# The Variable Detection of Atmospheric Escape around the young, Hot Neptune
AU Mic b

Keighley E. Rockcliffe Department of Physics and Astronomy, Dartmouth College,
Hanover, NH 03755, USA  Elisabeth R. Newton Department of Physics and
Astronomy, Dartmouth College, Hanover, NH 03755, USA  Allison Youngblood NASA
Goddard Space Flight Center, Greenbelt, MD 20771, USA  Girish M. Duvvuri
Department of Astrophysical & Planetary Sciences, University of Colorado
Boulder, Boulder, CO 80303, USA  Peter Plavchan Department of Physics and
Astronomy, George Mason University, Fairfax, VA 22030, USA  Peter Gao Earth
and Planets Laboratory, Carnegie Institution for Science, 5241 Broad Branch
Road, NW, Washington, DC 20015, USA  Andrew W. Mann Department of Physics and
Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599,
USA  Patrick J. Lowrance IPAC, MS 220-6, California Institute of Technology,
Pasadena, CA 91125, USA

###### Abstract

Photoevaporation is a potential explanation for several features within
exoplanet demographics. Atmospheric escape observed in young Neptune-sized
exoplanets can provide insight into and characterize which mechanisms drive
this evolution and at what times they dominate. AU Mic b is one such
exoplanet, slightly larger than Neptune ($4.19$ R⊕). It closely orbits a $23$
Myr pre-Main Sequence M dwarf with a period of $8.46$ days. We obtained two
visits of AU Mic b at Lyman-$\alpha$ (Ly$\alpha$) with HST/STIS. One flare
within the first HST visit is characterized and removed from our search for a
planetary transit. We present a non-detection in our first visit followed by
the detection of escaping neutral hydrogen ahead of the planet in our second
visit. The outflow absorbed $\sim 30$% of the star’s Ly$\alpha$ blue-wing
$2.5$ hours before the planet’s white-light transit. We estimate the highest
velocity escaping material has a column density of $10^{13.96}$ cm-2 and is
moving $61.26$ km s-1 away from the host star. AU Mic b’s large high energy
irradiation could photoionize its escaping neutral hydrogen in $44$ minutes,
rendering it temporarily unobservable. Our time-variable Ly$\alpha$ transit
ahead of AU Mic b could also be explained by an intermediate stellar wind
strength from AU Mic that shapes the escaping material into a leading tail.
Future Ly$\alpha$ observations of this system will confirm and characterize
the unique variable nature of its Ly$\alpha$ transit, which combined with
modeling will tune the importance of stellar wind and photoionization.

††software:  astropy (The Astropy Collaboration et al., 2018), batman
(Kreidberg, 2015), cos_flares (Feinstein et al., 2022), emcee (Foreman-Mackey
et al., 2013), lightkurve (Lightkurve Collaboration et al., 2018), lyapy
(Youngblood et al., 2016), matplotlib (Hunter, 2007), numpy (Harris et al.,
2020), scipy (Virtanen et al., 2020), stistools
(https://github.com/spacetelescope/stistools)

##  1 Introduction

Thousands of exoplanets within the Milky Way have been discovered with transit
photometry over the last twenty years, with significant contributions from
Kepler and now TESS
111https://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html. A
significant feature of the exoplanet population is the “radius gap”. The gap,
defined by the relative lack of planets with radii between $1.5$ and $2$ R⊕,
separates two distinct populations of exoplanets: super-Earths and sub-
Neptunes (Fulton & Petigura, 2018; Owen & Wu, 2017; Fulton et al., 2017; Owen
& Wu, 2013). A leading theory is that atmospheric escape produced the gap,
where a population of larger and less dense planets closely orbited their host
stars and subsequently lost envelope mass over time, leaving behind cores with
either little-to-no atmosphere (super-Earths) or smaller – a few % by mass –
atmospheres (sub-Neptunes) (e.g., Jin et al., 2014; Lopez & Fortney, 2013). On
the other hand, Lee & Connors (2021) suggest that the radius gap is a product
of delayed gas accretion during exoplanet formation, and not of atmospheric
escape or other evolutionary processes.

Another feature is the “hot Neptune desert”, a region in exoplanet
radius–period space with a paucity of Neptune-sized planets with short orbital
periods (P${}_{\text{p}}\lesssim 3$ days; Lundkvist et al., 2016; Lecavelier
Des Etangs, 2007). We expect the exoplanets born within the desert to be rocky
core planets with large gaseous envelopes that quickly evolve out of the
desert. As shown in Owen & Lai (2018) and Mazeh et al. (2016), the desert
could be a consequence of atmospheric escape and orbital migration. These
large, low density planets are part of the atmospheric escape story that
formed the previously mentioned radius gap. These two features and their
contested origins motivate continued study of atmospheric escape.

Any atmosphere can experience mass loss. The Earth loses hydrogen from its
upper atmosphere at roughly $3$ kg s-1, a negligible amount compared to the
Earth’s atmospheric mass and replenishment (Catling & Zahnle, 2009). Earth’s
mass loss can be attributed to the sum influence of several atmospheric escape
processes: Jeans escape, charge exchange escape, and polar wind escape. For
exoplanets, hydrodynamic escape is widely thought to be the primary
atmospheric escape process that formed the hot Neptune desert and radius gap.
Hydrodynamic escape occurs when there is an injection of heat to the upper
atmosphere of a planet (thermosphere, exosphere), causing an outflow of gas to
escape the planet’s gravity. The heating mechanism is one of the key
uncertainties surrounding hydrodynamic escape. Photoevaporation – hydrodynamic
escape externally driven by high-energy stellar radiation – was the
unchallenged theory for years (Owen, 2019). Recently, however, core-powered
mass loss – hydrodynamic escape internally driven by radiation from a cooling
planetary core – was posed as a viable candidate (Ginzburg et al., 2018). Both
schemes are able to reproduce the radius gap, and predict the same planetary
core properties and similar slopes in planetary radius–period–insolation space
(Owen & Wu, 2017; Gupta & Schlichting, 2019; Rogers & Owen, 2021).
Alternatives, like impact-driven atmospheric escape, have also been proposed
(Wyatt et al., 2020). Photoevaporation and core-powered mass loss differ in a
few ways that suggest we may be able to tease them apart observationally:
outflow strength, timescale, and different slopes in planetary
radius–period–host mass space. Rogers et al. (2021) describes the theoretical
similarities and differences between the two mechanisms in more detail.

We can use observations of atmospheric escape at different system ages and
host masses to narrow down which mechanism is primarily responsible for
shaping the exoplanet population. Specifically, observations of atmospheric
escape in young systems ($<1$ Gyr) will not only help us figure out what
mechanism dominates mass loss, but will explore at what age atmospheres are
lost, how a planet’s environment influences mass loss, and whether mass loss
rates used in demographic studies are consistent with measurements.

Atmospheric escape has been observed using Far-Ultraviolet (FUV) transmission
spectra, which contain the stellar Lyman-$\alpha$ emission line (Ly$\alpha$)
at $1215.67$ Å. A host star’s Ly$\alpha$ emission has a high likelihood of
interacting with any intervening neutral hydrogen, and any escaping neutral
hydrogen from a transiting exoplanet’s upper atmosphere will partially absorb
the incident Ly$\alpha$ radiation. Interstellar clouds of neutral hydrogen
(ISM) along our line of sight completely absorb the central portion of the
emission line unless the star is moving fast enough to Doppler-shift the
Ly$\alpha$ line away from its rest-wavelength. It follows that in planetary
systems with low-to-moderate radial velocities – including all young systems –
any planetary absorption signature will only be observable in the profile
wings (i.e., we are only able to observe high-velocity escaping material).
Although theory predicts these outflows escape at $\sim 10$s of km s-1, which
would be well within the ISM absorption of Ly$\alpha$ and thus unobservable,
several acceleration mechanisms (e.g., stellar wind ram pressure, charge
exchange, radiation pressure) have been proposed and modeled that can boost
some of the planetary wind to $\sim 100$s of km s-1 (McCann et al., 2019;
Bourrier et al., 2018; Bourrier & Lecavelier des Etangs, 2013).

Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) can
be used to obtain high signal-to-noise observations at Ly$\alpha$ at times
surrounding the white-light transit of a planet. If planetary absorption at
Ly$\alpha$ is detected, the planet’s hydrogen mass loss rate and the outflow
geometry and velocity can be constrained. For hot Jupiters, the inferred mass
loss rates are low relative to their planetary masses, so atmospheric escape
has a negligible effect on the evolution of large Jupiter-massed planets
(e.g., Lecavelier des Etangs et al., 2012; Vidal-Madjar et al., 2003). Mass
loss is thought to be more significant for Neptune-sized planets. There are
four close-orbiting Neptunes with detections of escaping neutral hydrogen
using Ly$\alpha$ transmission spectroscopy: Gl 436b (dos Santos et al., 2019;
Lavie et al., 2017; Ehrenreich et al., 2015; Kulow et al., 2014), GJ 3470b
(Bourrier et al., 2018), HD 63433c (Zhang et al., 2022a), and HAT-P-11b (Ben-
Jaffel et al., 2022). In these Neptunes, Ly$\alpha$ attenuation in the
profile’s blue-wing extends beyond the duration of the white-light transit,
indicating that neutral hydrogen is escaping and traveling towards the
observer in a large cometary tail-like cloud.

Figure 1: A panel of exoplanet demographics information from the NASA
Exoplanet Archive as of August 2022. Non-specified, field-age planets are
represented by the light blue contours and light blue triangles. Specified
planets have been searched for atmospheric escape. Filled circles indicate at
least one published detection of hydrogen and/or helium escape. The x’s
indicate hydrogen/helium escape non-detections. Among the detections/non-
detections, field-age planets are dark blue, whereas young planets are red.
The black star represents AU Mic b, with its range in bulk density showing its
spread in mass measurements. The leftmost panel shows the distribution of
exoplanets in radius and period. The center panel is exoplanet radius versus
its X-ray to ultraviolet irradiation (Foster et al., 2022). The rightmost
panel shows exoplanet radius versus bulk density limited to planets with
$\sigma_{\rho}<0.1\rho$.

Gl 436b, GJ 3470b, and HAT-P-11b all belong to field age systems with ages
$>1$ Gyr. It has been suggested, based on recent constraints on the orbital
structures of Gl 436b and GJ 3470b, that these older planets experiencing mass
loss may have undergone late migration after some gravitational disturbance to
its original far-away orbit (Bourrier et al., 2022; Stefànsson et al., 2022).
HD 63433c is the only young planet with a detection of escaping neutral
hydrogen. Two other young Neptunes, HD 63433b and K2-25b, have Ly$\alpha$
transit observations, neither of which exhibit escaping neutral hydrogen
(Zhang et al., 2022a; Rockcliffe et al., 2021). This provokes interesting
questions about the detectability or presence of atmospheric escape in young
Neptune-sized planets. Rockcliffe et al. (2021) describe multiple scenarios to
reconcile the detected escaping atmospheres with the non-detections. For
example, is the amount of ionizing radiation or strength of the stellar wind
coming from a young star too great to allow a large planetary neutral hydrogen
outflow to develop? These questions warrant more Ly$\alpha$ transit
observations of young exoplanet atmospheres.

Table 1: AU Mic system properties.

Properties (Symbol) | Value | Units | Reference
---|---|---|---
Earth-system distance (d) | $9.722100\pm 0.0004625$ | pc | Gaia Collaboration et al. (2018)
Age ($\tau$) | $22\pm 3$ | Myr | Mamajek & Bell (2014)
Right ascension ($\alpha$) | 20:45:09.87 | hh:mm:ss | …
Declination ($\delta$) |  $-$31:20:32.82 | dd:mm:ss | …
Spectral type | M1Ve |  | Turnbull (2015)
Bolometric luminosity (L${}_{\text{bol}}$) | $0.09$ | L⊙ | Plavchan et al. (2009)
Stellar mass (M⋆) | $0.50\pm 0.03$ | M⊙ | Plavchan et al. (2020)
Stellar radius (R⋆) | $0.75\pm 0.03$ | R⊙ | White et al. (2019)
Stellar rotation period (P⋆) | $4.863\pm 0.010$ | days | Torres et al. (1972)
Radial velocity (v⋆) | $8.7\pm 0.2$ | km s-1 | Lannier et al. (2017)
Epoch (t0) | $2458330.39080^{+0.00058}_{-0.00057}$ | BJD | Gilbert et al. (2022)
Transit duration | $3.56^{+0.60}_{-0.46}$ | hours | Gilbert et al. (2022)
Planetary mass measurements (M${}_{\text{p}}$) | $11.7^{+5.0}_{-5.0}$ | M⊕ |  Zicher et al. (2022)${}^{\text{a}}$
… | $17.0^{+5}_{-5}$ | M⊕ |  Martioli et al. (2021)${}^{\text{b}}$
… | $17.1^{+4.7}_{-4.5}$ | M⊕ |  Klein et al. (2021)${}^{\text{a}}$
… | $20.12^{+1.57}_{-1.72}$ | M⊕ |  Cale et al. (2021)${}^{\text{a}}$
Planetary radius (R${}_{\text{p}}$) | $4.19^{+0.24}_{-0.22}$ | R⊕ | Gilbert et al. (2022)
Orbital period (P${}_{\text{p}}$) | $8.4630004^{+0.0000058}_{-0.0000060}$ | days | Gilbert et al. (2022)
Semi-major axis (a) | $0.0644^{+0.0056}_{-0.0054}$ | AU | Gilbert et al. (2022)

aafootnotetext: Mass measured using radial velocity monitoring.

bbfootnotetext: Mass measured using transit-timing variations.

AU Mic is an M1Ve star in the $\beta$ Pic moving group (Zuckerman & Song,
2004) with a reliably constrained age of $23\pm 3$ Myr (Mamajek & Bell, 2014).
At $9.79\pm 0.04$ pc, it is one of the closest pre-main sequence stars to
Earth. Two exoplanets transiting AU Mic have been discovered using data from
TESS (Gilbert et al., 2022; Martioli et al., 2021; Plavchan et al., 2020). AU
Mic b orbits closer to its host, with a period of $8.46$ days. An overview of
AU Mic’s system parameters, excluding AU Mic c, is given in Table 1. Gilbert
et al. (2022) measured AU Mic b’s radius as $4.19$ R⊕, placing it on the edge
of the hot Neptune desert as shown in the left-most panel of Figure 1. We
expect planets of this size (indicating a large gaseous envelope) and orbital
period (highly irradiated) to be experiencing significant photoevaporation.
This and the star’s youth and proximity to Earth prompt the detailed study of
AU Mic b’s potentially escaping atmosphere. We obtained Ly$\alpha$ transits of
AU Mic b with HST/STIS (HST-GO-15836; PI: Newton). These observations are
presented in Section 2. We analyze the presence and impact of an observed
stellar flare in Section 3. After accounting for the flare, we search for the
presence of planetary absorption in Ly$\alpha$ and other emission line light
curves in Section 4. We confirmed that AU Mic c does not transit during our
observations. We also shifted the white-light mid-transit time for each visit
(the zero hour mark in Figures 6, 7, 8, and 9) in line with recent transit-
timing variation analyses for the AU Mic system (Wittrock et al., 2022). We
construct the high energy environment of AU Mic b, and estimate its mass loss
rate and the impact of photoionization in Section 5. We summarize and discuss
our results in Section 6.

##  2 Far-UltraViolet Observations

###  2.1 New observations corresponding to two transits of AU Mic b

We obtained FUV observations of AU Mic using a $0.2$″ x $0.2$″ aperture on
HST’s STIS instrument. HST observed the AU Mic system on 2 July 2020 (Visit 1)
and 19 October 2021 (Visit 2), corresponding to two transits of AU Mic b. Six
science exposures were taken per transit, each exposure covering the
observable window of an HST orbit ($2000-3000$ s). STIS was in its FUV multi-
anode microchannel array configuration (FUV-MAMA). We used the E140M echelle
grating, which has a resolving power of $\sim 45800$ and wavelength coverage
from $1144-1729$ Å. All science observations were made in TIME-TAG mode, where
each photon detected by the instrument has a time-stamp. The time-stamps
allowed us to split each science exposure into smaller sub-exposures prior to
data extraction and reduction. This was done using the inttag function from
the stistools Python package
(v1.3.0)222https://github.com/spacetelescope/stistools. For our flare analysis
in Section 3, we used $30$ s sub-exposures. Shorter sub-exposures were too low
signal. We used 10 sub-exposures ($\sim 241$ or $275$ s each) per orbit for
our light curve analysis in Section 4. We extracted and reduced these data
with stistools.x1d.x1d, which utilizes the calstis pipeline (v3.4). We allowed
the pipeline to find the best extraction location per echelle order in the
calibrated, flat-fielded exposures. The extraction locations per echelle order
varied by less than a pixel between each orbit. The same extraction and
reduction procedure was used on the sub-exposures. Each reduced spectrum
contains 44 echelle orders.

The pipeline uncertainties correlate with $\sqrt{\text{N}}$, where N is the
total photon count per wavelength bin. This uncertainty estimate is inaccurate
for small counts, which is the case for the lower signal-to-noise sub-
exposures. As in Rockcliffe et al. (2021), we recalculated the errors for each
sub-exposure spectrum using Equation 1, an estimation of the confidence limit
of a Poisson distribution, and the total counts reported in the GROSS
spectrum. These uncertainties were converted from counts into flux units using
a multiplicative factor inferred by comparing the GROSS and flux-calibrated
spectra. The calstis errors were used for the full-orbit spectra, which are
high signal-to-noise.

$\sigma\approx 1-\sqrt{\text{N}+0.75}$ (1)

###  2.2 Investigating breathing

Figure 2: Visits 1 and 2 Ly$\alpha$ light curves folded on the HST orbital
period ($95.42$ min). Each color corresponds to sub-exposures from a single
HST orbit. Only sub-exposures from consecutive orbits are plotted (and
considered in fitting the trend). The best-fit polynomial is shown by the
dashed line.

Before analysis, we sought to remove HST “breathing” - thermal fluctuations
that cause variability in the telescope optics, impacting the throughput on
the timescale of an HST orbit ($95.42$ min). For each transit, we created a
light curve of consecutive orbits for the integrated Ly$\alpha$ line flux in
each sub-exposure ($10$ per orbit). Ly$\alpha$ was integrated over
$1214.0-1217.0$ Å (excluding the remnant airglow region between $1215.4$ and
$1215.7$ Å). Ly$\alpha$ is the highest signal-to-noise emission line in our
data and thus the most preferred region to search for systematics. However, we
note that our detrending process may overcorrect potential planetary and
stellar variability on the – relatively short – timescale of an HST orbit.

Figure 2 shows the Ly$\alpha$ light curves for Visits 1 and 2 folded on HST’s
period and the corresponding best-fit polynomials. The flux values are
normalized by the mean flux per HST orbit. The best-fit per light curve was
determined by selecting the polynomial order that gave the smallest Bayesian
Information Criteria (BIC). Both transits deviate from a flat line, which
corresponds to variability over the course of an HST orbit and confirms the
presence of “breathing”. To detrend, we divided the best-fit polynomial out of
each folded light curve (non-consecutive orbits included). The same process
was used to detrend each FUV emission line light curve because HST breathing
has been characterized as an achromatic effect. Most emission line light
curves were consistent with a flat line when folded.

###  2.3 Archival FUV observations

We reference archival HST/STIS observations of AU Mic published by Pagano et
al. (2000). Four science exposures were taken on 06 September 1998, which does
not correspond to an AU Mic b transit (HST-GO-7556; PI: Linsky). The observing
set-up was the same as our observations: $0.2$″ x $0.2$″ aperture, FUV-MAMA
configuration, E140M grating, TIME-TAG mode. The same extraction, reduction,
and breathing-check processes were used on these data.

###  2.4 Looking for planetary absorption with Ly$\alpha$ and other emission
line spectra

Figure 3: The Ly$\alpha$ spectra of AU Mic observed by HST/STIS in September
1998 (left, archival), July 2020 (center, Visit 1), and October 2021 (right,
Visit 2). The gray shaded areas indicate our blue- and red-wing integration
regions.

Figure 3 depicts the observed Ly$\alpha$ spectra for each new visit alongside
the archival data. The ISM absorbs the line core ($\sim 1215.67$ Å), leaving
the wings for analysis. Although Ly$\alpha$ observations of high radial
velocity stars are becoming more common (Youngblood et al., 2022; Schneider et
al., 2019), young stars in particular are low in velocity and as such do not
experience significant Doppler shifting of spectral lines. AU Mic’s low
velocity ensures that the Ly$\alpha$ line core is unobservable at Earth due to
absorption by the ISM. Both the archival and Visit 2 data have residual
geocoronal emission within the wavelengths fully absorbed by the ISM. Due to
the high spectral resolution of STIS echelle data, this is not important for
our analysis.

Although the Visit 1 Ly$\alpha$ spectra remain fairly consistent throughout
the transit, the flare addressed in Section 3 is encapsulated in its first
orbit. Due to the flare’s short duration, it is washed out by the full-orbit
exposure time and a flux increase is not visible. The flare still has the
ability to impact our search for planetary absorption, however, and this first
orbit cannot be considered devoid of any contamination despite its stable
appearance. When discussing the full-orbit spectra, we ignore this orbit.

Over all three visits to AU Mic, the extended blue-wing ($\lambda<1215$ Å)
remains stable. This may indicate that the blue-wing is relatively impervious
to stellar activity. The same cannot be said for the extended red-wing
($\lambda>1216.1$ Å), which shows variations of up to $10\%$ percent in the
archival, Visit 1, and Visit 2 data (see Figure 8). The inner red-wing – where
we are looking for planetary absorption ($1215.8<\lambda<1216.1$ Å;
$32.1<v<106$ km s-1) – shows similar fluctuations across the three visits. It
may be that the entirety of the Ly$\alpha$ red-wing is more sensitive to
stellar activity than its blue counterpart. For that reason, we hesitate to
associate a decrease in the Ly$\alpha$ red-wing flux up to about $10\%$ with
planetary absorption.

Table 2: Best-fit parameters with $1-\sigma$ uncertainties for the in-transit (Visit 2, first orbit) and out-of-transit (Visit 2, sixth orbit) Ly$\alpha$ spectra: characterizing the intrinsic Ly$\alpha$ line, the ISM absorption, and the planetary absorption.  Parameter (Units) | In-Transit Value | Out-of-Transit Value
---|---|---
v${}_{\text{n}}$ (km s-1) | … | $-7.29^{+0.92}_{-0.89}$
log10A${}_{\text{n}}$ (erg s-1 cm-2 Å-1) | … | $-10.87^{+0.03}_{-0.03}$
FW${}_{\text{n}}$ (km s-1) | … | $140.54^{+2.82}_{-2.74}$
v${}_{\text{b}}$ (km s-1) | … | $-7.37^{+1.18}_{-1.18}$
log10A${}_{\text{b}}$ (erg s-1 cm-2 Å-1) | … | $-11.64^{+0.02}_{-0.02}$
FW${}_{\text{b}}$ (km s-1 ) | … | $386.12^{+6.03}_{-5.87}$
ISM log10N${}_{\text{H I}}$ | … | $18.38^{+0.01}_{-0.01}$
b (km s-1) | … | $12.34^{+0.27}_{-0.29}$
v${}_{\text{H I}}$ (km s-1) | … | $-22.98^{+0.23}_{-0.23}$
pl log10N${}_{\text{H I}}$ | $13.96^{+0.03}_{-0.03}$ | …
b${}_{\text{pl}}$ (km s-1) | $61.05^{+2.24}_{-2.24}$ | …
v${}_{\text{pl}}$ (km s-1) | $-61.26^{+2.45}_{-2.74}$ | …

We expect the majority of escaping planetary material to be moving at $10$s of
km s-1. Hydrodynamic models show that radiation and stellar wind pressure can
accelerate escaping neutral hydrogen up to these velocities directed radially
outward from the host star (McCann et al., 2019; Bourrier et al., 2018). This
draws our attention to the inner blue-wing ($1215<\lambda<1215.5$ Å;
$-165.2<v<-41.9$ km s-1) which could be experiencing flux variations due to
absorption by planetary neutral hydrogen flowing away from the host star. The
archival spectra do not show any significant changes within this region. The
Visit 1 spectra display a small amount of variability at the shorter
wavelength edge of our blue-wing region. The Visit 2 spectra, however, show a
gradual $30\%$ increase in the blue-wing flux over the course of the planet’s
transit.

Assuming the flux behavior is due to absorption by escaping planetary neutral
hydrogen, we fit the observed Ly$\alpha$ profile with an intrinsic stellar
component, an ISM absorption component, and a planetary absorption component.
We used the Python package lyapy (Youngblood & Newton, 2022), which
encompasses a model that combines the aforementioned emission and absorption
components and a fitting algorithm that uses emcee as the MCMC sampler
(Foreman-Mackey et al., 2013). A thorough description of the lyapy model and
how it can be used to reconstruct cool star Ly$\alpha$ emission profiles can
be found in Youngblood et al. (2016) and Section 4.1 of Raetz et al. (2020).

First, we reconstructed AU Mic’s Ly$\alpha$ emission line using the last orbit
from Visit 2 (see right panel of Figure 4), which we assume is out-of-transit
for the planetary neutral hydrogen. The timing of absorption in comparison to
the planet’s white-light transit is discussed more thoroughly in Sections 4
and 6. We varied every stellar and ISM profile parameter with uniform priors
except for the ISM deuterium-to-hydrogen ratio, which we fixed to $1.5\times
10^{-5}$ (Linsky et al., 2006). The best-fit parameters that recreated our
observed Ly$\alpha$ profile can be found in Table 2. Our results do not agree
within uncertainties with the reconstructed AU Mic Ly$\alpha$ profile from
Youngblood et al. (2016) (see their Table 1). However, our best-fit values
agree within a few $\sigma$ at most and the stability of M dwarf Ly$\alpha$
emission at young ages has not been fully explored.

We modified the absorption model within lyapy to include a Voigt profile
characterizing the excess absorption due to the proposed planetary outflow.
This profile is only able to characterize the high velocity outflow that is
visible in our observations. All information regarding the low velocity
planetary material is lost due to ISM absorption. The profile is parameterized
by column density, Doppler broadening, and a velocity centroid associated with
the intervening planetary neutral hydrogen. These three parameters were varied
during our fit to the in-transit spectrum, whereas our best-fit Ly$\alpha$
emission and ISM absorption values from the out-of-transit profile were fixed.
We estimate the high velocity planetary neutral hydrogen has a column density
of log10N${}_{\text{H I}}=13.96^{+0.03}_{-0.03}$ and is moving
$-61.26^{+2.45}_{-2.74}$ in the stellar rest frame. Our column density should
be treated as a lower limit on the total neutral hydrogen column density of
the outflow. The left panel of Figure 4 shows the best-fit planetary
absorption scaled to the figure’s y-axis along with the best-fit to the
observed spectrum. We investigate this in-transit absorption further by
integrating over the region and analyzing the light curve in Section 4.

Figure 4: The AU Mic Ly$\alpha$ spectra “in-transit” on the left (Visit 2
first orbit) and “out-of-transit” on the right (Visit 2 sixth orbit). The
observed data is shown by the black line. The blue dashed line is the
reconstructed stellar Ly$\alpha$ line. The Voigt profile fit for the planetary
absorption scaled to the y-axis of the figure is represented by the red dotted
line. The blue line is the best fit damped Ly$\alpha$ profile, with its
$1-\sigma$ uncertainty shown by shaded blue regions around the line. The gray
shaded regions indicate areas of the data that were masked before being run
through our fitting algorithm.

Figure 5 shows the archival, Visit 1, and Visit 2 spectra for the N V, O I, Si
IV, He II, and C I species. Although there are more emission lines present in
the data (see Table 3 and Figures 10 and 11), we focus on these five species
for tracing stellar activity and our search for planetary atmospheric escape.
FUV spectroscopic studies of M dwarfs have shown that N V and Si IV can trace
stellar activity, which can help identify when flux changes are not planetary
in nature (Loyd et al., 2018b; Loyd & France, 2014). Alternatively, O I, He
II, and C I are relatively insensitive to flares. O I and C I are of recent
interest as potential tracers of the evolution of the C/O ratio in exoplanet
atmospheres (Owen, 2022). O I, C I and C II have been used to trace
atmospheric escape previously in several hot Jupiters, as well as the hot
super Earth $\pi$ Men c (García Muñoz et al., 2021).

As expected, the Visit 1 flare causes substantial increases in the emission
line fluxes for N V and Si IV, whereas O I and C I do not. He II also
experiences an enhancement due to the flare. In Visit 2, N V and He II have a
similar flux increase during the fifth orbit, which also corresponds to the
increase observed in the Ly$\alpha$ blue-wing in Figure 3 but does not last
through the sixth orbit. When compared to the archival spectra, this behavior
is not representative of the typical noise in N V and He II emission. Light
curves for these two species are presented in Section 4 and compared to the
Ly$\alpha$ line behavior. O I shows consistent spectral variation across the
archival, Visit 1, and Visit 2 spectra, making it difficult to discern the
presence of planetary absorption. Similarly, C I is too low signal-to-noise to
draw any conclusion about carbon in transmission. Their light curves are also
shared in Section 4.

Figure 5: The emission line spectra of AU Mic observed by HST/STIS in September 1998 (left, archival), July 2020 (center, Visit 1), and October 2021 (right, Visit 2). The gray shaded areas indicate our integration regions. The orbits correspond to the same colors indicated in Figure 3. Table 3: AU Mic FUV emission lines confidently identifiable in this work’s HST/STIS spectra, cross-referenced with NIST (Kramida et al., 2021), the CHIANTI Atomic Database (Del Zanna et al., 2021; Dere et al., 1997), and Feinstein et al. (2022). The table includes line location(s), integration region, and formation temperature.  Species |  $\lambda$ (Å) |  $\Delta\lambda$ (Å) | $\log_{10}(T/\text{K})$
---|---|---|---
C III | $1175.7$ | $1174.5-1177.0$ | $4.8$
Si III | $1206.51$ | $1206.3-1206.7$ | $4.7$
H I (Ly$\alpha$) | $1215.67$ | $1214.0-1217.0$ | $4.5$
N V |  $1238.82$, $1242.80$ |  $1238.6-1239.0$, $1242.6-1243.0$ | $5.2$
O I |  $1302.2$, $1304.84$, $1306.01$ |  $1302.05-1302.35$, $1304.7-1305.0$, $1305.8-1306.15$ | $3.8$
C II |  $1334.53$, $1335.71$ |  $1334.45-1334.75$, $1335.45-1335.95$ | $4.5$
Fe XXI | $1354.07$ | $1353.8-1354.4$ | $7.1$
Si IV |  $1393.76$, $1402.77$ |  $1393.45-1394.05$, $1402.4-1403.15$ | $4.9$
C IV |  $1548.20$, $1550.774$ |  $1547.9-1548.5$, $1550.6-1551.0$ | $4.8$
He II | $1640.40$ | $1640.2-1640.65$ | $4.9$
C I |  |  $1656.27$, $1656.93$, $1657.01$, $1657.38$,
---
$1657.91$, $1658.12$
$1656.0-1658.25$ | $3.8$

##  3 Flare Analysis

###  3.1 Emission line flare light curves

Before looking for a planetary signature, we needed to characterize and remove
any host star variability from our observations. A substantial increase in AU
Mic’s flux in several emission lines and its FUV continuum occurred during the
first orbit of Visit 1, initially identified by eye. Figure 6 shows the
diversity in flaring behavior of the highest signal-to-noise emission lines
(listed in Table 3). We used $30$ s sub-exposures for comprehensive sampling
of the flare. We did not model these light curves as we did with Ly$\alpha$
and the continuum presented in Section 3.2.

As shown in Figure 6, C III, Si IV and C IV exhibit the strongest emission
during the peak of the flare, followed by Si III and C II. Most emission lines
return to quiescent fluxes relatively quickly ($\sim 2$ min). A notable
exception is He II, which remains elevated over the entirety of the exposure
and returns to quiescence by the second exposure (not pictured). The Visit 1
flare caused greater flux increases in every overlapping emission line
examined between this work and Feinstein et al. (2022). However, caution
should be taken when comparing fluxes observed with STIS and COS, as STIS has
focus issues that impact the flux calibration of narrow slit observations
(Riley et al., 2018; Proffitt et al., 2017). The one flare we observe in our
$\sim 7$ hours of non-consecutive HST orbits is at odds with the $2.5$ hour-1
AU Mic FUV flare rate presented in Feinstein et al. (2022) and potentially
agrees with the $2$ day-1 estimate from Gilbert et al. (2022) based on visible
light data. Although we did not conduct further analysis, characterizing this
flare and comparing it to other AU Mic flares observed with STIS and COS would
further knowledge of flare diversity from an individual star and help identify
systematic differences between the STIS and COS instruments.

Figure 6: Light curves for the first orbit of Visit 1 split into $30$ s sub-
exposures for various emission lines from Table 3.

###  3.2 Ly$\alpha$ and continuum flare modeling

Flares and other forms of stellar activity can mask or masquerade as planetary
signals in transit photometry and transmission spectroscopy. Loyd & France
(2014) surveyed 38 cool stars with HST/COS and STIS spectra, characterizing
their variability in the ultraviolet and the potential for masking planetary
signals. They concluded that most F-M stars will allow for confident
detections of planets larger than Jupiter, with M dwarfs potentially lowering
that limit to Neptune-to-Saturn-sized planets.

We modeled the Visit 1 flare in order to characterize its potential to mask
the transit of AU Mic b. For this analysis, we focused on the Ly$\alpha$
emission line because it is the highest signal emission line in the data and
because of its relevance to our search for atmospheric escape in transmission.
We also modeled the FUV continuum behavior during the flare for comparison
(continuum defined in A.1).

Figure 7: Continuum (top, left) and Ly$\alpha$ (bottom, left) light curves for
the first two orbits of Visit 1. The light blue points are the $30$ s sub-
exposures, and the blue line is the fitted flare model. Continuum and
Ly$\alpha$ in- (red) and out-of-flare (blue) spectra are shown in the top-
right and bottom-right panels, respectively.

We adapted the open source Python code cos_flares from Feinstein et al.
(2022)333https://github.com/afeinstein20/cos_flares/tree/paper-version written
for analyzing flares in HST/COS data to be compatible with our STIS data. We
fit the Visit 1 flare light curve using a skewed Gaussian, represented by
Equation 2 where $\omega$ parameterizes the amplitude, $t$ is time, $\xi$ is
the average time in the flare light curve, and $\eta$ is a dimensionless
version of time related to the aforementioned parameters and the skewness of
the light curve. The skewed Gaussian model was chosen because it provided the
best fit to the Ly$\alpha$ light curve compared to the white-light flare model
and the skewed Gaussian convolved with the white-light flare model. Figure 7
shows the resulting fit to the Ly$\alpha$ flare. We allowed for multiple peaks
in the flare to be modeled and fit, which is shown by the small increase in
flux after the flare.

$F(t)\sim\frac{1}{\omega\sqrt{2\pi}}\left(e^{-(t-\xi)^{2}/(2\omega)^{2}}\right)\left[1+\text{erf}\left(\frac{\eta}{\sqrt{2}}\right)\right]$
(2)

###  3.3 Flare energy and duration

We calculated the flare energy, equivalent duration, and maximum time the
flare could mask a $10\%$ planetary transit.

Absolute flare energy, $E$, is the total energy released by the flare at the
star within the spectral feature. It is given by Equation 3:

$E=4\pi d^{2}\int\left(F_{f}(t)-F_{q}(t)\right)dt$ (3)

where $d$ is the distance to AU Mic, and $F_{fl}$ and $F_{q}$ are the flaring
and quiescent fluxes (Davenport et al., 2014; Hawley et al., 2014). The
difference in flaring and quiescent flux is integrated over the time it takes
for the flux to return to quiescence. We classified the first two orbits of
Visit 1 as flaring, and the remaining out-of-transit orbit at the end of the
visit as quiescent.

We calculated a total flare energy of $7.11\times 10^{32}$ erg for Ly$\alpha$,
and $2.57\times 10^{34}$ erg for the continuum. Our continuum flare energy is
$100$ times larger than the median flare energy characterized in Feinstein et
al. (2022) for AU Mic. It is also $1000-10000$ times larger than the median
FUV flare energy found by surveying M stars (Loyd et al., 2018a, b).

The equivalent duration, $t_{eq}$, is given by Equation 4. Similar to an
equivalent width, it characterizes the amount of time for which the star would
have to emit 100% of its quiescent flux in order to match the total energy of
the flare. The flare’s equivalent duration was estimated as $278$ s ($0.0772$
hours) for Ly$\alpha$, and $43515$ s ($12.1$ hours) for the continuum.

$t_{eq}=\int\left(\frac{F_{f}(t)-F_{q}(t)}{F_{q}(t)}\right)dt$ (4)

The maximum masking time bears the most importance to our search for AU Mic b
in transmission. We calculated the amount of time the flare was above $110\%$
of the quiescent Ly$\alpha$ flux, effectively washing out a $10\%$ planetary
transit depth. We chose $10\%$ as a conservative estimate for the potential
size of the exosphere. We found that this flare contaminated the Ly$\alpha$
light curve for about $5731$ s, or $1.5$ HST orbits. This occurred 7 hours
before AU Mic b’s white-light mid-transit, so we do not expect the increase in
flux from the flare to deter us from observing a planetary signal in Visit 1.

##  4 AU Mic’s Light Curves

We examined the temporal behavior of AU Mic’s flux in different regions of its
FUV spectrum (i.e., the Ly$\alpha$ emission line and the several metal lines
listed in Table 3). In Section 3 we concluded that the flare only impacts the
first orbit of Visit 1, so we removed the contaminated orbit and examined the
Visit 1 and 2 light curves separately for signs of planetary absorption.

###  4.1 Ly$\alpha$ light curve

The presence or absence of absorption in the Ly$\alpha$ line over the course
of AU Mic b’s transit can indicate whether or not neutral hydrogen is escaping
from the planet’s upper atmosphere. After the detrending process described in
Section 2, we created two Ly$\alpha$ light curves per transit by summing the
flux in the blue-wing ($1215.0-1215.5$ Å) and the red-wing ($1215.8-1216.1$
Å). The errors were summed in quadrature. Visit 1 exposures were normalized by
the sixth orbit, which occurs $17$ hours after mid-transit and $>20$ hours
after the flare. Visit 2 was normalized by the average of the fifth and sixth
orbits. We also included archival HST/STIS observations of AU Mic from
September 1998 which do not coincide with an AU Mic b or c transit, normalized
by the last orbit from this visit. These light curves are shown in Figure 8.

Figure 8: The archival (left, black), Visit 1 (center, blue), and Visit 2
(right, red) light curves for the blue- (top) and red-wing (bottom) of the
Ly$\alpha$ line. The first orbit from Visit 1 is not included because of the
flare. Visit 1’s sixth, and final, orbit is not included but is represented by
the horizontal line at a flux of 1. The gray points represent the sub-
exposures. Samples from the posterior distribution of light curve fits to the
Visit 2 blue-wing are shown by the pink lines. The white-light transit
duration is shown by the gray shaded region.

The Ly$\alpha$ blue-wing shows a $\sim 5\%$ increase in emission during Visit
1 (center-top panel of Figure 8). For this reason, we do not attempt to fit
for a planetary transit in this light curve. We present possible explanations
for this in Sections 4.2 and 6. As discussed in Section 2, the Ly$\alpha$ red-
wing exhibits consistent flux changes of up to $10\%$ across all three HST
visits. These fluctuations occur at different times in relation to the
planetary ephemeris – from $100$s to within a few hours outside of transit –
leading us to conclude that these are changes in the intrinsic stellar
Ly$\alpha$ emission.

The Visit 2 Ly$\alpha$ blue-wing light curve exhibits extended absorption
starting at least four hours prior to the white-light mid-transit. The blue-
wing flux decrease lasts for about four hours and is completely recovered by
the conclusion of white-light transit. If the decrease in flux is due to
absorption in AU Mic b’s atmosphere, that implies that the neutral hydrogen is
moving ahead of the planet and is expanding radially away from the host star.
We pose physical explanations for the bulk of the escaping atmosphere to
transit before the planet in Section 6. Although slight Ly$\alpha$ absorption
prior to planet transit has been observed in other systems, like GJ 3470b, it
has never been observed to this magnitude (Bourrier et al., 2018).

Table 4: Fixed Light Curve Parameters (Gilbert et al., 2022).  Parameter | Value | Units
---|---|---
$P_{\text{p}}$ | $8.4630004$ | days
$a$ | $0.0644$ | AU
$i$ | $89.18$ | degrees
$e$ | $0.12$ |
$w$ | $88.528$ | degrees

We used batman to model a planetary transit for the Visit 2 blue-wing and
emcee to explore parameter space using Markov Chain Monte Carlo (MCMC). batman
models a transit for a fully opaque circle, not allowing for more diverse
atmospheric geometries. We initialized the batman model with measured system
parameters (see Table 4). Only the planetary radius at Ly$\alpha$ and the mid-
transit time were free parameters. The mid-transit time had a uniform prior
constrained to within 5 hours of the white-light mid-transit time. The
planetary radius at Ly$\alpha$ was limited to positive values (no negative
transit depths). The 60 sub-exposures associated with Visit 2 were fit using
80 MCMC walkers and 200000 steps. There was a burn-in of 50000 steps. We did
the same for the Visit 2 red-wing, but the opaque disk model provides a poor
fit to our data due to its long duration and small flux decrease.

The best-fit $R_{\text{p}}/R_{\star}$ value for the blue-wing light curve is
$0.52\pm 0.01$ ($0.39\pm 0.008$ R⊙). The Ly$\alpha$ blue-wing mid-transit time
is $2.5\pm 0.24$ hours before the white-light mid-transit time. Figure 8
includes example light curves pulled from the MCMC posteriors as pink lines. A
model that allows for non-circular geometries and/or transparency of the
transiting object along with data corresponding to the beginning of the
absorption signal would be required to better fit our blue-wing light curve.

We used the formalism presented in Owen et al. (2023) to estimate the geometry
and kinematics of the escaping planetary material. Although they model a
trailing tail of neutral hydrogen, the same physics applies to a leading tail
– our observations of AU Mic b correspond to a flipped version of Figure 1
from Owen et al. (2023). We used their Equations 10 and 11 for transit depth
and duration, respectively, to calculate a tail length of $9.69\times 10^{10}$
cm ($1.39$ R⊙) and height of $2.22\times 10^{10}$ cm ($0.32$ R⊙). From their
Equation 2, we estimated the velocity of the bulk of escaping material –
before acceleration by interactions with the environment – to be $20$ km s-1.
Unfortunately we are unable to probe this velocity observationally for the AU
Mic system due to the ISM absorption at the Ly$\alpha$ core (see Section 2.4),
but Ly$\alpha$ observations of high radial velocity systems allow transits to
occur at these lower velocities, as do transits of uncontaminated emission
lines (e.g., He $10830$ Å). As specified by Owen et al. (2023), we treat these
calculations as rough estimates to be tested by future sophisticated models.

###  4.2 Metal line light curves

Figure 9: The archival (left, black), Visit 1 (center, blue), and Visit 2
(right, red) light curves for several FUV emission lines. The first orbit from
Visit 1 is not included because of the flare. Visit 1’s sixth, and final,
orbit is not included but is represented by the horizontal line at a flux of
1. The gray points represent the sub-exposures. The white-light transit
duration is shown by the gray shaded region.

The search for atomic metals has been ongoing in some of the hottest giant
planet atmospheres. Detections of atomic sodium, potassium, and calcium have
come from optical and infrared observations (e.g., Zhang et al., 2022b;
Hoeijmakers et al., 2020; Yan et al., 2019). Using HST/STIS, neutral and
ionized metals (mostly sodium) have been detected in the ultraviolet for
several Hot Jupiters (Sing et al., 2019; Alam et al., 2018; Sing et al., 2016;
Nikolov et al., 2014). With HST/COS, metal absorption extending past the Roche
lobe has been detected for WASP-12b, showing that these ionized metals can be
carried far away from the planet by atmospheric escape (Haswell et al., 2012;
Fossati et al., 2010). Hot Neptunes, despite being more vulnerable to an
escaping atmospheric outflow that could carry heavier atoms, have remained
undetected in metal lines with the exception of sodium detected in WASP-166b
(Seidel et al., 2022, 2020) and a potential detection of C I in HAT-P-11b
(Ben-Jaffel et al., 2022).

Our AU Mic observations have a high enough signal-to-noise to look for
transits of AU Mic b’s escaping atmosphere in the host’s metal emission lines.
Figure 9 shows the light curves during Visits 1 and 2 for N V, O I, Si IV, He
II, and C I. All lines show decreasing flux around AU Mic b’s mid-transit in
Visit 1 except the slight emission shown by Si IV. It may be that the flare
has a longer lasting impact on these metal lines as opposed to the one-orbit
impact estimated for Ly$\alpha$ and so they are still evolving towards
quiescence during the planetary transit.

The Visit 2 N V, O I, He II and C I light curves have a similar shape to the
Visit 2 Ly$\alpha$ light curves in Figure 8, but with much lower signal-to-
noise. N V and He II, two lines where we do not expect to see planetary
material, exhibit the most pronounced transit-like behavior. The transit-like
depth is reduced when the flux normalization is changed from the average
between the fifth and sixth orbits to just the sixth orbit. The transit-like
shape is also exhibited by the archival N V and He II light curves, which are
well out of transit. As in Duvvuri et al. (2023), we speculate that the metal
line variability is due to some uncharacterized stochastic stellar activity
potentially linked to magnetic heating processes within AU Mic’s atmosphere.
We encourage the use of this data in combination with future UV programs
targeting M dwarfs to further investigate this non-flaring behavior.

The O I and C I light curves are of utmost interest when searching for
planetary metal transits (Owen, 2022). Although the O I and C I light curves
in Figure 9 depict transit-like behavior, we hesitate to characterize this as
planetary absorption 1) because of the low signal from these lines and 2)
because the behavior coincides with potential stellar activity signatures in
the other emission lines presented. HST/COS will be more successful
characterizing planetary metal line absorption than STIS. A metal outflow
search is currently underway for AU Mic b using COS, which can be compared to
these data to more definitively distinguish between planetary and stellar
signatures (Feinstein, in prep).

##  5 AU Mic b’s High Energy Environment

We investigated the planet’s high energy irradiation to place constraints on
how much mass it is potentially losing and how much of it is staying neutral.
We define high energy irradiation as the quiescent radiation received between
$5-1170$ Å, which covers the X-ray through the EUV. ROSAT observed AU Mic’s
quiescent X-ray luminosity to be $2.51\times 10^{29}$ erg s-1, corresponding
to a flux of $21500$ erg s-1 cm-2 at AU Mic b (Table 3; Chadney et al., 2015).

Much of the star’s EUV spectrum is inaccessible due to obscuration by the
intervening interstellar medium. Duvvuri et al.
(2021)444https://github.com/gmduvvuri/dem_euv modeled AU Mic’s EUV spectrum
using the differential emission measure technique. This method provides an
estimate for the radiation from plasma at a specific temperature. They
calculated an EUV flux of $8420$ erg s-1 cm-2 at AU Mic b. The combined XUV
irradiation of the planet is about $29900$ erg s-1 cm-2.

Chadney et al. (2015) include X-ray and EUV luminosity measurements for a
flaring AU Mic. Using the observed flare values from their Table 3, the
combined flaring XUV irradiation of AU Mic b is $71500$ erg s-1 cm-2.

###  5.1 Planetary mass-loss rate

The amount of mass escaping the planet is often estimated by assuming the
amount of high energy radiation received directly translates to heating the
atmosphere, leading to a bulk flow of gas that overcomes the planet’s
gravitational potential. This is referred to as the energy-limited regime.
There are two other photoevaporation regimes that may apply: recombination-
limited and photon-limited (Owen & Alvarez, 2016). The flow timescale to
recombination timescale ratio determines which regime applies to a planet.
This ratio is largely governed by the planet’s density and incident high
energy flux. Figure $1$ in Owen & Alvarez (2016) shows how the three
photoevaporation regimes depend on a planet’s mass and radius. Given AU Mic
b’s XUV irradiation of $29900$ erg s-1 cm-2, it will likely follow the top
left or bottom right panels depending on the atmosphere’s heating efficiency.

A typical source of uncertainty is the planet’s mass. This is difficult to
measure with extreme precision and is yet more difficult for planets with
active hosts, like AU Mic, due to contamination from stellar variability.
There are a few mass measurements reported for AU Mic b: $11.7\pm 5.0$
M⊕(Zicher et al., 2022), $17.1^{+4.7}_{-4.5}$ M⊕ (Klein et al., 2021) and
$20.12^{+1.57}_{-1.72}$ M⊕ (Cale et al., 2021) from radial velocities, and
$17\pm 5$ M⊕ from transit-timing variations (Martioli et al., 2021).

AU Mic b has a radius of $2.60\times 10^{9}$ cm and a potential mass range of
$6.99-12.0\times 10^{28}$ g. With a heating efficiency of $0.1$ (top left
panel of Figure 1; Owen & Alvarez, 2016), AU Mic b will be within the energy-
limited regime no matter its mass. However, if its atmosphere has a higher
heating efficiency (bottom right panel of Figure 1; Owen & Alvarez, 2016),
then the planet could enter the photon-limited regime. During periods of high
stellar activity, if a lower mass AU Mic b’s XUV irradiation reaches $\gtrsim
10^{5}$ erg s-1 cm-2, then the planet could enter the recombination-limited
regime. For this reason, we present AU Mic b’s energy-limited mass loss rate
as a possible scenario but the true mass loss rate could be smaller or larger
by a few orders of magnitude and will vary on short and long timescales.

The energy-limited regime is given by Equation 5, which is dependent on the
incident high energy radiation ($F_{\text{XUV}}$), the planet’s radius
($R_{\text{p}}$) and mass ($M_{\text{p}}$), the atmosphere’s heating
efficiency ($\eta$), and a correction factor ($K_{\text{eff}}$, Equation 6).
$K_{\text{eff}}$ corrects for the difference in gravitational potential at the
planet’s radius versus its Roche lobe where the atmosphere needs to escape.

$\dot{M}=\eta\frac{\pi
R^{3}_{\text{p}}F_{\text{XUV}}}{GM_{\text{p}}K_{\text{eff}}}$ (5)

where:

$K_{\text{eff}}=\frac{(a/R_{\text{p}}-1)^{2}(2a/R_{\text{p}}+1)}{2(a/R_{\text{p}})^{3}}$
(6)

Assuming the properties listed in Table 1 and our quiescent XUV flux estimate,
we estimate the energy-limited mass loss rate to be $(22.5-38.7)\eta\times
10^{10}$ g s-1 for a mass range of $20.12-11.7$ M⊕. We have not assigned a
heating efficiency because it can vary widely across the exoplanet population
(0.1 - 0.6; Shaikhislamov et al., 2014). The range presented is $100$ times
larger than the AU Mic b mass loss rate estimated by Feinstein et al. (2022).

###  5.2 Photoionization rate

Radiation at wavelengths shorter than $912$ Å can ionize neutral hydrogen in
exoplanet atmospheres. Large fluxes at these energies have the ability to
ionize much of the gas that is escaping a planet. The observability of the
atmosphere at Ly$\alpha$ depends on how much of the escaping material remains
neutral for a long enough time to be accelerated to velocities that result in
absorption in the line’s blue- and red-wings. To get an idea for how
significantly photoionization impacts AU Mic b, we estimated the
photoionization rate with the following equation that quantifies the amount of
ionization events per unit time ($\Gamma_{\text{ion}}$; count s-1):

$\Gamma_{\text{ion}}=\int^{911.8\text{ \AA}}_{0\text{
\AA}}\frac{F_{\text{XUV}}(\lambda)\sigma_{\text{ion}}(\lambda)}{hc}\lambda
d\lambda$ (7)

where $F_{\text{XUV}}$ is AU Mic b’s wavelength-dependent XUV irradiation, and
$\sigma_{\text{ion}}$ is the photoionization cross-section (cm2) defined by

$\displaystyle\sigma_{\text{ion}}=$ $\displaystyle 6.538\times
10^{-32}\left(\frac{29.62}{\sqrt{\lambda}}+1\right)^{-2.963}$
$\displaystyle\times(\lambda-28846.9)^{2}\lambda^{2.0185}.$ (8)

We split Equation 7 into separate integrals over the X-ray ($5<\lambda\leq
100$ Å) and EUV ($100<\lambda\leq 912$ Å) spectral regions and summed them to
get a photoionization rate of $4.01\times 10^{-4}$ s-1. Inverting the
photoionization rate characterizes the amount of time a typical neutral
hydrogen atom stays neutral before interacting with an ionizing photon - the
neutral hydrogen lifetime. A short neutral hydrogen lifetime indicates a
smaller neutral atmosphere and likely a smaller Ly$\alpha$ transit depth and
shorter transit duration.

At AU Mic b’s orbital distance, the neutral hydrogen lifetime is about $0.692$
hours (almost $42$ minutes) during quiescence, and decreases by about $50\%$
during a flare. This value is short compared to the benchmark planet Gl 436b,
which has a neutral hydrogen lifetime of 14 hours and consequently a large
trailing neutral hydrogen tail (Bourrier et al., 2016). It is not entirely
impossible to observe planets with short neutral hydrogen lifetimes, however,
as shown by the detection of neutral hydrogen around GJ 3470b (0.9 hours;
Bourrier et al., 2018).

Owen et al. (2023) provide a theoretical framework that explains Ly$\alpha$
detections and non-detections of atmospheric escape with photoionization and
the host star’s tidal influence. For example, the young Neptune K2-25b
experiences enough XUV irradiation to have escaping material that is ionized
and unobservable at Ly$\alpha$ resulting in a repeatable non-detection
(Rockcliffe et al., 2021). A similar planet, HD 63433c, is less irradiated and
is more likely to have escaping material detected at Ly$\alpha$ (Zhang et al.,
2022a). There has not yet been Ly$\alpha$ observations of atmospheric escape
on the same planet that vary to the degree we present in this work.

###  5.3 Recombination rate

If AU Mic b’s neutral hydrogen outflow is dense enough, the photoionization
from the Visit 1 flare – and other instances of increased stellar emission –
would be overcome by the recombination of ionized hydrogen back into its
neutral state. In this case, we would not expect the flare to cause the non-
detection of a Ly$\alpha$ transit in Visit 1. To test this, we estimated the
recombination rate of AU Mic b’s outflow and compared it to the flare
photoionization rate from Section 5.2.

The neutral hydrogen column density of $10^{13.96}$ cm-2 estimated in Section
2.4 is a lower limit since it only characterizes the fastest escaping
material. For this reason, we use the mass loss rate calculated in Section 5.1
and conservation of mass to estimate the total neutral hydrogen content of the
outflow. Equation 9 exhibits this relationship, with $\rho$ representing the
density of neutral hydrogen in the outflow ($\rho=n_{\text{H I}}m_{\text{H
I}}$), $r$ being some arbitrary distance from the planet, and $v$ as the
outflow velocity ($20$ km s-1 from Section 4.1).

$\dot{M}=\rho(4\pi r^{2})v$ (9)

Equation 9 can be rearranged to solve for the number density of neutral
hydrogen

$n_{\text{H I}}=\frac{\dot{M}}{(4\pi r^{2})m_{\text{H I}}v}$ (10)

which gives an estimate of $10^{9.04}$ cm-3 at the planet’s white-light
radius. The timescale for recombination is given by Equation 11, where
$\alpha$ is the recombination coefficient (assumed to be the Case A
coefficient of $\alpha=4.2\times 10^{-13}$ cm3 s-1).

$t_{\text{rec}}=(\alpha n_{\text{H I}})^{-1}$ (11)

Our resulting recombination timescale estimate is about $0.62$ hours. This is
roughly double the neutral hydrogen lifetime due to a flare’s photoionization
rate from Section 5.2, which indicates that even the densest parts of AU Mic
b’s outflow will not have enough time to recombine during a flare to be
visible in Ly$\alpha$ transmission. The Visit 1 flare occurs about $6.6$ hours
prior to AU Mic b’s white-light transit and about $4.1$ hours prior to the
planetary absorption seen in Visit 2. The $4.1$ hour difference between flare
and potential neutral hydrogen tail transit is more than enough time for the
neutral hydrogen to recombine. However, the Ly$\alpha$ blue-wing mid-transit
time from Section 4.1 is highly unconstrained since we do not observe the
ingress of the planetary material in Visit 2. It is entirely possible that a
leading neutral hydrogen outflow is ionized by the Visit 1 flare and thus
rendered unobservable at Ly$\alpha$. Stellar activity and photoionization
could play into our non-detection of a transit in Visit 1 versus a strong
signal in Visit 2, which we discuss in Section 6.

##  6 Summary & Discussion

###  6.1 Visit 1

The Visit 1 Ly$\alpha$ spectra showed little to no evidence for absorption
from intervening planetary material – with the majority of its changes
occurring in the red-wing. These red-wing flux changes can be seen in all
three visits presented in Figure 3 and do not depend on time away from
planetary transit, leading us to believe they are caused by stellar activity.
The Visit 1 metal line spectra showed similar amounts of stellar
contamination, which more easily washes out planetary absorption at the lower
line fluxes.

We characterized the flare observed in the first exposure of Visit 1. While
the flare was energetic enough to hide any planetary absorption in Ly$\alpha$
and other emission lines, its duration was estimated to be $1.5$ HST orbits –
much shorter than the expected planetary signal, and occurring $7$ hours
before the white-light transit.

Figure 8 shows the Visit 1 Ly$\alpha$ red-wing behavior is typical and
consistent with the flux changes seen across all visits. The Ly$\alpha$ blue-
wing does exhibit some enhancement in Visit 1, likely attributable to stellar
activity. The metal line Visit 1 light curves in Figure 9 show decreasing flux
behavior after the initial flare in the first orbit. We cannot positively
identify or rule out a planetary absorption signature in the Visit 1 light
curves, Ly$\alpha$ or metals, because of our inability to effectively
characterize the stellar contamination present.

###  6.2 Visit 2

The Visit 2 Ly$\alpha$ blue-wing in Figure 3 features a stark increase in flux
as opposed to the nominal red-wing flux changes. This blue-wing behavior is
not present in either Visit 1 or the archival spectra. We attribute this
behavior to intervening planetary neutral hydrogen that is transiting ahead of
AU Mic b and is being accelerated away from the star. We reconstructed the
“out-of-transit” stellar Ly$\alpha$ line using Visit 2’s last orbit. This
best-fit emission line profile and the subsequent best-fit ISM properties were
combined with an additional absorption component to fit the “in-transit”
behavior of Visit 2’s first orbit. We conclude that the planetary neutral
hydrogen has a column density lower limit of $10^{13.96}$ cm-2, and some of
the material has been accelerated to a speed of $61.26$ km s-1 radially away
from the star.

The Ly$\alpha$ light curves presented in Section 4 reinforce this picture. The
Ly$\alpha$ blue-wing light curve was modeled and fit with an opaque circular
transiting object to characterize the size and timing of the escaping
material. We find that the escaping neutral hydrogen is about $0.52$
$R_{\star}$ ($0.39$ R⊙). This is just an estimate as we are limited by the
geometry of our transit model, but this shows a large neutral hydrogen cloud
is needed to explain the Ly$\alpha$ blue-wing behavior. Following Owen et al.
(2023), we estimate the escaping material to be sculpted into a leading tail
of length $1.39$ R⊙ and height $0.32$ R⊙ with an outflow velocity of $20$ km
s-1 before acceleration.

The Visit 2 metal line spectra and light curves do not show any significant
behavior beyond what could be explained by stellar activity. While the N V and
He II Visit 2 light curves in Figure 9 look similar to the Ly$\alpha$ blue-
wing light curve in Figure 8, this could be because of a flux increase later
in the visit. The second and third orbits within the Si IV light curve do show
some flux variations that may be indicative of stellar activity occurring
throughout the visit. O I and C I are too low signal-to-noise to detect
transiting planetary material.

###  6.3 Bigger picture

While no planetary absorption could be definitively identified in Visit 1,
Visit 2 indicates planetary neutral hydrogen is escaping ahead of AU Mic b and
being accelerated away from the host star. Lavie et al. (2017) reported slight
changes in the shape of Gl 436b’s escaping atmosphere shown by its changing
Ly$\alpha$ transit shape across eight epochs, but detection of the outflow is
repeatable. Our work on AU Mic b is the first time a variable atmospheric
escape signature in Ly$\alpha$ has been observed to greater magnitude – going
from undetectable to detectable.

McCann et al. (2019) used 3D hydrodynamic modeling of planetary outflows
within varying stellar wind environments to show the geometry of the outflow
changes with stellar wind strength. They predicted that an intermediate
stellar wind strength could shape a time-variable “dayside arm” of planetary
material. The intermediate strength stellar wind balances against the
planetary outflow, creating fluid instabilities that result in a growing
dayside arm that eventually detaches from the planet (Figure 12, McCann et
al., 2019). This “burping” scenario could explain our observation of
Ly$\alpha$ absorption ahead of AU Mic b’s transit in Visit 2 and its time-
dependence also explains why we do not see Ly$\alpha$ absorption in Visit 1.
If this is the case, this work presents the first observational evidence of
the burping behavior predicted by McCann et al. (2019) and affirms the power
of Ly$\alpha$ planet transits in characterizing stellar wind environments.

The potential intermediate stellar wind strength argued above is at odds with
the extreme stellar wind strength scenarios depicted in Carolan et al. (2020)
and Cohen et al. (2022). Carolan et al. (2020), motivated by the unknown
stellar wind environment of exoplanets orbiting M dwarfs, simulated AU Mic b’s
outflow within different stellar wind strengths. Using 3D hydrodynamics, they
varied AU Mic’s mass loss rate and found that AU Mic b’s Ly$\alpha$ transit
could be nearly undetectable in the most extreme case, a stellar mass loss
rate of $1000$ $\dot{\text{M}}_{\odot}$. Cohen et al. (2022) used a global
magnetosphere magnetohydrodynamic code (BATS-R-US; Tóth et al., 2012; Powell
et al., 1999) to simulate AU Mic b’s escaping neutral hydrogen atmosphere
within a time-varying stellar wind environment and output corresponding
Ly$\alpha$ absorption light curves. The atmosphere’s response varied over the
course of the planet’s orbit, which contributed to the planet’s Ly$\alpha$
light curves changing shape from transit to transit. This builds off of the
work done by Harbach et al. (2021) to model the magnetohydrodynamic
interactions between a planetary outflow and varying stellar wind conditions.
They found that planetary Ly$\alpha$ transit signatures could vary on short
(hour-long) timescales due to the outflow actively changing shape throughout
the orbit under its local stellar wind conditions (see their Figure 6). These
works show that magnetized stellar wind strength, at least in part, could
explain the difference we see between our AU Mic b Ly$\alpha$ light curves
although neither present an explanation for the Ly$\alpha$ absorption
occurring ahead of the white-light transit.

Photoionization is another major factor in the observability of planetary
neutral hydrogen. The short Ly$\alpha$ transit duration of GJ 3470b is caused
by the quick photoionization of its outflow (Bourrier et al., 2018), and the
inability to detect K2-25b and HD 63433b at Ly$\alpha$ is thought to be caused
by the near total photoionization of their outflows (Owen et al., 2023). Given
AU Mic’s penchant for flaring, AU Mic b could be experiencing variable amounts
of ionizing radiation. We showed in Section 5 that neutral hydrogen could be
photoionized within 42 minutes of escaping AU Mic b, before being accelerated
to observable speeds, just from AU Mic’s quiescent radiation. This is
consistent with the short, yet largely unconstrained, Ly$\alpha$ transit
duration we observe in Visit 2. During a flare, the neutral hydrogen lifetime
could become as short as 22 minutes and further impact the observability of a
Ly$\alpha$ transit. We do not know to what extent self-shielding from
photoionization and radiation pressure are also involved (Bourrier et al.,
2015; Bourrier & Lecavelier des Etangs, 2013).

The data presented in this work can tune future FUV observation plans to
better sample AU Mic b’s transit – probing before the white-light transit and
further constraining its Ly$\alpha$ transit shape. These observations would
help answer questions about the timing of AU Mic b’s Ly$\alpha$ transit, how
frequent and to what magnitude the transit varies, the impact of stellar wind
and flares, and observing the escape of metals. Its drastic change in
Ly$\alpha$ light curve behavior makes AU Mic b a prime candidate for continued
characterization of its environment and modeling of its atmosphere. We could
distinguish between the potential stellar wind and flare scenarios posed above
by confirming the repeatability of the Ly$\alpha$ transit ahead of the planet.
Applying increasingly sophisticated simulations to this system will help us
learn more about the extreme behavior of close-in planets around young stars.

We sincerely thank Dr. Hans R. Müller, Dr. Brian Chaboyer, and Dr. James Owen
for their help and guidance throughout the progress of this work. The authors
appreciate the support, care, and community provided by the graduate students
within Dartmouth College’s Department of Physics & Astronomy. We would like to
express our sincere appreciation for Nova, Jacques, Margot, Charlie, Edmund,
and Nessie who have begrudgingly accepted our transition back to in-person
work. We will miss you, Charlie. Welcome to the family Jonah and Theo! This
research is based on observations made with the NASA/ESA Hubble Space
Telescope obtained from the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5–26555. These observations are associated with HST-
GO-15836. Support for program HST-GO-15836 was provided by NASA through a
grant from the STScI. CHIANTI is a collaborative project involving George
Mason University, the University of Michigan (USA), University of Cambridge
(UK) and NASA Goddard Space Flight Center (USA).

##  Appendix A Additional spectrum information

###  A.1 Far-Ultraviolet Continuum

The FUV continuum observed by HST/STIS using the E140M grating was defined as
a combination of the overlapping continuum presented in Feinstein et al.
(2022) and low-signal regions identified by eye: $1152.602-1155.579$,
$1159.276-1163.222$, $1164.565-1173.959$, $1178.669-1188.363$,
$1195.162-1196.864$, $1201.748-1203.862$, $1227.056-1236.921$,
$1262.399-1263.967$, $1268.559-1273.974$, $1281.396-1287.493$,
$1290.494-1293.803$, $1307.064-1308.703$, $1319.494-1322.910$,
$1330.349-1332.884$, $1337.703-1341.813$, $1341.116-1350.847$,
$1356.5-1370.5$, $1372.5-1392.0$, $1395.2-1401.0$, $1404.5-1521.5$,
$1522.5-1532.5$, $1535.0-1545.0$, $1553.0-1560.0$, $1562.5-1638.5$,
$1642.5-1655.5$, $1658.0-1670.0$, $1672.5-1700.0$ Å.

Figure 10: AU Mic’s quiescent spectrum – the last orbit from Visit 1.
Continued in Figure 11. Figure 11: AU Mic’s quiescent spectrum – the last
orbit from Visit 1.

HST/STIS

## References

  * Alam et al. (2018) Alam, M. K., Nikolov, N., López-Morales, M., et al. 2018, AJ, 156, 298
  * Ben-Jaffel et al. (2022) Ben-Jaffel, L., Ballester, G. E., Muñoz, A. G., et al. 2022, Nature Astronomy, 6, 141
  * Bourrier et al. (2015) Bourrier, V., Ehrenreich, D., & Lecavelier des Etangs, A. 2015, A&A, 582, A65
  * Bourrier & Lecavelier des Etangs (2013) Bourrier, V., & Lecavelier des Etangs, A. 2013, A&A, 557, A124
  * Bourrier et al. (2016) Bourrier, V., Lecavelier des Etangs, A., Ehrenreich, D., Tanaka, Y. A., & Vidotto, A. A. 2016, A&A, 591, A121
  * Bourrier et al. (2018) Bourrier, V., Lecavelier des Etangs, A., Ehrenreich, D., et al. 2018, A&A, 620, A147
  * Bourrier et al. (2022) Bourrier, V., Zapatero Osorio, M. R., Allart, R., et al. 2022, A&A, 663, A160
  * Cale et al. (2021) Cale, B. L., Reefe, M., Plavchan, P., et al. 2021, AJ, 162, 295
  * Carolan et al. (2020) Carolan, S., Vidotto, A. A., Plavchan, P., Villarreal D’Angelo, C., & Hazra, G. 2020, MNRAS, 498, L53
  * Catling & Zahnle (2009) Catling, D. C., & Zahnle, K. J. 2009, Scientific American, 300, 36
  * Chadney et al. (2015) Chadney, J. M., Galand, M., Unruh, Y. C., Koskinen, T. T., & Sanz-Forcada, J. 2015, Icarus, 250, 357
  * Cohen et al. (2022) Cohen, O., Alvarado-Gómez, J. D., Drake, J. J., et al. 2022, ApJ, 934, 189
  * Davenport et al. (2014) Davenport, J. R. A., Hawley, S. L., Hebb, L., et al. 2014, ApJ, 797, 122
  * Del Zanna et al. (2021) Del Zanna, G., Dere, K. P., Young, P. R., & Landi, E. 2021, ApJ, 909, 38
  * Dere et al. (1997) Dere, K. P., Landi, E., Mason, H. E., Monsignori Fossi, B. C., & Young, P. R. 1997, A&AS, 125, 149
  * dos Santos et al. (2019) dos Santos, L. A., Ehrenreich, D., Bourrier, V., et al. 2019, A&A, 629, A47
  * Duvvuri et al. (2023) Duvvuri, G. M., Pineda, J. S., Berta-Thompson, Z. K., France, K., & Youngblood, A. 2023, AJ, 165, 12
  * Duvvuri et al. (2021) Duvvuri, G. M., Sebastian Pineda, J., Berta-Thompson, Z. K., et al. 2021, ApJ, 913, 40
  * Ehrenreich et al. (2015) Ehrenreich, D., Bourrier, V., Wheatley, P. J., et al. 2015, Nature, 522, 459
  * Feinstein et al. (2022) Feinstein, A. D., France, K., Youngblood, A., et al. 2022, AJ, 164, 110
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, Publications of the Astronomical Society of the Pacific, 125, 306
  * Fossati et al. (2010) Fossati, L., Haswell, C. A., Froning, C. S., et al. 2010, ApJ, 714, L222
  * Foster et al. (2022) Foster, G., Poppenhaeger, K., Ilic, N., & Schwope, A. 2022, A&A, 661, A23
  * Fulton & Petigura (2018) Fulton, B. J., & Petigura, E. A. 2018, AJ, 156, 264
  * Fulton et al. (2017) Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ, 154, 109
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * García Muñoz et al. (2021) García Muñoz, A., Fossati, L., Youngblood, A., et al. 2021, ApJ, 907, L36
  * Gilbert et al. (2022) Gilbert, E. A., Barclay, T., Quintana, E. V., et al. 2022, AJ, 163, 147
  * Ginzburg et al. (2018) Ginzburg, S., Schlichting, H. E., & Sari, R. 2018, MNRAS, 476, 759
  * Gupta & Schlichting (2019) Gupta, A., & Schlichting, H. E. 2019, MNRAS, 487, 24
  * Harbach et al. (2021) Harbach, L. M., Moschou, S. P., Garraffo, C., et al. 2021, ApJ, 913, 130
  * Harris et al. (2020) Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357\.  https://doi.org/10.1038/s41586-020-2649-2
  * Haswell et al. (2012) Haswell, C. A., Fossati, L., Ayres, T., et al. 2012, ApJ, 760, 79
  * Hawley et al. (2014) Hawley, S. L., Davenport, J. R. A., Kowalski, A. F., et al. 2014, ApJ, 797, 121
  * Hoeijmakers et al. (2020) Hoeijmakers, H. J., Seidel, J. V., Pino, L., et al. 2020, A&A, 641, A123
  * Hunter (2007) Hunter, J. D. 2007, Computing in science & engineering, 9, 90
  * Jin et al. (2014) Jin, S., Mordasini, C., Parmentier, V., et al. 2014, ApJ, 795, 65
  * Klein et al. (2021) Klein, B., Donati, J.-F., Moutou, C., et al. 2021, MNRAS, 502, 188
  * Kramida et al. (2021) Kramida, A., Yu. Ralchenko, Reader, J., & and NIST ASD Team. 2021, NIST Atomic Spectra Database (ver. 5.9), [Online]. Available: https://physics.nist.gov/asd [2022, September 11]. National Institute of Standards and Technology, Gaithersburg, MD., ,
  * Kreidberg (2015) Kreidberg, L. 2015, PASP, 127, 1161
  * Kulow et al. (2014) Kulow, J. R., France, K., Linsky, J., & Loyd, R. O. P. 2014, ApJ, 786, 132
  * Lannier et al. (2017) Lannier, J., Lagrange, A. M., Bonavita, M., et al. 2017, A&A, 603, A54
  * Lavie et al. (2017) Lavie, B., Ehrenreich, D., Bourrier, V., et al. 2017, A&A, 605, L7
  * Lecavelier Des Etangs (2007) Lecavelier Des Etangs, A. 2007, A&A, 461, 1185
  * Lecavelier des Etangs et al. (2012) Lecavelier des Etangs, A., Bourrier, V., Wheatley, P. J., et al. 2012, A&A, 543, L4
  * Lee & Connors (2021) Lee, E. J., & Connors, N. J. 2021, ApJ, 908, 32
  * Lightkurve Collaboration et al. (2018) Lightkurve Collaboration, Cardoso, J. V. d. M., Hedges, C., et al. 2018, Lightkurve: Kepler and TESS time series analysis in Python, Astrophysics Source Code Library, , , ascl:1812.013
  * Linsky et al. (2006) Linsky, J. L., Draine, B. T., Moos, H. W., et al. 2006, ApJ, 647, 1106
  * Lopez & Fortney (2013) Lopez, E. D., & Fortney, J. J. 2013, ApJ, 776, 2
  * Loyd & France (2014) Loyd, R. O. P., & France, K. 2014, ApJS, 211, 9
  * Loyd et al. (2018a) Loyd, R. O. P., Shkolnik, E. L., Schneider, A. C., et al. 2018a, ApJ, 867, 70
  * Loyd et al. (2018b) Loyd, R. O. P., France, K., Youngblood, A., et al. 2018b, ApJ, 867, 71
  * Lundkvist et al. (2016) Lundkvist, M. S., Kjeldsen, H., Albrecht, S., et al. 2016, Nature Communications, 7, 11201
  * Mamajek & Bell (2014) Mamajek, E. E., & Bell, C. P. M. 2014, MNRAS, 445, 2169
  * Martioli et al. (2021) Martioli, E., Hébrard, G., Correia, A. C. M., Laskar, J., & Lecavelier des Etangs, A. 2021, A&A, 649, A177
  * Mazeh et al. (2016) Mazeh, T., Holczer, T., & Faigler, S. 2016, A&A, 589, A75
  * McCann et al. (2019) McCann, J., Murray-Clay, R. A., Kratter, K., & Krumholz, M. R. 2019, ApJ, 873, 89
  * Nikolov et al. (2014) Nikolov, N., Sing, D. K., Pont, F., et al. 2014, MNRAS, 437, 46
  * Owen (2022) Owen, J. 2022, in Bulletin of the American Astronomical Society, Vol. 54, 208.05
  * Owen (2019) Owen, J. E. 2019, Annual Review of Earth and Planetary Sciences, 47, 67
  * Owen & Alvarez (2016) Owen, J. E., & Alvarez, M. A. 2016, ApJ, 816, 34
  * Owen & Lai (2018) Owen, J. E., & Lai, D. 2018, MNRAS, 479, 5012
  * Owen & Wu (2013) Owen, J. E., & Wu, Y. 2013, ApJ, 775, 105
  * Owen & Wu (2017) —. 2017, ApJ, 847, 29
  * Owen et al. (2023) Owen, J. E., Murray-Clay, R. A., Schreyer, E., et al. 2023, MNRAS, 518, 4357
  * Pagano et al. (2000) Pagano, I., Linsky, J. L., Carkner, L., et al. 2000, ApJ, 532, 497
  * Plavchan et al. (2009) Plavchan, P., Werner, M. W., Chen, C. H., et al. 2009, ApJ, 698, 1068
  * Plavchan et al. (2020) Plavchan, P., Barclay, T., Gagné, J., et al. 2020, Nature, 582, 497
  * Powell et al. (1999) Powell, K. G., Roe, P. L., Linde, T. J., Gombosi, T. I., & De Zeeuw, D. L. 1999, Journal of Computational Physics, 154, 284
  * Proffitt et al. (2017) Proffitt, C. R., Monroe, T., & Dressel, L. 2017, Status of the STIS Instrument Focus, Instrument Science Report STIS 2017-01 (v1), 30 pages, ,
  * Raetz et al. (2020) Raetz, S., Stelzer, B., Damasso, M., & Scholz, A. 2020, A&A, 637, A22
  * Riley et al. (2018) Riley, A., Monroe, T., & Lockwood, S. 2018, Impacts of focus on aspects of STIS UV Spectroscopy, Instrument Science Report STIS 2018-6, 25 pages, ,
  * Rockcliffe et al. (2021) Rockcliffe, K. E., Newton, E. R., Youngblood, A., et al. 2021, AJ, 162, 116
  * Rogers et al. (2021) Rogers, J. G., Gupta, A., Owen, J. E., & Schlichting, H. E. 2021, MNRAS, 508, 5886
  * Rogers & Owen (2021) Rogers, J. G., & Owen, J. E. 2021, MNRAS, 503, 1526
  * Schneider et al. (2019) Schneider, A. C., Shkolnik, E. L., Barman, T. S., & Loyd, R. P. 2019, ApJ, 886, 19
  * Seidel et al. (2020) Seidel, J. V., Ehrenreich, D., Bourrier, V., et al. 2020, A&A, 641, L7
  * Seidel et al. (2022) Seidel, J. V., Cegla, H. M., Doyle, L., et al. 2022, MNRAS, 513, L15
  * Shaikhislamov et al. (2014) Shaikhislamov, I. F., Khodachenko, M. L., Sasunov, Y. L., et al. 2014, ApJ, 795, 132
  * Sing et al. (2016) Sing, D. K., Fortney, J. J., Nikolov, N., et al. 2016, Nature, 529, 59
  * Sing et al. (2019) Sing, D. K., Lavvas, P., Ballester, G. E., et al. 2019, AJ, 158, 91
  * Stefànsson et al. (2022) Stefànsson, G., Mahadevan, S., Petrovich, C., et al. 2022, ApJ, 931, L15
  * The Astropy Collaboration et al. (2018) The Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123
  * Torres et al. (1972) Torres, C. A. O., Ferraz Mello, S., & Quast, G. R. 1972, Astrophys. Lett., 11, 13
  * Tóth et al. (2012) Tóth, G., van der Holst, B., Sokolov, I. V., et al. 2012, Journal of Computational Physics, 231, 870
  * Turnbull (2015) Turnbull, M. C. 2015, arXiv e-prints, arXiv:1510.01731
  * Vidal-Madjar et al. (2003) Vidal-Madjar, A., Lecavelier des Etangs, A., Désert, J. M., et al. 2003, Nature, 422, 143
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods
  * White et al. (2019) White, R., Schaefer, G., Boyajian, T., et al. 2019, in American Astronomical Society Meeting Abstracts, Vol. 233, American Astronomical Society Meeting Abstracts #233, 259.41
  * Wittrock et al. (2022) Wittrock, J. M., Dreizler, S., Reefe, M. A., et al. 2022, AJ, 164, 27
  * Wyatt et al. (2020) Wyatt, M. C., Kral, Q., & Sinclair, C. A. 2020, MNRAS, 491, 782
  * Yan et al. (2019) Yan, F., Casasayas-Barris, N., Molaverdikhani, K., et al. 2019, A&A, 632, A69
  * Youngblood & Newton (2022) Youngblood, A., & Newton, E. R. 2022, allisony/lyapy: First release created for citation purposes in the literature, Zenodo, vv1.0.0, Zenodo, doi:10.5281/zenodo.6949067
  * Youngblood et al. (2022) Youngblood, A., Pineda, J. S., Ayres, T., et al. 2022, ApJ, 926, 129
  * Youngblood et al. (2016) Youngblood, A., France, K., Loyd, R. O. P., et al. 2016, ApJ, 824, 101
  * Zhang et al. (2022a) Zhang, M., Knutson, H. A., Wang, L., et al. 2022a, AJ, 163, 68
  * Zhang et al. (2022b) Zhang, Y., Snellen, I. A. G., Wyttenbach, A., et al. 2022b, A&A, 666, A47
  * Zicher et al. (2022) Zicher, N., Barragán, O., Klein, B., et al. 2022, MNRAS, 512, 3060
  * Zuckerman & Song (2004) Zuckerman, B., & Song, I. 2004, ARA&A, 42, 685