# Mind the Gap I: H$\alpha$ Activity of M Dwarfs Near the Partially/Fully
Convective Boundary and a New H$\alpha$ Emission Deficiency Zone on the Main
Sequence

Wei-Chun Jao Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303, USA  Todd J. Henry RECONS Institute, Chambersburg, PA
17201, USA  Russel J. White Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303, USA  Azmain H. Nisak Astronomy Department
Wesleyan University
Middletown, CT 06459, USA  Hodari-Sadiki Hubbard-James Department of Physics
and Astronomy
Georgia State University
Atlanta, GA 30303, USA  Leonardo A. Paredes Department of Physics and
Astronomy
Georgia State University
Atlanta, GA 30303, USA  Department of Astronomy/Steward Observatory
University of Arizona
Tucson, AZ 85721, USA  Vanders B. Lewis, Jr  Department of Physics and
Astronomy
Georgia State University
Atlanta, GA 30303, USA

###### Abstract

Since identifying the gap in the H-R Diagram (HRD) marking the transition
between partially and fully convective interiors, a unique type of slowly
pulsating M dwarf has been proposed. These unstable M dwarfs provide new
laboratories in which to understand how changing interior structures result in
potentially observable activity at the surface. In this work, we report the
results of the largest high-resolution spectroscopic H$\alpha$ emission survey
to date spanning this transition region, including 480 M dwarfs observed using
the CHIRON spectrograph at CTIO/SMARTS 1.5-m. We find that M dwarfs with
H$\alpha$ in emission are almost entirely found 0 to 0.5 magnitude above the
top edge of the gap in the HRD, whereas effectively no stars in and below the
gap show emission. Thus, the top edge of the gap marks a relatively sharp
activity transition and there is no anomalous H$\alpha$ activity for stars in
the gap. We also identify a new region at 10.3 $<M_{G}<$ 10.8 on the main
sequence where fewer M dwarfs exhibit H$\alpha$ emission compared to M dwarfs
above and below this magnitude range. Careful evaluation of literature results
indicates that 1) rotation and H$\alpha$ activity distributions on the main
sequence are closely related, and 2) fewer stars in this absolute magnitude
range rotate in less than $\sim$13 days than populations surrounding this
region. This result suggests that the most massive fully convective stars lose
their angular momentum faster than both partially convective stars and less
massive fully convective stars.

Hertzsprung Russell diagram (725) — M dwarf stars (982) — Stellar activity
(1580) — Stellar rotation (1629) — High resolution spectroscopy (2096)

††facilities: CTIO:1.5m (CHIRON)††software: Matplotlib (Hunter, 2007), NumPy
(Van der Walt, Colbert & Varoquaux, 2011), astropy (Astropy Collaboration et
al., 2013, 2018), SciPy (Virtanen et. al., 2020) and TOPCAT (Taylor, 2005)

##  1 Introduction

The main sequence gap on the Hertzsprung–Russell diagram (HRD) reported by Jao
et al. (2018) marks the interior structure transition between partially
convective and fully convective interiors in M dwarfs. Stars above the gap are
more massive and have an interior like the Sun, with a radiative zone and a
convection layer, resulting in an $\alpha\Omega$ magnetic dynamo (Charbonneau,
2014). Stars below the gap are less massive, have fully convective interiors,
and a different $\alpha^{2}$ dynamo (Chabrier & Küker, 2006). After the
announcement of the discovery of the gap, MacDonald & Gizis (2018), Baraffe &
Chabrier (2018), and Feiden et al. (2021) found that stars in the gap with
masses between 0.34 and 0.36 M⊙ experience a period of structural instability
and radial pulsations caused by non-equilibrium 3He fusion in the stellar
core; this results in intermittent mixing between the core and envelope
convection zones. Those efforts match earlier theoretical work by van Saders &
Pinsonneault (2012), who dubbed the resulting process the “convective kissing
instability”. This suggests that the interiors of stars in the gap are more
complex than stars above and below the gap, and may have up to three layers of
energy transport: a convective core with an overlying radiative zone, which is
in turn surrounded by a convective envelope. The underlying physics of this
3He instability drives slow pulsations in stellar radii and luminosities that
are thought to produce the gap in the HRD. Mansfield & Kroupa (2021) showed
the effects of these oscillations on the evolutionary tracks of these gap
stars on the HRD. The overall result of these modeling efforts indicates that
the low mass stars in the gap are likely unique on the main sequence.

Stellar dynamos are driven by differential rotation and convection, but
several questions arise when considering unstable stars in the gap: What
stellar dynamos occur for stars having not one, but two layers of convective
energy transport that shift over time? Do they have “switching” magnetic
dynamos, changing between $\alpha\Omega$ and $\alpha^{2}$, depending on the
stage along their stellar evolutionary paths? Do they exhibit enhanced
activity at the surface beyond typical rotation-induced activity? Although
detailed theoretical work has not yet been done to understand the complete
ramifications these unstable interiors, and whether or not they trigger
enhanced surface activity, some circumstantial evidence has been presented.

The tachocline is the boundary between the radiative interior and the outer
convective zone. Gilman (2005) argued that the tachocline plays a significant
role in creating magnetic patterns observed in photospheres, which
consequently resulting in spot activity. Donati et al. (2008) and Reiners &
Basri (2009) showed that stars with masses close to 0.34–0.36 $M_{\odot}$ are
likely to experience abrupt changes in their large-scale magnetic topologies,
which can also trigger activity signatures at the surface. Hence, it is
possible, perhaps even likely, that stars in the gap could have different
photometric and spectroscopic characteristics from stars on either side of the
gap because of their unique and changing interior structures.

In this first of a series of papers entitled “Mind the Gap”, we target stars
close to the narrow transition boundary between partially and fully convective
M dwarfs to evaluate their spectroscopic and photometric properties. Here we
present new results of high-resolution spectroscopic observations for 480
stars close to the gap to understand their H$\alpha$ emission/absorption
behavior. We also evaluate complementary data available in the literature for
broader context. For our spectroscopic survey, we outline target selection in
$\S$2, followed by details of data acquisition and reduction in $\S$3. Our
assessment of these results is presented in $\S$4. We analyze results from
four previous studies that include large numbers of M dwarf H$\alpha$ and
magnetic measurements in $\S$5. Finally, in $\S$6 we report on a new feature
where we find a dearth of active M dwarfs is on the main sequence, and make a
first attempt to understand the cause of this H$\alpha$ emission deficiency.
We present our conclusions in $\S$9.

##  2 Target Selection

Figure 1: The sample of 2,249 M dwarf targets (black dots) meeting our
selection criteria are shown in a small region of the HRD (Jao & Feiden,
2020), where the thin black line traces the best-fit main sequence. The white
shading is the gap first reported in Jao et al. (2018), enhanced here to show
where the stellar density is lower than expected. The thick black line marks
the high-luminosity gap edge, hereafter referred to as “GE”. Details of
defining the main sequence and GE lines are given in Appendix A. The tilted
white region of the gap across the main sequence drives our selection of the
white-dashed parallelogram that is the region interest (ROI); this permits
evaluation of subsamples in incremental offsets above and below the GE. The
same parallelogram ROI is used throughout this work.

The main sequence gap in the HRD is narrow, with a width of at most $\sim$0.2
in $M_{G}$ and is tilted relative to the main sequence (Jao & Feiden, 2020).
The gap is not evident across the entire width of the main sequence, fading at
the blue and red ends where fewer stars are available for plotting. To select
targets close to this fine feature for this work, we focus on stars (1) with
$G_{BP}-G_{RP}$ color between 2.4 and 2.6 (roughly spectral types M3.0V to
M4.0V) and (2) within $\pm$0.5 mag of the gap, the upper edge of which is
defined by a fitted thick black line shown in Figure 1 and given in Table 6.
This fitted line is known as the gap edge, hereafter called ”GE”. Our region
of interest (ROI) is a parallelogram extending above and below the GE centered
at the widest part of the gap at $G_{BP}-G_{RP}$ = 2.5. The narrow color range
for our sample ensures that the selected stars have similar spectral energy
distributions and effective temperatures, thereby minimizing effects that
would come into play with a less homogeneous sample. The same parallelogram
ROI is used throughout this paper and outlined in various Figures.

For our spectroscopic survey, we selected presumably single stars in the ROI
that have high-quality astrometric data in the Gaia Early Data Release 3
catalog (EDR3, Gaia Collaboration et al., 2021). We applied four criteria to
select stars in fields that provide uncontaminated spectra so that any
detected activity can be considered coming from the targets. In total, 2,249
stars met our criteria; the entire target list is available electronically in
Table 1 and shown in Figure 1. The selection criteria are:

  1. 1.

distances within 100 pc: nearby stars

  2. 2.

RUWE $<$ 1.4: likely single stars

  3. 3.

$|b|>$ 10: away from the Galactic plane

  4. 4.

no source in EDR3 with $\Delta G_{RP}<$ 4.0 within 63″ of the target, thereby
providing minimal contamination within three pixels of the star in the TESS
(Transiting Exoplanet Survey Satellite) camera

Table 1: Selected M Dwarf Targets Close to the Gap name | units | description
---|---|---
source_id |  | source ID in Gaia EDR3
R.A. | deg | Right ascension in Gaia EDR3 epoch
Decl. | deg | Declination in Gaia EDR3 epoch
parallax | mas | parallax in Gaia EDR3
pmra | mas | proper motion in R.A. in Gaia EDR3
pmdec | mas | proper motion in Decl. in Gaia EDR3
RUWE |  | Renormalised Unit Weight Error
G | mag | magnitude in Gaia EDR3 G band
BP | mag | magnitude in Gaia EDR3 BP band
RP | mag | magnitude in Gaia EDR3 RP band

##  3 Spectroscopic Observations and Data Reduction

###  3.1 CHIRON Spectroscopic Observations

We observed 443 of the 2,249 stars using the CHIRON high-resolution
spectrograph (Tokovinin et al., 2013; Paredes et al., 2021) on the SMARTS
1.5-m telescope at Cerro Tololo Inter-American Observatory (CTIO). This is the
largest high-resolution spectroscopic survey to date that focuses on the
narrow transition zone between partially and fully convective low mass stars.
Because some targets were observed before we completed the target selection,
an additional 37 targets that don’t meet the 63″ contamination criterion are
also included. None of these have a contaminating source within CHIRON’s fiber
diameter of 2$\farcs$7, so in total we observed and present results for 480
stars. These stars have $G$ magnitudes of 8.2–13.9 and a mean parallax of 28
mas.

Observations were made at the 1.5-m between November 2018 and August 2022. Of
the four different resolutions available with CHIRON, 96% of the targets are
observed in the fiber mode with R = 28,000 that covers 4500-8300Å over 62
spectral orders. The remaining targets were observed using slicer mode with R
= 79,000 covering the same wavelengths over 59 orders. All targets have
estimated $V$ magnitudes brighter than 15, so exposure times of 900–1800
seconds were used, depending on brightness, to reach a mean S/N of 23. A ThAr
lamp image was taken immediately after each target for an exposure of 0.25 or
4 seconds to calibrate the wavelength for fiber and slicer modes,
respectively. We carried out standard data processing procedures that included
bias and flat field corrections, cosmic-ray removal, echelle order
extractions, wavelength calibrations using ThAr comparison lamps, and removal
of the blaze function. The details of data processing are fully discussed in
Paredes et al. (2021).

For this work, the key feature is the H$\alpha$ line found at 6562.8Å in air
in the rest frame. To pinpoint the feature, we do a barycentric correction
using the algorithm discussed in Wright & Eastman (2014) and provided via
their online
tool111https://astroutils.astronomy.osu.edu/exofast/barycorr.html. The radial
velocity (RV) of the star is then calculated based on a spectral cross-
correlation against Barnard’s star (M4.0V, Henry et al. 1994) and GJ 273
(M3.5V, Henry et al. 1994), for which we adopt radial velocities of $-$110.11
km s-1$\pm$0.2 m s-1 and 18.36 km s-1$\pm$0.3 m s-1, respectively from Fouqué
et al. (2018). To obtain RVs, a cross-correlation analysis is performed as
described in Irwin et al. (2018) and Nisak et al. (2022), using six different
orders in fiber mode: order 38 (6397.94—6471.62Å), 39 (6471.47—6546.00Å), 41
(6623.73—6699.99Å), 42 (6702.58—6779.74Å), 46 (7037.69—7118.67Å), and 53
(7712.50—7801.18Å). Similar wavelength coverage is used for data obtained in
the slicer mode, but the echelle orders are shifted two orders higher. The RV
of a target in each of the six orders is calculated relative to both of the RV
reference stars. After offsetting for the standard stars’ velocities, the two
sets of 6 values are then used to determine the final weighted mean RV and
error for each target. In total, we acquired 503 spectra of 480 targets, where
twenty-one targets have more than one epoch, and found a mean RV error of 1.8
km s-1. The RV measurements, as well results for H$\alpha$ equivalent width
and $v\sin i$ discussed next are given for our targets in Table 4.

###  3.2 Determining H$\alpha$ Equivalent Widths

After making the barycentric correction and consequent shift of the spectrum
to the rest frame for a given star, we measure the equivalent width (EW) of
the H$\alpha$ line to measure the star’s activity level. Measuring an EW value
is accomplished via the equation

$EW=\sum\left(1-\frac{F_{mean}(\lambda)}{F_{C}}\right)\Delta\lambda$ (1)

where $F_{mean}(\lambda)$ is the flux between F1 and F2 for the feature,
$F_{C}$ is the mean pseudo-continuum flux, and $\Delta\lambda$ is 0.023Å for
slicer mode data or for 0.094Å fiber mode data. Here we adopt the usual
convention with negative EW values for stars with H$\alpha$ in emission and
positive EW values for stars with H$\alpha$ in absorption. We calculate EW
errors using the relation given in Cayrel (1988).

To measure the H$\alpha$ EW values, a window centered on the feature and two
windows on either side representing the pseudo-continuum were defined. We
randomly selected 79 stars observed in fiber mode with well-defined H$\alpha$
absorption features as templates to define the windows, illustrated with
overlapping black lines in Figure 2. The same windows are used for stars
observed in the slicer mode. The wavelengths of the window edges are given in
Table 2; these windows are similar to those used in Gizis et al. (2002). For
all stars with emission except for GAI1439$+$1023 which has an emission fitted
within the default template, the central H$\alpha$ line window was extended to
include flux from the wings by visual comparison to the template. In these
cases, the windows of the pseudo-continuum on either side were shifted outward
to exclude flux from the strong emission, while maintaining the window widths.

Figure 2: Windows used to determine H$\alpha$ EW values. The black lines trace
spectra for 79 stars with H$\alpha$ absorption features and the red line
represents the mean spectrum for these stars. The red box is the nominal
spectral window used to measure the H$\alpha$ line, with the dashed line
marking the feature at 6562.8Å in air. The two blue boxes mark the windows for
the pseudo-continuum on either side. Wavelength values for all three window
edges are given in Table 2. Table 2: H$\alpha$ line

| left continuum | adopted line | right continuum
---|---|---|---
| C1 | C2 | F1 | F2 | C3 | C4
H$\alpha$ | 6557.7 | 6560.0 | 6562.1 | 6563.6 | 6566.2 | 6568.4

Note. — This table is available online electronically.

Note. — Units are Angstroms.

We note here that the H$\alpha$ equivalent width is often converted to the
ratio of H$\alpha$ luminosity and bolometric luminosity to account for the
changing continuum across the wide range of temperatures exhibited by M dwarfs
(West et al., 2008; Newton et al., 2017; Kiman et al., 2021). Even without
obtaining flux calibrated spectra, calculations can be done using the so-
called $\chi$ factor (Walkowicz et al., 2004; Douglas et al., 2014) to obtain
$L_{\alpha}/L_{bol}$ values, where $L_{\alpha}/L_{bol}=-EW\times\chi$. This
conversion is needed for the analysis of M dwarf samples spanning temperatures
corresponding to a color range from early to late M dwarfs of $\sim$4
magnitudes in $G_{BP}-G_{RP}$. However, the color range of our sample is only
a very narrow 0.2 magnitude in $G_{BP}-G_{RP}$, so conversions are not
necessary. In fact, converting EWs to $L_{\alpha}/L_{bol}$ would have errors
from this relation itself and introduce additional errors because the commonly
used relations to obtain $\chi$ use $V-I_{c}$ or $i-J$ colors rather than the
Gaia photometry used here. Consequently, the equivalent width presented in
this work can be interpreted as a direct tracer of H$\alpha$ luminosity
without any conversions.

###  3.3 Projected Rotational Velocities

We also measured the projected rotational velocities ($v\sin i$) for the
survey stars using the prescription described in Nisak et al. (2022). Before
we measured the $v\sin i$, we first established an empirical relation between
the width of the cross-correlation function (CCF) and $v\sin i$ by cross-
correlating each standard star spectrum against rotationally broadened
synthetic versions of itself using the rotational broadening routine in
PyAstronomy222https://github.com/sczesla/PyAstronomy. The CCF width of a
survey star is calculated from all six orders of the spectrum used to
determine its RV. Then, using the mean CCF width from the six orders and the
empirical relation, a mean $v\sin i$ is derived. As a check, three previously
known fast rotating stars were observed with CHIRON and measured using this
method, with our results and those from earlier work given in Table 3.3; in
eight cases out of nine, our values are consistent with previously published
values within the errors, with the single outlier that of GJ871.1A, for which
we suspect the value of Fouqué et al. (2018) is offset from the true value.
Given the spectral resolution of our observations, S/N of the spectra, and the
standard stars we use, we conservatively only report stars with $v\sin i$
faster than 10 km/s in fiber mode and 4 km/s in slicer mode. In total, only
seven stars in fiber mode have measurable rotation signatures, and no star in
slicer mode has $v\sin i$ faster than the threshold. Results are given in
Table 4.

Table 3: Known fast rotation stars

Target | This work | #1 | Ref1 | #2 | Ref2 | #3 | Ref3
---|---|---|---|---|---|---|---
|  $v\sin i$ (km/s)
TWA9B | 7.08(1.79) | 9.0(1.0) | 1 | 8.39(0.61) | 2 | 10.9(1.7) | 6
2MA0200-0840 | 15.13(1.75) | 12.2(2.1) | 5 | 16.1(2.1) | 4 | 15.2(1.4) | 4
GJ871.1A | 12.34(1.36) | 20.5(2.4) | 5 | 14.5(1.9) | 4 | 13.9(0.5) | 3

Note. — All results are in fiber modes. The $v\sin i$ errors are within
parentheses.

References. — 1. White & Hillenbrand (2004), 2. Scholz et al. (2007), 3.
Bailey et al. (2012), 4. Malo et al. (2014), 5. Fouqué et al. (2018), 6.
López-Valdivia et al. (2021)

Table 4: Results

source ID | Name | R.A. | Decl. | $\pi$ | RUWE | $G$ | $G_{BP}-G_{RP}$ | neighbor | # visit | decker | epoch | activity | RV | RVerr | $v\sin i$ | $v\sin i_{err}$ | EW | EWerr | CaH1 | binary
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | deg | deg | mas |  | mag | mag |  |  |  | years |  | km s-1 | km s-1 | km s-1 | km s-1 | Å | Å |  |
(1) | (2) | 3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | (21)
2336284229875185024 | GAI0007-2524 | 00:07:06.39 | -25:24:51.65 | 23.9587 | 1.28 | 13.718 | 2.595 | 0 | 1 | fiber | 2021.6584 | A | 12.98 | 0.07 |  |  | 0.31 | 0.02 | 0.458 |
4901109094112344192 | GAI0008-6401 | 00:08:26.69 | -64:01:09.09 | 30.4698 | 1.23 | 12.244 | 2.433 | 0 | 1 | fiber | 2021.5929 | A | -9.83 | 0.18 |  |  | 0.37 | 0.02 | 0.628 |
4991695142706265344 | GAI0012-4445 | 00:12:03.04 | -44:45:06.80 | 13.9347 | 1.15 | 13.938 | 2.444 | 0 | 1 | fiber | 2021.855 | A | 16.12 | 0.22 |  |  | 0.36 | 0.02 | 0.483 |
4901473650937640576 | GAI0012-6312 | 00:12:26.65 | -63:12:43.62 | 19.6865 | 1.16 | 13.928 | 2.449 | 0 | 1 | fiber | 2021.8551 | A | 46.85 | 0.16 |  |  | 0.3 | 0.02 | 0.729 |
4706483132131647232 | GAI0015-6759 | 00:15:45.06 | -67:59:38.22 | 53.2872 | 1.36 | 11.447 | 2.447 | 1 | 1 | slicer | 2018.92 | A | -30.79 | 0.02 |  |  | 0.24 | 0.01 | 0.573 |
2309132133824849152 | GAI0018-3450 | 00:18:44.75 | -34:50:19.47 | 42.033 | 1.38 | 11.791 | 2.577 | 0 | 1 | fiber | 2021.5956 | A | 24.89 | 0.06 |  |  | 0.34 | 0.02 | 0.559 |
2360419059860637184 | GAI0022-2230 | 00:22:24.06 | -22:30:42.37 | 17.3802 | 1.35 | 13.557 | 2.453 | 0 | 1 | fiber | 2021.6368 | A | 25.27 | 0.07 |  |  | 0.29 | 0.02 | 0.647 |
2423826899002038912 | GAI0027-1203 | 00:27:28.44 | -12:03:10.32 | 19.5732 | 1.19 | 13.763 | 2.421 | 0 | 1 | fiber | 2021.6885 | A | -30.56 | 0.26 |  |  | 0.19 | 0.02 | 0.444 |
2528082144871347584 | GAI0028-0429 | 00:28:10.12 | -04:29:12.07 | 18.6548 | 1.16 | 13.716 | 2.556 | 0 | 1 | fiber | 2021.6175 | A | -10.93 | 0.3 |  |  | 0.2 | 0.02 | 0.566 |
2367344127690031744 | GAI0028-1700 | 00:28:17.67 | -17:00:59.72 | 18.6458 | 1.27 | 13.345 | 2.494 | 0 | 1 | fiber | 2021.8634 | A | -18.12 | 0.66 |  |  | 0.25 | 0.01 | 0.687 | 1

Note. — Column (9): Stars meeting our selection criteria discussed in Table 1
have a code of 0; 37 additional stars have a code of 1. Column (10): number of
observations. Column (11): spectra were taken with CHIRON in fiber or slicer
mode. Column (12): epoch of RV measurement. Column (13): “A” indicates
H$\alpha$ in absorption and “E” indicates in emission. Column (16): projected
rotational velocities. Column (21): Possible binaries. The full table is
available electronically online.

##  4 Results

Figure 3: (Left): Active stars (red dots) and inactive stars (blue dots) on
the enhanced HRD, identified using H$\alpha$ equivalent widths (EW) in CHIRON
spectra. Eight equal size zones are outlined inside the ROI. The gap edge (GE)
is shown with a short heavy black line , and the best-fit main sequence line
is shown with a long thin black line. (Center): The absolute values of EWs for
active stars are plotted as a function of the size of red circles. The single
active star represented by the very small red circle below the GE is
GAI0406-5011 with a very low EW$=-0.18$Å. (Right): The EWs of inactive stars
are indicated by the size of blue circles; all have similar EWs.

###  4.1 Activity Distribution Across the Gap

Previous studies of M dwarf H$\alpha$ activity have often sorted samples by
spectral types, colors, or estimated masses (e.g., Gizis et al. (2002); West
et al. (2008); Walkowicz & Hawley (2009)), and samples were analyzed using
one-dimensional graphs. However, to study H$\alpha$ activity across the gap, a
two-dimensional feature, we plot active and inactive targets on the two-
dimensional HRD shown in Figure 3 so that we can understand how both colors
and luminosities relate to H$\alpha$ activity, and map activity relative to
the gap and the across the main sequence. This figure shows that effectively
all active stars identified by this work, shown with red points, are above the
GE. The only active star (GAI0406-5011) clearly below the GE has weak
H$\alpha$ emission, with an of EW$=-0.18$Å; this star appears to be single
based on Gaia catalog and the CCF peak. Our result suggests that effectively
all active stars in our survey are partially convective, whereas fully
convective stars show no H$\alpha$ emission. As a result, instead of finding
an H$\alpha$ activity anomaly in the gap, we find that the activity
distribution is sharply divided at the GE. In other words, even though stars
in the gap have changing interior structures and slowly pulsate, their
H$\alpha$ activity does not differ from other fully convective stars. In
addition, most active stars are found above the best-fit main sequence line in
Figure 3.

To further investigate the H$\alpha$ emission distribution for our targets, we
divide the ROI into eight equal-sized smaller zones. As shown in Figure 3, we
outline four zones (A–D) above and four below (E–H) the GE, with the width of
each zone approximately the width of the gap, which corresponds to zone E. The
percentages of active stars in each zone are given in Table 5, which shows
that the number of active stars clearly drops below the GE. In zones A–D,
there are 50 active stars out of 334, indicating that 15% exhibit H$\alpha$
emission. In zones E–H, there are only 2 active stars out of 146, or 1%. There
is only one star (GAI0516-3846) in zone E that is active, but that star is
barely in zone E, found only 0.002 mag below the GE, and given the magnitude
error may be above the line. If we exclude this target, there is only one
active star (GAI0406-5011) in the bottom half of the ROI, as shown in Figure
3.

Table 5: Statistics for Samples of Stars in 8 Zones Near the Main Sequence Gap

| Sample Numbers | Mean CaH1 EWs | Mean Galactic Velocities
---|---|---|---
Zone | Total Stars | Active Stars | Inactive Stars | % Active | % Active |  $\langle$CaH1$\rangle$ | $\sigma_{CaH1}$ |  $\langle$Ttotal$\rangle$ | $\sigma_{V}$
| # | # | # |  |  | Å | Å | $km~{}sec^{-1}$ | $km~{}sec^{-1}$
A | 87 | 15 | 72 | 17.2${}^{+4.8}_{-3.2}$ | 15.0$\pm$2.3 | 0.52 | 0.10 | 42.6 | 23.2
B | 80 | 13 | 67 | 16.2${}^{+4.7}_{-3.2}$ | 0.53 | 0.14 | 41.7 | 23.1
C | 85 | 15 | 70 | 17.6${}^{+5.4}_{-3.6}$ | 0.54 | 0.09 | 40.8 | 24.8
D | 82 | 7 | 75 | 8.5${}^{+4.5}_{-2.5}$ | 0.58 | 0.15 | 38.0 | 22.4
E (gap) | 57 | (1) | 56 | (1.8${}^{+4.2}_{-0.8}$) | 1.4$\pm$1.0 | 0.57 | 0.14 | 41.1 | 20.7
F | 38 | 1 | 37 | 2.6${}^{+5.4}_{-0.6}$ | 0.58 | 0.18 | 41.4 | 20.6
G | 31 | 0 | 31 | 0 | 0.61 | 0.13 | 47.4 | 21.2
H | 20 | 0 | 20 | 0 | 0.58 | 0.09 | 42.5 | 24.1

Note. — The gap corresponds to zone E and is highlighted in bold. The
parentheses indicate that this zone contains one star, only 0.002 mags below
the line. Quantities enclosed with $\langle\rangle$ are mean values in each
zone. $T_{total}$ represents the a total Galactic velocity,
$\sqrt{U^{2}+V^{2}+W^{2}}$. $\sigma_{X}$ values indicate the standard
deviations for CaH1 EW and $T_{total}$ in each zone. The percentage errors are
calculated using the binomial distribution discussed in Burgasser et al.
(2003) for a sample size of fewer than 100 stars in each bin.

###  4.2 Age Evaluations of the Observed Stars Via Metallicities and
Kinematics

Stellar activity in M dwarfs at a given color is often related to age because
young stars are generally more active than old, low metallicity, inactive
subdwarfs (Jao et al., 2011; Clements et al., 2017). Because all of our
targets fall in a narrow color range, here we investigate whether or not the
active stars in our sample are younger than the inactive stars by using
stellar metallicity and kinematics as proxies for age.

The metallic molecular hydride bands, i.e., FeH, MgH, and CaH, are indicators
of M dwarf metallicity (Bessell, 1982; Gizis, 1997) and can be used to
evaluate relative metallicities of stars rather than their absolute
metallicities. For example, CaH band strength indices can be calculated to
separate low metallicity subdwarfs from dwarfs, as discussed in Reid et al.
(1995) and Gizis (1997). Here we use the CaH1 band at 6380–6390Å for the
sample stars as a measurement of their relative metallicities. Usually the
pseudo-continuum on either side of the molecular band is used to calculate the
CaH1 index, and the lower the value determined for the index, the lower the
metallicity. However, our spectra contain one side of the commonly used
pseudo-continuum at 6345–6355Å defined in Gizis (1997), and the other side of
the pseudo-continuum at 6410–6420Å is in a different echelle order. Our
spectra are not flux calibrated, so stitching the orders is not
straightforward. Instead of using continuum windows to calculate a CaH1 index,
here we measure the EW of the CaH1 feature using the EW as defined in section
3.2. A large EW means a deeper or stronger CaH1 band, which implies a larger
ratio of line opacity to continuum opacity ($n(CaH1)/n(H^{-})$) or lower
metallicity (Bessell, 1982).

Figure 4 shows the CaH1 band strength distribution of our sample in the HRD
and Table 5 lists the mean CaH1 EWs in each region from A to H. There is a
hint that there may be two metallicity groups — one including the A to C
regions with mean EWs of 0.52–0.54 and the other the remaining regions from D
to H with mean EWs of 0.57–0.61. However, the standard deviations in the
regions span 0.09–0.18, implying that the metallicity spread in the entire ROI
is certainly not as distinct as the H$\alpha$ activity shown in Figure 3. In
addition, the right panel of Figure 3 shows that the active stars identified
via H$\alpha$ emission have CaH1 EWs of $\sim$0.4–0.8, whereas inactive stars
span a wider range from $\sim$0.2–1.2, with perhaps proportionally a few more
stars at lower EW values. Overall, the CaH1 strengths for active and inactive
stars do not differ significantly, which we interpret to mean that metallicity
is not a significant factor affecting the activity distribution in Figure 3 we
see for H$\alpha$ in stars found in this narrow ROI.

Figure 4:  (Left): The CaH band strength distribution for our targets in the
enhanced HRD. This Figure is similar to Figure 3, but the two dark lines are
omitted to show the contrast and distribution of the points. Smaller CaH1 EW
values correspond to shallower CaH band strengths and higher metallicities.
(Right) The EWs of H$\alpha$ and CaH1 features for active (red dots) and
inactive stars (blue dots). The two arrows mark the directions of relatively
older and younger stars.

The other commonly used method to compare relative ages in a stellar sample is
to evaluate their kinematics. The Galactic velocities of main sequence dwarfs
and halo subdwarfs are different (Hawley et al., 1996; Gizis, 1997; Zhang et
al., 2021) because, on average, low metallicity halo subdwarfs have faster
Galactic velocities after billions of years of dynamic heating. In this work,
we calculate the Galactic UVW velocities of our targets relative to the local
standard of rest, for which the solar motion of (11.1, 12.24, 7.25) km s-1 are
adopted from (Schönrich et al., 2010). To calculate UVW values, coordinates,
parallaxes, and proper motions are taken from Gaia DR3, and radial velocities
are from this work. As shown in Figure 5, we find that the active stars are
almost all within the solid line region marking 1$\sigma$ offsets from the
mean velocity ellipsoid for M dwarfs, where we have adopted the mean UVW
values of (1$\pm$47, 14$\pm$32, 0$\pm$28) km s-1 from Zhang et al. (2021).
Inactive stars, however, exhibit relatively wider velocity distributions, with
nearly all falling inside the 2$\sigma$ offset region. While the distribution
is more dispersed for the inactive stars than for the active stars, the
inactive stars are still much slower than the velocity ellipsoid of halo
subdwarfs, which have mean UVW values of (5$\pm$173, -248$\pm$77, 6$\pm$89) km
s-1 (Zhang et al., 2021). Kinematically, all of the stars in our sample appear
to be thin or thick disk stars, and none appear to be halo subdwarfs. Table 5
presents the mean total Galactic velocities
($T_{total}=\sqrt{U^{2}+V^{2}+W^{2}}$) in each region, all of which fall in a
narrow range of 38–48 km s-1, with dispersions in each region of 20–25 km s-1.
As with the metallicity evaluation, there is no strong correlation between
Galactic velocities and H$\alpha$ measurements, indicating that activity is
not reflected in the kinematics across the various regions in the ROI.

Figure 5: The Galactic UVW velocities of our targets are shown in two panels.
The two black ellipses are centered on the UVW values of (1, 14, 0) km s-1 for
M dwarfs from Zhang et al. (2021). The ellipses trace 1$\sigma$ (solid line)
and 2$\sigma$ (dotted line) regions of the dispersions with (47, 32, 28) km
s-1(Zhang et al., 2021). Red dots are active stars, and blue dots are inactive
stars. The location of mean UV values for cool subdwarfs (5, $-$248) in the
left panel is off the left side of the plot. The velocities presented here are
relative to the local standard of rest given in Schönrich et al. (2010).

###  4.3 Spectroscopic Binaries

Among the 480 stars in our sample, we identify 11 spectroscopic binary
candidates in this work. Three stars show H$\alpha$ emission and the remaining
eight stars exhibit H$\alpha$ absorption features. All show more than one peak
in the CCF when measuring radial and rotational velocities based on single
spectroscopic observations, so they are persumably double-lined spectroscopic
binaries with orbits that could be determined with additional observations.
Both radial and rotational velocities for such systems are calculated based on
the higher CCF peak in the reduction. Our targets were selected to have low
RUWE ($<$1.4), and none of these stars are listed in the non-single stars list
for Gaia DR3 (Gaia Collaboration et al., 2022). This implies they all have
undetected astrometric perturbations through results derived for Gaia DR3, and
that they are potentially nearly equal-mass binaries. These 11 systems are
noted in Table 4.

##  5 Other Large Surveys Related to M Dwarf H$\alpha$ Activity

There are several large surveys of H$\alpha$ activity in M dwarfs in the
literature, all of which span larger portions of the HRD compared to the
tightly focused region explored here. Here we consider, chronologically, four
previous studies to understand H$\alpha$ activity for M dwarfs along the main
sequence in order to place the H$\alpha$ activity for our sample in broader
context among larger populations of similar low mass stars.

###  5.1 Newton 2017

Newton et al. (2017), hereafter N17, studied H$\alpha$ activity for 2,074
nearby M dwarfs with a mean parallax of 59.5 mas. After crossmatching their
sample against Gaia EDR3 results to select stars with RUWE$<$1.4 and excluding
targets noted as “binary” in their paper, there remain 1,249 M dwarfs that
will be examined here, most of which are presumably single. Their reported
H$\alpha$ EWs are from their own measurements and 27 earlier references; how
they adopted EWs from various sources and calibrated the EWs are discussed in
their work. They defined an H$\alpha$ EW threshold of $-$1Å as the dividing
value between “inactive” and “active” stars, and an activity flag was assigned
to each star in their Table 1. Only 12 stars are found in both N17 and our
sample. Of these, one star, GAI1019+1952, is flagged as active by both N17 and
us, and the remaining 11 stars are identified as inactive.

The distributions of their active (red dots) and inactive (blue dots) stars
are shown on the HRD in the first three panels of Figure 6. Because we study
H$\alpha$ activity across this two dimensional graph, we split the main
sequence into four regions labeled 1 to 4 as shown in the full main sequence
in the final, right panel of Figure 6. These regions are divided using
polynomials so that there are two regions above (2 and 4) and two regions
below (1 and 3) the best fitted line of the main sequence. There are also two
regions above (1 and 2) and two below (3 and 4) the GE. Details of generating
and defining these lines are discussed in Appendix C.

It is evident in the first panel of Figure 6 that the majority of active M
dwarfs in N17 are in regions 3 and 4, below the GE. Interestingly, most active
stars lie above the median main sequence line, falling in regions 2 and 4.
Some are even above the upper envelope of the main sequence, likely indicative
of their youth because we have excluded known close binaries in this plot. The
insets in Figure 6 illustrate the region around the gap in the main sequence,
with the heavy black line indicating the GE. Although their work contains over
a thousand presumably single M dwarfs, there are only eight active stars
falling inside our ROI. Seven of the eight are above the transition boundary,
falling in the ROI’s upper right corner, and only one active star is just
below the transition line. The entire region below the GE is essentially void
of active stars. The second panel of Figure 6 shows that inactive stars are
evenly distributed on either side of the fitted main sequence all along the
main sequence, and the inset illustrates that some inactive stars are found
above and below the GE. Overall, the distributions of active and inactive
stars within the ROI are similar in our work presented here and N17.

Next, we examine regions 3 and 4 below the GE. The ratio of inactive stars in
regions 4 and 3 is 147:187 (0.79:1), and the ratio of active stars in regions
4 and 3 is 114:65 (1.75:1). Thus, there are proportionally many more active
stars above the fitted main sequence than below. The broader perspective of M
dwarf activity from N17 shown in Figure 6 is that most active M dwarfs are
fully convective, and in fact, there are no active stars found region 1, which
is above the GE but below the median main sequence. This dearth of active
stars in region 1 differs from our work and two other efforts discussed later
in this section because all three efforts have identified active M dwarfs in
region 1. Recall that the large sample reported in N17 results from an
ensemble of 27 different efforts, so we suspect there may be biases due to
sample selection or observations that have precluded the identification of
active stars in region 1.

Figure 6: The HRD of nearby M dwarfs from Newton et al. (2017). The left plot
is for M dwarfs flagged as “active” in Newton et al. (2017) and the center-
left plot is for “inactive” M dwarfs. The center-right plot merges the samples
in the two left panels. The main sequence is divided into four regions, shown
in the right plot. Black lines in these four plots represent the GE (short
heavy line), the fitted main sequence, and the upper and lower envelopes of
the main sequence. The polynomial coefficients of these fitted lines are given
in Appendix C. The insets highlight a region around our ROI, which is shown as
a dashed parallelogram tracing the full ROI defined in Figure 1.

###  5.2 Jeffers 2018

The CARMENES survey targets nearby M dwarfs to monitor their long-term radial
velocity variations to detect exoplanets. Recently, Jeffers et al. (2018),
hereafter J18, released rotation and activity results of more than 2,200 M
dwarfs using the rich CARMENES data. We cross-match their sample against Gaia
EDR3 met the following criteria: 1) 1.5$<G_{BP}-G_{RP}<$4, 2) the parallax
error is less than 10% of the parallax, 3) RUWE$<$1.4, and 4) removing known
spectroscopic binaries noted in J18. A total of 1,177 stars with a mean
parallax of 60.2 mas in EDR3 are shown in Figure 7. We use the H$\alpha$ EW
limit of -0.5Å discussed in Jeffers et al. (2018) to separate active and
inactive stars, and we identify 333 active stars and 844 inactive stars. A
total of 14 active stars from J18 are within our ROI, and three of them are
below the transition boundary, which is slightly more than the active stars
identified by us and N17. Our nineteen stars are overlapped with J18. Among
them, two stars, GAI0505-1200 and GAI1019+1952, are identified as active by
both J18 and us. One star, GAI1722+0531, shows H$\alpha$ emission with EW of
-0.35Å by us but -0.11 by J18. That means this star became active in 2022. All
the rest overlapped targets are inactive from both works.

In comparison to results from N17 in Figure 6, more early active M dwarfs are
identified in J18 than in N17, especially in region 1. The ratio of active
stars in regions 2 and 1 is 2.87 (95:33) in J18, but the ratio for N17 is
infinity (49:0). However, similar to N17, fewer active stars from J18 are in
region 3 than in region 4. For stars below the GE, we found that the ratio of
inactive stars in regions 4 and 3 is 101:143 (0.71:1), and the ratio of active
stars is 81:51 (1.58:1). Hence, these ratios are consistent with the results
in N17, where active stars tend to be above the fitted main sequence,
especially for stars with $M_{G}$ between 10 and 12.

Figure 7: Selected M dwarfs from Jeffers et al. (2018) in the HRD. Symbols and
lines are defined in Figure 1 and Figure 6.

###  5.3 Zhang 2021

####  5.3.1 Stars in the ROI

Zhang et al. (2021), hereafter Z21, released chromospheric activities of
738,476 spectral M-type stars, including both dwarfs and giants, based on the
LAMOST (Large Sky Area Multi-Object Fibre Spectroscopic Telescope) low and
medium resolution spectral surveys. By following the three-step Gaia data
quality selecting criteria discussed in Lindegren et al. (2018) and Jao et al.
(2018), we matched 541,124 entries in Z21 with good astrometric data, and a
total of 68,141 entries are flagged with H$\alpha$ emissions by Z21. However,
we found many stars have multiple entries in their catalog because of multi-
epoch observations, and some stars have inconsistent spectral energy
distributions. Two example stars are given in Figure 8. Although all spectra
are classified as M type, the highlighted spectra appear not as M dwarfs. We
think the spectral misclassification could be caused by 1) misplaced fibers,
2) flux and telluric lines calibrations, or 3) mislabeled object
identifications. Because their released H$\alpha$ activity results are results
of their incorrect spectral classifications, spectra of non-M dwarfs have been
mixed in their results.

Figure 8: LAMOST spectra of two stars with multi-epoch observations. All
spectra are normalized and shifted by an integer. These two stars are
classified as M-type in Z21, and obviously, red lines are not M dwarfs. Both
targets are inactive.

Thus, because some stars have been misclassified as M dwarfs in Z21, we re-
classify their spectra in order to make a similar H$\alpha$ activity
distribution figure like Figure 6 and 7. We use the same EDR3 selecting
criteria discussed in section 2 to select stars with high-quality astrometric
data. We then retrieve spectra from the LAMOST DR6 for limited stars within
100 pc within our ROI as our base sample and use the Sloan Digital Sky Survey
(SDSS) M dwarf standard star templates released in Bochanski et al. (2007) to
re-classify their spectral types. After re-classifying their spectra, we
identify 639 M dwarfs within 100 pc from 751 spectra. Instead of using the
H$\alpha$ activity flag reported in Z21 to identify active and inactive stars,
we re-identify the H$\alpha$ profile by fitting a skewed Gaussian function
between 6,538 and 6,750Å. The peak of the skewed Gaussian, negative or
positive, is an initial indicator of the activity, and we later visually
inspect all spectra to distinguish H$\alpha$ emission and absorption. These
stars then serve as our reference stars to set the activity limits to separate
active and inactive stars for a much larger sample.

In Z21, they measured various parameters for the H$\alpha$ line, including EW
(EWHa), S/N (SNHa), and height (Height) of the H$\alpha$ line, as well as the
S/N of the spectrum (SNr). Using a combination of these parameters, Z21 set
criteria to indicate active and inactive stars among their 738,476 stars.
Because the 639 M dwarfs are our base sample, we will redefine the criteria to
select active and inactive stars. Without re-measuring these parameters
discussed above, we continue to adopt these parameters given in Z21 and
present new limits in Figure 10(a), where active stars have 1) “EWHa” $>$
0.58Å, 2) “SNHa” $>$16, 3) “Height” $>$ 2.5, 4) SNr $>$7.7, and 5) EWHa $>$
e_EWHa. Thus, these criteria are optimized for mid-M dwarfs, and two active
stars identified by Z21 do not meet the criteria as seen in the left plot of
Figure 10(a). This is because both stars have relatively low SNHa.

Forty-nine active and 590 inactive stars within the ROI are identified using
the new criteria shown in Figure 9. We can see inactive stars spread
throughout this ROI. The active stars, however, are generally in the top half
of the ROI, especially above the fitted main sequence. Five active stars are
in the bottom half of the ROI, much more than the active stars identified by
N17, J18, and this work. Nonetheless, the percentage of active stars remains
low in the bottom half of the ROI, and there is no activity anomaly in the
gap.

There are a total of 67 overlapped stars between Z21 and this work. Four
stars, GAI0128+1617, GAI1407+0311, GAI1556+0254, and GAI1722+0531 are
identified as active by both projects. Three additional stars (GAI0552-0305,
GAI0915+1414, and GAI1452+0629) were also marked as active by Z21, but our
spectra indicate they are inactive. We extract spectra for these three stars
from LAMOST and found that only GAI0552-0305 is active, which is just above
the gap ($M_{G}=10.08$ and $G_{BP}-G_{RP}=$2.5). This star may have become
inactive during our observation. All the rest of overlapped targets are
identified as inactive by both projects.

Figure 9: Active and inactive stars in LAMOST are selected using our new
criteria. This figure is similar to Figure 1

####  5.3.2 Apply new criteria to the entire M dwarfs on the main sequence

Figure 10(b) compares activity criteria defined by Z21 and new criteria by us
in different parameter spaces. Although Z21 noted that stars with EWHa greater
than 0.75Å are selected as active stars, this figure shows the limit they used
is $\sim$0.3Å. By applying the new criteria to entire dwarfs in Z21 without
re-classifying the spectra types and re-measuring H$\alpha$ parameters of
333,044 stars with $G_{BP}-G_{RP}>$ 1.6 and $M_{G}>$6.0 in Gaia EDR3, we
determine 18,472 stars are active, and the remaining are inactive. Their
distributions are shown in Figure 11, where the top panels are inactive stars,
and the bottom panels are active stars.

Ninety-five percent of stars are inactive, distributed throughout the main
sequence without showing any specific pattern. The fitted distribution of
inactive stars shown as a blue dashed line generally follows the fitted main
sequence, so the distribution or populations of inactive stars represents the
main sequence. In contrast to inactive stars in Figure 11, the distributions
of active stars, which is 5% of the sample, in the HRD are mainly composed of
two different bands where one band is the dwarfs on the main sequence, and the
other is possibly equal mass unresolved binaries elevated above the main
sequence. Active stars above the gap are mostly in region 2 (defined in Figure
6), and the density contrast between regions 1 and 2 is high. This indicates
active stars above the gap are mostly elevated above the fitted main sequence.
The best-fitted distribution for active stars is a red dashed line in the
bottom panel. Unlike the best-fitted line for inactive stars, the fitted line
for active stars does not match the main sequence and is shifted 0.07 mag
redder in $G_{BP}-G_{RP}$ color at about $M_{G}\sim$10\. For active stars
below the gap, we can see the distribution is gradually curved to match the
distribution of the main sequence. In general, the distributions of active and
inactive stars from Z21 in the HRD are consistent with the distributions based
on results from N17 and J18 shown in Figure 6 and 7.

The rightmost two plots in Figure 11 are histograms for inactive and active
stars. The two dash-dotted lines represent their distributions fitted by using
a skewed Gaussian function. We can see that the distribution of inactive stars
is relatively smooth, but surprisingly, there seems to be a prominent dip at
$M_{G}\sim$10.5 in the histogram for active stars. We will discuss more of
this newly identified activity dip in section 6.

Figure 10: Active and inactive stars in different H$\alpha$ parameter spaces,
i.e, EWHa, SNHa, Height, and SNr. (a) New criteria based on re-classified 639
M dwarfs within 100 pc. New limits are marked in black dashed lines. The blue
and red dots represent inactive and active stars determined by Z21,
respectively. The colored regions are defined as active stars using the new
criteria defined in this work. (b) The top panel is for inactive stars (blue
dots), and the bottom panel is for active stars (red dots) originally flagged
in Z21. The dashed lines mark the new criteria given in (a). This shows some
of the active stars flagged by Z21 won’t be identified as active by our new
criteria. Figure 11: Distributions of inactive (top panel) and active (bottom
panel) stars in the HRD from the LAMOST using our new criteria. The two left
plots are scattering plots for inactive and active stars. The center four
plots are two-dimensional histograms with a bin size of $\sim$0.05 magnitude
at $M_{G}$ and $G_{BP}-G_{RP}$. The two-dimensional histograms for active
stars are in linear scale, but in log scale for inactive stars. Four black
lines are the same lines defined in Figure 6 are shown in two of the center
plots, and they are served as a guide for the distribution of the main
sequence and the gap. The red and blue dashed lines represent the best-fitted
distribution for active and inactive stars, respectively. The right two plots
are the histograms of $M_{G}$ with a bin size of 0.05 mag. Two dash-dotted
lines represent the fitted distribution for inactive and active stars.

###  5.4 Reiners 2022

Reiners et al. (2022), hereafter R22, reported mean-surface magnetic fields of
292 nearby M dwarfs in the CARMENES project and an additional 22 stars from
the literature. The mean parallax of this sample is 98.5 mas, so their work
comprises the nearest M dwarfs among all works discussed in this manuscript.
They found a linear power law relation between the magnetic fields and
$L_{H\alpha}$ in their Figure 9, and a magnetic field of $\sim$1800 G could
separate fast and slow rotators. Hence, using this magnetic field limit, we
could separate their sample into two populations: one contains fast-rotating
stars with relatively stronger magnetic fields and high H$\alpha$
luminosities, and the other group has relatively weaker magnetic fields and
H$\alpha$ luminosities. We then plot their samples using this limit to
separate these two populations in the HRD in Figure 12.

The left plot of Figure 12 shows they have 27 slow rotators with $\langle
B\rangle<$ 1800 G within the ROI, and they have only one faster rotator with
$\langle B\rangle>$ 1800 G within the ROI. Unlike the three other works
discussed in this section, the relatively small sample size within the ROI
from R22 is hard for us to study and compare activity within our ROI.
Nonetheless, by examining the activity distribution across the main sequence,
we find slow rotators with $\langle B\rangle<$ 1800 G are generally
distributed on either side of the main sequence, but fast rotators with
$\langle B\rangle>$ 1800 G are elevated in the top half of the best fitted
main sequence or region 2 and 4, with a few exceptions at the lower main
sequence.

In summary, all four earlier works from N17, J18, Z21, and R22 show active
partially convective stars are mostly elevated above the main sequence, but
active fully convective stars are on either side of the main sequence. Other
than the samples in Z21, the other three works don’t have enough stars within
our ROI. However, all these works consistently show active stars are mostly in
the top half of the ROI, and the bottom half of the ROI, including stars in
the gap, lacks active stars.

Figure 12: M dwarfs from Reiners et al. (2022) in the HRD. The left plot shows
stars with $\langle B\rangle<$ 1800 G in open circles, and the center plot is
for stars with $\langle B\rangle>$ 1800 G in filled circles. Because of the
relation between magnetic fields and H$\alpha$ fluxes, the distributions shown
here are proxies of H$\alpha$ lines. The right plot shows the entire samples
in Reiners et al. (2022) and the strengths of magnetic fields in colors. The
black lines and ROI are defined in Figure 1 and Figure 6.

##  6 A dip in the H-alpha activity distribution

###  6.1 confirmation of the activity dip

This activity dip in Figure 11 is seen using our revised criteria to define
active and inactive stars. We found that when we use the active and inactive
stars originally flagged by Z21 (See Appendix A), both old and revised
selection criteria yield the same dip at the same location. In spite of that,
we understand a sampling bias could also create an expected distribution dip.
For example, West et al. (2011) studied a large number of M dwarfs using data
from SDSS, which has similar observational approaches and goals as the LAMOST,
and reported a selection bias in their SDSS sample so that a population gap is
seen on the main sequence. However, the smooth distribution of inactive stars
shown in Figure 11 likely eliminates sampling biases in LAMOST.

This activity dip mainly comes from stars within 200 pc in Z21. For stars
beyond 200 pc or stars fainter than $M_{G}\sim$10.6, the number of stars drops
rapidly because of the magnitude limit from LAMOST. To further confirm this
activity dip, we select two equal-volume samples to compare: distances of
0–158.7 and 158.7–200 pc. We found this activity dip is seen at the same
location regardless of the sample. Besides, LAMOST data also include stars in
nearby young clusters, i.e, Pleiades, M44, and M67. After stars in those parts
of the sky are excluded, the activity dip still exists at the same location on
the main sequence.

Finally, the dip in the histogram can also be identified in $M_{BP}$ and
$M_{RP}$ at a range of 12.0–12.25 and 9.0 – 9.55, respectively. The dip is the
most prominent in $M_{RP}$ because Gaia’s RP filter has the highest
transmission at H$\alpha$ among all three Gaia filters. Consequently, we can
reproduce this activity dip using various samples. We note that this activity
dip can’t be identified in N17 and 18, and we suspect these two works have
relatively smaller sample sizes to reveal this feature.

###  6.2 In-depth analysis of the activity dip

Figure 13: (Left): The activity dip is marked as a square bracket on the
enhanced HRD. This bracket is shown in all four plots. A stellar low-density
region first identified in Jao & Feiden (2020, 2021) is marked in yellow. The
dashed box is our ROI. (Center Left): A portion of the two-dimensional
histogram of active stars in the bottom panel of Figure 11. (Center Right): A
histogram of active stars. Both center left and center right plots are the
same as the right two plots in the bottom row of Figure 11. (Right): A
distribution of percentages of active stars. The inset plot covers a larger
range of this distribution. Red dashed lines are the second-order polynomial
fits of the percentages vs $M_{G}$ from 9 to 12 magnitude.

Figure 13 illustrates the location of the activity dip on the HRD. In the left
plot of this figure, this activity dip appears to overlap a low-density region
on the main sequence first identified by Jao & Feiden (2020) and Jao & Feiden
(2021). This low-density region is not as prominent as the gap but is
statistically significant. The cause of this low-density region is yet to be
known, and we have no prior reason to relate this H$\alpha$ activity dip to
this low-density region. Here, we only highlight the coincidence of these two
features on the lower main sequence.

Other than studying the number of active stars in each bin, we show the
percentage distribution of active stars in Z21 in the inset in the right plot
of Figure 13. The percentage distribution peaks at $M_{G}\sim$6, and decreases
till $M_{G}\sim$8, where it corresponds to the M0V. Then, the percentage rises
until about $M_{G}\sim$12 and decreases again till the end of the main
sequence. The fall and rise of the percentage of active stars could be related
to the chromospheric activities, the line strengths between H$\alpha$ and the
continuum, and the LAMOST survey’s incompleteness toward the end of the main
sequence. Nonetheless, there is a prominent activity dip between $M_{G}=$ 10.3
and 10.8, and we estimate 3% of fewer stars are active compared to the best-
fitted distribution at $M_{G}\sim$10.6 or at the deepest dip.

The activity dip marked as square brackets in all four plots in Figure 13 is
just below the gap, and this region overlaps a large portion of the bottom
half of our ROI. Consequently, our almost null H$\alpha$ emission detection in
the bottom half of the ROI is consistent with the activity dip in Figure 13.
In other words, stars in this activity dip region are fully convective M
dwarfs. When Z21 used spectral sub-types to study the percentages of active M
dwarfs on the main sequence, they reported a similar drop at M4 (see their
Figure 4), but they thought this was due to a change in the magnetic dynamo
mechanism at the partially and fully convective boundary. However, based on
the markings in Figure 13, this region is lower than the gap or boundary.

Thus, putting this all together, we find that the most luminous fully
convective M dwarfs, those with $M_{G}$ between 10.3 and 10.8 appear less
active than stars above and below this $M_{G}$ range. In other words, some
most massive fully convective M dwarfs have their H$\alpha$ activities ceased,
or no emission can be detected by the resolution and observation limits of
CHIRON and LAMOST.

##  7 Rotation and H$\alpha$ Emission Relative to the Activity Dip

Stellar activity and rotation or flares are known to have a broken power law
relation (Reiners et al., 2014; Newton et al., 2017; Wright et al., 2018;
Reinhold & Hekker, 2020; Namekata et al., 2021). To further understand their
relations, we select two recent works333Popinchalk et al. (2021) also
assembled a large number of rotation periods for young and field stars. The
reason for excluding it in finding the cause of this dip is fully discussed in
Appendix B.3. from Lu et al. (2022), and Reinhold & Hekker (2020) that contain
a large number of rotation periods from two different projects.

###  7.1 Lu et al. (2022) — Linking Activity and Rotation

Figure 14: Stars from Lu et al. (2022) on the HRD. The left and right plots
are for stars with $P_{rot}>$ and $P_{rot}<$ 10 days, respectively. Lu et al.
(2022) showed that 5% of the periods longer than 10 days and 50% of the
periods shorter than 10 days are possibly incorrect.

Lu et al. (2022), hereafter L22, reported rotation periods for over 40,553
stars measured using the Zwicky Transient Facility (ZTF). Two distributions of
their targets on the HRD after matching Gaia DR3 are shown in Figure 14, and
the mean parallax is 3.8 mas. In this figure, we split their sample into two
groups, $P_{rot}>10$ and $<10$ days. We can see that both groups are obviously
elevated above the best-fitted main sequence in regions 2 and 4, and
relatively fewer stars are in regions 1 and 3. Apparently, this distribution
is strikingly similar to those active stars in N17, J18, and Z21 and stars
with $\langle B\rangle>$ 1800 G in R22. ZTF is a ground-based observation, so
large and prominent spot modulations could preferably be detected. Hence,
those spot modulations detected by ZTF are closely relative to active stars,
and we would assume most of these stars could be considered active.

L22 stated that 50% of the rotation periods less than 10 days are possibly
incorrect, and 5% of the periods longer than 10 days are erroneously measured
in their work, so it is hard for us to take advantage of this rich dataset to
investigate this activity dip further. Furthermore, we don’t have enough
relatively fast rotators or potential inactive stars to compare with. In spite
of these challenges, the distribution of stars in L22 indicates a strong
connection between rotation and stellar activity on the HRD.

###  7.2 Reinhold & Hekker (2020) — Linking H$\alpha$ activity to Fast
Rotators

Figure 15: The entire sample in Reinhold & Hekker (2020) is shown in the left
plot. Because their targets include various young and old dwarfs selected in
different K2 Campaigns, we only focus on stars falling between the upper and
lower envelopes of the main sequence. Stars excluded from our statistics are
plotted in black dots. The two left plots are for stars with periods greater
(blue dots) or less (red dots) than the critical period ($P_{crit}$). The
right plot shows the percentage of fast rotation stars in each bin of $\Delta
M_{G}$=0.25 in a black line. The error bars are calculated using the same
method discussed in Table 5. The blue bands mark the H$\alpha$ activity dip in
LAMOST. The green line is the number of fast rotators in each bin. Inserted
plots highlight stars within the ROI in this work.

Reinhold & Hekker (2020), hereafter RH20, reported rotation periods of more
than 29,860 stars from the $Kepler$ K2 Campaigns from 0 to 18 with a mean
parallax of 5.1 mas from Gaia DR3, so results from their large numbers of M
dwarfs provide another avenue to understand H$\alpha$ activity distribution on
the main sequence. Because of the experimental design of the K2 mission, all
targets are mainly in the ecliptic plane and include a few young clusters like
Pleiades, M44, M67, and small portions of Hyades and Taurus-Auriga. We only
consider stars with RUWE$<$1.4 that fall between the upper and lower envelopes
of the main sequence to represent the overall population of the main sequence
stars. Figure 15 shows these selected 24,836 targets with $M_{G}>$ 7 on the
HRD. Unlike stars in L22, targets with long periods in RH20 are distributed on
either side of the best-fitted main sequence. Therefore, we can assume stars
in RH20 potentially contain both active and inactive stars, but L22 mostly
contains active stars.

####  7.2.1 Split stars in RH20 into fast and slow rotators

The broken power law relations between rotation and activity are fully
discussed and presented in Reiners et al. (2014) and Newton et al. (2017),
using X-ray and H$\alpha$ fluxes, respectively. The other difference between
these two works is whether the Rossby number is used to represent this
relation or not. Nonetheless, the X-ray or H$\alpha$ activity is saturated
when the Rossby number or rotational period is less than a critical value. As
discussed in Jao et al. (2022), we face challenges in determining the
convective turnover time, which is used to obtain the Rossby number.
Furthermore, Douglas et al. (2014) showed the broken power laws of X-ray and
H$\alpha$ activities for stars in young clusters have almost the same Rossby
number or critical value at the kink. Hence, instead of using the critical
Rossby number reported for the H$\alpha$ line in Newton et al. (2017), we
adopt the critical value reported in Reiners et al. (2014) based on X-ray
activities so that we can avoid the difficulties of obtaining convective
turnover time and eventually the Rossby number.

The breakpoint or the critical value is at
$\log(L_{X}/L_{bol})$=$\log(kR^{\alpha}P^{\beta})$=$-$3.14 (Reiners et al.,
2014), where R is the radius of a star in solar radius, P is the period in
days, $k=1.86\times 10^{-3}$, $\alpha=-$4, and $\beta=-$2\. Apparently, it
shows although the breakpoint is a fixed value for the activity-rotation
relation, it also depends on stellar radius and period. As a result, for a
given star, we would need to estimate its critical rotational period,
$P_{crit}$, so that we can compare its measured rotational period to
$P_{crit}$ to understand how active a star is. This also means the $P_{crit}$
is not a fixed value but depends on stellar radii. Without knowing their true
H$\alpha$ EWs or fluxes, this method can only distinguish potential saturated
and un-saturated X-ray or H$\alpha$ activities. Also, because all the
H$\alpha$ activity studies separate targets into two groups, active and
inactive, using the $P_{crit}$, we could also help us to split stars in RH20
into two groups of fast and slow rotators.

We calculate stellar radii for stars in RH20 based on the empirical $M_{G}$
and radius relation in Pecaut & Mamajek (2013). We then can obtain the
$P_{crit}$ for a given target based on the broken power law relation in
Reiners et al. (2014). Stars with measured rotational periods greater than
$P_{crit}$ are shown in blue dots in the left of Figure 15. Stars rotate
faster than the $P_{crit}$ are shown in red in the middle plot of Figure 15.

We can see that slow-rotation stars ($P_{rot}>P_{crit}$) are distributed
evenly on either side of the best-fitted main sequence or in all four regions.
The number of slow rotators decreases toward the lower main sequence. In
contrast, fast-rotation stars are mostly elevated above the main sequence for
stars above the gap in region 2, but fast-rotation stars below the gap can be
seen on either side of the main sequence in region 3 and 4, especially toward
the end of the main sequence. Consequently, the distributions of slow and
fast-rotation stars on the main sequence are strikingly similar to the
distribution of H$\alpha$ inactive and active stars shown in N17, J18, and
Z21. The distribution of the fast rotators in RH20 is also similar to the left
plot in Figure 14.

####  7.2.2 Connect H$\alpha$ activity and stellar rotation

For stars in the ROI, the distributions of slow and fast-rotation stars in
Figure 15 also resemble the H$\alpha$ activity distribution we found in Figure
3. Slow rotators and H$\alpha$ inactive stars above the GE are distributed on
either side of the ROI, but the fast rotators and H$\alpha$ active stars are
distributed mainly in the top half of the ROI and above the best-fitted main
sequence in region 2. No rotation anomaly is seen for stars in the gap or zone
E. Consequently, rotation and H$\alpha$ activities are closely related not
only in a mathematical relation but in their distributions on the HRD.

The right plot in Figure 15 shows the percentage of fast rotators as a black
line in a bin of $\Delta M_{G}=$0.25. This curve shows the percentages of fast
rotators are relatively lower in the range of $M_{G}=$ 10.3 and 10.8 than
those stars in the bin of $M_{G}\sim$10.9. This implies fewer stars in this
range rotate faster than the $P_{crit}$, which is about 13 days if
$M_{G}=$10.5 is used. The location is surprisingly identical to the H$\alpha$
activity dip highlighted in blue boxes. More importantly, this fast-rotator
deficient region is outside of the main sequence gap, so the cause of the
deficiency is not due to interior instability.

Furthermore, targets from Z21 and RH20 have no overlap. Targets in Z21 are all
over the northern sky, but targets in RH20 are mainly in the ecliptic plane.
Yet, the dips identified from these two datasets are at the same location on
the main sequence. This further demonstrates that stellar rotation and
H$\alpha$ activities are strongly related. A slow or no rotation star produces
a weaker H$\alpha$ line or absorption in the atmosphere, and a fast rotator
generates stronger dynamos to potentially saturate H$\alpha$ line. Pass et al.
(2022) used wide binaries to identify ages of M dwarfs with rotation periods
and found M dwarfs with masses between 0.2 and 0.3M⊙ spin down in roughly
three stages: $P_{rot}<$2 days at 600 Myrs, 2$<P_{rot}<$10 days at 1–3 Gyrs,
and rapidly spin down at older ages. The H$\alpha$ activity dip and low
percentage of faster rotators in the range of $M_{G}=$ 10.3 and 10.8, where
these stars are fully convective stars, are close to the estimated upper mass
limit in Pass et al. (2022). Therefore, some of the M dwarfs with ages older
than 3 Gyrs in this magnitude range have spun down rapidly, so fewer stars are
active and fast rotators.

We understand the percentage distribution of active stars in Figure 11 is
different from the percentage distribution of fast rotators in Figure 15. This
is mainly because 1) the split of fast and slow rotators in RH20 can only help
us identify potential saturated or un-saturated H$\alpha$ fluxes, and 2) RH20
has incompleteness of slow rotators, especially in the lower main sequence.
Hence, the percentage of active stars in Figure 11 rises the most at
$\sim$20%, but the percentage of fast rotators in Figure 15 can rise up to
100%. However, when we focus on the numbers of fast rotators between $M_{G}=$
9.5 and 11, we still have fewer fast rotators in this region, and the location
is overlapped with the activity dip in Z21. Based on the work in L22 and RH20,
we propose the H$\alpha$ activity dip results from lacking fast rotators in
this mass range.

##  8 The possible cause of the activity dip

The leading model to explain the stalled or reduced spin down for partially
convective stars with masses between 0.4 $M_{\odot}$ and 0.8 $M_{\odot}$ is
the transfer of angular momentum from the radiative core to the convective
envelope to compensate for the angular momentum loss due to wind braking
(Spada & Lanzafame, 2020). In other words, wind braking develops differential
rotation or velocity gradient, where the angular velocity of the radiative
zone is greater than the angular velocity of the convective zone.
Observationally, this model has generally accounted for the rotation stalling
of some stars in nearby clusters (Curtis et al., 2020; Dungee et al., 2022),
but this two-zone model is designed for stars that are only partially
convective. However, the concept of transferring angular momentum from the
core, or the lack of it, could be applied to fully convective stars. As
discussed in Dungee et al. (2022), due to the disappearance of the radiative
core for fully convective stars, they may lose the reservoirs of angular
momentum in the radiative core. Consequently, the wind braking could expedite
the spin down for these early types of fully convective stars. The more stars
spin down fast, the fewer H$\alpha$ emissions can be detected in the result of
the activity dip we see in Figure 11. According to the ${}^{3}He$ instability
model (Baraffe & Chabrier, 2018), M dwarfs with masses of 0.3 –
0.32$M_{\odot}$ could briefly form a radiative zone approximately between the
ages of 40 and 250 Myrs, then the radiative zone disappears and stars become
fully convective throughout their life. For M dwarfs with masses less than
0.3$M_{\odot}$, no radiative core has ever been formed, so there is no
additional angular momentum reservoir in their entire life. Consequently, we
speculate that the activity dip could also relate to the disappearance of the
radiative core for potential young stars with masses between 0.3 and
0.32$M_{\odot}$ as they evolve. However, the connection to the ${}^{3}He$
instability encounters two challenges: 1) stars with such a young age in this
mass range would mostly be elevated higher than the main sequence, so they
won’t be included in our analysis, and 2) this age range is much younger than
the spin down age determined empirically by Pass et al. (2022).

##  9 Summary

We carefully select and observe 480 M dwarfs on either side of the gap to
understand how the interior instability may affect their H$\alpha$ activities.
Our high-resolution spectroscopic survey results, the largest high-resolution
survey focusing on this tight transition zone, show the H$\alpha$ emission is
almost not detectable for stars in the bottom half of our ROI, with a few
exceptions close to the red edge of the ROI based on results in J18 and Z21.
This implies that stars in the gap don’t show excessive H$\alpha$ emissions
compared to stars above and below the gap, and observationally the H$\alpha$
activity has a sharp transition at the GE. Because the gap marks the interior
transition, those active stars are mostly partially convective, and stars in
and below the gap are mostly inactive. This relatively sharp activity
transition is different from results from a large survey of Ly$\alpha$ and
X-ray of M dwarfs by Linsky et al. (2020), where they found no abrupt changes
at or near the boundary in Ly$\alpha$ and X-ray fluxes.

Our targets have relatively consistent ages and metallicities based on studies
of CaH1 strength and galactic kinematics, but their true ages or metallicities
may still differ. Hence, we still have heterogeneous stars within the ROI. As
we know that the 3He instability can make their interior structure change
depending on their ages, so we should have a wide variety of interior
structures for stars in the gap. Yet, their interior differences are not
reflected in the H$\alpha$ activities.

Furthermore, the majority of active stars are in the top half of our ROI and
are also above the best-fitted main sequence or in region 2 in Figure 6. This
kind of shifted distribution for active stars can also be seen in N17, J18,
and Z21. Based on a large number of low and median resolution spectra from
LAMOST in Z21, we determine active stars are shifted up to $\sim$0.07 mag
redder in $G_{BP}-G_{RP}$ for stars at $M_{G}=$10\. However, the distribution
of active stars below the gap generally matches the curvature of the main
sequence.

The causes of active stars shifting redder for stars above the gap are yet to
be known, but a similar shift can also be identified for fast-rotation stars,
as shown in Figure 15. We note that the term “fast” or “slow” rotators we
refer to here are all relative depending on stellar masses. We think all the
active stars are fast rotators, so that is why the distributions of fast
rotators and active stars on the HRD are almost the same. In other words, for
stars within the ROI, the H$\alpha$ emissions we detected in this and other
works are primarily the result of fast rotation and not caused by interior
instability.

Fast rotators often have spots, and the starspot model by Somers et al. (2020)
suggested that starspots could make low-mass stars in the Pleiades redder
depending on the spot coverage. However, the presence of starspots doesn’t
always mean the presence of an H$\alpha$ emission. For example, the solar
spectrum has an H$\alpha$ absorption (Wallace et al., 2011), but still has
spots. The formation mechanism of the H$\alpha$ line in M dwarf atmosphere is
intertwined between rotation, chromospheric density, magnetic activities, and
photosphere temperature (Basri, 2021). We don’t know whether all these active
stars flagged by this work and others have starspots present on their
surfaces. Even if all these active stars have starspots, that will imply most
stars have a similar spot coverage to make these active stars above the gap
consistently shift redder. On the other hand, Jackson & Jeffries (2014) showed
an opposite shift in colors for stars with starspots. So how the starspots
affect their colors is not clear, but our result seems to match the model
proposed by Somers et al. (2020) if the cause of the color shift is starspots.

For stars below the gap with $M_{G}>11$, active fully convective stars
generally follow the curvature of the main sequence, and the shift disappears.
If we adopt the model by Somers et al. (2020) that starspots can make
partially convective stars redder, the presence of starspots on these fully
convective stars would appear to have minimum or no impact on their
$G_{BP}-G_{RP}$ colors. Berdyugina (2005) also showed the spot temperature
contrast with respect to the photospheric temperature is less than 500 K for
dwarfs cooler than 3500 K. Hence, the starspot’s contrast on the photosphere
would have minimal effect on the effective temperature, so $G_{BP}-G_{RP}$
color differences between active and inactive stars appear to be
indistinguishable for stars fainter than $M_{G}\sim$11\. We also show this
unique curved distribution is strikingly similar to stellar rotations on the
main sequence, so we demonstrate the activity and rotation are not only
closely related mathematically but also similarly distributed on the HRD.

Finally, while we study the H$\alpha$ activities using the LAMOST data, we
unveil some stars at 10.3$<M_{G}<$10.8 lack H$\alpha$ emissions. The
percentage of active stars drops a few percent within this magnitude range.
This $M_{G}$ region is also overlapped with the bottom half of our ROI, where
only one active star is identified from this work. Z21 discussed that the
activity dip might be caused by changing the magnetic dynamo mechanism at the
boundary, but our work shows the activity dip is below the gap. Based on the
large number of rotation periods presented in RH20, we found this activity dip
coincides with a region where fewer stars rotate faster than $P_{crit}$
periods. This implies some of the most massive fully convective stars spin
down rapidly, so fewer stars become active. However, the link between
H$\alpha$ activity dip and rotation dip is based on the current large survey
of nearby M dwarfs from the K2 mission. We lack all rotation periods for
unbiased and completed late M dwarfs. Only after both their rotation and
H$\alpha$ lines are measured can we further understand and explain this newly
identified H$\alpha$ activity dip on the lower main sequence.

We would like to thank Liyun Zhang, Zhong-Rui Bai, and Luqian Wang for their
help with the LAMOST data. We also thank Emily Pass and Gregory Feiden for
their suggestions. This work was supported by the NASA Astrophysics Data
Analysis Program (ADAP) under grant 20-ADAP20-0288. We have used data from the
CHIRON spectrograph on the SMARTS 1.5m telescope, which is operated as part of
the SMARTS Consortium by RECONS (www.recons.org) members, and with the
assistance of staff, especially Roberto Aviles, and Rodrigo Hinojosa, at Cerro
Tololo Inter-American Observatory. This research has made use of the SIMBAD
database, operated at CDS, Strasbourg, France. 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. Guoshoujing Telescope (the
Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a
National Major Scientific Project built by the Chinese Academy of Sciences.
Funding for the project has been provided by the National Development and
Reform Commission. LAMOST is operated and managed by the National Astronomical
Observatories, Chinese Academy of Sciences. This research has made use of
NASA’s Astrophysics Data System.

##  Appendix A Active and inactive Stars in Z21

Without using our new H$\alpha$ selecting criteria discussed in section 5.3,
the entire active and inactive stars flagged by Z21 in the HRD are shown in
Figure 16. The dip for active stars at $M_{G}$ 10.5 in the histogram is also
seen. This demonstrates no matter what criteria are used, the percentage of
active stars at $M_{G}$ 10.5 is low. The best-fitted distributions for active
and inactive stars are almost identical to the best-fitted distributions in
Figure 16. Averagely, active stars above the gap are 0.05 mag redder than the
best-fitted main sequence.

Figure 16: This figure is the same as Figure 11, but all active stars flagged
by Z21 are shown. The histogram dip at $M_{G}\sim$10.5 is still seen. In
contrast, the histogram of inactive stars continues to be smooth as the
distribution seen in Figure 11. This shows identifying this dip is not related
to how the active/inactive stars are selected.

##  Appendix B A few additional large surveys

Two additional large H$\alpha$ surveys for M dwarfs and one work with a large
number of rotation periods discussed next are excluded from our analysis.

###  B.1 Kiman 2019

Kiman et al. (2019), hereafter K19, reported H$\alpha$ activities of more than
74,000 M and L dwarfs by matching targets in SDSS and Gaia DR2. However, this
large sample has a mean parallax of 3.77 mas or a mean distance of 265 pc.
There are only 3 stars with distances less than 100 pc in our ROI after we
apply the following selecting criteria: 1) RUWE $<$1.4, 2)
photometric_sample_subred $=$1, 3) astrometric_sample $=$1, 4)
$\pi/\pi_{error}>$10, 5) no Gaia EDR3 source of $\Delta G_{RP}<$4.0 within the
4′′, where the SDSS fiber has a 3′′ diameter. In total, there are 1,671 in
this region, and 71 stars are flagged active by K19. Compared to the samples
in N17, J18, Z21, and this work, the K19 sample could potentially include more
unresolved close binaries because the mean distance is far, and almost all
stars are fainter than $V=$15 mag. Nonetheless, all active and inactive stars
within our ROI are shown in Figure 17, and K19 has significantly more active
stars in the bottom half of this ROI. We think because the distance cutoff is
different from others, the results in K19 are different than others. Besides,
their sample includes M dwarfs selected from West et al. (2011), where they
had a non-uniform sample selection, so obvious sampling gaps can be seen in
their color-magnitude Diagram and HRD (West et al., 2011; Kiman et al., 2019).
Hence, it is difficult to apply their results to understand stars in the ROI.

Figure 17: The left figure shows active (red dots) and inactive (blue dots)
stars reported in Kiman et al. (2019) in our ROI. The top right and the bottom
right figures are histograms of estimated V magnitudes and distances
respectively for stars shown in the left figure. The red and blue histograms
are for active and inactive stars, respectively.

###  B.2 Anthony 2022

Anthony et al. (2022) reported H$\alpha$’s EW of 122 M dwarfs in the Southern
Continuous Viewing Zone (CVZ) of the TESS mission using low-resolution
spectra, and the mean parallax is 25.9 mas. Only 14 targets are within our
ROI. A total of 12 stars with H$\alpha<-$0.5Å are identified as active, but no
active M dwarfs are within our ROI. Seven of the 12 active stars are fully
convective stars.

###  B.3 Popinchalk 2021

Popinchalk et al. (2021) presented 8,296 rotational periods for field stars
and stars in young clusters with various ages in their Table 3. The
distributions of these two populations on the HRD are shown in Figure 18. We
can see that the number of field stars within the highlighted box is
noticeably lower than the stars above and below this box. Thus, they don’t
have enough stars with this particular region to conduct statistics. As for
young stars, the ”main sequences” of different ages of clusters don’t follow
the main sequence of nearby stars. The lower band of the ”main sequence” is
mainly composed of stars from Pleiades, Praesepe, and Hyades, and the upper
band is mainly from stars in the Upper-Sco moving group. Fields stars below
the gap may have been selected from various biases, so the star density is
low. Therefore, stars are undersampled in 10.3$<M_{G}<$10.8 in comparison with
Reinhold & Hekker (2020) and Lu et al. (2022).

Figure 18: Field stars (black dots in the left plot) and young stars (red dots
in the right plot) in clusters with rotational periods from Popinchalk et al.
(2021). The blue boxes indicate the activity dip in Figure 13.

##  Appendix C The Best fitted Main sequence

Here we present 1) the best-fitted top edge of the gap or GE, 2) the best-
fitted main sequence, and 3) the upper and lower envelopes of the main
sequences using data in Gaia EDR3. To generate these best-fitted lines, the
algorithms and target selection used to generate the enhanced HRD discussed in
Jao & Feiden (2020) are applied for stars in Gaia EDR3. In order to
approximately use a fitted line to represent the two-dimensional gap, we fit a
straight line to represent the top edge of the gap shown in Figure 3. The
upper and lower envelopes cover 90% of the populations at a given
$G_{BP}-G_{RP}$ color using a skewed Gaussian curve to represent the
population. The peak of the distribution indicates the best-fitted main
sequence at this given color. All the best-fitted polynomial coefficients for
these lines are given in Table 6.

Table 6: Coefficients of the polynomials used to generate the best-fitted main
sequence, the gap, and envelopes

coeff. | MS | top of the gap | upper envelope | lower envelope
---|---|---|---|---
a0 | 19.10849382 | 7.86323529 | -13.58268031 | 13.12750985
a1 | -95.44879765 | 0.90252101 | 57.62576454 | -46.72259226
a2 | 214.54030704 |  | -79.81685633 | 90.64589118
a3 | -219.30493198 |  | 64.86365682 | -82.39866903
a4 | 87.35269064 |  | -31.37744697 | 40.94150742
a5 | 35.52596873 |  | 8.88026358 | -11.26957046
a6 | -61.88803250 |  | -1.34570736 | 1.61207258
a7 | 34.78644351 |  | 0.08384474 | -0.09356802
a8 | -10.88510027 |  |  |
a9 | 2.00794707 |  |  |
a10 | -0.20466398 |  |  |
a11 | 0.00891475 |  |  |

Note. — The relations are valid at 0.8$\leq$$G_{BP}-G_{RP}$$\leq$4.0 for the
MS and two envelopes, and 2.3$\leq$$G_{BP}-G_{RP}$$\leq$2.9 for the gap. All
relations have the format of
$M_{G}=\sum_{n=0}^{order}a_{n}\times(G_{BP}-G_{RP})^{n}$.

## References

  * Anthony et al. (2022) Anthony, F., Núñez, A., Agüeros, M. A., et al. 2022, AJ, 163, 257. doi:10.3847/1538-3881/ac6110
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33. doi:10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123. doi:10.3847/1538-3881/aabc4f
  * Bailey et al. (2012) Bailey, J. I., White, R. J., Blake, C. H., et al. 2012, ApJ, 749, 16. doi:10.1088/0004-637X/749/1/16
  * Baraffe & Chabrier (2018) Baraffe, I. & Chabrier, G. 2018, A&A, 619, A177. doi:10.1051/0004-6361/201834062
  * Basri (2021) Basri, G. 2021, An Introduction to Stellar Magnetic Activity, by Basri, Gibor. ISBN: 978-0-7503-2130-3. IOP ebooks. Bristol, UK: IOP Publishing, 2021. doi:10.1088/2514-3433/ac2956
  * Berdyugina (2005) Berdyugina, S. V. 2005, Living Reviews in Solar Physics, 2, 8. doi:10.12942/lrsp-2005-8
  * Bessell (1982) Bessell, M. S. 1982, PASA, 4, 417. doi:10.1017/S1323358000021329
  * Bochanski et al. (2007) Bochanski, J. J., West, A. A., Hawley, S. L., et al. 2007, AJ, 133, 531. doi:10.1086/510240
  * Burgasser et al. (2003) Burgasser, A. J., Kirkpatrick, J. D., Reid, I. N., et al. 2003, ApJ, 586, 512. doi:10.1086/346263
  * Cayrel (1988) Cayrel, R. 1988, The Impact of Very High S/N Spectroscopy on Stellar Physics, 132, 345
  * Charbonneau (2014) Charbonneau, P. 2014, ARA&A, 52, 251. doi:10.1146/annurev-astro-081913-040012
  * Chabrier & Küker (2006) Chabrier, G. & Küker, M. 2006, A&A, 446, 1027. doi:10.1051/0004-6361:20042475
  * Clements et al. (2017) Clements, T. D., Henry, T. J., Hosey, A. D., et al. 2017, AJ, 154, 124. doi:10.3847/1538-3881/aa8464
  * Cram & Mullan (1979) Cram, L. E. & Mullan, D. J. 1979, ApJ, 234, 579. doi:10.1086/157532
  * Curtis et al. (2020) Curtis, J. L., Agüeros, M. A., Matt, S. P., et al. 2020, ApJ, 904, 140. doi:10.3847/1538-4357/abbf58
  * Donati et al. (2008) Donati, J.-F., Morin, J., Petit, P., et al. 2008, MNRAS, 390, 545. doi:10.1111/j.1365-2966.2008.13799.x
  * Douglas et al. (2014) Douglas, S. T., Agüeros, M. A., Covey, K. R., et al. 2014, ApJ, 795, 161. doi:10.1088/0004-637X/795/2/161
  * Dungee et al. (2022) Dungee, R., van Saders, J., Gaidos, E., et al. 2022, ApJ, 938, 118. doi:10.3847/1538-4357/ac90be
  * Feiden et al. (2021) Feiden, G. A., Skidmore, K., & Jao, W.-C. 2021, ApJ, 907, 53. doi:10.3847/1538-4357/abcc03
  * Fouqué et al. (2018) Fouqué, P., Moutou, C., Malo, L., et al. 2018, MNRAS, 475, 1960. doi:10.1093/mnras/stx3246
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1. doi:10.1051/0004-6361/202039657
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Arenou, F., Babusiaux, C., et al. 2022, arXiv:2206.05595
  * Gilman (2005) Gilman, P. A. 2005, Astronomische Nachrichten, 326, 208. doi:10.1002/asna.200410378
  * Gizis (1997) Gizis, J. E. 1997, AJ, 113, 806. doi:10.1086/118302
  * Gizis et al. (2002) Gizis, J. E., Reid, I. N., & Hawley, S. L. 2002, AJ, 123, 3356. doi:10.1086/340465
  * Irwin et al. (2018) Irwin, J. M., Charbonneau, D., Esquerdo, G. A., et al. 2018, AJ, 156, 140. doi:10.3847/1538-3881/aad9a3
  * Hawley et al. (1996) Hawley, S. L., Gizis, J. E., & Reid, I. N. 1996, AJ, 112, 2799. doi:10.1086/118222
  * Henry et al. (1994) Henry, T. J., Kirkpatrick, J. D., & Simons, D. A. 1994, AJ, 108, 1437. doi:10.1086/117167
  * Houdebine & Mullan (2015) Houdebine, E. R. & Mullan, D. J. 2015, ApJ, 801, 106. doi:10.1088/0004-637X/801/2/106
  * Houdebine et al. (2017) Houdebine, E. R., Mullan, D. J., Bercu, B., et al. 2017, ApJ, 837, 96. doi:10.3847/1538-4357/aa5cad
  * Hubbard-James et al. (2022) Hubbard-James, H.S. et al. 2022, submitted to AJ
  * Hunter (2007) Hunter, J.D., 2007, Computing in Science & Engineering, 9, 90
  * Jackson & Jeffries (2014) Jackson, R. J. & Jeffries, R. D. 2014, MNRAS, 445, 4306. doi:10.1093/mnras/stu2076
  * Jao et al. (2011) Jao, W.-C., Henry, T. J., Subasavage, J. P., et al. 2011, AJ, 141, 117. doi:10.1088/0004-6256/141/4/117
  * Jao et al. (2018) Jao, W.-C., Henry, T. J., Gies, D. R., & Hambly, N. C. 2018, ApJ, 861, L11
  * Jao & Feiden (2020) Jao, W.-C. & Feiden, G. A. 2020, AJ, 160, 102. doi:10.3847/1538-3881/aba192
  * Jao & Feiden (2021) Jao, W.-C. & Feiden, G. A. 2021, Research Notes of the American Astronomical Society, 5, 124. doi:10.3847/2515-5172/ac053a
  * Jao et al. (2022) Jao, W.-C., Couperus, A. A., Vrijmoet, E. H., et al. 2022, ApJ, 940, 145. doi:10.3847/1538-4357/ac9cd8
  * Jeffers et al. (2018) Jeffers, S. V., Schöfer, P., Lamert, A., et al. 2018, A&A, 614, A76. doi:10.1051/0004-6361/201629599
  * Linsky et al. (2020) Linsky, J. L., Wood, B. E., Youngblood, A., et al. 2020, ApJ, 902, 3. doi:10.3847/1538-4357/abb36f
  * Kiman et al. (2019) Kiman, R., Schmidt, S. J., Angus, R., et al. 2019, AJ, 157, 231. doi:10.3847/1538-3881/ab1753
  * Kiman et al. (2021) Kiman, R., Faherty, J. K., Cruz, K. L., et al. 2021, AJ, 161, 277. doi:10.3847/1538-3881/abf561
  * Kirkpatrick et al. (1991) Kirkpatrick, J. D., Henry, T. J., & McCarthy, D. W. 1991, ApJS, 77, 417. doi:10.1086/191611
  * Kraft (1967) Kraft, R. P. 1967, ApJ, 150, 551. doi:10.1086/149359
  * Lindegren et al. (2018) Lindegren, L., Hernández, J., Bombrun, A., et al. 2018, A&A, 616, A2. doi:10.1051/0004-6361/201832727
  * López-Valdivia et al. (2021) López-Valdivia, R., Sokal, K. R., Mace, G. N., et al. 2021, ApJ, 921, 53. doi:10.3847/1538-4357/ac1a7b
  * Lu et al. (2022) Lu, Y. L., Curtis, J. L., Angus, R., et al. 2022, AJ, 164, 251. doi:10.3847/1538-3881/ac9bee
  * MacDonald & Gizis (2018) MacDonald, J. & Gizis, J. 2018, MNRAS, 480, 1711. doi:10.1093/mnras/sty1888
  * Malo et al. (2014) Malo, L., Artigau, É., Doyon, R., et al. 2014, ApJ, 788, 81. doi:10.1088/0004-637X/788/1/81
  * Medina et al. (2022) Medina, A. A., Winters, J. G., Irwin, J. M., et al. 2022, ApJ, 935, 104. doi:10.3847/1538-4357/ac77f9
  * Pecaut & Mamajek (2013) Pecaut, M. J. & Mamajek, E. E. 2013, ApJS, 208, 9. doi:10.1088/0067-0049/208/1/9
  * Mansfield & Kroupa (2021) Mansfield, S. & Kroupa, P. 2021, A&A, 650, A184. doi:10.1051/0004-6361/202140536
  * Mohanty & Basri (2003) Mohanty, S. & Basri, G. 2003, ApJ, 583, 451. doi:10.1086/345097
  * Namekata et al. (2021) Namekata, K., Maehara, H., Honda, S., et al. 2021, Nature Astronomy, 6, 241. doi:10.1038/s41550-021-01532-8
  * Newton et al. (2017) Newton, E. R., Irwin, J., Charbonneau, D., et al. 2017, ApJ, 834, 85. doi:10.3847/1538-4357/834/1/85
  * Nisak et al. (2022) Nisak, A. H., White, R. J., Yep, A., et al. 2022, AJ, 163, 278. doi:10.3847/1538-3881/ac63c3
  * Paredes et al. (2021) Paredes, L. A., Henry, T. J., Quinn, S. N., et al. 2021, AJ, 162, 176. doi:10.3847/1538-3881/ac082a
  * Passegger et al. (2018) Passegger, V. M., Reiners, A., Jeffers, S. V., et al. 2018, A&A, 615, A6. doi:10.1051/0004-6361/201732312
  * Pass et al. (2022) Pass, E. K., Charbonneau, D., Irwin, J. M., et al. 2022, ApJ, 936, 109. doi:10.3847/1538-4357/ac7da8
  * Popinchalk et al. (2021) Popinchalk, M., Faherty, J. K., Kiman, R., et al. 2021, ApJ, 916, 77. doi:10.3847/1538-4357/ac0444
  * van Saders & Pinsonneault (2012) van Saders, J. L. & Pinsonneault, M. H. 2012, ApJ, 751, 98. doi:10.1088/0004-637X/751/2/98
  * Reid et al. (1995) Reid, I. N., Hawley, S. L., & Gizis, J. E. 1995, AJ, 110, 1838. doi:10.1086/117655
  * Reiners & Basri (2009) Reiners, A. & Basri, G. 2009, A&A, 496, 787. doi:10.1051/0004-6361:200811450
  * Reiners et al. (2014) Reiners, A., Schüssler, M., & Passegger, V. M. 2014, ApJ, 794, 144. doi:10.1088/0004-637X/794/2/144
  * Reiners et al. (2018) Reiners, A., Zechmeister, M., Caballero, J. A., et al. 2018, A&A, 612, A49. doi:10.1051/0004-6361/201732054
  * Reiners et al. (2022) Reiners, A., Shulyak, D., Käpylä, P. J., et al. 2022, A&A, 662, A41. doi:10.1051/0004-6361/202243251
  * Reinhold & Hekker (2020) Reinhold, T. & Hekker, S. 2020, A&A, 635, A43. doi:10.1051/0004-6361/201936887
  * Scholz et al. (2007) Scholz, A., Coffey, J., Brandeker, A., et al. 2007, ApJ, 662, 1254. doi:10.1086/518361
  * Schönrich et al. (2010) Schönrich, R., Binney, J., & Dehnen, W. 2010, MNRAS, 403, 1829. doi:10.1111/j.1365-2966.2010.16253.x
  * Soderblom (1982) Soderblom, D. R. 1982, ApJ, 263, 239. doi:10.1086/160498
  * Somers et al. (2020) Somers, G., Cao, L., & Pinsonneault, M. H. 2020, ApJ, 891, 29. doi:10.3847/1538-4357/ab722e
  * Spada & Lanzafame (2020) Spada, F. & Lanzafame, A. C. 2020, A&A, 636, A76. doi:10.1051/0004-6361/201936384
  * Stepien (1994) Stepien, K. 1994, A&A, 292, 191
  * Taylor (2005) Taylor, M. B. 2005, Astronomical Data Analysis Software and Systems XIV, 347, 29
  * Tokovinin et al. (2013) Tokovinin, A., Fischer, D. A., Bonati, M., et al. 2013, PASP, 125, 1336. doi:10.1086/674012
  * Van der Walt, Colbert & Varoquaux (2011) van der Walt, S., Colbert, S.C., Varoquaux, G., 2011, Computing in Science & Engineering, 13, 22
  * Virtanen et. al. (2020) Virtanen, P., Gommers, R., Oliphant, T.E., et al., 2020, Nature Methods, 17, 261
  * Walkowicz et al. (2004) Walkowicz, L. M., Hawley, S. L., & West, A. A. 2004, PASP, 116, 1105. doi:10.1086/426792
  * Walkowicz & Hawley (2009) Walkowicz, L. M. & Hawley, S. L. 2009, AJ, 137, 3297. doi:10.1088/0004-6256/137/2/3297
  * Wallace et al. (2011) Wallace, L., Hinkle, K. H., Livingston, W. C., et al. 2011, ApJS, 195, 6. doi:10.1088/0067-0049/195/1/6
  * West et al. (2008) West, A. A., Hawley, S. L., Bochanski, J. J., et al. 2008, AJ, 135, 785. doi:10.1088/0004-6256/135/3/785
  * West et al. (2011) West, A. A., Morgan, D. P., Bochanski, J. J., et al. 2011, AJ, 141, 97. doi:10.1088/0004-6256/141/3/97
  * White & Hillenbrand (2004) White, R. J. & Hillenbrand, L. A. 2004, ApJ, 616, 998. doi:10.1086/425115
  * West et al. (2015) West, A. A., Weisenburger, K. L., Irwin, J., et al. 2015, ApJ, 812, 3. doi:10.1088/0004-637X/812/1/3
  * Wright & Eastman (2014) Wright, J. T. & Eastman, J. D. 2014, PASP, 126, 838. doi:10.1086/678541
  * Wright et al. (2018) Wright, N. J., Newton, E. R., Williams, P. K. G., et al. 2018, MNRAS, 479, 2351. doi:10.1093/mnras/sty1670
  * Zhang et al. (2021) Zhang, L.-Y., Meng, G., Long, L., et al. 2021, ApJS, 253, 19. doi:10.3847/1538-4365/abd7a8
  * Zhang et al. (2021) Zhang, S., Luo, A.-L., Comte, G., et al. 2021, ApJ, 908, 131. doi:10.3847/1538-4357/abcfc5