11institutetext:  Department of Space Research and Space Technology, Technical
University of Denmark, Elektrovej 328, 2800 Kgs. Lyngby, DK
11email<EMAIL_ADDRESS>22institutetext: Department of Astronomy,
University of Michigan, 1085 S. University Ave., 323 West Hall, Ann Arbor, MI
48109, US 33institutetext: Exoplanets and Stellar Astrophysics Lab, NASA
Goddard Space Flight Center, Greenbelt, MD 20771, US 44institutetext: Center
for Astrophysics and Space Astronomy, University of Colorado, 389 UCB,
Boulder, CO 80309, US 55institutetext: Department of Astrophysical and
Planetary Sciences, University of Colorado, 2000 Colorado Avenue, Boulder, CO
80309, US 66institutetext: Center for Astrophysics $|$ Harvard & Smithsonian,
60 Garden Street, Cambridge, MA 02138, US 77institutetext: Bridgewater State
University, 131 Summer St., Bridgewater, MA 02325, US 88institutetext:
Laboratory for Atmospheric and Space Physics, 1234 Innovation Drive, Boulder,
CO 80303, US 99institutetext: Max Planck Institute for Astronomy, Königstuhl
17, 69117 Heidelberg, DE 1010institutetext: Department of Astronomy, The
University of Texas at Austin, Austin, TX 78712, US 1111institutetext:
Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL
60637, US 1212institutetext: School of Information and Physical Sciences,
University of Newcastle, Callaghan, NSW, AU 1313institutetext: Southwest
Research Institute, 6220 Culebra Rd., San Antonio, TX 78238, US
1414institutetext: Department of Physics and Astronomy, Vanderbilt University,
Nashville, TN 37235, US 1515institutetext: Department of Astronomy, University
of Maryland, 4296 Stadium Drive, College Park, MD 20742, US 1616institutetext:
Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, NL
1717institutetext: SRON Netherlands Institute for Space Research, Niels
Bohrweg 4, 2333 CA Leiden, NL 1818institutetext: Hamburger Sternwarte,
Gojenbergsweg 112, D-21039, Hamburg, DE 1919institutetext: NHFP Sagan Fellow

# High-energy spectra of LTT 1445A and GJ 486
reveal flares and activity

H. Diamond-Lowe${}^{\href https://orcid.org/0000-0001-8274-6639}$ 11 G. W.
King${}^{\href https://orcid.org/0000-0002-3641-6636}$ 22 A.
Youngblood${}^{\href https://orcid.org/0000-0002-1176-3391}$ 33 A.
Brown${}^{\href https://orcid.org/0000-0003-2631-3905}$ 44 W. S.
Howard${}^{\href https://orcid.org/0000-0002-0583-0949}$ 551919 J. G.
Winters${}^{\href https://orcid.org/0000-0001-6031-9513}$ 6677 D. J.
Wilson${}^{\href https://orcid.org/0000-0001-9667-9449}$ 88 K.
France${}^{\href https://orcid.org/0000-0002-1002-3674}$ 445588 J. M.
Mendonça${}^{\href https://orcid.org/0000-0002-6907-4476}$ 11 L. A.
Buchhave${}^{\href https://orcid.org/0000-0003-1605-5666}$ 11 L.
Corrales${}^{\href https://orcid.org/0000-0002-5466-3817}$ 22 L.
Kreidberg${}^{\href https://orcid.org/0000-0003-0514-1147}$ 99 A. A.
Medina${}^{\href https://orcid.org/0000-0001-8726-3134}$ 1010 J. L.
Bean${}^{\href https://orcid.org/0000-0003-4733-6532}$ 1111 Z. K. Berta-
Thompson${}^{\href https://orcid.org/0000-0002-3321-4924}$ 55 T. M. Evans-
Soma${}^{\href https://orcid.org/0000-0001-5442-1300}$ 991212 C.
Froning${}^{\href https://orcid.org/0000-0001-8499-2892}$ 1313 G. M.
Duvvuri${}^{\href https://orcid.org/0000-0002-7119-2543}$ 1414 E. M.-R.
Kempton${}^{\href https://orcid.org/0000-0002-1337-9051}$ 1515 Y.
Miguel${}^{\href https://orcid.org/0000-0002-0747-8862}$ 16161717 J. S.
Pineda${}^{\href https://orcid.org/0000-0002-4489-0135}$ 88 C.
Schneider${}^{\href https://orcid.org/0000-0002-5094-2245}$ 1818

(Received)

The high-energy radiative output, from the X-ray to the ultraviolet, of
exoplanet host stars drives photochemical reactions and mass loss in the upper
regions of planetary atmospheres. In order to place constraints on the
atmospheric properties of the three closest terrestrial exoplanets transiting
M dwarfs, we observe the high-energy spectra of the host stars LTT 1445A and
GJ 486 in the X-ray with XMM-Newton and Chandra and in the ultraviolet with
HST/COS and STIS. We combine these observations with estimates of extreme
ultraviolet flux, reconstructions of the Ly$\alpha$ lines, and stellar models
at optical and infrared wavelengths to produce panchromatic spectra from 1
Å–20 $\mu$m for each star. While LTT 1445Ab, LTT 1445Ac, and GJ 486b do not
possess primordial hydrogen-dominated atmospheres, we calculate that they are
able to retain pure CO2 atmospheres if starting with 10, 15, and 50% of
Earth’s total CO2 budget, respectively, in the presence of their host stars’
stellar wind. We use age–activity relationships to place lower limits of 2.2
and 6.6 Gyr on the ages of the host stars LTT 1445A and GJ 486. Similar to
previous work, we find that optical observations fail to predict high-energy
activity: despite both LTT 1445A and GJ 486 appearing inactive at optical
wavelengths, we detect flares at ultraviolet and X-ray wavelengths for both
stars. In particular, GJ 486 exhibits two flares with absolute energies of
1029.5 and 1030.1 erg (equivalent durations of $4357\pm 96$ and $19724\pm 169$
s) occurring three hours apart, captured with HST/COS G130M. Based on the
timing of the observations, we suggest that these high-energy flares are
related and indicative of heightened flaring activity that lasts for a period
of days, but our interpretations are limited by sparse time-sampling.
Consistent high-energy monitoring is needed to determine the duration and
extent of high-energy activity on individual M dwarfs, as well as the
population as a whole.

###### Key Words.:

stars: low-mass — stars: flare — stars: activity — ultraviolet: stars —
ultraviolet: planetary systems — X-rays: stars

##  1 Introduction

The Kepler mission (Borucki et al., 2010), which operated from 2009–2013,
determined that small planets ($<4\ \mathrm{R_{\oplus}}$) are the most
abundant in the Galaxy (Fressin et al., 2013; Fulton et al., 2017). The
Transiting Exoplanet Survey Satellite (TESS, launched 2018 and continuing to
operate; Ricker et al., 2015) along with ground-based transit and radial
velocity facilities detect small planets orbiting our closest stellar
neighbors and determine the radii and masses of these worlds (e.g., Mayor et
al., 2003; Nutzman & Charbonneau, 2008; Quirrenbach et al., 2010; Mahadevan et
al., 2010; Cosentino et al., 2012; Gillon et al., 2013; Irwin et al., 2015;
Seifahrt et al., 2016; Schwab et al., 2016; Bouchy et al., 2017; Artigau et
al., 2014). Now, the James Webb Space Telescope (JWST, launched 2021) is
providing unprecedented insight into the atmospheres of small worlds (e.g.,
Lustig-Yaeger et al., 2023; Greene et al., 2023; Zieba et al., 2023; Moran et
al., 2023; Lim et al., 2023; May et al., 2023; Zhang et al., 2024).

A common thread among all small planets whose atmospheres we are currently
able to study with state-of-the-art observatories is that they orbit M dwarfs,
a stellar type with masses and radii below 0.6$\times$ that of the Sun and
effective temperatures below 3900 K. While the small sizes, low masses, and
large population of nearby M dwarfs allow for relative ease of small planet
detection, their extended pre-main-sequence phases, persistent activity and
flaring, and high-energy fluxes threaten to permanently alter or destroy the
atmospheres of those small planets (e.g., Segura et al., 2010; Seager &
Deming, 2010; Teal et al., 2022; Chen et al., 2021; Howard et al., 2023).

Stellar ultraviolet photons drive photochemistry in the upper atmospheres of
planets, where remote sensing techniques of exoplanet atmospheres, such as
transmission spectroscopy, are most sensitive. The first evidence for
photochemistry outside the solar system was recently detected in the
atmosphere of a hot Jupiter (Tsai et al., 2023), demonstrating the importance
of understanding complex photochemical reactions when interpreting planetary
atmospheres. The relative proportions of far- to near-UV (FUV=912–1700 Å;
NUV=1700–3200 Å) flux are particularly important for determining the balance
of molecular species, such as H2O, CH4, CO2, CO, O2, and O3, in planetary
atmospheres (Tian et al., 2014; Harman et al., 2015; Rugheimer et al., 2015).

High energy flux at X-ray (=1–100 Å) and extreme ultraviolet (EUV=100–912 Å)
wavelengths drives atmospheric mass loss and has the potential to completely
strip small planets of their primordial atmospheres (Lopez et al., 2012; Owen
& Wu, 2017). This process occurs during the highly-active saturation phase of
young stars on timescales of around 100 Myr (Lopez & Fortney, 2013; Owen & Wu,
2013), but mass loss from EUV photons may persist on Gyr timescales (King &
Wheatley, 2021), and complete atmospheric stripping can continue out to 10 Gyr
with active flaring (France et al., 2020). Small planets on tight orbits
around M dwarfs are also vulnerable to atmospheric stripping by stellar wind
(Cohen et al., 2015; Garraffo et al., 2016, 2017).

Results from the large MUSCLES program demonstrated that M dwarfs that are
similar in size, mass, and temperature, produce a range of fluxes in the UV,
making the scaling of one M dwarf’s high-energy flux to another highly
uncertain (France et al., 2016; Youngblood et al., 2017; Melbourne et al.,
2020). When determining whether or not a terrestrial planet retains an
atmosphere, having the exact high-energy output from its host M dwarf is
essential, as is work to determine its high-energy past. In this work we
provide a snapshot of the UV and X-ray outputs of the two closest M dwarfs to
host transiting terrestrial planets: LTT 1445A and GJ 486. To capture the high
energy spectra of these stars we use the unique spectral coverage and
resolving power of the Hubble Space Telescope, coupled with X-ray information
from XMM-Newton and Chandra. Both LTT 1445A and GJ 486 are considered to be
old, inactive M dwarfs based on their measured rotation periods and optical
activity indicators such as H$\alpha$ and Ca ii H & K. However, M dwarfs that
are quiet at optical wavelengths are known to flare at higher energies (e.g.,
Loyd et al., 2018; Jackman et al., 2024). A flare from LTT 1445A at X-ray
wavelengths has already been reported in Brown et al. (2022).

At the time of writing, there are two known planetary companions orbiting LTT
1445A and one planetary companion orbiting GJ 486 (Winters et al., 2019;
Trifonov et al., 2021; Winters et al., 2022; Caballero et al., 2022). All
three planets have masses and radii consistent with terrestrial bulk
compositions (Table 1). Ground-based optical transmission spectroscopy of LTT
1445Ab rules out solar-composition atmospheres down to 1 bar of surface
pressure (Diamond-Lowe et al., 2023). Ground-based high-resolution
transmission spectroscopy of GJ 486b rules out clear H/He-dominated
atmospheres as well as clear 100% water vapor atmospheres (Ridden-Harper et
al., 2023). JWST transmission spectroscopy of GJ 486b rules out much higher
mean molecular weight atmospheres at 1 bar of surface pressure (Moran et al.,
2023). The same JWST data may suggest a water-rich atmosphere on this planet,
however the interpretation of these results is degenerate with the presence of
star-spots in the transmission spectrum. Upcoming results from JWST emission
spectroscopy (GO 1743, PI Mansfield; and 2807 PI Berta-Thompson) and
transmission spectroscopy (GO 2515, PI Batalha) will provide further clues to
the atmospheric status of LTT 1445Ab and GJ 486b. To complete the atmospheric
picture of these planets we need measurements of the high energy spectra of
their host stars to pass to photochemical and mass loss models. Whether or not
these planet have atmospheres, and what those atmospheres or rocky surfaces
look like, depends on their high-energy stellar environments (Louca et al.,
2023).

The paper is laid out as follows: In Sect. 2 we provide information on the
observations that go into this work. In Sect. 3 we present the time series
analysis of our data. In Sect. 4 we put all of the measured and estimated flux
together to build a panchromatic spectrum of our targets. We provide an
analysis of detected flares in Sect. 5. We discuss our results as they pertain
to the planets orbiting LTT 1445A and GJ 486, as well as a discussion of M
dwarf ages and activity in Sect. 6. We conclude with Sect. 7. The resulting
spectra of LTT 1445A and GJ 486 are available for download as high level
science products (HLSPs) on the mstarpanspec page (doi:
10.17909/t9-fqky-7k61).

##  2 Observations

We observe the ultraviolet to optical spectra, from 1065–5700 Å, of the two
closest M dwarfs to host transiting terrestrial exoplanets, LTT 1445A and GJ
486. We use a combination of HST/COS and HST/STIS (GO 16722, PI H. Diamond-
Lowe and Co-PI G. King; GO 16701, PI A. Youngblood and Co-PI K. France) to
make these observations and achieve almost complete spectral coverage in this
range.

To capture the far-ultraviolet (FUV=912–1700 Å) we use COS/G130M with a
central wavelength of 1222 Å and COS/G160M with a central wavelength of 1533
Å. Using COS/G130M at 1222 Å places the Ly$\alpha$ line in the gap between the
A and B segments, which is required as part of the bright object protections
for COS. We capture near-ultraviolet (NUV=1700–3200 Å) flux using COS/G230L
with a central wavelength of 2950 Å. While COS provides higher sensitivity to
key transition region lines in the FUV and NUV, the segment gap in the
COS/G230L NUV spectrum is rather large, spanning 2113–2785 Å. To fill in this
gap we use STIS/G230L with a central wavelength of 2376 Å. In order to connect
the UV spectra to optical spectra, we take a brief observation with STIS/G430L
with a central wavelength of 4300 Å.

Though Ly$\alpha$ emission makes up about 85% of FUV flux for M dwarfs (France
et al., 2016), the bulk of the Ly$\alpha$ line core is absorbed by neutral
hydrogen in the interstellar medium before we can observe it. For nearby
bright M dwarfs it is possible to reconstruct Ly$\alpha$ flux from the
observed red and blue wings of the Ly$\alpha$ line (Youngblood et al., 2016),
but for most inactive M dwarfs it is prohibitively expensive to capture enough
signal in the wings of the Ly$\alpha$ line to perform a reconstruction. Though
LTT 1445A and GJ 486 are considered inactive M dwarfs, they are close enough
to capture enough Ly$\alpha$ flux in the wings of the Ly$\alpha$ profile to
perform the reconstruction. To make these observations we use STIS/G140M with
a central wavelength of 1222 Å and a narrow 52$\times$0.2′′ slit to avoid
geocoronal Ly$\alpha$ contamination, which is prevalent at Ly$\alpha$
wavelengths and would leak into the larger $2.5^{\prime\prime}$ aperture of
COS. For both targets we gather STIS/G140M data over three orbits, combining
observations from the GO 16701 and 16722 programs. These observations are
inspected separately but combined from the two GO Programs in order to boost
S/N for the Ly$\alpha$ reconstruction.

For the highest-energy part of the spectrum, we use X-ray data from XMM-Newton
and the Chandra X-ray Observatory. Chandra has the high spatial resolution
necessary to separate LTT 1445A from the more active LTT 1445BC binary
companion 7′′ away. With a PSF of 15′′ XMM-Newton cannot resolve LTT 1445A
from the companion stars. For LTT 1445A we use X-ray measurements from the
Chandra ACIS-S instrument described in Brown et al. (2022), as well as an
additional set of observations taken in 2023 (Obs IDs 23377, PI Brown; 27882,
PI Howard).

For GJ 486 we use XMM-Newton since it can provide broader spectral coverage in
the X-ray. We observed GJ 486 for 30 ks with XMM-Newton and the EPIC-pn camera
as part of GO 16722 (PI Diamond-Lowe, Co-PI King). The apparent visual
magnitude of GJ 486 is faint enough that we use all three EPIC cameras with
the thin optical blocking filters, and in full frame mode. We also make use of
the simultaneous Optical Monitor (OM) observation taken with the UVW1 filter,
however there were issues with these data, as outlined in Sect. 5.2. We also
obtained Chandra HRC-I data for GJ 486 (31.5 ks; Obs IDs 26210, 27799, 27942;
PI Youngblood) which provide additional measurements of the quiescent soft-X-
ray emission. All these instruments sample similar energy ranges between 0.1
and 10 keV (corresponding to a wavelength range of 1.2–120 Å), with lower
energy limits of 0.1, 0.16, and 0.3 keV for Chandra HRC-I, XMM-Newton, and
Chandra ACIS respectively. However, the Chandra ACIS detector has lost
significant sensitivity below 1 keV because of molecular contamination.

No currently operating observatory can capture extreme UV (EUV=100–912 Å) data
of our targets, however this wavelength range is critical for estimates of
atmospheric escape rates (King & Wheatley, 2021). We therefore use a
differential emission measure (DEM; Duvvuri et al., 2021) to estimate the EUV
flux from LTT 1445A and GJ 486 from measured flux at UV and X-ray wavelengths.

##  3 Time series of LTT 1445A and GJ 486

All HST data used in this work, with the exception of the STIS/G430L
observations, were taken in TIME-TAG mode, meaning that we can turn these
observations into time series. We use the *corrtag*.fits in the case of COS
and *tag*.fits files in the case of STIS, which have the time and detector
location of each detected photon. We present the resulting time series of LTT
1445A and GJ 486 in Figs. 1 and 2, respectively. Negative counts are due to
imperfect background subtraction.

We detect by eye one flare in the LTT 1445A COS/G160M data set and two flares
in the GJ 486 COS/G130M data set (shaded regions in Figs. 1 and 2). As in
Diamond-Lowe et al. (2021), we use the costools splittag and x1dcorr functions
to create our own x1d files that separate out the flare data from the
quiescent data. We combine all x1d quiescent data together to create our
panchromatic spectra (Sect. 4). Flare data from multiple flares are not
combined; each flare is processed separately to determine flare properties
(Sect. 5). We additionally detect what may be a small flare in the LTT 1445A
COS/G130M observations (top middle panel of Fig. 1), however our flare
analysis (discussed in depth in Sect. 5) does not find the flux to be
statistically different from the baseline flux. We do not exclude this data
from the spectral analysis.

Figure 1: Time series of LTT 1445A observations used in this analysis from GO
Programs 16722 and 16701 (program and visit number specified on right-hand
side), presented in chronological order. Count rates are provided in 1-second
time bins (light orange) and 1-minute time bins (dark orange). The instrument,
grating, and detector are given in the first panel of a set of exposures. The
shaded grey region shows a flare; these data are excluded from the
panchromatic spectrum (Sect. 4) but analyze the flare data separately in Sect.
5. Figure 2: Same as Fig. 1 but for GJ 486.

##  4 Panchromatic spectra of LTT 1445A and GJ 486

To produce panchromatic spectra of LTT 1445A and GJ 486 we combine HST UV
measurements, X-ray measurements from XMM-Newton and Chandra X-ray
Observatory, an estimation of the EUV output using the differential emission
measure (DEM) method, a reconstruction of the Ly$\alpha$ line, and an
extension of the spectra into the infrared with BT-Settl (CIFIST) models
(Allard et al., 2003; Caffau et al., 2011). Following previous works (France
et al., 2016; Loyd et al., 2016; Diamond-Lowe et al., 2021, 2022), we outline
the steps to producing our panchromatic spectra here. High level science
products are available on the mstarpanspec page of the MAST
archive111https://archive.stsci.edu/hlsp/mstarpanspec. In this section we work
only with the quiescent data, after having removed the flare data during the
time series analysis (Sect. 3). We provide stellar parameters used throughout
this work in Table 1.

Table 1: Parameters for the LTT 1445A and GJ 486 systems used in this work

Star | Unit | LTT 1445A | GJ 486
---|---|---|---
Distance | pc | $6.8638\pm 0.0012$ | $8.0791\pm 0.0021$
Radius | $R_{\odot}$ | $0.265^{+0.011}_{-0.010}$ | $0.328\pm 0.011$
Mass | $M_{\odot}$ | $0.257\pm 0.014$ | $0.323\pm 0.015$
$T_{\text{eff}}$ | K | $3340\pm 150$ | $3340\pm 54$
Planet |  | b | c | b
Radius | $R_{\oplus}$ | $1.305^{+0.066}_{-0.061}$ | $1.147^{+0.055}_{-0.054}$ | $1.305^{+0.063}_{-0.067}$
Mass | $M_{\oplus}$ | $2.87^{+0.26}_{-0.25}$ | $1.54^{+0.20}_{-0.19}$ | $2.82^{+0.11}_{-0.12}$
Density | g cm-3 | $7.1^{+1.2}_{-1.1}$ | $5.57^{+0.68}_{-0.60}$ | $7.0^{+1.2}_{-1.0}$
$a$ | AU | $0.03813^{+0.00068}_{-0.00070}$ | $0.02661^{+0.00047}_{-0.00049}$ | $0.01734^{+0.00026}_{-0.00027}$
$T_{\text{eq}}$ | K | $424\pm 21$ | $508\pm 25$ | $701\pm 13$
222Distance values are from Gaia Data Release 3 (Gaia Collaboration et al.,
2023), otherwise values for the LTT 1445A system are from Winters et al.
(2022) and values for GJ 486 are from Trifonov et al. (2021).

###  4.1 Ultraviolet

We directly measure the far- and near-UV output of LTT 1445A and GJ 486 with
HST/COS and STIS. Between these two instruments we have almost complete
coverage of the UV spectrum, with the exception of the Ly$\alpha$ line and
regions contaminated by geocoronal airglow.

Using a list of pre-identified geocoronal emission
lines333https://www.stsci.edu/hst/instrumentation/cos/calibration/airglow, we
identify contamination in our spectra from N i at 1134.980 Å and 1200 Å and
from O i at 1302–1307 Å and 1355.6 Å (Feldman et al., 2001). We zero-out flux
in regions where we identify airglow contamination in the stellar spectra. We
note that there are models and tools for modeling and removing contamination
from O i airglow lines at 1302–1307 Å (Bourrier et al., 2018; Cruz Aguirre et
al., 2023), however we find that modeling and removing the O i contamination
can introduce spurious flux into our spectra, while we see no evidence of
underlying stellar spectral features that need to be preserved.

We measure the flux in prominent UV transition region lines by fitting Voigt
models convolved with the COS line spread function (LSF) corresponding to the
the correct lifetime position for the data to each spectral line. To redefine
the LSF from pixels to wavelength we follow instructions in the STScI COS
Jupyter notebook on working with COS
LSFs444https://spacetelescope.github.io/COS-Notebooks/LSF.html. We use the
open-source pyspeckit (Ginsburg & Mirocha, 2011; Ginsburg et al., 2022) to
construct the Voigt model, and we estimate uncertainties in the model fit by
exploring the parameter space with the open-source dynesty nested sampler
(Speagle, 2020). For blended lines, such as C iii, we fit a combination of
Voigt models simultaneously. For lines with well-separated peaks, such as N v,
we fit each peak separately, and then sum them for further analysis. We
provide a sample of fitted line fluxes in Figs. 3 and 4.

Integrated surface fluxes are provided in Table 2 for LTT 1445A and Table 3
for GJ 486. We compute the surface fluxes as
$F_{\mathrm{Surf}}=F_{\mathrm{Obs}}\times\ (d/R_{\mathrm{s}})^{2}$, where
$F_{\mathrm{Obs}}$ is the integrated observed flux, $d$ is the stellar
distance, and $R_{\mathrm{s}}$ is the stellar radius. Values and uncertainties
for $d$ and $R_{\mathrm{s}}$ for each target are provided in Table 1. We
propagate the uncertainties in $d$ and $R_{\mathrm{s}}$ through to the
reported surface fluxes, however the resulting flux uncertainties are
dominated by fitting the convolved Voigt profiles to the data.

Figure 3: Sample of measured UV lines with fitted Voigt models for LTT 1445A.
The sample covers UV lines from all three COS gratings used (G130M, G160M, and
G230L). Lines that are blended, e.g., C iii and Mg ii are fit with combined
Voigt models, where as well-separated lines, e.g., N v and Si iv are fit with
individual models. Voigt models are made with pyspeckit (Ginsburg et al.,
2022) and we explore the model parameter space with dynesty (Speagle, 2020).
For lines  Figure 4: Same as Fig. 3 but for GJ 486. Table 2: Measured Emission
Lines from LTT 1445A with HST/COS

| Grating | Total Exposure Time | Line | Line Centersa | log10(Surface Flux)b | log10($T$)a
---|---|---|---|---|---|---
|  | (s) |  | (Å) | (erg cm-2 s-1) |
FUV | G130M | 7657 | C iii * | 1174.933, 1175.263, 1175.711, | $2.99\pm 0.12$ | 4.9
1175.987, 1176.37
Si iii * | 1206.555 | $2.85\pm 0.07$ | 4.8
N v * | 1238.821, 1242.804 | $2.99\pm 0.06$ | 5.3
Si ii * | 1264.738 | $1.99\pm 0.29$ | 4.5
C ii * | 1334.532, 1335.707 | $3.10\pm 0.06$ | 4.6
G160M | 6830 | O v | 1371.296 | $1.73\pm 0.66$ | 5.4
Si iv * | 1393.755, 1402.772 | $2.95\pm 0.14$ | 4.9
O iv | 1401.163 | $1.84\pm 0.64$ | 5.1
| C iv * | 1548.187, 1550.775 | $3.61\pm 0.09$ | 5.1
| He ii | 1640.474 | $3.20\pm 0.19$ | 4.9
|  |  | Al ii | 1670.788 | $2.89\pm 0.34$ | 4.5
NUV | G230L | 540 | Mg ii * | 2796.350, 2803.531 | $4.79\pm 0.08$ | 4.2

555Lines with $*$ are used to compute the DEM function (see Sect. 4.4 and Fig.
11).
a Values from CHIANTI database v10.1 (Dere et al., 2023)
bSurface fluxes (erg cm-2 s-1) are calculated by scaling the observed flux by
the distance $d$ and stellar radius $R_{\mathrm{s}}$ of LTT 1445A:
$F_{\mathrm{Surf}}=F_{\mathrm{Obs}}\times\ (d/R_{\mathrm{s}})^{2}$. For
multiple lines, we report the combined surface flux.

Table 3: Measured Emission Lines from GJ 486 with HST/COS

| Grating | Total Exposure Time | Line | Line Centersa | log10(Surface Flux)b | log10($T$)a
---|---|---|---|---|---|---
|  | (s) |  | (Å) | (erg cm-2 s-1) |
FUV | G130M | 7610 | C iii * | 1174.933, 1175.263, 1175.711, | $3.8\pm 0.07$ | 4.9
1175.987, 1176.37
Si iii * | 1206.555 | $3.04\pm 0.08$ | 4.8
N v * | 1238.821, 1242.804 | $3.27\pm 0.07$ | 5.3
Si ii * | 1264.738 | $2.58\pm 0.24$ | 4.5
C ii * | 1334.532, 1335.707 | $3.71\pm 0.06$ | 4.6
G160M | 6753 | O v | 1371.296 | $1.20\pm 0.51$ | 5.4
Si iv * | 1393.755, 1402.772 | $2.52\pm 0.12$ | 4.9
O iv | 1401.163 | $1.41\pm 0.54$ | 5.1
| C iv * | 1548.187, 1550.775 | $3.29\pm 0.07$ | 5.1
| He ii | 1640.474 | $2.74\pm 0.15$ | 4.9
|  |  | Al ii | 1670.788 | $2.6\pm 0.23$ | 4.5
NUV | G230L | 552 | Mg ii * | 2796.350, 2803.531 | $4.53\pm 0.08$ | 4.2

666Same as Table 2 but for GJ 486. DEM shown in Fig. 12.

###  4.2 Ly$\alpha$

The core of the Ly$\alpha$ line is attenuated by resonant scattering of
neutral hydrogen in the interstellar medium (ISM), however for bright enough
stars it is possible to measure the wings of the Ly$\alpha$ profile, and then
“reconstruct” the intrinsic Ly$\alpha$ line (Youngblood et al., 2016, 2021,
2022). An alternative method for stars not bright enough to perform the
reconstruction is to use known correlations between other UV lines to
“estimate” the Ly$\alpha$ flux (Youngblood et al., 2017; Diamond-Lowe et al.,
2021, 2022). LTT 1445A and GJ 486 are both bright enough to do a Ly$\alpha$
reconstruction, which we use in the panchromatic spectra. We also compare the
reconstructed Ly$\alpha$ flux to the estimated Ly$\alpha$ flux from UV-UV line
correlations.

We combine three STIS/G140M measurements and take a weighted average to build
up S/N for the Ly$\alpha$ reconstruction (Figs. 5 and 6). In the case of LTT
1445A, one of the three observations, from GO 16722 Visit 03, appeared to
contain about 1.5$\times$ the flux of the other two observations; we posit
that this additional flux may be associated with the flare that preceded the
observation by 48 hours (Fig. 1). A further discussion of prolonged stellar
activity can be found in Sect. 6.3.

Figure 5: Reconstruction of the intrinsic Ly$\alpha$ flux of LTT 1445A (grey)
using the best fit (light orange) to the measured wings of the Ly$\alpha$
profile observed with STIS/G140M (orange 1$\sigma$ error bars; Youngblood et
al., 2016).  Figure 6: Same as Fig. 5 but for GJ 486.

For comparison, we estimate Ly$\alpha$ flux for LTT 1445A from UV-UV line
correlations found in the MUSCLES sample (Youngblood et al., 2017). In
addition to demonstrating the ability of the UV-UV correlations to recover the
data-driven Ly$\alpha$ reconstruction, this method additionally provides a
useful comparison of the UV flux from transition region lines observed with
different COS gratings, which cannot be used simultaneously. As demonstrated
in Fig. 7, the UV-UV correlation values for Ly$\alpha$ estimated from
individual transition region lines agree well with each other, and the
resulting average Ly$\alpha$ estimate agrees well with the reconstructed
Ly$\alpha$ value. Similar to previous work (e.g., Diamond-Lowe et al., 2022),
we conservatively estimate the uncertainty of the individual Ly$\alpha$
estimates using the rms of the correlations from Youngblood et al. (2017), and
take the final estimate as the mean value and the mean uncertainty.

On the other hand, in the case of GJ 486, there is a potential discrepancy
between the UV-UV correlation values for Ly$\alpha$ from transition region
lines measured with the COS/G130M grating and those measured with the
COS/G160M and G230L gratings (Fig. 8). During observations with the COS/G130M
grating we detect two large flares (Fig. 2). These flares are removed from the
data and analyzed separately in Sect. 5, but the remaining “quiescent” data
may still represent an elevated activity state (more on this in Sect. 6.3).
The discrepancy between “quiescent” UV estimates of Ly$\alpha$ suggests that
we have not actually observed GJ 486 in true quiescence with the COS/G130M
grating. For the purposes of comparison with the Ly$\alpha$ reconstruction, we
only use the lines observed with COS/G160M and COS/G230L, which were observed
about a week after the COS/G130M observations. The UV-UV correlation values
for Ly$\alpha$ estimated from the COS/G160M and G230L lines agree with the
Ly$\alpha$ value at the 2$\sigma$ level.

The reconstructed Ly$\alpha$ profiles for LTT 1445A and GJ 486 are included in
the final panchromatic spectrum. Properties derived from the reconstruction
are provided in Table 4, along with a comparison to the UV-UV correlation
method.

Figure 7: Deriving the Ly$\alpha$ flux of LTT 1445A using a reconstruction
from the wings of the Ly$\alpha$ profile observed with the STIS/G140M grating
(orange 1$\sigma$ band; Youngblood et al., 2016) and using UV-UV line
correlations with other measured UV lines with the COS instrument (orange
points with 1$\sigma$ errors, and the average 1$\sigma$ grey band; Youngblood
et al., 2017; Diamond-Lowe et al., 2021, 2022). In the case of LTT 1445A we
find that individual transition region lines agree with each other, and with
the reconstructed value.  Figure 8: Same as Fig. 7 but for GJ 486. In this
case we find a discrepancy between the lines observed with COS/G130M and those
observed with COS/G160M and COS/G230L. It is possible that this discrepancy is
due to the large flares observed during the COS/G130M observations. We only
use lines observed with COS/G160M and COS/G230L (darker purple points with
1$\sigma$ errors) to estimate the Ly$\alpha$ flux with the UV-UV correlation
method. The Ly$\alpha$ values from the reconstruction and the UV-UV estimation
agree to within 2$\sigma$.  Table 4: Ly$\alpha$ values for LTT 1445A and GJ
486

| LTT 1445A | GJ 486
---|---|---
| Reconstruction from STIS/G140M
log10(Surface Flux) (erg/cm2/s) | $5.27^{+0.08}_{-0.06}$ | $4.88^{+0.04}_{-0.03}$
log10(N(H i)) (cm-2) | $17.8\pm 0.1$ | $17.8\pm 0.1$
H i radial velocity (km/s) | $13.2^{+3.4}_{-2.8}$ | $-18.1^{+1.3}_{-2.0}$
| Estimate from UV-UV Correlations
log10(Surface Flux) from Si iii (erg/cm2/s) | $5.37\pm 0.23$ | $5.48\pm 0.23$
log10(Surface Flux) from N v (erg/cm2/s) | $5.30\pm 0.35$ | $5.49\pm 0.35$
log10(Surface Flux) from Si ii (erg/cm2/s) | $5.02\pm 0.30$ | $5.52\pm 0.30$
log10(Surface Flux) from C ii (erg/cm2/s) | $5.48\pm 0.40$ | $5.84\pm 0.40$
log10(Surface Flux) from Si iv (erg/cm2/s) | $5.39\pm 0.38$ | $5.14\pm 0.38$
log10(Surface Flux) from C iv (erg/cm2/s) | $5.36\pm 0.32$ | $5.15\pm 0.32$
log10(Surface Flux) from He ii (erg/cm2/s) | $5.47\pm 0.32$ | $5.23\pm 0.32$
log10(Surface Flux) from Mg ii (erg/cm2/s) | $5.43\pm 0.19$ | $5.22\pm 0.19$
log10(Surface Flux) mean (erg/cm2/s) | $5.35\pm 0.31$ |  $5.19\pm 0.30$a
777Log surface fluxes calculated using distances and stellar radii from Table
1.
a For GJ 486 we find that lines measured with the COS/G130L grating give
systematically higher estimates of the Ly$\alpha$ flux. Given that two large
flares were removed from the data taken with this grating, it is possible that
the transition region lines we measure with COS/G130L are not completely
representative of a quiescent state. We therefore report the Ly$\alpha$
estimate from the UV-UV correlations only with lines in the G160M and G230L
gratings for LTT 1445A.

###  4.3 X-ray

Detecting X-ray flux for most inactive mid-to-late M dwarfs is challenging as
their apparent brightness at these wavelengths is typically faint. LTT 1445A
and GJ 486 are close enough that X-ray detections are possible. We use Chandra
to measure X-ray flux from LTT 1445A and both Chandra and XMM-Newton to
measure X-ray flux from GJ 486. We detect X-rays flares for both stars, which
are discussed in more detail in Sect. 5. Similar to the UV data, we remove the
flare points from the time-series X-ray data to measure quiescent X-ray flux
levels. The quiescent X-ray flux measurements are used to construct the
panchromatic spectra and inform the DEM estimate of the EUV (Sect. 4.4).
Quiescent and flare values from the X-ray observations are provided in Tables
5 and 6 for LTT 1445A and GJ 486, respectively.

For LTT 1445A we use Chandra observations published in Brown et al. (2022), as
well as a new set of observations presented here (Fig. 9, Table 5). The first
set of observations, obtained in 2021, distinctly show a flare. An extensive
analysis of this flare is reported in Brown et al. (2022) and we do not repeat
the process here. We observed LTT 1445A again on 2023 Aug 2 (Obs ID 27882, PI
Howard) and did not detect a flare. Estimation of X-ray flux parameters
involves spectral fitting using the XSPEC v12.12 software (Arnaud, 1996).
Count rates are converted to flux values in erg s-1 cm-2 using the best-fit
single-temperature VAPEC spectrum for an optically thin coronal plasma,
assuming a hydrogen column density of 1019 cm-2, sub-solar metallicities, and
stellar distance provided in Table 1. A full description of how we choose the
sub-solar abundances can be found in Sect. 4.3 of Brown et al. (2022). We take
the 2023 observations as representative of LTT 1445A’s typical X-ray state,
and divide the flux into three broad spectral bins for use in the DEM (Sect.
4.4). We use only the 2023 observations in the GJ 486 panchromatic spectrum.

For GJ 486 we are able to use XMM-Newton, which has better sensitivity at
lower energies. We observed GJ 486 for 32 ks on 2021 Dec 23 with the European
Photon Imaging Camera (EPIC). A few short periods of high background flaring
associated with energetic Solar protons are excluded (Walsh et al., 2014),
using the standard processes888As outlined in the SAS threads:
https://www.cosmos.esa.int/web/xmm-newton/sas-threads. Our extracted light
curves of GJ 486 are displayed in Fig. 10, with results for three different
energy bands: “full” (0.2–2.4 keV), “soft” (0.2–0.65 keV), and “hard”
(0.65–2.4 keV). These light curves show evidence of flares, which we describe
in more detail in Sect. 5.2.

We extracted separate EPIC-pn spectra for the quiescent epochs of the
observation and the biggest flare, which occurred halfway through the time
series. The S/N of the second peak was too low to warrant fitting, but this
section of the observation was excluded from the quiescent spectrum. We fit
the data using a two temperature APEC model, where the temperatures were
forced to be the same across the quiescent and flaring spectra, due to the
latter only containing five spectral bins. However their respective
normalizations are allowed to vary, such that the substantial change in the
spectral shape can be accounted for in the fit. We again use the same sub-
solar abundances from Brown et al. (2022) for these fits, noting that our best
fit fixes the Fe abundance, as this parameter becomes unconstrained when
allowed to vary. We use C-statistics when performing the fit (Cash, 1979).
From the best-fit model, we calculate the flux in several broad energy ranges
for use in reconstructing the DEM (Sect. 4.4).

We also have observations of GJ 486 using the Chandra HRC-I detector obtained
on 2023 Apr 4, Jul 13, and Jul 15. These observations appear to show quiescent
emission and the corresponding X-ray luminosity, and we estimate the emission
measures assuming a coronal temperature of 0.19 keV (2.2 MK)999See Brown et
al. (2023) for a discussion on quiescent M dwarf coronal temperatures, because
the HRC-I has minimal energy resolution and does not provide a temperature
directly.

Figure 9: X-ray observations of LTT 1445A using Chandra ACIS-S4. Observations
from 2021 (top panel) were already reported in Brown et al. (2022). The 2021
observations distinctly show a flare. We use the observations from 2023 (Obs
ID 27882, PI Howard) as representative of the typical X-ray state of LTT 1445A
(bottom panel). Figure 10: XMM-Newton EPIC light curve of GJ 486 from the 2021
Dec 23 observation. The count rates are coadded across the three EPIC cameras
(pn, MOS1 and MOS2). The three panels show the count rate in three bands:
0.2–2.4 keV (top), 0.2–0.65 keV (middle), 0.65–2.4 keV (bottom). Table 5:
X-ray Source Properties for LTT 1445A

| Chandra ACIS-S4
---|---
| 2021 | 2021 | 2023
| Quiescent | Flare | All
Exp. time (ks) | 12.2 | 6.66 | 29.75
Source counts (ct) | 4.9 | 177 | 50
Count rate (ct/ks) | 0.4 ± 0.2 | 26.6 ± 2.0 | 1.68 ± 0.25
X-ray Flux (10-13 erg/cm2/s) | 0.066 ± 0.033 | 3.61 ± 0.27 | 0.51 ± 0.08
Characteristic Temperature (keV) | 0.5a | 1.02$\pm$0.10 | 0.55$\pm$0.20
log10(LX) (erg/s) | 25.57${}^{+0.18}_{-0.30}$ | 27.31 ± 0.03 | 26.46 ± 0.04
101010Values from Brown et al. (2022). Log fluxes calculated assuming stellar
distance provided in Table 1.
a We assume this temperature from the measurement from the elevated flux post-
flare. It is in agreement with the 2023 observations.

Table 6: X-ray Source Properties for GJ 486

| XMM-Newton EPIC-pn | Chandra HRC-I
---|---|---
| Quiescent | Flare 1 | All
Energy range (keV) | 0.2–2.4 | 0.1–10
Wavelength range (Å) | 5.2–62 | 1.2–124
Obs ID (PI) | 0892010101 (Co-PI King) | 26210/27799/27942 (Youngblood)
Exp. time (ks) | 26.02 | 1.73 | 31.54
Source counts (ct) | 109±15 | 33.2±6.4 | 55.8 ± 7.8
Count rate (ct/ks) | 4.18±0.57 | 19.2±3.7 | 1.77 ± 0.25
X-ray Flux (10-14 erg/cm2/s) | $0.80^{+0.68}_{-1.64}$ | $4.35^{+0.61}_{-0.83}$ | 1.88 ± 0.27
Temperature 1 (keV) | $0.115^{+0.022}_{0.021}$ | 0.19 (assumed)
Temperature 2 (keV) | $0.783^{+0.097}_{0.099}$ | n/a
log10(LX) (erg/s) | $25.797^{+0.035}_{-0.099}$ | $26.531^{0.057}_{0.092}$ | 26.17 ± 0.07
111111The “Flare 1” spectrum also includes the underlying quiescent emission
at that epoch. The spectrum for the second flare had insufficient signal to
warrant fitting. Flux is the unabsorbed flux at Earth. Log luminosities
calculated assuming stellar distance provided in Table 1.

###  4.4 Extreme ultraviolet

There is no currently operating observatory that can detect extreme
ultraviolet (EUV = 100–912Å) flux from LTT 1445A and GJ 486. Energetic photons
approaching 912Å are increasingly absorbed by neutral hydrogen in the ISM,
making it nearly impossible to detect photons at 912Å for stars other than the
Sun. The Extreme-Ultraviolet Explorer (EUVE; Craig et al., 1997), which
functioned from 1992–2001, could measure EUV flux from nearby, highly
energetic stars, but neither LTT 1445A nor GJ 486 were observed by this
mission. Instead, in order to estimate the EUV flux from LTT 1445A and GJ 486,
we leverage the measured transition lines we detect in the UV, as well as the
X-ray measurements, in order to construct a DEM function for our targets.

The DEM method takes advantage of the fact that a smoothly varying function
with respect to temperature can be fit to the DEMs calculated for observed
emission lines in the data; the fitted function can then be used to back out
the flux we should measure from emission lines where no data are available,
such as those at EUV wavelengths. There are many examples of DEM applications
in stellar astrophysics (e.g., Kashyap & Drake, 1998; Sanz-Forcada et al.,
2003). Here we follow the application of the DEM method to cool dwarf stars
(Duvvuri et al., 2021), with several examples now available (e.g., Diamond-
Lowe et al., 2021, 2022; Wilson et al., 2021; Feinstein et al., 2022; Duvvuri
et al., 2023). The DEM method relies on several assumptions, for example that
each temperature component of the stellar atmosphere can be treated as an
optically thin plasma in collisional ionization equilibrium, which can limit
the method, but without another way to access the EUV spectra of inactive M
dwarfs, the DEM method is the current state-of-the-art for estimating EUV flux
for our targets. We note that it is also possible to estimate the EUV flux by
scaling from the Ly$\alpha$ line (Linsky et al., 2014) or the Si iv and N v
lines (France et al., 2018). Diamond-Lowe et al. (2021) found agreement
between these scaling methods and the DEM method for the inactive M dwarf LHS
3844. Here we opt for the DEM method because it utilizes measured flux across
the UV and X-ray.

Following methods outlined in Duvvuri et al. (2021) and improving upon code
developed in Diamond-Lowe et al. (2021) and Diamond-Lowe et al. (2022), we
construct a DEM for LTT 1445A and GJ 486. For each observed UV line and X-ray
band we calculate a “local DEM” that is the local average DEM value required
to reproduce the observed flux given the method’s assumptions. We use the
CHIANTI atomic database v10.1 to retrieve the maximum formation temperature
and emissivity contribution functions for each ion (Dere et al., 1997, 2023).
For the X-ray bands we use the CHIANTI database to find every ion that emits
in each band, and sum their emissivity contribution functions. We use the peak
of this summed function to determine a peak formation temperature. The
exception is the Chandra HRC-I observation for GJ 486, which does not have any
energy resolution, so we take the assumed coronal temperature of 2.2MK as the
peak formation temperature. We fit a 5th-order Chebyshev polynomial to the
local DEMs, and use the dynesty dynamic nested sampler to explore the
parameter space within the prior bounds. We set priors on the Chebyshev
polynomial coefficients as prescribed in Duvvuri et al. (2021), as well as
include the free parameter $s$ to characterize unknown systematic
uncertainties. The resulting DEM functions for LTT 1445A and GJ 486 are shown
in Figs. 11 and 12, respectively.

We note that because we do not have any measured EUV constraints for our
targets, it is likely that the fitted DEM will over-predict the EUV flux (Del
Zanna et al., 2002). This over-prediction is non-uniform and therefore cannot
be corrected with a simple scaling. Duvvuri et al. (2021) find an
overestimation by a factor of $\sim$5 for stars where they could compare
results with and without measured EUV DEMs. In the case of LTT 1445A and GJ
486 we do not have direct flux measurements at EUV wavelengths, so this error
is unavoidable and we cannot know how much the EUV flux is over-estimated in
our analysis. However, we do note that by sampling the parameters that
describe the DEM function, a lack of data increases the resulting uncertainty.
This is most apparent in the case of LTT 1445A where we do not have as much
temperature-coverage for the DEM function in the range of 6.0 $<$ log10($T$)
$<$ 6.5. The resulting LTT 1445A spectrum is more likely to suffer from the
over-prediction noted by Del Zanna et al. (2002), however the fitted DEM also
has a greater uncertainty, and so the EUV flux error of the resulting spectrum
encompasses a factor of 5 at the 1$\sigma$ level in almost all EUV flux bins,
and at the 2$\sigma$ level in all EUV flux bins.

Figure 11: Differential emission measures (DEM) with 1$\sigma$ uncertainties
derived from measured UV flux from HST/COS and X-ray flux from Chandra ACIS of
LTT 1445A. We show the 5th-order Chebyshev polynomial best fit to the local
DEMs along with shaded regions representing the 1$\sigma$ and 2$\sigma$
uncertainties for the fit. Figure 12: Same as Fig. 11 but for GJ 486. All
X-ray DEMs are derived from XMM-Newton observations, except for the single
point from Chandra HRC-I.

###  4.5 Optical and infrared

To fill in the optical and infrared end of the panchromatic spectra we use BT-
SETTL (CIFIST) models that cover the optical to infrared part of the spectrum
out to 20 $\mu$m (Allard et al., 2003, 2007, 2011, 2012, 2013; Barber et al.,
2006; Caffau et al., 2011) accessed from the Spanish Virtual Observatory
database repository121212http://svo2.cab.inta-csic.es/theory/main/ (Bayo et
al., 2008). The grid of stellar spectra are interpolated to the published
values of effective temperature $T_{\text{eff}}$ and surface gravity log($g$)
for LTT 1445A (Winters et al., 2019, 2022) and GJ 486 (Trifonov et al., 2021;
Passegger et al., 2019).

Blue-ward of $\sim$6000 Å model spectra of M dwarfs do not accurately re-
produce measured stellar flux (e.g., Fontenla et al., 2016). To determine how
reliably we can append a stellar model to the HST data, we compare the
STIS/G430L observations with spectral data from Gaia DR3
BP/RP131313https://gaia-dpci.github.io/GaiaXPy-website/
DOI v2.1.0: 10.5281/zenodo.8239995 (Gaia Collaboration et al., 2023), as well
as the interpolated stellar model. The STIS/G430L and Gaia data agree where
they overlap in wavelength. The interpolated BT-Settl (CIFIST) model broadly
agrees with the Gaia spectra down to $\sim$5500Å but at shorter wavelengths
the model over-predicts the amount of flux measured by HST/STIS G430L and Gaia
DR3 (Fig. 13).

We also compare interpolated stellar spectra from PHOENIX (Husser et al.,
2013) and SPHINX (Iyer et al., 2023) models, which also over-predict the
stellar flux at short wavelengths. This over-prediction of flux by stellar
models is one reason why having measurements from STIS/G430L out to 5700Å is
so valuable, especially for M dwarfs. We choose to use the BT-Settl (CIFIST)
models because the PHOENIX models do not extend far enough into the infrared
and the SPHINX models have less agreement with the Gaia and HST data. To
complete our panchromatic spectra, we append BT-Settl (CIFIST) models
interpolated to the parameters of LTT 1445A and GJ 486 to the red end of the
HST spectra.

Figure 13: Comparison of flux measured with HST/STIS and the G430L grating,
Gaia DR3 spectra, and model spectra from SPHINX (Iyer et al., 2023), PHOENIX
(Husser et al., 2013), and BT-Settl (Caffau et al., 2011) interpolated to the
published parameters of LTT 1445A. No relative scaling was performed. The
STIS/G430L and Gaia XP data agree where they overlap. We use the BT-Settl
model in the panchromatic spectrum.

###  4.6 Putting it all together

For both LTT 1445A and GJ 486 we provide panchromatic spectra representing the
quiescent state of each star. These spectra range from 1 Å–20 $\mu$m and are
available on the mstarpanspec high level science product (HLSP) page of the
MAST archive141414https://archive.stsci.edu/hlsp/mstarpanspec. As with
previous works, the panchromatic spectra are available in four different
versions:

  * •

Variable resolution reflecting different instrument and model resolutions

  * •

Constant resolution binned to 1 Å

  * •

Variable resolution, adaptively binned to remove negative flux

  * •

Constant resolution at 1 Å, adaptively binned to remove negative flux

Characteristic spectral properties for LTT 1445A and GJ 486 are provided in
Table 7, and panchromatic spectra are shown in Figs. 14 and 15.

Figure 14: Panchromatic spectrum of LTT 1445A from 1 Å–20 $\mu$ constructed
from empirical data in the X-ray, UV, and blue optical (HST/COS and STIS,
Chandra), estimates of the EUV (using the DEM method), a Ly$\alpha$ line
reconstruction, and models of the optical and infrared (BT-Settl). Figure 15:
Panchromatic spectrum of GJ 486 from 1 Å–20 $\mu$ constructed from empirical
data in the X-ray, UV, and blue optical (HST/COS and STIS, Chandra, XMM-
Newton), estimates of the EUV (using the DEM method), a Ly$\alpha$
reconstruction, and models of the optical and infrared (BT-Settl). Table 7:
Derived spectrum values

| Wavelength | LTT 1445A | GJ 486
---|---|---|---
log10($L_{\text{Bol}}$) | 1Å–20$\mu$m | 31.49 | 31.66
$f$(XUV) | 1–912Å | -3.45 | -4.55
$f$(FUV) | 912–1700Å | -4.33 | -4.64
$f$(XUVage) | 5–1700 | -3.40 | -4.30
$f$(NUV) | 1700–3200Å | -4.20 | -4.41
FUV/NUV | — | 0.75 | 0.58
Ly$\alpha$/FUV | — | 0.57 | 0.49
|  |  LTT 1445Ab |  LTT 1445Ac |  GJ 486b
FXUV,p (erg/cm2/s) | 1–912Å | $2.67\times 10^{3}$ | $5.49\times 10^{3}$ | $1.50\times 10^{3}$
151515We compute $f$(band) = log10($L_{\mathrm{band}}/L_{\mathrm{Bol}}$),
where $L_{\text{Bol}}$ is in units of erg s-1. The value FXUV,p is the
integrated XUV flux (1–912Å) received by each planet, assuming orbital
distance $a$ from Table 1. We provide the value $f$(XUVage) becuase it is used
to calculate stellar ages in Sect. 6.2 based on the XUV activity–age
relationship from Engle (2024).

##  5 Flare analysis

Both LTT 1445A and GJ 486 exhibit flares in the UV and X-ray observations.
These data are not simultaneous, nor do they cover the same wavelengths, so we
cannot determine broadband flare characteristics (e.g., flare temperatures;
Berger et al., 2023; Jackman et al., 2023). We also cannot compare the flare
energies between the UV and X-ray flares. We therefore address the UV and
X-ray flares separately.

###  5.1 UV flares

Following the works of Loyd & France (2014) and Loyd et al. (2018) we use the
costools package provided by STScI in order to flux-calibrate the time-series
data. We detect one partial flare from LTT 1445A with the COS/G160M grating
(Fig. 1). Unfortunately we did not catch the peak of this flare, only a
partial decay at the beginning of an orbit. Without any constraints on the
flare peak we cannot constrain the duration or energy of this flare, and we
therefore do not provide any further analysis.

In the HST observations of GJ 486 we see two flares, both with the COS/G130M
grating (Fig. 2). For the first flare we have data before, during, and after
the flare. The second flare is much larger and there is a gap in the data when
the flare starts due to a change in FP-POS, however we do capture the flare
peak. For neither flare do we observe a complete return to the pre-flare
quiescent flux level. For both of GJ 486’s flares we employ the continuous
flare model from Tovar Mendoza et al. (2022), which is an upgrade to the
piece-wise analytic model for classical flares from Davenport et al. (2014).
The Tovar Mendoza et al. (2022) flare model is a convolution of a Gaussian
function with the sum of two exponential functions. The choice of a Gaussian
function is physically motivated by the rapid rise in continuum emission, and
the double exponential describes the rapid and then more gradual decay back to
quiescence (Hawley & Pettersen, 1991; Kowalski et al., 2013; Hawley et al.,
2014; Davenport et al., 2014; Jackman et al., 2018, 2019).

Tovar Mendoza et al. (2022) provide an analytic flare model based on
photometric optical data from the Kepler survey. This analytic model can be
scaled by an amplitude, a characteristic timescale, and a central time to fit
to new flares. We find that the analytic model fits the first GJ 486 flare
reasonably well, but does not provide a good fit to the second, larger flare,
which appears to have a longer rise timescale. It is possible that because the
analytic model is derived using fits to optical flare data, it is not directly
applicable to flares at broad UV wavelengths (Berger et al., 2023). Feinstein
et al. (2022) also find that the analytic optical model does not match high-
energy UV flares detected from the active star AU Mic. We therefore determine
a new model fit to each flare following the methods in Tovar Mendoza et al.
(2022), rather than use the analytic form derived from Kepler photometry.

A full derivation of the flare model can be found in Tovar Mendoza et al.
(2022), so here we only reproduce the final flare equation, after the
convolution of the Gaussian and exponential functions has been applied:

$\text{Flare}(t)=\frac{\sqrt{\pi}AC}{2}\left[\begin{array}[]{l}F_{1}\left(\begin{array}[]{l}e^{-D_{1}t_{\text{rel}}+\left(\frac{B}{C}+\frac{D_{1}C}{2}\right)^{2}}\\\
\quad\times\
erfc\left(\frac{B-t_{\text{rel}}}{C}+\frac{D_{1}C}{2}\right)\end{array}\right)\\\\[21.52771pt]
\quad+\quad
F_{2}\left(\begin{array}[]{l}e^{-D_{2}t_{\text{rel}}+\left(\frac{B}{C}+\frac{D_{2}C}{2}\right)^{2}}\\\
\quad\times\
erfc\left(\frac{B-t_{\text{rel}}}{C}+\frac{D_{2}C}{2}\right)\end{array}\right)\\\\[4.30554pt]
\end{array}\right]$ (1)

where

  * •

$A$ is the flare amplitude;

  * •

$B$ is the central position of the Gaussian function;

  * •

$C$ is the Gaussian rise timescale;

  * •

$D_{1}$ is the rapid decay phase timescale;

  * •

$D_{2}$ is the slow decay phase timescale;

  * •

$F_{2}$ is defined as 1 – $F_{1}$, which describes the relative importance of
the exponential decay terms $D_{1}$ and $D_{2}$; and

  * •

$erfc$ is the complementary error function from scipy.special.

The flare model is a function of relative time $t_{\text{rel}}$, which is the
unitless value defined as

$t_{\mathrm{rel}}=\frac{t-t_{\mathrm{cen}}}{t_{1/2}}$ (2)

where $t$ is time, $t_{\text{cen}}$ is a central time that is close to the
time of the flare peak, though not exactly at the flare peak due to the
convolution, and $t_{1/2}$ is the characteristic timescale (Kowalski et al.,
2013). This scaling to a relative time is useful when fitting multiple flares
because the priors for the flare function variables only need to be defined
once, as opposed to being tailored to each flare.

Again following Tovar Mendoza et al. (2022), we determine the best-fit flare
model for each flare by performing the following steps:

  1. 1.

Subtract off the median out-of-flare flux such that the baseline is at 0.

  2. 2.

Fit the flare using the analytic flare model from Tovar Mendoza et al. (2022)
to determine initial flare scaling parameters: amplitude, central time, and
characteristic timescale.

  3. 3.

Scale the flare by the initial flare scaling parameters and fit for the flare
model variables $A$, $B$, $C$, $D_{1}$, $D_{2}$, and $F_{1}$.

  4. 4.

Fix the best fit flare model variables and then again fit for the flare
scaling parameters to get the best-fit flare model.

In both flare cases we do not capture enough data post-flare to see the flux
return to the nominal pre-flare flux level; we therefore only use the pre-
flare flux level to compute the median out-of-flare flux. We use the emcee
package built into the lmfit optimizing package to explore the parameter space
(Foreman-Mackey et al., 2013; Newville et al., 2016). We run the emcee for
50,000 steps with a 5,000 step burn in and determine convergence by checking
the integrated auto-correlation time. We report our best-fit values in Table
8.

To compare the two flares we detect from GJ 486 with those from other works
(e.g., Loyd et al., 2018), we use the best-fit flare model and the median out-
of-flare flux value to compute the absolute energy $E$ (the integrated flux
during the flare minus the quiescent flux) and equivalent duration $\delta$
(the flare energy normalized by the quiescent energy) for each flare, using
the standard equations for these values (Loyd et al., 2018). Because we do not
observe the return to the quiescent flux level after either flare, in both
cases we extend the best-fit model past the end of the observations in order
to compute the absolute energies and equivalent widths. We also compute flare
parameters from the best-fit flare models, such as time of the flare peak,
flare amplitude, and flare fwhm (Table 8).

Figure 16: We detect two flares in the time series of the COS/G130M data for
GJ 486. Dark purple points highlight the data that we consider to be “in
flare,” as opposed to the lighter purple “quiescent” data. Dark purple lines
are the best-fit flare models (Eqn. 1, Table 8), created from a continuous
flare model based on the work of Tovar Mendoza et al. (2022). The first flare
(Flare 1; top) has an absolute energy of 1029.5 erg cm-2 s-1 and an equivalent
duration of 4357$\pm$96 s, while the second flare (Flare 2; bottom) is larger,
with an absolute energy of 1030.1 erg cm-2 s-1 and an equivalent duration of
19724$\pm$169 s.  Table 8: GJ 486 flare properties

| Unit | Flare 1 | Flare 2
---|---|---|---
Wavelength range | Å | 1065–1367 | 1065–1367
Flare start–enda | s | 1730–2161 | 1300–2690
Flare durationa | s | 431 | 1390
Median quiescent flux | erg cm-2 s-1 | $9.02\times 10^{-15}$ | $8.89\times 10^{-15}$
|  | Flare model parameters
$t_{\text{cen}}$ | s | $1809.60\pm 0.80$ | $1438.22\pm 0.89$
$t_{1/2}$ | s | $36.2\pm 1.8$ | $89.6\pm 1.7$
$A$ | — | $1.28\pm 0.19$ | $1.50\pm 0.10$
$B$ | — | $-0.182\pm 0.041$ | $-0.164\pm 0.020$
$C$ | — | $0.364\pm 0.061$ | $0.536\pm 0.026$
$D_{1}$ | — | $0.015\pm 0.017$ | $0.226\pm 0.014$
$D_{2}$ | — | $1.16\pm 0.13$ | $1.8\pm 0.16$
$F_{1}$ | — | $0.0327\pm 0.0058$ | $0.0988\pm 0.0067$
|  | Derived flare properties
Time of peak flarea | s | $1814$ | $1457$
Flare amplitude | erg cm-2 s-1 | $2.34\times 10^{-13}$ | $8.36\times 10^{-13}$
FWHM | s | $47$ | $123$
Absolute energy ($E_{\text{COS/G130M}}$) | erg | $3.065\pm 0.068\times 10^{29}$ | $1.368\pm 0.012\times 10^{30}$
Equivalent duration ($\delta$) | s | $4357\pm 96$ | $19724\pm 169$
161616A description of the flare model parameters can be found in Sect. 5.1.
Derived flare properties are computed from the best-fit flare models.
a Flare times are relative to the observation start time. We do not observe
the start of Flare 2, so time values are approximate.

We additionally inspect how the two flares affect individual transition lines
in the FUV observed with the COS/G130M grating. Recall that at the start of
the analysis we removed time-series data containing the flares from the rest
of the observations used to make the panchromatic spectrum. We now use the
removed flare data to create FUV spectra and fit the line profiles of observed
transition region lines using the same methods as described in Sect. 4.1.

We compare the flux density of each line between the quiescent state and each
flare state (Fig. 17). The flare data are shown in purple, with purple lines
representing the best-fit Voigt line profiles convolved with the COS LSF.
These are compared to the best-fit line profiles from the quiescent data
(black lines). The transition region lines are ordered from lower to higher
formation temperatures. It is not surprising that the more energetic Flare 2
shows a larger increase in individual transition region lines than Flare 1.
Note that observations for Flare 2 used FP-POS 4, which does not cover the Si
iii line. The greatest increases in line flux are for lines forming at
intermediate temperatures of 4.5 $>$ log10(T) $>$ 5.0: C ii, Si iii, and C iii
(France et al., 2016; Loyd et al., 2018). In Flare 2 we also see emission from
the coronal FUV line Fe XXI at 1354 Å.

Figure 17: Transition region lines detected with COS/G130M for GJ 486 during
the two observed flares. The purple line profiles and fits are constructed
from data taken during the “in flare” phase of each flare. The black line
profiles are the quiescent states; they are the same quiescent profiles in the
top and bottom rows, but note the change in y-axes. Flare 2 was observed using
FP-POS 4, which misses the Si iii line at 1206.5Å.

###  5.2 X-ray flares

LTT 1445A flared during the 2021 Chandra observations and was analyzed in
detail in Brown et al. (2022). We reproduce the flare time series in Fig. 9,
along with the quiescent time series taken in 2023 and used in the
panchromatic spectrum in this work. The flare flux is about 55$\times$ greater
than the average quiescent level just prior to the flare, and about 7$\times$
greater than the quiescent level observed two years later in 2023. The
characteristic single-temperature fits to these spectra show significantly
hotter plasma present during the flare than in quiescence (see Table 5).

The LTT 1445A datasets obtained in ACIS VFAINT mode (Fig. 9) were tested for
source variability using the CIAO tool glvary171717glvary CIAO thread:
cxc.cfa.harvard.edu/ciao/threads/variable/. This tool searches for variability
using the Gregory-Loredo algorithm (Gregory & Loredo, 1992), which tests for
nonrandom grouping of the event times across multiple time bins. The glvary
tool is regularly used to test for variability in the major Chandra source
catalogs and provides a variability index (VARINDEX) which ranges from 0 to
10, with values of 5 or above indicating a variable source. The 2021
observation with its large flare has a VARINDEX of 10. The 2023 observation,
while less dramatic, is also definitely variable with a VARINDEX of 7. The
variability seen in the 2023 dataset seems to be typical for LTT 1445A.

For GJ 486 we catch flares with the XMM-Newton EPIC-pn camera, as shown in
Fig. 10. The biggest flare occurs about halfway through the observation, and
is clearly visible in the harder energies (bottom panel), with only a smaller,
non-significant rise in the soft band (middle panel). Our spectral fits in
Sect. 4.3 indicate a 5.5$\times$ increase in the overall flux during the
flare, with the bulk of that rise coming through an increase in the higher of
the two temperature components. This “hardening” of the X-ray emission is
typical of flares at these wavelengths (e.g., Reale et al., 2001; Pye et al.,
2015).

Two small peaks in the following $\sim$7 ks are also possibly associated with
flaring, with both rises only seen in the hard band and not the soft. The
first is not statistically above the basal level, and was not excluded from
the quiescent epoch in our spectral fits in Sect. 4.3. The peak of the second
does show a clear significant rise above the quiescent level. The signal was
too low to warrant fitting a separate spectrum, but this epoch was not
included the quiescent spectrum.

We attempted to search for evidence of the flaring in the simultaneous near-UV
data taken with the OM. Looking at the raw image mode count rates shows
evidence of a possible rise shortly after the midpoint of the observation.
However, the data also show major problems. While much of the background in a
single exposure shows $\sim$10 counts per pixel, there are many with $>$10,000
counts spread all across the image. While suggestive of guiding issues and/or
the source being too bright, there is still a source visible in the correct
position on the image, and the hallmarks of typical OM saturated sources are
not present. The problems seen in the OM data lead the later parts of the
standard reduction chains to fail. We do not consider this data further.

###  5.3 Flare frequency

Based on the observed flares and Poisson counting statistics we make rough
approximates of flare frequencies. Optical activity indicators suggest that
both LTT 1445A and GJ 486 can be considered inactive stars. From two sectors
of TESS data on GJ 486, a visual inspection does not reveal any flares. The
TESS photometric light curve for LTT 1445A is contaminated by an active binary
companion $7^{\prime\prime}$ away; there are many flares in the LTT 1445A TESS
light curve, but their origin is likely from LTT 1445B and C, and the three
components cannot be disentangled to determine the flare origins.

From the two GJ 486 flares observed in the FUV with the COS/G130M grating
(observations that lasted a total of 7610 s), we derive a flare frequency
$23\pm 5$ flares/day with absolute energy $E\geq 10^{29.5}$ erg and equivalent
duration $\delta\geq 4,300$ s. We can compare this estimate directly to work
by Loyd et al. (2018), who used observations with the same COS/G130M grating
to perform a statistical analysis of flares in sample of 10 active and
inactive M dwarfs. We find that the derived flare frequency for GJ 486 in this
work is similar to what we expect for typically active M dwarfs when comparing
absolute energies (Loyd et al., 2018). However, Loyd et al. (2018) demonstrate
that flare frequencies for inactive and active M dwarfs are statistically
indistinguishable when comparing flares in relative units, such as equivalent
duration. When comparing the derived flare frequency for GJ 486 to the Loyd et
al. (2018) sample we find that the supposedly inactive GJ 486 flares at a rate
of more than 10$\times$ that of the stars in the Loyd et al. (2018) sample.
For LTT 1445A we detect a flare, but because we cannot determine its energy or
duration, we cannot derive a UV flare rate.

The relationship between flare energy in the UV and X-ray is not well
established, with only limited information available regarding the relative
strengths of a single flare event across the electromagnetic spectrum
(MacGregor et al., 2021). Simultaneous observations in X-ray and FUV did
observe flares on Proxima Centauri and found a coherent increase in the
derived DEM corresponding to the X-ray and FUV regimes (Fuhrmeister et al.,
2022). While we do observe X-ray flares for both LTT 1445A and GJ 486, these
are not the counterparts to the UV flares, which were observed at different
times. The X-ray time series data are not flux-calibrated, meaning that we
cannot derive X-ray flare frequency rates.

##  6 Discussion

###  6.1 Planetary atmospheres

A driving motivation for capturing the high-energy flux from exoplanet-hosting
M dwarfs and producing self-consistent panchromatic spectra is to gain a
holistic understanding of their terrestrial planets’ atmospheres. High energy
flux from M dwarfs influence both photochemistry and atmospheric escape from
the upper atmospheres of orbiting planets (Catling & Kasting, 2017;
Kubyshkina, 2024). The photoevaporation theory of atmospheric evolution posits
that the terrestrial exoplanets we observe today may have started off with
primordial hydrogen-rich atmospheres that were subsequently lost due to
hydrodynamic escape (Owen & Wu, 2013; Lopez & Fortney, 2013; Luger et al.,
2015; Owen et al., 2020). Hydrodynamic escape is driven by the absorption of
stellar high energy radiation in the upper atmospheres of planets. As hydrogen
is driven away, it can drag heavier material along with it, leading to loss of
atomic and molecular species such as O, H2O, and CO2 (Zahnle & Kasting, 1986;
Pepin, 1991; Odert et al., 2018; Lammer et al., 2018). Photodissociation of
H2O can continuously fuel hydrodynamic escape, and in the extreme lead to
complete dessication of the planet (Luger & Barnes, 2015), as perhaps is the
case for Venus (e.g., Gillmann et al., 2009).

Early hydrodynamic escape is rapid, and can last from a few thousand years to
a few Myr after formation, depending on a planet’s initial water content and
atmospheric composition, and the stellar high energy flux. Hyrodynamic escape
can result in the complete loss of atmospheric atomic hydrogen, as well as
losses of a few to a few thousands of bars of heavier species, again depending
on the initial conditions. For example, in a study focused on the terrestrial
exoplanet TRAPPIST-1c orbiting a late-type M dwarf, Teixeira et al. (2024)
impose initial water contents of 0.01 to 100 Earth oceans on TRAPPIST-1c, and
find that hydrodynamic escape can last for 1000 years to 10 Myr resulting in a
loss of CO2 ranging from 0.1 to 1000 bars.

The measured radii and masses of the terrestrial planets LTT 1445Ab, LTT
1445Ac, and GJ 486b result in high bulk densities that are inconsistent with
H/He-rich atmospheres (Trifonov et al., 2021; Winters et al., 2022), and,
based on hydrodynamic escape models, we do not expect these worlds to
currently retain primordial H/He-dominated atmospheres accreted from the
protoplanetary nebula (Kubyshkina & Vidotto, 2021). It is possible, however,
that these worlds have secondary atmospheres consisting of heavier molecular
material than hydrogen that is not so easily lost. Secondary atmospheres can
arise from material that was sequestered in the mantle during formation and
outgassed later on timescales of a few Gyr (e.g., Marty & Dauphas, 2003), or
else delivered by comets or asteroids (Raymond et al., 2007; Ciesla et al.,
2015; O’Brien et al., 2018). Secondary atmospheres can still be sculpted and
removed by stellar wind, which is particularly relevant for terrestrial
exoplanets on short orbital periods around M dwarf stars (e.g., Garraffo et
al., 2017). It is also possible that LTT 1445Ab, LTT 1445Ac, and GJ 486b are
airless rocks (e.g., Kreidberg et al., 2019; Crossfield et al., 2022; Zieba et
al., 2023; Zhang et al., 2024).

To connect the measured X-ray and EUV radiation from the M dwarfs LTT 1445A
and GJ 486 to the atmospheric mass loss of their terrestrial exoplanets, we
employ a toy model following the steps of (Teixeira et al., 2024). We skip the
the rapid hydrodynamic escape phase since the mass loss is heavily dependent
on initial water content, for which we do not have accurate estimates, and it
is clear from radius-mass measurements that LTT 1445Ab, LTT 1445Ac, and GJ
486b do not have hydrogen-dominated atmospheres. We instead focus on whether
or not pure CO2 secondary atmospheres on these worlds can survive to the
present day in the presence of stellar wind, though atmospheres can also be
sculpted and stripped over long timescales via thermal processes such as Jeans
escape (Van Looveren et al., 2024). Our toy model does not include rates of
mantle outgassing or the possibility of magnetic fields on the planets, which
can shield atmospheres from stellar ions.

We use the X-ray luminosity–age relationship developed by Engle (2024) for
M2.5–6.5 dwarfs to get an estimate of the X-ray luminosity over time for the
two targets, up until their current estimated ages (details on stellar ages to
follow in Sect. 6.2). We then calculate the stellar mass loss rates following
Teixeira et al. (2024), who derive their stellar mass-loss rate relationship
from Wood et al. (2021):

$\dot{M_{\text{s}}}=\frac{\mathcal{A}}{10^{3.42}}F_{\text{X,surf}}^{0.77}$ (3)

where $\mathcal{A}$ is the stellar surface area in solar units, and
$F_{\text{X,surf}}$ is the X-ray surface flux of the star. The result is the
stellar mass loss rate in units of solar mass loss rate, which we take as
$1.26\times 10^{12}\,\text{g/s}$.

From the stellar mass loss rate we calculate the planetary atmospheric mass
loss rate due to stellar wind stripping as

$\dot{M}_{\text{atm}}=0.025\left(\frac{R_{\text{p}}}{a}\right)^{2}\dot{M_{\text{s}}}$
(4)

where $R_{\text{p}}$ is the planetary radius and $a$ is the planetary semi-
major axis (Dong et al., 2018; Teixeira et al., 2024). The factor of 0.025 is
borrowed from the TRAPPIST-1 system because we do not have MHD models of LTT
1445A or GJ 486, however they are also M dwarfs and their planetary orbital
distances are similar to those of the TRAPPIST-1 planets (Agol et al., 2021).

When executing the toy models we assume pure CO2 atmospheres for LTT 1445Ab,
LTT 1445Ac, and GJ 486b, since CO2 is a common atmospheric molecule with
advantages for atmospheric retention: it has a high mean molecular weight and
a rapid cooling timescale that makes it resilient to thermal escape (Gordiets
& Kulikov, 1985; Johnstone et al., 2021; Van Looveren et al., 2024). For each
planet we start with a pure CO2 atmosphere equal to 5–50% of Earth’s total
estimated CO2 budget of 1022 mol (Sleep & Zahnle, 2001; Foley & Smye, 2018).
Though we do not take into account outgassing rates, Teixeira et al. (2024)
find that most of the outgassing takes place in the first Gyr. For each time
step, we compute the planetary atmospheric mass loss rate from the stellar
mass loss rate, and subtract the result from the remaining CO2 in the
atmosphere.

Figure 18: Results of the toy model describing CO2 mass loss from each
terrestrial planet, assuming initial atmospheres of pure CO2 5–50% that of
Earth’s total estimated CO2 content of $10^{22}$ mol (Sect. 6.1). The vertical
orange and purple lines, along with the shaded regions, are the estimated
stellar ages with uncertainties (discussed in Sect. 6.2). Whether or not each
planet maintains a CO2 atmosphere with surface pressure of $\gtrapprox 1$ bar
depends on the initial CO2 content, the planetary orbital period, and the
stellar age and activity history. The model does not take into account CO2
outgassing rates—we assume all of the CO2 outgasses at the start of the model
time steps—or magnetic fields, which may be able to shield secondary
atmospheres from loss.

We present the results of our toy model in Fig. 18. Whether or not the planets
LTT 1445Ab, LTT 1445Ac, and GJ 486b, can retain CO2-rich atmospheres is
dependent on their initial atmospheric CO2 content, their orbital distances,
and the age of their host stars. So long as LTT 1445Ab has an initial CO2
budget of at least 10% that of Earth’s, it should be able to maintain a CO2
atmosphere of at least 1 bar of surface pressure. LTT 1445Ac, which orbits
closer to the host star, needs at least 15% of Earth’s CO2 budget to maintain
an atmosphere of almost 1 bar of surface pressure. Finally, GJ 486b orbits the
closest to its host star, making its atmosphere the most susceptible to loss;
GJ 486b needs an initial CO2 content of at least 50% of Earth’s current CO2
content to maintain a CO2-rich atmosphere of at least 1 bar of surface
pressure.

Without knowing the initial compositions of LTT 1445Ab, LTT 1445Ac, and GJ
486b or the activity history of their host stars, we cannot know a priori
whether or not they have atmospheres today. Determining whether or not these
planets have atmospheres can place upper limits on their initial water
contents (e.g. Kreidberg et al., 2019). One scaling relation called the
“cosmic shoreline” compares the (estimated) cumulative XUV radiation received
by a planet and its escape velocity under assumptions of energy-limited escape
(Zahnle & Catling, 2017). All three planets considered in this work lie close
to the $I_{\text{XUV}}\propto v_{\text{esc}}^{4}$ relationship, implying that
all three planets have undergone hydrogen-stripping but are not necessarily
bare rocks. Observational programs looking at LTT 1445Ab and GJ 486b in
secondary eclipse with JWST/MIRI LRS spectroscopy (GO Program 1743, PI
Mansfield; and 2807 PI Berta-Thompson) and in transmission with JWST/NIRSpec
BOTS (GO Program 2512, PI Batalha) may soon provide the answer for these two
worlds.

###  6.2 Stellar ages

It is notoriously difficult to determine the ages of M dwarfs. They spend
hundreds of Gyr on the main sequence (Choi et al., 2016), and once they are
stably fusing hydrogen in their cores, their measurable properties like
luminosity, effective temperature, and radius remain constant on cosmological
timescales; in other words, longer than the age of the universe. This means
that stellar evolutionary models are poor predictors of M dwarf age, even with
well-constrained stellar properties in the Gaia era (Gaia Collaboration et
al., 2016, 2023; Eastman et al., 2023).

One promising avenue is to apply the age–rotation or age–activity
relationships that exist for main sequence stars, and set constraints
specifically for M dwarfs (Wright & Drake, 2016; Wright et al., 2018). The
fact that older main sequence stars have longer rotation periods and decreased
activity relative to younger main sequence stars is well-documented (e.g.,
Schatzman, 1962; Skumanich, 1972; Barnes, 2003; Newton et al., 2016; Pineda et
al., 2021). Using a series of dating methods to pinpoint the ages of a
precious sample of M dwarfs, Engle & Guinan (2023) establish age–rotation
relationships for early- to mid-M dwarfs, which are then expanded to
age–activity relationships (Engle, 2024). Here we apply some of these
relationships to LTT 1445A and GJ 486.

Both LTT 1445A and GJ 486 have long rotation periods: $85\pm 22$ and $130.1\pm
1.6$ days, respectively (Trifonov et al., 2021; Winters et al., 2022); and low
activity: only weak measurements of H$\alpha$ and Ca ii H & K (Astudillo-Defru
et al., 2017; Hojjatpanah et al., 2019; Winters et al., 2019). These long
rotation periods and weak activity indicators broadly put LTT 1445A and GJ 486
in the category of “old, inactive” M dwarfs, but here we attempt to derive
more quantitative ages. Using the age–rotation relationships for M2.5–6.5
dwarfs with rotation period greater than 24 days, we estimate that the ages of
LTT 1445A and GJ 486 are $5\pm\text{Univ}$ and $7.8\pm 4.8$ Gyr, respectively
Engle & Guinan (2023), where we use the limit of “Univ” to mean that the
uncertainties extend to the age of the universe. We also note that additional
work on GJ 486 finds a significantly shorter stellar rotation period of
$49.9\pm 5.5$ days (Caballero et al., 2022), which translates to a stellar age
of $3.7^{+5.1}_{-\text{Univ}}$ (Engle & Guinan, 2023).

The unconstrained age of LTT 1445A is due to the difficulty in measuring its
rotation period; the value of $P_{\text{rot}}=85\pm 22$ is derived from the
mass-rotation period relation for inactive M dwarfs (Newton et al., 2017). LTT
1445A is the primary member of a hierarchical stellar triple, with a binary
pair roughly 7′′ away. The binary stars are more active and have rapid
rotation periods, making it difficult to distinguish the much longer rotation
period of LTT 1445A (Winters et al., 2022). Based on an analysis of galactic
kinematics and flare rates of a volume complete sample of mid-to-late M
dwarfs, (Medina et al., 2022) determine broad age bins based on stellar
rotation period: mid-to-late M dwarfs with $10<P_{\text{rot}}<90$ days are
$5.6\pm 2.7$ Gyr, and those with $P_{\text{rot}}>90$ days are $12.9\pm 3.5$
Gyr. These age-bin estimates agree with those found using the age–rotation
relation from Engle & Guinan (2023).

We are better able to constrain the ages of LTT 1445A and GJ 486 using their
high-energy spectra and age–activity relationships (Engle, 2024). We opt to
use the log($L_{\text{X-UV (5--1700\AA)}}/L_{\text{bol}}$) activity–age
relation because this is the best defined in terms of wavelength range. We
integrate the panchromatic spectra from 5–1700 Å and find that LTT 1445A has
an age of $3.7^{+\text{Univ}}_{-1.5}$ Gyr and GJ 486 has an age of
$10.5^{+\text{Univ}}_{-3.9}$ Gyr. The upper and lower bounds of the stellar
age are conservative: we take the integrated X-UV (5–1700Å) flux plus and
minus 1$\sigma$ errors on the panchromatic spectrum and compare these against
the 1$\sigma$ errors in the activity–age relationship from Engle (2024). We
take the outer-most ages that take into account the uncertainty in the
integrated spectrum and the activity–age relation. We place lower limits on
the ages of LTT 1445A and GJ 486 at 2.2 and 6.6 Gyr, respectively.

Conservatively, we cannot put an upper bound on the age of LTT 1445A and GJ
486, however the $1\sigma$ lower age bounds are still useful. For example,
based on their flare-rate analysis as a function stellar rotation period,
Medina et al. (2022) determine a transition age for mid-to-late M dwarfs from
a saturated to unsaturated flaring state at $2.4\pm 0.3$ Gyr, though we note
that this result is based on optical flares in the TESS data. If this
transition age is true for UV flares, then GJ 486 is in a state of decreased
activity and relatively low flaring, while LTT 1445A may be in the process of
transitioning between the saturated and decreasing activity states. The UV
flare rate we deduce for GJ 486 is significantly higher than what we expect
for an inactive star, suggesting that high-energy flare rates may remain high
as optical flare rates decrease.

###  6.3 Evidence of prolonged elevated activity

We do not have access to long-term high-cadence monitoring of a large sample
of inactive M dwarfs at high-energy wavelengths. Rather, what we present here
are high-cadence observations in spurts from HST. Based on these non-
contiguous observations, we posit that supposedly “inactive” M dwarfs like LTT
1445A and GJ 486 not only produce more high-energy flares per day than in the
optical, but also that those flares produce prolonged periods of heightened
flux output, perhaps lasting as long as several days, and may be the result of
observing during a high-activity period. Here we present evidence for this
conjecture.

We look first at GJ 486 because for this star we observe two flares and are
able to model them and derive their absolute energies and equivalent
durations. It is well-documented that stars that are considered inactive at
optical wavelengths still flare in the FUV (Loyd et al., 2018; Froning et al.,
2019; Loyd et al., 2020; Diamond-Lowe et al., 2021; Jackman et al., 2024). The
star GJ 674 is considered inactive with a rotation period of 30 days, no
H$\alpha$ in emission, and an approximate age of 0.1 to a few Gyr (Bonfils et
al., 2007; Newton et al., 2018), and yet multiple flares, the largest having
an absolute energy of $E=10^{30.75}$ erg and an equivalent duration of
$>30,000$ s, were observed up by HST COS/G130M (Froning et al., 2019). By
comparison, GJ 486 has an even longer rotation period of 130 days and a lower
age limit of 6.6 Gyr, and two flares with absolute energies $E=10^{29.5}$ and
$E=10^{30.1}$ erg and equivalent durations of $4357\pm 96$ and $19724\pm 169$
s were observed with the same grating within three hours. Old and quiet M
dwarfs like GJ 486 can still produce high energy flares, but what is
surprising is that we derive a flare frequency roughly 10$\times$ that of the
broader M dwarf population (Loyd et al., 2018), with the caveat that we are
very much in the regime of small sample statistics based on the limited time-
sampling of our observations. We find it more plausible that we caught GJ 486
in a period of heightened flare activity than this being the true flare
frequency for this star.

We additionally posit that this period of heightened activity in GJ 486 lasts
at least a week. We observed the two flares from GJ 486 in the same HST visit,
only three hours apart (Fig. 2), perhaps suggesting that both flare events
originate from the same activated region of the stellar surface. We showed in
Sect. 4.2 and Fig. 8 that even after removing the flare data from the
COS/G130M observations, the UV-UV line correlations with Ly$\alpha$ suggest
that lines measured from the “quiescent” time series were in fact excited. The
next set of UV observations of GJ 486 taken six days later with COS/G160M and
COS/G230L, also appear systematically higher that what we estimate for the
Ly$\alpha$ flux using the reconstruction method (Youngblood et al., 2016). The
STIS/G140M observations that provide the data for the Ly$\alpha$
reconstruction were taken almost exactly one year apart—three months before
the COS/G130M observations were we observe the flares and eight months after
the COS/G160M and COS/G130M observations—yet they agree incredibly well. Our
final line of evidence for prolonged activity comes from the LTT 1445A data,
where we observed the tail end of a flare with COS/G160M. We do not know how
big this flare was, but two days later we observed LTT 1445A with STIS/G140M,
and this observation gives 1.5$\times$ higher flux than STIS/G140M
observations taken six weeks before (Fig. 1). It is of course also possible
that these older M dwarfs might exhibit sporadic rather than periodic
activity. Indeed, previous searches did not find strong evidence for
persistent flare periodicity in TESS data, though short-term periodic cycles
may exist (Howard & Law, 2021).

If there are indeed times of heightened stellar activity, whether periodic or
not, in older quiet M stars, this affects our ability to determine their ages
based on age–activity relations. X-ray and UV measurements of stars generally
come from a handful of observations. Wherever a star happens to be in its
activity cycle when we observe it will affect the resulting estimated age when
using age–activity relations. A good example of this are the three X-ray
states—“quiescent,” “flare,” and “elevated”—of LTT 1445A reported by Brown et
al. (2022), and the resulting placement of the star on the X-ray–age
relationship based on each state (Fig. 4 of that paper). Poor time-sampling of
high-energy stellar observations are likely contributing to the scatter in the
activity–age relationships at both X-ray and UV wavelengths.

Ultimately, we have exhausted the detective work we can do with our non-
contiguous and non-overlapping observations. Additional HST campaigns to
capture more flares are risky—even with these observations, LTT 1445A and GJ
486 do not flare as reliably as a younger, truly active stars like AU Mic
(Feinstein et al., 2022). What is needed is a space mission with a high-energy
monitoring campaign of a large catalog of M dwarfs. Consistent time-sampling
of M dwarfs at high energy would allow us to determine the periodic nature of
activity on older, quiet stars, as well as tighten constraints on
age–activity–rotation relationships for M dwarf stars, which would in turn
provide the most accurate stellar ages we are likely to get for these long-
lived low-mass stars.

There are proposed missions to monitor large samples of stars, including M
dwarfs, in the X-ray (Advanced X-ray Imaging Satellite, or AXIS; Corrales et
al., 2023) and the EUV (Extreme-ultraviolet Stellar Characterization for
Atmospheric Physics and Evolution, or ESCAPE; France et al., 2022). The ESCAPE
mission in particular has the goal of EUV monitoring for a sample of M dwarfs
with direct application to understanding terrestrial exoplanet atmospheres and
the impacts of stellar variability on those atmospheres. The impact of M dwarf
activity on observations of terrestrial exoplanets is becoming increasingly
important in the JWST era due to stellar contamination of transmission spectra
(e.g., Lustig-Yaeger et al., 2023; Moran et al., 2023; May et al., 2023; Lim
et al., 2023). It will take a statistical monitoring survey of M dwarfs at
high-energy to push our understanding M dwarf activity periodicity, ages, and
impact on terrestrial exoplanet atmospheres to the point where we can
eventually answer questions of exoplanet habitability.

##  7 Conclusions

In this work we combine data from HST COS and STIS (GO Programs 16722 and
16701), XMM-Newton (ObsID 23377), and Chandra (ObsIDs 23377, 27882, 26210,
27799, 27942), as well as interpolated BT-Settl (CIFIST) models to produce
self-consistent panchromatic spectra of LTT 1445A and GJ 486 from 1Å–20$\mu$m.
To fill in an observational gap at EUV wavelengths we use the DEM method to
estimate EUV flux (Duvvuri et al., 2021), and we use the wings of the
Ly$\alpha$ line to reconstruct the full profile (Youngblood et al., 2016).

Both LTT 1445A and GJ 486 are considered inactive based on the long rotation
periods and optical activity indicators, but we detect flares in both stars at
UV and X-ray wavelengths, suggesting a flare frequency rate higher than
predicted for inactive stars. The flare frequency distribution we derive from
the two UV flares detected from GJ 486 based on their equivalent durations is
$\sim$10$\times$ larger than the larger population of active and inactive M
dwarfs (Loyd et al., 2018), despite the fact that this star is optically quiet
(Trifonov et al., 2021). The high-energy activity we see in both M dwarfs,
despite a lack of activity from optical indicators, continues the conclusions
of previous works that optical observations fail to predict high-energy
activity (Loyd et al., 2018; Jackman et al., 2024). We consider that this
high-energy activity is variable, and may not be captured in a single
measurement. A lack of high-energy monitoring of M dwarfs is therefore
preventing us from seeing the bigger activity picture. We do not know whether
the high-energy activity we observe is periodic or sporadic. Only taking
snapshots of stars at high-energy will also contaminate age–activity
relations, which are some of the best ways to constrain M dwarf ages (Wright &
Drake, 2016; Engle, 2024).

Variable high-energy activity will also affect our interpretation of planetary
atmospheres. LTT 1445Ab, LTT 1445Ac, and GJ 486b have lost any primordial
hydrogen-dominated atmospheres they may have had, but higher mean molecular
weight secondary atmospheres are still possible. Efforts to determine the
atmospheric status of a sample of terrestrial exoplanets orbiting M dwarfs is
underway (e.g., the Hot Rocks Survey, JWST GO Program 3730; PI H. Diamond-
Lowe, Co-PI J. M. Mendonça), with a top recommendation by the Working Group on
Strategic Exoplanet Initiatives with HST and JWST to “understand the
prevalence and diversity of atmospheres on rocky-M dwarf worlds” (Redfield et
al., 2024). As noted by the working group report, detecting and characterizing
terrestrial exoplanet atmospheres must go side-by-side with characterizing
their M dwarf hosts. Measuring and monitoring high-energy flux from M dwarf is
the next step to determining the ages, mass loss rates, and activity cycles of
these key exoplanet hosts.

###### Acknowledgements.

This paper includes data gathered with the Cosmic Origins Spectrograph and the
Space Telescope Imaging Spectrograph on board the Hubble Space Telescope. This
research has used data obtained by the Chandra X-ray Observatory and software
provided by the Chandra X-ray Center (CXC) in the CIAO application package. We
make use of the CHIANTI database and open-source python code. CHIANTI is a
collaborative project involving George Mason University, University of
Michigan (USA), University of Cambridge (UK), and NASA Goddard Space Flight
Center (USA). This publication makes use of VOSA, developed under the Spanish
Virtual Observatory (https://svo.cab.inta-csic.es) project funded by
MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00. VOSA has
been partially updated by using funding from the European Union’s Horizon 2020
Research and Innovation Programme, under Grant Agreement no. 776403
(EXOPLANETS-A). 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. This job has made use of the
Python package GaiaXPy, developed and maintained by members of the Gaia Data
Processing and Analysis Consortium (DPAC), and in particular, Coordination
Unit 5 (CU5), and the Data Processing Centre located at the Institute of
Astronomy, Cambridge, UK (DPCI). We thank Thea Kozakis for participation in
the proposal for GO Program 16722, and Daria Kubyshkina for a helpful
discussion of hydrodynamic mass loss. We thank the anonymous referee for their
comments, which led to improvements in this paper. H.D.-L. acknowledges
support from the Carlsberg Foundation, grant CF22-1254. G.W.K. and L.C.
acknowledge support through NASA grant HST-GO-16722.002-A. A.Y. acknowledges
support through NASA grant HST-GO-16701.001-A administered by Space Telescope
Science Institute. A.B. acknowledges Chandra grants GO1-22005X and GO2-23002X
to the University of Colorado. Y.M. acknowledges funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement no. 101088557, N-GINE). C.S.
acknowledges grant DLR 50 OR 2205.
Facilities used in this work are: HST (STIS, COS); CXO (ACIS, HRI); XMM-Newton
(EPIC).
Software used in this work: astropy (Price-Whelan et al., 2018); CIAO
(Fruscione et al., 2006); dynesty (Speagle, 2020); emcee (Foreman-Mackey et
al., 2013); lmfit (Newville et al., 2016); XSPEC (Arnaud, 1996)

## References

  * Agol et al. (2021) Agol, E., Dorn, C., Grimm, S. L., et al. 2021, , 2, 1
  * Allard et al. (2007) Allard, F., Allard, N. F., Homeier, D., et al. 2007, A&A, 474, L21
  * Allard et al. (2003) Allard, F., Guillot, T., Ludwig, H.-G., et al. 2003, in Brown Dwarfs, ed. E. Martín, Vol. 211, 325
  * Allard et al. (2011) Allard, F., Homeier, D., & Freytag, B. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 448, 16th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, ed. C. Johns-Krull, M. K. Browning, & A. A. West, 91
  * Allard et al. (2012) Allard, F., Homeier, D., & Freytag, B. 2012, Philosophical Transactions of the Royal Society of London Series A, 370, 2765
  * Allard et al. (2013) Allard, F., Homeier, D., Freytag, B., Schaffenberger, W., & Rajpurohit, A. S. 2013, Memorie della Societa Astronomica Italiana Supplementi, 24, 128
  * Arnaud (1996) Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17
  * Artigau et al. (2014) Artigau, É., Kouach, D., Donati, J.-F., et al. 2014, in Ground-based and Airborne Instrumentation for Astronomy V, Vol. 9147, 914715
  * Astudillo-Defru et al. (2017) Astudillo-Defru, N., Delfosse, X., Bonfils, X., et al. 2017, A&A, 600, A13
  * Barber et al. (2006) Barber, R. J., Tennyson, J., Harris, G. J., & Tolchenov, R. N. 2006, MNRAS, 368, 1087
  * Barnes (2003) Barnes, S. A. 2003, ApJ, 586, L145
  * Bayo et al. (2008) Bayo, A., Rodrigo, C., Barrado Y Navascués, D., et al. 2008, A&A, 492, 277
  * Berger et al. (2023) Berger, V. L., Hinkle, J. T., Tucker, M. A., et al. 2023, arXiv e-prints, arXiv:2312.12511
  * Bonfils et al. (2007) Bonfils, X., Mayor, M., Delfosse, X., et al. 2007, A&A, 474, 293
  * Borucki et al. (2010) Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977
  * Bouchy et al. (2017) Bouchy, F., Doyon, R., Artigau, É., et al. 2017, The Messenger, 169, 21
  * Bourrier et al. (2018) Bourrier, V., Ehrenreich, D., Lecavelier des Etangs, A., et al. 2018, A&A, 615, A117
  * Brown et al. (2022) Brown, A., Froning, C. S., Youngblood, A., et al. 2022, AJ, 164, 206
  * Brown et al. (2023) Brown, A., Schneider, P. C., France, K., et al. 2023, AJ, 165, 195
  * Caballero et al. (2022) Caballero, J. A., González-Álvarez, E., Brady, M., et al. 2022, A&A, 665, A120
  * Caffau et al. (2011) Caffau, E., Ludwig, H. G., Steffen, M., Freytag, B., & Bonifacio, P. 2011, Sol. Phys., 268, 255
  * Cash (1979) Cash, W. 1979, ApJ, 228, 939
  * Catling & Kasting (2017) Catling, D. C. & Kasting, J. F. 2017, Atmospheric Evolution on Inhabited and Lifeless Worlds
  * Chen et al. (2021) Chen, H., Zhan, Z., Youngblood, A., et al. 2021, Nature Astronomy, 5, 298
  * Choi et al. (2016) Choi, J., Dotter, A., Conroy, C., et al. 2016, ApJ, 823, 102
  * Ciesla et al. (2015) Ciesla, F. J., Mulders, G. D., Pascucci, I., & Apai, D. 2015, ApJ, 804, 9
  * Cohen et al. (2015) Cohen, O., Ma, Y., Drake, J. J., et al. 2015, ApJ, 806, 41
  * Corrales et al. (2023) Corrales, L., Stassun, K. G., Cunningham, T., et al. 2023, arXiv e-prints, arXiv:2311.07674
  * Cosentino et al. (2012) Cosentino, R., Lovis, C., Pepe, F., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8446, Proc. SPIE, 84461V
  * Craig et al. (1997) Craig, N., Abbott, M., Finley, D., et al. 1997, ApJS, 113, 131
  * Crossfield et al. (2022) Crossfield, I. J. M., Malik, M., Hill, M. L., et al. 2022, ApJ, 937, L17
  * Cruz Aguirre et al. (2023) Cruz Aguirre, F., Youngblood, A., France, K., & Bourrier, V. 2023, ApJ, 946, 98
  * Davenport et al. (2014) Davenport, J. R. A., Hawley, S. L., Hebb, L., et al. 2014, ApJ, 797, 122
  * Del Zanna et al. (2002) Del Zanna, G., Landini, M., & Mason, H. E. 2002, A&A, 385, 968
  * Dere et al. (2023) Dere, K. P., Del Zanna, G., Young, P. R., & Landi, E. 2023, ApJS, 268, 52
  * Dere et al. (1997) Dere, K. P., Landi, E., Mason, H. E., Monsignori Fossi, B. C., & Young, P. R. 1997, A&AS, 125, 149
  * Diamond-Lowe et al. (2022) Diamond-Lowe, H., Kreidberg, L., Harman, C. E., et al. 2022, AJ, 164, 172
  * Diamond-Lowe et al. (2023) Diamond-Lowe, H., Mendonça, J. M., Charbonneau, D., & Buchhave, L. A. 2023, AJ, 165, 169
  * Diamond-Lowe et al. (2021) Diamond-Lowe, H., Youngblood, A., Charbonneau, D., et al. 2021, AJ, 162, 10
  * Dong et al. (2018) Dong, C., Jin, M., Lingam, M., et al. 2018, Proceedings of the National Academy of Science, 115, 260
  * Duvvuri et al. (2023) Duvvuri, G. M., Cauley, P. W., Aguirre, F. C., et al. 2023, AJ, 166, 196
  * Duvvuri et al. (2021) Duvvuri, G. M., Sebastian Pineda, J., Berta-Thompson, Z. K., et al. 2021, ApJ, 913, 40
  * Eastman et al. (2023) Eastman, J. D., Diamond-Lowe, H., & Tayar, J. 2023, AJ, 166, 132
  * Engle (2024) Engle, S. G. 2024, ApJ, 960, 62
  * Engle & Guinan (2023) Engle, S. G. & Guinan, E. F. 2023, ApJ, 954, L50
  * Feinstein et al. (2022) Feinstein, A. D., France, K., Youngblood, A., et al. 2022, AJ, 164, 110
  * Feldman et al. (2001) Feldman, P. D., Sahnow, D. J., Kruk, J. W., Murphy, E. M., & Moos, H. W. 2001, J. Geophys. Res., 106, 8119
  * Foley & Smye (2018) Foley, B. J. & Smye, A. J. 2018, Astrobiology, 18, 873
  * Fontenla et al. (2016) Fontenla, J. M., Linsky, J. L., Garrison, J., et al. 2016, ApJ, 830, 154
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306
  * France et al. (2018) France, K., Arulanantham, N., Fossati, L., et al. 2018, ApJS, 239, 16
  * France et al. (2020) France, K., Duvvuri, G., Egan, H., et al. 2020, AJ, 160, 237
  * France et al. (2022) France, K., Fleming, B., Youngblood, A., et al. 2022, Journal of Astronomical Telescopes, Instruments, and Systems, 8, 014006
  * France et al. (2016) France, K., Loyd, R. O. P., Youngblood, A., et al. 2016, ApJ, 820, 89
  * Fressin et al. (2013) Fressin, F., Torres, G., Charbonneau, D., et al. 2013, ApJ, 766, 81
  * Froning et al. (2019) Froning, C. S., Kowalski, A., France, K., et al. 2019, ApJ, 871, L26
  * Fruscione et al. (2006) Fruscione, A., McDowell, J. C., Allen, G. E., et al. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6270, Observatory Operations: Strategies, Processes, and Systems, ed. D. R. Silva & R. E. Doxsey, 62701V
  * Fuhrmeister et al. (2022) Fuhrmeister, B., Zisik, A., Schneider, P. C., et al. 2022, A&A, 663, A119
  * Fulton et al. (2017) Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ, 154, 109
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1
  * Garraffo et al. (2016) Garraffo, C., Drake, J. J., & Cohen, O. 2016, ApJ, 833, L4
  * Garraffo et al. (2017) Garraffo, C., Drake, J. J., Cohen, O., Alvarado-Gómez, J. D., & Moschou, S. P. 2017, ApJ, 843, L33
  * Gillmann et al. (2009) Gillmann, C., Chassefière, E., & Lognonné, P. 2009, Earth and Planetary Science Letters, 286, 503
  * Gillon et al. (2013) Gillon, M., Jehin, E., Fumel, A., Magain, P., & Queloz, D. 2013, in European Physical Journal Web of Conferences, Vol. 47
  * Ginsburg & Mirocha (2011) Ginsburg, A. & Mirocha, J. 2011, PySpecKit: Python Spectroscopic Toolkit, Astrophysics Source Code Library, record ascl:1109.001
  * Ginsburg et al. (2022) Ginsburg, A., Sokolov, V., de Val-Borro, M., et al. 2022, AJ, 163, 291
  * Gordiets & Kulikov (1985) Gordiets, B. F. & Kulikov, Y. N. 1985, Advances in Space Research, 5, 113
  * Greene et al. (2023) Greene, T. P., Bell, T. J., Ducrot, E., et al. 2023, Nature, 618, 39
  * Gregory & Loredo (1992) Gregory, P. C. & Loredo, T. J. 1992, ApJ, 398, 146
  * Harman et al. (2015) Harman, C. E., Schwieterman, E. W., Schottelkotte, J. C., & Kasting, J. F. 2015, ApJ, 812, 137
  * Hawley et al. (2014) Hawley, S. L., Davenport, J. R. A., Kowalski, A. F., et al. 2014, ApJ, 797, 121
  * Hawley & Pettersen (1991) Hawley, S. L. & Pettersen, B. R. 1991, ApJ, 378, 725
  * Hojjatpanah et al. (2019) Hojjatpanah, S., Figueira, P., Santos, N. C., et al. 2019, A&A, 629, A80
  * Howard et al. (2023) Howard, W. S., Kowalski, A. F., Flagg, L., et al. 2023, ApJ, 959, 64
  * Howard & Law (2021) Howard, W. S. & Law, N. M. 2021, ApJ, 920, 42
  * Husser et al. (2013) Husser, T. O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6
  * Irwin et al. (2015) Irwin, J. M., Berta-Thompson, Z. K., Charbonneau, D., et al. 2015, in Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, Vol. 18, 18th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, 767–772
  * Iyer et al. (2023) Iyer, A. R., Line, M. R., Muirhead, P. S., Fortney, J. J., & Gharib-Nezhad, E. 2023, ApJ, 944, 41
  * Jackman et al. (2024) Jackman, J. A. G., Shkolnik, E. L., Loyd, R. O. P., & Richey-Yowell, T. 2024, arXiv e-prints, arXiv:2406.15308
  * Jackman et al. (2023) Jackman, J. A. G., Shkolnik, E. L., Million, C., et al. 2023, MNRAS, 519, 3564
  * Jackman et al. (2019) Jackman, J. A. G., Wheatley, P. J., Bayliss, D., et al. 2019, MNRAS, 485, L136
  * Jackman et al. (2018) Jackman, J. A. G., Wheatley, P. J., Pugh, C. E., et al. 2018, MNRAS, 477, 4655
  * Johnstone et al. (2021) Johnstone, C. P., Lammer, H., Kislyakova, K. G., Scherf, M., & Güdel, M. 2021, Earth and Planetary Science Letters, 576, 117197
  * Kashyap & Drake (1998) Kashyap, V. & Drake, J. J. 1998, ApJ, 503, 450
  * King & Wheatley (2021) King, G. W. & Wheatley, P. J. 2021, MNRAS, 501, L28
  * Kowalski et al. (2013) Kowalski, A. F., Hawley, S. L., Wisniewski, J. P., et al. 2013, ApJS, 207, 15
  * Kreidberg et al. (2019) Kreidberg, L., Koll, D. D. B., Morley, C., et al. 2019, Nature, 573, 87
  * Kubyshkina (2024) Kubyshkina, D. 2024, arXiv e-prints, arXiv:2402.13931
  * Kubyshkina & Vidotto (2021) Kubyshkina, D. & Vidotto, A. A. 2021, MNRAS, 504, 2034
  * Lammer et al. (2018) Lammer, H., Zerkle, A. L., Gebauer, S., et al. 2018, Astronomy and Astrophysics Review, 26, 2
  * Lim et al. (2023) Lim, O., Benneke, B., Doyon, R., et al. 2023, ApJ, 955, L22
  * Linsky et al. (2014) Linsky, J. L., Fontenla, J., & France, K. 2014, ApJ, 780, 61
  * Lopez & Fortney (2013) Lopez, E. D. & Fortney, J. J. 2013, ApJ, 776, 2
  * Lopez et al. (2012) Lopez, E. D., Fortney, J. J., & Miller, N. 2012, ApJ, 761, 59
  * Louca et al. (2023) Louca, A. J., Miguel, Y., Tsai, S.-M., et al. 2023, MNRAS, 521, 3333
  * Loyd & France (2014) Loyd, R. O. P. & France, K. 2014, ApJS, 211, 9
  * Loyd et al. (2016) Loyd, R. O. P., France, K., Youngblood, A., et al. 2016, ApJ, 824, 102
  * Loyd et al. (2018) Loyd, R. O. P., France, K., Youngblood, A., et al. 2018, ApJ, 867, 71
  * Loyd et al. (2020) Loyd, R. O. P., Shkolnik, E. L., France, K., Wood, B. E., & Youngblood, A. 2020, Research Notes of the American Astronomical Society, 4, 119
  * Luger & Barnes (2015) Luger, R. & Barnes, R. 2015, Astrobiology, 15, 119
  * Luger et al. (2015) Luger, R., Barnes, R., Lopez, E., et al. 2015, Astrobiology, 15, 57
  * Lustig-Yaeger et al. (2023) Lustig-Yaeger, J., Fu, G., May, E. M., et al. 2023, Nature Astronomy, 7, 1317
  * MacGregor et al. (2021) MacGregor, M. A., Weinberger, A. J., Loyd, R. O. P., et al. 2021, ApJ, 911, L25
  * Mahadevan et al. (2010) Mahadevan, S., Ramsey, L., Wright, J., et al. 2010, in Proc. SPIE, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, 77356X
  * Marty & Dauphas (2003) Marty, B. & Dauphas, N. 2003, Earth and Planetary Science Letters, 206, 397
  * May et al. (2023) May, E. M., MacDonald, R. J., Bennett, K. A., et al. 2023, ApJ, 959, L9
  * Mayor et al. (2003) Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20
  * Medina et al. (2022) Medina, A. A., Winters, J. G., Irwin, J. M., & Charbonneau, D. 2022, ApJ, 935, 104
  * Melbourne et al. (2020) Melbourne, K., Youngblood, A., France, K., et al. 2020, AJ, 160, 269
  * Moran et al. (2023) Moran, S. E., Stevenson, K. B., Sing, D. K., et al. 2023, ApJ, 948, L11
  * Newton et al. (2017) Newton, E. R., Irwin, J., Charbonneau, D., et al. 2017, ApJ, 834, 85
  * Newton et al. (2016) Newton, E. R., Irwin, J., Charbonneau, D., et al. 2016, ApJ, 821, 93
  * Newton et al. (2018) Newton, E. R., Mondrik, N., Irwin, J., Winters, J. G., & Charbonneau, D. 2018, AJ, 156, 217
  * Newville et al. (2016) Newville, M., Stensitzki, T., Allen, D. B., et al. 2016, Lmfit: Non-Linear Least-Square Minimization and Curve-Fitting for Python
  * Nutzman & Charbonneau (2008) Nutzman, P. & Charbonneau, D. 2008, PASP, 120, 317
  * O’Brien et al. (2018) O’Brien, D. P., Izidoro, A., Jacobson, S. A., Raymond, S. N., & Rubie, D. C. 2018, Space Sci. Rev., 214, 47
  * Odert et al. (2018) Odert, P., Lammer, H., Erkaev, N. V., et al. 2018, Icarus, 307, 327
  * Owen et al. (2020) Owen, J. E., Shaikhislamov, I. F., Lammer, H., Fossati, L., & Khodachenko, M. L. 2020, Space Sci. Rev., 216, 129
  * Owen & Wu (2013) Owen, J. E. & Wu, Y. 2013, ApJ, 775, 105
  * Owen & Wu (2017) Owen, J. E. & Wu, Y. 2017, ApJ, 847, 29
  * Passegger et al. (2019) Passegger, V. M., Schweitzer, A., Shulyak, D., et al. 2019, A&A, 627, A161
  * Pepin (1991) Pepin, R. O. 1991, Icarus, 92, 2
  * Pineda et al. (2021) Pineda, J. S., Youngblood, A., & France, K. 2021, ApJ, 918, 40
  * Price-Whelan et al. (2018) Price-Whelan, A. M., Sipőcz, B. M., Günther, H. M., et al. 2018, AJ, 156, 123
  * Pye et al. (2015) Pye, J. P., Rosen, S., Fyfe, D., & Schröder, A. C. 2015, A&A, 581, A28
  * Quirrenbach et al. (2010) Quirrenbach, A., Amado, P. J., Mandel, H., et al. 2010, in Proc. SPIE, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, 773513
  * Raymond et al. (2007) Raymond, S. N., Scalo, J., & Meadows, V. S. 2007, ApJ, 669, 606
  * Reale et al. (2001) Reale, F., Peres, G., & Orlando, S. 2001, ApJ, 557, 906
  * Redfield et al. (2024) Redfield, S., Batalha, N., Benneke, B., et al. 2024, arXiv e-prints, arXiv:2404.02932
  * Ricker et al. (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003
  * Ridden-Harper et al. (2023) Ridden-Harper, A., Nugroho, S. K., Flagg, L., et al. 2023, AJ, 165, 170
  * Rugheimer et al. (2015) Rugheimer, S., Kaltenegger, L., Segura, A., Linsky, J., & Mohanty, S. 2015, ApJ, 809, 57
  * Sanz-Forcada et al. (2003) Sanz-Forcada, J., Brickhouse, N. S., & Dupree, A. K. 2003, ApJS, 145, 147
  * Schatzman (1962) Schatzman, E. 1962, Annales d’Astrophysique, 25, 18
  * Schwab et al. (2016) Schwab, C., Rakich, A., Gong, Q., et al. 2016, in Proc. SPIE, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, 99087H
  * Seager & Deming (2010) Seager, S. & Deming, D. 2010, ARA&A, 48, 631
  * Segura et al. (2010) Segura, A., Walkowicz, L. M., Meadows, V., Kasting, J., & Hawley, S. 2010, Astrobiology, 10, 751
  * Seifahrt et al. (2016) Seifahrt, A., Bean, J. L., Stürmer, J., et al. 2016, in Proc. SPIE, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, 990818
  * Skumanich (1972) Skumanich, A. 1972, ApJ, 171, 565
  * Sleep & Zahnle (2001) Sleep, N. H. & Zahnle, K. 2001, J. Geophys. Res., 106, 1373
  * Speagle (2020) Speagle, J. S. 2020, MNRAS, 493, 3132
  * Teal et al. (2022) Teal, D. J., Kempton, E. M. R., Bastelberger, S., Youngblood, A., & Arney, G. 2022, ApJ, 927, 90
  * Teixeira et al. (2024) Teixeira, K. E., Morley, C. V., Foley, B. J., & Unterborn, C. T. 2024, ApJ, 960, 44
  * Tian et al. (2014) Tian, F., France, K., Linsky, J. L., Mauas, P. J. D., & Vieytes, M. C. 2014, Earth and Planetary Science Letters, 385, 22
  * Tovar Mendoza et al. (2022) Tovar Mendoza, G., Davenport, J. R. A., Agol, E., Jackman, J. A. G., & Hawley, S. L. 2022, AJ, 164, 17
  * Trifonov et al. (2021) Trifonov, T., Caballero, J. A., Morales, J. C., et al. 2021, Science, 371, 1038
  * Tsai et al. (2023) Tsai, S.-M., Lee, E. K. H., Powell, D., et al. 2023, Nature, 617, 483
  * Van Looveren et al. (2024) Van Looveren, G., Güdel, M., Boro Saikia, S., & Kislyakova, K. 2024, A&A, 683, A153
  * Walsh et al. (2014) Walsh, B. M., Kuntz, K. D., Collier, M. R., et al. 2014, Space Weather, 12, 387
  * Wilson et al. (2021) Wilson, D. J., Froning, C. S., Duvvuri, G. M., et al. 2021, ApJ, 911, 18
  * Winters et al. (2022) Winters, J. G., Cloutier, R., Medina, A. A., et al. 2022, AJ, 163, 168
  * Winters et al. (2019) Winters, J. G., Medina, A. A., Irwin, J. M., et al. 2019, AJ, 158, 152
  * Wood et al. (2021) Wood, B. E., Müller, H.-R., Redfield, S., et al. 2021, ApJ, 915, 37
  * Wright & Drake (2016) Wright, N. J. & Drake, J. J. 2016, Nature, 535, 526
  * Wright et al. (2018) Wright, N. J., Newton, E. R., Williams, P. K. G., Drake, J. J., & Yadav, R. K. 2018, MNRAS, 479, 2351
  * Youngblood et al. (2017) Youngblood, A., France, K., Loyd, R. O. P., et al. 2017, ApJ, 843, 31
  * Youngblood et al. (2016) Youngblood, A., France, K., Loyd, R. O. P., et al. 2016, ApJ, 824, 101
  * Youngblood et al. (2022) Youngblood, A., Pineda, J. S., Ayres, T., et al. 2022, ApJ, 926, 129
  * Youngblood et al. (2021) Youngblood, A., Pineda, J. S., & France, K. 2021, ApJ, 911, 112
  * Zahnle & Catling (2017) Zahnle, K. J. & Catling, D. C. 2017, ApJ, 843, 122
  * Zahnle & Kasting (1986) Zahnle, K. J. & Kasting, J. F. 1986, Icarus, 68, 462
  * Zhang et al. (2024) Zhang, M., Hu, R., Inglis, J., et al. 2024, ApJ, 961, L44
  * Zieba et al. (2023) Zieba, S., Kreidberg, L., Ducrot, E., et al. 2023, Nature, 620, 746