New and Improved Lyα Reconstructions for M and K Dwarfs

The Lyα emission line is the brightest UV emission line in M and K dwarf spectra and serves as an important tool for studies of stellar chromospheres, the interstellar medium, and exoplanet atmospheres. However, Lyα observations have proven difficult due to the strong absorption by the interstellar medium, necessitating a reconstruction of the intrinsic stellar line from the observed spectrum. We have performed new Lyα reconstructions on the MUSCLES Treasury Survey stars, incorporating improved parameterizations for the intrinsic line wings and line core. We present an analysis of how the updated Lyα fluxes could impact photochemical and atmospheric escape studies and flux–flux scaling relations with other chromospheric emission lines such as Ca ii H and K. We find the overall intrinsic Lyα flux of our star sample decreases by as little as 10% to as much as ∼5× fainter compared to previous findings. The exception to this flux decrease is the M dwarf GJ 581, whose Lyα flux increased by 4%. These results will likely have a limited impact on the aforementioned studies that rely on Lyα fluxes.


Introduction
H I Lyα (Lyα, 1215.67Å) is one of the most studied UV emission lines from low-mass stars due to it being a tracer of magnetic activity and an important input in models of exoplanet atmospheric escape (Schaefer et al. 2016) and photochemistry (Rugheimer et al. 2015).Lyα photons serve as a main driver for photochemical interactions in exoplanet atmospheres and Lyα influences the atmospheric composition of exoplanets orbiting M and K dwarfs, promising targets for atmospheric characterization with the James Webb Space Telescope (JWST) due to their large numbers and favorable star-to-planet size ratios.Additionally, Lyα photons also serve as a proxy for estimating host star extreme-ultraviolet emission (EUV) flux (100-912 Å; Linsky et al. 2014), a primary driver for some exoplanets losing their atmospheres over a period of time (Lammer et al. 2003;Luger & Barnes 2015).
Lyα photons regulate the chemistry of molecules like CO 2 and H 2 O, where they participate in photochemical reactions that can lead to an accumulation of abiotic O 2 in the upper atmosphere of the planet (Domagal-Goldman et al. 2014).Since these molecules also serve as potential biosignatures, it is important to be able to distinguish between abiotic and biotic sources in a planet's atmosphere as the search for life continues to intensify now with the launch of JWST (Quanz et al. 2022;Thompson et al. 2022).In exoplanet atmospheric escape studies, EUV photons heat upper planetary atmospheres, potentially leading to significant atmospheric mass loss in extreme cases (Lammer et al. 2003).There is currently no instrument available to measure the EUV spectral range directly but since portions of the EUV emission are formed at temperatures near Lyα the Lyα stellar flux can be helpful for estimating or reconstructing the EUV emission required by models of exoplanetary atmospheric escape models.Lyα can also be useful for estimating other UV fluxes through empirical fluxflux relationships such as those from Cincunegui et al. (2007), Suárez Mascareño et al. (2015), and Melbourne et al. (2020), a potentially valuable input to photochemical models under some limitations (Teal et al. 2022).
Lyα observations are considerably thwarted by the interstellar medium (ISM) due to resonant scattering between the photons emitted by the target star and neutral H I atoms in the ISM, necessitating a reconstruction of the intrinsic Lyα spectrum (Wood et al. 2005).Additionally, there has been increasing evidence that Lyα emission lines of low-mass stars display selfreversal, a flux decrease in the line core, caused by complex radiative transfer effects and if not accounted for, could lead to an overestimation of the intrinsic Lyα flux (Youngblood et al. 2022).
In this work, we update the Lyα reconstructions of the MUSCLES Treasury Survey (France et al. 2016;Loyd et al. 2016;Youngblood et al. 2016) by incorporating self-reversal into the model of the intrinsic line profile.In Section 2, we describe the methodology used to reconstruct the Lyα intrinsic profiles.In Section 3, we describe our results and in Section 4, we discuss the implications of our results.Finally, we summarize our work in Section 5.

Methodology
In order to recover the Lyα intrinsic profile, it is necessary to correct for the ISM attenuation in all of our targets.We downloaded the HST STIS G140M/E140M source spectra (v2.2) from the Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (MUSCLES) high-level science products (HLSP) page. 5We applied the normalization factors listed in the FITS files (NORMFAC keyword) in order to correct the STIS flux calibration (see the HLSP README file).We removed residual geocoronal Lyα emission in the E140M spectra simply by masking those regions from the fit.For the reconstruction technique, we closely followed the procedure and model of Youngblood et al. (2022), where we assumed a Voigt profile for the stellar emission line with self-reversal and a Voigt profile for the ISM absorption line.Specifically, the self-reversal component was modeled using a Voigt absorption profile whose width and velocity centroid matched the stellar emission line.This differs from the original model used in Youngblood et al. (2016) that used two Gaussians for the stellar emission line with no selfreversal.
To obtain the reconstructed Lyα profile, we multiply the ISM absorption and stellar emission components using the code lyapy6 (Figure 1).The typical number of samples is 7,200,000 for each of our targets and the Markov Chain Monte Carlo (MCMC) ran for 50 autocorrelation lengths for all targets.For most of our targets, we used a single ISM absorption component with the exception of ò Eri and Proxima Centauri, which require additional components because of the presence of additional ISM, astrospheric, and/or heliospheric absorption (Wood et al. 2021).Astrospheric and heliospheric absorption trace the buildup of H I at the region where the stellar wind and the local ISM interact and is only visible from certain viewing angles (Wood et al. 2001).The presence of excess absorption results in an overall poor Lyα reconstruction fit for both of these targets unless accounted for in the model as an extra absorption component.For ò Eri's astrospheric component (Table 1), the H I column density value (∼2 × 10 17 cm −2 ) is larger than may be physically realistic for astrospheric absorption, but still fits overall well with the data.The STIS spectra, best-fit models, and reconstructed intrinsic Lyα profiles are shown in Figure 1 and the best-fit parameters and intrinsic Lyα fluxes are listed in Table 1 and Table 2.
Following the methods of Linsky et al. (2014), we calculated coarse EUV spectra.Briefly, Linsky et al. (2014) established a scaling relation between stellar Lyα flux and coarse EUV spectra (100-1170 Å) based on stellar observations of FGKM dwarfs for the 100-400 Å and 912-1170 Å regions and a semiempirical solar model from Fontenla et al. (2014) for the 400-912 Å region.Note that we use Gaia distance values for each target, which were not available for Youngblood et al. (2016).To reflect these new flux changes, both the updated Lyα and EUV spectra were spliced into the most recent (v2.2) MUSCLES spectra found on the MUSCLES HLSP site.These new spectral energy distributions are available as v2.5 on the same site.

Results
We compared the reconstructed Lyα fluxes of this work with those of Youngblood et al. (2016), and we find that all but one of our fluxes is smaller (Figure 2).Most of the M dwarfs' new fluxes are 10%-35% fainter, with the exception of GJ 1214 and Note.The list of the best-fit parameters for our sample (except GJ 551, which can be found in Table 2) including the spectral type (Loyd et al. 2016)     GJ 581.GJ 1214 is ∼2× fainter, and GJ 581 is 4% brighter.
The most substantial flux differences lie with three of the four K dwarfs, which are 3-5× fainter than the fluxes presented in Youngblood et al. (2016).The fourth K dwarf, ò Eri, is only 17% fainter.
We attribute these differences in flux primarily to the inclusion of self-reversal in our model.Although there are other changes in our model compared to the one used in Youngblood et al. (2016), such as the use of a Voigt profile to model the stellar emission line, we infer that the inclusion of self-reversal in our model dominates, because the stars with deeper selfreversal tend to show greater departures from the original MUSCLES reconstructions.Youngblood et al. (2016) noticed that GJ 1214ʼs reconstructed flux was lower than the other M dwarfs of the MUSCLES sample, consistent with the earlier finding of France et al. (2013), and assumed that the poor data quality was responsible.In order to roughly match the expected Lyα flux value based on the high-quality Mg II flux, they scaled up the amplitude parameter of their fit by a factor of 2.4 and hence increased the intrinsic Lyα flux by this amount.However, considering the large error bars on GJ 1214ʼs Lyα flux, we determine GJ 1214ʼs flux is roughly consistent with the other M dwarfs, and therefore no correction factor is needed.
The Lyα flux uncertainties presented in this work are smaller compared to those found in Youngblood et al. (2016).This is likely because the flux uncertainty computation method used by Youngblood et al. (2016) did not consider correlations between the parameters, leading to overestimated uncertainties.
We also find greater self-reversal depths in the K dwarfs than in the M dwarfs.This is visually apparent in Figure 1 and reflected in the larger self-absorption parameter values from Table 1.Similar trends between self-reversal and spectral type are found in Youngblood et al. (2022), and they posited that magnetic activity may be a contributing factor in self-reversal depth.This could explain why ò Eri, a young and active K dwarf, has less self-reversal than the other three older K dwarfs of this work.However, even though ò Eri is much more magnetically active than any of the M dwarfs in our sample, it still has a greater self-reversal depth than any of the M dwarfs, implying that fundamental stellar properties such as spectral type or mass are the primary driver of self-reversal depth.
However, we note that the K dwarfs in our sample, except for ò Eri, are more distant than the M dwarfs, generally with larger H I column densities.It is possible that the K dwarfs' larger ISM absorption, which obscures more of the line core, permits the MCMC sampler to explore larger self-reversal depths and lower H I column densities, when that may not reflect the actual properties of the line core.These excursions of the MCMC sampler trend the median values of the posteriors toward deeper self-reversal and lower H I column densities.This is supported by the results of Wilson et al. (2022), who performed various Lyα reconstructions of the white dwarf-M dwarf binary EG UMa at multiple velocities due to the binary motion Doppler shifting the Lyα emission line between strong and weak ISM attenuation regions.They found that the H I column density was underestimated for spectra where the line core was the most obstructed by the ISM and self-reversal was included in the model.It is challenging to measure accurate Lyα self-reversal depths for stars like those in this sample where the line core is completely obscured by the ISM.

Discussion
In this section we discuss the significance and implications of our results for exoplanet atmosphere models and stellar activity studies.Since photochemistry and atmospheric escape models rely heavily on the input of Lyα and EUV fluxes, it is important to assess their reliability.Compared to the EUV flux values calculated via the Linsky et al. (2014) scaling relations and reported in Youngblood et al. (2016), we observe that the Lyα-derived EUV flux values in this work are approximately 1.0×-2.2×smaller for all of our M dwarfs and 1.3×-6.7×smaller for all of our K dwarfs.Since the K dwarfs exhibit the largest Lyα flux differences and the EUV flux scales approximately linearly to the Lyα flux (Linsky et al. 2014), the K dwarf sample is the most significantly affected.The energylimited mass-loss rate also scales linearly with the EUV flux  Youngblood et al. (2016).The dashed colored lines represent constant flux ratios between the reconstructions of the two works.For example, the black 1:1 line shows perfect agreement, while the 0.2:1 line corresponds to a 5× smaller flux in this work than compared to Youngblood et al. (2016).
(e.g., Salz et al. 2016); this could imply that the calculated atmospheric mass-loss rates could change by up to a factor of 2× for the M dwarfs and up to 7× for the K dwarfs using the updated EUV flux values in this work compared to previously used values.We note that EUV flux systematic uncertainties on these stars are in the range of ∼10× -∼100× (e.g., Drake et al. 2020) and mainly stem from limited EUV flux measurements.Compared to these large systematic uncertainties, our updated EUV fluxes are unlikely to significantly affect any previous results that used the Youngblood et al. (2016) EUV fluxes.Melbourne et al. (2020) investigated the relationship between UV and optical chromospheric emission lines in order to estimate the UV emission from M dwarfs without direct UV data.They found scaling relationships between the normalized UV line luminosity and R' HK , S index , and log 10 (L Hα /L bol ) for nine UV spectral lines, including Lyα; Melbourne et al.Miguel et al. (2015), we find that our updated Lyα fluxes could potentially have an impact on the modeling of gaseous planet atmospheres but not as significant as the result they found.The smallest flux change considered in their work was 10× the Lyα flux while the largest flux difference described in this work is a 5× flux decrease.Peacock et al. (2022) examined the impact of Lyα flux and line profile shape at different degrees of self-reversal on the chemistry of oxic and anoxic terrestrial atmospheres.For the oxic atmosphere, they found lower concentrations of atmospheric gases with Lyα displaying no self-reversal compared to deep self-reversal.For the anoxic atmosphere, the most pronounced change was in the mesospheric CH 4 levels when Lyα has no self-reversal.This was a result of increased photolysis rates, where the effect is the most intense at the top of the planet's atmosphere.However, for both scenarios, the overall change in photolysis rates is less than a factor of 2 between line profile shapes with the highest and lowest degrees of self-reversal and do not significantly impact potentially detectable spectral features.Therefore, we conclude that the updated Lyα flux values of this work compared to the Youngblood et al. (2016) values would not cause significant changes in photochemical models of terrestrial planets.

Conclusion
We present new Lyα reconstructions of the 12 M and K dwarfs from the MUSCLES Treasury Survey using an improved reconstruction model that incorporates a Voigt profile with self-reversal for the stellar emission line.We found that the overall intrinsic Lyα flux decreased as a result of the improved treatment to the stellar emission line.The K dwarf sample exhibits the largest flux difference with a 3-5× flux decrease except for ò Eri, which showed a ∼17% flux decrease.The M dwarf samples largest flux difference lies with GJ 1214 with a ∼65% flux decrease but can be explained due to a scaling factor that was applied in Youngblood et al. (2016) and not applied in this work.The remaining M dwarfs show a flux difference ranging between 10% to 35% dimmer compared to the Youngblood et al. (2016) M dwarf flux values.The substantial flux differences between the K dwarfs and M dwarfs can be attributed to their spectral type since earlier spectral types appear to display deeper self-reversal in their line core compared to later spectral types (Youngblood et al. 2022).Photochemical and atmospheric escape models that use the MUSCLES data products updated by this work instead of any previous version will likely not significantly change.The results found in this work would imply a decrease in atmospheric mass-loss and photolysis rates by up to a factor of ∼5 due to their Lyα linear dependence.Exoplanet atmospheric spectra with current facilities may not be precise enough to distinguish between models based on these different Lyα fluxes.

Figure 1 .
Figure 1.Lyα reconstructions for the eight M dwarfs and four K dwarfs.The black histogram represents the STIS G140M/E140M data.The blue and purple dashed lines represent the reconstructed intrinsic emission line for the star, where the former represents the profile convolved with the instrument line spread function and the latter has not been convolved.The black dashed line shows the ISM absorption component, which when multiplied by the reconstructed emission line gives the best-fit profile (pink line).The gray-shaded regions highlight residual geocoronal emission that was masked from the fit.
and target distance obtained from Gaia Collaboration et al. (2023), denoted by d.F(Lyα) is the reconstructed stellar Lyα flux, F(EUV) is the extreme-UV flux computed using the reconstructed Lyα flux over Δλ=100-1170ÃA, V radial is the stellar radial velocity, log 10 A is the amplitude, FWHM L and FWHM G are the FWHM values of the Lorentzian and Gaussian components of the Voigt profile, p is the unitless self-reversal parameter, log 10 N(H I) is the ISM column density, b H I is the Doppler broadening parameter, V H I is the ISM HI radial velocity, and the remaining parameters are additional absorption parameters used on select stars.The prior probability distributions are defined underneath each parameter value where U represents a uniform distribution between a minimum and maximum value indicated in the parentheses and based on the parameter's likely value.Fixed parameter values are denoted by an equal sign.
551ʼs best-fit parameters including its spectral type(Loyd et al. 2016) and target distance obtained from GaiaCollaboration et al. (2023).F(Lyα) is the reconstructed stellar Lyα flux, F(EUV) is the extreme-UV flux computed using the reconstructed Lyα flux over Δ λ = 100-1170ÃA, V radial is the stellar radial velocity, log 10 A is the amplitude, FWHM L and FWHM G are the FWHM values of the Lorentzian and Gaussian components of the Voigt profile, p is the unitless self-reversal parameter, log 10 N(H I) is the ISM column density, b H I is the Doppler broadening parameter, V H I is the ISM HI radial velocity and the remaining parameters are additional absorption parameters used on select stars.The prior probability distributions are defined underneath each parameter value where U represents a uniform distribution between a minimum and maximum value indicated in the parentheses and based on the parameter's likely value.Fixed parameter values are denoted by an equal sign.

Figure 2 .
Figure 2. Comparison between the reconstructed Lyα fluxes of this work and those ofYoungblood et al. (2016).The dashed colored lines represent constant flux ratios between the reconstructions of the two works.For example, the black 1:1 line shows perfect agreement, while the 0.2:1 line corresponds to a 5× smaller flux in this work than compared toYoungblood et al. (2016).
(2020) obtained their Lyα fluxes from Youngblood et al. (2016) and Youngblood et al. (2017).Melbourne et al. (2020) reported uncertainties in the Lyα scaling relations of ∼0.4 dex (∼2.5×), which are of similar magnitude to the changes we report in our updated Lyα fluxes.We conclude that our updated flux values might not significantly alter the Melbourne et al. (2020) Lyα scaling relations, but a recalibration of those relations is deferred to future work.Miguel et al. (2015) and Peacock et al. (2022) explored the photochemical effects of Lyα on mini-Neptune and terrestrial atmospheres, respectively.Specifically, Miguel et al. (2015) analyzed the impact of varied Lyα flux intensities on the photochemistry of a mini-Neptune's atmosphere with different metallicity compositions.They find the most notable change for atmospheres with solar compositions, where the H 2 O mixing ratio changes by up to 5 orders of magnitude between 1000× Lyα and 0.0001× Lyα scenarios, due to the strong dependence between the H 2 O photolysis rate and incident Lyα flux.Based on

Table 1
Best-fit Parameters