# The Factory and the Beehive. IV. A Comprehensive Study of the Rotation X-ray
Activity Relation in Praesepe and the Hyades

Alejandro Núñez NSF MPS-Ascend Postdoctoral Research Fellow  Department of
Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027, USA
Marcel A. Agüeros Department of Astronomy, Columbia University, 550 West 120th
Street, New York, NY 10027, USA  Kevin R. Covey Department of Physics &
Astronomy, Western Washington University, Bellingham, WA 98225, USA  Stephanie
T. Douglas Department of Physics, Lafayette College, 730 High St, Easton, PA
18042, USA  Jeremy J. Drake Center for Astrophysics $|$ Harvard $\&$
Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Rayna Rampalli Department
of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA  Emily C.
Bowsher  Department of Astronomy, Columbia University, 550 West 120th Street,
New York, NY 10027, USA  Phillip A. Cargile Center for Astrophysics $|$
Harvard $\&$ Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Adam L.
Kraus Department of Astronomy, The University of Texas at Austin, Austin, TX
78712, USA  Nicholas M. Law Department of Physics and Astronomy, University of
North Carolina, Chapel Hill, NC 27599, USA

###### Abstract

X-ray observations of low-mass stars in open clusters are critical to
understanding the dependence of magnetic activity on stellar properties and
their evolution. Praesepe and the Hyades, two of the nearest, most-studied
open clusters, are among the best available laboratories for examining the
dependence of magnetic activity on rotation for stars with masses
$\buildrel<\over{\sim}$1 ${M_{\odot}}$. We present an updated study of the
rotation–X-ray activity relation in the two clusters. We updated membership
catalogs that combine pre-Gaia catalogs with new catalogs based on Gaia Data
Release 2. The resulting catalogs are the most inclusive ones for both
clusters: 1739 Praesepe and 1315 Hyades stars. We collected X-ray detections
for cluster members, for which we analyzed, re-analyzed, or collated data from
ROSAT, the Chandra X-ray Observatory, the Neil Gehrels Swift Observatory, and
XMM-Newton. We have detections for 326 Praesepe and 462 Hyades members, of
which 273 and 164, respectively, have rotation periods—an increase of
6$\times$ relative to what was previously available. We find that at
$\approx$700 Myr, only M dwarfs remain saturated in X-rays, with only
tentative evidence for supersaturation. We also find a tight relation between
the Rossby number and fractional X-ray luminosity
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ in unsaturated single members, suggesting
a power-law index between $-3.2$ and $-3.9$. Lastly, we find no difference in
the coronal parameters between binary and single members. These results
provide essential insight into the relative efficiency of magnetic heating of
the stars’ atmospheres, thereby informing the development of robust age-
rotation-activity relations.

Low mass stars (2050); Stellar activity (1580); X-ray stars (1823); Stellar
rotation(1629)

##  1 Introduction

In the interiors of low-mass stars (late-F dwarfs and later types), rotational
shear at the tachocline, the boundary between the radiative and convective
zones, is thought to power a dynamo (Parker, 1993; Charbonneau, 2014). This
dynamo generates magnetic field that rises to the stellar surface where a
fraction of the magnetic energy is dissipated and heats the corona to the
$\buildrel>\over{\sim}$106 K temperatures required to produce thermal X-rays.
Observations of GKM dwarfs with the Einstein Observatory found that their
X-ray luminosity ($L_{\mathrm{X}}$) is proportional to their rotational
velocity, confirming this connection between $L_{\mathrm{X}}$ and rotation
(Pallavicini et al., 1981; Pizzolato et al., 2003). Subsequent measurements of
$L_{\mathrm{X}}$, generally expressed as a fraction of the bolometric
luminosity, $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$, to remove the mass
dependence, have shown that $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ increases as
the stellar rotation period ($P_{\mathrm{rot}}$) decreases. This relation was
refined by Noyes et al. (1984), who examined chromospheric fluxes in terms of
the Rossby number, $R_{\mathrm{o}}$ = $P_{\mathrm{rot}}$/$\tau$, where $\tau$
is the convective turnover time. $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ then has
a power-law dependence on $R_{\mathrm{o}}$ such that
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ $\propto R_{\mathrm{o}}^{\beta}$, with
$\beta\approx-2$ (e.g., Randich, 2000; Wright et al., 2011; Núñez et al.,
2015; Thiemann et al., 2020). However, this holds only up to some threshold
$R_{\mathrm{o}}$, below which $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ is
$\approx$constant. For faster rotators, magnetic activity is saturated, i.e.,
it no longer depends on rotation speed (e.g., Stauffer et al., 1994; Pizzolato
et al., 2003; Wright et al., 2011; Núñez et al., 2015).

The cause(s) of the saturation of X-ray activity are not well established,
though several competing hypotheses have been formulated. A fundamental
challenge is determining whether saturation is caused by changes in the dynamo
efficiency, or is instead a consequence of fast rotation. The former could
result in saturation of the dynamo (e.g., Gilman, 1983; Blackman & Thomas,
2015), although this is contradicted by observations that not all activity
indicators appear to saturate, and that different indicators can saturate at
different $R_{\mathrm{o}}$ (e.g, Cardini & Cassatella, 2007; Mamajek &
Hillenbrand, 2008; Marsden et al., 2009). The latter could suggest that
saturation instead occurs in the coronal filling factor (Vilhu, 1984),
although here again, the observational evidence is not strong, as studies have
found that the coronal filling factor can be small in saturated X-ray emitters
(e.g., Testa et al., 2004). Very rapid rotation could also cause coronal loops
to become unstable due to the centrifugal force, a situation known as coronal
stripping, as a result of the Keplerian corotation radius getting close to the
stellar surface (Jardine & Unruh, 1999). Other work has explored additional
potential explanations, including changes in the underlying dynamo mechanism
(from a convective dynamo to an interface dynamo; see Barnes, 2003a, b).

Meanwhile, some studies have also found that, in the fastest rotators, X-ray
activity decreases relative to the saturation level, a phenomenon known as
supersaturation (Randich et al., 1996). These authors found a decrease in
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ for the fastest rotators ($v\sin i>$ 100
km s-1) in the $\approx$60 Myr-old open cluster $\alpha$ Persei. Subsequent
studies have claimed to observe supersaturation in FGK dwarfs (Stauffer et
al., 1997; Jeffries et al., 2011; Argiroffi et al., 2016), K dwarfs (Thiemann
et al., 2020), M dwarfs, and ultracool dwarfs (Alexander & Preibisch, 2012;
Cook et al., 2014).

Supersaturation is even less well understood than saturation. James et al.
(2000) and Jardine (2004) proposed that coronal stripping would explain both
saturation and supersaturation, while Stȩpień et al. (2001) argued that
supersaturation is caused by a decrease in the filling factor due to the
poleward migration of active regions in very fast rotators. Wright et al.
(2011) assembled a sample of 824 stars to study the dependence of
$L_{\mathrm{X}}$ on $R_{\mathrm{o}}$ and found that their data favored the
Stȩpień et al. (2001) hypothesis, even though the Keplerian corotation radius
and the excess polar updraft were both better predictors of
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ than either $P_{\mathrm{rot}}$ or
$R_{\mathrm{o}}$ for their supersaturated stars. However, supersaturation does
not appear to occur for chromospheric activity (e.g., Marsden et al., 2009;
Jackson & Jeffries, 2010), which argues against it being due to e.g., the
migration of active regions, and favors the coronal-stripping explanation.

Further complicating our understanding of the coronal rotation-activity
relation is the posited transition from a solar-type $\alpha\Omega$ dynamo in
stars with a radiative core and a convective outer layer to a turbulent or
$\alpha^{2}$ dynamo in fully convective M dwarfs. Wright & Drake (2016) and
Wright et al. (2018) found that fully convective M dwarfs follow the same
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$–$R_{\mathrm{o}}$ relation as their partly
convective counterparts, suggesting that fully and partly convective stars
have very similar dynamos, driven mostly by the interaction of rotation and
turbulent convection. This conclusion impugns the relevance of the shear at
the tachocline in driving the magnetic dynamo in partly convective stars.

Studies of the dependence of $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ on rotation
have mostly focused on mixed-aged samples of open cluster and/or of field
stars, where age effects are difficult to quantify (e.g., Randich et al.,
2000; Wright et al., 2011, 2018; Thiemann et al., 2020). Other studies have
instead focused on the single-aged populations in the handful of open clusters
currently observable with X-ray telescopes,111The small fields-of-view of the
current flagship X-ray observatories are poorly matched to the size of nearby
open clusters, while the low-mass members in more distant, smaller-on-the-sky
clusters require excessive exposure times. where the number of detected stars
is generally small (e.g., Douglas et al., 2014; Núñez et al., 2015, 2017).
There is a clear need for more data before we can reach a consensus view on
the age-dependence of the rotation–coronal activity relation or on the
reason(s) for saturation and supersaturation.

The approximately coeval Praesepe and Hyades clusters, each about 700 Myr old,
are the oldest open clusters within 250 pc, and thus the oldest accessible
ensembles of low-mass stars with a well-constrained age.222Douglas et al.
(2019) combined literature estimates for the age of Praesepe to assign the
cluster an age of 670$\pm$67 Myr, and used gyrochronology to determine that
the Hyades is 57 Myr older, or 727$\pm$75 Myr old. Fully characterizing
rotation and activity for the low-mass members of these two clusters is
therefore critical to constraining the age-rotation-activity relation,
particularly as Praesepe and the Hyades serve as a bridge of knowledge between
younger cluster stars and their older field-age cousins.

This paper is the fourth in a series focused on Praesepe and the Hyades. In
Agüeros et al. (2011, Paper I), we presented $P_{\mathrm{rot}}$ for 40
Praesepe members measured using Palomar Transient Factory (PTF; Law et al.,
2009; Rau et al., 2009) light curves. In Douglas et al. (2014, Paper II), we
combined literature $P_{\mathrm{rot}}$ and X-ray data with new and archival
optical spectra for members of both clusters to show that $L_{\mathrm{X}}$ and
$\mathrm{H}\alpha$ emission, a proxy for chromospheric activity, depend
differently on $R_{\mathrm{o}}$. In Kraus et al. (2017, Paper III), we
characterized a newly discovered eclipsing binary in Praesepe. Parallel to
this paper series, in Douglas et al. (2016, 2017, hereafter D16 and D17) we
added 48 new $P_{\mathrm{rot}}$ for Hyades members and 677 for Praesepe
members from an analysis of K2 (Howell et al., 2014) photometry. And in
Rampalli et al. (2021) we used two additional K2 campaigns to complete the
census of rotation in Praesepe, measuring new $P_{\mathrm{rot}}$ for 220 stars
and bringing the total number of $P_{\mathrm{rot}}$ for the cluster to 1013.

We begin below by revisiting the membership catalogs for the two clusters in
light of the information provided by the Gaia data, and particularly by its
Data Release 2 (GDR2; Gaia Collaboration et al., 2018a), in Section 2. We also
discuss the $P_{\mathrm{rot}}$ available for both clusters, using these to
calculate $R_{\mathrm{o}}$ for their members, as well as binary information
for stars in the two clusters. In Section 3 we present our analysis of the
extensive set of X-ray observations we have assembled for Praesepe and the
Hyades from the Röntgen Satellite (ROSAT), the Chandra X-ray Observatory
(Chandra), the Neil Gehrels Swift Observatory (Swift), and the X-ray Multi-
Mirror MissionNewton (XMM). We derive several stellar parameters for cluster
stars in Section 4. We present our results in Section 5 and conclude in
Section 6.

Table 1: Praesepe and Hyades Membership Catalogs Considered in This Work | # of Members
---|---
Provenance | Praesepe | Hyades
Legacy Catalogs | 1123 | 746
Cantat-Gaudin et al. (2018) | 719 |  $\cdots$
Gaia Collaboration et al. (2018b) | 937 | 508
Lodieu et al. (2019a) | 721 |  $\cdots$
Lodieu et al. (2019b)aaWe did not include the set of stars farther than 18 pc from the cluster center, as these authors considered this set to have a significant level of contamination. |  $\cdots$ | 556
Meingast & Alves (2019) |  $\cdots$ | 238
Röser et al. (2019) |  $\cdots$ | 976
Röser & Schilbach (2019) | 1393 |  $\cdots$
Ultra-cool DwarfsbbLate-M dwarfs and brown dwarfs found in the literature. See Section 2.3. | 12 | 21
Consolidated # of Members | 1739 | 1315

##  2 Constructing Our Membership Catalogs

###  2.1 Legacy Membership Catalogs

Douglas et al. (2014) and D17 based their Praesepe catalog on the cluster
membership probabilities $P_{\mathrm{mem}}$ calculated by Kraus & Hillenbrand
(2007). These $P_{\mathrm{mem}}$ were found for $>$106 sources in the field of
view of Praesepe using photometric and astrometric data. D17 considered the
Kraus & Hillenbrand (2007) 1130 stars with $P_{\mathrm{mem}}$ $\geq$ 50% as
bona fide cluster members. To these stars, D17 added 39 previously identified
Praesepe members too bright to be included in the Kraus & Hillenbrand (2007)
catalog, assigning these stars $P_{\mathrm{mem}}$ = 100%. As a starting point,
we took all stars from Kraus & Hillenbrand (2007) with $P_{\mathrm{mem}}$
$\geq$ 10% to be potential Praesepe members; we also added the 39 additional
stars from D17 as bona fide members.

As in D16, we adopted the Goldman et al. (2013) catalog for the Hyades and
supplement it with members identified through analysis of Hipparcos data
(Perryman et al., 1997). All but 13 Hyads identified through this analysis
were also identified by Goldman et al. (2013). In Goldman et al. (2013), stars
have discrete values for field contamination (100, 30, 17.5, or 1%). D16
adopted the invert of these values as $P_{\mathrm{mem}}$ and considered stars
with $P_{\mathrm{mem}}$ $\geq$ 70% (corresponding to contamination fraction
$\leq$ 30%) as bona fide members. As a starting point, we took all stars in
D16 with $P_{\mathrm{mem}}$ $>$ 0% to be potential Hyades members.

###  2.2 Gaia-based Membership Catalogs

Successive Gaia data releases have transformed our view of the membership of
stellar clusters. Table 1 lists the Gaia-based studies of Praesepe and the
Hyades that we considered, in addition to our legacy catalogs, to produce our
definitive membership catalogs, and the number of members included in each.
Our starting assumption was that the Gaia-based catalogs are correct, in that
they are likely to contain fewer contaminants than earlier catalogs—thanks in
part to Gaia’s higher spatial resolution—but are incomplete, in that Gaia data
either lack five-parameter solutions or have poor fits for unresolved binaries
(e.g., Belokurov et al., 2020). Gaia-based studies, therefore, exclude most
potential binaries from published cluster catalogs.

Figure 1: Decision process to consolidate our Praesepe and Hyades legacy
catalogs (described in Section 2.1) with the GDR2-based catalogs listed in
Table 1.

To produce our updated catalogs, we first cross-matched our legacy catalogs
against the GDR2-based catalogs using a 5″ matching radius. To account for the
large proper motions of Hyads, we also searched for GDR2 counterparts using a
matching radius between 5″ and 7″ and found 17 additional matches; we
inspected these visually using Aladin Sky Atlas.333We also tracked these 17
stars in our subsequent analysis. Ten of them have X-ray detections; none of
which stand apart from their spectral type cohort in their X-ray measurements.
We found two or more GDR2 stars within the matching radius of 161 Hyads and 80
Praesepe stars. We assumed the closest match to be the best match, except when
the radial distances of the potential matches were too similar. In such
instances, we guided our best match selection using GDR2 parallax, proper
motion, and photometry for each potential match. We resolved ambiguous matches
using this approach for 23 Hyads and 5 Praesepe stars. All in all, the median
closest matching radius was 1$\farcs$6 for Hyads and 0$\farcs$6 for Praesepe
stars.

Stars that appeared as members in our legacy catalogs and are included in any
of the GDR2 catalogs in Table 1 form the bulk of our final catalogs. There are
746 Hyads and 1123 Praesepe stars in this category. If, however, a star was
not in our legacy catalogs but is included as a member in any of the GDR2
catalogs, we added that star to our list of bona fide members for that
cluster. In Praesepe, there are 292 such stars in the core, and 312 in the
tidal tails. In the Hyades, the numbers are 143 and 405, respectively.

We then matched our catalog stars to Gaia Early Data Release 3 (GEDR3; Gaia
Collaboration et al., 2021, see Section 2.4) to obtain GEDR3 photometry and
GEDR3-based distances from Bailer-Jones et al. (2021). For stars without such
distances, we found either parallax or distance calculations in the
literature. For Hyades, we found 2 Hipparcos-based parallaxes in van Leeuwen
et al. (2007), 51 PPMXL-based parallaxes in Röser et al. (2011), and one
trigonometric parallax in Dittmann et al. (2014). We also found eight
spectroscopic distances in Lodieu et al. (2014), one photometric distance in
Robert et al. (2016), and two photometric distances in Schneider et al.
(2017). For all other stars missing distances (68 Praesepe stars and five
Hyads), we assigned them a distance equal to that of the cluster as a whole.
To estimate the distance of each cluster as a whole, we calculated the median,
16th, and 84th percentiles of the Bailer-Jones et al. (2021) distances.444We
excluded the tidal tail stars cataloged for both clusters (Meingast & Alves,
2019; Röser et al., 2019; Röser & Schilbach, 2019) to calculate these cluster
distances. The resulting cluster distances are 183.2${}^{+11.1}_{-13.7}$ pc
for Praesepe and 49.1${}^{+25.4}_{-7.7}$ pc for the Hyades; the 1$\sigma$
distance errors were approximated as the mean of the 16th and 84th
percentiles.

Figure 1 illustrates as a decision tree the steps described next to build our
cluster catalogs. To start, we compared the one-dimensional parallax distance
($\pm$2$\sigma$) of each star in our legacy catalogs to its cluster’s center
$\pm$twice the tidal radius, which we took to be 11.5 pc for Praesepe (Kraus &
Hillenbrand, 2007) and 10 pc for Hyades (Röser et al., 2011). If the star is
closer to or farther from us than these distances, indicating that it is
beyond twice the tidal radius for its cluster, we categorized that star as a
non-member.

We then checked whether a star that was rejected as a non-member in the step
above is considered a member in any of the GDR2 catalogs. We assumed that such
stars are bona fide members and therefore added them back in to our final
catalogs.

Lastly, we rejected stars from our legacy catalogs that passed the above
radial distance check but that have $P_{\mathrm{mem}}$ lower than the
thresholds used in D16 and D17: 70% for Hyades and 50% for Praesepe,
respectively (see Section 2.1). As these stars were not present in any of the
GDR2 catalogs and they have low $P_{\mathrm{mem}}$ in the legacy catalogs, we
consider them to have a high probability of being field contaminants.

Table 2 includes our consolidated catalog of Praesepe and Hyades stars. Column
7 of Table 2 specifies if a star is a member in our legacy catalogs, and
Columns 8–14 specify if a star is considered a cluster member in each of the
GDR2 catalogs. Our resulting catalogs include 1727 Praesepe members and 1294
Hyads. To these, we add ultracool dwarfs from the literature, as we explain
next.

Table 2: Overview of Columns in the Praesepe and Hyades Membership Catalog  Column | Description
---|---
1 | Name
2 | 2MASS designation
3 | Gaia EDR3 designation
4, 5 | R.A., Decl. for epoch J2000
6 | Cluster to which the star belongs
7 | Member in legacy catalog?
8 | Member in Cantat-Gaudin et al. (2018)?
9 | Member in Gaia Collaboration et al. (2018b)?
10 | Member in Lodieu et al. (2019a)?
11 | Member in Lodieu et al. (2019b)?
12 | Member in Meingast & Alves (2019)?
13 | Member in Röser & Schilbach (2019)?
14 | Member in Röser et al. (2019)?
15 | Ultracool dwarf in literature?
16, 17 | Distance and 1$\sigma$ uncertainty
18 | Source of distanceaaBJ: Bailer-Jones et al. (2021); C: Cluster distance; D: Dittmann et al. (2014); L: Lodieu et al. (2014); P: Pérez-Garrido et al. (2018); R11: Röser et al. (2011); R16: Robert et al. (2016); S: Schneider et al. (2017); vL: van Leeuwen et al. (2007); Z: Zhang et al. (2010).
19, 20 |  $K$-band magnitude and 1$\sigma$ uncertainty
21 | Source of $K$ magnitudebb2M: 2MASS; B: Boudreault et al. (2010); G: Derived from GEDR3 photometry; UL: UKIDSS LAS; UG: UKIDSS GCS.
22, 23 | Gaia EDR3 $G$ band magnitude and 1$\sigma$ uncertainty
24 | Source of $G$ magnitudecc2M: Derived from 2MASS photometry; G: GEDR3
25 | Gaia EDR3 $G_{\mathrm{BP}}-G_{\mathrm{RP}}$
26 | Binary flag: (0) no binary flag; (1) candidate binary;
| (2) confirmed binary
27 | Gaia EDR3 RUWE
28 | Rotation period $P_{\mathrm{rot}}$
29, 30 | X-ray energy flux $f_{\mathrm{X}}$ (0.1–2.4 keV) and 1$\sigma$ uncertainty
31 | Stellar mass
32 | Convective turnover time $\tau$
33, 34 |  $L_{\mathrm{bol}}$ and 1$\sigma$ uncertainty

###  2.3 Ultracool Dwarfs

To our consolidated cluster catalogs, we added ultracool dwarfs that were not
already included in our legacy catalogs or in the GDR2-based catalogs. These
are primarily late M and early-to-mid L dwarfs. We found twelve such Praesepe
stars in the literature: one M9 and four L0 type dwarfs from Boudreault et al.
(2010), one L0 found by Zhang et al. (2010), and four late M and two early-L
dwarfs from Manjavacas et al. (2020). To the Hyades catalog we added 21
objects: two late M and four early-L dwarfs cataloged by Lodieu et al. (2014),
one L3 found by Robert et al. (2016), two mid L found by Schneider et al.
(2017), and three late M and nine L dwarfs found by Pérez-Garrido et al.
(2018). Column 15 of Table 2 indicates whether a cluster star is an ultracool
dwarf from the literature.

Only eight ultracool dwarfs (one Praesepe and seven Hyads) have Bailer-Jones
et al. (2021) distances. For the others, we adopted either the distances from
the literature—which was the case for one Praesepe and 14 Hyads—or the cluster
distance as a whole (see Section 2.2).

The final tallies in our cluster catalogs are 1739 Praesepe stars and 1315
Hyads.

###  2.4 Photometry

As mentioned in Section 2.2, we matched our final catalog from Sections 2.2
and 2.3 against GEDR3 using a 3″ matching radius for stars in both clusters.
When we found more than one GEDR3 star within the matching radius, we compared
the $G$ magnitudes, when available, to determine the better match. In most
cases, the closest match was the best match.

Figure 2: CMDs for Praesepe (top panels) and Hyades (bottom). The left column
combines GEDR3 and either 2MASS, UKIDSS, or GEDR3-derived $K$ photometry to
produce a ($G-K$) color. The right column uses the
($G_{\mathrm{BP}}-G_{\mathrm{RP}}$) color from GEDR3. Our full catalog
consists of stars from our legacy catalog (gray circles, see Section 2.1),
Gaia DR2-based studies of cluster membership (blue $\times$ symbols, see
Section 2.2), and ultracool dwarfs from the literature (red squares, see
Section 2.3). The bottom left panel includes an inset to show the full red end
of the main sequence for Hyades in ($G-K$) color. We have a total of 1739
Praesepe members and 1315 Hyades members in our full catalog.

Figure 3: Same as in Figure 2, but this time indicating stars with no binary
flags with gray circles, and candidate/confirmed binaries with orange crosses.
Candidate/confirmed binaries constitute 31% of our Praesepe catalog and 23% of
our Hyades catalog.

We obtained GEDR3 magnitudes for 2684 members of the two clusters (1732 for
Praesepe, 1304 for the Hyades), ranging from $G$ = 2.7 to 21.1 mag. For seven
ultracool dwarf Praesepe members and eleven ultracool dwarf Hyads lacking a
GEDR3 counterpart, we derived $G$ magnitudes from Two Micron All-Sky Survey
(2MASS; Skrutskie et al., 2006) $J$ and $K$ magnitudes using the
transformations given by Riello et al. (2021). These ultracool dwarfs cover
the magnitude range $14.5<K<17.1$, and the derived $G$ magnitudes are in the
range $19.6<G<25.2$.

We also collected good quality (ph-qual A, B, or C) 2MASS $K$ magnitudes for
1669 Praesepe and 1274 Hyades members. The resulting coverage is $1.5<K<15.7$
mag. For the 111 Praesepe and Hyades stars lacking a good quality 2MASS $K$,
we searched for $K$ photometry from the United Kingdom InfraRed Telescope
(UKIRT) Infrared Deep Sky Survey (UKIDSS; Lawrence et al., 2007) data release
9, both from the Galaxy Clusters Survey (GCS) and Large Area Survey (LAS). We
found UKIDSS $K$ photometry for 41 additional Praesepe members and nine Hyads,
covering the magnitude range $9.8<K<18.8$.

There are nine Praesepe stars lacking good quality 2MASS/UKIDSS $K$
photometry. For these stars, we derived $K$ magnitudes from GEDR3 $G$ and
($G_{\mathrm{BP}}-G_{\mathrm{RP}}$) color using the transformations given in
Riello et al. (2021). There are also 20 Praesepe stars unmatched in
2MASS/UKIDSS. Ten of these are newly identified white dwarfs in the GDR2
catalogs, and five others are secondary stars in binaries unresolved by
2MASS/UKIDSS. Except for one of the white dwarfs and three of the secondary
stars—all lacking a ($G_{\mathrm{BP}}-G_{\mathrm{RP}}$) color, we derived
their $K$ magnitudes using the same transformations as above. The remaining
five unmatched stars are ultracool dwarfs, for which we adopt the $K$
magnitudes measured in Boudreault et al. (2010).

In the Hyades, there are 27 stars lacking good quality 2MASS/UKIDSS $K$
photometry. We derived their $K$ magnitudes using the transformations in
Riello et al. (2021) mentioned above. There are also five Hyads unmatched in
2MASS/UKIDSS. Three of these are newly identified white dwarfs in the GDR2
catalogs, and two are secondary stars in binaries unresolved by 2MASS/UKIDSS.
We derived their $K$ magnitudes using the same transformations as above. The
magnitude range of all derived $K$ magnitudes is $1.0<K<19.7$. Column 21 of
Table 2 identifies the source of the $K$ magnitude for each star.

All in all, we have $G$ photometry for all stars in our catalogs, and $K$
photometry for all but four Praesepe stars. The combined photometry covers the
color range $-0.9<$ ($G-K$) $<$ 10.4 mag. We calculated absolute $G$
magnitudes ($M_{G}$) for our cluster stars using the distances we adopted for
each, and an extinction correction for the Gaia $G$ band. We obtained the
latter by first calculating the total absorption in $V$ ($A_{V}$) using the
extinction tables by Schlafly & Finkbeiner (2011) assuming $R_{V}$ = 3.1 and
adopting a reddening of $E$($B-V$) = 0.035 for Praesepe (Douglas et al., 2019)
and 0.001 for the Hyades (Taylor, 2006). We then obtained the total absorption
in $G$ ($A_{G}$) using $A_{G}$/$A_{V}$ = 0.789 (Wang & Chen, 2019). The left
panels of Figure 2 show the $M_{G}$ – ($G-K$) color-magnitude diagram (CMD),
and the right panels, the $M_{G}$ – ($G_{\mathrm{BP}}-G_{\mathrm{RP}}$)
CMD555We collected ($G_{\mathrm{BP}}-G_{\mathrm{RP}}$) for 1724 Praesepe and
1301 Hyades stars, although we do not use this Gaia color in our analysis. for
both clusters.

###  2.5 Rotation Periods

The most up-to-date catalogs of rotation periods for the two clusters are
those of Rampalli et al. (2021) for Praesepe and Douglas et al. (2019) for the
Hyades. Both of these catalogs supplement ground-based $P_{\mathrm{rot}}$
measurements with large numbers of $P_{\mathrm{rot}}$ obtained from the five
K2 campaigns dedicated to the two clusters (C5, C16, and C18 to Praesepe, and
C4 and C13 to the Hyades). In total, we have $P_{\mathrm{rot}}$ measurements
for 1052 Praesepe members and 233 Hyads. Column 28 in Table 2 includes these
$P_{\mathrm{rot}}$ values.

###  2.6 Binary Flags

To identify binaries and multiple systems in the two clusters, we relied on
the binary flags from several previous studies. D16 and D17 obtained and
tabulated binary flags for members of Hyades and Praesepe, respectively.
Douglas et al. (2019) updated and complemented those flags and reported the
following individual flags: visual identification, UVW kinematic deviations
(for Hyades only), vertical distance from the main sequence on a Gaia CMD,
multiple periodicity from K2 periodograms, GDR2 radial velocity and proper
motion deviations, high GDR2 astrometric excess noise ($\epsilon_{i}>1$), and
confirmed binarity from the literature. Rampalli et al. (2021) further updated
these flags for Praesepe and replaced the $\epsilon_{i}>1$ flag with GEDR3’s
re-normalized unit weight error (RUWE) $>$ 1.2 to identify likely unresolved
binaries (see binary indicators in their Table 4).

In our catalog, we consider as _candidate_ binaries (Binary Flag = 1) stars
having at least one of the kinematics, CMD distance, radial velocity, proper
motion, or multiple periodicity flags. We consider as _confirmed_ binaries
(Binary Flag = 2) those confirmed in the literature. However, we ignore the
$\epsilon_{i}$ and the RUWE flags in Douglas et al. (2019) and Rampalli et al.
(2021), respectively, as we implement our own approach to using the most
recent GEDR3 spurious astrometry indicators (see our RUWE treatment in the
next paragraph). Also, we found ten Praesepe stars and seven Hyads for which
GEDR3 resolved two point sources and 2MASS only one. We assigned Binary Flag =
1 to these 17 stars. All in all, we have 456 candidate and 82 confirmed
binaries in Praesepe and 60 candidate and 238 confirmed binaries in Hyades.
Figure 3 shows the same CMDs as in Figure 2, this time highlighting with
orange crosses candidate/confirmed binaries. Column 26 of Table 2 includes our
binary flag for each star.

Lastly, we collected RUWE values for our stars666Both $\epsilon_{i}$ and RUWE
have their pros and cons in identifying spurious Gaia astrometry; we opted to
use only RUWE by virtue of its more sound and guaranteed distribution (with
peak at 1.0) across the full color-magnitude range of Gaia (see discussions in
Belokurov et al., 2020; Penoyre et al., 2020). The RUWE is a goodness-of-fit
measure of the single-star model fit to the source’s astrometry. If a star is
an unresolved binary and its center of light deviates from the assumed single-
star model, its RUWE will deviate significantly from 1.0 (e.g., Jorissen,
2019; Belokurov et al., 2020). Gaia cannot resolve separations
$\buildrel<\over{\sim}$0$\farcs$7 (Ziegler et al., 2018), which corresponds to
a semimajor axis $a~{}\approx~{}35$ au at the typical Hyad distance and
$\approx$130 au at the typical Praesepe star distance. Therefore, most stars
in our catalogs with high RUWE are likely to be “intermediate” binaries, i.e.,
with small enough separation ($0.1~{}{\lower
3.44444pt\hbox{$\buildrel<\over{\sim}$}}~{}a~{}{\lower
3.44444pt\hbox{$\buildrel<\over{\sim}$}}~{}80$ au) for the binary components
to have affected each other’s protoplanetary disks in the first 10 Myr (Rebull
et al., 2006; Meibom et al., 2007; Kraus et al., 2016; Messina et al., 2017,
S. T. Douglas et al. 2022, in preparation). They are unlikely to be tight,
tidally interacting binaries ($a~{}{\lower
3.44444pt\hbox{$\buildrel<\over{\sim}$}}~{}0.1$ au) because their center of
light will deviate minimally from the assumed single-star model ($a=0.1$ au
corresponds to $\delta\theta~{}\approx~{}2$ mas at the typical Hyad distance
and $\approx$0.5 mas at the typical Praesepe star distance), thus only
negligibly deviating RUWE from 1.0.

Typically, stars with RUWE $>$ 1.4 are considered to have high probability of
being unresolved binaries (e.g., Deacon & Kraus, 2020; Ziegler et al., 2020;
Kervella et al., 2022), although some studies have used a more conservative
$>$1.2 threshold to identify potential binaries (e.g., Pearce et al., 2020).
We use RUWE $>$ 1.4 to determine which stars with Binary Flag = 0 (i.e.,
assumed to be single) are potentially unresolved binaries. However, we do not
necessarily exclude them from the sample of single stars in our analysis,
because we do not have any additional information on their potential binarity.
Column 27 of Table 2 includes the RUWE for each star. In Praesepe, 52 (4%)
stars with Binary Flag = 0 and 129 (24%) with Binary Flag > 0 have RUWE $>$
1.4. For Hyades, the numbers are 152 (15%) and 131 (44%), respectively.

##  3 X-Ray data

Over the past few decades, Praesepe and the Hyades have been regularly
targeted by X-ray missions, and members of both clusters have also been
detected serendipitously. We collected data from ROSAT, Chandra, XMM-Newton,
and Swift. In some cases this required extracting sources from the X-ray
observations ourselves. In others, we relied on previously compiled lists of
X-ray detections, typically serendipitous source catalogs, which are
constructed from automated processing of archival pointings. We homogenized
these data to build a complete and uniform set of X-ray detections. To achieve
this, our approach was to use the reported count rates and our own energy
conversion factors (ECF; see Section 4.3) to obtain unabsorbed X-ray energy
fluxes, $f_{\mathrm{X}}$, in the 0.1–2.4 keV energy band.777We chose the most
restrictive energy bandpass out of the four X-ray observatories to homogenize
our data, which happens to be the ROSAT bandpass.. We then converted
$f_{\mathrm{X}}$ to $L_{\mathrm{X}}$ by using our adopted individual
distances. For Chandra, XMM, or Swift sources with enough X-ray counts, we
performed spectral analysis to extract unabsorbed $f_{\mathrm{X}}$ as well as
coronal temperature, coronal metal abundance, and, in some cases, neutral
hydrogen column density along the line of sight.

In the few instances in which the count rates were not reported, namely, some
ROSAT-based studies, we worked backwards from the reported $L_{\mathrm{X}}$,
distance, and ECF to estimate the count rates and then applied the procedure
described above to obtain our own $f_{\mathrm{X}}$ and $L_{\mathrm{X}}$
values. Figure 4 illustrates the number of Praesepe and Hyades stars detected
with at least one of the X-ray observatories.

Our full list of X-ray detections for Praesepe and Hyades stars is in Table 3.
If a star had more than one X-ray detection, we calculated the error-weighted
average of the $f_{\mathrm{X}}$ values and adopted it as the bona fide
$f_{\mathrm{X}}$ for that star. Columns 29 and 30 of Table 2 include the
$f_{\mathrm{X}}$ and 1$\sigma$ uncertainty for each cluster star with at least
one X-ray detection. In total, we have 504 individual X-ray detections for 326
Praesepe stars (two of which are ultracool dwarfs), and 603 for 464 Hyads
(three ultracool dwarfs). Only 3% of X-ray detections have questionable
quality (see Column 28 in Table 3).

In the next subsections, we explain in detail the X-ray source detection and
photometric extraction we performed with data from each X-ray observatory.

Figure 4: Venn diagrams illustrating the number of Praesepe (top panel) and Hyades (bottom panel) stars detected in X-rays with the four X-ray observatories. In our Praesepe catalog, 19% of stars are detected in X-rays. In our Hyades catalog, the number is 35%. Table 3: Overview of Columns in the X-ray Source Catalog  Column | Description
---|---
1 | External catalog source ID
2 | Provenance of X-ray informationaa1RXH; 2RXP; 2RXS; CSC; CIAO: Reduction of Chandra observation with CIAO; R95: Randich & Schmitt (1995); S01: Stelzer & Neuhäuser (2001); S95: Stern et al. (1995); SAS: Reduction of XMM observations with SAS; Swift.
3 | IAU Name
4 | Observation ID
5 | Instrument
6, 7 | R.A., Decl. for epoch J2000
8 | X-ray positional uncertainty
9 | Off-axis angle $\theta$
10 | Detection likelihood $L$bbFor CIAO sources, it is the source significance; for all others, it is the maximum likelihood.
11 | Net counts in the broad band
12, 13 | Net count rate and 1$\sigma$ uncertainty in broad band
14, 15 | Net count rate and 1$\sigma$ uncertainty in soft band
16, 17 | Net count rate and 1$\sigma$ uncertainty in hard band
18$-$20 | Definition of broad, soft, and hard bands
21 | Hardness ratio: (hard band $-$ soft band) /
| (hard band + soft band)
22 | Exposure time
23 | Variability flag: (0) no evidence for variability;
| (1) possibly variable; (2) definitely variable
24, 25 | Unabsorbed energy flux and 1$\sigma$ uncertainty in the
| 0.1–2.4 keV band
26 | Source of energy flux: (ECF) from applying ECF;
| (SpecFit) from spectral fitting
27 | X-ray flare removed?
28 | Quality Flagccm: likely mismatch to optical counterpart; x: likely extended source.
29 | Name of the optical counterpart
30 | Separation between X-ray source and optical counterpart

###  3.1 ROSAT Observations

####  3.1.1 ROSAT Sources from the Publicly Released Catalogs

We searched for X-ray counterparts to our cluster stars in the latest versions
of the three publicly released ROSAT catalogs: the Second ROSAT Source Catalog
of Pointed Observations with the Position Sensitive Proportional Counters
(PSPC) catalog (2RXP, ROSAT Consortium, 2000), the Second ROSAT All-Sky survey
(RASS) catalog (2RXS, Boller et al., 2016), and the ROSAT High-Resolution
Imager Pointed Observations catalog (1RXH, ROSAT Scientific Team, 2000). We
cross-matched these ROSAT catalogs and our cluster catalogs using a 50″
radius; this value was chosen to be large enough to account for the large
ROSAT positional errors. To estimate the number of likely false matches, we
shifted the X-ray source positions in steps of 50″ out to 10′ in all
directions and re-matched them to the cluster catalogs using the same 50″
radius used before. All resulting matches are assumed to be false. We found
that the median number of false matches is 30 ($\approx$8% of our matched
ROSAT sources) with a median offset of 34″. In our final ROSAT-cluster
catalogs matches, we consider those with radii $>$30′′ in Praesepe and $>$40′′
in Hyades to be likely false matches, and we exclude those from our X-ray
analysis, although we still include them in our consolidated catalog of X-ray
sources, with a “likely false match” flag (Quality Flag = “x”; Column 28 of
Table 3).

From the ROSAT catalogs, we obtained count rates and some other information
about the X-ray point sources, such as hardness ratios, detection likelihoods,
and variability flags, when available (see Table 3). We used the published
count rates, our own ECFs (see Section 4.3), and our adopted individual
distances to calculate $f_{\mathrm{X}}$ and $L_{\mathrm{X}}$ in the 0.1–2.4
keV energy band.

In the 2RXP catalog, we found X-ray counterparts for 78 Praesepe stars and 56
Hyads. Five Praesepe stars have a matching radius $>$30′′, and we flagged
these matches as likely false matches. All 56 Hyads, on the other hand, have a
matching radius $<$20′′. We also found six additional Praesepe and 90 Hyades
stars with X-ray counterparts at large ($>$20′) offset angles from the
instrument aimpoint. For these X-ray sources, 2RXP did not present count rate
uncertainties, and so we opted to ignore these X-ray sources. Also, one of the
sources matched to a Praesepe star has a source extent maximum likelihood
higher than its source detection maximum likelihood; we therefore flag this
source as a likely extended source in Table 3. Lastly, we found six additional
2RXP X-ray sources with ambiguous matches to stars in our catalogs. In these
cases, each X-ray source had either two Praesepe stars within a 15′′ radius or
two Hyads within a 40′′ radius roughly equidistant, and we opted to ignore
these X-ray sources, as it was not possible to determine the true optical
source of the X-ray detection.

In the 2RXS catalog, we found X-ray counterparts for nine Praesepe stars and
312 Hyads. One Praesepe star has a matching radius $>$30′′, and 19 Hyads have
a matching radius $>40$′′. We flagged these 20 matches as likely false
matches. Furthermore, five of the Praesepe matches and 35 of the Hyades
matches were also found in the 2RXP catalog, and we opted to adopt the X-ray
information for these 40 sources from the 2RXP catalog instead888The 2RXP
catalog was curated for point sources by both automatic algorithms and
detailed visual inspection. As such, we assume 2RXP to be a more reliable
source of X-ray information than 2RXS.. Lastly, we found nine additional 2RXS
X-ray sources with ambiguous matches to Hyads. In each case, the X-ray source
had two roughly equidistant Hyads within a 30′′ radius, and we opted to ignore
these X-ray sources, as it was not possible to determine the true optical
source of the X-ray detection. All in all, we include 2RXS sources for four
Praesepe stars and 277 Hyads, and their X-ray information is included in Table
3.

Lastly, in the 1RXH catalog, we found X-ray counterparts for one Praesepe star
and 22 Hyads. All matches to 1RXH have a matching radius $<$15′′, and none of
them were found in the 2RXP or the 2RXS catalogs.

####  3.1.2 ROSAT Sources from Independent Studies

To complement the ROSAT X-ray sources we found in the publicly released ROSAT
catalogs, we also searched for X-ray counterparts from ROSAT studies of
Praesepe and Hyades in the literature. Such studies sometimes included sources
that were otherwise rejected by the automatic pipelines of the ROSAT catalogs,
but that were otherwise acceptable knowing the nature of the X-ray emission
(i.e., hot plasma from the atmospheres of low-mass stars). We describe below
the individual ROSAT studies and the data we used from each one, which is
included in Table 3.

Stelzer & Neuhäuser (2001) used PSPC data publicly available as of 1998 Oct
and analyzed by Stelzer et al. (2000) to report 0.1–2.0 keV
quiescent999Stelzer et al. (2000) found X-ray flares in the detections of 12
Hyads. The $L_{\mathrm{X}}$ values Stelzer & Neuhäuser (2001) published for
these 12 stars exclude X-ray counts during the flares. $L_{\mathrm{X}}$ and
hardness ratio (HR) values for 181 Hyads in our catalog. We used
$L_{\mathrm{X}}$ and HR values published by Stelzer & Neuhäuser (2001) and the
distances adopted by these authors (from Hipparcos when available; otherwise,
46 pc) to calculate the corresponding X-ray count rates, using the formula ECF
= ($8.31+5.30~{}\times$ HR) $\times$ $10^{-12}$ erg cm-2 count-1, as adopted
in their work.

Of the 181 X-ray sources in Stelzer & Neuhäuser (2001), 126 are also in the
ROSAT catalogs, and we opted to adopt the X-ray information for these 126
sources from the ROSAT catalogs instead. Therefore, we used X-ray information
for only 55 Hyads from the Stelzer & Neuhäuser (2001) catalog.

Stern et al. (1995) used data from the RASS (Voges et al., 1999) to extract
X-ray point sources and match them to an optical catalog of 440 Hyads put
together by these authors. They found 187 matches to cluster stars and 24
matches to stars they considered nonmembers. For the former, they only
published $L_{\mathrm{X}}$ values in the 0.1–1.8 keV band, which were
calculated assuming a distance of 45 pc and an ECF of $6.0\times 10^{-12}$ erg
cm-2 count-1. For the latter, they instead published count rates in the
0.1–1.8 keV band. We converted the published $L_{\mathrm{X}}$ for cluster
stars back into count rates.

Table 4: Log of Chandra and XMM Observations of Praesepe and Hyades

Cluster | Instrument | ObsIDs | P.I. | Start | DurationaaExposure time before any filtering is applied. | Nominal Aimpoint | Roll | Filter/
---|---|---|---|---|---|---|---|---
|  |  |  | Date | (s) | $\alpha_{\rm J2000}$ | $\delta_{\rm J2000}$ | (°) | Data Mode
Praesepe | EPIC | 0101440401 | Pallavicini | 2000-11 | 48310 | 08:39:58.0 | +19:32:29.0 | 106.2 | Thick/MedbbThe first filter is for the MOS cameras and the second for the pn camera.
Praesepe | EPIC | 0721620101 | Agüeros | 2013-10 | 71800 | 08:39:00.0 | +19:57:00.0 | 103.0 | Thin1
Praesepe | ACIS-I | 17254–17257 | Drake, J. | 2015-05 | 191560 | 08:39:50.0 | +19:31:41.0 | 255.6–256.2 | VFaint
Praesepe | EPIC | 0863710201 | Núñez | 2021-04 | 32000 | 08:39:32.0 | +20:39:20.3 | 283.6 | Medium
Hyades | HRC-1 | 2554 | Ayres | 2001-12 | 17900 | 04:35:55.2 | +16:30:33.0 | 288.3 |  $\cdots$
Hyades | EPIC | 0762760601 | Agüeros | 2015-09 | 17000 | 04:33:27.0 | +13:02:43.5 | 82.3 | Thin1

Note. — This table is available in its entirety in the electronic edition of
the ApJ. Six rows are shown here for guidance regarding its form and content.

Of the 211 X-ray sources in Stern et al. (1995), 174 are also in the ROSAT
catalogs, and we opted to adopt the X-ray information for these 174 sources
from the ROSAT catalogs instead. Seven additional sources are also in the
Stelzer & Neuhäuser (2001) catalog, and we opted to adopt the X-ray
information for these seven sources from the latter catalog instead.
Furthermore, we found 18 of their sources to be nonmembers. Finally, we found
five sources with ambiguous optical counterparts, and we opted to ignore
those, as it was not possible to determine the true optical counterparts to
these five X-ray sources. In summary, we used X-ray information for only seven
Hyads from the Stern et al. (1995) catalog.

Randich & Schmitt (1995) surveyed Praesepe using the PSPC instrument aboard
ROSAT. These authors obtained 42 0.4–2.0 ks fields in a raster scan pattern
over two years of observations, detecting 68 stars in the Klein Wassink
(1927), Jones & Cudworth (1983), and Jones & Stauffer (1991) Praesepe
catalogs. For these 68 stars, Randich & Schmitt (1995) published X-ray count
rates in the 0.4–2.0 keV band.

Of the 68 X-ray sources in Randich & Schmitt (1995), 39 are in the ROSAT
catalogs, and we opted to adopt the X-ray information for these 39 sources
from the ROSAT catalogs instead. We also found two of their sources to be
nonmembers. Finally, we found one source with an ambiguous optical
counterpart, and we opted to ignore this source, as it was not possible to
determine its true optical counterpart. Therefore, we used X-ray information
for only 26 Praesepe stars from the Randich & Schmitt (1995) catalog.

Reid et al. (1995) published the results of three 30–40 ks PSPC observations
offset by 3–4∘ from the Hyades cluster center. These authors detected 20
Hyads, 19 of which are also considered members in our updated membership
catalog. However, we did not use any X-ray information from this X-ray
catalog. Nine of their sources are in the ROSAT catalogs, and we opted to
adopt the X-ray information for these sources from the ROSAT catalogs instead.
The remaining ten X-ray sources are all present in the Stelzer & Neuhäuser
(2001) catalog, and we opted to adopt the X-ray information for these sources
from the latter catalog.

###  3.2 Chandra Observations

####  3.2.1 Data from the Chandra Source Catalog

We searched for X-ray counterparts to our cluster stars in the latest version
of the Chandra Source Catalog (CSC 2.0, Evans et al., 2020a). We cross-matched
the CSC and our cluster catalogs using a 15″ radius. We found CSC counterparts
to ten Praesepe stars and nine Hyads, all have a matching radius $<$ 8″.
Eleven of these CSC sources were observed with an ACIS-I chip, six with an
ACIS-S chip, and two with the High Resolution Camera instrument. In Figure 5
we draw in blue the ACIS footprints of archival observations that include
sources matched to Praesepe stars.101010We do not show a figure with X-ray
observations of Hyads because they are are too scattered in the sky.

Like with ROSAT (see Section 3.1.1), we estimated the number of likely false
matches by shifting the X-ray source positions in steps of 25″ out to 3′ in
all directions and re-matched them to the cluster catalogs using the same 15″
radius used before. All resulting matches are assumed to be false. We found
that the median number of false matches is 2 ($\approx$10% of our matched CSC
sources) with a median offset of 10″. As such, we consider all our final CSC-
cluster catalogs matches to be true matches.

From the CSC, we obtained count rates in the 0.5–2.0 (soft), 2.0–7.0 (hard),
and 0.5–7.0 (broad) keV bands, plus some other information about the X-ray
point sources, such as detection likelihoods, and variability flags (see Table
3). We used the published count rates, our own ECFs (see Section 4.3), and our
adopted individual distances to calculate $f_{\mathrm{X}}$ and
$L_{\mathrm{X}}$ in the 0.1–2.4 keV band. Information about the original
Chandra observations that collected the data for these 19 CSC sources is shown
in Table 4.

Three of the CSC sources matched to Hyads have $>$300 net counts in the broad
band. For these sources we performed spectral analysis to extract unabsorbed
$f_{\mathrm{X}}$ as well as plasma parameters (see Section 3.5). The extracted
spectroscopic information is included in Table 5.

####  3.2.2 Chandra Source Extraction with CIAO

The CSC 2.0 only includes observations through the end of 2014. For Chandra
pointings obtained after this cutoff date, we performed our own data reduction
and source extraction using the Chandra Interactive Analysis of Observations
(CIAO, Fruscione et al., 2006, we used CIAO v.4.13 and CALDB v.4.9.5) tools.
Table 4 provides the basic information about all the Chandra pointings
described next.

##### New Chandra Observations

The central field of Praesepe was observed four separate times with the same
pointing and similar roll angle between 2015 May and 2015 Jun with the
Advanced CCD Imaging Spectrometer (ACIS; Garmire, 2003) for a total of 191.6
ks (Proposal 16200863, PI: J. Drake). The four ACIS-I chips were used in Very
Faint telemetry mode to improve the screening of background events and thus
increase the sensitivity of ACIS to faint sources (Vikhlinin, 2001). The
exposure-weighted average aimpoint of the 16$\farcm$9$\times$16$\farcm$9
ACIS-I field of view is
$\alpha=08^{\mathrm{h}}39^{\mathrm{m}}50.^{\mathrm{s}}2$,
$\delta=+19^{\circ}31^{\prime}05\farcs 0$0 (J2000). Figure 5 shows the
combined footprint of this observation, plus an archival Chandra observation
and new and archival XMM observations (see Section 3.3).

Two M dwarf Hyads, LP 415-19 (2MASS J04214435+2024105) and 2MASS
J04214586+2023446, half an arcminute apart, were observed 12 separate times
with the same pointing and varying roll angles between 2020 Nov and 2020 Dec,
for a total of 218.7 ks (Proposal 22200351, PI: Agüeros). We used the ACIS-S3
chip, plus optional S2, I0, and I1 chips, in Very Faint telemetry mode. The
exposure-weighted average aimpoint of the combined field of view is
$\alpha=04^{\mathrm{h}}21^{\mathrm{m}}45.^{\mathrm{s}}2$,
$\delta=+20^{\circ}23^{\prime}55\farcs 8$ (J2000). In addition to these two M
dwarfs, we detected another M dwarf, 2MASS J04213829+2018102, that
serendipitously fell within the field of view of the combined pointings.

The M dwarf Hyad 2MASS J04351354+2008014 was observed six separate times with
the same pointing and differing roll angles during between 2021 Jan and 2021
Oct, for a total of 175.1 ks (Proposal 22200351, PI: Agüeros). We used the
ACIS-S3 chip, plus optional S2, I0, and I1 chips, in Very Faint telemetry
mode. The exposure-weighted average aimpoint of the combined field of view is
$\alpha=04^{\mathrm{h}}35^{\mathrm{m}}13.^{\mathrm{s}}6$,
$\delta=+20^{\circ}07^{\prime}59\farcs 9$ (J2000).

Lastly, three K dwarf Hyads, StKM 1-393 (2MASS J03390791+2822560), BD+05 526
(2MASS J03400754+0552286), and HD 286363 (2MASS J03550142+1229081), and one G0
dwarf Hyad, HD 265537 (2MASS J06531311+2119128), were observed individually in
2020 and 2021 as part of the Chandra Cool Targets
program111111https://cxc.harvard.edu/proposer/CCTs.html (Proposal 20201075,
PI: Agüeros). In each observation, we used the ACIS-S3 chip in Very Faint
telemetry mode. Each star was observed for 10.0 ks.

##### Using CIAO on the New Chandra Observations

We performed the following steps on each one of the recent Chandra
observations. We started by running chandra_repro. We did not use very faint
correction, as we wanted to avoid excluding potentially good events in
modestly bright point sources. Next, we corrected the absolute astrometry of
the observations. To do this, we ran wavdetect with a false-probability
threshold of 10-6 on the observations to produce a conservative list of point
sources. We then used a list of high quality (ph_qual = AAA) 2MASS sources and
the tool reproject_aspect to register the astrometry of the observations to
the astrometric frame of 2MASS. We used a 3″ matching radius and residual
rejection limit of 0$\farcs$6.

In the cases where observations were broken down into several pointings, we
ran the steps above on the longest pointing, and then we ran wavdetect and
reproject_aspect on the rest of the pointings to register their astrometry to
that of the longest pointing. Next, we merged the individual pointings using
merge_obs and produced merged events in the soft, hard, and broad bands.

We created point-spread function (PSF) maps for the observations. In the cases
with more than one pointing, we combined the individual PSF maps using
dmimgfilt and selecting the minimum PSF map size out of the individual
pointings at each pixel. This last step allows us to detect point sources that
may be smaller than the mean size, but still larger than the local PSF in the
individual pointing maps.

Subsequently, we ran wavdetect for the three energy bands using the PSF map
and using a less stringent false-probability threshold of 10-5, to allow for a
non-negligible number of spurious sources to be included in the initial source
candidate list. We consolidated the resulting three lists of sources by
matching them against each other using a 2″ matching radius for sources with
off-axis angle $\theta<$5 ′ and 4″ for sources with $\theta>$ 5′. For matched
sources, we adopted the source region description, in order of priority, from
the broad, soft, or hard band list. We then visually inspected the
consolidated source list to discard sources that overlapped significantly with
others or sources characterized by ellipse regions that deviated significantly
from the local PSF (e.g., minor axis $\approx$0″). Next, we used a 15″
matching radius to find optical counterparts in our cluster catalogs for the
X-ray sources. The largest offset radius was 6$\farcs$5 (for a source at an
off-axis angle of $\approx$9′); all other offset radii were below 3$\farcs$5.

We ran srcflux to extract X-ray source count rates for the three energy bands.
We then used our own ECFs (see Section 4.3) and our adopted individual
distances to calculate $f_{\mathrm{X}}$ and $L_{\mathrm{X}}$ in the 0.1–2.4
keV band. Three of our sources extracted with CIAO have $>$300 net counts in
the broad band. As for the bright CSC sources described above, we performed
spectral analysis on these sources to extract unabsorbed $f_{\mathrm{X}}$
values as well as plasma parameters (see Section 3.5). The extracted
spectroscopic information is included in Table 5.

Figure 5: Left: Footprints of X-ray observations in the field of view of
Praesepe: three with the Chandra ACIS camera and 24 with the XMM EPIC camera.
Red footprints indicate observations for which one of the co-authors is the
P.I., and blue footprints, other publicly available observations. The gray
circles indicate cluster members. A black plus symbol indicates the cluster
center. Each XMM footprint represents the combined contours of the usable
parts of the EPIC pn and MOS cameras. Right: Zoomed out view of Praesepe, to
display eight additional footprints (one Chandra and seven XMM) along a tidal
tail of Praesepe, including one at $\delta>$ +50∘, and six that completely
overlap. A PanSTARRS color image serves as the background on both panels.

Lastly, we ran glvary on each source, which searches for X-ray variability
using the Gregory-Loredo algorithm. We inspected the light curves of the six
sources we have with a probability of variability $\geq$0.9 (considered to be
definitely variable). We found X-ray flares in five of the six light curves.
In such cases, we filtered them out (see Section 3.6) and then re-ran srcflux
to re-extract the X-ray photometry and properties of the sources.

In total, we matched X-ray sources from these recent Chandra observations to
19 Praesepe stars and eight Hyads in our catalogs. Table 3 includes the X-ray
information for these 27 X-ray sources.

###  3.3 XMM-Newton Observations

####  3.3.1 Data from the XMM Serendipitous Source Catalog

We searched for X-ray counterparts to our cluster stars in the latest version
of the XMM Serendipitous Source Catalog (4XMM-DR11, Webb et al., 2020) from
observations with the EPIC instrument. We cross-matched the list of individual
detections (which use the detid naming convention) in the 4XMM catalog and our
cluster catalogs using a 15″ radius. We found 4XMM counterparts to 315
Praesepe stars and 110 Hyads. Like with CSC (see Section 3.2.1), we estimated
the number of likely false matches by shifting the X-ray source positions in
steps of 25″ out to 5′ in all directions and re-matched them to the cluster
catalogs using the same 15″ radius used before. We found the median number of
false matches to be 21 ($\approx$5% of our matched 4XMM sources) with a median
offset of 10″. In our final 4XMM-cluster catalogs matches, we flag those with
radii $>$10″—there are eight Praesepe matches (all for the same star) in this
category—as likely false matches. All 110 Hyad matches, on the other hand,
have matching radii $<$6″.

From 4XMM, we obtained count rates in the basic energy bands 1 through 5,
which together span the energy range 0.2–12.0 keV, and then combined bands 1
through 3 to create a soft band, 4 and 5 to create a hard band, and 1 through
5 to create the broad band. Additionally, we obtained some other information
about the X-ray sources, such as detection likelihoods and variability flags
(see Table 3). We used the published count rates, our own ECF (see Section
4.3), and our adopted individual distances to calculate $f_{\mathrm{X}}$ and
$L_{\mathrm{X}}$ in the 0.1–2.4 keV band. Information about the original XMM
observations that collected the data for these 425 4XMM sources is shown in
Table 4.

Of the 4XMM X-ray sources matched to cluster stars, 129 had $>$300 net counts
in the broad band for the pn camera or $>$500 net counts in the broad band for
the combined pn and MOS cameras. For these sources we performed spectral
analysis to extract unabsorbed $f_{\mathrm{X}}$ as well as plasma parameters
(see Section 3.5). The extracted spectroscopic information is included in
Table 5.

We inspected the light curves for all 4XMM sources with flags indicating
variability. We found 28 sources with X-ray flares in their light curves. In
such cases, we filtered the flare events out (see Section 3.6) and then re-
extracted the X-ray photometry and properties of the sources. Table 3 includes
the X-ray information for all the 4XMM sources.

####  3.3.2 XMM Source Extraction with SAS

The 4XMM-DR11 catalog only includes observations through the end of 2020. For
the XMM pointing we obtained after this cutoff date, we performed our own data
reduction and source extraction using the XMM Science Analysis System (SAS
v19.0, Gabriel et al., 2004) tools. Table 4 provides the basic information
about this XMM recent pointing.

Furthermore, due to the automated nature of the 4XMM-DR11 catalog pipeline,
some faint point-like sources may have been discarded as spurious detections.
As some of our cluster stars are expected to be very X-ray faint, we performed
our own data reduction of ten archival XMM observations, all targeting the
cluster core, to verify that no X-ray faint source be left behind.

##### New XMM Observation

The slow-rotating Praesepe K3 dwarf JS 297 (2MASS J08393203+2039203) was
observed in 2021 Apr for 32.0 ks (Proposal 86371, PI: Núñez). We used the EPIC
cameras with the medium filter. The aimpoint of the field of view is
$\alpha=08^{\mathrm{h}}39^{\mathrm{m}}32.^{\mathrm{s}}0$,
$\delta=+20^{\circ}39^{\prime}20\farcs 3$ (J2000) and the roll angle is
283$\fdg$6\. In addition to this K dwarf, we detected ten other Praesepe
dwarfs (one F, one G, one K, and seven M types) that serendipitously fell
within the field of view of this observation, as we describe next.

##### Using SAS on New and Archival XMM Observations

We used SAS to reduce the recent observation—plus ten archival observations
targeting the core of Praesepe—with the most up-to-date calibration. We
started by applying standard filters to event files. Next, we created filtered
event files for the three EPIC cameras by excluding times when the global
count rate in the MOS1 camera increased beyond $\approx$2.5 counts sec-1.
Finally, we used the edetect_chain task to perform source detection on both
MOS and pn images simultaneously. The algorithm in edetect_chain runs a
sliding box source detection (eboxdetect), then computes maximum likelihood
analysis to prune the initial source list (emldetect).

The 4XMM SAS pipeline uses the five basic energy bands 0.2–0.5, 0.5–0.1,
1.0–2.0, 2.0–4.5, and 4.5–12.0 keV (bands 1 through 5) for source detection
and extraction. We used instead the broader energy bands 0.2–2.0 and 2.0–12.0,
plus the total band 0.2–12.0 keV. We adopted these three bands, which
correspond to 4XMM bands 6, 7, and 8, as the soft, hard, and broad bands,
respectively. An image with a broader energy band will include a higher number
of source counts than one with a narrower band; for a very faint source, this
increase in source counts may be significant. Therefore, the source detection
routines may be able to pick up fainter sources in broader bands. At the same
time, a broadband image will also include a higher number of background
counts. As a compromise, we increased the detection likelihood threshold in
the detection algorithm from 6—the value used in the automatic SAS pipeline—to
8. Furthermore, although edetect_chain performs simultaneous source detection
across all bands and detectors, we did not require sources to be detected in
all three cameras. As, for example, there are several dead chips on the MOS1
camera, this would severely limit our available area for detection.

We cross-matched the resulting X-ray source list with our cluster catalogs
using a 15″ tolerance radius. From the new XMM observation (not included in
the 4XMM catalog), we matched eleven X-ray sources to Praesepe counterparts.
One of these matched sources had enough source counts to perform spectral
analysis (see Section 3.5). Table 3 includes information for these eleven
sources.

From our SAS reductions of the archival observations of the core of Praesepe,
we found 34 X-ray counterparts to Praesepe stars that are not present in the
4XMM catalog. The maximum likelihood values for these 34 sources are in the
range 8.2–140.0; the source with the highest likelihood was detected only with
the pn camera. Table 3 includes information for these 34 sources. One of the
34 sources has a likelihood of being an extended source of 9.1, and we
therefore flag this source as a likely extended source in this Table.

###  3.4 Data from the Swift XRT Point Source Catalog

We searched for X-ray counterparts to our cluster stars in the latest version
of the Swift XRT Point Source Catalog (2SXPS, Evans et al., 2020b). This
catalog includes observations through 2018 Aug, which covers eleven
observations from our proposal to observe low-mass Hyads (Proposal 1215128,
PI: Agüeros). We cross-matched 2SXPS and our cluster catalogs using a 15″
radius. We found 2SXPS counterparts to six Praesepe stars and 59 Hyads. Like
with ROSAT (see Section 3.1.1), we estimated the number of likely false
matches by shifting the X-ray source positions by 25″ out to 3′ in all
directions and re-matched them to the cluster catalogs using the same 15″
radius used before. We found that the median number of false matches is one
($\approx$2% of our matched 2SXPS sources) with a median offset of 10″. None
of our 2SXPS matches merited a “likely mismatch” flag (Column 28 of Table 3).

From the 2SXPS catalog we obtained count rates in the 0.3–1.0, 1.0–2.0, and
2.0-10.0 keV bands. We then combined the first two bands to create the soft
band, adopted the third band as the hard band, and combined all three bands to
create the broad band. Additionally, we obtained some other information about
the X-ray sources, such as hardness ratios, detection likelihoods, and
variability flags (see Table 3). We used the published count rates, our own
ECF (see Section 4.3), and our adopted individual distances to calculate
$f_{\mathrm{X}}$ and $L_{\mathrm{X}}$ in the 0.1–2.4 keV band.

Three of the 2SXPS sources had $>$300 source counts in the broad band. For
these sources, we performed spectral analysis to extract unabsorbed
$f_{\mathrm{X}}$ as well as plasma parameters (see Section 3.5). The extracted
spectroscopic information is included in Table 5.

###  3.5 X-ray Spectral Fitting and Properties

We performed spectral analysis on six Chandra, three Swift, and 130 XMM
sources, for a total of 139. To be included in spectral fitting, we required
an X-ray source to have at least 300 counts121212We performed spectral fitting
on sources between 100 and 300 counts, but obtained poor statistical results.
We therefore excluded sources with $<$300 counts from our spectral analysis.
in either Chandra ACIS, Swift XRT, or XMM EPIC pn cameras; we also included
XMM sources with at least 500 combined counts in the three EPIC cameras.

Figure 6: X-ray spectral fitting parameters for X-ray sources with $>$300
counts, using a one-temperature APEC model and setting the neutral hydrogen
column density to the typical value for each cluster (see Section 3.5). The
panels show the coronal metal abundance with respect to Solar (top row) and
coronal temperature (bottom row) as a function of ($G-K$) color (left column),
$R_{\mathrm{o}}$ (middle column), and $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$
(right column). Gray circles indicate single members, and orange $\times$
symbols, candidate/confirmed binaries. The dash horizontal lines in the left
column indicate the parameter values we assumed for the APEC model we used to
derive our own ECFs to apply to low-count X-ray sources (see Section 4.3).
Most K and M dwarfs have metal abundance less than $\approx$0.2, whereas F and
G dwarfs have a large spread in abundance, from $\approx$0.1 up to
$\approx$0.9. Plasma temperature is constrained between 0.4 and 1.0 keV for
all dwarfs. Table 5: Spectral Fits for the Highest X-Ray Count Chandra, Swift,
and XMM Sources

Source ID | IAU Name | $kT$ | Metal | $N_{\mathrm{H}}$ | Flux | $\chi^{2}_{\nu}$ | d.o.f.
---|---|---|---|---|---|---|---
|  |  | Abund. | ($10^{21}$) | ($10^{-14}$) |  |
|  | (keV) |  | (cm-2) | (erg cm-2 s-1 ) |  |
107851101010001 | 4XMM J041802.0+181522 | 0.68$\pm$0.02 | 0.54$\pm$0.08 |  $\cdots$ | 41.36$\pm$3.05 | 1.99 | 227
107619211010001 | 4XMM J083656.2+185747 | 0.76$\pm$0.03 | 0.09$\pm$0.02 |  $\cdots$ | 5.83$\pm$0.45 | 1.06 | 121
107216201010012 | 4XMM J083915.7+200413 | 0.61$\pm$0.05 | 0.05$\pm$0.02 |  $\cdots$ | 3.58$\pm$0.56 | 0.81 | 53
$\cdots$ | XMMU J083952.7+203046 | 0.72$\pm$0.09 | 0.05$\pm$0.03 | 1.08$\pm$0.36 | 4.68$\pm$1.44 | 0.71 | 49
$\cdots$ | CXOU J042138.5+201809 | 0.98$\pm$0.07 | 0.27$\pm$0.13 |  $\cdots$ | 4.61$\pm$1.25 | 1.51 | 24

Note. — Results of all acceptable spectral fits for our highest-count X-ray
sources using a one-temperature APEC model. All fits included the XSPEC model
tbabs to account for ISM extinction, and we give the best fit atomic hydrogen
column density $N_{\mathrm{H}}$ in the cases where freeing this parameter
resulted in a better fit. We also show the derived unabsorbed flux in the
0.1–2.4 keV band. Finally, we give for each fit its reduced chi-square
($\chi^{2}_{\nu}$) and degrees of freedom (d.o.f.). This table is available in
its entirety in the electronic edition of the ApJ. Five rows are shown here
for guidance regarding its form and content.

Of the 139 X-ray spectra, 75 are of Praesepe stars and 64 are of Hyads,
including 89 total spectra for candidate/confirmed binaries. Also, seven of
the 139 are cluster giants, and one is a candidate white dwarf–M6 dwarf binary
(2MASS J03040207+0045512, Becker et al., 2011). We excluded these eight non-
main-sequence stars from our analysis.

We used the CIAO tool Sherpa (v. 4.13.0, Freeman et al., 2001; Burke et al.,
2021) to perform the spectral analysis. We fitted the spectra with an XSPEC
one-temperature (1T) APEC optically thin plasma emission spectrum model. We
combined the APEC model with ISM absorption model TBabs to account for
extinction by neutral atomic hydrogen ($N_{\mathrm{H}}$). We binned the
spectra by 20 counts per bin for sources with more than 1000 counts, and by
15, for those with fewer than 1000 counts. We then fitted the spectra using
the $\chi^{2}$ statistic with the Gehrels variance function and Sherpa’s
levmar optimization method. We obtained 1$\sigma$ confidence intervals of all
free parameters by computing the co-variance matrices.

Most XMM sources had up to three spectra from the same observation, one EPIC
pn and two MOS spectra. In such cases, we performed the spectral fit for each
source using all available spectra simultaneously.

For each source, we ran the fit twice. First, we ran it by setting the
$N_{\mathrm{H}}$ parameter to that of the star’s cluster: 1.50$\times 10^{20}$
cm-2 for Praesepe and 5.50$\times 10^{18}$ cm-2 for Hyades, derived using our
adopted $E$($B$-$V$) values for the two clusters (see Section 2.4) and
$N_{\mathrm{H}}$[cm${}^{-2}/A_{v}$] = 1.79 $\times 10^{21}$ (Predehl &
Schmitt, 1995). Then, we freed the $N_{\mathrm{H}}$ parameter and ran the fit
again. We considered the fit with the reduced $\chi^{2}$ statistic
($\chi_{\nu}^{2}$) closest to unity as the best fit. Only eleven of the 139
X-ray sources had a better spectral fit with a free $N_{\mathrm{H}}$
parameter. The resulting $N_{\mathrm{H}}$ in these eleven spectra are between
0.2 and fifteen times the value for the cluster, except one case, for which
$N_{\mathrm{H}}$ is two orders of magnitude larger than that of the Hyades
cluster. This X-ray source with unexpectedly large $N_{\mathrm{H}}$ is matched
to the white dwarf–M6 binary mentioned above.

From each spectral fit, we also obtained values for the plasma temperature kT,
metal abundance with respect to the Sun, and the unabsorbed energy flux in the
0.1–2.4 keV band. Column 26 of Table 3 identifies the X-ray sources for which
we used spectral fitting to calculate their $f_{\mathrm{X}}$. Table 5 shows
the fit results for each of the 139 X-ray sources, including the
$\chi_{\nu}^{2}$ statistic and the degrees of freedom. Figures of our spectral
fits are publicly available from the Columbia University Academic Commons, an
online research repository.131313Available at
https://doi.org/10.7916/dtws-0x90.

Figure 6 shows the metal abundance (top row) and plasma temperature (bottom
row) parameters resulting from our spectral fits, drawn against ($G-K$) color
(left column), $R_{\mathrm{o}}$ number (middle column, see Section 4.2), and
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ (right column, see Section 4.3) for main-
sequence stars in the two clusters. There is a clear trend for metal
abundances to remain less than $\approx$0.2 with respect to Solar for most K
and M dwarfs ($G-K>1.8$). F and G dwarfs ($G-K$ $\buildrel<\over{\sim}$ 1.8),
on the other hand, show a large spread in abundance, from $\approx$0.1 up to
$\approx$0.9, with an average value of $\approx$0.4. This trend is true for
both single (gray circles) and binary stars (orange $\times$ symbols). Plasma
temperature, on the other hand, appears to be constrained between 0.4 keV (4.6
MK) and $\approx$1.0 keV (11.6 MK) for all low-mass stars, with an average
value of $\approx$0.7 keV (8.1 MK).

###  3.6 Removing X-ray Flares

Some of the X-ray observations used in our work have exposure times long
enough ($\buildrel>\over{\sim}$30 ks) to increase the probability of catching
a transient stellar flare. During an X-ray flare, the X-ray emission of a star
increases significantly from the quiescent level, in some extreme cases up to
7000 times, for a couple to a few hours (e.g., Osten et al., 2010). Therefore,
including the emission from the flare in the calculation of the energy flux of
a source would inflate the flux value from the expected quiescent level—the
latter being the more representative measurement of the magnetic activity
level of a low-mass star. To obtain the most representative energy flux values
for stars in our two clusters, we removed X-ray flares whenever possible from
our X-ray source calculations.

First, we examined the X-ray light curves of sources with variability flags
indicating a high probability of a variable source, as these are the ones most
likely to include an X-ray flare. Next, we identified the flare time interval
of each X-ray flare, which we defined as the time with a rapid increase in the
count rate to at least 3$\sigma$ from the quiescent level and lasting for at
least $\approx$2 ks (half an hour). We then generated new event files by
removing counts that occurred during the flaring time intervals. Finally, we
re-extracted X-ray source parameters and photometry from the new event files.

All in all, we removed flares from five Chandra and 27 XMM sources. The
average change in source count rate from pre- to post-flare removing was a
decrease of $\approx$12%. Seven of these 32 sources had an unexpected higher
count rate after we removed flares. We found that in all seven cases—all from
the 4XMM catalog—we removed, in addition to an X-ray flare, noisy light curve
edges caused possibly by a faulty X-ray background extraction in the 4XMM
automated reduction pipeline, which resulted in episodes of negative count
rates in the original light curve.

Column 27 of Table 3 indicates whether we removed an X-ray flare from each
source to calculate its X-ray parameters and photometry. Figures of the X-ray
light curves with identified flares are publicly available from the Columbia
University Academic Commons.13

##  4 Deriving Stellar Properties

###  4.1 Stellar Masses and Bolometric Luminosities

We calculated stellar masses $m$ and bolometric luminosities
($L_{\mathrm{bol}}$) for main-sequence members of both clusters using the
empirical $m$– and log($L_{\mathrm{bol}}$)–$M_{G}$ relations of E.
Mamajek.141414Version 2021.03.02. Available at
http://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt. Much
of this table comes from Pecaut & Mamajek (2013). We linearly interpolated
between the $M_{G}$ values in the empirical relation to obtain $m$ and
log($L_{\mathrm{bol}}$) values. The calculated $m$ values are in the range
0.09–2.28 ${M_{\odot}}$ for Praesepe and 0.08–2.47 ${M_{\odot}}$ for Hyades.
Column 31 in Table 2 includes $m$, and columns 33 and 34, $L_{\mathrm{bol}}$
and its 1$\sigma$ uncertainty.

For nine of the ultracool dwarfs that we found in the literature (seven in
Praesepe and two in the Hyades), we adopted $m$ published by those authors
(see Section 2.3), instead of relying on the $m$–$M_{G}$ relation above. These
nine values are in the range 0.05–0.11 ${M_{\odot}}$.

Lastly, although we calculated $m$ and $L_{\mathrm{bol}}$ for
candidate/confirmed binaries, we recognize that these two quantities are
likely over-estimated for these stars, as there is more than one light source
contributing to the brightness of the spatially unresolved stellar source.

###  4.2 Rossby Numbers

Studies of the rotation-activity relation typically express rotation in a
mass-independent manner by substituting the Rossby number $R_{\mathrm{o}}$ for
$P_{\mathrm{rot}}$, as was first demonstrated by (Noyes et al., 1984). $R_{o}$
is given by $P_{\mathrm{rot}}$/$\tau$, where $\tau$ is the convective overturn
time. We used the empirical mass–log($\tau$) relation of Wright et al. (2018),
which is based on $P_{\mathrm{rot}}$ and X-ray luminosity measurements for
almost 850 stars in the mass range 0.08–1.36 ${M_{\odot}}$. Column 32 in Table
2 includes our $\tau$ estimates. With those $\tau$ values, we calculated
$R_{o}$ for cluster stars with a measured $P_{\mathrm{rot}}$.

###  4.3 X-ray Luminosities

Most of the X-ray sources matched to Praesepe and Hyades stars do not have
enough source counts to derive $f_{\mathrm{X}}$ from spectral fitting (see
Section 3.5). For these low-count X-ray sources, we calculated ECFs using the
tool WebPIMMS151515https://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3pimms/w3pimms.pl to convert the instrumental count rates into
unabsorbed $f_{\mathrm{X}}$ in the 0.1–2.4 keV energy band. We calculated the
ECFs using a one-temperature thermal APEC model (Smith et al., 2001) with a
plasma temperature161616The PIMMS models only have solutions for discrete
values of the input parameters. The closest of these discrete values to our
average plasma temperature is 0.6845 keV, and to our average metal abundances
are 0.2 and 0.4 Solar. of 0.6845 keV and setting the following inputs specific
for each X-ray source:

  * •

the X-ray instrument used, namely, Chandra’s ACIS-I, ACIS-S, and HRC
detectors, ROSAT’s PSPC and HRI cameras, Swift’s XRT camera, and XMM’s pn and
MOS EPIC cameras;

  * •

the Chandra cycle in which the source was detected171717We used
https://cxc.harvard.edu/toolkit/pimms.jsp for Chandra’s ECFs, because it
accounts for the evolution of the effective areas of the Chandra detectors.;

  * •

the filter used with the XMM EPIC cameras (thin, medium, or thick filters);

  * •

the energy bands of the instrumental count rates, which are generally
instrument-specific and thus different for the different X-ray missions; plus,
for the case of the ROSAT catalogs we used the energy bands reported therein;

  * •

the $N_{\mathrm{H}}$ value assumed for each open cluster (see Section 3.5);
and

  * •

a plasma metal abundance16 of 0.2 for stars with ($G-K$) $>$ 1.8 and 0.4 for
stars with ($G-K$) $\leq$ 1.8 (see Section 3.5).

Table 6: ECFs Used For the Low-Count X-Ray Sources

Observatory | Instrument | Energy | Other | Praesepe | Hyades
---|---|---|---|---|---
|  | BandaaThe original energy band of the instrumental count rate values. | DescribersbbCycle number for Chandra; catalog for ROSAT: R95 is Randich & Schmitt (1995), S95 is Stern et al. (1995), and S01 is Stelzer & Neuhäuser (2001); operation mode for Swift; and filter type for XMM. | Abundance 0.2 | Abundance 0.4 | Abundance 0.2 | Abundance 0.4
Chandra | ACIS-I | 0.5–7.0 | Cycle 4 | $\cdots$ |  $\cdots$ | 7.314E$-$12 | 6.462E$-$12
|  |  | Cycle 8 | 9.956E$-$12 | 8.842E$-$12 | 9.672E$-$12 | 8.584E$-$12
|  |  | Cycle 9 | 9.972E$-$12 | 8.856E$-$12 |  $\cdots$ |  $\cdots$
|  |  | Cycle 15 | $\cdots$ |  $\cdots$ | 1.278E$-$11 | 1.140E$-$11
|  |  | Cycle 16 | 1.529E$-$11 | 1.370E$-$11 |  $\cdots$ |  $\cdots$
| ACIS-S | 0.5–7.0 | Cycle 3 | $\cdots$ |  $\cdots$ | 4.240E$-$12 | 3.798E$-$12
|  |  | Cycle 8 | $\cdots$ |  $\cdots$ | 5.354E$-$12 | 4.740E$-$12
|  |  | Cycle 9 | 5.554E$-$12 | 4.918E$-$12 |  $\cdots$ |  $\cdots$
|  |  | Cycle 13 | $\cdots$ |  $\cdots$ | 6.048E$-$12 | 5.342E$-$12
|  |  | Cycle 14 | 6.084E$-$12 | 5.554E$-$12 | 6.082E$-$12 | 5.372E$-$12
|  |  | Cycle 20 | $\cdots$ |  $\cdots$ | 2.020E$-$11 | 1.843E$-$11
|  |  | Cycle 21 | $\cdots$ |  $\cdots$ | 1.808E$-$11 | 1.647E$-$11
|  |  | Cycle 22 | $\cdots$ |  $\cdots$ | 2.120E$-$11 | 1.947E$-$11
| HRC | 0.1–10.0 | Cycle 3 | $\cdots$ |  $\cdots$ | 8.218E$-$12 | 8.126E$-$12
|  |  | Cycle 4 | $\cdots$ |  $\cdots$ | 8.140E$-$12 | 7.980E$-$12
ROSAT | PSPC | 0.1–2.0 | 2RXS/2RXP | 1.141E$-$11 | 1.101E$-$11 | 6.950E$-$12 | 7.314E$-$12
|  | 0.4–2.0 | R95 | 1.630E$-$11 | 1.431E$-$11 |  $\cdots$ |  $\cdots$
|  | 0.1–1.8 | S95 | $\cdots$ |  $\cdots$ | 6.928E$-$12 | 7.294E$-$12
|  | 0.1–2.0 | S01 | $\cdots$ |  $\cdots$ | 6.904E$-$12 | 7.266E$-$12
| HRI | 0.2–2.4 | 1RXH | 3.578E$-$11 | 3.258E$-$11 | 3.074E$-$11 | 2.880E$-$11
Swift | XRT | 0.3–10.0 | PC | 3.202E$-$11 | 2.976E$-$11 | 2.998E$-$11 | 2.804E$-$11
XMM | pn | 0.2–12.0 | Thin | 1.559E$-$12 | 1.511E$-$12 | 1.322E$-$12 | 1.315E$-$12
|  |  | Medium | 1.632E$-$12 | 1.560E$-$12 | 1.425E$-$12 | 1.390E$-$12
|  |  | Thick | 2.248E$-$12 | 2.094E$-$12 | 2.055E$-$12 | 1.935E$-$12
| MOS | 0.2–12.0 | Thin | 7.186E$-$12 | 6.800E$-$12 | 6.452E$-$12 | 6.204E$-$12
|  |  | Medium | 7.454E$-$12 | 6.996E$-$12 | 6.800E$-$12 | 6.462E$-$12
|  |  | Thick | 9.322E$-$12 | 8.634E$-$12 | 8.686E$-$12 | 8.102E$-$12

Note. — All ECFs have units erg cm-2 cts-1 and produce unabsorbed
$f_{\mathrm{X}}$ values in the 0.1–2.4 keV band. We calculated two sets of
ECFs using a 1T APEC model: one set adopted a metal abundance of 0.2 (columns
5 and 7), and another set adopted a metal abundance of 0.4 (columns 6 and 8).
See Section 4.3 for more details.

Table 6 lists all the ECFs we used for the different X-ray point sources in
our X-ray catalog. Columns 24 and 25 in Table 3 include our $f_{\mathrm{X}}$
values for each X-ray source and their 1$\sigma$ uncertainties, and Column 26
identifies the X-ray sources for which we derived $f_{\mathrm{X}}$ using our
ECFs. We do not calculate $f_{\mathrm{X}}$ for X-ray sources with Quality Flag
= “m” or “x” (Column 28 in Table 3).

There are 106 Hyads and 79 Praesepe stars with more than one $f_{\mathrm{X}}$
(and up to four). For these stars, we calculated the $f_{\mathrm{X}}$ range as
a fraction of the mean:
($f_{\mathrm{X}}$${}_{\mathrm{,max}}-$$f_{\mathrm{X}}$,min) /
$f_{\mathrm{X}}$,mean. The median value is 0.45, with 16th and 84th
percentiles of 0.15 and 1.12. Eleven stars have values beyond 1.6 (and up to
2.8). In all eleven cases, the time span of the detections is between 15 and
25 years. We suspect, therefore, that we may be capturing Solar-type activity
cycles in these stars. However, a study of such activity cycles is beyond the
scope of this project.

For stars with more than one $f_{\mathrm{X}}$, we used the error-weighted mean
$f_{\mathrm{X}}$ as the adopted $f_{\mathrm{X}}$ for the star. Lastly, we
converted $f_{\mathrm{X}}$ into $L_{\mathrm{X}}$ using our adopted distances.
For each cluster star detected in X-rays, columns 29 and 30 in Table 2 include
the adopted $f_{\mathrm{X}}$ value and its 1$\sigma$ uncertainty.

Figure 7: Comparison of $L_{\mathrm{X}}$ values derived for Hyads in Freund et
al. (2020) (abscissa) vs. our $L_{\mathrm{X}}$ values for the same stars
(ordinate). We account for the difference in energy range (their 0.2–12.0 keV
vs. our 0.1–2.4 keV) by increasing their $L_{\mathrm{X}}$ values by 16.3%.
Hyads for which we removed X-ray flares before computing their
$L_{\mathrm{X}}$ are highlighted with red circles. The gray solid line is the
1:1 relation, and the gray dashed line is offset from the 1:1 relation by 11%,
which corresponds to the median offset in luminosity between our
$L_{\mathrm{X}}$ values and those in Freund et al. (2020).

Freund et al. (2020) calculated $L_{\mathrm{X}}$ values for Hyads From
Chandra, ROSAT, and XMM detections. If a star had more than one X-ray
detection, these authors assigned it a “best” X-ray detection to derive its
$L_{\mathrm{X}}$, instead of combining them like we did. This results in our
sample having $L_{\mathrm{X}}$ uncertainties smaller than theirs for several
stars. Also, they did not account for potential flares in their X-ray
detections like we did, which results in several of these flaring Hyads having
lower $L_{\mathrm{X}}$ in our catalog. Furthermore, in their ECFs, these
authors assumed an APEC temperature of 0.2725 keV and a metal abundance of 1.0
for all stars, compared to our temperature of 0.6845 keV and abundance of 0.2
or 0.4.

To compare our $L_{\mathrm{X}}$ values against those in Freund et al. (2020)
for the same stars, we had to account for the difference in energy ranges used
to calculate $L_{\mathrm{X}}$ (their 0.2–12.0 keV vs. our 0.1–2.4 keV). Using
PIMMS, we found that one must increase $f_{\mathrm{X}}$ by 16.3% to go from
0.2–12.0 keV to 0.1–2.4 keV, everything else being equal. After applying this
correction, we found a median offset in luminosity of $\approx$11% between our
$L_{\mathrm{X}}$ values and theirs, with our values being larger on average.
Figure 7 compares our $L_{\mathrm{X}}$ to those in Freund et al. (2020),
highlighting stars for which we removed flares $L_{\mathrm{X}}$ (filled red
circles). The systematic offset between our $L_{\mathrm{X}}$ and those of
Freund et al. (2020) can be explained by the difference in assumed APEC
parameter values: increasing the plasma temperature from 0.2725 keV to 0.6845
keV increases the resulting $f_{\mathrm{X}}$ values by up to 20%, and
decreasing the plasma abundance from 1.0 to 0.2 decreases the resulting
$f_{\mathrm{X}}$ values by up to 5%.

##  5 Results and Discussion

###  5.1 X-ray Spectral Parameters

Beginning with the Advanced Satellite for Cosmology and Astrophysics (ASCA)
and Extreme Ultraviolet Explorer (EUVE) missions, studies of both low- and
high-resolution EUV and X-ray spectra of low-mass stars have revealed that the
chemical composition of the corona differs from that of the underlying
photosphere (e.g., Drake et al., 1996; Brinkman et al., 2001; Güdel, 2007;
Testa, 2010). Long documented in the case of the Sun, this chemical abundance
anomaly is referred to as the “First Ionization Potential (FIP) Effect”:
elements with low FIP (FIP $\leq 10$ eV, e.g., Si, Mg, Fe) are enhanced by
factors of 2–4 relative to elements with high FIP (FIP $\geq 10$ eV, e.g., N,
Ne, Ar). In the stellar case, stars with fairly low, solar-like magnetic
activity levels exhibit a solar-like FIP effect (e.g., Drake et al., 1997).
Instead, more active stars exhibit the reverse, and the low FIP metals are
generally depleted relative to high-FIP elements (e.g., Brinkman et al., 2001;
Drake & Kashyap, 2001).

More recent studies with high-resolution X-ray spectra have also uncovered a
spectral type dependence of the FIP effect, and it is not yet clear whether
the depletion or enhancement of metals is mostly controlled by magnetic
activity level (e.g., Telleschi et al., 2005; García-Alvarez et al., 2009), or
by the change in outer convection zone properties with spectral type (e.g.,
Wood & Linsky, 2010; Wood et al., 2012; Wood & Laming, 2013).

The FIP and inverse FIP effects are not yet fully understood, but are likely
related to one or more mechanisms of coronal heating (e.g. Drake et al., 2002;
Testa et al., 2015). The most promising model to date cites the ponderomotive
force on ions in the chromosphere associated with magnetohydrodynamic waves
(Laming, 2015).

Our results show a clear correlation between spectral type and coronal metal
abundance. In our sample of Praesepe and Hyades stars, K and M dwarfs ($G-K\
{\lower 3.44444pt\hbox{$\buildrel>\over{\sim}$}}\ 1.8$) display very low
abundances, whereas F and G dwarfs ($G-K\ {\lower
3.44444pt\hbox{$\buildrel<\over{\sim}$}}\ 1.8$) display higher abundances (see
upper left panel of Figure 6). We find similar correlations with
$R_{\mathrm{o}}$ and $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$: fast rotators
($R_{\mathrm{o}}$ ${\lower 3.44444pt\hbox{$\buildrel<\over{\sim}$}}~{}0.2$)
have very low abundances, and vice versa (upper middle panel), and the more
active stars ($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ ${\lower
3.44444pt\hbox{$\buildrel>\over{\sim}$}}~{}10^{-4}$) have very low abundances,
and vice versa (upper left panel).

As will be shown in Section 5.3, spectral type, $R_{\mathrm{o}}$, and
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ are tightly correlated in our sample of
$\approx$700 Myr old stars, as most fast rotating stars with high activity
levels are K and M types, whereas most slowly spinning stars with moderate to
low activity are F and G types. Therefore, we cannot completely disentangle
activity level, rotation, and spectral type from their relation to coronal
abundance in our sample. Nonetheless, we note that abundance has a tighter
correlation with spectral type than with activity level, as evidenced by a
clear shift from $\buildrel<\over{\sim}$0.2 to an average $\approx$0.4
abundance in both ($G-K$) color space and $R_{\mathrm{o}}$ space, the latter
being a function of the stellar mass dependent $\tau$ parameter. Furthermore,
a significant fraction of K dwarfs have similar slow rotation and low activity
levels as G dwarfs, and yet in Figure 6 it is clear that all K dwarfs have
abundance levels comparable to those of the fast rotating, highly active M
dwarfs instead.

Studies have also found mean coronal temperature to decrease with decreasing
magnetic activity levels (see review by Telleschi et al., 2005). In our
sample, we observe a correlation between temperature and
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ (see lower right panel of Figure 6).
Temperature increases by a factor of $\approx$2.5 as
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ increases by $\approx$3 orders of
magnitude. In a similar study, Singh et al. (1999) found on a sample of ten
low-mass field stars that temperature increased by a factor of $\approx$4
while $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ increased by three orders of
magnitude. Thus, in our sample, coronal temperature appears to be slightly
less sensitive to activity levels.

A similar correlation can be observed between temperature and $R_{\mathrm{o}}$
(bottom middle panel), where stars with higher $R_{\mathrm{o}}$, i.e. slower
rotation rates and, consequently, lower activity levels, display lower coronal
temperatures, more so for single stars than for binaries. The bottom left
panel of Figure 6, on the other hand, shows a very weak correlation between
coronal temperature and ($G-K$) color. Rising temperature with increasing
color (i.e. later spectral types) can be discerned for binaries. For single
stars, the mean temperature of later types is higher, but this is accompanied
by a larger spread in values.

For the most part, however, single and binary stars display very similar
behaviors in Figure 6. This result appears to contradict that of Pye et al.
(1994), who showed binary K dwarf Hyads being at least twice as X-ray bright
as their single brethren. We note that there is a significant gap in our
coverage of K and early M dwarfs (1.8 ${\lower
3.44444pt\hbox{$\buildrel<\over{\sim}$}}~{}G-K~{}{\lower
3.44444pt\hbox{$\buildrel<\over{\sim}$}}~{}3.5$) with X-ray spectral fitting
parameters: in this spectral range we have only four single stars, but we have
17 binaries. And indeed, in that range binaries appear to have higher coronal
temperatures than the single cohort, but with only four single stars to
compare against, we cannot affirm that with a high level of confidence.

Figure 8: $P_{\mathrm{rot}}$ vs. ($G-K$) color for single Praesepe (top panel)
and Hyades (bottom panel) stars. Circles indicate stars with an
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ measurement. Gray triangles indicate stars
without X-ray data. The circles are color-coded according to their $\log$
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ following the colorbar at the bottom left.
Symbols with black edges are single stars with RUWE > 1.4.

####  5.1.1 The Color–Rotation Plane for Single Stars

In Figure 8, we plot single Praesepe and Hyades members in
($G-K$)–$P_{\mathrm{rot}}$ space, with color indicating
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$. Stars that remain undetected in X-rays
are indicated with gray triangles. We note in both clusters (although more so
in Praesepe due to its broader $P_{\mathrm{rot}}$ coverage) that mid F to
early G dwarfs can have similar $P_{\mathrm{rot}}$ values to some early-to-mid
M dwarfs ($\approx$M3 to M5), and yet the latter have much higher levels of
magnetic activity. Furthermore, early-to-mid M dwarfs have
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ spanning up to $\approx$1 order of
magnitude, and yet their $P_{\mathrm{rot}}$ values span over 2 orders of
magnitude ($\approx$5 hr up to $\approx$25 d). Evidently, some saturation
mechanism is preventing the fastest rotators from increasing their X-ray
emission beyond a certain $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ level, as we
will see more clearly in Section 5.3.

Lastly, stars with RUWE $>$ 1.4 do not stand out in the
($G-K$)–$P_{\mathrm{rot}}$ plane (highlighted with black edges in Figure 8).
If these high-RUWE stars are indeed unresolved intermediate binaries, Figure 8
tells us that their spin down evolution has not been greatly affected, if at
all, by the companion.

###  5.2 The Distribution of X-Ray Emission

Figure 9 shows the relation between X-ray emission, in the form of
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ (upper panels) and $L_{\mathrm{X}}$ (lower
panels), and ($G-K$) color for Praesepe (left panels) and Hyades (right
panels) stars. We calculate in Table 7 the $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$
and $L_{\mathrm{X}}$ median, 16th, and 84th percentiles of several spectral
type ranges for both single and binary stars.
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ follows a narrow increasing
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$-color relation from F through early G
types, then spreads—if not remaining flat—between early G and early M types,
and then narrows again beyond early M types. This is true for both Praesepe
and Hyades stars, as well as single (gray circles) and candidate/confirmed
binary (orange $\times$ symbols) stars. For the latter, there is a larger
spread in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ compared to singletons at the
relatively flat $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ region between early G and
early M types.

In $L_{\mathrm{X}}$ space (bottom panels), we find a global trend for later
spectral types to have lower $L_{\mathrm{X}}$, which is not surprising as the
latter depends on the stellar luminosity and the size of the stellar corona
and, thus, on $m$ and radius. We note that mid M dwarfs can have equivalent
$L_{\mathrm{X}}$ levels as some F and early G dwarfs, even though F types can
have stellar radii $\approx$5 times larger than mid M types, and hence, up to
25 times larger surface areas. The small sizes of the highly active M dwarfs
in our sample is compensated by their brighter X-ray emission reflected by
their smaller $R_{\mathrm{o}}$ and largely saturated activity (see Section
5.3). As we found that coronal temperatures varied only weakly across spectral
types (see bottom left panel of Figure 6), this brighter emission cannot
simply be due to hotter coronae in the M dwarfs. The brighter X-ray emission
from M dwarfs is therefore likely driven by higher number of active regions
and/or a significant difference in magnetic topology (e.g., Lang et al.,
2012).

Table 7: $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and $L_{\mathrm{X}}$ Statistics

Sample | Sp. Type | $N_{\star}$ | log $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ | log $L_{\mathrm{X}}$
---|---|---|---|---
Praesepe
Singles | F0–F4 | 8 | $-5.39^{+0.44}_{-0.48}$ | 28.88${}^{+0.52}_{-0.47}$
| F5–F9 | 12 | $-4.60^{+0.12}_{-0.23}$ | 29.20${}^{+0.22}_{-0.11}$
| G0–G4 |  $\cdots$ |  $\cdots$ |  $\cdots$
| G5–G9 | 8 | $-4.67^{+0.23}_{-0.12}$ | 28.71${}^{+0.34}_{-0.07}$
| K0–K4 | 19 | $-4.51^{+0.58}_{-0.18}$ | 28.66${}^{+0.35}_{-0.35}$
| K5–K9 | 12 | $-4.45^{+0.72}_{-0.15}$ | 28.27${}^{+0.71}_{-0.19}$
| M0–M3.0 | 37 | $-3.43^{+0.59}_{-0.65}$ | 28.44${}^{+0.68}_{-0.47}$
| M3.5–M5 | 50 | $-3.00^{+0.33}_{-0.24}$ | 28.48${}^{+0.46}_{-0.27}$
Binaries | F0–F4 | 11 | $-5.51^{+0.64}_{-0.40}$ | 29.17${}^{+0.16}_{-0.50}$
| F5–F9 | 18 | $-4.80^{+0.34}_{-0.57}$ | 29.22${}^{+0.31}_{-0.34}$
| G0–G4 | 12 | $-4.48^{+0.22}_{-0.22}$ | 29.19${}^{+0.60}_{-0.11}$
| G5–G9 | 12 | $-4.55^{+0.38}_{-0.14}$ | 29.05${}^{+0.31}_{-0.14}$
| K0–K4 | 22 | $-4.45^{+0.26}_{-0.31}$ | 28.68${}^{+0.43}_{-0.28}$
| K5–K9 | 11 | $-4.39^{+0.88}_{-0.20}$ | 28.35${}^{+0.86}_{-0.17}$
| M0–M3.0 | 26 | $-3.23^{+0.39}_{-0.54}$ | 29.21${}^{+0.21}_{-0.56}$
| M3.5–M5 | 33 | $-2.97^{+0.25}_{-0.18}$ | 28.57${}^{+0.51}_{-0.33}$
Hyades
Singles | F0–F4 | 17 | $-5.06^{+0.24}_{-0.43}$ | 29.15${}^{+0.21}_{-0.38}$
| F5–F9 | 20 | $-4.61^{+0.11}_{-0.17}$ | 29.27${}^{+0.12}_{-0.17}$
| G0–G4 | 7 | $-4.41^{+0.07}_{-0.19}$ | 29.16${}^{+0.26}_{-0.03}$
| G5–G9 | 11 | $-4.37^{+0.14}_{-0.28}$ | 29.02${}^{+0.13}_{-0.26}$
| K0–K4 | 20 | $-4.45^{+0.12}_{-0.12}$ | 28.61${}^{+0.15}_{-0.16}$
| K5–K9 | 17 | $-4.62^{+0.44}_{-0.12}$ | 28.07${}^{+0.27}_{-0.23}$
| M0–M3.0 | 50 | $-3.30^{+0.37}_{-0.92}$ | 28.60${}^{+0.43}_{-0.68}$
| M3.5–M5 | 95 | $-3.02^{+0.29}_{-0.35}$ | 28.52${}^{+0.34}_{-0.71}$
Binaries | F0–F4 | 8 | $-5.51^{+0.10}_{-0.24}$ | 28.92${}^{+0.08}_{-0.12}$
| F5–F9 | 15 | $-4.53^{+0.13}_{-0.26}$ | 29.41${}^{+0.17}_{-0.08}$
| G0–G4 | 10 | $-4.60^{+0.16}_{-0.15}$ | 29.16${}^{+0.22}_{-0.12}$
| G5–G9 | 18 | $-4.46^{+0.13}_{-0.25}$ | 29.07${}^{+0.41}_{-0.31}$
| K0–K4 | 32 | $-4.42^{+0.36}_{-0.15}$ | 28.74${}^{+0.44}_{-0.19}$
| K5–K9 | 18 | $-4.20^{+1.06}_{-0.41}$ | 28.75${}^{+0.91}_{-0.75}$
| M0–M3.0 | 33 | $-3.14^{+0.25}_{-0.52}$ | 29.00${}^{+0.36}_{-0.37}$
| M3.5–M5 | 53 | $-2.86^{+0.26}_{-0.40}$ | 28.59${}^{+0.45}_{-0.56}$

Note. — The quoted values are median, 16th, and 84th percentiles.

Figure 9: $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ (top panels) and
$L_{\mathrm{X}}$ (bottom) vs. ($G-K$) color for Praesepe (left panels) and
Hyades (right) stars. Gray circles indicate single members, and orange
$\times$ symbols, candidate/confirmed binaries. Stars, both single and binary,
follow a narrow increasing $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ sequence from F
through early G that then spreads between G and early M types, and narrows
again beyond early M types.

####  5.2.1 X-Ray Emission of Singles vs. Binaries

In Section 5.1, we noted that there were only small differences in the X-ray
emission characteristics, namely, coronal abundance and temperature, between
single and binary stars. To better visualize any systematic difference between
singles vs. binaries in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and
$L_{\mathrm{X}}$, we performed 1,000 Monte Carlo iterations of $\Delta$ median
log $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ = (median log
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)${}_{\mathrm{binaries}}~{}-$ (median log
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)singles for each spectral type range in
Table 7. At each iteration, we added noise to all
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ measurements, drawn from a Gaussian with
width equal to the uncertainty of each measurement, and re-measured the median
value. We repeated the same process in log $L_{\mathrm{X}}$ space. We show in
Figure 10 the mean and standard deviation of $\Delta$ from our Monte Carlo
results for each cluster and spectral type range.

If we consider the case of unresolved binary systems including two X-ray
emitters, their unresolved $L_{\mathrm{X}}$ would be higher compared to those
for single stars. In the scenario of their total X-ray emission coming from
two stars each with activity levels commensurate to those of single stars,
their total $L_{\mathrm{X}}$ would be twice that of an equivalent single star.
On the other hand, in the scenario of the binary components having experienced
past and/or present interactions, resulting in inflated levels of activity,
their total $L_{\mathrm{X}}$ would be even greater than that of the previous
scenario. In both scenarios, our measured $L_{\mathrm{bol}}$ would also be
inflated for unresolved binaries, as our $L_{\mathrm{bol}}$ are derived from
$M_{G}$ (see Section 4.1). In the extreme case of equal mass binary systems,
their total $L_{\mathrm{bol}}$ would be inflated anywhere between 20% and 60%
(assuming that equal mass binaries lie 0.375 in $M_{G}$ above the single main
sequence, see, e.g., Rampalli et al., 2021) compared to their hypothetical
individual $L_{\mathrm{bol}}$ values. All in all, for the scenario of binaries
without inflated activity, the combined effect would be
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ anywhere between 1.2 and 1.7$\times$
higher for binaries than for singles, or up to $\approx$0.2 orders of
magnitude.

The top panel shows that binaries and singles have similar
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ values—the largest differences are smaller
than 0.5 orders of magnitude, and most differences are within 0.2 orders of
magnitude, both above and below zero. We believe these minor differences can
be explained mostly by the small sample sizes and by the inherent noise around
measuring the X-ray emission of a main-sequence dwarf, by virtue of both
short-term (e.g., flaring) and long-term (e.g., Solar-type activity cycles)
variability. Such inherent noise in our result obscures the expected intrinsic
over-luminosity of binaries in the hypothetical scenario described above.

Figure 10: Top: Mean value, plus 95% confidence interval, of the median log
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ for binaries minus the median log
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ for single members in Praesepe (green
circles) and Hyades (brown triangles) for each spectral type bin of Table 7,
using a Monte Carlo simulation. Bottom: Same as above, but in log
$L_{\mathrm{X}}$ space. We find only marginal differences in X-ray
activity—more evident in $L_{\mathrm{X}}$ space and for a couple of spectral
type bins—between the single and binary populations.

The result in $L_{\mathrm{X}}$ space is almost identical, with two marginal
exceptions. First, K5–K9 binaries in the Hyades are $\approx$0.7 orders of
magnitude more luminous than their single counterparts. Pye et al. (1994) had
found that the X-ray luminosity function of K binaries in the Hyades was
almost one order of magnitude more luminous than that of their single
counterparts. Our result, therefore, partly supports their conclusion. Second,
M0–M3 binaries in Praesepe are $\approx$0.8 orders of magnitude more luminous
than their single counterparts.

In both of these exceptions, the significant over-luminosity of the binary
sample cannot be explained only by assuming that we are capturing two or more
individual—and unresolved—X-ray emitters in our binary $L_{\mathrm{X}}$
measurements. Instead, such over-luminosity suggests that binaries have higher
magnetic activity levels than single stars at those spectral type ranges.
Their rotational information partly corroborates this: In our sample of K5–K9
Hyads, four out of the nine known binaries with known $P_{\mathrm{rot}}$ are
fast rotators ($\leq$5 d), whereas all seven singles with known
$P_{\mathrm{rot}}$ are slow rotators ($\geq$10 d). It is still puzzling that
the highlighted exceptions are for only one specific spectral type range and
for stars in only one of the two clusters. In any event, we caution the reader
about the small sizes of our spectral type subsamples in Table 7, which may
lead to uncertain statistical results.

A potential additional piece of evidence of inflated magnetic activity could
be found in the fraction of X-ray variable/flaring stars in our full sample of
X-ray detections. The most magnetically active stars are expected to have more
common flaring episodes (e.g., Kowalski et al., 2009), and thus have a higher
probability of getting caught flaring or displaying large variability during
an X-ray observation. Of the 963 X-ray sources we have with a variability
flag, 9% are flagged as definitely variable: 36 are single members and 47 are
binaries. As such, we find no strong preference for binaries to have signs of
variability or flaring in X-rays over single members.

Figure 11: Same as Figure 9, but plotting only stars with no binary flags.
Circles indicate stars for which we have a $P_{\mathrm{rot}}$, and gray
triangles, stars without $P_{\mathrm{rot}}$. The circles are color-coded
according to the $P_{\mathrm{rot}}$ value using the colorbar in the top right
panel. Symbols with black edges are single stars with RUWE $>$ 1.4. Stars
appear to plateau in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ between early G and
early M spectral types, even as they display increasing $P_{\mathrm{rot}}$
toward later types.

Similar to Figure 9, Figure 11 shows $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$
(upper panels) and $L_{\mathrm{X}}$ (lower panels) as a function of ($G-K$)
color for stars in our sample, this time only including stars identified as
single cluster members. Colored circles are stars with $P_{\mathrm{rot}}$
measurements, identified by the color map in the upper left panel, and
triangles are stars without $P_{\mathrm{rot}}$. Both clusters reveal a trend
of increasing $P_{\mathrm{rot}}$ with increasing ($G-K$) color for stars in
the relatively flat $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ region between early G
and early M spectral types. For spectral types later than $\approx$M3, roughly
coinciding with the transition between partially and fully convective stellar
interiors (Chabrier & Baraffe, 1997), almost all stars display fast rotation
($P_{\mathrm{rot}}$ $\ll$ 10 d) and high $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$.
Furthermore, both F and mid-to-late M dwarfs can have equivalent
$P_{\mathrm{rot}}$ values, and yet stars in the latter cohort display
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ values that are two orders of magnitude
higher than the F dwarfs in the same cluster.

Interestingly, and analogous to what we find in the color–$P_{\mathrm{rot}}$
plane (Figure 8), there is no significant offset in
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ or $L_{\mathrm{X}}$ between single stars
with RUWE $\leq$ 1.4 and $>$ 1.4. The latter—highlighted with black edges in
Figure 11—could be unresolved intermediate binaries (see Section 2.6), which
means that their X-ray detections could be a combination of X-ray emission
from two (or more) separate sources. In the extreme case of two equally X-ray
bright emitters, their $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and
$L_{\mathrm{X}}$ values would appear over-luminous compared to their single
counterparts by 0.3 in log space, everything else remaining equal. Such a
relatively small difference is largely obscured by the intrinsic noise in our
sample data. However, the fact that there is no widespread large X-ray over-
luminosity in stars with RUWE $>$ 1.4 suggests that levels of magnetic
activity in these potential binaries are not inflated compared to those in
single stars.

####  5.2.2 X-Ray Outlier in the Hyades

The F8 Hyad HD 50554 (2MASS J06544283+2414441) appears under-luminous in
X-rays by at least two orders of magnitude compared to its peers (log
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$$=-6.83$, log [$L_{\mathrm{X}}$/erg s-1]
$=26.9$; see right panels of Figure 9). Sanz-Forcada et al. (2010) estimated
an age of 12.2 Gyr for this star, and Kains et al. (2011), 4.7 Gyr, based on a
surrounding debris disk detected in the far infrared. Our faint
$L_{\mathrm{X}}$ value for this star appears to corroborate an age much older
than that of the Hyades. We included this star in our Hyades catalog because
it is considered a trailing tail star in the Röser et al. (2019) GDR2 Hyades
catalog. However, these authors noted that almost 14% of trailing tail stars
in their catalog are statistically expected to be contaminants. Given the
estimated ages in the literature and its significant under-luminosity in
X-rays, we consider this star a likely contaminant in our Hyades membership
catalog, and therefore exclude it from our calculations in Table 7.

###  5.3 The Relationship Between X-Ray Emission and Rotation

A more direct way to analyze the link between coronal activity and rotation in
low-mass stars is by characterizing the relationship between
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and $R_{\mathrm{o}}$ (see section 4.2). We
break down our sample of cluster stars into single and binary stars, both for
each cluster and combined, to characterize the
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ relation.

To obtain a very clean sample of single stars, we exclude those with RUWE $>$
1.4, the latter considered to be likely unresolved intermediate binaries (see
Section 2.6). Instead, we include these high-RUWE stars in our sample of
cluster binaries. As we noted in Section 5.2.1, the X-ray emission from high-
RUWE stars may be dominated, partially or entirely, by only one of the members
of the potential binary system. As we cannot resolve the system in X-rays or
optically, we therefore consider these stars as potential contaminants in our
analysis of the rotation-activity relation in single stars.

We also exclude cluster stars with $m\geq 1.3$ ${M_{\odot}}$ ($\approx$F5 type
and earlier) to probe the $R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$
relation. Although main-sequence stars with $m$ up to $\approx$1.6
${M_{\odot}}$($\approx$F0 type) can have an outer convective zone (Böhm-
Vitense & Dettmann, 1980), their magnetic activity ceases to be correlated
with rotation. It is, thus, not dominated by a solar-like dynamo, but by
fossil magnetic fields instead (e.g., Böhm-Vitense et al., 2002; Kochukhov,
2003; Walter & Linsky, 1986; Wolff & Heasley, 1987).

We parameterize the $R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$
relationship as a flat region connected to a power law. For stars with
$R_{\mathrm{o}}$ $\leq{R_{\mathrm{o}}}_{\mathrm{,sat}}$, activity is
constant—i.e., saturated—and equal to
($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)sat. Above
${R_{\mathrm{o}}}_{\mathrm{,sat}}$, activity declines as a power law with
index $\beta$, and is, therefore, unsaturated. Functionally, this corresponds
to

$\frac{L_{\mathrm{X}}}{L_{\mathrm{bol}}}=\left\\{\begin{array}[]{l
l}\left(\frac{L_{\mathrm{X}}}{L_{\mathrm{bol}}}\right)_{\mathrm{sat}}&\quad\textrm{if
$R_{\mathrm{o}}\leq R_{\mathrm{o,sat}}$}\\\
CR_{\mathrm{o}}^{\beta}&\quad\textrm{if $R_{\mathrm{o}}$ >
$R_{\mathrm{o,sat}}$}\end{array}\right.$ (1)

where $C$ is a constant. This model has been widely used in the literature
(e.g., Randich 2000, Wright et al. 2011, Douglas et al. 2014, Núñez et al.
2015).

We use the open-source Markov-chain Monte Carlo (MCMC) package emcee (Foreman-
Mackey et al., 2013) to fit this three-parameter model to our data. Like in
the emcee implementation by Magaudda et al. (2020), we allow for a nuisance
parameter $f$ to account for underestimated errors.181818See
https://emcee.readthedocs.io/en/develop/user/line/. We assume flat priors over
each parameter and use 300 walkers, each taking 5,000 steps in their MCMC
chain, to infer maximum likelihood parameters. Our results are presented in
Figure 12. The posterior distributions for each parameter and 2D correlations
between pairs of parameters from each fit are included in a Figure Set in
Appendix A; 200 random samples from these distributions are shown in Figure
12, along with the maximum a posteriori model. In all cases, the nuisance
factor $f$ converges to $\approx$0.1, which suggests that our
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ uncertainties are underestimated by no
more than $\approx$10%.

The ($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)sat, $R_{\mathrm{o}}$,sat, and
$\beta$ parameters corresponding to the maximum a posteriori model are
presented in Table 8 for the six subsamples we show in Figure 12, and are also
annotated in each panel in the Figure. The stated values correspond to the
50th percentiles of the results and the uncertainties are the 16th and 84th
percentiles. We selected these percentiles to be consistent with 1$\sigma$
Gaussian uncertainties, even though our one-dimensional 1D posterior
probability distributions are not Gaussian.

Table 8: Rossby–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ Relation Fitting Results Sample | $N_{\star}$ | ($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)sat | $R_{\mathrm{o,sat}}$ | $\beta$
---|---|---|---|---
|  | ($10^{-3}$) |  |
Singles
Praesepe | 114 | 1.04$\pm$0.10 | 0.18$\pm$0.02 | $-3.24^{+0.34}_{-0.38}$
Hyades | 63 | 0.73${}^{+0.11}_{-0.12}$ | 0.23$\pm$0.03 | $-3.93^{+0.68}_{-0.74}$
All | 177 | 0.92${}^{+0.07}_{-0.08}$ | 0.19$\pm$0.02 | $-3.43^{+0.33}_{-0.36}$
Binaries & with RUWE $>$ 1.4
Praesepe | 107 | 1.10${}^{+0.14}_{-0.15}$ | 0.13${}^{+0.03}_{-0.02}$ | $-2.22^{+0.28}_{-0.40}$
Hyades | 98 | 0.94$\pm$0.11 | 0.18$\pm$0.03 | $-2.82^{+0.38}_{-0.46}$
All | 205 | 1.03$\pm$0.09 | 0.15$\pm$0.02 |  $-2.50\pm$0.29

Figure 12: $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ vs. $R_{\mathrm{o}}$ for stars
in Praesepe (left column), Hyades (middle), and both clusters (right). The top
row shows single stars, and the bottom row shows candidate/confirmed binaries.
This latter set includes stars with no binary flags but with RUWE $>$ 1.4
(indicated with solid black circles). Single stars are color-coded by their
$m$ following the colorbar in the top left panel. The solid black line in each
panel is the maximum a posteriori fit from the MCMC algorithm, and the gray
lines are 200 random samples from the posterior probability distributions. The
fit result of the three parameters, ($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)sat,
$R_{\mathrm{o}}$,sat, and $\beta$, are annotated in each panel. We show in the
Appendix the marginalized posterior probability distributions from the MCMC
analysis for each fit. The power-law index $\beta$ in the unsaturated regime
for single stars is significantly steeper than that for binary stars, the
latter being closer to the canonical $\beta\approx-2$ from other studies in
the literature.

####  5.3.1 X-Ray Emission and Rotation in Singles vs. Binaries

Figure 13: $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ vs. $R_{\mathrm{o}}$ for single
stars in Praesepe and Hyades, highlighting the different spectral types in
each panel. The background gray symbols in all panels are the combined sample
of single FGKM dwarfs in both Praesepe and Hyades, but excluding those with
RUWE $>$ 1.4. The solid black line in all panels is the maximum a posteriori
fit from the MCMC algorithm for the full sample of single Praesepe and Hyades
stars (see top right panel of Figure 12). At the age of Praesepe and Hyades,
fully convective dwarfs (M3.5 and later) remain saturated in X-rays, whereas
most early-to-mid M dwarfs and all late-F, G, and K dwarfs have spun down into
the unsaturated regime.

Stars in close binary systems may have their spin down history affected by the
companion, leading to circularized orbits and synchronized $P_{\mathrm{rot}}$,
the latter resulting in either faster or slower rotation than their single
stellar counterparts at the same age (Counselman, 1973; Meibom & Mathieu,
2005; Zahn, 2008; Fleming et al., 2019). This could lead to higher or lower
X-ray activity in binaries, compared to coeval single stars. For example, and
as we noted in Section 5.2.1, Pye et al. (1994) found that K dwarf binaries in
the Hyades are more than twice as luminous as their single counterparts. Also,
if the binaries are close enough to each other, it is also possible that their
magnetic fields may directly interact.

Based on our fits in Section 5.3, the relationships between coronal activity
and $R_{\mathrm{o}}$ are mostly similar for both our single and binary
subsamples. ($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)${}_{\mathrm{sat}}\approx
10^{-3}$ in all subsamples, with singles vs. binaries agreeing within
1$\sigma$ in their saturation level. The $R_{\mathrm{o}}$,sat thresholds fall
within the approximate narrow range 0.13–0.23, also agreeing within 1$\sigma$.
However, $\beta$ is steeper for single stars than for binaries: $\beta$ falls
between $-3.24$ and $-3.93$ for single stars, and between $-2.22$ and $-2.82$
for binaries.

As we discussed in Section 5.2.1, if we assumed that both components in
unresolved binaries are X-ray emitters, their combined X-ray emission and
$M_{G}$ would translate into higher ($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)sat
for binaries than for singles. For unresolved binaries, their $R_{\mathrm{o}}$
values are smaller than for equivalent single stars by anywhere between
$\approx$10% and 50%, as our $\tau$ are derived from stellar masses, which in
turn are derived from $M_{G}$ (see Section 4.1). The combined, almost uniform
upward shift in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and rightward shift in
$R_{\mathrm{o}}$ for binaries in the
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ plane would translate
into a negligible change in $\beta$ compared to single stars. This shift would
only affect $R_{\mathrm{o}}$,sat, increasing it by up to 50%.

In Table 8 (and Figure 12) we see that the binary subsamples have higher
($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$)sat than the single counterparts by no
more than 1.3$\times$, and their values agree within 1$\sigma$ with one
another. The large spread in activity in the saturated regime in all
subsamples may be partially hiding what would otherwise be a more
statistically significant over-luminosity of binaries over singles in this
regime.

On the other hand, in the subsamples of Praesepe stars and of combined (i.e.,
“All”) cluster stars, $\beta$ values are shallower for binaries than for
singles, disagreeing by at least 1$\sigma$, and $R_{\mathrm{o}}$,sat values
are statistically equivalent for both binaries and singles. Only in the
Hyades, the singles and binaries subsamples have $\beta$ within 1$\sigma$:
$3.93^{+0.68}_{-0.74}$ vs. $-2.82^{+0.38}_{-0.46}$, respectively. Freund et
al. (2020) found $\beta=-2.12\pm 0.60$ in their Hyades study of
$f_{\mathrm{X}}$/$f_{\mathrm{bol}}$ vs. $R_{\mathrm{o}}$, which is
statistically closer to our $\beta$ for binary Hyads than for single Hyads. We
note that these authors did not exclude X-ray flares from their calculations
of X-ray emission and did not systematically apply binary flags to their
sample of stars.

Both the persistent shallower $\beta$ values in our binaries subsamples and
the indistinguishable $R_{\mathrm{o}}$,sat values in both singles and binaries
may be driven by the larger scatter—both in
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and $R_{\mathrm{o}}$—in their unsaturated
regime compared to our subsamples of single stars, which leads to a poorer
power-law fit. In our unresolved binaries, there is no way to appropriately
assign $L_{\mathrm{X}}$ and $L_{\mathrm{bol}}$ values to the individual
components of the binary systems. Even if we assume a first order approach and
split $L_{\mathrm{X}}$ evenly between the binary components, we are still left
with the complication of assigning $R_{\mathrm{o}}$ to only one of them, as
the adopted $P_{\mathrm{rot}}$ only captures one rotating signal. In short,
the ambiguity in the X-ray emission level of stars flagged as binaries or with
RUWE $>$ 1.4 makes the sample presented in the bottom row of Figure 12
inappropriate to study the
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ relation in stars with
secular angular momentum evolution.

####  5.3.2 Saturation and Supersaturation

As we noted earlier, the level of saturation in
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ lies at $\approx$10-3 for all the
subsamples we examined. There is a large spread, a little over one order of
magnitude, in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ in the saturated regime,
particularly in our sample of Praesepe stars. This finding is similar to the
large sample in Wright et al. (2011), in which a mix of cluster and field
stars have a saturated $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ value of
$\approx$10-3 and a spread of about 1.5 orders of magnitude.

We inspected the X-ray nature of stars that are either too under- or over-
luminous in the saturated regime, to determine whether systematic issues were
contributing to the spread in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$. We find no
correlation between $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and X-ray observatory
or source counts. That is, the under/over-luminosity is not a function of
X-ray instrument or exposure times, which leads us to believe that the noise
in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ in the saturated regime is intrinsic to
the stars, due perhaps to unaccounted X-ray flaring or to activity cycles
similar to that observed in the Sun.

To test for supersaturation, a phenomenon usually observed in stars with
$R_{\mathrm{o}}$ $\buildrel<\over{\sim}$ 0.02, we add a secondary power law of
index $\beta_{\mathrm{sup}}$ connected to the flat region in Equation 1 for
$R_{\mathrm{o}}$ $<$ $R_{\mathrm{o}}$,sup, where $R_{\mathrm{o}}$,sup is the
threshold $R_{\mathrm{o}}$ value between supersaturation and saturation. The
results and figures of our MCMC routine on the modified five-parameter (the
three parameters in Equation 1 plus $\beta_{\mathrm{sup}}$ and
$R_{\mathrm{o}}$,sup) model are included in Appendix B.

For our subsamples of single cluster stars, $\beta_{\mathrm{sup}}$ falls
anywhere between 0.23 and 0.76 and $R_{\mathrm{o}}$${}_{\mathrm{,sup}}\approx
0.01$. Such values of $\beta_{\mathrm{sup}}$ could indicate that stars with
$R_{\mathrm{o}}$ $<$ $R_{\mathrm{o}}$,sup are supersaturated and, thus,
experiencing a reduced amount of X-ray activity by virtue of their extremely
fast rotation. However, we recognize that both $\beta_{\mathrm{sup}}$ and
$R_{\mathrm{o}}$,sup are not nearly as constrained as $R_{\mathrm{o}}$,sat and
$\beta$ in the unsaturated regime—both the random samples from the posterior
probability distributions and the marginalized posterior probability
distributions can attest to this. We therefore recognize these results as only
tentative evidence for supersaturation.

Lastly, for our subsamples of binary cluster stars, $\beta_{\mathrm{sup}}$ is
statistically indifferent from zero, and ${R_{\mathrm{o}}}_{\mathrm{,sup}}$ is
virtually unconstrained. If it is true that binaries show no signs of
supersaturation while single stars do, then this could be interpreted as
evidence for inflated levels of coronal activity in binaries with extremely
fast rotation.

####  5.3.3 Spectral Type vs. Rotation and Activity

Figure 13 shows our sample of single Praesepe and Hyades stars combined (gray
circles), highlighting with colored symbols in each panel different spectral
types. As can be seen in the right-most panel, _all_ stars in the hypothetical
supersaturated regime ($R_{\mathrm{o}}$ $\buildrel<\over{\sim}$ 0.01) have
spectral types later than M3.5, i.e., the fully convective stars. The smallest
$R_{\mathrm{o}}$ in our sample of single stars is 0.002 ($P_{\mathrm{rot}}$
$\approx$ 7h), for the M5 and M7.5 dwarfs 2MASS J05003894+2422581 and
J04351354+2008014, respectively. The latter, in particular, appears
significantly brighter than its super fast rotating peers
($L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ = 4.8$\times 10^{-3}$). This, in spite of
the fact that we removed an X-ray flare from its detection to calculate its
quiescent $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ (see Section 3.6). It is
possible, therefore, that we observed this ultracool dwarf during an episode
of large variability and flaring activity, which would explain its over-
luminosity compared to the other M dwarfs in the supersaturated regime.

We noted in Figure 8 the narrow slow-rotating sequence for single stars
spanning the mid F to early M spectral types illustrating the one-to-one
relationship between spectral type and rotation in Praesepe and the Hyades.
Now, Figure 13 highlights the large spread in X-ray activity, as measured by
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$, in these same stars. All late-F, G, and K
dwarfs have practically the same $R_{\mathrm{o}}$, and yet they cover roughly
one order of magnitude in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$. Early M dwarfs
(M0–M3.5) cover one order of magnitude in $R_{\mathrm{o}}$ space and two
orders of magnitude in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$. Lastly, mid- and
late M dwarfs (M3.5–M7), the fully convective cohort, span two orders of
magnitude in $R_{\mathrm{o}}$ space (with $P_{\mathrm{rot}}$ values from
$\approx$5 hr up to $\approx$30 d), while their spread in
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ spans _only_ one and a half orders of
magnitude (right-most panel in Figure 13).

As our sample of Praesepe and Hyades stars is approximately coeval, we can
safely assume that within the same spectral type range, the cause of the
spread in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ is not a function of age. In the
current paradigm of angular momentum driving the level of magnetic activity in
low-mass stars, our findings illustrate the strong dependence of
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ on $R_{\mathrm{o}}$ in unsaturated, partly
convective dwarfs. On the other hand, in the cohort of fully convective
dwarfs, a very large range in $R_{\mathrm{o}}$ translates into only a modest
range in $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$. It would be easy to hold their
fully convective nature responsible for this behavior. However, we may just be
observing an age at which only the fully convective—and a few partially
convective—stars remain saturated and, thus, restricted in their activity
levels by whatever mechanisms drive the saturated regime.

##  6 Conclusion

The Hyades and Praesepe form a crucial bridge between very young open clusters
and field-age stars in the study of the evolution of rotation and activity in
low-mass stars. We re-visit these two clusters to expand our understanding of
the connection between rotation and coronal activity at their critical stellar
age.

We start by combining several membership catalogs, including our own legacy
catalogs and GDR2-based catalogs, and consolidating literature binary
information on these stars. We produce a Praesepe catalog with 1739 members
and a Hyades catalog with 1315 members. For these members, we collect GEDR3
$G$ and 2MASS $K$ and photometry and astrometry to derive stellar parameters,
including stellar mass and $L_{\mathrm{bol}}$. Next, we consolidate
$P_{\mathrm{rot}}$ measurements from the literature for stars in both
clusters.

To produce a comprehensive catalog of coronal activity, we search for X-ray
detections of cluster members with the ROSAT, Chandra, Swift, and XMM
observatories, both archival and new observations. We rely on the archival
serendipitous catalogs of each observatory to obtain the X-ray flux of each
detection. For ten XMM pointings, we perform our own data reduction to add 34
very faint X-ray sources that were not included in the XMM serendipitous
catalog. Additionally, we reduce seven new observations from Chandra and XMM
that were taken after the cutoff dates of the serendipitous catalogs.

We derive $f_{\mathrm{X}}$ values for each X-ray detection from the
instrumental count rates using our own ECFs. For 139 X-ray sources with
sufficient counts, we perform spectral analysis instead to derive
$f_{\mathrm{X}}$ along with coronal temperature and metal abundance. For the
32 sources in which we identify flares in their X-ray light curves, we first
remove counts from the flare events before calculating their $f_{\mathrm{X}}$.
We find no difference in the coronal parameters of binary and nonbinary
cluster members. We also find a very weak correlation between spectral type
and coronal temperature, and a slightly stronger positive correlation between
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ and coronal temperature. More importantly,
we find that coronal abundance displays a strong correlation with stellar
spectral type: G and early-K dwarfs have typical abundance values of