FUMES. II. Lyα Reconstructions of Young, Active M Dwarfs
DDraft version February 26, 2021
Typeset using L A TEX preprint style in AASTeX62
FUMES. II. Ly α Reconstructions of Young, Active M Dwarfs
Allison Youngblood,
1, 2
J. Sebastian Pineda, and Kevin France
1, 3, 4 Laboratory for Atmospheric and Space Physics, University of Colorado, 600 UCB, Boulder, CO 80309, USA NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA Department of Astrophysical and Planetary Sciences, University of Colorado, UCB 389, Boulder, CO 80309, USA Center for Astrophysics and Space Astronomy, University of Colorado, 389 UCB, Boulder, CO 80309, USA
ABSTRACTThe H I Ly α (1215.67 ˚A) emission line dominates the far-UV spectra of M dwarf stars,but strong absorption from neutral hydrogen in the interstellar medium makes observingLy α challenging even for the closest stars. As part of the Far-Ultraviolet M-dwarfEvolution Survey (FUMES), the Hubble Space Telescope has observed 10 early-to-midM dwarfs with ages ranging from ∼
24 Myr to several Gyrs to evaluate how the incidentUV radiation evolves through the lifetime of exoplanetary systems. We reconstruct theintrinsic Ly α profiles from STIS G140L and E140M spectra and achieve reconstructedfluxes with 1- σ uncertainties ranging from 5% to a factor of two for the low resolutionspectra (G140L) and 3-20% for the high resolution spectra (E140M). We observe broad,500-1000 km s − wings of the Ly α line profile, and analyze how the line width dependson stellar properties. We find that stellar effective temperature and surface gravityare the dominant factors influencing the line width with little impact from the star’smagnetic activity level, and that the surface flux density of the Ly α wings may be usedto estimate the chromospheric electron density. The Ly α reconstructions on the G140Lspectra are the first attempted on λ/ ∆ λ ∼ α line. Young, low-gravity stars have the broadestlines and therefore provide more information at low spectral resolution to the fit tobreak degeneracies among model parameters. Keywords:
M dwarf stars, stellar atmospheres, interstellar absorption, planet-hostingstars INTRODUCTIONFar-ultraviolet (FUV) photons (912-1700 ˚A) drive photochemistry and heating in planetary upperatmospheres due to the large, wavelength-dependent absorption cross sections of molecules through-out the FUV (e.g., Segura et al. 2005; Loyd et al. 2016). Using the
Hubble Space Telescope ( HST ),the Far-Ultraviolet M-dwarf Evolution Survey (FUMES; HST-GO-14640) has measured the FUVspectral energy distributions of early-to-mid M dwarfs ranging in age from 24 Myr to field age ( ∼ [email protected] a r X i v : . [ a s t r o - ph . S R ] F e b Gyr) to determine how stellar magnetic activity evolves with age and to better inform exoplanetatmosphere evolution studies (Pineda et al. accepted ). In particular, a large ratio of incident FUV tonear-ultraviolet (NUV; 1700-3200 ˚A) flux on a planet can lead to the abiotic production of oxygen andozone, possible biosignatures (see reviews by Meadows et al. 2018 and Schwieterman et al. 2018). Mdwarfs have intrinsically faint FUV and NUV emission from their cool photospheres, but high levelsof magnetic heating (e.g., non-radiative heating) make bright chromospheric and transition regionemission lines that raise the FUV/NUV flux ratio two to three orders of magnitude higher than forsolar-type stars.H I Ly α (1215.67 ˚A) is the brightest M dwarf emission line in the UV (France et al. 2013), and istherefore required for a thorough accounting of the stellar UV energy budget. Yet, neutral hydrogengas in the ISM completely attenuates the inner ∼ − of the Ly α line core for even theclosest stars. To determine the intrinsic stellar emission, the Ly α line must be reconstructed from theobserved wings. Historically, this has been done at high spectral resolving power ( λ /∆ λ > I absorption line (-82 km s − from H I ) can be resolved from the H I absorption line (e.g.,Wood et al. 2005). Resolving the optically thin D I line places strong constraints on the propertiesof the highly optically thick H I line: column density, radial velocity, and Doppler broadening.France et al. (2013) showed that reliable reconstructions can be performed at lower resolving power( λ /∆ λ ∼ λ /∆ λ ∼ I absorption trough is completely unresolved.The higher sensitivity of the G140L spectra compared to higher resolution STIS gratings (G140M,E140M, and E140H) eases the detection of the important Ly α line, expanding the volume of Mdwarfs for which Ly α emission can potentially be studied. Higher sensitivity also allows for themeasurement of very broad Ly α wings ( ∼ − ), which have been long known for theSun (Morton & Widing 1961) and for M dwarfs (Gayley 1994; Youngblood et al. 2016). The broadwings are the result of partial frequency redistribution, which occurs because Ly α is a highly opticallythick resonance line (Milkey & Mihalas 1973; Basri et al. 1979). Photons from the lower opacity lowertransition region escape in the line core, whereas photons from the higher opacity chromosphere mustdiffuse out into the broad wings to escape. Matching the observed wing strength of emission lines likeLy α is a notoriously difficult problem for stellar models, especially for M dwarf models (see Fontenlaet al. 2016; Peacock et al. 2019a; Tilipman et al. 2020). More detailed observational constraintssupport the upcoming generation of stellar models that include chromospheres and transition regions(Peacock et al. 2019b; Tilipman et al. 2020).The intensity of the chromospheric emission line wings compared to the line core is controlledprimarily by the pressure scale height (Ayres 1979), with an inverse dependence on surface gravity.For main sequence stars, this means that more massive stars have brighter wings, as shown by Wilson& Bappu (1957) for Ca II H&K. However, there is likely a small dependence on magnetic activity(Ayres 1979; Gayley 1994), with more active stars exhibiting stronger wings. Combining the young,active M dwarf sample of FUMES, two well-known active M dwarfs from the literature (ProximaCentauri and AU Mic), and the more inactive M dwarf sample from the MUSCLES Treasury Survey(France et al. 2016; Youngblood et al. 2016; Loyd et al. 2016), we address the magnitude of magneticactivity’s effect on the observed Ly α wing strength of M dwarf stars.In Section 2, we briefly describe the FUMES observations and reductions, and in Section 3 wethoroughly describe the Ly α reconstructions. These results are used in the main FUMES analysis Table 1.
FUMES TargetsName Other Spectral d P rot
M R T eff
Age STISName Type (pc) (d) (M (cid:12) ) (R (cid:12) ) (K) gratingG 249-11 M4 29.14 52.8 a e G140LHIP 112312 WW PsA M4.5 20.86 2.4 b f E140MGJ 4334 FZ And M5 25.33 23.5 a g G140LLP 55-41 M3 37.04 53.4 a e G140LHIP 17695 M4 16.8 3.9 b f E140MLP 247-13 M3.5 35.04 1.3 c h G140LGJ 49 M1 9.86 18.6 d i G140LGJ 410 DS Leo M0 11.94 14.0 d h G140LCD -35 2722 M1 22.4 1.7 b f G140LHIP 23309 M0 26.9 8.6 b f G140L
Note —Distances (d) from Gaia Data Release 2 (Brown et al. 2018); spectral types, effectivetemperatures (T eff ), masses (M), and radii (R) from Pineda et al. accepted . References —(a) Donati et al. (2008), (b) Hartman et al. (2011), (c) Messina et al. (2010),(d) Newton et al. (2016), (e) Gagn´e & Faherty (2018), (f) Bell et al. (2015), (g) Irwin et al.(2011), (h) Shkolnik & Barman (2014), (i) Miles & Shkolnik (2017). (Pineda et al. accepted ). In Section 4, we analyze the broad Ly α wings and the implications forunderstanding M dwarf atmospheres. In Section 5, we summarize our findings. OBSERVATIONS AND REDUCTIONSUsing the STIS spectrograph onboard
HST , we observed 10 M dwarfs as part of the The Far-Ultraviolet M-dwarf Evolution Survey (FUMES) survey (GO 14640; PI: J. S. Pineda). Properties ofthe targets are listed in Table 1 and discussed in more detail in Paper I (Pineda et al. accepted ).Two of the targets, LP 55-41 and G 249-11, were detected at low signal-to-noise ratio (SNR), and wedo not attempt Ly α reconstructions for them. Custom reductions were performed using stistools following Loyd et al. (2016), including the exclusion of flares from the extracted spectra of GJ 4334,GJ 410, and HIP 17695. See Pineda et al. ( under review ) for more details. Ly α RECONSTRUCTIONS3.1.
The Model
Our model is comprised of two components: the stellar emission component and the ISM absorp-tion component. We tested different functions for the intrinsic stellar emission, including multiple,superimposed Gaussians, and found that a single Voigt profile in emission fits both the line coreand the broad wings best. We use the astropy Voigt1D function, which is based on the computa-tion from McLean et al. (1994). We assume no self-reversal because past results have shown that https://stistools.readthedocs.io/en/latest/ the Ly α self-reversal of M dwarfs is small (Wood et al. 2005; Guinan et al. 2016), if present at all(Youngblood et al. 2016; Bourrier et al. 2017; Schneider et al. 2019). Given that the Ly α line center,the region in the spectrum where the self-reversal appears, is usually entirely hidden by the ISM andnot well-constrained by the reconstruction, we assume no self-reversal is present. The Voigt emissionline model component has four free parameters: F λemission = V ( λ, V radial , A, F W HM L , F W HM G ) , (1)where V radial is the radial velocity of the emission line (km s − ), A is the Lorentzian amplitude (ergcm − s − ˚A − ; note that we parameterize it in all tables as log A), and FWHM L and FWHM G (km s − ) are the full-width at half maximum values for the Lorentzian and Gaussian components,respectively. For use with Voigt1D , V radial , FWHM L , and FWHM G are converted to ˚A. For thereconstructions on the E140M spectra where Ly α and Si III are not blended, Equation 1 is used, butfor the G140L spectra where the two lines are blended, F λemission = F λemission,HI + F λemission,SiIII .We assume a single ISM absorbing cloud as such low-resolution spectra (300 km s − ) are not ableto distinguish between ∼ − separated clouds. Youngblood et al. (2016) demonstrated thatassuming a single-velocity ISM does not significantly impact the reconstructed Ly α flux. For theISM component (used for Ly α only), we model the H I and D I absorption lines each as Voigt profileswith linked parameters using the code lyapy (Youngblood et al. 2016): F λabsorption = V ( λ, V HI , log N ( HI ) , b HI ) × V ( λ, V DI , log N ( DI ) , b DI ) . (2)V HI is the radial velocity (km s − ) and is assumed to be the same for both H I (1215.67 ˚A) and D I(1215.34 ˚A) (V HI = V DI , so V HI is the reported parameter). log N is the logarithm of the columndensity (cm − ) where N(HI) and N(DI) are linked by the parameter D/H, the deuterium to hydrogenratio: N(DI) = N(HI) × D/H. D/H is fixed to 1.5 × − (Linsky et al. 2006), so log N(HI) is thereported parameter. The Doppler parameter b controls the width of the absorption line, and we link b HI and b DI so that b DI = b HI / √ b HI is the reported parameter. In order to reduce the number offree parameters for the G140L reconstructions, b HI was fixed at 11.5 km s − based on the standardT=8000 K ISM (Wood et al. 2004; Redfield & Linsky 2004).To model the observed (attenuated) profile, we multiply the emission and absorption models (Equa-tions 1 & 2) and convolve with the instrument line spread function (LSF) provided by STScI forthe appropriate grating and slit combinations to recover the true physical parameters and accountfor the non-Gaussian wings of the G140L LSF: F λ = ( V emission × V absorption ) (cid:126) LSF. (3)3.2.
Fitting procedure and results
To reconstruct the Ly α profiles, we used a likelihood-based Bayesian calculation and a Markov-Chain Monte Carlo (MCMC) method ( emcee ; Foreman-Mackey et al. 2013) to simultaneously fitthe model (Equation 3) to the observed spectra. We assume uniform (flat) priors for all parameters https://github.com/allisony/lyapy https://emcee.readthedocs.io/en/latest/ except for a logarithmic prior for the Doppler b value (Youngblood et al. 2016), and a Gaussianlikelihood ln L = − N (cid:88) i ( y i − y model,i ) σ y i + ln(2 πσ y i ) , (4)where N is the total number of spectral data points y i with associated uncertainties σ y i , and y model,i corresponds to Equation 3. We maximize the addition of ln L and the logarithm of our priors with emcee . We used 50 walkers, ran for 50 autocorrelation times ( ∼ -10 steps), and removed anappropriate burn-in period based on the behavior of the walkers.Tables 3-7 show all of our model parameters with the assumed priors (uniform or logarithmic) withina bounded range and the 2.5, 15.9, 50, 84.1, and 97.5 percentiles as determined from the marginalizedposterior distributions. We present the median (50th percentile) as the best fit parameter values.The best fit (median) and 68% and 95% confidence intervals on the reconstructed Ly α and Si III fluxes were determined from the entire ensemble (i.e., a histogram of all the Ly α or Si III fluxes fromthe MCMC chain). Often the median parameter values do not create a self consistent solution, sowe obtain the best fit models and reconstructed profiles from the median flux in each wavelengthbin from the ensemble of models and reconstructed profiles. Figure 1 shows the best fit modeland reconstructed profile for the HIP 23309 data, and Figure 2 shows the marginalized and jointprobability distributions of the fitted parameters for HIP 23309. Similar figures for the other starsare available in the figure set in the online journal.In the rest of this section, we make note of any irregularities or the source of any constraints imposedon the reconstructions on a star-by-star basis. Most of the FUMES Ly α spectra were obtained withthe low-resolution G140L STIS grating ( λ /∆ λ ∼ I and D I ISM absorption linesare unresolved. Resolving the D I absorption is useful for constraining the ISM model parameters(column density, Doppler b value, and radial velocity), so we provide constraints on these parametervalues with outside information when necessary to aid convergence to a best-fit solution. Theseconstraints include stellar radial velocities from SIMBAD, predicted ISM radial velocities from theLocal ISM Kinematic Calculator (Redfield & Linsky 2008), predicted H I column densities for thelocal interstellar cloud (LIC) (Redfield & Linsky 2000), and measured H I column densities fromnearby sightlines collated from Wood et al. (2005), Youngblood et al. (2016), and Youngblood et al.(2017). GJ 4334 — The fit had to be restricted to log N(HI) > N(HI) < N(HI) < N(HI) restricted to lie between 17.8-19, the best fit log N(HI) = 18.03 is inagreement with the LIC model log N(HI) = 18.04 prediction and measurements of nearby sightlines(log N(HI)=17.9-18.5).
HIP 17695 — Despite the high spectral resolution obtained for this target, the fit is not consistentwith probable log N(HI) values ( > N(HI) value low ( < http://lism.wesleyan.edu/LISMdynamics.html http://lism.wesleyan.edu/ColoradoLIC.html Figure 1.
HIP 23309 best fit Ly α reconstruction. In the upper two panels, the STIS data with 1- σ errorbars are shown in black, the best model fit (intrinsic Ly α profile folded through the ISM) is shown in pinkwith 1 σ error bars shown in dark shaded gray and 2 σ error bars in light shaded gray. The dashed blue lineshows the best fit intrinsic Ly α profile with 1- and 2- σ error bars (dark and light shaded blue, respectively),and the dotted black line shows the Si III best fit profile. The bottom panel shows the residuals ((data-model)/(data uncertainty)) for the best fit model (pink in the upper panels) that best fits the data (black inthe upper panels). The horizontal dashed line is centered at zero, and the dotted lines are centered at ± Figure 2.
One- and two-dimensional projections of the sampled posterior probability distributions, referredto as marginalized and joint distributions, respectively, of the nine parameters for HIP 23309. Contours inthe joint distributions are shown at 0.5-, 1-, 1.5-, and 2- σ , and the histograms’ dashed black vertical linesshow the 16th, 50th, and 84th percentiles of the samples in each marginalized distribution. The text aboveeach histogram shows the median ± the 68% confidence interval. which may be unphysically low based on knowledge of the local ISM (Wood et al. 2005), althougha value < N(HI)= 17.93, and allow the MCMC to pile up near the lower boundary. We note that O V (1218.3 ˚A) isclearly detected in the Ly α red wing. LP 247-13 — We constrain the log N(HI) parameter to be between 18.3-19.0 (the fit prefers < N(HI) = 18.31 for a foreground star (Dring et al. 1997).
GJ 49 — The fit reveals 4 different local maxima with no clear global maximum. We discard thesolutions with a low log N(HI) = 17.7 value and a high log N(HI) = 18.7 value, because nearbysightlines indicate log N(HI) = 18.0-18.3. We also rule out the solution with the >
100 km s − dif-ference between V HI and V radial . With these restrictions on N(HI) and V HI in place (see priors inTable 3), we ran the MCMC for the presented solution. GJ 410 — The posterior distribution for this star’s fit is wide, as the 95% confidence interval spansa factor of 15 in Ly α flux. Nearby sightlines indicate log N(HI) lies in the range of 17.6-18.6, andthe solution’s log N(HI) = 18.32 is in agreement with this range.3.3.
Analysis of the reconstruction quality
The quality of the E140M reconstructions is high, but for many of our G140L reconstructions, >
32% of the residuals lie outside of the ± σ range (Figure 1 and the extended figure set in theonline journal). This indicates either that the data uncertainties are underestimated or that themodel is misspecified. In general, the data appear well-fit by the model, but a Durbin-Watson test(Durbin & Watson 1950) reveals some positive autocorrelation in the residuals. For half of our stars(HIP 23309, GJ 410, LP 247-13, HIP 112312), the Durbin-Watson statistic ( dw ) is between 1.5-1.8(where 2 represents no autocorrelation and 0 represents perfect positive autocorrelation) and for theothers (GJ 49, CD -35 2722, GJ 4334, HIP 17695) dw = 1.1-1.4. This autocorrelation of the residualscan be partially accounted for by a group of weak, unresolved emission lines present around 1190-1210˚A that are not included in our model. Based on detailed spectra of the Sun (Curdt et al. 2001) andprominent lines in high quality M dwarf spectra like AU Mic (Pagano et al. 2000; Ayres 2010) andGJ 436 (dos Santos et al. 2019), these lines include S III (1190, 1194, 1201, 1202 ˚A), Si II (1190, 1193,1194, 1197 ˚A), N I (1200, 1201 ˚A), Si III (1206 ˚A), and H (1209 ˚A) . There are fewer unresolvedemission lines in the blue wing of the Ly α line, including O V (1218 ˚A) and S I (1224, 1229, 1230˚A). This creates an apparent asymmetry (see the solar spectrum from Woods et al. 1995), whereasour model is symmetric about the line center. We have included only the strongest of these adjacentemission lines (Si III at 1206 ˚A) in our model as the others are ill-constrained by our spectra.We have tested adding a scatter term ( f ) to our model to account for underestimated data uncer-tainties, which is implemented by replacing the σ i terms in Equation 4 with σ i + f . We find thatfor our higher quality fits (e.g., HIP 23309), the fitted result was the same. For our lowest qualityfit (GJ 49), there was a large difference in the reconstructed flux, but the quality of the fit was notimproved as the structure in the residuals remained. Therefore, we do not present the fits with thescatter term in this work. We conclude that the model is missing a component, such as the weakemission lines and/or continuua in the line wings mentioned above.GJ 49’s reconstruction quality is the worst of our sample; and we note that its reconstructedLy α flux should be interpreted with caution. We postulate that the reason this star’s fit is sounconstrained is because of its Ly α line’s narrow intrinsic width (see Section 4.3) and the high SNRof its spectrum. GJ 49’s observed spectrum has higher SNR around the Ly α line than any of ourother G140L spectra, and this precision increases the visibility of features not covered by our model.Other FUMES targets with wider intrinsic line widths (and lower SNR) may swamp the signals fromunresolved emission lines and/or continuua. Despite large scatter in the residuals, GJ 49’s Ly α andSi III flux measurements appear to be consistent with other FUMES targets of similar rotation period(Pineda et al. accepted ). Note that in dos Santos et al. (2019), this line is labeled as Si IV , but is most likely H as labeled in the SUMERsolar spectral atlas (Curdt et al. 2001). Regarding our fitted radial velocity parameters, we note that the relative accuracy of the STISMAMA’s wavelength solution is reported in the STIS Instrument Handbook as 0.25-0.5 pixels (37-74km s − for the G140L grating; 0.8-1.6 km s − for the E140M grating), and the absolute wavelengthaccuracy is 0.5-1 pixel (74-148 km s − for G140L; 1.6-3.3 km s − for E140M). We find that the quotedrelative wavelength accuracy can easily describe the offsets between our fitted H I and Si III radial ve-locites (accounting for the 68% confidence interval on those values). The quoted absolute wavelengthaccuracy can account for almost all of the offsets between the literature stellar radial velocities andour fitted radial velocities. The exception is GJ 4334, which has some disagreement in the literatureover its radial velocity (-40 ± − from Newton et al. 2014; -16.5 ± − from Terrien et al.2015; -11.9 km s − from West et al. 2015). This discrepancy is not large enough to account for the ∼ − offset between our fitted radial velocities and the literature values. However, GJ4334’s velocity difference between the fitted radial velocity and the fitted ISM radial velocity is inagreement with the velocity difference of the Newton et al. (2014) radial velocity and predicted ISMvelocity (6.0 ± − ; Redfield & Linsky 2008), lending confidence to our fit and supporting thepossibility that the absolute wavelength accuracy for GJ 4334’s STIS observation is poorer than istypical.To test the accuracy of the reconstructions based on the G140L spectra, we degraded the resolutionof our E140M spectra (HIP 112312 and HIP 17695) to the resolution of the G140L spectra byconvolving with the G140L LSF and rebinning to match the G140L dispersion. Tables 6-7 showthe results of the E140M (native resolution) and degraded resolution reconstructions for these twostars. There is substantial overlap between the native and degraded reconstructed Ly α fluxes at the68% (for HIP 17695) and the 95% confidence interval (for both). The uncertainties with the G140L-quality reconstruction are much larger than for the E140M reconstructions, as expected. Whencomparing the individual fitted parameter values, we find that the G140L-quality reconstructionsdo not always agree with their higher resolution counterparts. For HIP 17695, agreement betweenthe individual fitted parameters is generally good, but not for HIP 112312. We provide confidenceintervals for all of our G140L reconstruction parameters (Tables 3-5), but note that they shouldbe interpreted with caution and may not reflect the true parameters that could be revealed withhigher-resolution spectra. This may be because the G140L posterior distributions are generally verywide, and we report the median parameter values as the best-fit values, even though combining themedian parameter values does not always yield a self-consistent best-fit to the data. However, thisexercise in comparing E140M reconstructions with degraded resolution reconstructions shows thatthe reconstructed Ly α fluxes overlap within at least the 95% level. DISCUSSION4.1.
The Wilson-Bappu effect and Ly α line widths Our STIS G140L reconstructed spectra of M dwarfs show their broad, ∼ − Ly α wingsin detail (Figure 3). As demonstrated in Ayres (1979), the widths of chromospheric emission lines likeCa II H&K, Mg II h&k, and Ly α are predominantly controlled by the stellar temperature distributionrather than chromosphere dynamics or magnetic heating. This explains the remarkable Wilson-Bappu correlation between absolute stellar magnitude and FWHM for the Ca II H&K emission cores(Wilson & Bappu 1957) and other chromospheric emission lines (McClintock et al. 1975; Cassatellaet al. 2001) across many orders of magnitude of stellar bolometric luminosity. In Figure 4, we show0 Figure 3.
Reconstructed Ly α profiles (corrected for stellar distance and radius) with the effect of instru-mental broadening removed (with the exception of the Sun, whose line profile inside ± − . that our data support a similar correlation ( ρ =0.72; p=0.0015) between bolometric luminosity andLy α FWHM, albeit over a much smaller parameter space than explored by Wilson & Bappu (1957).Ayres (1979) notes that stellar magnetic activity (e.g., due to non-radiative heating) does playa role in the widths of chromosphere emission lines, with greater activity corresponding to widerlines, in addition to the stronger influences of stellar effective temperature, surface gravity, andelemental abundance compared to hydrogen. Ayres (1979) and Linsky (1980) present a linear modelof chromospheric emission line width as a function of chromospheric heating (i.e., activity as measuredby the flux of a chromospheric emission line), effective temperature, surface gravity, and elementalabundance. To determine which stellar properties are most responsible for our observed Ly α widths,we construct a linear model based on our observations. We select surface gravity, Si III luminosityas a fraction of bolometric luminosity (a general “activity” proxy), and effective temperature aspredictor variables. Because we are examining a hydrogen line, we do not include a metallicity term.We scale each variable (by subtracting the mean and dividing by the standard deviation), constructa correlation matrix, and calculate the eigenvalues and eigenvectors via principal component analysis(PCA) (Table 4). Only the first two principal components (PCs) or eigenvectors have eigenvalues1 Figure 4.
Intrinsic Ly α FWHM (km s − ) versus stellar bolometric luminosity, plotted analogously toWilson & Bappu (1957), and color coded by Ly α luminosity as a fraction of bolometric luminosity. The effectof instrument line broadening has been removed. The Pearson correlation coefficient ( ρ =0.72, p=0.0015)demonstrates a statistically significant correlation over this narrow range of parameter space. > | ρ | > p < and PC in the linear model of Ly α width.We perform a multiple linear regression to relate our previously determined PCs to a responsevariable, the Ly α full width at 20% maximum flux (FW ), a term that is analogous to W(K ) fromAyres (1979). Regression coefficients are reported in Table 4. Simplifying the linear model expressionsinto the original unscaled predictor variables rather than PCs, we find that for the Ly α emission line:log F W = − .
29 log g + 0 .
09 log L ( SiIII ) L ( bol ) + 2 .
13 log T eff − . , (5)where FW is in ˚A, g is in cm s − , L(SiIII)/Lbol is unitless, and T eff is in K. There are somesimilarities in the coefficients between this paper’s Equation 5 and Equation 8 from Linsky (1980)(log W(K ) = -0.25 log g + 0.25 log F + 1.75 log T eff + 0.25 log A met , where F is the scalednon-radiative heating rate and A met is the metal abundance), such as the sign and magnitude of eachcoefficient being roughly the same. Dissimilarities are likely due to the differences in terms ( F and A met ) and parameter ranges in the sample stars. In this analysis, the stars used have log g between2 Table 2.
Principal Component Analysis SummaryCorrelation coefficients with Predictor Variables Regression coefficients ( β )Eigenvector g L(SiIII)/Lbol T eff
Response Variable(PC) Eigenvalue ρ p ρ p ρ p FW PC × − × − β =0.60PC × − β =0.10PC Note —The principal components (PCs) are related to the scaled predictor variables as follows: PC = − g + 0.60 log L(SiIII)/Lbol + 0.36 log T eff ; PC = − g − L(SiIII)/L(bol) +0.85 log T eff ; PC = − g − L(SiIII)/Lbol − T eff . ρ is the correlationcoefficient and p is the probability of no correlation between the PCs and predictor variables. We define asignificant correlation as | ρ | > p < FW = PC × β + PC × β . The intercept coefficient on the regression is vanishinglysmall ( < − ) and is dropped. The linear model’s predicted FW is significantly and positively correlatedwith the measured values ( ρ =0.76, p =6.5 × − ). L(SiIII)/Lbol between -7.5 and -5.0, and T eff between 3000-3900 K. The observed rangeof FW values is 0.6-3.8 ˚A.As is the case for Ca II , stellar activity appears to be a minor factor in the width of Ly α , also indi-cated by the lack of correlation between FW and L(Ly α )/L bol ( ρ =-0.06, p =0.82) or L(SiIII)/L bol ( ρ =0.29, p =0.27). The more dominant factors are surface gravity and effective temperature, indicatedby the correlation coefficients between FW and T eff ( ρ =0.50; p =0.05) or g ( ρ =-0.51; p =0.04).From Figure 3, we find that in general, the M dwarfs with larger Ly α wing flux values tend to bemore active. The “inactive” MUSCLES M dwarfs (as determined by optical activity indicators suchas Ca II; France et al. 2016) have the narrowest profiles, and Proxima Centauri has a surprisinglynarrow profile given its known levels of moderate activity (Robertson et al. 2013, 2016; Davenportet al. 2016; Howard et al. 2018). For example, Proxima Centauri’s log L(SiIII)/L bol = -6.2 com-pared to the -7.2 to -7.5 values for the inactive MUSCLES M dwarfs GJ 832, GJ 581, and GJ 436.However, as discussed, these line widths are dominated by stellar structure, and in general, lowersurface gravity (i.e., young) M dwarfs tend to be more active.4.2.
Chromospheric electron density estimates from Ly α observations The electron density in the line forming region (the chromosphere for the Ly α broad wings) isa main factor in controlling the width of the Ly α line (Gayley 1994). We estimate chromosphereelectron density values, which are a valuable constraint for stellar models, using the formalism fromGayley (1994) that explicitly relates the surface flux density of the Ly α broad wings to chromosphericelectron density and other stellar properties: F wing (∆ λ ) ≈ F peak, (cid:12) ∆ λ (cid:16) n e n e, (cid:12) (cid:17) g (cid:12) g T chromo K J c, (cid:12) J c , (6)3 Figure 5.
Surface gravity vs. surface flux density (erg cm − s − ˚A − ) at ± α line center.Lines of constant electron density (log n e ) are shown in gray under the approximation from Gayley (1994)(Equation 6, with T chromo = 7500 K, and J c = J c, (cid:12) ). Note that the Sun’s measured electron density is10 cm − (Song 2017) and GJ 832’s is 10 cm − (Fontenla et al. 2016). where F wing (∆ λ ) is the Ly α surface flux density at ∆ λ ˚A from line center, F peak, (cid:12) is the peak solarLy α flux ( ∼ × erg cm − s − ), n e is the chromospheric electron density, g is the surface gravity, T chromo is the chromospheric temperature, and J c is the Balmer continuum flux. Each parameter isnormalized to the solar ( (cid:12) ) value. Stars with larger electron densities and hotter chromospheres willhave broader wings, but the wing intensity is diminished for stars with greater surface gravity andgreater Balmer continuum flux.Figure 5 shows the Ly α surface flux densities of the FUMES targets, the MUSCLES M dwarfs(France et al. 2016), Proxima Centauri and AU Mic (Youngblood et al. 2017), and the Sun(SORCE/SOLSTICE; McClintock et al. 2005), plotted against surface gravity. Lines of constantelectron density are drawn on the plot using Equation 6. We assume T chromo and J c are both equiv-alent to solar values ( T chromo = 7500K; J c = 1.7 × erg cm − s − ˚A − sr − ). For stars with knownchromospheric electron densities, the Gayley (1994) approximation works well. The Sun’s electrondensity log n e =11 cm − (Song 2017), and GJ 832’s log n e =10 cm − (Fontenla et al. 2016), areboth in agreement with the gray curves in Figure 5.4We find that LP 247-13, a 625 Myr M2.7V star, has a chromospheric electron density similar tothe Sun. All of the FUMES targets (“active” stars) have electron densities larger than that of the“inactive” M dwarfs from the MUSCLES survey, except for GJ 176. We note that GJ 176 is the least“inactive” of the MUSCLES stars as it is the most rapidly rotating (P rot =39.5 day, Robertson et al.2015) and is possibly younger than 1 Gyr based on its large X-ray luminosity (Guinan et al. 2016;Loyd et al. 2018). 4.3. STIS G140L and future Ly α observations The presented Ly α reconstructions are the first based on λ/ ∆ λ ∼ I absorption completely unresolved. Using the STIS G140L mode provides some observationaladvantages including avoiding prohibitively long exposure times of higher resolution STIS modes forM dwarf targets deemed too hazardous for the COS instrument (Bright Object Protections ). Basedon the six M dwarfs presented here, we find that the precision of Ly α reconstructions performed onSTIS G140L spectra can range from 5% to 100% at the 68% confidence level (Figure 6). At the95% confidence level, the precisions range from ∼
10% to a factor of nine. There appears to beno dependence of these precisions on the SNR of the observed spectrum; we note that all G140LLy α emission lines were detected at high SNR (90-250 integrated over the line). Rather, our threeG140L targets with the largest reconstructed flux uncertainties (GJ 4334, GJ 49, and GJ 410) are alsothe G140L targets with the lowest surface flux in the Ly α wings, or in other words, the narrowestprofiles. We hypothesize that for narrow profiles (Ly α surface flux at ± (cid:46) erg cm − s − ˚A or F W < λ/ ∆ λ ∼ ∼ α fluxes for young, active Mdwarfs with precisions comparable to G140M spectra, but the precision is much lower than what isobtainable with high SNR G140M or E140M spectra.Adopting FW > α reconstructionswith G140L, Equation 5 may be useful for guiding future observers toward whether or not G140L issuitable for a Ly α reconstruction for a particular M dwarf. Surface gravity and effective temperature,two of the three stellar parameters in Equation 5, are readily available in the literature for manyM dwarfs. The third parameter, L (SiIII)/ L (bol), is not available for most M dwarfs, but can beestimated from the stellar rotation period (Pineda et al. accepted ) or common activity indicators like R (cid:48) HK or L (H α )/ L (bol) (Melbourne et al. 2020).Figure 6 shows how the observed Ly α fluxes compare to the reconstructed (intrinsic) fluxes. Theobserved fluxes were obtained simply by integrating over the observed, ISM-attenuated Ly α profiles.In some cases, the observed Ly α fluxes are only 10-50% less than the reconstructed fluxes, while in Figure 6.
The reconstructed Ly α flux as observed at Earth are plotted against the Ly α surface flux density(erg cm − s − ˚A − at ± left panel ) and Ly α full width at 20% maximum ( F W ; rightpanel ) for the FUMES targets. All but two stars were observed with the STIS G140L grating ( λ/ ∆ λ ∼ λ/ ∆ λ ∼ α flux density obtained by integrating over the observed (ISM-attenuated)Ly α spectra. The gray vertical lines indicate the apparent size of several factors of uncertainty (200%, 100%,50%, 30%, and 10%). others they are a factor of a few to an order of magnitude less. The dominant factor in the fluxdifferences is the column density of the ISM absorbers and the radial velocity of the ISM absorbersrelative to the stellar radial velocity. A small radial velocity offset between the star and ISM, andlarger column densities will result in larger flux differences between observed and reconstructed.Figure 6 may give the reader a sense of whether or not performing a reconstruction on G140LLy α spectra is worthwhile for their science goals. SUMMARYAs part of the Far Ultraviolet M-dwarf Evolution Survey (FUMES), we have reconstructed theintrinsic Ly α profiles of 8 early-to-mid M dwarfs spanning a range of young to field star ages fromlow and moderate resolution spectra taken with HST ’s STIS spectrograph. The Ly α and Si III fluxesderived in this paper are incorporated into Paper I of the FUMES survey (Pineda et al. accepted ),which describes the flux evolution of FUV spectral lines with stellar age and rotation period forearly-to-mid M dwarfs. We summarize our findings here:1. We present the first demonstration of Ly α reconstruction on low, λ/ ∆ λ ∼ I absorption trough from the ISM is completely unresolved. We find that6 the 1- σ precision in the reconstructed Ly α flux can be 5-10% in the best case (young M dwarfs)and a factor of two in the worst case (field age M dwarfs). The precision is not correlated withSNR of the observation, rather, it depends on the intrinsic broadness of the stellar Ly α line.Young, low-gravity stars have the broadest lines and therefore provide more information at lowspectral resolution to the fit to break degeneracies among model parameters.2. Our high SNR, low resolution Ly α spectra detect the extremely broad wings ( ∼ − ) at SNR=7-14 per resolution element, and we see large differences in the width of Ly α fromstar to star. We confirm past findings that the line width is predominantly correlated with thefundamental stellar parameters surface gravity and effective temperature, rather than magneticactivity.3. Ly α surface flux density ∼ α surface fluxdensity approximation from that work using GJ 832’s spectrum from Youngblood et al. (2016);Loyd et al. (2016) and modeled electron density from Fontenla et al. (2016).The data presented here were obtained as part of the HST
Guest Observing program lyapy . Facilities:
HST
Software:
Astropy(Robitailleetal.2013),IPython(Perez&Granger2007),Matplotlib(Hunter2007),NumPyandSciPy(vanderWaltetal.2011),lyapy(Youngbloodetal.2016),emcee(Foreman-Mackeyetal.2013), triangle (Foreman-Mackey et al. 2014), statsmodels (Seabold & Perktold 2010).REFERENCES
Ayres, T. R. 1979, The Astrophysical Journal,228, 509, doi: 10.1086/156873Ayres, T. R. 2010, ApJS, 187, 149,doi: 10.1088/0067-0049/187/1/149Basri, G. S., Linsky, J. L., Bartoe, J.-D. F.,Brueckner, G., & van Hoosier, M. E. 1979, TheAstrophysical Journal, 230, 924,doi: 10.1086/157151Bell, C. P. M., Mamajek, E. E., & Naylor, T. 2015,MNRAS, 454, 593, doi: 10.1093/mnras/stv1981Bourrier, V., Ehrenreich, D., Allart, R., et al.2017, A&A, 602, A106,doi: 10.1051/0004-6361/201730542Brown, A. G. A., Vallenari, A., Prusti, T., et al.2018, Astronomy & Astrophysics, 616, A1,doi: 10.1051/0004-6361/201833051 Cassatella, A., Altamore, A., Badiali, M., &Cardini, D. 2001, Astronomy and Astrophysics,374, 1085, doi: 10.1051/0004-6361:20010816Curdt, W., Brekke, P., Feldman, U., et al. 2001,A&A, 375, 591,doi: 10.1051/0004-6361:20010364Davenport, J. R. A., Kipping, D. M., Sasselov, D.,Matthews, J. M., & Cameron, C. 2016, ApJL,829, L31, doi: 10.3847/2041-8205/829/2/L31Donati, J.-F., Morin, J., Petit, P., et al. 2008,Monthly Notices of the Royal AstronomicalSociety, 390, 545,doi: 10.1111/j.1365-2966.2008.13799.xdos Santos, L. A., Ehrenreich, D., Bourrier, V.,et al. 2019, A&A, 629, A47,doi: 10.1051/0004-6361/201935663 Table 3.
Prior Probabilities, Best Fits, and Confidence Intervals for G140LParameter GJ 4334 GJ 49V radial
U(-100; 300) U(-150; 150)(km s − ) [142.4, 153.0, 166.7, 178.0, 188.9] [43.8, 50.9, 52.8, 54.0, 55.1]log A U(-18.5, 8) U(-14; -10)(erg cm − s − ˚A − ) [-12.99, -12.89, -12.72, -12.36, -10.95] [-11.93, -11.07, -10.52, -10.32, -10.26]FWHM L U(1; 1000) U(1; 1000)(km s − ) [8.6, 37.9, 57.5, 73.6, 88.1] [9.3, 10.1, 12.6, 23.7, 62.3]FWHM G U(1; 1000) U(1; 1000)(km s − ) [167.4, 209.5, 253.7, 293.4, 327.1] [178.8, 181.8, 187.7, 208.4, 277.2]log N(H I ) U(17.8; 19) U(17.7; 18.5)(cm − ) [17.81, 17.87, 18.03, 18.25, 18.58] [17.81, 18.29, 18.44, 18.49, 18.50]b HI − )V HI U(0; 300) U(0; 150)(km s − ) [188.9, 214.7, 223.1, 227.8, 233.4] [47.0, 72.4, 72.8, 73.1, 73.3]V SiIII
U(-60; 400) U(-250; 250)[195.5, 221.6, 247.7, 270.6, 292.7] [76.2, 90.0, 104.2, 118.7, 132.9]A
SiIII
U(-16; -12) U(-16; -13)[-14.94, -14.85, -14.75, -14.61, -14.37] [-14.55, -14.49, -14.44, -14.37, -14.30]FWHM
SiIII
U(1; 700) U(1; 700)[130.1, 202.1, 277.0, 344.4, 416.7] [253.0, 300.1, 349.5, 400.6, 453.1]F(Ly α ) [5.47, 5.87, 7.03, 10.96, 59.54] [0.46, 1.56, 2.49, 3.07, 3.28](erg cm − s − ) × − × − F(Si III) [1.78, 1.93, 2.11, 2.28, 2.44] [5.06, 5.27, 5.50, 5.71, 5.90](erg cm − s − ) × − × − Note —U represents a uniform prior within the bounds. Other values are fixed values. On the secondline: [2.5%, 15.9%, 50%, 84.1%, 97.5%].Dring, A. R., Linsky, J., Murthy, J., et al. 1997,The Astrophysical Journal, 488, 760Durbin, J., & Watson, G. S. 1950, Biometrika, 37,409, doi: 10.1093/biomet/37.3-4.409Fontenla, J., Witbrod, J., Linsky, J. L., et al.2016, The Astrophysical Journal, 830, 154Foreman-Mackey, D., Hogg, D. W., Lang, D., &Goodman, J. 2013, Publications of theAstronomical Society of the Pacific, 125, 306,doi: 10.1086/670067Foreman-Mackey, D., Ryan, G., Barbary, K., et al.2014, doi: 10.5281/zenodo.11020 France, K., Froning, C. S., Linsky, J. L., et al.2013, The Astrophysical Journal, 763, 149,doi: 10.1088/0004-637X/763/2/149France, K., Loyd, R., Youngblood, A., et al. 2016,Astrophysical Journal, 820,doi: 10.3847/0004-637X/820/2/89Gagn´e, J., & Faherty, J. K. 2018, ApJ, 862, 138,doi: 10.3847/1538-4357/aaca2eGayley, K. G. 1994, The Astrophysical Journal,431, 806, doi: 10.1086/174531Guinan, E. F., Engle, S. G., & Durbin, A. 2016,ApJ, 821, 81, doi: 10.3847/0004-637X/821/2/81 Table 4.
Prior Probabilities, Best Fits, and Confidence Intervals for G140LParameter GJ 410 LP247-13V radial
U(-250; 250) U(-250; 250)(km s − ) [0.8, 8.7, 16.8, 25.5, 36.8] [84.8, 91.6, 101.3, 110.2, 115.3]log A U(-18.5; -8) U(-18; -8)(erg cm − s − ˚A − ) [-11.6, -11.38, -11.04, -10.44, -9.3] [-12.27, -12.19, -12.0, -11.58, -11.04]FWHM L U(1; 1000) U(1; 1000)(km s − ) [3.8, 13.8, 27.3, 40.2, 51.6] [22.6, 41.6, 66.7, 82.7, 91.4]FWHM G U(1; 1000) U(1; 1000)(km s − ) [158.4, 181.8, 204.7, 226.6, 246.6] [17.5, 72.2, 118.1, 153.6, 178.3]log N(H I ) U(17.5; 19) U(18.3; 19)(cm − ) [18.05, 18.18, 18.32, 18.48, 18.68] [18.3, 18.31, 18.35, 18.42, 18.50]b HI − )V HI U(-200; 200) U(-250; 250)(km s − ) [71.4, 72.7, 73.6, 74.7, 76.0] [74.4, 76.0, 78.8, 84.4, 88.4]V SiIII
U(-160; 350) U(-250; 250)(km s − ) [-33.7, -11.8, 9.8, 31.6, 53.6] [121.1, 143.8, 166.6, 188.7, 209.8]A SiIII
U(-16; -12) U(-16; -13)(erg cm − s − ˚A − ) [-14.28, -14.19, -14.1, -13.99, -13.75] [-14.50, -14.43, -14.36, -14.28, -14.20]FWHM SiIII
U(1; 700) U(1; 700)(km s − ) [113.1, 197.5, 257.5, 313.7, 374.1] [268.3, 325.2, 391.3, 464.7, 539.7]F(Ly α ) [0.82, 1.05, 1.58, 3.21, 11.95] [3.06, 3.39, 4.42, 8.16, 17.17](erg cm − s − ) × − × − F(Si III) [7.32, 8.02, 8.76, 9.48, 10.16] [6.53, 6.91, 7.31, 7.72, 8.10](erg cm − s − ) × − × − Note —U represents a uniform prior within the bounds. Other values are fixed values. On thesecond line: [2.5%, 15.9%, 50%, 84.1%, 97.5%].Hartman, J. D., Bakos, G. ´A., Noyes, R. W., et al.2011, The Astronomical Journal, 141, 166,doi: 10.1088/0004-6256/141/5/166Howard, W. S., Tilley, M. A., Corbett, H., et al.2018, ApJL, 860, L30,doi: 10.3847/2041-8213/aacaf3Hunter, J. D. 2007, Computing in Science &Engineering, 9, 90, doi: 10.1109/MCSE.2007.55Irwin, J., Berta, Z. K., Burke, C. J., et al. 2011,ApJ, 727, 56, doi: 10.1088/0004-637X/727/1/56Linsky, J. L. 1980, Annual Review of Astronomyand Astrophysics, 18, 439,doi: 10.1146/annurev.aa.18.090180.002255 Linsky, J. L., Draine, B. T., Moos, H. W., et al.2006, The Astrophysical Journal, 647, 1106,doi: 10.1086/505556Loyd, R. O. P., France, K., Youngblood, A., et al.2016, The Astrophysical Journal, 824, 102,doi: 10.3847/0004-637X/824/2/102—. 2018, The Astrophysical Journal, 867, 71,doi: 10.3847/1538-4357/aae2bdMcClintock, W., Linsky, J. L., Henry, R. C., &Moos, H. W. 1975, The Astrophysical Journal,202, 733, doi: 10.1086/154026 Table 5.
Prior Probabilities, Best Fits, and Confidence Intervals for G140L (continuation of Table 3)Parameter CD 35-2722 HIP 23309V radial
U(-250; 250) U(-250; 250)(km s − ) [70.3, 93.3, 99.1, 104.7, 110.1] [110.4, 114.5, 118.0, 121.6, 125.1]log A U(-18, -8) U(-18; -8)(erg cm − s − ˚A − ) [-12.79, -12.75, -12.70, -12.63, -12.51] [-12.26, -12.23, -12.20, -12.17, -12.14]FWHM L U(1; 1000) U(1; 1000)(km s − ) [162.3, 186.2, 201.5, 215.3, 227.9] [122.8, 129.0, 135.6, 142.5, 149.7]FWHM G U(1; 1000) U(1; 5000)(km s − ) [236.6, 294.7, 327.9, 359.9, 387.3] [421.6, 438.7, 455.3, 472.5, 489.6]log N(H I ) U(17.5; 19) U(17.5; 19)(cm − ) [17.52, 17.60, 17.78, 17.98, 18.21] [17.61, 17.71, 17.80, 17.88, 17.96]b HI − )V HI U(-250; 250) U(-250; 250)(km s − ) [-66.2, -58.3, 38.2, 59.0, 67.9] [47.5, 72.0, 74.7, 76.7, 78.8]V SiIII
U(-250; 250) U(-250; 250)[-7.5, 8.7, 25.1, 42.1, 67.9] [96.3, 107.5, 118.1, 128.5, 138.6]A
SiIII
U(-16; -13) U(-16; -13)[-14.28, -14.23, -14.17, -14.11, -14.03] [-13.86, -13.82, -13.77, -13.72, -13.64]FWHM
SiIII
U(1; 700) U(1; 700)[338.8, 409.7, 477.8, 548.6, 616.4] [201.1, 243.0, 276.1, 306.9, 336.5]F(Ly α ) [2.30, 2.37, 2.50, 2.72, 2.99] [5.03, 5.21, 5.40, 5.60, 5.82](erg cm − s − ) × − × − F(Si III) [1.26, 1.32, 1.37, 1.43, 1.49] [1.85, 1.93, 2.01, 2.10, 2.17](erg cm − s − ) × − × − Note —U represents a uniform prior within the bounds. Other values are fixed values. On the secondline: [2.5%, 15.9%, 50%, 84.1%, 97.5%].McClintock, W. E., Rottman, G. J., & Woods,T. N. 2005, Solar Physics, 230, 225,doi: 10.1007/s11207-005-7432-xMcLean, A. B., Mitchell, C. E. J., & Swanston,D. M. 1994, Journal of Electron Spectroscopyand Related Phenomena, 69, 125,doi: 10.1016/0368-2048(94)02189-7Meadows, V. S., Reinhard, C. T., Arney, G. N.,et al. 2018, Astrobiology, 18, 630,doi: 10.1089/ast.2017.1727 Melbourne, K., Youngblood, A., France, K., et al.2020, AJ, 160, 269,doi: 10.3847/1538-3881/abbf5cMessina, S., Desidera, S., Turatto, M., Lanzafame,A. C., & Guinan, E. F. 2010, A&A, 520, A15,doi: 10.1051/0004-6361/200913644Miles, B. E., & Shkolnik, E. L. 2017, AJ, 154, 67,doi: 10.3847/1538-3881/aa71abMilkey, R. W., & Mihalas, D. 1973, TheAstrophysical Journal, 185, 709,doi: 10.1086/152448 Table 6.
Prior Probabilities, Best Fits, and Confidence Intervals for HIP 112312 (E140M)Parameter Native Resolution Degraded (G140L) ResolutionV radial
U(-250; 250) U(-100; 100)(km s − ) [-3.2, -2.2, -1.1, 0.0, 1.1] [16.1, 23.2, 31.6, 39.3, 46.1]log A U(-18; -8) U(-18; -8)(erg cm − s − ˚A − ) [-11.15, -11.13, -11.10, -11.07, -11.04] [-11.89, -11.82, -11.70, -11.44, -10.81]FWHM L U(1; 1000) U(1; 1000)(km s − ) [37.8, 40.1, 42.6, 45.1, 47.5] [44.9, 90.9, 122.9, 143.8, 158.1]FWHM G U(1; 1000) U(1; 1000)(km s − ) [216.3, 221.3, 226.4, 231.6, 236.5] [4.4, 22.5, 71.5, 127.8, 165.3]log N(H I ) U(17.5; 19) U(17.5; 19.0)(cm − ) [18.24, 18.26, 18.28, 18.3, 18.33] [17.52, 17.61, 17.82, 18.08, 18.39]b HI ln (5; 20) ln (5; 20)(km s − ) [10.2, 11.4, 12.2, 12.7, 13.2] [5.6, 8.3, 13.0, 17.3, 19.4]V HI U(-250; 250) U(-100; 100)(km s − ) [-10.3, -9.9, -9.5, -9.0, -8.6] [-27.7, -15.1, 0.7, 15.0, 23.5]F(Ly α ) [2.02, 2.08, 2.14, 2.21, 2.29] [1.22, 1.31, 1.48, 1.90, 3.17](erg cm − s − ) × − × − Note —U represents a uniform prior within the bounds. Other values are fixed values. On the secondline: [2.5%, 15.9%, 50%, 84.1%, 97.5%].Morton, D. C., & Widing, K. G. 1961, TheAstrophysical Journal, 133, 596,doi: 10.1086/147062Newton, E. R., Charbonneau, D., Irwin, J., et al.2014, The Astronomical Journal, 147, 20,doi: 10.1088/0004-6256/147/1/20Newton, E. R., Irwin, J., Charbonneau, D.,Berta-Thompson, Z. K., & Dittmann, J. A.2016, The Astrophysical Journal, 821, L19,doi: 10.3847/2041-8205/821/1/L19Pagano, I., Linsky, J. L., Carkner, L., et al. 2000,ApJ, 532, 497, doi: 10.1086/308559Peacock, S., Barman, T., Shkolnik, E. L.,Hauschildt, P. H., & Baron, E. 2019a, TheAstrophysical Journal, 871, 235,doi: 10.3847/1538-4357/aaf891Peacock, S., Barman, T., Shkolnik, E. L., et al.2019b, The Astrophysical Journal, 886, 77,doi: 10.3847/1538-4357/ab4f6fPerez, F., & Granger, B. E. 2007, Computing inScience & Engineering, 9, 21,doi: 10.1109/MCSE.2007.53 Redfield, S., & Linsky, J. L. 2000, TheAstrophysical Journal, 534, 825,doi: 10.1086/308769Redfield, S., & Linsky, J. L. 2004, ApJ, 602, 776,doi: 10.1086/381083Redfield, S., & Linsky, J. L. 2008, TheAstrophysical Journal, 673, 283,doi: 10.1086/524002Robertson, P., Bender, C., Mahadevan, S., Roy,A., & Ramsey, L. W. 2016, ApJ, 832, 112,doi: 10.3847/0004-637X/832/2/112Robertson, P., Endl, M., Cochran, W. D., &Dodson-Robinson, S. E. 2013, ApJ, 764, 3,doi: 10.1088/0004-637X/764/1/3Robertson, P., Roy, A., & Mahadevan, S. 2015,The Astrophysical Journal, 805, L22,doi: 10.1088/2041-8205/805/2/L22Robitaille, T. P., Tollerud, E. J., Greenfield, P.,et al. 2013, Astronomy & Astrophysics, 558,A33, doi: 10.1051/0004-6361/201322068 Table 7.
Prior Probabilities, Best Fits, and Confidence Intervals for HIP 17695 (E140M)Parameter Native Resolution Degraded (G140L) ResolutionV radial