# Evolution of X-ray Activity in $<25$ Myr Old Pre-Main Sequence Stars

Konstantin V. Getman Department of Astronomy & Astrophysics
Pennsylvania State University
525 Davey Laboratory
University Park, PA 16802, USA  Eric D. Feigelson Department of Astronomy &
Astrophysics
Pennsylvania State University
525 Davey Laboratory
University Park, PA 16802, USA  Gordon P. Garmire Huntingdon Institute for
X-ray Astronomy
LLC, 10677 Franks Road
Huntingdon, PA 16652, USA  Patrick S. Broos Department of Astronomy &
Astrophysics
Pennsylvania State University
525 Davey Laboratory
University Park, PA 16802, USA  Michael A. Kuhn Department of Astronomy
California Institute of Technology
Pasadena, CA 91125, USA  Thomas Preibisch Universitäts-Sternwarte München
Ludwig-Maximilians-Universität
Scheinerstr. 1, 81679, München, Germany  Vladimir S. Airapetian American
University
4400 Massachusetts Avenue NW
Washington, DC 20016 USA  NASA/GSFC/SEEC
Greenbelt, MD, 20771, USA

(Accepted for publication in ApJ, June 10, 2022)

###### Abstract

Measuring the evolution of X-ray emission from pre-main sequence (PMS) stars
gives insight into two issues: the response of magnetic dynamo processes to
changes in interior structure and the effects of high-energy radiation on
protoplanetary disks and primordial planetary atmospheres. We present a sample
of 6,003 stars with ages 7–25 Myr in ten nearby open clusters from Chandra
X-ray and Gaia-EDR3 surveys. Combined with previous results in large samples
of younger ($\lesssim 5$ Myr) stars in MYStIX and SFiNCs star forming regions,
mass-stratified activity-age relations are derived for early phases of stellar
evolution. X-ray luminosity ($L_{X}$) is constant during the first few Myr,
possibly due to the presence of extended X-ray coronas insensitive to temporal
changes in stellar size. $L_{X}$ then decays during the 7–25 Myr period, more
rapidly as stellar mass increases. This decay is interpreted as decreasing
efficiency of the $\alpha^{2}$ dynamo as radiative cores grow and a solar-type
$\alpha\Omega$ dynamo emerges. For more massive 3.5–7 M⊙ fully radiative
stars, the X-ray emission plummets indicating lack of an effective magnetic
dynamo. The findings provide improved measurements of high energy radiation
effects on circumstellar material, first the protoplanetary disk and then the
atmospheres of young planets. The observed X-ray luminosities can be so high
that an inner Earth-mass rocky, unmagnetized planet around a solar-mass PMS
star might lose its primary and secondary atmospheres within a few-several
million years. PMS X-ray emission may thus have a significant impact on
evolution of early planetary atmospheres and the conditions promoting the rise
of habitability.

††facilities: CXO, Gaia††software: ACIS Extract (Broos et al., 2010), R (R
Core Team, 2020), XSPEC (Arnaud, 1996)

##  1 Introduction

Pre-main-sequence (PMS) stars are fully or partially convective, rapidly
rotating young stars that exhibit enhanced magnetic activity, which indicates
the presence of powerful magnetic dynamos. Evidence includes cool starspots
covering considerable fractions of the surface, high surface magnetic fields,
and magnetic reconnection flares producing $\sim$1,000–10,000 times more X-ray
emission than the contemporary Sun (Bouvier et al., 1993; Donati et al., 1997;
Feigelson & Montmerle, 1999; Güdel, 2004; Preibisch et al., 2005; Feigelson,
2010; Gregory et al., 2010; Stelzer, 2017).

Figure 1: Temporal evolution of stellar bolometric luminosity and radius for 7
stellar masses as predicted by the PARSEC 1.2S evolutionary models. The
corresponding Hayashi-Henyey and Henyey-ZAMS evolutionary boundaries are
depicted by the small circle and square symbols, respectively. The black solid
lines indicate linear regression fits to the model data within the $t=$ 7–25
Myr age span of the open clusters of interest in the current study.
Corresponding inferred slopes $b$ for the $L_{bol}\propto t^{b}$ and
$R_{\star}\propto t^{b}$ relations within this age range are listed in Table
7.

But, except for very low mass stars that remain fully convective, the interior
of stars change dramatically before they arrive at the Zero Age Main Sequence
(ZAMS). This evolution was calculated in the prescient study of Iben (1965)
and is shown in Figure 1 using modern PARSEC 1.2S evolutionary models (Bressan
et al., 2012; Chen et al., 2014). Stars around a solar mass first contract
with falling bolometric luminosities along Hayashi tracks for $10-15$ Myr
years. We will call this the early-PMS (e-PMS) phase. The star then enters the
late-PMS (l-PMS) phase when the surface temperature rapidly increases, the
outer layer contraction slows, and the luminosity rises somewhat. A core
radiative zone, already emerging during the e-PMS phase, now occupies most of
the volume and mass of the interior.

This l-PMS phase, sometimes called the Henyey track, lasts a few million years
for solar-mass stars. At the end of the l-PMS phase, core convection might
emerge briefly due to 12C burning, after which the star settles on the Zero
Age Main Sequence (ZAMS) with continuous hydrogen burning. The duration of
these phases is strongly mass-dependent with higher mass stars rapidly leaving
the e-PMS Hayashi track and migrating across the Hertzsprung-Russell diagram
in the l-PMS phase in $\lesssim 1$ Myr (right panels of Figure 1).

The l-PMS phase is relatively poorly studied because large and reliable star
samples are difficult to obtain. Many star clusters have dispersed, the
infrared-excess protoplanetary disks have disappeared, and the stars have
drifted away from their natal molecular clouds which themselves may have
dissipated (Kuhn et al., 2019; Alexander et al., 2014; Richert et al., 2018;
Feigelson, 1996). There are no conveniently nearby l-PMS samples such as the
e-PMS Orion Nebula cluster at distance $d\simeq 0.4$ kpc or lower mass groups
Taurus-Auriga or Ophiuchus around $d\simeq 0.15$ kpc. The nearest l-PMS
samples $-$ such as the $\beta$ Pic and TW Hya moving groups and the Sco-Cen
Association $-$ are spread broadly across the sky, inhibiting the study of
large samples of l-PMS stars facilitated by compact clusters.

Consequently, there is limited empirical evidence for the effects of the
interior changes on surface magnetic activity. It is widely believed that
fully convective e-PMS (and late-M main sequence) stars generate magnetic
fields through a distributed turbulent $\alpha^{2}$-type magnetic dynamo
rather than solar-type tachoclinal $\alpha\Omega$-type dynamos (Durney et al.,
1993; Yadav et al., 2015; Cohen et al., 2017; Warnecke & Käpylä, 2020). It is
unclear whether $\alpha^{2}$ dynamos will grow fields up to equipartition
strength or whether they will saturate at weaker levels. The morphology of the
fields emerging onto the surface of e-PMS stars phase may be distinctive;
Cohen et al. (2017) predict they are concentrated at high-latitudes; this is
seen in some e-PMS stars (Donati et al., 2007) but not others (Argiroffi et
al., 2017).

In the X-ray band where magnetic activity is readily investigated, one sample
of l-PMS stars has been studied: $\sim 400$ stars in the 13 Myr old cluster
NGC 869 = h Per at a distance of $d\simeq 2.5$ kpc. Here Argiroffi et al.
(2016) find a dependence of X-ray luminosity on rotation for 1–2 M⊙,
suggesting that activity in stars is now powered by a $\alpha\Omega$-type
dynamo.

In the present study, we investigate the X-ray emission from the e-PMS through
the l-PMS phases in more detail with a larger and more diverse sample: 6,003
young stars in 10 open clusters at distances $0.3\lesssim d\lesssim 2.5$ kpc
with ages ranging from 7 to 25 Myr (Table 1). This sample is combined with our
earlier MYStIX (Massive Young Star-Forming Complex Study in Infrared and
X-Ray) and SFiNCs (Star Formation In Nearby Clouds) surveys of 40,041 e-PMS
stars (ages 0.5–5 Myr) in 42 star forming regions at distances $0.3\lesssim
d\lesssim 3$ kpc (Feigelson et al., 2013; Getman et al., 2019). Large samples
are needed to distinguish dependencies on mass, age and rotation in the
presence of scatter produced by flare variability. Here all of these samples
are observed with the same instrument and analyzed in a homogeneous fashion,
capture stars with different masses (including the rare intermediate mass
stars) at different stages of their PMS evolution.

Our characterization of mass-stratified X-ray activity-age relations in early
stellar evolution from $0.5$ to $25$ Myr has one astronomical goal and two
astrophysical goals:

  1. 1.

It fills a ‘missing link’ in the activity-rotation-age relations for solar-
type stars (Skumanich, 1972a). For the PMS phases, it is important to add
stellar mass as a variable due to strong dependence of interior structure on
mass (Figure 1). Past empirical measurements of the mass-stratified evolution
of X-ray activity have little information between the e-PMS and ZAMS phases
(Preibisch & Feigelson, 2005; Gregory et al., 2016). Our cluster sample is
large enough that, with careful statistical analysis, we can provide
distribution functions of X-ray activity measures rather than just first
moment (e.g. median value) summaries. Our much larger cluster sample should
offer more accurate estimates of mass-stratified X-ray activity as a function
of age.

  2. 2.

Our current study, with a larger cluster sample and a range of ages, can
verify the evidence of Argiroffi et al. (2016) that the transition from
$\alpha^{2}$ to $\alpha\Omega$ dynamos in the stellar interior has
observational consequences in stellar X-ray activity, as outlined above.

  3. 3.

The high fluence X-ray radiation of PMS stars will penetrate deep into nearby
molecular environments. For the e-PMS phase, it is well-established that the
X-rays ionize the protoplanetary disk and have a major role in its dissipation
(Alexander et al., 2014). For the l-PMS phase when disk gas is mostly gone,
the X-rays may have significant effects on the primordial atmospheres of
close-in planets. Lammer et al. (2003) was the first to show that stellar
X-ray and ultraviolet irradiation will dominate thermal evaporation in
atmospheric loss, although their original calculation has been revised in
later studies (reviewed by Owen (2019)). Our empirical findings can assist the
analytical studies like the one by Johnstone et al. (2021a) who use mass-
stratified changes in the X-ray activity as inputs for their calculations on
early planetary atmospheres.

The paper is organized as follows. Past studies on the X-ray evolution in PMS
stars are reviewed in §2. The sample of ten 7–25 Myr-old open clusters and
associated Chandra X-ray data and reduction procedures are described in §3.
Stellar membership assignments for the open clusters are based on a
combination of Chandra and Gaia properties (§4). Properties of the open
clusters and their stellar members are derived in §§5-6. The younger e-PMS
MYStIX and SFiNCs stars supplementing our l-PMS sample are described in §7.
Results on X-ray-mass-age relations are presented in §§8-9 and Appendix
sections B-C. Comparison with past results on the X-ray evolution in PMS stars
is presented in §10. Astrophysical implications for dynamos and surface
activity are discussed in §11, and implications for ionization of disks and
planetary atmospheres are discussed in §12. Companion studies will analyze the
l-PMS X-ray activity dependence on stellar rotation, and will investigate the
presence of mega- and super-flares in l-PMS stars that are common in e-PMS
MYStIX/SFiNCs stars (Getman & Feigelson, 2021).

##  2 Past Studies on X-ray Evolution in PMS Stars

Preibisch & Feigelson (2005) introduce two different approaches to study the
age-dependence of the stellar X-ray luminosity ($L_{X}$). One (approach A)
deals with $L_{X}$ changes over a short time range, first 10 Myr of stellar
evolution, based on the single X-ray dataset of stars in Orion Nebula (COUP;
Getman et al., 2005) with the assumption that the related isochronal age
spread of $\sim 10$ Myr in the Orion Nebula is real. The stellar sample is
limited to lightly-absorbed Orion stars that are likely members of the Orion
Nebula Cluster (ONC). In contrast, the second approach (B) relies on median
stellar X-ray luminosities and ages for several stellar clusters, spanning a
wide age range of a few Gyr. These include very young $t<10$ Myr clusters ONC,
NGC 2264, and Chameleon; older $t=$ 100–600 Myr open clusters Pleiades and
Hyades; and field stars. One of the major findings of this study is a double-
slope decay of X-ray activity in 0.5–1.2 M⊙ stars: mild decay $L_{X}\propto
t^{-0.3}$ over the first 10 Myr of stellar evolution (based on approach A)
followed by much faster decay of $L_{X}\propto t^{-0.75}$ over the large age
range of a few Gyr (approach B). But the authors note that “Comparison [of
ONC] with the NGC 2264 and Chamaeleon I clusters suggests there may be no
decay at all during the PMS phase [i.e., based on approach B]”.

Using approach A, Gregory et al. (2016) extend the X-ray activity evolution
studies towards five young clusters, ONC, NGC 2264, IC 348, NGC 2362, and NGC
6530 (the latter is the primary ionizing cluster of Lagoon Nebula). The X-ray
datasets for all but one cluster were taken from our MYStIX project (Feigelson
et al., 2013). In the stellar mass range of Preibisch & Feigelson (2005)
(0.1–2 M⊙), the inferred slopes $b$ in the $L_{X}\propto t^{b}$ relation
appear similar within errors between the two studies. But Gregory et al.
report slightly steeper decay for more massive 2–3 M⊙ stars. Overall, Gregory
et al. find that the PMS stars on Henyey tracks undergo faster X-ray activity
changes due to the development of radiative cores.

Table 1: Sample of 10 Late-PMS Open Clusters

Region | $l$ | $b$ | $N_{mem}$ | $D$ | $\sigma_{D}$ | $A_{V}$ | Age | $M_{lim}$
---|---|---|---|---|---|---|---|---
| deg | deg |  | pc | pc | mag | Myr | M⊙
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
NGC1502 | 143.6742 | 7.6567 | 256 (231) | 1078 | 13 | 2.1 | 7 | 0.7
NGC2169 | 195.6189 | -2.9264 | 104 (90) | 959 | 6 | 0.7 | 7 | 0.4
IC2395 | 266.6473 | -3.6082 | 246 (179) | 717 | 4 | 0.5 | 9 | 0.4
NGC3293 | 285.8533 | 0.0726 | 944 (743) | 2552 | 34 | 0.9 | 11 | 0.7
NGC869aaNGC 869 = h Per; NGC 884 = $\chi$ Per | 134.6311 | -3.7401 | 1370 (1096) | 2451 | 22 | 1.7 | 13 | 1.0
NGC884aaNGC 869 = h Per; NGC 884 = $\chi$ Per | 135.0176 | -3.5958 | 1294 (895) | 2475 | 23 | 1.7 | 13 | 1.0
NGC4755 | 303.2035 | 2.5031 | 1219 (1003) | 2101 | 14 | 1.2 | 15 | 0.7
NGC1960 | 174.5388 | 1.0702 | 406 (358) | 1192 | 13 | 0.8 | 22 | 0.7
NGC3766 | 294.1170 | -0.0231 | 1968 (1291) | 2074 | 15 | 0.8 | 22 | 0.7
NGC2232 | 214.4996 | -7.4062 | 117 (117) | 319 | 1 | 0.2 | 25 | 0.4

Note. — Column 1: Cluster name. Columns 2-3: Galactic coordinates for the
cluster center in degrees. Column 4: Total number of cluster members
identified across entire Chandra fields (§§4 and 5) and presented in Table 4;
totaling 7,924 X-ray and non-X-ray stars. The values enclosed in the
parentheses indicate stellar members, located in the central parts of the
clusters (except for the most sensitive Chandra mosaic of the nearest NGC 2232
cluster) and employed in the analyses of the X-ray-mass-age relations (§§8-9
and Appendix C); totaling 6,003 X-ray and non-X-ray stars. Columns 5-6: Median
cluster distance from the Sun and its 68% bootstrap error, derived in §4.
Columns 7-8: Cluster average extinction in visual band and cluster age,
derived in §5. Column 9: Mass completeness limits for our cluster member
samples, derived in §5.

But the approach A that rests on individual stellar ages may be questionable.
Debates have waged for decades over interpretation of observed age spreads in
rich clusters, such as ONC (e.g., Reggiani et al., 2011). The difficulties of
interpretation are due to various observational and theoretical reasons such
as photometric variability, multiplicity, accretion history, binarity,
extinction uncertainty, veiling from accretion, scattering and absorption by
disks, stellar interiors model uncertainty, and distance uncertainty
(Preibisch, 2012; Getman et al., 2014b, and references therein). Due to
possibly unaccounted magnetic effects, old generation PMS evolutionary models
may provide inconsistent ages between intermediate- and low-mass stars, a
phenomenon referred as “radius inflation” (Richert et al., 2018, and
references therein). For instance, the HRD diagrams in Figure 3 of Gregory et
al. (2016) show clear isochronal age biases between the intermediate- and low-
mass stellar members of NGC 2264 and IC 348. While recent studies do provide
strong evidence for the presence of astrophysical age spreads in rich nearby
star forming regions and individual clusters, these generally do not exceed 1
Myr per 1 parsec scale (Reggiani et al., 2011; Getman et al., 2014b, a;
Beccari et al., 2017; Getman et al., 2018a), which is much smaller than for
instance, $\Delta t\gtrsim 10$ Myr per 2 parsec scale of ONC assumed in their
method A by Preibisch & Feigelson (2005); Gregory et al. (2016).

Tu et al. (2015); Johnstone et al. (2021a) consider temporal mass-stratified
changes in the X-ray activity of young and older stars using a different,
semi-analytical-empirical, approach. The analytical part includes a
modification of the angular momentum evolution model by Gallet & Bouvier
(2015), which takes into consideration three major physical processes, such as
star-disk interaction, momentum loss due to stellar wind, and redistribution
of angular momentum in stellar interior. With the knowledge of the angular
momentum, fractional X-ray luminosity ($R_{X}=L_{X}/L_{bol}$) is then
predicted assuming (based on past empirical results) two regimes (“saturation”
and “non-saturation”) described as two different power-law dependencies of
$R_{X}$ on Rossby number (ratio of rotation period to convective turnover
time). Various model parameters are adjusted based on the comparison of the
model outcomes with the stellar X-ray and rotation empirical data for clusters
of different ages. For a wide age range of up to a few Gyr, Tu et al. (2015)
and Johnstone et al. (2021a) calculate and provide X-ray luminosity temporal
tracks for stars in mass ranges near 1 M⊙ and 0.1–1.2 M⊙, respectively. Within
the 0.5–25 Myr age range (targeted by our current paper), Tu et al. (2015);
Johnstone et al. (2021a) use empirical data sets for only a handful of
clusters: X-ray data for $\sim 2$ Myr old Taurus cloud stars and 13 Myr old h
Per cluster; stellar rotation data for $\sim 2$ Myr old Lagoon Nebula stars
and 13 Myr old h Per cluster.

Unlike in Tu et al. (2015); Johnstone et al. (2021a), the investigation of the
X-ray evolution here is based solely on empirical data. We improve the
previous studies of Preibisch & Feigelson (2005); Gregory et al. (2016); Tu et
al. (2015); Johnstone et al. (2021a) by expanding significantly the X-ray
stellar samples, from a few clusters per study to a dozen nearby, very young
0.5–5 Myr stellar clusters/groups from our previously published Chandra
MYStIX/SFiNCs projects (Feigelson et al., 2013; Getman et al., 2017, and see
§7 in the current paper) combined with the new Chandra X-ray data for 10
nearby, older 7–25 Myr open clusters (§3). Due to the aforementioned problems
with age spreads we further apply approach B rather than approach A to our
data.

Table 2: X-ray Sources Towards 10 Open Clusters

Region | CXOU J | R.A. | Decl. | $C_{net}$ | $\sigma_{net}$ | $PFlux$ | $ME$ | Group
---|---|---|---|---|---|---|---|---
|  | deg | deg | cnts | cnts | ph cm-2 s-1 | keV |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
NGC1502 | 040628.63+621745.1 | 61.619304 | 62.295876 | 24.3 | 6.7 | -5.640 | 3.8 | 10
NGC1502 | 040632.61+621612.3 | 61.635902 | 62.270094 | 10.4 | 5.3 | -6.012 | 4.9 | 10
NGC1502 | 040635.11+622057.9 | 61.646325 | 62.349421 | 8.0 | 3.5 | -5.677 | 2.1 | 10
NGC1502 | 040638.68+621951.4 | 61.661188 | 62.330956 | 7.9 | 4.3 | -6.153 | 2.9 | 10
NGC1502 | 040639.70+621928.8 | 61.665445 | 62.324694 | 15.8 | 5.2 | -5.863 | 1.6 | 5
NGC1502 | 040643.05+622040.0 | 61.679393 | 62.344472 | 2181.3 | 47.1 | -3.719 | 1.6 | 7
NGC1502 | 040643.15+622025.4 | 61.679799 | 62.340410 | 33.5 | 7.1 | -5.535 | 1.7 | 5

Note. — This table is available in its entirety (14,222 X-ray sources) in
machine-readable form in the online journal. These Chandra-X-ray source
positions and photometric quantities are provided by the ACIS Extract package.
Column 1: Cluster name. Column 2: IAU designation. Columns 3-4: Right
ascension and declination (in decimal degrees) for epoch J2000.0. The X-ray
photometric quantities listed in Columns 5-8 are calculated in the $(0.5-8)$
keV band. Columns 5-6: Net counts and average of the upper and lower
1-$\sigma$ errors. Column 7: $\log$ of apparent photometric flux as the ratio
of the net counts to the mean Auxiliary Response File value (product of the
local effective area and quantum efficiency) and exposure time. Column 8:
Background-corrected median photon energy. Column 9: Source class: Groups 5-10
(§4).

##  3 Target Sample And Chandra Data Reduction

Our sample comprises ten rich, nearby, 7–25 Myr-old open clusters listed in
Table 1 in order of increasing age. They were selected from the literature
based on age, proximity and richness. The table lists refined numbers of
cluster members and cluster distances, extinctions, and ages based on the
analyses presented later in §§4 and 5.

Table 8 in Appendix A provides information about 37 observations of these
clusters made by the Chandra X-ray Observatory. Eight clusters were
specifically targeted by Chandra during observation Cycles 20-21 as part of
this large GO/GTO program (PIs, Getman and Garmire). Data for two clusters,
NGC 3293 and NGC 869, were obtained from the Chandra archive; previous results
for these clusters were reported by Preibisch et al. (2017), Argiroffi et al.
(2016), and Townsley et al. (2019).

All observations were performed using Chandra’s Advanced CCD Imaging
Spectrometer imaging array (ACIS-I; Garmire et al., 2003). Numerous
$17\arcmin\times 17\arcmin$ images from four contiguous CCD chips were aimed
at the centers of these clusters. All but three observations were taken in
Very Faint Timed Exposure mode; ObsIDs 9912, 9913, and 12021 were taken in
Faint mode.

Figure 2: Gaia astrometry for X-ray and non-X-ray sources towards NGC 1502.
Source classes discussed in the text are color coded as: red (Group 1), pink
(Group 2), orange (Group 3), grey (Group 4), green (Group 5), blue (Group 6),
cyan (Group 7), and purple (Group 8). Figure legends give the number of stars
in each group. Panels a, b, c: Proper motion diagrams for X-ray sources with
increasing astrometric uncertainties: $<0.2$, 0.2–0.4 and $>0.4$ mas yr-1. The
green circle defining the initial cluster membership is discussed in the text.
Panel d: Gaia parallax as a function of magnitude for the X-ray sources. The
solid and dashed lines show the median and $2\times MADN$ spread for Group 5
sources with accurate astrometry. Panels e, f, g, h: Similar to panels a-d but
for the non-X-ray sources. Panel i: Spatial distribution of Group 1, 2, 5, and
6 cluster member candidates. The $\times$ symbols mark sources, located at the
edges of the Chandra ACIS-I fields, that are excluded from our mass stratified
activity-age analyses. The complete figure set for all the ten open clusters
is available in the full electronic version of the paper.  Figure 3: Gaia
astrometry of X-ray and non-X-ray sources towards NGC 869 = h Per. See Figure
2 caption for explanation.  Figure 4: Gaia color-magnitude diagrams and mass
functions for cluster member stars in NGC 1502 (upper panels) and NGC 869
(lower panels). Panels a and c: CMDs for X-ray and non-X-ray classes. Groups 1
through 8 are color coded as in Figure 2 and brown $+$ symbols are distant
cluster members from C20. Typical Gaia EDR3 photometric uncertainties are
depicted in the left-upper corners of the figure panels. Legends provide the
number of stars in each group. The black curve represents the best fit PARSEC
1.2S evolutionary models for the Group 1, 2, 5, and 6 stars. Corresponding
stellar masses are indicated by black markers. X-ray and non-X-ray stars (even
from Groups 1, 2, 5 and 6) that are located to the left of the purple dashed
lines are omitted from the member lists. Panels b and d: Histogram of the mass
function of member stars (Groups 1, 2, 5, and 6 stars located to the right of
the purple dashed lines on the CMD panels). Histogram error bars are
approximations to 95% confidence intervals of a Poissonian distribution
(Gehrels, 1986). The gray curve shows the best-fit theoretical IMF from
Maschberger (2013). The complete figure set for all the ten open clusters is
available in the electronic version of the paper.  Table 3: Gaia-EDR3
Properties Of Non-X-ray And X-ray Sources Towards 10 Open Clusters

Region | R.A. | Decl. | Group | $\omega$ | $\sigma_{\omega}$ | $\mu_{\alpha\star}$ | $\sigma_{\mu_{\alpha\star}}$ | $\mu_{\delta}$ | $\sigma_{\mu_{\delta}}$ | $G$ | $\sigma_{G}$ | $B-R$ | $\sigma_{BR}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| deg | deg |  | mas | mas |  |  |  |  | mag | mag | mag | mag
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14)
NGC1502 | 61.970594 | 62.327418 | 1 | 0.955 | 0.018 | -0.870 | 0.021 | -0.791 | 0.018 | 12.864 | 0.003 | 0.909 | 0.005
NGC1502 | 61.960166 | 62.329657 | 1 | 0.954 | 0.014 | -0.790 | 0.017 | -0.693 | 0.015 | 12.359 | 0.003 | 0.838 | 0.005
NGC1502 | 61.988023 | 62.308490 | 1 | 0.997 | 0.119 | -0.430 | 0.139 | -0.725 | 0.122 | 17.922 | 0.007 | 2.506 | 0.054
NGC1502 | 61.931138 | 62.326292 | 1 | 0.937 | 0.015 | -0.660 | 0.018 | -0.842 | 0.015 | 10.285 | 0.003 | 0.795 | 0.005
NGC1502 | 61.928628 | 62.327341 | 1 | 0.955 | 0.014 | -0.720 | 0.017 | -0.946 | 0.015 | 9.545 | 0.003 | 0.739 | 0.005

Note. — This table is available in its entirety in the machine-readable form
in the online journal. It presents 10,534 stars in Groups 1, 2, 3, 5, 6, 7,
and 8, of which 7,924 are cluster members from Groups 1, 2, 5, and 6 (see the
membership list in Table 4). Column 1: Cluster name. Columns 2-3: Gaia right
ascension and declination (in decimal degrees) for epoch J2000.0. Column 4:
Group assignment. Columns 5-10: Gaia parallax and proper motions and their
uncertainties. Proper motions are in mas yr-1. Columns 11-14: Gaia magnitude
and color and their uncertainties.

X-ray data analysis closely followed procedures from our earlier projects
studying young stellar populations (e.g., Kuhn et al., 2013; Getman et al.,
2017; Townsley et al., 2019), and is briefly summarized here. The suite of
ACIS Extract and related tools described by Broos et al. (2010, 2012) provides
very sensitive and reliable identification of faint X-ray sources in Chandra
images. A deep catalog of candidate sources is obtained from bumps in a
smoothed map of the field based on maximum likelihood deconvolution using the
known spatially variable telescope point-spread function. Local background
levels are iteratively calculated for each candidate source. This candidate
source identification procedure is performed on the merged image from multiple
exposures (Table 8).

A global astrometric correction to the pointing direction is made by removing
any offset between bright X-ray sources and Gaia-DR2 counterparts. This allows
sub-arcsecond positional accuracy for on-axis sources. Photons are extracted
for each candidate source in small regions scaled to the local point-spread
function, typically containing 90% of the expected photons. Local background
rates are subtracted to give net source counts. The local exposure time is
obtained from the merged exposure map.

A variety of X-ray properties are then calculated from the extracted events:
net count rate corrected for local exposure time and point-spread function
tails; source locations with errors depending on off-axis angle and net count
rate; probability of source existence based on Poisson distributions for the
source and background photon rates; hypothesis tests for variability in the
photon arrival times using a Kolmogorov–Smirnov test; apparent photomeric
flux; and median energy of the net counts.

For NGC 3293 and NGC 869, the same reduction procedures were performed by
Preibisch et al. (2017); Townsley et al. (2019), and the final X-ray data
products were shared with us by these authors.

A total of 14,222 candidate X-ray sources were identified across the ten open
clusters. Table 2 presents their locations and X-ray photometric quantities.
These X-ray sources consist of PMS cluster members of interest here,
extragalactic contaminants and Galactic field contaminants. Our classification
of the sources is described in the next section.

##  4 Cluster Membership

We identify members of these young clusters by combining results from the
Chandra source catalog in Table 2 and results from the public Early Data
Release 3 (EDR3) of the Gaia mission (Gaia Collaboration et al., 2016, 2021).
Gaia EDR3 offers an all-sky, deep astrometric and photometric source catalog
in the visual band. All cluster members we identify have Gaia counterparts but
only a fraction are detected with Chandra; thus both X-ray and non-X-ray stars
can be members. Membership is constrained to lie within the Chandra fields
listed in Table 8 of Appendix A. Since these are lightly absorbed clusters
without nebula background emission (unlike MYStIX and SFiNCs clusters embedded
in star forming regions), a cluster census down to some limiting stellar mass
can be obtained from a magnitude limited survey. Thus if contaminants can be
effectively removed, the Gaia-based sample will be complete above this
limiting mass.

The steps of cluster member identification are outlined here and illustrated
for two clusters in Figures 2-4. Similar figures for all ten clusters are
available in the online figure sets.

First, Gaia-EDR3 (Gaia Collaboration et al., 2021) and Chandra catalog source
positions (Table 2) are cross-correlated within a constant search radius of
$1\arcsec$. Most Chandra sources are localized to better than $1\arcsec$; a
very small fraction of X-ray sources may miss their Gaia counterpart due to
the large point spread function at the outer regions of the ACIS-I field. Out
of 14,222 X-ray sources $5,027$ have Gaia counterparts.

Second, since the X-ray emission of cool members of such young open clusters
is expected to be elevated $\sim 100-1000$ times above typical main sequence
levels (Preibisch & Feigelson, 2005), the X-ray sources with Gaia counterparts
represent a reliable subsample of cluster members. We constrain this initial
sample to stars with accurate Gaia proper motions, $\sigma_{\mu_{\alpha}}<0.2$
mas/yr. A circle in the proper motion diagram is then drawn where these X-ray
emitting stars are most concentrated as shown in Figures 2a and 3a. The
circle, chosen to have radius $R_{cl,pm}$ as 1.3 normalized median absolute
deviations (MADNs), includes $60-90$% of such X-ray stars. This is a
conservative choice as many Chandra-Gaia cluster members with less accurate
proper motions lie outside the circle (panels b and c in Figures 2-3). But a
small circle reduces contamination of non-cluster members in the Gaia survey.

Third, we estimate the distance to each cluster. The parallax of the cluster
is chosen to be the median parallax of this initial member sample, and the
distance is the inverse of this median. None of the individual stellar
parallaxes are negative so the median of parallaxes or inverse parallaxes
(stellar distances) produce the same results. The uncertainty of the distance
is obtained from the 68% quantiles of a bootstrap resampling of parallaxes.
These distances and uncertainties are listed in Table 1.

These distances are highly reliable. Getman et al. (2019) show that for
different parts of the Orion A cloud, such simple distance estimates are
consistent within 1% with the probabilistic distance estimates by Bailer-Jones
et al. (2018). Cluster distances inferred from weighted median and mean
parallaxes (Kuhn et al., 2019) lie within the 95% confidence intervals of our
values. Stars with Gaia re-normalized unit weight errors (RUWE) in excess of
1.4 (a threshold considered as a possible indicator of poor Gaia astrometric
solution) represent only $\lesssim 6$% in these stellar samples and do not
affect our cluster distance estimates.

In addition to the uncertainty of the median parallax, we define a spread of
parallax values about the median to be two normalized median absolute
deviations of these values, $PlxSpread=2\times MADN$. This spread is used
below for identification of additional members, and is shown as a band of
dashed lines in panels d and h of Figures 2-3.

We now classify all Chandra-Gaia and non-Chandra-Gaia sources located within
the Chandra fields into the following 10 groups. These are visually shown
using different color symbols in Figures 2-3. Group assignments for X-ray
sources are listed in Table 2.

Groups 1 (red), 2 (pink), and 3 (orange): These are non-Chandra Gaia sources
with proper motion uncertainties of $\sigma_{\mu_{\alpha}}<0.2$ mas/yr,
$0.2<\sigma_{\mu_{\alpha}}<0.4$ mas/yr, and $\sigma_{\mu_{\alpha}}>0.4$
mas/yr, respectively whose proper motion values lie inside the $R_{cl,pm}$
circle and their parallax confidence intervals intercept the $PlxSpread$ band
(panels e-h). After inspection of their photometric properties (e.g., Figure
4), we find that the Group 1 stars are typically higher mass ($>1-2$ M⊙)
cluster members and many Group 2 stars are lower mass ($<1$ M⊙) cluster
members. Group 3 stars include both low mass ($<0.5-0.8$ M⊙) cluster member
candidates and foreground and background contaminants.

Group 4 (gray): This contains the remaining non-Chandra Gaia stars within the
Chandra fields (panels e-h). These are mostly field stars unrelated to the
open clusters.

Groups 5 (green) and 6 (blue): These are Chandra-Gaia stars with their
parallax confidence intervals intercepting the $PlxSpread$ band and their
proper motion positions lying inside (Group 5) and outside (Group 6) the
$R_{cl,pm}$ circle, shown in panels a-d. Gaia photometry indicates that the
Group 5 objects are mainly cluster members with masses $>0.5$ M⊙ and the Group
6 includes both $<2$ M⊙ cluster members and stellar contaminants.

Groups 7 (cyan) and 8 (purple): Chandra-Gaia stars with their lower (upper)
error-bar on parallax being above (below) the $PlxSpread$ band (panels h and
d) for Group 7 (Group 8). The Group 7 is predominantly foreground stars and
the Group 8 is predominantly background stars.

Groups 9 and 10. Group 9 comprises Chandra-Gaia sources without astrometry
information. Some may be very low-mass cluster members and some may be
contaminants. Group 10 incorporates Chandra sources without Gaia counterparts.
The vast majority of these are extragalactic contaminants or spurious (noise)
X-ray sources. These groups are not shown in the figures.

Table 3 presents Gaia astrometric and photometric properties for non-X-ray
(groups 1, 2, and 3) and X-ray (groups 5, 6, 7, and 8) sources towards the ten
open clusters. Among those, Groups 1, 2, 5, and 6 contain the vast majority of
cluster member candidates.

Table 4: Stellar Properties Of Non-X-ray And X-ray Members Of 10 Open Clusters

Region | R.A. | Decl. | Group | $\log(T_{eff})$ | $M$ | $\log(L_{bol})$ | $\log(L_{X})$ | $\log(L_{X,up})$ | F1 | Ph | F2
---|---|---|---|---|---|---|---|---|---|---|---
| deg | deg |  | K | $M_{\odot}$ | $L_{\odot}$ | erg s-1 | erg s-1 |  | HRD |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
NGC1502 | 62.257371 | 62.385897 | 2 | 3.54 | 0.55 | -0.82 |  $\cdots$ | 29.54 | 1 | 1 | 0
NGC1502 | 61.944486 | 62.153143 | 1 | 4.04 | 2.40 | 1.55 |  $\cdots$ | 29.76 | 1 | 5 | 0
NGC1502 | 61.577576 | 62.266908 | 2 | 3.57 | 0.71 | -0.62 |  $\cdots$ | 29.80 | 1 | 1 | 0
NGC1502 | 61.904523 | 62.509605 | 1 | 3.55 | 0.63 | -0.72 |  $\cdots$ | 29.77 | 1 | 1 | 0
NGC1502 | 62.374648 | 62.351225 | 2 | 3.54 | 0.54 | -0.83 |  $\cdots$ | 29.73 | 1 | 1 | 0
NGC1502 | 61.665573 | 62.324773 | 5 | 3.69 | 1.25 | 0.02 | 29.91 |  $\cdots$ | 1 | 2 | 0
NGC1502 | 61.679861 | 62.340361 | 5 | 3.72 | 1.40 | 0.21 | 30.24 |  $\cdots$ | 1 | 2 | 0
NGC1502 | 61.758327 | 62.315094 | 5 | 3.66 | 1.05 | -0.20 | 29.80 |  $\cdots$ | 0 | 2 | 0
NGC1502 | 61.764918 | 62.335727 | 6 | 3.54 | 0.54 | -0.83 | 29.42 |  $\cdots$ | 0 | 1 | 0
NGC1502 | 61.769816 | 62.227697 | 5 | 3.75 | 1.55 | 0.45 | 30.49 |  $\cdots$ | 1 | 2 | 0

Note. — This table is available in its entirety (7,924 cluster members) in the
machine-readable form in the online journal. Only sources from Groups 1, 2, 5,
and 6 with available mass estimates are presented. And only lower-mass stars
with colors redder than the purple dashed lines in Figure 4a,c are included.
Out of the total 7,924 cluster members, 6,003 are located in the central parts
of the clusters (Column 10 flag $=0$), and are included in the science
analysis of the X-ray-mass-age relations (§§8-9 and Appendix C). Column 1:
Cluster name. Columns 2-3: Gaia right ascension and declination (in decimal
degrees) for epoch J2000.0. Column 4: Source class: groups 1, 2 (non-X-ray
stars), and groups 5, 6 (X-ray stars). Columns 5-7: Stellar effective
temperature, mass, and bolometric luminosity derived from the Gaia color-
magnitude diagrams (Figure 4a,c). Columns 8-9: X-ray luminosity (for X-ray
members; groups 5 and 6) and upper limits to X-ray luminosity (for non-X-ray
members; groups 1 and 2). Column 10: A flag indicating whether the star is
located inside ($=0$) or outside ($=1$) the spatial circle around the cluster
center depicted in Figures 2i and 3i. Column 11: The evolutionary status of
the star on the Hertzsprung–Russell diagram based on the predictions of the
PARSEC 1.2S evolutionary models: $=1$ \- Hayashi track; $=2$ or $=3$ \- Henyey
track; $\geq 4$ \- ZAMS and beyond. Column 12: A flag indicating sources with
inconsistency ($=1$) between the Gaia $G$-band, and BP and RP photometry.
There are 595 stars with F2$=1$; of those 485 are located within the central
cluster regions, i.e., have F1$=0$.

Due to the degradation of the Chandra ACIS-I point source sensitivity with
increasing distance from the detector center the fraction of X-ray detections
of cluster members decreases considerably in the outer regions of the
detector. For this reason, the cluster member candidates lying outside of a
$R=7.5\arcmin$ circle around the cluster centers ($\times$ symbols in Figures
2i and 3i) for all but one (NGC 2232) clusters will be ignored from the
analyses of mass-stratified activity-age relations presented later in §§8-9
and Appendix C. The outer members will be retained in the case of NGC 2232
because this nearest region offers the best point source X-ray sensitivity
among our open clusters (see Column 9 in Table 1).

In a final step to reduce contamination by field stars, we require that
cluster members lie close to the PMS and main sequence isochrones on the Gaia
color-magnitude diagram (Figure 4). We fit Group 1, 2, 5, and 6 stars with the
PARSEC 1.2S evolutionary models (Bressan et al., 2012; Chen et al., 2014) at
the same time omitting faint objects with blue colors as possible stellar
contaminants. These are objects located to the left of the dashed purple
curves depicted in panels a and c of Figure 4. These purple curves are chosen
to follow the best-fit isochrones shifted towards bluer colors by the typical
confidence interval for the colors of faint sources.

The result of these selection criteria is a sample of 7,924 young stars (from
Groups 1, 2, 5, and 6) in the ten clusters with ages 7–25 Myr. These stars are
listed in Table 4, whose content is described below. Omitting cluster members
lying outside the spatial circles in Figures 2i and 3i gives a sub-sample of
6,003 cluster members further employed in the analyses of mass-stratified
activity-age relations (§§8-9 and Appendix C).

##  5 Cluster and member properties

Cluster absorption and ages are estimated as follows. The extinction
coefficients from Luhman & Esplin (2020) are used to redden theoretical PARSEC
1.2S isochrones on the Gaia color-magnitude diagram for a range of absorptions
and ages. These curves are fitted to the Gaia EDR3 photometry data of the
cluster members using minimum chi-squared estimation weighted with the
$G_{BP}-G_{RP}$ errors. The CMD positions of the brightest stars, typically
with $M>2$ M⊙, are more sensitive to the changes in the cluster extinctions
while the positions of the lower-mass stars are more sensitive to the changes
in the cluster ages.

The inferred cluster distances (§4), average extinctions in visual band,
cluster ages, and numbers of the cluster members $-$ Group 1, 2, 5, and 6
sources located to the right of the dashed purple lines on the CMD diagrams
(Figure 4a,c) $-$ are summarized in Table 1. Galactic coordinates for the
cluster centers are also provided.

Effective temperatures, bolometric luminosities, and masses for individual
cluster members are obtained through a comparison of the observed $G$-band
absolute magnitudes with theoretical predictions for the best-fit reddened
PARSEC 1.2S isochrone. Table 4 lists these Gaia-based stellar properties
together with flags indicating source’s proximity to the cluster centers. An
additional flag indicates the evolutionary phase of each star: e-PMS Hayashi
track, l-PMS Henyey track, or ZAMS. The boundaries between these phases are
shown as large symbols in Figure 1.

According to Riello et al. (2021), the ${BP}$-band flux of some faint Gaia-
EDR3 objects ($G_{BP}>(20.3-20.9)$ mag) may be overestimated. Because of this
effect our cluster member lists may miss true very low mass young stars with
their CMD positions shifted to the locus of background stars (Figure 4). Among
the 7,924 open cluster members (Table 4), 13% and 5% have $G_{BP}$ magnitudes
in excess of 20.3 and 20.9, respectively. Ignoring these stars from the CMD
fitting does not change the inferred cluster ages. The mass and bolometric
luminosity estimates of such stars are not affected since these are based on
the $G$-band magnitudes only.

Following Riello et al. (2021), we also checked our open cluster members with
high EDR3 blend fraction ($\beta>0.1$) for possible contamination from nearby
sources. Among 7,924 cluster members, there are only 68 cases of “target”
stars with $\beta>0.1$ lying near (within 1.05$\arcsec$) a potential
“blending” Gaia-EDR3 source, where $F_{G,target}/F_{G,blending}<4$. Vast
majority of such stars are members of two distant and rich clusters, NGC 4755
and NGC 3766. Ignoring such stars from the analysis of X-ray evolution (§9)
does not affect any science results.

Evans et al. (2018); Riello et al. (2021) suggest that high excess in the sum
of the Gaia BP-band and RP-band fluxes relative to the G-band flux may
indicate that star’s photometry is susceptible to the effects of source
crowding and/or nebulosity. We find that 7% of our 7,924 open cluster members
have their corrected BP and RP flux excesses as
$|C^{\star}|>5\sigma_{C^{\star}}$ (Riello et al., 2021; Anders et al., 2022),
indicating inconsistency between the G-band, and BP and RP photometry. In
Table 4, such stars can be identified through the selection $F2=1$. We
verified that these stars affect neither the CMD fitting nor X-ray evolution
results (§9).

See Appendix C of Getman & Feigelson (2021) and §7 for details on applying
PARSEC 1.2S models to derive MYStIX/SFiNCs e-PMS stellar properties.

Once individual masses are estimated, they can be considered as an ensemble to
examine the Initial Mass Function (IMF). This can give confidence that our
cluster memberships are complete above a limiting mass. IMF histograms for NGC
1502 and NGC 869 are shown in panels b and d of Figure 4. They are fitted to
Maschberger (2013) generalized log-log formulation of the IMF. Our membership
analysis delivers cluster member mass distributions consistent with the power
law tail of Maschberger’s IMF. To obtain mass completeness limits, starting
from low masses of 0.2 M⊙, mass cutoffs are iteratively increased until the
Anderson-Darling goodness-of-fit test shows statistically acceptable fits
($p>0.05$) between the unbinned c.d.f.’s for the data and Maschberger’s model.
The mass completeness limit for each cluster is listed in Table 1; these are
generally around $0.4-0.7$ M⊙ but are higher for two distant and more absorbed
clusters, NGC 869 and NGC 884. Our cluster memberships represent roughly 20%
of the total intrinsic cluster population and 80% of the cluster mass.

Finally, we note that these clusters were subject to previous membership
analysis with a multi-stage statistical techniques applied to the Gaia DR2
(Evans et al., 2018) catalog without considering any Chandra sources (Cantat-
Gaudin & Anders, 2020; Cantat-Gaudin et al., 2020, hereafter C20). All but a
handful of C20 members located inside the Chandra ACIS-I fields have
counterparts belonging to our Groups 1, 2, 5, and 6. Those without
counterparts (none or a few C20 members per cluster) generally have astrometry
discrepancies between the Gaia DR2 and EDR3 catalogs111See, for instance, a
DR2-EDR3 parallax discrepancy in a NGC 1502 at
$(\alpha,\delta)=(61.937884,62.317771)$.. Due to the improved accuracy of the
Gaia-EDR3 data and availability of Chandra-X-ray data, our member lists
provide numerous new low-mass cluster members that were not located by C20.
Our catalogs increase the cluster census within the Chandra fields by factors
$1.6$ (NGC 2232), $(2-3)$ (NGC 1502, NGC 2169, NGC 1960, IC 2395), and $(3-6)$
for most distant clusters (NGC 3293, NGC 884, NGC 3766, NGC 4755, NGC 869).
C20 members which reside outside the Chandra fields, ranging from a dozen to a
hundred stars per cluster, are added to the Gaia CMDs in Figure 4a,c (brown
$+$). Their color-magnitude positions are in complete agreement with those of
our Groups 1, 2, 5, and 6.

##  6 X-ray Luminosities and Upper Limits

For younger members of MYStIX/SFiNCs star forming regions in the e-PMS phase
(§7), intrinsic X-ray luminosities were derived using the non-parametric
method XPHOT (Getman et al., 2010) based on a concept that is similar to the
long-standing use of color–magnitude diagrams in optical and infrared
astronomy. However, XPHOT requires the presence of both soft ($<2$ keV) and
hard ($>2$ keV) X-ray photons. The members of the ten l-PMS open clusters
considered here are generally lightly absorbed and older than the
MYStIX/SFiNCs stars with lower flare activity. They thus often lack hard X-ray
photons. The XPHOT method could be applied to roughly half of the cluster
members.

Table 5: X-ray Spectral Fits Of Stacked Data

Sample |  $ME$ range | $NC$ | $\chi^{2}_{\nu}$ | dof | $N_{H}$ | $kT_{2}$ | $EM_{1}$ | $EM_{2}$ | Flux
---|---|---|---|---|---|---|---|---|---
|  |  |  |  | $10^{22}$ |  | $10^{52}$ | $10^{52}$ | $10^{-15}$
| (keV) | (cnts) |  |  | (cm-2) | (keV) | (cm-3) | (cm-3) | (erg s-1 cm-2)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
NGC1502_S1 | $[0.9-1.5]$ | 1278 | 1.5 | 57 | 0.42 | $1.6\pm 0.2$ | $0.12\pm 0.06$ | $10.79\pm 2.55$ | 6.88
NGC1502_S2 | $[1.5-1.7]$ | 1283 | 0.7 | 56 | 0.42 | $2.8\pm 0.8$ | $3.18\pm 3.14$ | $10.43\pm 5.90$ | 9.49
NGC1502_S3 | $[1.7-3.4]$ | 1263 | 1.1 | 55 | 0.42 | $4.3\pm 0.6$ | $0.04\pm 0.03$ | $11.96\pm 1.61$ | 8.61
NGC2169_S1 | $[1.0-1.5]$ | 874 | 0.9 | 34 | 0.14 | $2.0\pm 0.5$ | $7.57\pm 6.15$ | $7.90\pm 3.28$ | 7.65
NGC2169_S2 | $[1.5-1.6]$ | 944 | 1.2 | 37 | 0.14 | $6.0\pm 3.1$ | $27.22\pm 10.79$ | $7.60\pm 3.43$ | 18.65
NGC2169_S3 | $[1.6-1.8]$ | 633 | 1.4 | 23 | 0.14 | $3.2\pm 0.5$ | $0.01\pm 0.00$ | $15.12\pm 2.86$ | 11.78
IC2395_S1 | $[1.0-1.5]$ | 1468 | 0.9 | 61 | 0.10 | $2.3\pm 0.5$ | $1.02\pm 0.62$ | $4.55\pm 1.80$ | 8.19
IC2395_S2 | $[1.5-1.6]$ | 1512 | 0.9 | 65 | 0.10 | $2.9\pm 0.6$ | $11.91\pm 11.90$ | $20.33\pm 4.68$ | 37.13
IC2395_S3 | $[1.6-4.2]$ | 1414 | 1.0 | 65 | 0.10 | $6.2\pm 2.6$ | $6.35\pm 3.06$ | $3.91\pm 2.42$ | 11.73
NGC3293_S1 | $[0.7-1.3]$ | 1375 | 1.4 | 53 | 0.18 | $5.0\pm 1.5$ | $17.63\pm 3.80$ | $0.18\pm 0.06$ | 2.08
NGC3293_S2 | $[1.3-1.5]$ | 1381 | 1.0 | 59 | 0.18 | $6.6\pm 3.4$ | $10.80\pm 8.74$ | $6.24\pm 2.24$ | 2.83
NGC3293_S3 | $[1.5-5.3]$ | 1354 | 1.0 | 64 | 0.18 | $6.6\pm 2.0$ | $1.96\pm 1.86$ | $11.71\pm 4.59$ | 2.43
NGC869_S1 | $[0.8-1.3]$ | 6726 | 1.0 | 195 | 0.34 | $2.5\pm 0.5$ | $17.81\pm 2.66$ | $3.27\pm 1.54$ | 1.63
NGC869_S2 | $[1.3-1.5]$ | 6713 | 1.1 | 195 | 0.34 | $3.1\pm 0.4$ | $8.68\pm 4.29$ | $12.56\pm 2.83$ | 2.23
NGC869_S3 | $[1.5-5.6]$ | 6626 | 1.2 | 228 | 0.34 | $6.8\pm 1.4$ | $2.70\pm 2.55$ | $11.16\pm 1.42$ | 2.08
NGC884_S1 | $[0.9-1.6]$ | 2102 | 1.2 | 105 | 0.34 | $2.7\pm 0.6$ | $7.36\pm 6.89$ | $2.05\pm 1.89$ | 1.69
NGC884_S2 | $[1.6-1.8]$ | 2100 | 1.0 | 109 | 0.34 | $2.9\pm 0.4$ | $0.20\pm 0.10$ | $19.88\pm 5.46$ | 2.59
NGC884_S3 | $[1.8-5.8]$ | 2090 | 1.1 | 125 | 0.34 | $7.1\pm 2.3$ | $0.02\pm 0.01$ | $5.13\pm 4.43$ | 1.99
NGC4755_S1 | $[0.6-1.5]$ | 2688 | 1.3 | 111 | 0.24 | $3.7\pm 1.7$ | $10.40\pm 3.68$ | $1.86\pm 1.09$ | 1.73
NGC4755_S2 | $[1.5-1.7]$ | 2675 | 0.8 | 115 | 0.24 | $3.7\pm 0.7$ | $4.76\pm 4.66$ | $12.46\pm 2.32$ | 2.91
NGC4755_S3 | $[1.7-6.6]$ | 2660 | 1.2 | 148 | 0.24 | $17.3\pm 8.1$ | $4.18\pm 2.90$ | $7.38\pm 1.61$ | 2.33
NGC1960_S1 | $[0.8-1.4]$ | 1101 | 1.1 | 47 | 0.16 | $2.4\pm 1.1$ | $6.05\pm 2.96$ | $1.47\pm 1.19$ | 3.02
NGC1960_S2 | $[1.4-1.7]$ | 1088 | 1.1 | 44 | 0.16 | $2.9\pm 0.7$ | $1.18\pm 1.16$ | $6.80\pm 2.13$ | 3.99
NGC1960_S3 | $[1.7-5.8]$ | 1030 | 1.3 | 47 | 0.16 | $5.6\pm 3.2$ | $1.39\pm 0.66$ | $4.94\pm 2.36$ | 4.56
NGC3766_S1 | $[0.6-1.4]$ | 3218 | 1.2 | 124 | 0.16 | $3.6\pm 0.7$ | $14.28\pm 1.65$ | $0.32\pm 0.08$ | 1.84
NGC3766_S2 | $[1.4-1.6]$ | 3208 | 1.0 | 140 | 0.16 | $3.9\pm 0.9$ | $12.55\pm 4.20$ | $5.91\pm 2.23$ | 2.37
NGC3766_S3 | $[1.6-6.5]$ | 3123 | 1.1 | 182 | 0.16 | $10.3\pm 2.5$ | $0.01\pm 0.01$ | $7.15\pm 0.63$ | 1.82
NGC2232_S1 | $[0.9-1.4]$ | 302 | 1.8 | 9 | 0.04 | $2.8\pm 4.9$ | $3.55\pm 3.54$ | $1.02\pm 0.64$ | 27.27
NGC2232_S2 | $[1.4-1.5]$ | 293 | 1.4 | 9 | 0.04 | $2.0\pm 0.3$ | $0.30\pm 0.20$ | $4.58\pm 3.39$ | 86.96
NGC2232_S3 | $[1.5-2.1]$ | 211 | 0.9 | 10 | 0.04 | $2.6\pm 0.4$ | $0.33\pm 0.33$ | $4.18\pm 0.58$ | 38.57

Note. — Column 1: Cluster name and spectral stratum id. Columns 2: Range of
X-ray source median energies. Column 3: Total number of net (background-
corrected) X-ray counts in a spectrum. Columns 4-5: Reduced $\chi^{2}$ for the
overall spectral fit and degrees of freedom. Column 6: Fixed value of
cluster’s X-ray column density. Column 7: Inferred temperature of the hot
plasma component and its 1 $\sigma$ error. Columns 8-9: Inferred emission
measures and their 1 $\sigma$ errors for each plasma component. Column 10:
Inferred absorption corrected incident X-ray flux in the 0.5–8 keV band.

For all X-ray detected cluster members (regardless the presence/absence of
XPHOT estimates), we obtain factors converting the apparent X-ray photometric
fluxes given in Table 2 to intrinsic X-ray luminosities by assuming the stars
have similar spectra. Individual X-ray spectra are stacked in three energy
bands and the stacked spectra are fitted with optically thin thermal plasma
models. Stacked luminosities are then obtained using Gaia-based cluster
distances (Table 1). Individual stellar X-ray luminosities are then estimated
from their contributed fraction of the stacked spectrum. Only young stars with
X-ray net counts $<500$ counts belonging to the Groups 5 and 6 (Table 2) are
included in the spectral stacking.

Figure 5: Fitting plasma models to X-ray spectra to derive X-ray luminosities
for the NGC 1502 and NGC 869 clusters. Panels a, b, and c: Spectral fitting of
the stacked X-ray spectra of Group 5 and 6 cluster members that have soft,
intermediate, and hard hardness ratios. Panels e, f, and g: Similar for NGC
869 members. The hot plasma components have typical temperatures around 2 keV,
3 keV and 4-7 keV, respectively, in addition to a cool plasma component with
$0.7$ keV. Panels d and h: Cluster member X-ray luminosities as a function of
angular distance from the cluster center. The local regression fit to the
lower envelope is used to estimate X-ray upper limits to undetected cluster
members. Group 5 members are shown in green, Group 6 in blue, and Groups 7, 8,
9, and 10 (mostly extragalactic contaminants) in gray. The complete figure set
for the ten open clusters is available in the electronic version of the paper.

The sources’ X-ray median energy (Table 2) is employed to separate the stars
into three energy bands. The choice of the three energy bands varies from
cluster to cluster with the goal to accumulate similar numbers of X-ray counts
per merged spectrum. Individual X-ray spectra are merged and grouped according
to the procedure described in the ACIS Extract User Guide222
http://personal.psu.edu/psb6/TARA/ae_users_guide.pdf..

Spectral fitting is performed with the XSPEC package (Arnaud, 1996). Grouped
spectra were fitted using the $\chi^{2}$ statistic with two-temperature VAPEC
plasma emission models (Smith et al., 2001) subject to TBABS absorption (Wilms
et al., 2000). We assumed the following typical coronal elemental abundances
for PMS or extremely active stars (Güdel et al., 2007). These are defined as
relative to the solar photospheric abundances from Anders & Grevesse (1989, as
default abundance table in XSPEC): C = 0.45, N = 0.788, O = 0.426, Ne = 0.832,
Mg = 0.263, Al = 0.5, Si = 0.309, S = 0.417, Ar = 0.55, Ca = 0.195, Fe =
0.195, Ni = 0.195. Occasionally, elemental abundances were varied to fit
prominent spectral lines.

Based on the spectral analyses of the Chandra and EUVE data for very young
($t\sim(1-3)$ Myr) ONC and much older ($t>(0.06-1)$ Gyr) nearby stars,
Preibisch et al. (2005); Sanz-Forcada et al. (2003) suggest the presence of a
“fundamental” coronal structure with plasma temperature of around $8-10$ MK.
Assuming that such a “fundamental”, high-density, low-temperature coronal
structure exists in PMS stars as a common feature of coronally active stars,
we fix the cool temperature component at a similar value of 0.7 keV ($8$ MK).

The X-ray column density was fixed at the average cluster extinction value
(Table 1) assuming a gas-to-dust ratio from Zhu et al. (2017).

Table 5 lists the spectral fit results. For each stacked spectrum, it gives
the range of source’s X-ray median energy, total number of X-ray net counts,
quality of the overall fit, column density, temperature of the hot plasma
component, emission measures, and incident absorption corrected X-ray flux for
the overall stacked spectrum. This flux is derived using the XSPEC command
flux assuming zero absorption.

The total intrinsic luminosity for the overall stacked spectrum ($L_{X,tot}$)
is the product of such flux and $4\pi D^{2}$, where $D$ is the distance to the
cluster from the Sun. The sum of the apparent photomeric fluxes ($PFlux$;
Table 2) for all the sources, whose data are included in the stacked spectrum,
gives the total apparent flux for the overall stacked spectrum
($PFlux_{tot}$). The X-ray luminosity of an individual source ($L_{X,i}$)
included in the stacked spectrum is then estimated as the product of its
apparent photometric flux from Table 2 and the conversion factor
$L_{X,tot}/PFlux_{tot}$.

Figure 5 illustrates the fitted X-ray spectra for NGC 1502 and NGC 869. The
resulting inferred stellar X-ray luminosities are listed in Table 4. No biases
are found upon comparison of the X-ray luminosities obtained from the spectral
stacking and XPHOT procedures.

The ratio of the “hot” to “cool” emission measures does not depend on cluster
age, but indicates the dominance of the hot plasma in the majority of the S2
(medium hardness) and S3 (high hardness) spectra likely due to the presence of
larger flares (Table 5).

Upper limits to the X-ray luminosities of the non-X-ray members (Groups 1 and
2) are obtained from the X-ray faint source luminosity sensitivity for each
cluster. The effect of the reduced Chandra point source sensitivity with
increasing off-axis angle (Feigelson et al., 2002) is taken into
consideration. Panels d and h in Figure 5 show detected X-ray luminosities as
a function of off-axis angle for Group 5 and 6 cluster members, as well as
X-ray sources unrelated to the clusters (Groups 7-10). The latter X-ray
luminosities were obtained as above with the incorrect assumption that the
sources lie in the star clusters. The red curves show likelihood-based local
quadratic regression fits to the lower envelope data of the X-ray luminosity
distribution generated using the locfit.robust function from the R CRAN locfit
package (Loader, 1999, 2020). Using these curves, upper limits to the X-ray
luminosity based on the source’s angular distances from the cluster centers
are assigned to non-X-ray cluster members (Groups 1 and 2). The inferred upper
limits are listed in Table 4.

##  7 MYStIX/SFiNCs Stars

The interpretation of the 7–25 Myr clusters (with many PMS stars) examined
here greatly benefits from comparison to previously reported X-ray studies of
0.5–5 Myr stellar clusters (with mostly e-PMS stars) in the MYStIX and SFiNCs
projects. The MYStIX (Feigelson et al., 2013) Chandra survey covers 20 regions
dominated by multiple O-type stars at typical distances $1.5\leq d\leq 2.5$
kpc, while the SFiNCs (Getman et al., 2017) survey covers 22 regions dominated
by single O- or multiple B-type stars at typical distances $0.3\leq d\leq 0.8$
kpc. The original catalogs of over 40,000 MYStIX and SFiNCs probable cluster
members in the 42 star forming regions are provided in Broos et al. (2013);
Getman et al. (2017).

Numerous MYStIX/SFiNCs-based papers on methodology and topics of cluster
formation and stellar activity have been published. Related to the current
project, Getman et al. (2014b, 2018b); Richert et al. (2018); Getman &
Feigelson (2021) calculate stellar masses and cluster ages using various
theoretical evolutionary models. The MYStIX/SFiNCs cluster ages range between
0.5 Myr and 5 Myr. For the current study we adopt stellar masses and cluster
ages that are based on the PARSEC 1.2S evolutionary models (Appendix C in
Getman & Feigelson, 2021).

Stellar extinctions, effective temperatures, masses, and bolometric
luminosities were derived using near-IR color-magnitude diagrams. However,
MYStIX/SFiNCs cluster memberships do not include Gaia-selected stars due to
the absorption and nebulosity associated with these embedded e-PMS
populations. This can lead to systematic biases such as an excess of
high-$L_{X}$ stars in the X-ray luminosity function in MYStIX/SFiNCs
populations. This bias should be less pronounced in our older clusters where
X-ray upper limits are treated.

Table 6 gives inferred stellar and X-ray properties for the MYStIX and SFiNCs
samples. Out of 40,041 MYStIX/SFiNCs stellar members, mass estimates are
available for 26,681 most massive members. Out of these 26,681 most massive
members, X-ray luminosity estimates are available for 16,011 most massive and
X-ray luminous members.

Table 6: Stellar Properties of MYStIX and SFiNCs Members

Region | Source | R.A. | Decl. | $ME$ | $A_{V}$ | $t$ | $\log(T_{eff})$ | $M$ | $\log(L_{bol})$ | $\log(L_{X})$ | Evol
---|---|---|---|---|---|---|---|---|---|---|---
|  | deg | deg | ke) |  | Myr | K | $M_{\odot}$ | $L_{\odot}$ | erg s-1 | phase
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
be59 | 000033.87+672446.2 | 0.141150 | 67.412846 | 2.6 | 9.3 | 0.9 | 3.66 | 1.0 | 0.35 | 31.1 | 1
be59 | 000036.43+672658.5 | 0.151798 | 67.449596 | 1.9 | 5.3 | 1.7 | 3.70 | 1.7 | 0.56 | 31.0 | 2
be59 | 000045.20+672805.8 | 0.188345 | 67.468297 | 1.7 | 5.1 | 1.7 | 3.69 | 1.4 | 0.43 |  $\cdots$ | 1
be59 | 000046.19+672358.2 | 0.192477 | 67.399503 | 1.6 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 30.4 |  $\cdots$
be59 | 000050.10+672721.4 | 0.208781 | 67.455954 | 1.8 | 4.1 | 2.0 | 3.59 | 0.7 | -0.27 | 30.1 | 1

Note. — This table is available in its entirety (40,041 MYStIX/SFiNCs members)
in the machine-readable form in the online journal. Column 1: Star forming
region. Column 2: Source’s IAU designation. This identifier is used in the
MYStIX and SFiNCs member tables of Broos et al. (2013) and Getman et al.
(2017). Columns 3-4: Right ascension and declination (in decimal degrees) for
epoch J2000.0. Column 5: X-ray median energy in the $(0.5-8)$ keV band. Column
6. Visual extinction. Column 7. Stellar age estimated from the $Age_{JX}$
chronometer (Getman et al., 2014b). Columns 8-10. Stellar effective
temperature, mass, and bolometric luminosity derived from $JHK$ color-
magnitude diagrams. Column 11: X-ray luminosity in the $(0.5-8)$ keV band.
Column 12: The evolutionary status of the star on the Hertzsprung–Russell
diagram based on PARSEC 1.2S model tracks (Figure 1): 1 = Hayashi track; 2 or
3 = Henyey track; $\geq 4$ = ZAMS.

##  8 PMS X-ray Emission Dependence on Mass

Main sequence stellar activity is primarily a function of rotation (Skumanich,
1972b). But e-PMS activity depends on bulk properties like mass, surface area
and volume (Preibisch et al., 2005; Preibisch & Feigelson, 2005; Telleschi et
al., 2007). The evolution of interior structure during the l-PMS phase shown
in Figure 1 is also strongly dependent on mass. For these reasons, it is
essential that our study of the evolution of X-ray emission consider mass
strata separately. We treat both the e-PMS-dominated population from the
MYStIX/SFiNCs surveys (§7) and the older l-PMS stars in ten 7–25 Myr open
clusters presented here.

Figures 6 shows three measures of X-ray emission as a function of stellar mass
for the 16,011 MYStIX/SFiNCs stellar members with available mass and X-ray
luminosity estimates. These measures are the $(0.5-8)$ keV-band X-ray
luminosity $L_{X}$ useful for measuring ionizing fluence on the environment,
$L_{X}/L_{bol}$ giving the ratio of magnetic activity to bolometric stellar
output, and $F_{X}$ giving the ratio of the X-ray luminosity to the stellar
surface area.

The points are displayed in three colors representing three phases of early
stellar evolution demarcated in Figure 1: the e-PMS Hayashi track for low mass
stars with M$\lesssim$2 M⊙, the l-PMS Henyey track for masses $2\lesssim
M\lesssim 4$ M⊙, and the ZAMS for masses $4\lesssim M\lesssim 100$ M⊙. Widely
used linear fits to the $L_{X}-M$ relation for e-PMS stars are shown from the
Orion COUP (blue; Preibisch et al., 2005) and Taurus XEST (red; Telleschi et
al., 2007) surveys. But the $L_{X}-M$ pattern is complicated and is better
modeled by the black curves showing B-spline regression fits to the $25$%,
$50$% (median), and $75$% quartiles of the X-ray measure distribution. These
curves are generated using R CRAN package cobs (Ng & Maechler, 2007, 2020).

Figure 6: X-ray emission quantities as functions of stellar mass for $16,011$
stellar members of the MYStIX/SFiNCs regions. The stars are color-coded
according to their evolutionary status in the Hertzsprung-Russell diagram:
stars on the Hayashi track (teal), Henyey track (orange), and ZAMS or beyond
(blue). The black curves are spline fits to the 25%, 50% and 75% quartiles of
the X-ray distribution. In the first panel, the straight lines are regression
fits from Preibisch et al. (COUP; 2005) (blue) and Telleschi et al. (XEST;
2007) (red) surveys

.

Figure 7 shows $L_{X}-M$ distributions for the ten 7–25 Myr clusters treated
here. This is one of the principal observational results of this study. These
plots include both ACIS (points) and non-ACIS (triangles indicating upper
limits)333 Upper limits are not available for the MYStIX/SFiNC sample as
reliable Gaia memberships cannot be obtained due to absorption and nebulosity.
Based on the X-ray luminosity function (XLF) and IMF analyses (Kuhn et al.,
2015; Getman & Feigelson, 2021), the X-ray samples from different
MYStIX/SFiNCs regions are approximately complete above different mass
thresholds.. Approximate mass completeness limits obtained from the cluster
IMF distributions (Figure 4) are marked by vertical grey lines, and smoothed
quartiles of the MYStIX/SFiNCs $L_{X}-M$ distribution from Figure 6 are shown
as black curves.

Figure 7: X-ray luminosities as a function of stellar mass for members of the
ten open clusters in Table 1. The vertical gray line shows the mass
completeness limit for each cluster. The purple curves show smoothed Kaplan-
Meier quartiles of the luminosity distributions (see text). The black quartile
curves from the MYStIX/SFiNCs surveys are reproduced from the left panel of
Figure 6. The last panel collects the median curves from the other panels to
facilitate comparison among the clusters.

It is difficult to visually compare the cluster $L_{X}-M$ distributions given
the wide range of luminosities and different fractions of non-detections. To
assist in this comparison we calculate smooth curves representing the median
values (solid purple curves), and the 25% and 75% quartiles (dashed purple
curves) of the $L_{X}$ values as a function of mass. These curves are
calculated as follows. Adaptive stellar mass bins are introduced to accumulate
$N_{tot}/10$ stars per bin, where $N_{tot}$ is the total number of stars per
cluster included in this analysis. To treat both X-ray detections and upper
limits, we use the nonparametric Kaplan-Meier estimator (KM; Kaplan & Meier,
1958) for the $L_{X}$ distributions in each stellar mass bin. The KM
calculations are made with R CRAN package survival (Therneau, 2020). Local
quadratic fits using R’s loess (Cleveland et al., 1992) are then calculated to
provide smoothed representations of the $25$%$-50$%$-75$% KM quartiles.

For mass bins with high fractions of X-ray nondetections, the KM 25% and 50%
(and sometimes even the 75% level) quartiles may be unavailable. The median
curves are superposed in the last panel to help compare the cluster $L_{X}-M$
patterns.

Three important results emerge from both the MYStIX/SFiNCs and the older
cluster $L_{X}-M$ relationships.

1. The e-PMS $L_{X}-M$ relation in the MYStIX/SFiNCs surveys is not well-described by a power law. Dozens of studies have adopted the $L_{X}\propto M^{1.7}$ relation from the Taurus sample of Telleschi et al. (2007) as a valid parameterization of how magnetic activity increases with stellar mass for stars on the Hayashi track. But the left panel of Figure 6 shows this is an inadequate description of a more complex distribution.

The power law is a reasonable fit to the median $L_{X}$ in the 0.3–2 M⊙ range
of our MYStIX/SFiNCs. But this masks a $\sim 30$-fold range in $L_{X}$ at any
mass, and a bifurcation between a minority of stars around $\log L_{X}\simeq
30.5-31.0$ erg s-1 and a majority of stars around $29.5-30.5$ erg s-1. The
upper fork can be attributed to the capture of individual super- and mega-
flares in the Chandra exposures (Getman & Feigelson, 2021). This bimodality is
more prominent for masses below 0.5 M⊙ where the $L_{X}-M$ relation for most
stars steepens considerably. Recall that the MYStIX/SFiNCs samples are missing
most of the low mass stellar population of their clusters, and the true
$L_{X}$ distributions will have more low $L_{X}$ values than shown in Figure
6. The bifurcation and steepening in the $L_{X}$ dependence on mass,
inconsistent with a simple power law relation, is also seen in the dependence
of $L_{X}/L_{bol}$ and $F_{X}$ on mass.

These wide and non-Gaussian spreads can not reasonably be attributed to
inaccuracies in X-ray measurements, or mass, or usage of different mass-scales
based on different evolutionary models, i.e., PARSEC 1.2S (here) versus Siess
et al. (2000) (as in Preibisch et al. (2005); Telleschi et al. (2007)). Visual
inspection of Figure 3 in Preibisch et al. (2005) indicates that the $L_{X}-M$
relationship showed a wide spread and diverged from a single power law at
lower masses ($<0.4$ M⊙). The latest census of Taurus e-PMS stars based on the
Gaia catalog indicates that the XEST Taurus sample used by Telleschi et al.
(2007) was deficient in $0.2-0.6$ M⊙ stars (Luhman, 2018). This may be
responsible for their overestimation of the $L_{X}-M$ relation at low masses.

2. The median X-ray luminosities of l-PMS stars in our open clusters are weaker than median luminosities from e-PMS stars at all masses. This is seen in the comparison of smooth distributions shown in the last panel of Figure 7. This drop in X-ray luminosity continues through the l-PMS phase. The difference between the median $L_{X}$ values of the open clusters and MYStIX/SFiNCs clusters increases from a factor of $\simeq$3 drop for $t\simeq 7$ Myr to a factor of $\simeq$6 at $t\simeq 25$ Myr.

3. At any given age, intermediate mass stars on the l-PMS Henyey track have higher X-ray luminosities than either lower mass Hayashi track or higher mass ZAMS stars. This is seen in Figure 7 where the highest luminosities are orange points.

The last panel’s smooth distributions show narrow peaks in X-ray luminosities
at intermediate masses compared to other masses. In particular, higher-mass
stars in the range $M\gtrsim 1-3$ M⊙ have X-ray luminosities plummeting with
increasing stellar mass. These X-ray luminosity decreases take place for stars
that are completing their changes on the Henyey track or already reside on the
ZAMS.

The combination of the above effects causes a distinctive drift of the
$\log(L_{X})-\log(M)$ turnover point with age. Again this is best seen in the
smooth median $L_{X}-M$ curves in the last panel of Figure 7.

In summary, the historically reported strong correlation of X-ray luminosity
with mass for e-PMS Hayashi track stars with $M\lesssim 3$ M⊙ is confirmed,
but a simple power law relationship does not apply. Most stars exhibit a
relation steeper than $L_{X}\propto M^{1.8}$ while other stars are dominated
by powerful flares and show a shallower relation. The median X-ray
luminosities decline gradually as stars begin passage along the l-PMS Henyey
track and then plummet rapidly as they approach the ZAMS. We find definite
systematic decreases in surface magnetic activity as the interior changes from
fully convective to mostly radiative energy transport. Overall, it is clear
that the X-ray activity of the stars diminishes with increasing age and the
Henyey/ZAMS stars experience the most drastic X-ray activity changes. We
quantify these changes in §9.

Finally, we note that our discussion of l-PMS activity evolution has been
limited to X-ray luminosities with no mention of $L_{X}/L_{bol}$ and $F_{X}$.
Plots of these quantities against mass for the 7–25 Myr open clusters show
complex structure changes (such plots are omitted from this paper). Often the
changes in X-ray emission are overwhelmed by bolometric luminosity and stellar
radius changes (Figure 1). $L_{X}/L_{bol}$ and $F_{X}$ have long proved useful
in plots against stellar rotational measures on the main sequence in
discussions of saturation and tachoclinal dynamo processes (Güdel, 2004). But
they are not useful for the l-PMS phase when luminosities and radii are
rapidly changing.

##  9 PMS X-ray Emission Dependence on Age

We now address how the X-ray emission of ensembles of stars evolves from the
fully convective e-PMS phase through the l-PMS changes and settling on the
ZAMS. Here we stratify stellar masses into a few bins. This is challenging
because, due to differing distances and Chandra observation sensitivities,
X-ray detections are complete to different limiting masses in a sample of PMS
clusters. The addition of Gaia-only members does not fully alleviate this
difficulty as the Gaia survey also has a distance-dependent sampling effect.
The results of this analysis presented in Figure 8 show the mass-stratified
evolution of the X-ray luminosity for the stellar groups from MYStIX/SFiNCs
regions and our 7–25 Myr open clusters.

For the e-PMS phase, the analysis is limited to the nearby MYStIX/SFiNCs
stellar samples with better sensitivities towards low-mass stars and
completeness limits down to $0.5-0.75$ M⊙.444 The included MYStIX/SFiNCs
regions are (in order of increasing distance from the Sun out to $d\simeq 1$
kpc; see Table 1 in Getman & Feigelson (2021)): IC 348, OMC 2-3, ONC Flanking
Fields, Orion Nebula, NGC 2068, W 40, LkHα 101, NGC 2264, IC 5146, Cep B, RCW
36, NGC 7160, Be 59, NGC 2362, and Lagoon Nebula. Each region is shown as a
gray point in Figure 8. We also consider lightly-absorbed (X-ray median energy
$<2$ keV) sub-populations from the deep Chandra surveys of Orion Nebula
(COUP), MYStIX-NGC2264, and SFiNCs-IC348, which exhibit even better
completeness limits down to $0.1-0.4$ M⊙ (black points).

For the l-PMS phase, the analysis is limited to mass strata in each cluster
where the cluster’s IMF completeness limit is below the lower boundary of the
mass stratum and the KM estimator is able to produce a 50% quartile value with
uncertainty. This avoids low mass samples that are dominated by X-ray upper
limits.

Figure 8: Temporal evolution of X-ray luminosity for four mass strata.
Corresponding mass bins are given in the figure legends. e-PMS stellar samples
from nearby MYStIX/SFiNCs regions are shown as grey points with error bars
representing 68% confidence intervals on median (solid squares). 25% and 75%
quartiles are shown for samples with $>20$ stars (open triangles). Stars from
the lightly-absorbed e-PMS sub-populations are marked by black points. The
l-PMS open clusters are depicted by colored points with 68% error bars on the
50% quartiles (solid circles) of the KM estimators. 25% and 75% quartiles are
shown only for samples with over 20 stars (open triangles); 25%-quartile KM
estimators are often not available due to high numbers of X-ray upper limits.
The black lines indicate linear regression fits to the median X-ray
luminosities of the open clusters. The regression fit results are listed in
Table 7. The legends also list the numbers of stars in the open clusters,
whose stellar masses lie within the mass range of interest, and the fractions
of X-ray detections. The flag ”Y” indicates that the mass completeness limit
(Table 1) is below the mass range of interest, the 50% quartile of the KM
estimator is available, and the cluster’ median $L_{X}$ is plotted and
involved in the regression calculation.

Historically, a power law relation $L_{X}\propto t^{b}$ has been used to
characterize the decay of magnetic activity. From the Orion Nebula Cluster
COUP study, Preibisch & Feigelson (2005) report, for instance, $b\simeq-0.32$
in the 0.4–1 M⊙ range over the age range $0.1-10$ Myr, and a steeper decline
$b\simeq-0.75$ when older ZAMS stars are included. In Figure 8, we find that
the power law model does provide good fits to the evolution of X-ray
luminosities during the l-PMS phase. Results from weighted least squares
regression, using the R lm function (Sheather, 2009), for $L_{X}\propto t^{b}$
in the age range 7–25 Myr are listed in Table 7.

Table 7: Evolution of $L_{X}$, $F_{X}$, $L_{X}/L_{bol}$, $L_{bol}$, and
$R_{\star}$ in 7–25 Myr-old Stars

Mass Stratum | Quantity | $N_{clusters}$ | $N_{stars}$ | $\log(a)$ | $b$ |  $p$-val
---|---|---|---|---|---|---
$M_{\odot}$ |  |  |  |  |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7)
$0.75-0.9$ | $L_{X}$ | 7 | 352 | $30.42\pm 0.19$ | $-0.66\pm 0.17$ | 0.01
$0.75-0.95$ | $L_{X}$ | 7 | 443 | $30.41\pm 0.18$ | $-0.63\pm 0.15$ | 0.01
$0.75-1$ | $L_{X}$ | 7 | 538 | $30.20\pm 0.21$ | $-0.46\pm 0.18$ | 0.05
$1-2$ | $L_{X}$ | 9 | 2021 | $31.62\pm 0.44$ | $-1.78\pm 0.41$ | 0.00
$1-3.5$ | $L_{X}$ | 6 | 1008 | $31.46\pm 0.21$ | $-1.79\pm 0.19$ | 0.00
$1-3.5$ | Q85% $L_{X}$ | 10 | 3271 | $31.03\pm 0.35$ | $-0.67\pm 0.30$ | 0.06
$3.5-5$ | Q85% $L_{X}$ | 5 | 224 | $32.48\pm 0.46$ | $-2.25\pm 0.42$ | 0.01
$3.5-7$ | Q85% $L_{X}$ | 7 | 374 | $34.06\pm 0.84$ | $-3.65\pm 0.88$ | 0.01
$0.75-0.9$ | $L_{X}/L_{bol}$ | 7 | 352 | $-2.85\pm 0.19$ | $-0.44\pm 0.17$ | 0.05
$0.75-0.95$ | $L_{X}/L_{bol}$ | 7 | 443 | $-2.81\pm 0.21$ | $-0.49\pm 0.18$ | 0.04
$0.75-1$ | $L_{X}/L_{bol}$ | 8 | 966 | $-2.73\pm 0.44$ | $-0.62\pm 0.39$ | 0.16
$1-2$ | $L_{X}/L_{bol}$ | 10 | 2488 | $-0.87\pm 0.38$ | $-3.14\pm 0.39$ | 0.00
$1-3.5$ | $L_{X}/L_{bol}$ | 7 | 1630 | $0.16\pm 0.53$ | $-4.55\pm 0.48$ | 0.00
$1-3.5$ | Q85% $L_{X}/L_{bol}$ | 10 | 3271 | $-2.65\pm 0.25$ | $-0.71\pm 0.23$ | 0.01
$3.5-5$ | Q85% $L_{X}/L_{bol}$ | 5 | 224 | $-3.14\pm 0.50$ | $-2.65\pm 0.45$ | 0.01
$3.5-7$ | Q85% $L_{X}/L_{bol}$ | 7 | 374 | $-4.36\pm 1.17$ | $-1.76\pm 1.04$ | 0.15
$0.75-0.9$ | $F_{X}$ | 7 | 352 | $7.18\pm 0.19$ | $-0.22\pm 0.17$ | 0.24
$0.75-0.95$ | $F_{X}$ | 7 | 443 | $7.23\pm 0.19$ | $-0.27\pm 0.17$ | 0.18
$0.75-1$ | $F_{X}$ | 7 | 538 | $6.96\pm 0.21$ | $-0.03\pm 0.18$ | 0.88
$1-2$ | $F_{X}$ | 9 | 2021 | $8.54\pm 0.42$ | $-1.83\pm 0.40$ | 0.00
$1-3.5$ | $F_{X}$ | 6 | 1008 | $8.51\pm 0.31$ | $-1.95\pm 0.29$ | 0.00
$1-3.5$ | Q85% $F_{X}$ | 10 | 3271 | $7.44\pm 0.26$ | $-0.18\pm 0.23$ | 0.45
$3.5-5$ | Q85% $F_{X}$ | 5 | 224 | $9.39\pm 0.42$ | $-2.69\pm 0.38$ | 0.01
$3.5-7$ | Q85% $F_{X}$ | 7 | 374 | $9.29\pm 0.58$ | $-2.61\pm 0.61$ | 0.01
0.75,0.8,0.9 | $L_{bol}$ |  $\cdots$ |  $\cdots$ | -0.15,-0.17,-0.39 | -0.43,-0.35,-0.03 |  $\cdots$
0.95,1,1.5 | $L_{bol}$ |  $\cdots$ |  $\cdots$ | -0.56,-0.77,0.14 | 0.20,0.47,0.52 |  $\cdots$
2,3.5,5,7 | $L_{bol}$ |  $\cdots$ |  $\cdots$ | 1.29,2.11,2.68,3.07 | -0.03,0.02,0.08,0.22 |  $\cdots$
0.75,0.8,0.9 | $R_{\star}$ |  $\cdots$ |  $\cdots$ | 0.26,0.25,0.23 | -0.26,-0.22,-0.20 |  $\cdots$
0.95,1,1.5 | $R_{\star}$ |  $\cdots$ |  $\cdots$ | 0.22,0.20,0.57 | -0.18,-0.15,-0.32 |  $\cdots$
2,3.5,5,7 | $R_{\star}$ |  $\cdots$ |  $\cdots$ | 0.36,0.27,0.35,0.36 | -0.15,0.03,0.07,0.16 |  $\cdots$

Note. — Column 1: Mass stratum. Column 2: X-ray luminosity ($L_{X}$ in units
erg s-1), X-ray surface flux ($F_{X}$ in units erg s-1 cm-2), median for lower
mass stars and 85% quantiles for higher mass stars (Appendix §C). Bolometric
luminosity ($L_{bol}$ in units $L_{\odot}$) and stellar radius ($R_{\star}$ in
units $R_{\odot}$) are from PARSEC 1.2S evolutionary models. Columns 3-4:
Numbers of open clusters and cluster members. Columns 5-7: Results from the
linear regression fits for the relations $Q=a\times t_{Myr}^{b}$ within the
7–25 Myr age range, where Q is one of the above stellar quantities. The
results include the intercept and slope with 68% errors, and $p$-value for the
hypothesis of zero slope.

Four findings emerge:

1. For the X-ray detected MYStIX/SFiNCs stars in the low-mass range 0.75–1 M⊙, within the first few Myr of evolution, their X-ray luminosities do not exhibit any statistically significant temporal changes; the median X-ray luminosities remain at a constant level of $\log(L_{X})\sim 30.3$ erg s-1. The young stars within these mass and age ranges are still on Hayashi tracks; they are fully convective and keep gravitationally contracting. Since their X-ray luminosities are at a constant level, their surface fluxes rise drastically with time at the pace of the decline of their squared stellar radii. The associated astrophysical issue we consider in §11 is: What causes the X-ray luminosity to remain nearly constant while the fully convective star keeps contracting?

2. In contrast, the X-ray luminosities of the low-mass 0.75–1 M⊙ members of the open clusters decline with time slightly during the 7–25 Myr period, but the effect is statistically significant. The majority of the stars in clusters younger than 15 Myr are still descending Hayashi tracks (e-PMS phase). But for older clusters, Henyey stars start significantly contributing or even dominating the stellar samples. The median X-ray luminosities decrease from $\log(L_{X})\sim 29.8$ erg s-1 (at 7 Myr) to $\log(L_{X})\sim 29.5$ erg s-1 (at 25 Myr). The associated slope $b$ in the $L_{X}\propto t^{b}$ relation is around $b\sim-0.6$. This temporal trend is similar to the rate of decrease of stellar volume $V\propto R_{\star}^{3}$ based on the PARSEC 1.2S models (Figure 1, Table 7). The associated astrophysical issue is: What causes the X-ray power to scale with stellar volume?

3. Within the mass ranges 1–2 M⊙ and 1–3.5 M⊙, the open cluster stars are predominantly located on either Henyey (l-PMS phase) or ZAMS tracks. The stellar radii exhibit complex temporal behaviours — some are rising, some are still decreasing, and some are roughly constant. The X-ray luminosity undergoes a rapid plunge. The slope of the $L_{X}\propto t^{b}$ relation is $b\simeq-1.8$. What causes the X-ray power to plunge in stars undergoing most significant interior changes?

4. For the highest mass range available to us, $3.5\lesssim M\lesssim 7$ M⊙, the stars are entirely on the ZAMS. X-ray luminosities are so low that the Kaplan-Meier estimator does not give a median value; we measure instead the temporal behavior of the 85% quantile of the $L_{X}$ KM estimator. These stars show an even more rapid decay rate than the 1–3.5 M⊙ mass stratum. The decay slope for the 85% quantile of $L_{X}$ changes from $b\sim-0.7$ in 1–3.5 M⊙ stars to $b\simeq-[2-4]$ in more massive stars. Appendix C details these changes. Why does X-ray luminosity keep nosediving in more massive ZAMS stars?

The X-ray activity evolution results given above are based on the entire
sample of 6,003 young stars located within the central regions of the ten open
clusters (Table 4). These results are listed in Table 7. For the sample culled
of 485 stars with inconsistent $G$-band vs. BP- and RP-band photometry, the
inferred X-ray luminosity decay slopes are $b=(-0.7\pm 0.2,-0.4\pm 0.2,-2.0\pm
0.4,-1.8\pm 0.2)$ for the mass strata $M=(0.75-0.9),(0.75-1),(1-2),(1-3.5)$
M⊙, respectively, and are statistically indistinguishable from the ones given
in Table 7.

##  10 Comparison With Previous Literature

Using approach A (i.e., relying on ages for individual stars; §2), for the
first $\sim 10$ Myr of PMS evolution Preibisch & Feigelson (2005) and Gregory
et al. (2016) report a mild decay in the stellar X-ray luminosity with the
slopes $b$ in the $L_{X}\propto t^{b}$ relation as $b\sim-0.3$ and
$b\sim-0.5$, for the 0.4–1 M⊙ and 1–2 M⊙ mass ranges, respectively. Gregory et
al. (2016) further find a steeper decay slope for more massive stars, e.g.,
$b=-1.19\pm 0.35$ in 2–3 M⊙ stars.

Our results differ from those in two ways: 1) we do not find any X-ray
luminosity decreases within the first few Myr of PMS evolution; 2) but for the
time interval after 7 Myr, we find significantly faster $L_{X}$ decays in $>1$
M⊙ stars (Table 7).

Our results are more consistent with the outcomes of the approach B in
Preibisch & Feigelson (2005). In this case, the authors mention no indications
for $L_{X}$ changes within the first few Myr of evolution and derive a steeper
decay slope of $b=-0.75$ for 0.5–1.2 M⊙ stars after 7 Myr.

Qualitatively, our results are consistent with the findings of Gregory et al.
(2016) that the X-ray luminosity decays faster in more massive PMS stars.

Figure 9: Comparison with the modeling results of Johnstone et al. (2021a).
Temporal evolution of the 25-50-75% quartiles for the X-ray luminosity in 3
mass bins. The mass ranges are given in figure legends. Our empirical points
from the current study, as medians with 68% confidence intervals (black points
with error bars) and 25-75% quartiles for $N>20$ stellar samples (green
triangles), are the same as in Figure 8. For the modeled data of Johnstone et
al. (2021a), median and its 68% confidence intervals (red points with error
bars) and 25-75% quartiles (red lines).

For e-PMS age ranges, Tu et al. (2015); Johnstone et al. (2021a) calibrate
their analytic rotation evolution approach against X-ray and rotation
empirical data of only two similar-aged young ($\sim$2 Myr) star forming
regions, Taurus cloud and Lagoon Nebula. For the l-PMS age range of interest
here, 7–25 Myr, their calibration includes only one $\sim 13$ Myr old cluster,
h Per. The outcome from the model of Johnstone et al. (2021a) and our
empirical results are compared in Figure 9. For the modelled data of Johnstone
et al., we calculate 25-50-75% quartiles and 68% confidence intervals on
median $L_{X}$ based on their on-line electronic data-set entitled
“TrackGrid_Distribution”. The following main inconsistencies between the model
and empirical results are evident. First, the empirical distributions of X-ray
luminosities have higher spreads (interquartile ranges) than the modeled
distributions. For l-PMS stars such wide X-ray radiation spreads can be
explained by possible dependencies of $L_{X}$ on rotation, with faster
rotators having systematically high X-ray luminosities (e.g., Tu et al.,
2015). Second, for the first few Myr (at least up to 3 Myr), the model
predicts a monotonic decrease in $L_{X}$, while the empirical data show nearly
constant (within statistical uncertainties) X-ray emission. Third, for $<0.95$
M⊙ stars in the $>10$ Myr age range, there is an indication for possible
slightly steeper temporal decline of the empirical median $L_{X}$. Forth,
closer to one-solar mass $>7$ Myr stars, the empirical data give
systematically lower median X-ray luminosities.

Our future Chandra projects will be targeting more open clusters within the
age ranges 5–7 Myr and 25–150 Myr for further improvements of the empirical
trends and comparison with the models. Johnstone et al. (2021a) are encouraged
to use our data for calibration and refinement of their models.

##  11 Discussion: Interior Dynamos and Surface Activity

The evolution of PMS stars is strongly mass-dependent as they proceed from the
e-PMS Hayashi track to the rapid crossing of the Hertzsprung-Russell diagram
during the l-PMS phase (Figure 1). We therefore divide our discussion into
mass strata considered earlier.

The 0.75–1 M⊙ stars For this mass range, the X-ray detected stellar
populations for nearby MYStIX/SFiNCs star forming regions are nearly complete
in mass and all stars are still descending Hayashi HRD tracks. In contrast to
most previous results (Preibisch & Feigelson, 2005; Gregory et al., 2016; Tu
et al., 2015; Johnstone et al., 2021a), we find that the X-ray luminosity
levels of these lower mass e-PMS stars remain nearly constant in time during
the first few Myr of evolution (at least at $\sim(0.5-3)$ Myr). The surface
fluxes rapidly increase with time simply as consequences of decreasing radii
during the gravitational contraction phase of a fully convective PMS star. Our
finding suggests that at this evolutionary stage, the X-ray levels do not
respond to the temporal changes in the size of a star.

In addition, previous work has found no correlation between $L_{X}$ and
rotation rate during the fully convective e-PMS phase (Preibisch et al., 2005;
Alexander & Preibisch, 2012; Henderson & Stassun, 2012). The independence of
surface magnetic activity to rotation rates, the high levels of X-ray emission
during the e-PMS phase with $\log L_{X}/L_{bol}\simeq-3$ to $-4$, and similar
behaviors of older fully convective late-dM stars (Magaudda et al., 2021),
lead to the conclusion that magnetic activity processes may be saturated. We
will discuss this issue for the ten older open clusters in our forthcoming
companion paper concentrated on measuring ZTF and TESS stellar rotation
periods.

But in low-mass e-PMS stars, it is not clear which stage is saturated:
interior dynamos, surface filling factors, or some process above the stellar
surface such as centrifugal stripping of X-ray coronal structures (Vilhu,
1984; Jardine & Unruh, 1999; Pizzolato et al., 2003; Wright et al., 2011a). It
is possible that a combination of some of these processes is responsible for
the X-ray saturation.

Qualitatively, the link between interior field generation and the observed
X-ray emission is clear. Fields generated in the interior dynamo, probably a
distributed $\alpha^{2}$ dynamo process, erupt onto the stellar surface where
reconnection commonly occurs as field loop footprints are twisted by turbulent
cells. Getman & Feigelson (2021) and Getman et al. (2021) find that super- and
mega-flares are common during the e-PMS phase for all stellar masses. The
surface fields confine hot X-ray emitting plasma as the flare developed with
the hotter plasma component originating in higher-altitude coronal loops and
cooler plasma dominating in the lower-altitude corona. This is in line with
the dynamic MHD simulations of Cohen et al. (2017). The simulations suggest
that surface magnetic fields in fully convective fast rotating stars may be
concentrated in high-latitude areas leading to formation of large-scale
dipolar coronal structures that due to their strong magnetic fields would be
able to confine hot X-ray emitting plasma. This is alternative to the
scenarios relying on the saturation of surface filling factors or dynamos.

A few lines of independent empirical evidence based on our COUP and
MYStIX/SFiNCs data favor the scenario of Cohen et al. (2017). First, the Orion
COUP data show that the emission measure of the hot ($T\sim 20-60$ MK) plasma
component dominates that of the cool ($T\sim 10$ MK) component by a factor of
3 in low mass e-PMS stars (Preibisch et al., 2005; Getman et al., 2010).
Second, plasma modeling of COUP and MYStIX/SFiNCs super- and mega-flares
provide strong evidence for the existence of giant X-ray hot flaring coronal
structures extending $0.5-10$ R⋆ above the stellar surface (Favata et al.,
2005; Getman et al., 2008, 2021). In diskless stars, the heights of such
structures can often exceed one corotation radius indicating that the
structures may withstand the effects of centrifugal forces, thanks to the high
strengths of their associated large-scale magnetic fields (Getman et al.,
2008). Third, in the current study, we find that the X-ray luminosity is
insensitive to the age and stellar size changes. This is in line with the idea
that the higher altitudes of X-ray emitting structures imply less dependence
on the properties of the surface far below the giant polar loops.

As the 0.75–1 M⊙ stars progress into the l-PMS phase represented by our open
cluster members, the X-ray luminosity starts with a drop sometime between 3
and 7 Myr. While we have a gap in our age coverage during this interval, the
drop is evident in Figure 8. The X-ray luminosity continues to fall slowly
during the following 7–25 Myr period. During this period, the PARSEC 1.2S
interior models indicate that the bolometric luminosity continues to fall and
reaches a minimum while the radius continues to decrease (Figure 1). X-ray
luminosity changes with time as the stellar volume does.

The explanation for this change in X-ray behavior is unclear. Perhaps, unlike
the MYStIX/SFiNCs e-PMS regime, the convective dynamo finally becomes
responsive to changes in stellar volume and produces weaker surface fields and
consequently weaker X-ray flares. And/or perhaps the smaller stellar surface
is unable to sustain the enormous polar loops responsible for the strongest
X-ray flares. A simplistic model might be that the X-ray coronal scale height
is proportional to the stellar radius so that $L_{X}\propto V_{loop}\propto
V_{star}$.

The 1–2 M⊙ stars In this mass range, most of the open cluster members lie on
the l-PMS Henyey track and or (for the 20–25 Myr cluster) have reached the
ZAMS. These are the most X-ray luminous stars in the clusters, as indicated by
a sharp peak in the $L_{X}-M$ diagrams in Figure 7. Figure 7 (last panel),
Figure 8 (lower left panel), and Table 7 show that the X-ray luminosity is now
decreasing rapidly during the 7–25 Myr period roughly as $L_{X}\propto
t^{-1.8}$. This is consistent with the decay for older stars on the main
sequence: Maggio et al. (1987) and Güdel et al. (1997) obtain $L_{X}\propto
t^{-1.5}$ for G-type field stars and members of old open clusters with ages
between $\gtrsim$70 Myr and 9 Gyr. Feigelson et al. (2004) report
$L_{X}\propto t^{-2}$ for magnetically active M-, K-, and G-type Galactic
stars. The magnetic activity of these main sequence stars is believed to be
driven by the tachoclinal $\alpha\Omega$ dynamo. The great majority of older
main sequence stars lie on the unsaturated locus of the X-ray activity $-$
rotation diagrams (Maggio et al., 1987; Güdel et al., 1997).

This similar decay law between our open cluster stars and main sequence stars
in this mass range suggests that the $\alpha\Omega$ dynamo now dominates over
the $\alpha^{2}$ dynamo during the l-PMS phase: a fundamental transition has
occurred in the magnetic field generation with observable consequences in the
X-ray band. Like in the contemporary Sun, the bulk of our 1–2 M⊙ l-PMS stars
have developed radiative zones, but the outer parts are convective. Hints of
changes in the large scale magnetic topologies of such stars, from simple
(i.e., dipolar) axisymmetric to more complex (i.e., octopolar) non-
axisymmetric, support this transition (Gregory et al., 2014, 2016). For NGC
869, Argiroffi et al. (2016) reach a similar conclusion based on their
discovery of a handful of unsaturated 1–1.4 M⊙ stars on the activity-rotation
diagram.

It is interesting to note that for older (70 Myr – 9 Gyr) solar-mass stars
Güdel et al. (1997) report a strong negative correlation between the
temperature of the hot X-ray emitting plasma component and stellar age,
implying that the frequency of larger X-ray flares associated with hotter
plasma is decreasing with age. Our 7–25 Myr old l-PMS stars (averaged across
all masses) have Chandra-based median hot temperature component of $\sim 40$
MK (Table 5) and fit nicely into the ASCA-based hot temperature versus age
relation of Güdel et al. (1997). And so do the 440 Myr and 210 Myr old solar-
mass stars $\epsilon$ Eri and Kepler-63, whose XMM-Newton-based hot plasma
temperatures range between 9 and 12 MK (Coffaro et al., 2020, 2022). Since the
heights of X-ray flaring coronal structures on young stars, older active
stars, and the Sun positively correlate with plasma temperature (Figure 7 in
Getman et al., 2021), it is reasonable to propose that the X-ray coronas of
our solar-mass l-PMS stars are more extended than those of older ($t>70$ Myr)
solar-mass stars, but are not as large as the coronas of solar-mass e-PMS
stars. Our future work on X-ray super-flares from l-PMS stars will provide
more quantitative treatment of this issue.

Coffaro et al. (2020, 2022) also find that the X-ray cycle amplitudes of
$\epsilon$ Eri and Kepler-63 are the smallest (compared to several older
solar-mass stars with known X-ray cycles) and their surfaces may be profusely
(60-100%) covered by solar-type X-ray emitting magnetic structures (such as
active region cores and flares). Careful analyses of mass-stratified X-ray
spectral stacking, mass-stratified super-flare energies and frequencies, and
rotation rates for l-PMS stars need to be performed in order to examine
whether the solar-mass l-PMS stars exhibit similar X-ray surface saturation.

The higher-mass 2–7 M⊙ stars Samples of MYStIX/SFiNCs e-PMS stars are likely
incomplete above $2$ M⊙ and involvement of Gaia data will not recover all
young members due to often high and variable source extinctions and effects of
high source crowding and background nebula emission (Getman et al., 2019).
Nevertheless, the upper envelopes of apparent X-ray distributions for e-PMS
MYStIX/SFiNCs stars seem still higher than those of l-PMS (Figure 12).

The X-ray luminosity keeps decreasing as $L_{X}\propto t^{-1.8}$ when 1–2 and
2–3.5 M⊙ l-PMS stars are combined. Many of the 2–3.5 M⊙ stars reach ZAMS but
remain partially convective. It is likely that as their 1–2 M⊙ siblings they
are now powered by the $\alpha\Omega$ dynamo.

$L_{X}$ falls precipitously during the l-PMS phase (Figure 12). For these
masses, most of the l-PMS stars are undetected by Chandra (Figure 7, all
panels) so it is difficult to quantify this dropoff. Fitting a power law to
the upper envelope of the $L_{X}$ distribution suggests that $b\simeq-2$ to
$-4$ in the $L_{X,85\%}\propto t^{b}$ relationship (Table 7). The dropoff is
more dramatic in the 3.5–7 M⊙ interval than in the 1–3.5 M⊙ (Appendix C).

Vast majority of the 3.5–7 M⊙ stars are fully radiative and already reached
the main sequence; a few are approaching their post-main sequence regime
(Figure 1). Many of them are A- and late-B type stars. Our findings of
diminishing X-ray emission levels are consistent with the well known fact that
such stars lack both the convection zones driving magnetic activity in lower-
mass stars and the strong radiation driven stellar winds with shocks
responsible for X-ray emission in O- and early B-type stars (e.g., Güdel &
Nazé, 2009; Stelzer et al., 2009; Drake et al., 2014; Nuñez et al., 2021).
Occasionally, the X-ray emission is detected from some of such systems and
probably is not produced by the massive primary, but rather by lower mass
unresolved secondaries in multiple systems (Stelzer et al., 2005, 2009).

##  12 Discussion: Effects on the molecular environs on PMS stars

###  12.1 X-ray effects on protoplanetary disks

High fluence ionizing PMS X-ray radiation is predicted to penetrate deep into
molecular environments and substantially increase the degree of ionization,
stimulate magnetorotational instability and associated turbulence, create
conditions necessary for launching a magnetocentrifugal disk wind and a
collimated jet, induce non-equilibrium ion-molecular chemistry, and sputter
grain surfaces (e.g., Glassgold et al., 2000; Fromang et al., 2002; Shang et
al., 2002; Ilgner & Nelson, 2006; Gressel et al., 2013; Cleeves et al., 2017;
Dupuy et al., 2018; Waggoner & Cleeves, 2019, 2022).

X-rays are expected to play an important role in photoevaporative flows and
dispersal of protoplanetary disks (reviewed by Williams & Cieza, 2011;
Alexander et al., 2014; Ercolano & Pascucci, 2017). Disk photoevaporation
linked to high-energy X-ray and ultraviolet radiation from the central star is
now directly detected in a number of systems (Alexander et al., 2014; Picogna
et al., 2019). X-rays seem most important in the final stages of disk
dispersal (Owen et al., 2013). There is some empirical evidence that X-rays
heat disks and diminish accretion due to photoevaporation of disks (Drake et
al., 2009; Flaccomio et al., 2018; Flaischlen et al., 2021).

Within the framework of the hydrodynamic escape model by Owen et al. (2012),
the X-ray driven gas removal rate in the disk around a $1$ M⊙ young star is
$\dot{M}_{phot}=6\times 10^{-9}\times(L_{X}/10^{30})^{1.14}$ M⊙ yr-1. Figure 9
shows that for star age of 1 Myr, $L_{X}$ is $10^{30.2}$ erg s-1 based on the
MYStIX/SFiNCs data but $10^{30.6}$ erg s-1 based on the modeling of Johnstone
et al. (2021a). There is thus a factor of 3 discrepancy between the disk gas
rates expected from our empirical MYStIX/SFiNCs data and modeling by Johnstone
et al. (2021a).

The bifurcation of e-PMS stars on the $\log(L_{X})-\log(M)$ plane around
$\log(L_{X})\sim 30.5$ erg s-1 (Figure 6) is partially due to the presence of
numerous large X-ray flares. The occurrence rate of super ($E_{X}>10^{34}$
erg) and mega ($E_{X}>10^{36.2}$ erg) flares in solar-mass e-PMS stars is
$\sim 200$ and $\sim 2$ flares per star per year, respectively (Getman &
Feigelson, 2021). Large flares from PMS stars may significantly impact the
physical and chemical evolution of circumstellar disks. Possible observational
signatures of such an impact have been detected from the disk around the young
solar-mass star IM Lupi via time-dependent flux variations of H13CO+ (J=3-2)
ion in the sub-mm band observed by ALMA (Cleeves et al., 2017). The thermo-
chemical disk models suggest that the formation of this ion is highly
sensitive to the ionization rate of the disk through the formation of
H${}_{3}^{+}$, which reacts with the abundant molecules CO and N2 to produce
H13CO+ and N2H+, respectively (Rab et al., 2017; Waggoner & Cleeves, 2022).
Disk chemistry simulations involving a large X-ray flare with the duration
from several hours to 2 days predict enhanced ion abundances for up to 20 days
(Cleeves et al., 2017). However, to date no X-ray observations have been
performed in the same epoch as disk ion abundance variability (Cleeves et al.,
2017). Simultaneous X-ray and sub-mm observations are required to test these
scenarios.

Over the typical 5 Myr disk-lifetime (Richert et al., 2018), the disk around a
solar-mass star is predicted to be irradiated by 1 billion super- and mega-
flares with X-ray energies $34<\log(E_{X})<38$ erg (Getman & Feigelson, 2021).
Such large flares are expected to be accompanied by fast and energetic coronal
mass ejections propagating at a few thousands of km s-1 (Alvarado-Gómez et
al., 2022). Such fast CMEs are expected to initiate strong shocks and drive
high fluence hard spectra stellar energetic particles, mostly protons,
penetrating the equatorial regions of the disk at over 100 AU from the star,
and igniting significant ionization with efficient production of H13CO+ and
N2H+ ions on a time scale of a few weeks (Rab et al., 2017, 2020; Hu et al.,
2022).

The present open cluster observations contribute little to the X-ray effects
on disks as the disks are mostly gone by $5-7$ Myr (Richert et al., 2018).

###  12.2 Impact of X-ray and associated EUV emission on primordial planetary
atmospheres

As shown in Figure 8, the median time-averaged X-ray luminosity for 1–2 M⊙
stars and the 75% $L_{X}$ quartile for 0.75–1 M⊙ PMS stars can reach up to
$3\times 10^{30}$ erg s-1 in the first few Myr of evolution. Assuming that
$L_{EUV}\sim 4\times L_{X}$ in the $100-1200$ Å band, the total X-ray and EUV
(XUV) power for many solar-mass e-PMS stars may exceed $10^{31}$ erg s-1. This
is over 1000 times higher than the current Sun’s time-averaged XUV luminosity
of $1.5\times 10^{28}$ erg s-1 (Airapetian et al., 2020; Johnstone, 2020).
While this enhanced XUV flux declines during the l-PMS phase in a mass-
dependent fashion (§9) when protoplanetary disks have mostly dissipated, the
PMS XUV irradiance should have significant impact on atmospheric evolution of
primary atmospheres of protoplanets and young exoplanets.

The stellar XUV radiation is absorbed by atmospheric gas producing excitation,
dissociation, and ionization of atmospheric species. Photoionization generates
photoelectrons with energies sufficient for the subsequent ionization and
excitation of atomic and molecular hydrogen. These photoelectrons excite
secondary electrons that lose their excess kinetic energy via Coulomb
collisions with the ambient atmospheric particles, and contribute to the
heating and expansion of exoplanetary upper atmospheres (Glocer et al., 2012;
Airapetian et al., 2017). This in turn can drive several thermal, nonthermal,
and chemical escape processes forming the ionosphere and thermosphere
(Airapetian et al., 2020; Gronoff et al., 2020).

The XUV driven heating rate depends critically on the chemical composition of
the primordial planetary atmosphere because different atmospheric species have
different wavelength-dependent absorption cross sections. Hydrogen-rich
primordial atmospheres of protoplanets around PMS stars efficiently absorb
stellar radiation shortward of 1120 Å via molecular and atomic hydrogen. XUV
driven heating increases the temperature at the exobase, the atmospheric
layer, where the particle mean free path is comparable to the pressure scale
height. In this layer, energetic particles from the tail of Maxwellian
distribution move with outgoing velocity exceeding the planet’s escape
velocity and thus escape into space. The escape rate is controlled by the
Jean’s escape parameter $\lambda_{C}$, represented by the ratio of
gravitational energy to the mean particle’s thermal energy. For a pure
hydrogen atmosphere, the hydrodynamic escape occurs at $\lambda_{C}<3.5$ or at
the exospheric temperatures over 4,200 K.

However, the atmosphere should also contain rock vapor formed due to frequent
impacts in the early phase of evolution of protoatmospheres (Canup, 2004).
This may raise the temperature in excess of 21,000 K required for the onset of
hydrodynamic escape via adiabatic expansion (Massol et al., 2016).

Recent hydrodynamic and magnetohydrodynamic models provide satisfactory
agreement with observational signatures of atmospheric escape from hot giant
and mini-Neptune exoplanets (Johnstone, 2020; García Muñoz et al., 2021;
Shaikhislamov et al., 2020; Khodachenko et al., 2021; Zhang et al., 2022). In
particular, the measurement of Ly$\alpha$ absorption during transits of mini-
Neptune HD 63433c orbiting at 0.145 AU from a young (440 Myr) solar-like G5
star leads to an estimate of the hydrodynamic escape of a hydrogen rich
atmosphere at $3\times 10^{10}$ g s-1 (Zhang et al., 2022). The stellar XUV
fluence is estimated to be $\sim 1000$ times of the Sun’s XUV flux at 1 AU. HD
63433c has a surface gravity of the Earth and is thus a reasonable
representative case for a rocky exoplanet orbiting within $\sim 0.1$ AU. Its
inferred atmospheric escape rate is close to a theoretical calculation of
$\sim 1.5\times 10^{10}$ g s-1 from an Earth-like steam (H2O-rich) atmosphere
subject to similar level of irradiation (Johnstone, 2020).

According to Lammer et al. (2014), a protoplanet with an Earth-mass rocky core
can capture hydrogen envelopes between $\sim 5\times 10^{22}$ g and $\sim
1.5\times 10^{24}$ g. The hydrogen rich atmosphere of an Earth mass planet
exposed to the 1000$F_{X,Sun}$ flux at 1 AU from an e-PMS host star will
escape at the rate of $3\times 10^{10}$ g s-1, which suggests that the planet
will lose its primary atmosphere within $0.1-2$ Myr, considerably shorter than
the span of the e-PMS phase for stars with masses $\geq 2.5$ M⊙ stars (Figure
1). We thus find that e-PMS XUV radiation may lead to the loss of the entire
primordial atmosphere of rocky planets orbiting within $\sim 1$ AU.

The atmospheric loss discussed so far is driven by a continuous
“characteristic” XUV flux from a superposition of weak flares. Mega-flares
with X-ray energies of $>10^{36}$ erg are superposed on this characteristic
emission and can be individually studied in Chandra observations. They have
occurrence rates of a few flares per year from solar-mass e-PMS stars,
contributing an additional $10-20$% to the characteristic X-ray fluence of
e-PMS stars (Getman & Feigelson, 2021). Mega-flares produce more energetic
X-rays that will penetrate more deeply into the planetary atmosphere. If the
response of the planetary atmosphere escape to the additional ionization is
much slower than the mega-flare timescale ($\sim 1$ day), then the total
effect of the mega-flares will be modest. But if the response is rapid, then
the effects can be substantial.

Rapid atmospheric loss of a primary atmosphere will have other effects on the
planetary evolution. At typical distances of $\sim$1 AU atmospheric loss
drives magma ocean crystallization, while close-in exoplanets will undergo
strong tidal heating (Kite & Barnett, 2020). At this stage, if an Earth-like
planet is massive enough, its mantle convection can drive formation of crustal
rock and water oceans with subsequent volcanic and tectonic outgassing forming
a secondary atmosphere. The mantle redox state affects the volatile
partitioning during mantle melting and its volatile speciation close to the
surface (Ortenzi et al., 2020). Mantle oxygen fugacity also plays a
significant role in specifying the atmospheric thickness. Earth-like planets
with high oxygen fugacity can regenerate a high mean molecular weight
(N2-CO2-H2O rich) atmosphere.

Recent studies suggest that the fate of secondary atmospheres forming during
$\sim$30 Myr after the loss of the primary atmosphere strongly depends on the
stellar XUV flux and is not sensitive to CO2 abundance (Johnstone et al.,
2021b). For XUV fluxes of $\sim 30\times$ solar, even in the case of 100% CO2
abundance the atmosphere will experience significant hydrodynamic escape.

At stellar ages $\sim 10$ Myr, we find that l-PMS stars with masses 0.75–1 M⊙
and 1–2 M⊙ have typical median $\log(L_{X})$ of 29.7 erg s-1 and 75%-quartiles
up to $\log(L_{X})\sim 30.2$ erg s-1 (§9). Assuming the X-ray-to-EUV
conversion of $L_{EUV}=4\times L_{X}$, the XUV luminosities of many $\sim 10$
Myr solar-mass l-PMS stars would be in the range $(150-550)\times
L_{XUV,{\odot}}$. At such high XUV fluxes, the photoionization driven energy
deposition will drive hydrodynamic escape of secondary atmospheres at the
rates $\sim 3\times 10^{9}$ g s-1 from an unmagnetized planet and $\gtrsim 7$
times lower rates from a magnetized Earth-like planet. This suggests a dense
100 bar CO2-rich atmosphere will evaporate in $\sim$10 Myr (unmagnetized) and
$\sim 100$ Myr (magnetized case) unless it is replenished by internal dynamics
processes including volcanic, tectonic processes and tidally induced
outgassing. We thus conclude that l-PMS XUV emission may (partially) remove
the early secondary atmosphere as well as the primordial atmosphere of an
Earth mass planet unless the planet migrated to 1 AU from the outer regions of
the disk at $\geq$ 5 AU (Batygin & Laughlin, 2015) and its secondary
atmosphere can be replenished during its evolution.

##  13 Future Work

The current paper is the first of a series of planned studies based on the
Chandra study of magnetic activity in 7–25 Myr and older ZAMS star clusters.

First, we will examine the relation of $L_{X}$ to stellar rotation in our
l-PMS clusters. Rotation period analyses for numerous l-PMS stars are underway
using lightcurves from the TESS satellite and Zwicky Transient Facility
survey. Both $L_{X}$ and $P_{rot}$ are evolving rapidly during the l-PMS
phase, and the distribution of stellar angular momenta splits into slow- and
rapidly-rotating tracks (Barnes, 2003; Wright et al., 2011b; Vidotto et al.,
2014). Argiroffi et al. (2016) has examined X-ray and rotation in NGC 869 = h
Per and found hints that by $\sim 13$ Myr some young stars have drifted
towards the “non-saturation” locus on the activity-age plane, a manifestation
of possible changes in internal dynamos. Our deeper X-ray sensitivity for h
Per, and expansion to other l-PMS clusters of different ages, should give
samples sufficiently rich to capture the effects of rapid changes in stellar
structure on surface activity as stars approach the ZAMS.

Second, we will extend the Chandra findings on super- and mega-flares in the
e-PMS phase (Getman & Feigelson, 2021; Getman et al., 2021) to the ten
clusters in the l-PMS phase. These studies provide a homogeneous methodology
to quantify the discovery, frequencies, energetics, and flare loop geometries
of powerful X-ray flares. Combining flare properties for the younger e-PMS
MYStIX and SFiNCs cluster members to the older l-PMS open clusters discussed
here will extend empirical relations on flare evolution and magnetic loop
geometries. Flares in the l-PMS phase are particularly important for
understanding effects of X-rays on planetary atmospheres (§12.2).

Third, we will extend our Chandra observations to older clusters in the 25–150
Myr age range. The $\alpha\Omega$ dynamo should now be the sole process for
generating surface magnetic fields of many $>0.7$ M⊙ PMS stars. The decay of
characteristic and flare XUV luminosities can be quantified for improved
modeling of planetary atmospheres. Fast- and slow-rotating stars may have
different XUV evolutions.

##  14 Conclusions

Using new Chandra observations of $\sim 6000$ stellar members of 10 open
clusters with ages 7–25 Myr, we have improved characterization of magnetic
activity for the late pre-main sequence (l-PMS) phase of stellar evolution. In
addition to quantifying the evolution of X-ray activity in young stars for a
range of stellar masses (§§8-9), the results give insight into two
astrophysical issues: the response of magnetic dynamo processes to rapid l-PMS
changes in interior structure (§§1, 11), and the effects of high-energy
radiation on protoplanetary disks and primordial planetary atmospheres (§12).

Our expanded sample of stars in the 7–25 Myr age range benefits from a joint
analysis of X-ray emitting and X-ray non-emitting cluster members from Chandra
and Gaia surveys (§§3-6, Table 5). These are then combined with previous
studies of e-PMS MYStIX and SFiNCs star forming regions (§7, Table 6) for a
systematic study of mass-stratified magnetic activity measurement in the wider
age range of 0.5–25 Myr that covers the e-PMS, l-PMS, and ZAMS phases (§8, 9).
The samples are analyzed in a homogeneous fashion with statistical methods
correctly treating X-ray nondetections. Due to wide scatter in X-ray
luminosities, X-ray luminosity function quantiles, as well as medians, are
provided when available (Figures 6-7, Appendix).

The results improve the previous studies of mass-stratified activity-age
relations such as Preibisch & Feigelson (2005) and Gregory et al. (2016). We
do not find decreases in X-ray luminosity during the e-PMS phase and report
steeper temporal decays for later l-PMS phases (§10). Our empirical
distributions of PMS X-ray luminosities have wider spreads, large $L_{X}-t$
slope differences for the e-PMS phase, and small systematic differences in the
median $L_{X}$ for the l-PMS phase than those derived from semi-analytic
rotation evolution models (Johnstone et al., 2021a).

In §11 we discuss the magnetic origin of the inferred activity-age trends.
X-ray luminosity is constant during the e-PMS phase despite strong drops in
stellar luminosity and radius. This may indicate that extended X-ray emitting
loops are insensitive to stellar size. The X-ray luminosity decays rapidly
during the 7–25 Myr period: $L_{X}\propto t^{-0.5}$ for $<1$ M⊙ stars,
$L_{X}\propto t^{-1.8}$ for 1–3.5 M⊙ stars, and $L_{X}\propto t^{-4}$ and
steeper for intermediate-mass stars. This is attributed to decreasing
efficiency of the $\alpha^{2}$ dynamo at $<1$ M⊙ regime, switch to
$\alpha\Omega$ dynamo at 1–3.5 M⊙ regime as radiative cores grow, and the lack
of any dynamo as the more massive stars become fully radiative.

Our findings provide improved empirical inputs into calculations of the
effects of high energy radiation on the young stellar environment, first the
protoplanetary disk and then the atmospheres of young planets (§12). A few
estimations are made. The disk around a solar-mass e-PMS star can be
photoevaporated within a few Myr years; but our empirical gas rate estimates
may be a few times lower than those based on the semi-analytic rotation
evolution approach of Johnstone et al. (2021a). X-ray luminosity values
inferred here for PMS stars imply a very rapid escape rate of a primordial
hydrogen-rich atmosphere in an Earth-like planet on a 1 AU-orbit around a
solar-mass e-PMS star of $\sim 3\times 10^{10}$ g s-1, suggesting a complete
loss of the atmosphere within 2 Myr. An early secondary CO2-rich atmosphere
might also be evaporated depending on the planet’s magnetization.

We thank the anonymous referee for his time and many useful comments that
improved this work. We thank L. Townsley (Penn State) for sharing with us the
Chandra data products for the open clusters NGC 3293 and NGC 869. This project
is supported by the Chandra grant GO9-20011X (K. Getman, Principal
Investigator) and the Chandra ACIS Team contract SV474018 (G. Garmire & L.
Townsley, Principal Investigators), issued by the Chandra X-ray Center, which
is operated by the Smithsonian Astrophysical Observatory for and on behalf of
NASA under contract NAS8-03060. The Chandra Guaranteed Time Observations (GTO)
data used here were selected by the ACIS Instrument Principal Investigator,
Gordon P. Garmire, of the Huntingdon Institute for X-ray Astronomy, LLC, which
is under contract to the Smithsonian Astrophysical Observatory; contract
SV2-82024. The work of T.P. was supported by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under project numbers
325594231 and 362051796. V.S. Airaoetian acknowledges support from the
NASA/GSFC Sellers Exoplanet Environments Collaboration (SEEC), which is funded
by the NASA Planetary Science Division’s Internal Scientist Funding Model
(ISFM). This work has made use of data from the European Space Agency (ESA)
mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data
Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

##  Appendix A Chandra Observations Of The 10 Open Clusters

This section presents Table 8 detailing the Chandra observations of the 10
open clusters.

Table 8: Log of Chandra-ACIS-I Observations

Cluster | ObsId | Exposure | R.A. | Decl. | Start Time | PI
---|---|---|---|---|---|---
|  | (ksec) | $\alpha_{J2000}$ | $\delta_{J2000}$ | (UT) |
(1) | (2) | (3) | (4) | (5) | (6) | (7)
NGC 1502 | 21138 | 66.6 | 04:07:50.00 | +62:19:54.00 | 2019-04-30T13:26:51 | G. Garmire
NGC 2169 | 21139 | 30.7 | 06:08:24.00 | +13:57:54.00 | 2018-12-10T08:15:05 | G. Garmire
NGC 2169 | 21997 | 33.3 | 06:08:24.00 | +13:57:54.00 | 2018-12-14T10:34:54 | G. Garmire
IC 2395 | 21137 | 23.8 | 08:42:30.00 | -48:07:00.00 | 2020-08-19T05:06:54 | G. Garmire
IC 2395 | 24613 | 41.5 | 08:42:30.00 | -48:07:00.00 | 2020-08-19T22:14:15 | G. Garmire
NGC 3293 | 16648 | 70.9 | 10:35:50.00 | -58:14:00.00 | 2015-10-07T10:13:16 | T. Preibisch
NGC 869 | 5407 | 41.1 | 02:19:02.20 | +57:07:12.00 | 2004-12-02T06:28:44 | N. Evans
NGC 869 | 9912 | 101.7 | 02:19:02.20 | +57:07:12.00 | 2009-11-11T07:20:00 | G. Micela
NGC 869 | 9913 | 36.7 | 02:19:02.20 | +57:07:12.00 | 2009-10-16T05:56:43 | G. Micela
NGC 869 | 12021 | 51.4 | 02:19:02.20 | +57:07:12.00 | 2009-11-08T22:58:35 | G. Micela
NGC 884 | 21172 | 25.7 | 02:22:00.40 | +57:07:40.00 | 2019-11-13T16:17:56 | K. Getman
NGC 884 | 21173 | 16.8 | 02:22:00.40 | +57:07:40.00 | 2020-03-30T03:23:21 | K. Getman
NGC 884 | 23070 | 24.7 | 02:22:00.40 | +57:07:40.00 | 2019-11-14T07:20:29 | K. Getman
NGC 884 | 23071 | 25.8 | 02:22:00.40 | +57:07:40.00 | 2019-11-15T10:07:30 | K. Getman
NGC 884 | 23072 | 19.8 | 02:22:00.40 | +57:07:40.00 | 2019-11-17T15:28:10 | K. Getman
NGC 884 | 23202 | 53.5 | 02:22:00.40 | +57:07:40.00 | 2020-03-31T14:11:34 | K. Getman
NGC 884 | 23203 | 15.9 | 02:22:00.40 | +57:07:40.00 | 2020-04-01T18:53:32 | K. Getman
NGC 4755 | 21169 | 45.5 | 12:53:40.00 | -60:22:05.00 | 2019-12-02T03:52:00 | K. Getman
NGC 4755 | 22889 | 47.4 | 12:53:40.00 | -60:22:05.00 | 2019-11-14T16:55:24 | K. Getman
NGC 4755 | 22890 | 49.4 | 12:53:40.00 | -60:22:05.00 | 2019-11-25T03:52:48 | K. Getman
NGC 1960 | 21168 | 17.8 | 05:36:18.00 | +34:08:24.00 | 2018-12-26T19:57:53 | K. Getman
NGC 1960 | 22031 | 21.8 | 05:36:18.00 | +34:08:24.00 | 2018-12-27T11:21:49 | K. Getman
NGC 1960 | 22032 | 14.9 | 05:36:18.00 | +34:08:24.00 | 2019-01-01T00:06:59 | K. Getman
NGC 1960 | 22033 | 11.9 | 05:36:18.00 | +34:08:24.00 | 2019-01-06T23:51:05 | K. Getman
NGC 3766 | 21170 | 49.4 | 11:36:14.00 | -61:36:30.00 | 2019-11-05T18:31:43 | K. Getman
NGC 3766 | 21171 | 24.7 | 11:36:14.00 | -61:36:30.00 | 2019-12-10T10:16:50 | K. Getman
NGC 3766 | 22891 | 88.9 | 11:36:14.00 | -61:36:30.00 | 2019-11-16T07:38:03 | K. Getman
NGC 3766 | 23094 | 24.7 | 11:36:14.00 | -61:36:30.00 | 2019-12-11T04:41:11 | K. Getman
NGC 2232 | 22895 | 9.9 | 06:27:56.15 | -05:01:53.30 | 2020-01-06T08:03:26 | G. Garmire
NGC 2232 | 22896 | 9.8 | 06:27:55.95 | -04:44:56.20 | 2020-01-06T11:10:33 | G. Garmire
NGC 2232 | 22897 | 9.8 | 06:29:04.60 | -05:01:50.50 | 2020-01-06T14:05:44 | G. Garmire
NGC 2232 | 22898 | 9.9 | 06:26:47.56 | -05:01:49.20 | 2020-01-11T02:48:39 | G. Garmire
NGC 2232 | 22899 | 9.7 | 06:27:55.77 | -04:27:46.80 | 2020-01-12T20:08:15 | G. Garmire
NGC 2232 | 22900 | 9.9 | 06:29:04.13 | -04:44:48.00 | 2020-01-17T01:11:08 | G. Garmire
NGC 2232 | 22901 | 9.8 | 06:26:47.73 | -04:44:47.08 | 2020-01-17T04:26:33 | G. Garmire
NGC 2232 | 22902 | 9.8 | 06:29:03.90 | -04:27:46.90 | 2020-01-17T07:21:49 | G. Garmire
NGC 2232 | 22903 | 9.9 | 06:26:47.69 | -04:27:47.90 | 2020-01-13T21:21:24 | G. Garmire

Note. — Column 1: Cluster name. Columns 2-3: Chandra-ACIS-I observation
identifier (ObsID) and net exposure time in kiloseconds. Columns 4-5: Aimpoint
of the Chandra observation in right ascension and declination. Column 6: Start
time of Chandra exposure. Column 7: Principal investigator of Chandra
observation.

##  Appendix B Evolution of Fractional X-ray Luminosity and X-ray Flux in PMS
Stars

In § 9 we report mass-stratified temporal evolution of PMS X-ray luminosity
and in § 11 we link these findings to possible changes in underlying interior
dynamos and X-ray coronal structures. In addition to the temporal evolution of
X-ray luminosity itself (Figure 8), here Figures 10 and 11 show the evolution
of X-ray luminosity normalized by the stellar bolometric luminosity and
stellar surface. As mathematical expressions of normalized X-ray luminosities,
their temporal changes can be explained by invoking the changes in the X-ray
luminosity and stellar interior.

For younger e-PMS MYStIX/SFiNCs stars, X-ray luminosities remain nearly
constant in time (Figure 8) but bolometric luminosities keep decreasing with
time (for vast majority of the stars) as stars travel along Hayashi tracks,
resulting in positive correlations between $L_{X}/L_{bol}$ and $t$ (Figure
10). For older open cluster stars, within the mass range 0.75–1 M⊙, the
temporal rise and decay of the bolometric luminosities for lower- and higher-
mass stars, respectively, counterbalance each other (Figure 1) resulting in
small integral temporal changes of $L_{bol}$ and similar decay slopes
$b\sim-0.6$ in the $L_{X}\propto t^{b}$ and $L_{X}/L_{bol}\propto t^{b}$
relations (Table 7). Within the mass range 1–3.5 M⊙, the bolometric
luminosities of open cluster stars, which lie mainly on Henyey or ZAMS tracks,
either keep rising with time or settle at a constant level, resulting on-
average in positive temporal changes and thus steeper decay slopes in the
$L_{X}/L_{bol}-t$ versus $L_{X}-t$ relations (Table 7).

Younger e-PMS MYStIX/SFiNCs stars are still gravitationally contracting, and
since their X-ray luminosities remain constant with time their X-ray fluxes
appear to increase with time (Figure 11). For older open cluster stars with
masses 0.75–1 M⊙, their surface areas keep decreasing with time as
approximately $\propto t^{-0.4}$ leading to a mild or no decay of stellar flux
(Table 7, Figure 11). Many 1–3.5 M⊙ open cluster stars are on Henyey or ZAMS
tracks; since they stop contracting, their $F_{X}-t$ and $L_{X}-t$ relations
exhibit similar decay slopes of $b\sim-2$ (Table 7).

Figure 10: Temporal evolution of fractional X-ray luminosity ($L_{X}/L_{bol}$)
for four mass strata. See Figure 8 for a detailed description.  Figure 11:
Temporal evolution of X-ray surface flux for four mass strata. See Figure 8
for a detailed description.

##  Appendix C Evolution of 85% Quantiles for X-ray Luminosities of High-mass
Stars

For the higher-mass $\gtrsim 3.5$ M⊙ ZAMS and post-ZAMS stars, the ratio of
the non-X-ray to X-ray stars is so high that only 85% quartiles are available
for the KM estimators of $L_{X}$, $L_{X}/L_{bol}$, and $F_{X}$. Linear
regression results are provided in Table 7 and we present here in Figure 12
plots showing the individual 7–25 Myr clusters. The decay of the X-ray
luminosity, fractional X-ray luminosity, and surface X-ray flux is much
stronger for the higher-mass stars (3.5–7 M⊙) than for the lower-mass stars
(1–3.5 M⊙).

Figure 12: Evolution of the 85% quantiles of the Kaplan-Meier estimator of the
X-ray luminosity (upper row), fractional X-ray luminosity (middle row), and
X-ray surface flux (bottom row) in three mass strata. See Figure 8 for
details.

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