# The high-energy spectrum of the nearby planet-hosting inactive mid-M dwarf
LHS 3844

Hannah Diamond-Lowe Center for Astrophysics $|$ Harvard & Smithsonian, 60
Garden St., Cambridge, MA 02138, USA  National Space Institute, Technical
University of Denmark, Elektrovej, 2800 Kgs. Lyngby, Denmark  Allison
Youngblood Laboratory for Atmospheric and Space Physics, 1234 Innovation Dr.,
Boulder, CO 80303, USA  David Charbonneau Center for Astrophysics $|$ Harvard
& Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  George King Department
of Astronomy, University of Michigan, 1085 S. University Ave., 323 West Hall,
Ann Arbor, MI 48109, USA  D. J. Teal Department of Astronomy, University of
Maryland, College Park, MD 20742, USA  Sandra Bastelberger Department of
Astronomy, University of Maryland, College Park, MD 20742, USA  Lia Corrales
Department of Astronomy, University of Michigan, 1085 S. University Ave., 323
West Hall, Ann Arbor, MI 48109, USA  Eliza M.-R. Kempton Department of
Astronomy, University of Maryland, College Park, MD 20742, USA

###### Abstract

To fully characterize the atmospheres, or lack thereof, of terrestrial
exoplanets, we must include the high-energy environments provided by their
host stars. The nearby mid-M dwarf LHS 3844 hosts a terrestrial world that
lacks a substantial atmosphere. We present a time-series UV spectrum of LHS
3844 from 1131 to 3215Å captured by HST/COS. We detect one flare in the FUV
that has an absolute energy of $8.96\pm 0.77\times 10^{28}$ erg and an
equivalent duration of $355\pm 31$ s. We extract the flare and quiescent UV
spectra separately. For each spectrum, we estimate the Ly$\alpha$ flux using
correlations between UV line strengths. We use Swift-XRT to place an upper
limit on the soft X-ray flux and construct a differential emission model to
estimate flux that is obscured by the interstellar medium. We compare the
differential emission model flux estimates in the XUV to other methods that
rely on scaling from the Ly$\alpha$, Si iv, and N textscv lines in the UV. The
XUV, FUV, and NUV flux of LHS 3844 relative to its bolometric luminosity is
log10($L_{\mathrm{band}}/L_{\mathrm{Bol}}$) = $-3.65$, $-4.16$, and $-4.56$,
respectively, for the quiescent state. These values agree with trends in high-
energy flux as a function of stellar effective temperature found by the
MUSCLES survey for a sample of early-M dwarfs. Many of the most
spectroscopically accessible terrestrial exoplanets orbit inactive mid-to-late
M dwarfs like LHS 3844. Measurements of M dwarf high-energy spectra are
preferable for exoplanet characterization but are not always possible. The
spectrum of LHS 3844 is a useful proxy for the current radiation environment
for these worlds.

††facilities: HST(COS), Swift(XRT)††software: astropy (Robitaille et al.,
2013; Price-Whelan et al., 2018), Atmos
(github.com/VirtualPlanetaryLaboratory/atmos), ChiantiPy (Dere et al., 1997,
2019), emcee (Foreman-Mackey et al., 2013), lmfit (Newville et al., 2016)

##  1 Introduction

Studying the atmospheres of terrestrial exoplanets can provide insights into
their histories and current processes that are not available from radius and
mass measurements alone. The most accessible terrestrial planet atmospheres
belong to worlds with high equilibrium temperatures ($T_{\mathrm{eq}}>400$ K)
that transit small ($<0.3\ M_{\odot}$), nearby ($<15$ pc) stars. These systems
provide large planet-to-star radius ratios $R_{\mathrm{p}}/R_{\mathrm{s}}$ and
high signal-to-noise ratio observing opportunities. The Transiting Exoplanet
Survey Satellite (TESS; Ricker et al., 2015), along with other ground-based
survey programs (e.g., Nutzman & Charbonneau, 2008; Gillon et al., 2013; Irwin
et al., 2015), is expanding the known sample of transiting terrestrial
exoplanets orbiting nearby mid-M dwarfs, and these worlds are becoming prime
targets for in-depth characterization.

Mid-M dwarfs have masses and radii that are typically 20% times that of the
Sun and exhibit stark differences from their G-type counterparts. M dwarfs
have extended pre-main-sequence phases (Baraffe et al., 2015) and remain
chromospherically active on long timescales (Newton et al., 2017). A large
fraction of M dwarf surfaces are covered by magnetic fields, which heat their
upper atmospheres and produce strong emission lines and flaring in these fully
convective stars (Saar & Linsky, 1985; Loyd et al., 2018; Wright et al.,
2018). For planets in orbit around young mid-M dwarfs, this adds up to a harsh
high-energy environment that can alter their atmospheric chemistry and even
strip their atmospheres altogether. Once a planet-hosting M dwarf settles onto
the main sequence and slows its rotation (around 2 Gyr), it provides a more
benign environment.

If a primordial planetary atmosphere survives the youthful stages of a mid-M
dwarf host star, or the planet outgasses a secondary atmosphere later on, the
high-energy M dwarf environment still plays a role in sculpting the planetary
atmosphere. Molecular photodissociation cross sections are wavelength-
dependent, so planetary atmospheric chemistry is highly sensitive to the
stellar spectral energy distribution (SED). For instance, the far-ultraviolet
(FUV = 912–1700 Å) to near-ultraviolet (NUV = 1700–3200 Å) flux ratio can
shift the abundances of key molecules for habitability studies like water,
methane, carbon dioxide, ozone, and diatomic oxygen by more than an order of
magnitude (Harman et al., 2015; Rugheimer et al., 2015; France et al., 2016).
While high-energy radiation may be damaging to biological material, there is
evidence that some amount is needed for abiogenesis (Ranjan et al., 2017).

Studies of the atmospheric escape of terrestrial exoplanets orbiting M dwarfs
are rooted in theoretical studies of what early Venus, Earth, and Mars might
have looked like in the presence of a young, more active Sun (e.g., Watson et
al., 1981; Zahnle et al., 1990). X-ray and extreme ultra-violet flux (X-ray =
1–100Å; EUV = 100–912Å; XUV = 1–912Å) are responsible for hydrodynamic escape,
by which photolysis of atmospheric molecules, namely water, can produce a
stream of escaping hydrogen that can drag heavier molecules with it. It
remains an open question whether or not terrestrial worlds around M dwarfs can
retain atmospheres. Knowing where the divide is between those that can and
those that cannot is a key piece of missing information when it comes to
identifying optimal terrestrial targets for atmospheric follow-up. This
divide, known as the cosmic shoreline, relies on many unknowns, including
high-energy stellar flux levels over planetary lifetimes (Zahnle & Catling,
2017).

In this work, we focus on the nearby mid-M dwarf LHS 3844, which hosts a
terrestrial exoplanet discovered by TESS (Vanderspek et al., 2019). Kreidberg
et al. (2019) observed nine orbits of the terrestrial exoplanet LHS 3844b with
100 hr of Spitzer time. From the phase-curve data, they determined that
surface pressures of 10 bars or higher are disfavored on this planet for a
range of atmospheric compositions. Clear, low mean molecular weight
atmospheres at surface pressures of 0.1 bars or greater are disfavored by
optical ground-based transmission spectroscopy (Diamond-Lowe et al., 2020). On
the basis of stellar wind and high-energy flux over the planetary lifetime of
LHS 3844b, Kreidberg et al. (2019) also disfavored tenuous high mean molecular
weight atmospheres, with a small area of parameter space allowed if such an
atmosphere can be continuously replenished. It appears that the terrestrial
world LHS 3844b does not have an atmosphere, and in this paper, we quantify
one likely contributor, namely the high-energy emission from its host star.

We do not know the high-energy history of LHS 3844, but we here provide a
current snapshot as an anchor for stellar evolution and atmospheric escape
models. In Section 2 we describe in detail our observations and resulting
data. We present an analysis of the observed FUV flare in Section 3 and the
steps to constructing a panchromatic spectrum for LHS 3844 in Section 4. We
discuss the implications of our data for the terrestrial exoplanet LHS 3844b
in Section 5. We conclude with Section 6. We provide a list of constants used
throughout this work in Table 1.

All of our data products are available as high-level science products (HLSPs)
at MAST via 10.17909/t9-fqky-7k61 (catalog 10.17909/t9-fqky-7k61).

Table 1: Constants for LHS 3844 and LHS 3844b Used in This Work

Constant | Unit | Value | Reference
---|---|---|---
Distance | pc | $14.8909\pm 0.0113$ | Gaia Collaboration et al. (2018)
Stellar radius | $R_{\odot}$ | $0.178\pm 0.012$ | Kreidberg et al. (2019)
Stellar mass | $M_{\odot}$ | $0.158\pm 0.004$ | Kreidberg et al. (2019)
Effective temperature | K | $3036\pm 77$ | Vanderspek et al. (2019)
Bolometric flux (at Earth) | erg cm-2 s-1 | $3.52\pm 0.33\times 10^{-10}$ | Kreidberg et al. (2019)
Spectral type |  | M4.5–M5 | Vanderspek et al. (2019)
Planet radius | $R_{\oplus}$ | $1.244\pm 0.006$ | Kreidberg et al. (2019)
Planet mass | $M_{\oplus}$ | $2.2\pm 1.0$ |  Chen & Kipping (2017)a
Semi-major axis | au | $0.00622\pm 0.00017$ | Vanderspek et al. (2019)
Equilibrium temperature | K | $805\pm 20$ | Vanderspek et al. (2019)

Note. — We primarily take values from the more recent Kreidberg et al. (2019)
study. When values are taken from Vanderspek et al. (2019), they are either
fixed or not used in the Kreidberg et al. (2019) analysis.

aWe use the Chen & Kipping (2017) relation to estimate the mass of LHS 3844b.

##  2 Observations

We observed the UV spectrum of the mid-M dwarf LHS 3844 ($V=15.3$, $K=9.1$)
from 1131 to 3215 Å with 10 orbits of the Hubble Space Telescope (HST) and the
Cosmic Origins Spectrograph (COS; GO Program 15704; PI: Diamond-Lowe). The 10
orbits were divided into three visits executed from 2019 August 7 to 2019
August 12. In order to cover the full wavelength range, we use three COS
gratings: G130M (centered at 1291 Å), G160M (1600 Å), and G230L (2950 Å). It
is not possible to observe with multiple COS gratings simultaneously. We spent
six orbits observing with the G130M grating, three with G160M, and one with
G230L.

COS has two separate detectors for observing the FUV (G130M and G160M) and NUV
(G230L), while the gratings all have different throughputs. The dark current
in the NUV detector is 2 orders of magnitude greater than that of the FUV
detector, leading to noisier NUV count rates. There is, however, detectable
stellar continuum flux in the NUV that is not present in the FUV. There is a
limit to the signal-to-noise ratio achievable with each grating due to fixed-
pattern noise in the COS detectors. This can be overcome by changing the
fixed-pattern position (FP-POS) between exposures. Each FP-POS shifts the
spectrum slightly in the dispersion direction so that the spectral features
fall on different parts of the detector. The FP-POS is changed during the
Earth occultations for the G130M and G160M gratings. For the G230L grating, it
is changed during the final orbit, hence the split into four separate
exposures with short data gaps (Figure 1). The allocation of the orbits by
grating was designed to achieve a signal-to-noise ratio of at least 4 in
prominent UV lines. A UV spectrum of the mid-M dwarf star GJ 1214 was scaled
to the distance and size of LHS 3844 in order to estimate the exposure times
needed in each grating (France et al., 2016). Table 2 provides details about
each observation.

We used the G130M and G160M gratings to observe prominent molecular lines in
the FUV and the G230L grating to observe lines in the NUV. We used the
FLASH=YES setting and TIME-TAG mode in order to maximize the exposure time on
LHS 3844 and create a time series in which to look for stellar variability and
flares. This observing strategy was based on the successful Measurements of
the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems
(MUSCLES; GO Program 13650) and Mega-MUSCLES (GO Program 15071) treasury
surveys (France et al., 2016; Froning et al., 2019).

Figure 1: Time series of observations of LHS 3844 taken with HST/COS for GO
Program 15704 (PI: Diamond-Lowe). Ten orbits of HST time were divided into
three visits. The start times of each exposure are indicated with a vertical
line and labeled in UTC. Blue data points with 1$\sigma$ Poisson error bars
are counts per second in 1 s time bins. Dark blue points are the same but
binned into 1 minute time bins. The $x$-axis measures the minutes from the
start of the exposure; all $x$-axis tick marks are at equal intervals of 10
minutes and labeled only once in the bottom left corner for clarity. Note the
change in the $y$-axis scale for the G230L exposure. The first exposure of
every visit is shorter to allow time for target acquisition before the start
of the exposure. A gray band in the first G130M exposure indicates the flare.
Table 2: Observations of LHS 3844 with HST/COS

Visit | Orbit | Grating | Central Wavelength | Wavelength Range | Resolution Range | Exposure Timea | FP-POS
---|---|---|---|---|---|---|---
|  |  | (Å) | (Å) | ($\times 10^{3}$) | (s) |
| 1 |  |  |  |  | 2661 | 3
1 | 2 | G130M | 1291 | 1131–1429 | 12–16 | 3120 | 3
| 3 |  |  |  |  | 3120 | 4
| 4 |  |  |  |  | 2661 | 3
2 | 5 | G130M | 1291 | 1131–1429 | 12–16 | 3120 | 4
| 6 |  |  |  |  | 3120 | 4
3 | 7 |  |  |  |  | 2614 | 2
8 | G160M | 1600 | 1407–1775 | 13–20 | 3120 | 3
9 |  |  |  |  | 3120 | 4
10 | G230L | 2950 | 1678–3215 | 2.1–3.9 | 4$\times$ 716 | 1, 2, 3, 4

Note. — Spectra taken with the G130M and G160M gratings were placed at
lifetime position four (LP4) on the FUV detector in accordance with
recommendations by the COS team to mitigate gain sag and extend the detector
lifetime.

a The first exposure of every visit is shorter to allow for time to acquire
the target.

##  3 Time Series of LHS 3844

The star LHS 3844 is considered inactive, with an H$\alpha$ equivalent width
of $0.12\pm 0.08$ Å and one detected optical flare at an energy of $1.30\times
10^{31}$ erg in the TESS bandpass, observed at a 2-minute cadence by TESS in a
27 day sector (Medina et al., 2020). However, M dwarfs are known to flare at
high energies even when relatively quiescent at optical wavelengths (Loyd et
al., 2018). We use the corrtag files associated with each HST/COS exposure to
construct a time series of LHS 3844 (Figure 1). We detect one flare in our
time series, observed with the G130M grating. We note that we could have
detected a flare in any of the orbits (in any of the gratings) but spent the
most time observing with G130M. We also note that the additional noise in the
G160M and G230L gratings means that the energy threshold for detecting flares
is higher in these gratings than in the G130M grating.

###  3.1 Flux-calibrating the time series

The corrtag files provide a count rate (counts per second) that we need to
flux-calibrate in order to calculate the flare properties, such as FWHM, peak
flux, time of peak flux, absolute energy, and equivalent duration. This is not
directly provided in the COS data products, so we start with the provided
corrtag files and manually perform the background subtraction detailed in
chapter 3.4.19 of the COS Data Handbook, version 4.0111COS Data Handbook v4.0,
Chapter 3.4.19. Then, following the work of Loyd & France (2014) and Loyd et
al. (2018), we use the x1d (spectral) data products, which include information
about the wavelength grid, calibrated flux, and net counts to back out an
effective area ($A_{\mathrm{eff}}$) for the COS detector. This allows us to
include the COS detector response in the time-series flux calibration.

Every detected photon event from the corrtag files has an associated
wavelength. We use this wavelength to calculate the photon energy and then
divide by the associated effective area. Finally, we bin these events in time
in order to achieve a time series of fluxes in erg cm-2 s-1. We assume Poisson
uncertainties for each counted photon and propagate these values though our
flux-calibration process to get the uncertainties on the fluxes in the time
series.

###  3.2 Absolute Energy and Equivalent Duration

Following Davenport et al. (2014), Hawley et al. (2014), and Loyd et al.
(2018), we compute the absolute FUV flare energy $E$ as

$E=4\pi d^{2}\int_{\mathrm{flare}}(F_{f}-F_{q})dt$ (1)

where $d$ is the distance to the star, $F_{f}$ is the flux during the flare,
and $F_{q}$ is the estimated quiescent flux. A related quantity, the
equivalent duration $\delta$, is calculated as

$\delta=\int_{\mathrm{flare}}\frac{F_{f}-F_{q}}{F_{q}}dt$ (2)

which is essentially the area under the flare.

In order to calculate the absolute energy and equivalent duration of the
flare, we need to (1) choose a flare duration to integrate over and (2)
estimate the quiescent flux level. We determine which points are included in
the flare by shifting the starting and ending points of the flare and then
calculating the flare energy at each shift. When shifting the start time of
the flare, we keep the end time constant, and vice versa. Once the energy is
stable to the change in flare duration over which we integrate, we have found
the extent in time of the flare. The points that we include in the flare range
from 1783 to 1916 s after the start of the exposure, giving a flare duration
of 133 s. To estimate the quiescent flux, we fit a quadratic function in time
to the out-of-flare flux. We present the flux-calibrated time series that
includes the observed flare in Figure 2, with the in-flare points highlighted
in orange and the estimate of the quiescent flux shown as a gray line.

Dedicated analyses of flare surveys perform flare injection-and-recovery tests
in order to estimate the completeness of flare detections for different energy
thresholds, as well as place uncertainties on the flare properties (Loyd et
al., 2018; Medina et al., 2020). Flare injection-and-recovery tests are
outside the scope of this work. We instead estimate the uncertainties in
absolute energy and equivalent duration of our single flare using a Monte
Carlo estimate. We shuffle each in-flare flux point around by an amount drawn
from a normal distribution centered on zero with a standard deviation equal to
the uncertainty in the flux. We do this 1000 times and at each iteration
calculate the absolute energy and equivalent duration. We take the standard
deviations of the resulting distributions of these values as their
uncertainties (Table 3). Needless to say, this is not a Bayesian approach, and
our uncertainties mostly capture decisions regarding the quiescent flux level
and flare duration.

###  3.3 FWHM, Peak Time, and Amplitude

We use the classical flare model from Davenport et al. (2014) to fit for the
FWHM,222Here FWHM is defined as the time span, including the rise and decay
portions of the flare, at which the flux is half of the maximum recorded flux
(Kowalski et al., 2013). the time of peak flux, and the amplitude of the
flare. From this classical flare model, we can also do a by-eye check for the
starting and ending times of the flare that we chose in the previous section.
The Davenport et al. (2014) flare model assumes that the quiescent state is at
zero, so we subtract off the quadratic fit to the quiescent flux before
fitting the flare model.

We use the open-source fitting package lmfit (Newville et al., 2016), which
includes a wrapper for the Markov Chain Monte Carlo (MCMC) package emcee
(Foreman-Mackey et al., 2013). When fitting the flare model to the data, we
weight the data by the flux uncertainties. We use 100 walkers and run the MCMC
for 5000 steps with a 300 step burn-in, at which point the chain length is
over 50 times the integrated autocorrelation time. The final fit for the
Davenport et al. (2014) flare model is presented as a red line in the inset of
Figure 2, with the associated values listed in Table 3.

Figure 2: Flux-calibrated time series of the first G130M exposure of visit 1
(GO Program 15704). Blue points with 1$\sigma$ error bars are flux-calibrated
using the COS corrtag and x1d files. Orange points highlight the flare, from
1783 to 1916 s after the start of the exposure. Time bins are 1 s. The gray
line is a quadratic fit to the out-of-flare data, which we take as the
quiescent flux level. The red line in the inset is a fit of the classic flare
model to the data (Davenport et al., 2014). The shaded orange region between
the flare and quiescent flux is the equivalent duration $\delta$. Table 3:
Properties of the FUV Flare from LHS 3844

| Unit | Value
---|---|---
Wavelength range | Å | 1131–1429
Flare start and end | s | 1783–1916
Flare duration | s | 133
Mean quiescent flux | erg cm-2 s-1 | $9.48\times 10^{-15}$
Absolute energy ($E$) | erg | 8.96 $\pm$ 0.77 $\times$ 1028
Equivalent duration ($\delta$) | s | 355 $\pm$ 31
FWHM | s | 7.9 $\pm$ 1.0
Time of peak flux | s | 1796.27 $\pm$ 0.48
Amplitude | erg cm-2 s-1 | 1.99 $\pm$ 0.24 $\times$ 10-13

Note. — This flare was detected with the G130M grism, which captured flux in
the range of 1131–1429Å. Values reported here represent that whole flux range.

###  3.4 Flare Rate

From a total of 17,802 s of observing time with the G130M grating, we can
place a rough upper limit on the FUV flare frequency of LHS 3844 at $4.9\pm
2.2$ flares day-1, assuming Poisson counting statistics and not accounting for
the noncontiguous nature of the G130M observations. The absolute energy and
equivalent duration are helpful in contextualizing the LHS 3844 flare against
other flaring M dwarfs. We find that if we take the upper limit flare
frequency from our detection, the values we calculate for $E$ and $\delta$ are
within the distribution uncertainties of inactive M stars in the MUSCLES
sample (Figure 3 of Loyd et al., 2018).

Using TESS data, Medina et al. (2020) detected one LHS 3844 flare and reported
a flare frequency of $2.4\pm 2.0\times 10^{-4}$ flares day-1 at or above
energies of $3.16\times 10^{31}$ erg in the TESS bandpass for LHS 3844. TESS
operates in the optical, so we cannot draw direct comparisons between the
flare frequency reported by Medina et al. (2020) and the upper limit we place
here because we do not know the bolometric flux of these flare events. There
are no concurrent observations between TESS and HST/COS to determine if the
FUV flare we detect had an observable optical counterpart. However, Medina et
al. (2020) found that the mid-M dwarfs in their sample follow a common flare
energy distribution with a power-law index of $-2$; i.e., low-energy flares
are more common than high-energy flares. If we can assume that the bolometric
flux of the low-energy flare we report here is lower than the bolometric flux
of the flare detected by Medina et al. (2020) in the TESS data, it is possible
that low-energy flares like the one we observe are actually fairly common on
LHS 3844. This would also be in line with the finding that even stars that are
considered inactive (EW${}_{\mathrm{Ca\ \textsc{ii}}}<2$Å) exhibit flares in
both the optical (Medina et al., 2020) and the UV (Loyd et al., 2018).

##  4 Panchromatic Spectrum of LHS 3844

Given the presence of a flare in the UV data, we construct two panchromatic
spectra for LHS 3844: a flare spectrum and a quiescent spectrum. However, data
that include the flare were only observed in the FUV with the G130M grating,
so the flare spectrum is a much rougher estimate of what the LHS 3844 flux
might look like during a relatively low-energy flare. The panchromatic spectra
we present from 1 to $1\times 10^{5}$Å is constructed from (1) Swift-XRT soft
X-ray data, (2) estimates of the EUV and Ly$\alpha$ flux, (3) HST/COS data in
the FUV and NUV, (4) a PHOENIX model in the optical to mid-infrared, and (5) a
blackbody tail out to 10 $\mu$m.

###  4.1 Separating the HST/COS quiescent and flare spectra

In order to excise the flare and its associated spectra from the G130M time
series, we use the costools333github.com/spacetelescope/costools splittag
function to create three new sets of corrtag files for the first G130M
exposure: one before the flare, one during the flare, and one after the flare.
We then use the x1dcorr function to get flux-calibrated spectra from each
corrtag set. These flux-calibrated spectra are akin to the x1d data products
provided by the HST/COS pipeline. To turn our homemade x1d files into x1dsum
files that combine multiple exposures taken with the same grating, we follow
the instructions from chapter 3.4.22 of the COS Data Handbook version
4.0,444COS Data Handbook v4.0, Chapter 3.4.22 which explains how to sum x1d
files by weighting by the data quality (DQ_WGT). In this way, we combine all
nonflare (quiescent) portions of the G130M exposures and leave the flare on
its own.

The G160M and G230L exposures are only applicable to the quiescent spectrum.
The G230L grating does not provide complete coverage of the NUV; there is a
gap in the data between 2125 and 2750Å. We take the average flux out to 300Å
on either side of the gap and take this as the nominal flux value in the gap.
There are no emission lines that fall in the data gap that would have been
visible over the data noise. A list of the emission lines that we measure,
along with which gratings we use and the total exposure times to measure them,
can be found in Table 4.

Table 4: Measured Emission Lines from LHS 3844 with HST/COS

| Grating | Total Exposure Time | Line | Line Centers | log10(Surface Flux)a | log10(Surface Flux)b | log($T$)d
---|---|---|---|---|---|---|---
|  | (s) |  | (Å) | (erg cm-2 s-1) |
FUV | G130M | 17,802 | C iii | 1175.59c | 3.22 $\pm$ 0.22 | 5.05 $\pm$ 0.20 | 4.8
Si iii | 1206.50 | 2.95 $\pm$ 0.06 | 4.63 $\pm$ 0.16 | 4.7
O v | 1218.34 | 3.45 $\pm$ 0.03 | —— | 5.3
N v | 1238.82, 1242.8060 | 3.30 $\pm$ 0.05 | 4.49 $\pm$ 0.18 | 5.2
Si ii | 1264.74 | 2.13 $\pm$ 0.14 | —— | 4.5
C ii | 1334.53, 1335.67 | 3.32 $\pm$ 0.22 | 4.59 $\pm$ 0.18 | 4.5
Si iv | 1393.72, 1402.74 | 3.07 $\pm$ 0.21 | 4.81 $\pm$ 0.14 | 4.9
G160M | 8854 | C iv | 1548.19, 1550.78 | 3.97 $\pm$ 0.05 | —— | 5.0
He ii | 1640.4 | 3.06 $\pm$ 0.54 | —— | 4.9
NUV | G230L | 2864 | Mg ii | 2796.35 | 4.19 $\pm$ 0.98 | —— | 4.5

Note. — Surface fluxes (erg cm-2 s-1) are calculated by scaling the observed
flux by the distance $d$ and stellar radius $R_{\mathrm{s}}$ of LHS 3844:
$F_{\mathrm{Surf}}=F_{\mathrm{Obs}}\times\ (d/R_{\mathrm{s}})^{2}$. We use
$d=14.8909\pm 0.0113$ pc and $R_{\mathrm{s}}=0.178\pm 0.012\ R_{\odot}$ (Gaia
Collaboration et al., 2018; Kreidberg et al., 2019). For double lines, we
present the combined surface flux. Some lines in the G130M grating are not
well constrained by the data during the flare due to a low signal-to-noise
ratio so we do not report them here. We do not have G160M or G230L
observations during the flare.

a Quiescent spectrum

b Flare spectrum

c There are six unresolved C iii transition lines here; we fit them as a
single broad line

d Peak formation temperatures from CHIANTI v7.0 (Landi et al., 2012)

###  4.2 Ly$\alpha$ estimation

The largest flux source in the UV is Ly$\alpha$, so having a measurement or
estimation of the Ly$\alpha$ flux is necessary to construct the UV spectrum of
LHS 3844. However, for all stars other than the Sun, Ly$\alpha$ emission is
absorbed by neutral hydrogen in the interstellar medium (ISM) before it can
reach our telescopes. The MUSCLES survey was able to gather enough flux in the
wings of the Ly$\alpha$ profiles of early-M stars to perform a reconstruction
of the line and thereby measure the flux (Youngblood et al., 2016). We make a
distinction between the MUSCLES method of Ly$\alpha$ reconstruction, and the
method we present here for Ly$\alpha$ estimation.

An additional barrier to measuring the Ly$\alpha$ flux from LHS 3844 comes
from the COS instrument. COS is optimal for measuring FUV flux (Green et al.,
2012; France et al., 2013), but because it is a slitless spectrograph, the
Ly$\alpha$ line becomes contaminated by geocoronal emission, whereby solar
photons interact with neutral hydrogen in Earth’s atmosphere and produce local
Ly$\alpha$ emission. The Space Telescope Imaging Spectrograph (STIS) on board
HST has a slit and can measure the wings of the Ly$\alpha$ profile (France et
al., 2016; Youngblood et al., 2016), but at a lower efficiency. Given how
faint LHS 3844 is in the UV, we found that it would take a prohibitive amount
of HST/STIS time (70 orbits) to build up enough signal-to-noise ratio in the
wings of the Ly$\alpha$ line to perform a reconstruction. We remove
contamination from the geocoronal Ly$\alpha$ emission, as well as the local
emission of N i (1200Å) and O i (1302, 1305, 1306Å), from the HST/COS UV
spectra by setting the flux values at the contaminated wavelengths to zero.

To estimate the Ly$\alpha$ flux from LHS 3844, we build upon the work of the
MUSCLES survey to establish correlations between UV fluxes of different
emission lines across their stellar sample. Though the early-M stars in the
MUSCLES sample have orders-of-magnitude variations in their measured line
fluxes, there exists statistically significant correlations between line
fluxes within a given star’s UV spectrum (Youngblood et al., 2017). Because
the MUSCLES survey successfully reconstructed the Ly$\alpha$ flux for their
sample and measured the UV–UV correlations between line strengths, including
the Ly$\alpha$ line, we can build upon this work in order to estimate the
Ly$\alpha$ flux from other measured UV lines.

We start by fitting Gaussian functions555We tried to fit Voigt functions to
the UV lines, which is theoretically the correct function to use, but because
our data have low signal-to-noise ratios, the extra free parameter made for an
indistinguishable fit but with larger uncertainties. convolved with the
appropriate COS line spread function (LSF)666COS LSF to each of the emission
lines listed in Table 4. Visuals of these fits are shown in Figures 3 and 4,
where we also separate out each transition. During the flare, the integrated
flux in measured G130M emission lines increased by a median factor of 55, with
no detectable trend with peak formation temperature that would point to which
region of the stellar atmosphere the flare originated from. Indeed, other work
finds that it is additional continuum flux that accounts for the overall rise
in stellar radiation during flares (Osten & Wolk, 2015). There was too little
signal-to-noise ratio in the short time span of the flare to measure O v and
Si ii emission.

Figure 3: Quiescent spectrum emission lines (thin light blue lines) listed in
Table 4, with subplots for each transition. The transition lines are fitted
with Gaussian functions convolved with COS LSFs (thick dark blue lines).
Figure 4: Same as Figure 3 but for the flare spectrum. Thin orange lines are
the observed flux density during the flare. Thick brown lines are the fitted
Gaussian functions convolved with COS LSFs. Note the difference in the x\- and
y-axes, as well as the lower signal-to-noise ratio.

We integrate under the fitted Gaussians to establish the line flux. We then
normalize the observed flux in each line to the surface flux of the star using
the stellar distance and radius and take the base-10 log. In this format, we
can use the UV–UV emission line relations established by Youngblood et al.
(2017) to estimate this value for Ly$\alpha$ according to

$\mathrm{log}_{10}(F_{\mathrm{Surf},\mathrm{UV_{1}}})=m\times\mathrm{log}_{10}(F_{\mathrm{Surf},\mathrm{UV_{2}}})+b$
(3)

where $F_{\mathrm{Surf},\mathrm{UV_{1}}}$ in this case is the Ly$\alpha$
surface flux, $F_{\mathrm{Surf},\mathrm{UV_{2}}}$ is the surface flux of the
lines we measure (Table 4), and $m$ and $b$ are taken from Table 9 of
Youngblood et al. (2017). Note that not all emission lines we present in the
LHS 3844 UV spectrum are included in the UV–UV scalings, so these are not
included in the Ly$\alpha$ estimate. To estimate the uncertainty in log10
Ly$\alpha$ surface flux, we compare the rms scatter about the best-fit lines
of the UV–UV scalings (Youngblood et al., 2017, Table 9) to the upper and
lower values we get by calculating Equation 3 with 1$\sigma$ upper and lower
bounds of the log10 surface flux of the measured UV lines. We take whichever
value is higher as the uncertainty in the estimated log10 Ly$\alpha$ surface
flux. In all cases, the rms values from Youngblood et al. (2017) are higher,
meaning that the uncertainties in our Ly$\alpha$ estimates are dominated by
the scatter in the UV–UV scalings, not by our measurements of emission lines
in the COS data. We take the mean of the individual line estimates and their
standard deviations to get our final Ly$\alpha$ flux estimates and
uncertainties (Figure 5) and present the values in Table 5.

Table 5: Ly$\alpha$ Surface Flux Estimates from Measured UV Lines

Emission | log10($F_{\mathrm{Surf},\mathrm{Ly}\alpha}$)a | log10($F_{\mathrm{Surf},\mathrm{Ly}\alpha}$)b
---|---|---
Line | erg cm-2 s-1 | erg cm-2 s-1
Si iii | $5.43\pm 0.23$ | $6.44\pm 0.23$
N v | $5.51\pm 0.20$ | $6.34\pm 0.20$
Si ii | $5.14\pm 0.30$ | —
C ii | $5.60\pm 0.40$ | $6.35\pm 0.40$
Si iv | $5.46\pm 0.38$ | $6.48\pm 0.38$
C iv | $5.59\pm 0.32$ | —
He ii | $5.40\pm 0.32$ | —
Mg ii | $4.98\pm 0.71$ | —
Mean | $5.39\pm 0.36$ | $6.40\pm 0.30$

Note. — Some lines that we measure, like C iii and O v, are not included in
the UV–UV scaling relations from Youngblood et al. (2017).

a Quiescent spectrum.

b Flare spectrum; only lines measured during the flare are used to estimate
the Ly$\alpha$ surface flux (erg cm-2 s-1) from the flare spectrum.

Figure 5: The Ly$\alpha$ flux estimates from UV–UV line emission correlations
found by Youngblood et al. (2017). Blue and teal bars with black error bars
are derived from the quiescent spectrum. The increase in surface flux during
the flare is shown cumulatively with the orange and red bars and gray error
bars. We take the mean of the individual line correlations and their
respective standard deviations to get our final Ly$\alpha$ flux estimates.

###  4.3 EUV Estimation

For stars other than the Sun, EUV (100–912 Å) is not observable with any
current telescope. Energies corresponding to 912Å and below can ionize neutral
hydrogen in the ISM, with energies approaching 912Å the most likely to be
absorbed. This makes detecting photons at 912Å nearly impossible for most
stars. The only dedicated EUV mission, the Extreme-Ultraviolet Explorer (EUVE;
Craig et al., 1997), which flew from 1992 to 2001, could measure emission
under 600Å for most nearby stars. EUVE captured spectra of several active M
dwarfs, including AU Mic, AD Leo, EV Lac, and Proxima Centauri. Another high-
energy observatory, the Far Ultraviolet Spectroscopic Explorer (FUSE; Moos et
al., 2000; Sahnow et al., 2000), operated from 1999 to 2007 and captured FUV
spectra from 900 to 1200Å. EUVE’s all-sky survey did not pick up any flux at
LHS 3844’s coordinates, and FUSE did not make any observations within 1∘ of
LHS 3844.

We present two methods for estimating the EUV flux of LHS 3844. The first
relies on scaling relations similar to those used in the previous section to
estimate the Ly$\alpha$ flux. The second method is more in-depth and involves
calculating the differential emission measure (DEM) for each of the
transitions we measure and from there backing out the flux from transitions we
do not measure.

####  4.3.1 Method 1: Scaling from UV line fluxes

We use UV–EUV scalings to estimate LHS 3844’s EUV flux from its UV spectrum.
The first scaling we attempt is based on measurements and models of the solar
spectrum, EUVE, and FUSE data and relates broad EUV bands to Ly$\alpha$ flux
(Linsky et al., 2014). The second scaling focuses on the Si iv and N v lines
in the FUV, measured by HST/COS and STIS, and relates them to the 90–360Å
range measured for active M dwarfs by EUVE (France et al., 2018). The Si iv
and N v lines are particularly suited to estimating the EUV because they form
in $\sim$105 K plasma, similar to the coronal region where the bulk of the EUV
radiation is emitted (Tilipman et al., 2021). The Si iv and N v lines do not
suffer from ISM extinction as do other FUV lines that form at lower
temperatures, like C ii (France et al., 2018). The results of these scalings
for both the quiescent and flare LHS 3844 spectra are shown in the left and
middle panels of Figure 6.

We find good agreement between the Linsky et al. (2014) and France et al.
(2018) methods where they overlap for the quiescent and flare spectra,
respectively. We use the RMS scatter about the Si iv and N v fits to calculate
the uncertainties in the estimated EUV flux, similar to how France et al.
(2018) calculated the error bars in Figure 6 of their paper. Overall, these
scaling methods are disfavored because they rely on scaling from either the
Ly$\alpha$ line, which we do not directly measure, or two FUV lines, which are
measured at low signal-to-noise ratio. Furthermore, these scalings are derived
from measurements of active M stars, whereas LHS 3844 is considered inactive.
However, it is encouraging that there is general agreement between the EUV
flux estimates.

Figure 6: The EUV estimates of LHS 3844 flux for the quiescent (blue) and
flare (orange) spectra. In the left panel, the EUV flux estimate is scaled
from the estimated Ly$\alpha$ flux (Section 4.3.1; Linsky et al., 2014). The
lines show the best EUV estimates, and the shaded regions indicate 1$\sigma$
uncertainties. In the middle panel, the EUV flux from 90 ti 360 Å is estimated
using the measured Si iv and N v emission in the HST/COS data (Section 4.3.1;
France et al., 2018). The lines and shaded regions are again the best
estimates and 1$\sigma$ uncertainties. The right panel shows the EUV flux
estimated from the DEM functions (Section 4.3.2). We intentionally used the
same binning as the Ly$\alpha$ scaling (left panel) for comparison. Lighter
blue and orange lines demonstrate the range of EUV estimates that arises if
the assumed soft X-ray flux is 1 to $1\times 10^{-9}$ times the derived upper
limit for LHS 3844 from Swift-XRT (see Section 5.1).

####  4.3.2 Method 2: DEM

The second method involves calculating the DEM of the detected UV transitions
and using their formation temperatures to construct a smoothly varying
function that allows us to estimate the fluxes of lines that we do not
measure. This process is described in detail in Duvvuri et al. (2021). This
method assumes that the plasma from which these high-energy transitions emit
photons is optically thin and in a state of collisional ionization equilibrium
(i.e., de-excitation due to collisions is negligible). As such, it is
necessary to also have the emissivity contribution function for each
transition, which we calculate with the ChiantiPy package,777ChiantiPy v0.9.5
which utilizes the CHIANTI atomic database, v9.0 (Dere et al., 1997, 2019).

To calculate the DEMs for the UV emission lines we measure, we start with the
equation

$I_{\mathrm{ul}}=\int_{T}G_{\mathrm{ul}}(T)\Psi(T)dT$ (4)

where $I_{\mathrm{ul}}$ is the intensity for each transition ($ul$ stands for
the transition from an “upper to lower” energy level), $G_{\mathrm{ul}}(T)$ is
the emissivity contribution function, $\Psi(T)$ is the DEM, and $T$ is the
temperature range over which a particular transition occurs. We assume a
solar-like electron density of $10^{8}$ when calculating the emissivity
contribution function. The emissivity contribution functions
$G_{\mathrm{ul}}(T)$ exhibit strong peaks in temperature where most of the
flux is concentrated, meaning that the integral in Equation 4 reflects a
narrow temperature range for a given transition region line. We place an
estimate of the DEM at the peak formation temperature of each transition line
by integrating over $G_{\mathrm{ul}}(T)$ and dividing the intensity by this
value (see Equation 8 of Duvvuri et al., 2021).

To fill out the DEM function, we require X-ray data to inform the highest peak
formation temperatures. Over two epochs in 2019, Swift-XRT observed LHS 3844
for a total of 31.8 ks (PI: Corrales), but it was too faint to detect.
Instead, we report a 95% confidence upper limit on the count rate of
$2.3\times 10^{-4}$ counts s-1, calculated using the Bayesian method detailed
in Kraft et al. (1991). Assuming a single-temperature plasma at 0.25 keV, this
count rate yields an upper limit on the unabsorbed observed flux of $1.1\times
10^{-14}$ erg cm-2 s-1 for the 0.2–2.4 keV band. This gives an upper limit
X-ray luminosity in the same band of $2.9\times 10^{26}$ erg s-1 and a
fractional luminosity $L_{\mathrm{X}}/L_{\mathrm{Bol}}$ of $3.1\times 10^{-5}$
assuming $L_{\mathrm{Bol}}=9.34\times 10^{30}$ erg s-1.

In order to translate the upper limit unabsorbed flux into a DEM, we again
start with Equation 4. However, where $I_{\mathrm{ul}}$ previously applied to
an individual transition that we measured, now $I_{\mathrm{ul}}$ represents
the X-ray intensity across 0.2–2.4 keV (5.2–62.0 Å). And instead of using
$G_{\mathrm{ul}}(T)$ for a particular transition, we now sum the emissivity
contribution functions for every ion transition in the band. We take the peak
of this summation of $G_{\mathrm{ul}}(T)$ functions as the peak formation
temperature for the X-ray band. We integrate the summed $G_{\mathrm{ul}}(T)$
function and divide the upper limit X-ray intensity by this value to get an
estimate of the X-ray DEM, which serves as an upper limit given the
nondetection by Swift-XRT.

We present our DEMs as a function of peak formation temperature in Figure 7.
We compare the DEMs from the quiescent line transitions to a scaled average of
DEM functions across the stellar sample reported by Sanz-Forcada et al.
(2003), which was a strategy used by Garcia-Sage et al. (2017) for the
$4.0<\mathrm{log}(T)<6.25$ temperature range of Proxima Centauri. However, the
stars used in the Sanz-Forcada et al. (2003) study were mostly active, Sun-
like stars, unlike LHS 3844, a relatively small and inactive star
($R=0.19R_{\odot}$; Vanderspek et al., 2019). We therefore do not adopt the
averaged Sanz-Forcada et al. (2003) DEM function for LHS 3844. Rather, we
include a point from the Sanz-Forcada et al. (2003) scaled average DEM at
$\mathrm{log}(T)=6.0$ where we have no constraining data, and then fit a
third-order polynomial to the DEMs (Louden et al., 2017). For the flare
spectrum, where we have fewer measured emission lines and no soft X-ray upper
limit, we scale the Sanz-Forcada et al. (2003) DEM function estimate to the
measured FUV DEMs and then use this scaling to increase the soft X-ray upper
limit before fitting the polynomial.

Figure 7: The DEMs for observed transition lines in the HST/COS UV spectrum of
LHS 3844. The X-ray data points are upper limits derived from Swift-XRT
observations. Blue points are DEMs from the quiescent spectrum, while orange
points are DEMs from the flare spectrum. We compare the quiescent DEMs to
those observed for active G stars by Sanz-Forcada et al. (2003), with purple
and pink lines and 1$\sigma$ error shading taken from an average across all
stars in their sample, and then scaled to the quiescent and flare DEMS,
respectively. The DEM function of the quiet Sun is plotted as a green dashed
line (Dere et al., 2019). The teal and red dotted lines are third-order
polynomial fits to the quiescent and flare DEM points, respectively. We
include a point from the Sanz-Forcada et al. (2003) scaled DEM function at
$\mathrm{log}(T)=6.0$ (purple and pink squares for the quiescent and flare
DEMs, respectively) in the unconstrained area of parameter space between
$\mathrm{log}(T)=5.5$ and $\mathrm{log}(T)=6.5$.

From the estimated DEM functions, we can back out the fluxes of lines that we
do not directly measure, for example, in the range from 100 to 912 Å. This
simply requires going back to Equation 4 and using the DEM function and the
emissivity contribution functions $G_{\mathrm{ul}}(T)$ from CHIANTI to
calculate the intensity for each transition. We take the top 10 transitions of
every ion in the CHIANTI database from 1 to 3215 Å and compute the associated
fluxes. We then insert these computed fluxes for high-energy wavelength ranges
in which we do not have measurements of LHS 3844 from either HST/COS
(1131–3215 Å) or Swift-XRT (5.2–62.0 Å). The DEM estimates of the EUV flux are
in agreement, to at least within an order of magnitude, with other EUV flux
estimates we attempted (Figure 6, right panel). We note that by using the DEM
to estimate the EUV flux, we do not include an estimate on the Lyman continuum
emission, which peaks at 911Å. In the Sun, the Lyman continuum accounts for
15% of the total EUV flux (Woods et al., 2009; Duvvuri et al., 2021).

We do not have data outside of the G130M grating for the flare spectrum. We
instead use the flare DEM function to estimate the flux densities of the
prominent lines that we observe in quiescence (C iv, He ii, Mg ii). For these
lines, we insert Gaussian profiles into the flare spectrum that integrate to
the estimated values. We do not insert Gaussian profiles for lines that fall
within the G130M grating but are not detected above the noise (Si ii, O v).

###  4.4 Optical and infrared

Redward of 3215 Å we use a PHOENIX model that has been interpolated to the
effective temperature and surface gravity of LHS 3844 (Husser et al., 2013).
We check that the interpolated model agrees with the available photometry. The
PHOENIX model extends out to 5 $\mu$m. Past this, up to 10 $\mu$m, we append a
blackbody curve at LHS 3844’s effective temperature. We scale the combined
PHOENIX and blackbody spectrum to the distance and stellar surface area of LHS
3844. We then compare the bolometric flux of the scaled PHOENIX and blackbody
spectrum to $F_{\mathrm{bol}}=3.52\times 10^{-10}$ erg cm-2 s-1 for LHS 3844
reported by Kreidberg et al. (2019) from an SED fit. We further scale the
spectrum such that it integrates to this $F_{\mathrm{bol}}$ value. (The scale
factor is 1.01, so this is not changing the spectrum significantly.) We check
that the scaled PHOENIX spectrum matches, to within the error bars, the COS
spectrum at the reddest NUV wavelengths, where we detect a small amount of
continuum flux from LHS 3844. We then append the optical and infrared portions
of the spectrum to the end of the HST/COS data set. The panchromatic quiescent
and flare spectra of LHS 3844 are shown in Figure 8.

Figure 8: Quiescent (blue) and flare (orange) spectra of LHS 3844 from 1 to
$1\times 10^{5}$Å. These panchromatic spectra combine UV transition region
lines measured with HST/COS, an upper limit on the soft X-ray flux, an
estimate of the EUV (100-912Å) using a DEM, a PHOENIX model (Husser et al.,
2013), and a blackbody curve. The flare spectrum is only directly measured in
the FUV (see Section 3), and the rest is estimated. There is a gap in the
quiescent NUV observations between 2125 and 2750Å, which we fill in with an
average of the flux from 300Å on either side of the gap, excluding the Mg ii
emission lines.

###  4.5 LHS 3844 compared to MUSCLES stars

The MUSCLES survey features few stars of similar spectral type to LHS 3844
(France et al., 2018). The upcoming extension to MUSCLES for low-mass stars,
Mega-MUSCLES (PI: Froning), will focus on this parameter space and so far
includes Barnard’s Star (France et al., 2020) and the late-M dwarf TRAPPIST-1
(Wilson et al., 2021). We present some quantitative qualities of the LHS 3844
spectrum in Table 6. We find that the quiescent LHS 3844 spectrum fits within
broad trends found for the MUSCLES stars. For instance, the FUV/NUV ratio for
LHS 3844 follows the trend toward higher FUV flux relative to NUV flux when
going from warmer to to cooler stellar effective temperatures (France et al.,
2016). The estimate of the quiescent Ly$\alpha$ line makes up $75\%\pm 18$% of
the FUV flux, which is in agreement with MUSCLES stars. We note that our
estimate of the XUV flux is higher than that of the MUSCLES stars. This is due
to the differences between using the Linsky et al. (2014) scalings from the
Ly$\alpha$ flux (France et al., 2016) and a DEM function, similar to what we
see for the EUV in Figure 6.

Table 6: Derived Values from the Spectrum of LHS 3844

| Wavelength (Å) | Valuea | Valueb
---|---|---|---
$\mathrm{log_{10}}(L_{\mathrm{Bol}})$ | 1 — $1\times 10^{5}$ | 30.97 | 30.97
$f$(XUV) | 1 — 912 | -3.65 | -2.49
$f$(FUV) | 912 — 1700 | -4.16 | -3.01
$f$(NUV) | 1700 — 3200 | -4.48 | -4.15
FUV/NUV | — | 2.11 | 13.81c
Ly$\alpha$/FUV | — | $0.74\pm 0.61$ | $0.54\pm 0.37$
FXUV,pd | 1 – 912 | $1.9\times 10^{4}$ | $2.8\times 10^{5}$
$\dot{M}$ (g s-1) | — | $7.7\times 10^{10}$ | $1.3\times 10^{12}$

Note. — Following France et al. (2016), $f$(band) =
log10($L_{\mathrm{band}}/L_{\mathrm{Bol}}$); $F_{\mathrm{Bol}}$ is $3.52\times
10^{-10}$ erg cm-2 s-1 (Kreidberg et al., 2019) in all cases.

a Quiescent spectrum.

b Flare spectrum.

c We have no way of estimating the continuum NUV flux during the flare, so the
integrated NUV flux is taken from the PHOENIX model and is therefore
underestimated.

d The XUV flux (erg cm-2 s-1) at the planet LHS 3844b, assuming $a=0.00622\pm
0.00017$ au (Vanderspek et al., 2019)

##  5 Discussion

###  5.1 The Soft X-ray Flux Upper Limit

Due to the nondetection of LHS 3844 by the X-ray observatory Swift-XRT, we use
an upper limit when constructing DEM functions for the quiescent and flare
spectra presented in this work. Because the upper limit on LHS 3844’s soft
X-ray flux informs the highest peak formation temperatures of the quiescent
and flare DEM functions (Figure 7), we wish to understand the impact of taking
the soft X-ray flux upper limit as the soft X-ray flux value. We
systematically decrease the soft X-ray flux and recalculate the DEMs and
resulting estimates for the integrated X-ray (1–100 Å) and EUV (100–912 Å)
flux for LHS 3844. We present the results of this exercise in Figure 9, as
well as illustrate the range of the resulting EUV flux estimates in Figure 6
(right panel). As expected, changing the soft X-ray flux has a strong effect
on the integrated X-ray flux, since the soft X-ray makes up a large portion of
this spectral range. However, once the soft X-ray flux is decreased to 1% of
the upper limit, the integrated X-ray flux remains stable. In the EUV, the
integrated flux changes by less than a factor of 2 in response to the
decreased soft X-ray flux in both the quiescent and flare cases. The XUV
(1–912 Å) flux, which is dominated by the EUV, changes by less than a factor
of 3. We are therefore comfortable taking the soft X-ray flux upper limit as
the nominal value.

Figure 9: Illustration of the response of the integrated X-ray (1–100 Å) and
EUV (100–912 Å) flux to the assumed soft X-ray flux. From Swift-XRT, we derive
an upper limit for the soft X-ray flux of $1.1\times 10^{-14}$ erg cm-2 s-1.
Here we take fractions of this upper limit and calculate how the integrated
X-ray and EUV flux responds.

###  5.2 Constraints on the Atmosphere of LHS 3844b

The highly irradiated terrestrial planet in orbit around LHS 3844 likely does
not have an atmosphere. Atmospheres with surface pressures greater than 10
bars are disfavored (Kreidberg et al., 2019), and clear, low mean molecular
weight atmospheres are disfavored down to 0.1 bar (Diamond-Lowe et al., 2020).
Tenuous high mean molecular weight atmospheres are not addressed empirically,
but theoretical arguments based on the stellar wind and high-energy radiation
that LHS 3844b receives strongly imply that this world is a bare rock
(Kreidberg et al., 2019).

Kreidberg et al. (2019) explored a parameter space for a final atmospheric
pressure of O2 on LHS 3844b after 5 Gyr of energy-limited atmospheric escape
based on an initial water abundance and LHS 3844’s XUV saturation fraction
(Figure 4 of that paper). They explored an XUV saturation fraction from
$10^{-4}$ to $10^{-2}$ and found a small area between 1 and $3\times 10^{-4}$
XUV saturation fraction that allows for a high mean molecular weight
atmosphere given the right initial water abundance. We can add more empirical
information to this argument. From an upper limit on LHS 3844’s soft X-ray
flux and an estimation of the EUV, we find that in its current quiescent
state, LHS 3844’s XUV output flux relative to bolometric is $2.2\times
10^{-4}$.

With a rotation period of 128 days and no observed H$\alpha$ emission, LHS
3844 is no longer in the saturation state exhibited by young stars (Wright et
al., 2018). Models of activity evolution predict that M dwarfs spend an
extended amount of time in the highly active pre-main-sequence phase before
settling onto the main sequence (Baraffe et al., 2002, 2015), meaning that LHS
3844’s XUV saturation fraction must have been higher than the fraction we see
currently (e.g., Luger & Barnes, 2015). The high-energy spectra we present in
this work are representative of the unsaturated regime of LHS 3844 and perhaps
similar mid-M dwarfs as well.

###  5.3 Mass-Loss Rate

We can also use our XUV estimate to calculate an atmospheric mass-loss rate
for LHS 3844b, supposing it had an extended low mean molecular weight
atmosphere, as it may have soon after formation (Owen & Wu, 2013; Lopez &
Fortney, 2013). For planets that end up on the terrestrial side of the planet
radius distribution gap (Fulton et al., 2017; Fulton & Petigura, 2018), it is
possible that they formed before the dissipation of the gas in the
protoplanetary nebula. In this case, the terrestrial planet core would be able
to accrete about 1% of its mass in hydrogen and helium (Owen et al., 2020).
Using the radius–mass relations of Chen & Kipping (2017), we estimate that LHS
3844b currently has a mass of 2.2 $M_{\oplus}$ and so may have accreted 0.02
$M_{\oplus}$ of low mean molecular weight material soon after formation.

Basic mass-loss equations for energy-limited escape show that hydrodynamic
escape from LHS 3844b would be rapid and efficient (e.g., Erkaev et al., 2007;
Lopez & Fortney, 2013; Salz et al., 2016; Johnstone et al., 2019). We
calculate the evaporation efficiency log${}_{10}(\eta_{\mathrm{eva}})$ to be
-0.51 (Salz et al., 2016), placing LHS 3844b solidly in the regime of
efficient atmospheric evaporation (compare to Figure 2 of Salz et al., 2016).
This is unsurprising, given that this is a terrestrial planet with a low
gravitational potential. Following the equations and simulation results of
Salz et al. (2016), we calculate the mass-loss rate for the hydrodynamical
regime using

$\dot{M}=\frac{3\beta^{2}\eta F_{\mathrm{XUV,p}}}{4KG\rho_{\mathrm{p}}}$ (5)

where we take $\eta=\eta_{\mathrm{eva}}$, $\beta$ relates the planet radius to
the radius at which XUV flux can be absorbed, $F_{\mathrm{XUV,p}}$ is the XUV
flux at the planet, $K$ is a correction factor because the mass only needs to
reach the Hill radius to escape, and $\rho_{\mathrm{p}}$ is the planet density
(Erkaev et al., 2007; Salz et al., 2016). At a distance of $0.00622\pm
0.00017$ au from LHS 3844 (Vanderspek et al., 2019), LHS 3844b receives
$1.9\times 10^{4}$ erg cm-2 s-1 in XUV flux when LHS 3844 is in its current
quiescent state. We find a hydrodynamic mass-loss rate of 7.7$\times 10^{10}$
g s-1. At this rate, it would take only 54 Myr for LHS 3844b to lose its
primordial low mean molecular weight atmosphere. We compare this mass-loss
rate to that of the Neptune-sized world GJ 436b, which has a tail of hydrogen
escaping at an estimated rate of 108-109 g s-1 (Ehrenreich et al., 2015).

###  5.4 Atmospheric Models

While LHS 3844b is unlikely to retain an atmosphere, the panchromatic spectrum
we present here for LHS 3844 can be an input to atmospheric models of planets
in inactive mid-M dwarf systems. For instance, we consider the case of a
hypothetical Earth-like planet in the habitable zone of the LHS 3844 system.
We use the quiescent and flare LHS 3844 spectra as inputs to the Atmos888
github.com/VirtualPlanetaryLaboratory/atmos coupled photochemical and climate
model (Arney et al., 2017) with updated opacities and molecular cross sections
(Grimm & Heng, 2015; Grimm et al., 2018; Gordon et al., 2017). The
nondetection of the UV continuum in the HST/COS data leads to negative flux
density values in this part of the spectrum, which can create instabilities in
the Atmos code. To avoid this, we create versions of the panchromatic spectra
that are binned and resampled to 1 Å such that negative flux density values
are eliminated but the overall flux is conserved.

We determine the steady-state temperature–pressure (T–P) profiles and mixing
ratios for molecular species under both the quiescent and flare states of LHS
3844. The quiescent and flare spectra result in negligible differences in the
T–P profiles, but yield significant differences in mixing ratios (Figure 10,
left panel). During the flare, additional ozone (O3) is produced in the upper
atmosphere, while oxygen (O2), water (H2O), and methane (CH4) are dissociated.

The T–P and abundance profiles are fed into a proprietary modified version of
the open-source Exo-Transmit code in order to produce model transmission
spectra (Kempton et al., 2017). With this modification, we are able to read in
vertically defined abundance profiles, as opposed to the equilibrium chemistry
tables defined on preset T–P grids provided with Exo-Transmit. Investigating
the timescale of the planet’s atmospheric response to the observed flare is
beyond the scope of this work. We note that studies of energetic flares on
active M dwarfs like AD Leo imply that they have a lasting affect on the
steady state of a planetary atmosphere that may be detectable in transmission
spectra (Venot et al., 2016). It is likely that LHS 3844 exhibited heightened
energetic flaring earlier in its lifetime, but it is not clear how long the
relatively small flare we observed in this work would impact a planet’s
atmosphere. Based on the T–P profiles we produce for the hypothetical planet
we consider here, we do not detect large differences in the resulting
transmission spectra (Figure 10, right panel).

Based on studies of high-energy flares on active M stars, it is likely that
low-energy stellar flares like the one observed in this work would leave
atmospheric O3 intact if it were to exist in a planetary atmosphere (Segura et
al., 2010; Tilley et al., 2019). We are also not likely to see the effects of
small stellar flares in the photochemical imprints they leave on planetary
atmospheres, though it has been suggested that early stellar activity is a
source of abiogenesis (Ranjan et al., 2017; Rimmer et al., 2018), which in
turn could alter atmospheric compositions on geological times, as with the
oxygenation of Earth by cyanobacteria. Atmospheric detections on terrestrial
exoplanets are therefore best understood in the context of high-energy stellar
radiation.

Figure 10: Photochemical models for an Earth-like planet in the habitable zone
of the LHS 3844 system, with LHS 3844’s quiescent and flare spectra as inputs.
Left: T–P profiles for the quiescent and flare cases (black solid and dashed
lines, respectively) along with mixing ratios for prominent molecules in
Earth’s atmosphere. Right: model transmission spectra derived from the
photochemical models. The dominant species contributing to various spectral
features are labeled.

##  6 Conclusion

We present the observed UV spectrum of LHS 3844 from 1131 to 3215Å using the
G130M, G160M, and G230L gratings of the COS instrument on board HST. During an
exposure with the G130M grating, we detected a low-energy FUV flare. We
separate the flare spectra from the quiescent spectra and present both in this
work, providing two different pictures of LHS 3844.

Because COS is a slitless spectrograph, we cannot directly observe the
prominent Ly$\alpha$ line due to absorption by neutral hydrogen in the ISM and
local geocoronal contamination. We instead use UV–UV scalings from the MUSCLES
survey to estimate the Ly$\alpha$ flux (France et al., 2016; Youngblood et
al., 2017). We estimate the EUV (100–912 Å) flux using both the Linsky et al.
(2014) and France et al. (2018) scalings, as well as a DEM function estimated
from detected UV emission lines. We place an upper limit on the soft X-ray
flux from Swift-XRT and include this in our estimates of the unmeasured high-
energy portions of the LHS 3844 spectrum. We find the DEM function estimates
to be a more self-consistent method of estimating the unmeasured XUV (1–912Å)
flux of LHS 3844, an inactive mid-M star. However, we do find agreement to
within an order of magnitude between the DEM and scaling methods where they
overlap in wavelength space. We find that our resulting band-integrated
measurements and estimates of the FUV, NUV, and XUV are in agreement with
those found for other M stars (France et al., 2013, 2016).

We estimate that the highly irradiated exoplanet LHS 3844b currently receives
$1.9\times 10^{4}$ erg cm-2 s-1 in XUV flux and would lose a primordial
hydrogen/helium atmosphere in 54 Myr. Keep in mind that this is the calculated
hydrodynamic mass-loss rate derived from the current XUV flux of LHS 3844.
This mid-M dwarf spent hundreds of millions of years in the the pre-main-
sequence phase (Reid & Hawley, 2005), and a further several gigayears in the
X-ray saturation state (Ribas et al., 2005; West et al., 2008; Stelzer et al.,
2013; Wright & Drake, 2016; Wright et al., 2018), during which its X-ray
output was higher than it is today. While LHS 3844b is likely a bare rock
(Kreidberg et al., 2019; Diamond-Lowe et al., 2020), we present atmospheric
models of a hypothetical Earth-like planet in the habitable zone of the LHS
3844 system. Models of the molecular abundances of such a planet exhibit
different responses to the LHS 3844 quiescent and flare spectra. Though the
atmosphere of this hypothetical planet would spend most of its time in the
conditions presented for the quiescent star, the high-energy radiation of LHS
3844 earlier in its lifetime would have looked more like the state we observe
it in during the flare.

The forthcoming Mega-MUSCLES survey will place LHS 3844 in the context of
other planet-hosting mid-M stars. Assessing terrestrial exoplanet atmospheres
requires knowledge of the high-energy environments provided by their host
stars. It may not be possible to measure the UV spectrum of every planet-
hosting M dwarf, and our ability to do so only lasts as long as HST can gather
data. There is no planned successor on the scale of HST in the UV, though
small satellites like the Colorado Ultraviolet Transit Experiment (Fleming et
al., 2018) and the Star-Planet Activity Research CubeSat (Scowen et al., 2018)
aim to measure the high-energy radiation of bright stars. There are also
efforts to broadly capture the UV behavior of M dwarfs from optical indicators
such as Ca ii and H$\alpha$ (Melbourne et al., 2020). Refining the high-energy
behavior of mid-M dwarfs is crucial for future efforts to understand the
atmospheres of the terrestrial worlds around them.

This paper includes data gathered with the Cosmic Origins Spectrograph on
board the Hubble Space Telescope. We thank HST Program Coordinator Patricia
Royle for assistance in scheduling these observations. We thank Amber Medina
for valuable conversations about stellar flares. We greatly appreciate the
thoughtful comments provided by the anonymous referee. Support for Program
15704 was provided by NASA through a grant from the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS5-26555. We also 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).
E.M.-R.K. and D.J.T. recognize support from STScI program No. 16135 and NSF
grant No. 2009095. This publication was made possible through the support of a
grant from the John Templeton Foundation. The opinions expressed here are
those of the authors and do not necessarily reflect the views of the John
Templeton Foundation.
. Data products are available as HLSPs at MAST via 10.17909/t9-fqky-7k61
(catalog 10.17909/t9-fqky-7k61).

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