Predicting the Extreme Ultraviolet Radiation Environment of Exoplanets Around Low-Mass Stars: GJ 832, GJ 176, GJ 436
Sarah Peacock, Travis Barman, Evgenya Shkolnik, Peter Hauschildt, E. Baron, Birgit Fuhrmeister
DDraft version October 18, 2019
Typeset using L A TEX twocolumn style in AASTeX62
PREDICTING THE EXTREME ULTRAVIOLET RADIATION ENVIRONMENT OF EXOPLANETS AROUNDLOW-MASS STARS: GJ 832, GJ 176, GJ 436
Sarah Peacock, Travis Barman, Evgenya L. Shkolnik, Peter H. Hauschildt, E. Baron,
4, 3 andBirgit Fuhrmeister University of Arizona, Lunar and Planetary Laboratory, 1629 E University Boulevard, Tucson, AZ 85721, USA School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85281, USA Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germany Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks, Rm 100, Norman, OK 73019-2061USA (Accepted October 17, 2019)
Submitted to ApJABSTRACTCorrect estimates of stellar extreme ultraviolet (EUV; 100 – 1170 ˚A) flux are important for studyingthe photochemistry and stability of exoplanet atmospheres, as EUV radiation ionizes hydrogen andcontributes to the heating, expansion, and potential escape of a planet’s upper atmosphere. Contam-ination from interstellar hydrogen makes observing EUV emission from M stars particularly difficult,and impossible past 100 pc, and necessitates other means to predict the flux in this wavelength regime.We present EUV – infrared (100 ˚A – 5.5 µ m) synthetic spectra computed with the PHOENIX atmo-spheric code of three early M dwarf planet hosts: GJ 832 (M1.5 V), GJ 176 (M2.5 V), and GJ 436(M3.5 V). These one-dimensional semiempirical nonlocal thermodynamic equilibrium models includesimple temperature prescriptions for the stellar chromosphere and transition region, from where ultra-violet (UV; 100 – 3008 ˚A) fluxes originate. We guide our models with Hubble Space Telescope far- andnear-UV spectra and discuss the ability to constrain these models using
Galaxy Evolution Explorer
UV photometry. Our models closely reproduce the observations and predict the unobservable EUVspectrum at a wavelength resolution of < Keywords: stars: activity, stars: chromospheres, stars: low-mass, ultraviolet: stars [email protected] a r X i v : . [ a s t r o - ph . S R ] O c t Peacock et al. INTRODUCTIONThe majority of known terrestrial-sized exoplanets lo-cated within the canonical habitable zone are foundorbiting M stars (Shields et al. 2016), including themost nearby, Proxima Centauri b (Anglada-Escud´e etal. 2016) and three of the seven TRAPPIST-1 systemplanets (Gillon et al. 2017). Due to their cool effectivetemperatures ( ∼ , CH , and H Oin the upper atmospheres of planets (Segura et al. 2005;Hu et al. 2012; Moses 2014; Rugheimer et al. 2015; Loydet al. 2016). For example, the strongest emitting line inthe FUV, Lyman α (Ly α ; 1215.7 ˚A), will generate hy-drocarbon hazes in the upper atmospheric layers as adirect result of dissociating methane in a planet’s iono-sphere (Trainer et al. 2006). At longer wavelengths, stel-lar near-UV (NUV; 1680 – 3008 ˚A) flux dissociates bothO and O . Analyzing single and repeated UV flareevents and from the M dwarf star, AD Leo, Segura et al.(2010) and Tilley et al. (2019) found that the combina-tion of UV radiation and protons is capable of depletingalmost all of the O on an Earth-like planet in an Mstar’s habitable zone in under 10 years.Close-in exoplanets become vulnerable to mass lossas stellar extreme-UV (EUV; 100 – 1170 ˚A) radiationionizes hydrogen. This process heats and expands theatmospheric layers above the planet’s thermosphere, po-tentially leading to ion pickup by the stellar wind or hy-drodynamic outflow of hydrogen (Lammer et al. 2007; Tian et al. 2008; Murray-Clay et al. 2009; Koskinen etal. 2010; Rahmati et al. 2014; Chadney et al. 2015; Tri-pathi et al. 2015). Depending on the amount of EUVflux they are exposed to, habitable zone planets aroundM stars can lose both oceans and significant fractions oftheir atmospheres within a few billion years (Luger &Barnes 2015). Correct estimates of stellar EUV flux areimportant for studying the stability of exoplanet atmo-spheres and the stability of the M star habitable zone.Observing in EUV wavelengths is extremely difficultdue to optically thick interstellar hydrogen absorbingmost of the spectrum between 400 – 912 ˚A (Barstow &Holberg 2007). While the quantity of absorption dueto the interstellar medium (ISM) is dependent on thedirection, short-wavelength UV observations are signifi-cantly affected for nearly all planet-hosting stars ( > Extreme Ultraviolet Explorer ( EUVE ) ob-served six active M stars with low signal-to-noise from100 – 400 ˚A (AD Leo, AU Mic, EV Lac, Proxima Cen-tauri, YY Gem, YZ CMI). The majority of the EUVemission from these stars is below the minimum de-tectable flux level for the instrument, so only strongemission lines including He II and highly ionized iron(Fe IX – XVI ) were identified (Craig et al. 1997). Noflux was observed from 350-912 ˚A. While current capa-bilities allow for FUV, NUV, and limited X-ray mea-surements, there are no operational instruments able toobserve stars other than the Sun in the EUV wavelengthrange.Due to the scarcity of EUV observations for M stars,studies have relied on using either the
EUVE spectrumof the very active M star, AD Leo (Segura et al. 2010;Wordsworth et al. 2010), or other proxies to determinethe flux in this wavelength regime. Current methodsto predict EUV flux include various empirical scalingrelationships (Linsky et al. 2014; Chadney et al. 2015;France et al. 2018) and semiempirical models to pro-duce synthetic EUV spectra (e.g. Lecavelier Des Etangs2007; Sanz-Forcada et al. 2011; Fontenla et al. 2016;Peacock et al. 2019). Stellar EUV spectra are char-acterized by many emission lines with large dynamicranges in flux, superimposed on a continuum markedwith distinct bound-free edges from continuous opacitysources. In a low activity solar spectrum, the strongestEUV emission lines peak at fluxes three orders of magni-tude larger than continuum levels (Tobiska 1996). Thislevel of detail is not encompassed in broadband scalingrelationships and can only be predicted with high res-olution synthetic spectra. The radiation in individualEUV emission lines penetrates planetary atmospheres at
UV-IR Spectrum of GJ 832, GJ 176, GJ 436 . In order to determine the temperature struc-ture in the full upper atmosphere and estimate realisticEUV spectra, X-ray and/or UV observations are neededto guide and validate semiempirical stellar models. It isimportant to note that the timescales for flares and mag-netic activity cycles occurring in the upper-atmosphericlayers of M stars ranges from seconds to years and re-sults in highly variable levels of measured X-ray and UVflux (Monsignori Fossi et al. 1996; Hawley et al. 2003;Stelzer et al. 2013; Loyd et al. 2018a,b). As a result,models based on non-contemporaneous X-ray and UVobservations will have potentially large uncertainties inthe predicted EUV spectra.Stellar X-ray measurements provide important infor-mation about the thermal structure in the outermost ∼ K coronal layers, where emission features of highlyionized species found in the XUV (1 – 912 ˚A) spectrumform. The EUV continuum and many FUV emissionlines, however, form at cooler temperatures deeper inthe stellar atmosphere in the chromosphere and transi-tion region. Estimating UV spectra using only X-rayobservations leads to systematically underpredicted linefluxes because the X-ray observations do not include thecontribution from the deeper atmospheric layers. For ex-ample, Sanz-Forcada et al. (2011) used emission measuredistribution coronal models with
XMM-Newton , Chan-dra , and
ROSAT
X-ray observations to compute syn-thetic XUV spectra of 82 late-F to mid-M planet hosts,but the spectra were found to underpredict observedFUV line strengths by up to a factor of 33 (France et al.2016; Louden et al. 2017). For a complete summary of previous semiempirical chromo-sphere models for Main Sequence stars, see Linsky (2017).
The majority of spectral features observed in the stel-lar UV spectrum form at temperatures ranging from 10 – 10 K (Sim & Jordan 2005). While FUV and NUV ob-servations lack major contribution from the corona (withnotable exception of the Fe
XII line at 1242 ˚A that formsnear 1.4 × K), they provide crucial informationabout the thermal structure in the chromosphere andtransition region, where a large fraction of EUV emis-sion is generated. Recently, Peacock et al. (2019) usedthe PHOENIX atmosphere code to predict the EUVthrough near-IR spectrum of the M8 star TRAPPIST-1, calibrating the models with two UV datasets. Themodels have temperature-pressure profiles qualitativelysimilar to the Sun, but without a corona. The modelsreproduce the UV observations well and predict EUVfluxes consistent with estimates calculated using em-pirical scaling relationships. However, as a result ofnot including the coronal flux contribution, they are es-timated to underpredict the spectrum at wavelengths <
300 ˚A. Fontenla et al. (2016) adapted their solar model(Fontenla et al. 2007, 2009, 2011, 2014, 2015) to producea full upper atmosphere model for the M1 star GJ 832that covers X-ray through optical wavelengths and pro-vides the first spectrally resolved EUV prediction forthis star.In this paper, we present 1D nonlocal thermodynamicequilibrium (non-LTE) synthetic spectra (EUV – IR,100 ˚A – 5.5 µ m) of three early-M planet host stars(GJ 832, GJ 176, GJ 436) that replicate both HubbleSpace Telescope ( HST ) and
Galaxy Evolution Explorer ( GALEX ) observations of each target. We show thatconstructing models with a simple temperature struc-ture can reproduce the UV continuum and many emis-sion features in high resolution
HST spectra. Thesemodels also predict the unobservable EUV spectrum, asthey include prescriptions for the stellar upper atmo-sphere, including the chromosphere and transition re-gion, where EUV, FUV, and NUV fluxes originate.In Section 2, we describe the construction and spec-ifications in our atmospheric models. In Section 3, wediscuss the properties and pre-existing observations ofour target stars that we use to guide our models. Weanalyze the computed spectra and compare them to op-tical and UV observations in Section 4. The syntheticEUV spectra are described in Section 5. In Section 6,we compare our models to flux estimates derived fromempirical scaling relationships and semiempirical mod-eling. Conclusions are given in Section 7. MODELWe build 1D stellar upper atmosphere models withprescriptions for the chromosphere and transition re-
Peacock et al.
Figure 1.
Temperature-column mass structures for mod-els of GJ 832 (blue), GJ 176 (orange), and GJ 436 (green)with prescriptions for the chromosphere and transition re-gion. The radiative-convective boundary in the photospherefor all three models occurs around 8 g cm − . Free parametersin the construction of the upper atmosphere are the columnmass at the base and top of the chromosphere: m Tmin andm TR , and the temperature gradient in the transition region: ∇ T TR (approximate locations labeled). The parameter val-ues for these models are given in Table 1. gion using the multi-level non-LTE code PHOENIX(Hauschildt 1993; Hauschildt & Baron 2006; Baron &Hauschildt 2007). PHOENIX has been used to study thediagnostic properties of strong chromospheric lines inthe optical spectrum of M stars (Hauschildt et al. 1996;Andretta et al. 1997; Short & Doyle 1998; Fuhrmeisteret al. 2005, 2006; Hintz et al. 2019) and to create EUV– IR spectra of the M8 star, TRAPPIST-1 (Peacock etal. 2019).For our models, we use a similar prescription to thatused in Peacock et al. (2019). We begin with a basephotosphere model in radiative-convective equilibriumthat corresponds to the effective temperature, surfacegravity, and mass of each star. We then superimposean increasing temperature distribution up to 8,000 K tosimulate a chromosphere and a steep temperature gradi-ent above 8,000 K to simulate the transition region (Fig-ure 1). At temperatures greater than ∼ Table 1.
Model ParametersModel ∇ T TR m TR m Tmin P out (K dyne − cm ) (g cm − ) (g cm − ) (dyne cm − )GJ 832 10 − . − . − . − . − . − plasma energy balance (Ayres 1979). In our models, weset the hottest layer at the top of the transition regionto be 200,000 K, since the majority of observed emis-sion lines in M star UV spectra form at or below thistemperature, e.g. Mg II ( ∼ . K), C II (10 . K),H I ( ∼ . K), Si IV (10 . K), He II ( ∼ . K),C IV (10 . K), N V (10 . K) (Sim & Jordan 2005).Heating mechanisms in M dwarf chromospheres arenot well understood. Acoustic heating, magnetic heat-ing, and back irradiation from coronal layers are allsuggested potential contributing processes (Narain &Ulmschneider 1996). For our models, we assume a lin-ear temperature rise with log(column mass) in boththe chromosphere and transition region. Previousworks have experimented with implementing nonlinearlog(column mass)-temperature profiles and found thatnonlinear temperature rises can be tailored to replicateindividual lines very well, but linear rises give the bestoverall continuum fit (Eriksson et al. 1983; Andrettaet al. 1997; Fuhrmeister et al. 2005). For example,Fuhrmeister et al. (2005) altered the structure of thelower chromosphere in order to better fit observationsof Na I D lines, but found that it resulted in worse fitmodels with significantly increased flux in the Balmerlines.In the construction of the upper atmosphere, we alterthree free parameters designating the depth at which theupper atmosphere is attached to the underlying photo-sphere and the thickness of both the chromosphere andtransition region (approximate locations labeled in Fig-ure 1). The specific parameters are the column mass atthe initial chromospheric temperature rise ( m T min ), thecolumn mass at the top of the chromosphere ( m T R ),and the temperature gradient in the transition region( ∇ T T R = | d T /d log P | ). We then use the prescriptionsselected for each model to calculate the outer pressure: P out = T max − T ch ∇ T T R + ( m T R ∗ g ) (1)where T max is the temperature at the top of the tran-sition region, set to 200,000 K, T ch is the temperature atthe base of the transition region, set to 8,000 K, and g is UV-IR Spectrum of GJ 832, GJ 176, GJ 436 Table 2.
Species computed in non-LTEElement Abundance Levels Total LinesI II III IV V VIH 12.0 30 · · · · · · · · · · · · · · · · · · · · · · · · · · ·
82C 8.43 230 85 79 36 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · the surface gravity of the star. For each star, we createa grid of 29 models varying m T min = 10 − – 10 − . gcm − , m T R = 10 − – 10 − g cm − , and ∇ T T R = 10 – 10 K dyne − cm .Different states of stellar activity are simulated by ad-justing where the chromospheric temperature rise is at-tached to the underlying photosphere model (Andretta& Giampapa 1995; Andretta et al. 1997). Higher activ-ity states, and therefore, higher UV continuum fluxes,are generated by shifting the temperature structure uni-formly inward, beginning the initial temperature rise atlarger column mass. Since many FUV emission featuresform at similar temperatures to those that are foundin the EUV spectrum (Kretzschmar et al. 2009), bothwavelength regimes are most sensitive to the same pa-rameters: ∇ T T R and m T R . A factor of 10 decrease in ∇ T T R or increase in m T R results in an order of magni-tude increase in the integrated flux density across EUVwavelengths and a factor of five increase in the inte-grated FUV flux density. Changes in m T min correspondto changes in the strength of the extended wings of Ly α and therefore the FUV pseudo-continuum, but have alarger effect on the NUV spectrum. Adjusting the depthof the chromosphere by shifting the position where thetemperature rise begins inwards by 10 g cm − increasesthe NUV flux density by a factor of three and the FUVflux density by up to a factor of two. Changes in m T min by itself have no effect on the computed EUV spectrum.2.1.
Microturbulent Velocity
Levels of microturbulent velocity ( v turb ) influence theintensity and wing shape of emission lines, particularlyaffecting hydrogen, sodium, and calcium lines (Jevre-movi´c et al. 2000). The turbulent surface of a stellarphotosphere induces disturbances in the overlying chro-mosphere that are propagated at the speed of sound.For our models, we set v turb to 2 km s − in the photo-sphere and 10 km s − at the top of the transition re-gion. We follow the same approach as Fuhrmeister et al.(2005) in setting the slope of v turb in the chromosphereand lower transition region to a fraction of the soundspeed in each layer, but not allowing this value to ex- Peacock et al. ceed 10 km s − . We select a value of 0.35 × v sound suchthat v turb smoothly transitions from 2 km s − in thephotosphere to the larger values in the chromosphere.2.2. Non-Local Thermodynamic Equilibrium RadiativeTransfer
In an M dwarf photosphere, temperatures are low anddensities are high, such that collisions dominate andLTE is an appropriate approximation for calculating thelevel populations of atoms and molecules. As temper-atures increase in the upper atmosphere and densitiesbecome very low, radiative rates exceed collisional ratesand radiative transfer is dominated by non-LTE effects.PHOENIX is equipped with current atomic level data(Dere et al. 1997; Kurucz 2014, 2017; Del Zanna et al.2015) suitable for these high temperatures and low den-sities and has the capacity to do multi-line non-LTEcalculations for many species. For our models, we con-sider a total of 15,355 levels and 233,871 emission lineswhen computing the set of 73 atoms and ions listed inTable 2 in full non-LTE radiative transfer using speciesand background opacities provided by the PHOENIXand CHIANTI v8 databases (Landi et al. 2006). Alsoincluded in our models are new bound-free molecularopacities described in Peacock et al. (2019) and millionsof optically thin atomic and molecular background linescalculated with assuming an LTE source function.2.3.
Partial Frequency Redistribution
Strong resonance lines are typically good indicators ofchromospheric activity. They are characterized as opti-cally thick lines with broad absorption wings that formin the photosphere and lower chromosphere with coresthat form in the upper chromosphere and transition re-gion. Since these lines dictate information regardingthe thermodynamic properties of the stellar upper at-mosphere and provide constraints on the Lyman contin-uum and EUV spectrum (Linsky et al. 2014; Shkolnik& Barman 2014), it is important to model these linesparticularly well.Complete frequency redistribution (CRD) accountsfor overlapping radiative transitions and is generally agood approximation to use when calculating the major-ity of line profiles. In strong resonance lines, however,coherent scattering of photons largely affects the shapeof the wings in the line profiles, requiring the inclusion ofpartial frequency redistribution (PRD) in the radiativetransfer calculations.As a part of Peacock et al. (2019), we added PRDcapabilities to PHOENIX and demonstrated the impor-tance of these calculations when computing the H I Ly α line in M stars. In this paper, we extend these cal-culations to additional strong resonance lines that are Figure 2.
Computed non-LTE profiles for GJ 832 assumingCRD (orange) versus PRD (blue) for Mg II k (top panel)and Ca II K (bottom panel) compared to high resolutionobserved spectra (black; top panel:
HST
STIS (France et al.2016), bottom: Keck/HIRES (Vogt 2011)). commonly used as chromospheric diagnostics: Mg II h & k and Ca II H & K. In Figure 2, we show the im-pact of including the PRD formalism when computingthe Mg II k and Ca II K line profiles in our model forGJ 832. When computed assuming CRD, the modelMg II k profile marginally overpredicts the wings andoverpredicts the strength of the observed line core bya factor of ∼
13. Observations of Mg II , however, arecontaminated by interstellar absorption, so direct com-parisons to the line core cannot be drawn. Estimatessuggest ∼
30% attenuation of the intrinsic Mg II linecore, affecting the line profiles from 2796.4 – 2796.6 ˚Aand 2803.6 – 2803.7 ˚A(France et al. 2013) as comparedto the nearly 100% interstellar absorption of the H I Ly α core (Youngblood et al. 2016). We find that the PRDcalculations decrease the flux in the Mg II line peaksand line core by nearly a factor of two, with marginaleffects on the strength of the wings.The CRD Ca II K profile slightly underpredicts theobserved profile, with the total line flux differing by afactor of 1.9. Computing Ca II in PRD increases thestrength of the wings and decreases the total line fluxby a factor of four. Since the PRD calculations worsenthe agreement to the observations for Ca II , we use theCRD formalism in computing this species in our models.The broad wings of Ly α extend far enough from theline center that using PRD to compute this line profiledrastically alters the FUV pseudocontinuum and influ- UV-IR Spectrum of GJ 832, GJ 176, GJ 436 II and Ca II in PRD versus CRDresults in negligible changes to the surrounding contin-uum, such that the special treatment of these lines doesnot have an effect on the choice of model that best re-produces the observations as a whole, and therefore doesnot effect the predicted EUV spectrum. In future work,we will explore a non-linear temperature rise in the chro-mosphere, in which the accuracy in modeling both Mg II and Ca II will play a more vital role in determining thestructure. TARGETSThere are few M stars that have observations in X-ray, UV, optical, and IR wavelengths. For this work,we modeled 3 M star planet hosts of different subtypesthat have UV spectroscopic observations and estimatesfor EUV fluxes calculated from empirical scaling rela-tionships with Ly α from the MUSCLES Treasury Sur-vey program (France et al. 2016; Youngblood et al. 2016;Loyd et al. 2016) as well as GALEX
UV photometric de-tections (Bianchi et al. 2011; Shkolnik & Barman 2014):
GJ 832 is an M1.5 V star that hosts two planets: a0.64 M
Jupiter planet at a semi-major axis of 3.56 au anda 5.4 M ⊕ super-Earth located in the canonical habitablezone (0.16 au) (Wittenmyer et al. 2014). Its age is uncer-tain, but a rotational period of 45.7 ± GJ 176 is a 3.62 Gyr (Sanz-Forcada et al. 2011)M2.5 V star that hosts an 8.3 M ⊕ planet orbiting at0.066 au (Butler et al. 2009; Forveille et al. 2009).Youngblood et al. (2016) calculated the column densityof H I in the interstellar medium along the line of sightto GJ 176 and found the value to be among the lowestcolumn densities measured in their sample of 11 M andK dwarfs. In the event of a new EUV telescope, thesmaller concentration of interstellar hydrogen in the di-rection of GJ 176 suggests that it would be a favorabletarget for follow-up EUV observations. GJ 436 is a 6 +4 − Gyr (Torres 2007) M3.5 V. Ly α transit observations of its Neptune-sized planet (23 M ⊕ ,0.287 au) discovered by Butler et al. 2004 show a 56%transit depth that is most likely caused by a large cloudof escaping hydrogen (Kulow et al. 2014; Ehrenreich etal. 2015). Since EUV radiation drives atmospheric es-cape, a synthetic stellar EUV spectrum is essential forunderstanding the star-planet interaction in this system. The effective temperature (T eff ) is a primary driverof spectral shape, especially affecting NUV and visiblewavelengths in M stars. There is significant variance inthe literature values of T eff for each target in our sam-ple. Effective temperatures for GJ 832 range from 3472K (Wittenmyer et al. 2014) – 3993 K (Gaia Collabora-tion et al. 2018), for GJ 176 range from 3416 K (Loydet al. 2016) – 3897 K (Gaia Collaboration et al. 2018),and for GJ 436 range from 3281 K (Loyd et al. 2016) –3660 K (Gaia Collaboration et al. 2018). We computedmodels with the range of literature values and calcu-lated synthetic visible and near-IR photometry over thesame wavelengths as the filter profiles for: HIP: BT,VT; Johnson: B, V, J, H, K; POSS-II: J, F, i; Gaia: G;2MASS: J, H, Ks, SDSS: g, r, i. We normalized thefluxes and compared the values to all available photo-metric detections (not including upper limits) returnedby the VizieR Photometry Viewer for each star withina 5” search radius. We used a χ test to identify thebest fit models to the photometry and to select our op-erational T eff for each star. The best fit models areshown in blue in Figure 3, along with the upper andlower end members. Our operational stellar parametersare listed in Table 3. COMPARISON OF MODELS TOOBSERVATIONSWe calibrate our models to replicate
HST
COS andSTIS observations taken as a part of the MUSCLESTreasury Survey (Version 2.1) France et al. (2016) andKeck High Resolution Echelle Spectrometer (HIRES)observations from Vogt (2011). We scale the high res-olution (∆ λ ∼ R (cid:63) /d and ac-count for radial velocity shifts, rotational broadening,and instrumental broadening before comparing to ob-servations.We determine the steepness of the temperature gra-dient in the transition region, ∇ T T R , by fitting obser-vations of emission lines with formation temperaturesgreater than 8,000 K (Si IV , He II , C IV , and N V ). Weuse the FUV and NUV psuedocontinuum and the wingsof Ly α , Mg II h & k , and Ca II H & K, which have forma-tion temperatures below 8,000 K, to determine m T min and m T R . Best fits were determined by eye and witha χ test using the mentioned diagnostic lines. As weare using a 1D simplified linear temperature structure tomodel a 3D object with spatially varying active regions,it is not expected that the models will reproduce all ob-served chromospheric lines well. A good match to theobserved UV continuum and many emission lines that http://vizier.u-strasbg.fr/vizier/sed/ Peacock et al.
Figure 3.
Flux-normalized PHOENIX synthetic spectra and synthetic photometry (circles) for the range of effective tempera-tures found in the literature (coldest: yellow, hottest: grey) compared to all available visible and near-IR photometric detectionsper star returned by the VizieR Photometry Viewer (red crosses). Best fit models are plotted in blue. Spectral resolution inthe spectra has been degraded for clarity.References for photometric detections –GJ832: 1,2,3,4,5,6,7,8,9,10,11; GJ176: 1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18; GJ436: 1,2,3,5,8,9,10,12,13,15,16,19,20References – (1) Cutri et al. 2003; (2) R¨oser et al. 2008; (3) Roeser et al. 2010; (4) Zacharias et al. 2012; (5) Neves et al. 2013;(6) Santos et al. 2013; (7) Bourg´es et al. 2014; (8) Gaidos et al. 2014; (9) Ward-Duong et al. 2015; (10) Altmann et al. 2017;(11) Schneider & Shkolnik 2018; (12) Soubiran et al. 2016; (13) Droege et al. 2006; (14) Huber et al. 2017; (15) Trifonov et al.2018; (16) Terrien et al. 2015; (17) Ofek 2008; (18) Ammons et al. 2006; (19) Lasker et al. 2008; (20) Triaud et al. 2014 cover a broad range of formation temperatures is indica-tive that the simplified upper atmospheric temperaturestructure and predicted spectrum are a good general ap-proximation for the star as a whole. The model param-eters that best replicate the
HST observations are givenin Table 1. 4.1.
Visible Spectrum
The emission strengths of Ca II H (3968.17 ˚A) & K(3933.66 ˚A) and H α (6562.8 ˚A) are commonly used in-dicators of chromospheric activity found in the visibleregion of a stellar spectrum. H α is a commonly useddiagnostic for solar-type stars since the nearby contin-uum emission is relatively weak and it typically hasbroad wings. However, for M type stars, H α can be acomplicated diagnostic of chromospheric activity since it progresses from presenting as an absorption featureto an emission feature with increasing activity (Gomesda Silva et al. 2011). The Ca II H & K doublet doesnot undergo the transition from absorption to emission,making it a more favorable diagnostic feature detectablefrom the ground. For example, while the H α absorptionspectra for the stars in this study imply that they areoptically inactive (Gizis et al. 2002), the strength of theCa II H & K emission cores and observations of UVflares indicate that they do display chromospheric ac-tivity (Vogt 2011; Shkolnik & Barman 2014; France etal. 2016; Loyd et al. 2018b).In M dwarfs, resonance lines of ions, including theCa II doublet, have very weak wings because the photo-sphere and lower chromosphere are mostly neutral. Theline cores of Ca II form in the upper chromosphere/lower UV-IR Spectrum of GJ 832, GJ 176, GJ 436 Table 3.
Stellar ParametersGJ 832 GJ 176 GJ 436Spectral Type . . M1.5 M2.5 M3.5 Age (Gyr) . . . . . . > +4 − T eff (K) . . . . . . . 3657 ± ± log(g) (cm s − ) . 4.7 ± ± M (cid:63) (M (cid:12) ) . . . . . . . 0.45 ± +0 . − .
062 3 R (cid:63) (R (cid:12) ) . . . . . . . . 0.499 ± ± ± [ F e/H ] . . . . . . . . . -0.17 ± -0.01 ± -0.03 ± v sin(i) (km s − ) · · · < +0 . − .
17 8 v rad (km s − ). . . 12.52 ± ± ± ± ± References —(1) Bailey et al. 2009; (2) Forveille et al. 2009; (3) von Braun et al. 2014; (4) Newton et al. 2016; (5) Sanz-Forcadaet al. 2011; (6) Torres 2007; (7) Loyd et al. 2016; (8) Lanotte et al. 2014; (9) Wittenmyer et al. 2014; (10) Santos et al. 2013;(11) von Braun et al. 2014; (12) Houdebine 2010; (13) Neves et al. 2014; (14) Gaia Collaboration et al. 2018
Figure 4.
Comparison of the PHOENIX spectra (blue, solid) to Ca II H (3968.17 ˚A) & K (3933.66 ˚A) Keck/HIRES observations(black, dashed) (Vogt 2011). Observations are converted to vacuum wavelengths and scaled to the stellar surface. The resolutionof the synthetic spectra has been reduced to that of the observations, ∆ λ = 0.05 ˚A. transition region between 5,000 and 20,000 K while theneighboring emission peaks form at cooler temperaturesdeeper in the atmosphere between 4,000 and 10,000 K.Since these lines yield information about the tempera-ture structure, before stellar UV spectral observationswere available, early semiempirical M dwarf chromo-sphere models were based on fitting ground-based Ca II K observations (Giampapa et al. 1982). More recently,Youngblood et al. (2017) found that the equivalentwidth of the Ca II K line could be used to estimate thestellar surface flux in several ultraviolet emission lines,including Ly α , and developed a scaling relationship toestimate EUV fluxes using time-averaged high resolu-tion Ca II observations.We compare our model spectra to Keck/HIRES ob-servations of Ca II H & K from Vogt (2011) in Figure4. Deviations of the synthetic spectra from the obser-vations in the continuum surrounding the Ca II doublet are related to the model parameter at the base of thechromosphere, m T min . Adjusting m T min to better fitthis region of the spectrum worsens the agreement of themodel to the NUV continuum and does not influence theEUV spectrum. For all three models, the far wings ofthe lines replicate the observations well, but the modelsunderpredict the observed emission cores by 45 – 70%.We attribute uncertainties in our estimated Ca II linesto the lack of ambipolar diffusion in the model. Am-bipolar diffusion is associated with coronal back-heatingand is important for determining the hydrogen ioniza-tion near where the cores of Ca II H & K are forming ( ∼ Peacock et al.
Figure 5.
Near-UV PHOENIX spectra (blue) at the spec-tral resolution of the
HST observations (black). Prominentemission features are labeled in the top panel. The
HST observations for GJ 176 and GJ 436 were taken with theG230L grating on STIS, while the spectrum for GJ 832 iscomprised of observations taken with the multiple gratingson both STIS and COS, including the high resolution gratingused to measure Mg II . Near Ultraviolet Spectrum
At low resolution (∆ λ ∼ II h (2802.7 ˚A) & k (2795.53 ˚A)doublet and a forest of Fe II emission lines spanning 2300– 2650 ˚A. The pseudo-continuum is shaped by molecu-lar opacity sources, most importantly: NH, CH, OH,and H . In Figure 5, we compare our synthetic spectrato HST observations taken as part of the MUSCLESTreasury survey. We find good general agreement inthe pseudo-continuum for all three stars. From 2375 –2630 ˚A, the pseudo-continuum is elevated by excess fluxfrom OH and H causing the models to overpredict theforest of Fe II lines. The models also overpredict a strongV II line at 2721 ˚A.The Mg II h & k lines are diagnostics of the chromo-spheric thermal structure located in the NUV region.The line cores form at temperatures around 10,000 K, the emission peaks at ∼ II H & K doublet in that both display weak wings,but the Mg II lines typically have stronger emission coresin M dwarfs. This is due to a higher abundance ofMg than Ca, a larger ionization potential of Mg+ thanCa+, and a weaker background photospheric spectrumat shorter wavelengths (Linsky 2017).Observations of Mg II are contaminated by interstel-lar absorption, estimated to attenuate 30 – 35% of theintrinsic line flux (France et al. 2013). Additional ab-sorption of Mg II lines has been observed in host starsduring the transit of exoplanets with escaping atmo-spheres, such as WASP-12b, attributed to metals in theexospheric cloud (Fossati et al. 2010). It is thereforepossible that the intrinsic Mg II emission profiles of GJ436 are further attenuated by the escaping atmosphereof its warm Neptune mass planet. Due to the low res-olution modes used on the G230L grating on COS andSTIS, corrections were not done for Mg II for any ofthe HST observations (France et al. 2016). Calculatedline fluxes for Mg II h & k for the models and obser-vations are given in Table 4. The spectral resolution ofthe models was reduced to that of the observations be-fore calculating the line fluxes. We have also increasedthe observed line fluxes by 30% in order to make a moreaccurate comparison to the intrinsic stellar values, andfind that our model predictions are within a factor of1.5 of the corrected Mg II fluxes for GJ 176 and GJ 436,and within a factor of ∼ Far Ultraviolet Spectrum
In Figure 6, we compare our synthetic FUV spectrato the MUSCLES composite
HST observations. We findgood general agreement with the FUV continuum, whichis shaped by recombination edges of Si, Mg, and Fe.The FUV spectrum is populated with emission linesthat form in both the chromosphere and transition re-gion, including H I , N V , C I , II & IV , O II & IV ,and Si IV (labeled in the top panel of Figure 6). In-dividual emission line profiles for H I Ly α , N V , C IV ,and Al II as compared to the observations are shown inFigure 7. Calculated emission line fluxes from both themodels and observations are given in Table 4. The mod-els reproduce H I Ly α , Si III , O IV , the N V doublet,and the C IV line at 1551 ˚A within a factor of 2.5 ofthe observations. However, due to the simplified lineartemperature structure, not all chromospheric lines arefit well. The models underpredict Si IV , O II , and theC IV line at 1548 ˚A by an order of magnitude. This im-plies that some EUV emission lines that form at similartemperatures in the lower transition region may also be UV-IR Spectrum of GJ 832, GJ 176, GJ 436 Table 4.
Line fluxes (erg cm − s − ) of select chromosphere and transition regionlinesSpecies λ GJ 832 GJ 176 GJ 436(˚A) Model
HST
Model
HST
Model
HST Si III I (Ly α ) a V V II b II b IV IV IV IV IV II II II k b II h b Note —Computed and observed emission line fluxes at the stellar surface and continuum normalized.
HST fluxes are calculatedfrom the MUSCLES v2.1 panchromatic spectral energy distributions that maintain the native instrument resolutions and havebeen scaled by d /R star . a Observed Ly α fluxes are calculated using the reconstructed profile from Youngblood et al. (2016). b Observed emission line fluxes have been corrected for an estimated 30% absorption by interstellar Mg II and C II . underpredicted. The agreement between the syntheticspectra and each of the aforementioned lines can be im-proved by decreasing the temperature gradient in thetransition region and reducing the thickness of the chro-mosphere. Making these adjustments, however, worsensthe agreement with other FUV emission lines and ele-vates the EUV – FUV pseudocontinuum by up to anorder of magnitude. Since our final spectra are a goodmatch to the observed UV continuum and many emis-sion lines that form at temperatures found across theentire upper atmosphere, we conclude that the simpli-fied temperature structures and predicted EUV spectraare good general approximations for each star.The strongest emission line in the FUV spectrum isthe Ly α resonance line. For most M dwarfs, it con-tributes up to 75% of the total flux in the FUV region(France et al. 2013). Unfortunately, observations of theLy α line for any star other than the Sun are heavilycontaminated by both geocoronal airglow and interstel-lar hydrogen absorbing nearly all of the line core. Inorder to determine the intrinsic stellar line profile, ob-servations must be reconstructed using interstellar pa-rameters along the line of sight to the star (Wood et al. 2005; France et al. 2013; Youngblood et al. 2016). Inthe top panels of Figure 7, we show both the raw HST observations and the Youngblood et al. (2016) recon-structions. Our models closely reproduce the wings ofLy α in the raw HST observation, but present with a selfreversed core that results in calculated Ly α line fluxes1.6 – 2.5 × less than the reconstructed profiles. Whilethe absorption in the raw HST observations is due tocontamination, the central reversal in our models is adirect result of non-LTE effects.In the ultraviolet spectrum, non-LTE effects becomeimportant as the source function deviates from thePlanck function in both the chromosphere and transitionregion. When allowing for departures from LTE, opti-cally thick lines that form at various depths in a stellaratmosphere (e.g. Ly α , Mg II , Ca II ) can present in emis-sion with a self-reversed core. Observations of the Sunin both active and quiescent states show self-reversalsin Ly α , Mg II h & k , and Ca II H & K lines (Linsky& Avrett 1970; Fontenla et al. 1988; Staath & Lemaire1995; Tian et al. 2009). In M dwarf stars, inverted coresare observed in high resolution measurements of Mg II Peacock et al.
Figure 6.
Comparison of the far-UV PHOENIX spectra (blue) to the MUSCLES composite
HST spectra (black). Both spectraare convolved to a resolution of 1 ˚A. Prominent emission features are indicated in the top panel. h & k (France et al. 2013) and some Ca II H & K lines(Rauscher & Marcy 2006).While Mg II h & k form at slightly cooler temper-atures than Ly α , they have similar line profiles in theobserved solar spectrum (Donnelly et al. 1994; Lemaireet al. 1998). Due to their similarities in the Sun, obser-vations of the Mg II doublet have been used to estimatethe shape of the central portion of the Ly α profile forM stars after fitting the ISM absorption (Wood et al.2005). Low instrument resolution, however, can maskthe existence of an inverted core in Mg II lines. For ex-ample, in Wood et al. (2005), HST observations of Mg II h & k and the corresponding best fit Ly α profiles for fiveM stars do not include a central reversal, but when uti-lizing a high resolution grating, observations of GJ 832from France et al. 2013 do show a central reversal inMg II (Figure 2).Contamination of the stellar Ly α emission line fromthe geocoronal feature can be circumvented if observinga high radial velocity target. For example, the M1 star,Kapteyn’s Star, has a radial velocity (V = +245 km s − )such that Ly α is Doppler shifted 0.99 ˚A away from thegeocoronal contribution. Guinan et al. (2016) obtainedhigh resolution HST observations of the Ly α region ofKapteyn’s Star and determined the stellar emission pro- file presented with a faint self-reversal in the line core.Analysis of the same spectrum by Youngblood et al.(2016), however, fit the line with a Gaussian-shaped pro-file with no self-reversal. Additional high resolution ob-servations of Ly α from high radial velocity M stars (e.g.A. Schneider et al., in prep.) as well as high resolutionMg II observations would help determine the actual Ly α line profile and intrinsic flux from M stars.Modeling efforts by Fontenla et al. (2016) also predictinverted cores in both the Mg II doublet and Ly α forGJ 832. The smaller depths of the central reversal inthe Kapteyn’s Star observation and the Fontenla et al.(2016) model lead us to believe our models could be un-derpredicting the flux in the core of Ly α by up to 40%if the intrinsic profile does not contain any central re-versal. We attribute uncertainty in the model Ly α lineprofiles to the parameterization in the transition regionand the lack of ambipolar diffusion and a corona in ourmodel. Peacock et al. (2019) found that this reversal isvery sensitive to ∇ T T R , with less steep temperature gra-dients resulting in shallower reversals in the Ly α profile.As mentioned in Section 4.1, the base of the transitionregion is determined by where hydrogen becomes fullyionized. Adding a corona above the transition regionleads to back irradiation from the 10 K plasma, pho-
UV-IR Spectrum of GJ 832, GJ 176, GJ 436 Figure 7.
Select FUV emission line profiles from the PHOENIX spectra (blue) compared to
HST spectra (black) continuumnormalized and scaled to the surface of the star. In the top panels, the raw H I Ly α observation (black) is contaminated byinterstellar absorption. The reconstructed profiles from Youngblood et al. 2016 are plotted in red. The central reversal inthe model Ly α profiles are a result of non-LTE effects. The suppression of the C IV ( ∼ ∇ T TR , m TR ), as the C IV lines form at slightly different temperatures found near thetop of the chromosphere and base of the transition region. toionizing the lower layers through ambipolar diffusionand affecting the collisional rates where the core is form-ing. 4.4. Near UV and Far UV Photometry
Existing
GALEX
FUV (1340–1811 ˚A) and NUV(1687–3008 ˚A) detections of the stars measured usingthe elliptical Kron aperture are presented in Table 5.We compute synthetic photometry for the models overthe same wavelength ranges as the
GALEX
FUV andNUV filter profiles and find that the calculated valuesmatch the FUV detections, but exceed the NUV due tothe overestimated Fe II lines from 2375 – 2630 ˚A. Wealso note that M stars are UV active and the GALEX and
HST observations were not taken contemporane-ously. It is therefore not necessarily expected that themodel that best reproduces the
HST data also matchthe
GALEX photometry within uncertainty. Model F
F UV and F
NUV for GJ 832 are 2.06 × − erg cm − s − ˚A and 12.41 × − erg cm − s − ˚A,respectively, falling within the uncertainty of the FUVdetection but overpredicting the F NUV by a factor of 1.3.For GJ 176, F
F UV = 1.81 × − erg cm − s − ˚A andF NUV = 11.09 × − erg cm − s − ˚A, matching themeasured F F UV and overpredicting the F
NUV detectionby a factor of 1.7. Our model for GJ 436 overpredictsthe singular F
NUV detection by a factor of 2.6, F
NUV = 3.05 × − erg cm − s − ˚A (Table 5). We plot thisinformation in Figure 8.The three prescribed parameters designating the tem-perature structure in the chromosphere and transitionregion for the three stars are nearly the same (Table 1).As a result of this degeneracy, the UV continuum slopein the models are very similar: F NUV,G /F F UV,G = 5 –6. Calculating this ratio with the
GALEX detections4
Peacock et al.
Table 5.
Band integrated UV flux densities in(10 − erg cm − s − ˚A − ) GALEX Detections Models F FUV F NUV F EUV F FUV F NUV
GJ 832 2.43 ± ± ± ± · · · ± Note — GALEX
FUV and NUV photometric detections mea-sured using the Kron aperture. Synthetic photometry from thePHOENIX models is calculated over λ EUV = 100–1170 ˚A andthe same wavelengths as the
GALEX
FUV ( λ FUV = 1340–1811˚A) and NUV ( λ NUV = 1687–3008 ˚A) filter profiles. for GJ 832 and GJ 176 both yield a ratio of ∼
4, sup-porting the plausibility that the upper atmospheres forthese stars are likely analogous. EXTREME ULTRAVIOLET SPECTRUMMany emission features in the EUV (100 – 1170 ˚A)spectrum form in the upper chromosphere and transi-tion region (e.g. He I (584 ˚A, 10 . K) O V (629.7 ˚A,10 . K), and H I Ly β (1025.7 ˚A, 10 . K) (Sim & Jordan2005)), with highly ionized lines forming in the corona(e.g. Fe IX (171 ˚A, 10 K) (Del Zanna et al. 2014)).Continuum emission forms in the chromosphere and in-cludes contributions from the H I Lyman, He I and He II continua.Our synthetic EUV spectra are presented in full reso-lution (∆ λ < I (912 ˚A), He I (504 ˚A), N II (418 ˚A),K II (392 ˚A), O II (353 ˚A), He II (228 ˚A). In additionto the many non-LTE emission features, also prominentare narrow, but very bright emission features for speciesnot included in the non-LTE set: Fe VII (246 ˚A), Ne IV (402 ˚A), Ca V (558 ˚A) and O VI (1031, 1038 ˚A). Thestrength of the lines computed in the LTE, particularlythose near 400 ˚A and 550 ˚A and the O VI lines near1030 ˚A are likely overpredicted by up to a factor of ten.On account of these lines, we suggest that the fluxes inthe 400 – 600 ˚A and 1000 – 1050 ˚A regions be taken asupper limits.The current models do not include a corona, andtherefore underpredict the flux from lines that form attemperatures greater than 2 × K. While the contin-uum and many EUV emission lines found between 200– 1170 ˚A form below this temperature, the 100 – 200˚A wavelength range in the
EUVE spectrum of the M2flare star, AU Mic, is filled with Fe
XIX – XXIII and Cr
Figure 8.
PHOENIX FUV–NUV spectra (blue) comparedto
GALEX photometry (red, crosses), with calculated syn-thetic photometry over the same wavelengths as the
GALEX filter profiles plotted as blue circles. These wavelength rangesare indicated in the bottom panel. Values for the
GALEX detections are listed in Table 5.XVIII – XXI lines which form at coronal temperatures(Monsignori Fossi et al. 1996).As a test to quantify the amount of EUV flux our syn-thetic spectra could be underestimating, we comparedour models to versions with example coronal spectraadded to them. We computed coronal spectra of AUMic (high activity) and the quiet Sun (low activity)with CHIANTI version 9.0 (Dere et al. 2019), using theDifferential Emission Measures (DEMs) of both objectsfrom the CHIANTI database (Del Zanna et al. 2002).We truncated the temperature minimums at 2 × K so that there was no duplication of the PHOENIXmodel structures. We scaled the computed AU Micspectrum and the quiet Sun spectrum to GJ 832, GJ436, and GJ 176, and added the CHIANTI spectra toeach PHOENIX spectrum. AU Mic is an active youngM star (12 Myr) with elevated levels of FUV and NUVemission (Robinson et al. 2001), and likely emits moreEUV flux than GJ 832, GJ 436, and GJ 176. The addi-tion of a scaled AU Mic coronal spectrum to our models
UV-IR Spectrum of GJ 832, GJ 176, GJ 436 Figure 9.
Full resolution EUV synthetic spectra and corresponding average flux densities in 100 ˚A wavelength bands (blue).Estimated EUV flux densities in 100 ˚A wavelength bands calculated using F EUV /F Lyα scaling relationships from Linsky et al.(2014) in the MUSCLES SEDs are overplotted in black. F
EUV estimates from France et al. (2018) are overplotted in orange. increases the EUV flux in the 100 – 200 ˚A region bya factor of 60, but only slightly impacts on the rest ofthe EUV spectrum, increasing the integrated flux over100 ˚A wavelength bands by factors of 1 – 5. Adding thescaled coronal spectrum of the quiet Sun to our modelschanges the EUV flux in each wavelength band by lessthan a factor of two, except in the 100 – 200 ˚A band,which increases by a factor of five. Integrating over 100– 1170 ˚A, the coronal flux contribution from either DEMincreases the overall EUV flux by 4 – 45%. Without theflux contribution from coronal lines, our models under-predict the EUV spectrum at <
200 ˚A by less than twoorders of magnitude and by less than a factor of five atwavelengths >
200 ˚A. In a future paper, we will incor-porate both a corona and the associated ambipolar dif-fusion to our models, exploring temperature structurestailored for the field age M stars. DISCUSSIONSince most of the EUV spectrum is unobservable dueto interstellar contamination, there are no observations of the stars in this study to directly compare our syn-thetic spectra against. Here, we compare our modelsto existing EUV estimates for the target stars calcu-lated with empirical scaling relationships or semiempir-ical stellar models and discuss the uncertainties associ-ated with each method:6.1.
Comparison of PHOENIX EUV Spectra to EUVEmpirical Scaling Relationships
In the MUSCLES spectral energy distributions(SEDs), Youngblood et al. (2016) calculated the EUVspectrum for each star using Ly α reconstructions inan F EUV /F Lyα scaling relationship from Linsky et al.(2014). This method predicts the EUV flux from 100 –1070 ˚A in 100 ˚A wavelength bands and is derived froma combination of observations and models. The scal-ings for wavelengths <
400 ˚A are calculated from
EUVE observations of M stars, while those from 912 – 1170˚A are determined from
FUSE observations of K5 – M5stars. The relationships for wavelengths between 400– 912 ˚A are computed from the Fontenla (2013) solar6
Peacock et al. models and may not be appropriate for M stars. Tocompute the EUV flux using this scaling relationship,observations of the Ly α line must be reconstructed, con-tributing additional uncertainty to the predicted values.The F EUV /F Lyα estimated SEDs are plotted in blackin Figure 9 and have an estimated accuracy of ∼ EUVE and
HST spectraof 104 F–M stars to develop a scaling relationship forF(90 – 360 ˚A) based on N V or Si IV observations. Whilethe FUV emission lines used in this relationship do notrely on reconstructions, uncertainties in correcting forthe ISM absorption in the EUVE spectra and difficultiesin measuring the continuum flux at these wavelengthsresult in uncertainties in the predicted EUV flux. TheEUV fluxes for the target stars calculated with this scal-ing relationship are plotted in orange in Figure 9 and areestimated to be accurate within a factor of two. Com-paring the France et al. (2018) scaling to the modelsacross the full 90 – 360 ˚A range, the fluxes agree withinfactors of 0.95 – 2.2.We also compare our model for GJ 436 to an EUVflux calculated in an F
EUV /F X scaling relationship de-rived in Chadney et al. (2015). This scaling is derivedfrom averaged solar EUV and X-ray observations takendaily over an 11 year period and estimates an EUVflux for 124 – 912 ˚A. Ehrenreich et al. (2015) calcu-lated F EUV = 2.34 × − erg cm − s − for GJ 436using X-ray observations of the star. The Linsky et al.(2014) Ly α scaling relationship is also derived from solarEUV observations, and yields a similar F(124 – 912 ˚A)= 2.1 × − erg cm − s − (Youngblood et al. 2016).Calculating the flux across the same wavelengths for oursynthetic spectrum for GJ 436 yields a twice larger valueof F EUV = 4.34 × − erg cm − s − .Empirical scaling relationships allow for general esti-mates of the unobservable EUV flux using observationsfrom accessible wavelengths, but are derived using ei-ther observations of the Sun or from a wide range ofspectral types. They are hindered by uncertainties inmeasuring the ISM absorption as well as noncontem-poraneous observations at wavelengths known to dis-play significant variability. They are further limited inboth wavelength resolution and versatility. Conversely,semiempirical stellar models can predict realistic EUVspectra at the high resolution needed for detailed stud-ies of the photochemistry and escape in exoplanet atmo- spheres and have the versatility to be used for a rangeof spectral type and activity state.6.2. Comparison of PHOENIX and Solar-StellarRadiation Physical Modeling tools GJ 832 Models
Fontenla et al. (2016) adapted their 1D non-LTEsemiempirical solar atmosphere model (SRPM) (Fontenlaet al. 2015) that reproduces observations of the Sun, in-cluding UV spectra, to compute the stellar spectrumof GJ 832 using their Solar-Stellar Radiation PhysicalModeling (SSRPM) tools. Similar to PHOENIX, theirmodels are comprised of a modified thermal structure inthe upper atmosphere added to an initial photosphericmodel with similar luminosity and spectral type as GJ832. The temperature-pressure profile is based on theirSRPM model and is divided into a chromosphere andlower transition region computed in a plane-parallel ap-proximation and an upper transition region and coronalmodel computed in a spherically-symmetric approxi-mation. The coronal SSRPM model extends to hottertemperatures than our PHOENIX model (0.2 MK), totheir maximum coronal temperature peaking at 2.7 MK.In both the PHOENIX and SSPRM models, solar el-emental abundances are assumed, and the calculationsinclude several species in full non-LTE radiative trans-fer in addition to millions of effectively thin backgroundatomic and molecular lines. In our PHOENIX model, weconsider 73 atoms and ions in full non-LTE, comparedto 55 species (including H – and H ) in the Fontenla etal. (2016) SSRPM model.We compare the thermal structure of our GJ 832model to the lower transition region, chromosphere andphotosphere profile for the SSRPM GJ 832 model inFigure 10. The GJ 832 models are both qualitativelyand quantitatively very similar in the photosphere, butthe chromospheric structure and onset of the thermallyunstable transition region differ. The thermal structurein the SSRPM model has a steep temperature rise in thelower chromosphere near P gas ≈
15 dynes cm − followedby a near-constant temperature plateau in the upperchromosphere similar to their solar model. The temper-ature plateau results from the balance of radiative losseswith non-radiative heating, and is where singly ionizedmetals are the dominant stages of ionization (Linsky2017). Our model employs a linear temperature risein log(column mass) for all chromospheric layers, whichcorresponds to a linear rise in log(P gas ) for this model,and similarly begins near P gas ≈
15 dyne cm − .As described in Section 4, the Mg II doublet is an im-portant diagnostic for the thermal profile in the chromo-sphere. We compare our PHOENIX model Mg II h & k profiles to the SSRPM model profiles, and the high res- UV-IR Spectrum of GJ 832, GJ 176, GJ 436 Figure 10.
Temperature vs. gas pressure distributions inthe lower transition region, chromosphere, and photospherefor the PHOENIX (blue) and the Fontenla et al. (2016) SS-RPM (red) GJ 832 models. The upper transition regionin the PHOENIX model extends to 2 × K. The finalSSRPM GJ 832 model structure is coadded with a coronaltemperature distribution that peaks around 2.7 × K. Figure 11. Mg II h & k profiles from the PHOENIX (blue)and SSRPM (red) models of GJ 832 compared to the highresolution STIS E230H observation (black). The observa-tions have not been corrected for interstellar absorption. olution STIS E230H observations from the MUSCLESSED in Figure 11. Both models display central reversalsdue to non-LTE effects. Since the observed profiles havenot been corrected for interstellar absorption a directcomparison to the core of the lines cannot be confidentlymade. The PHOENIX model computed in PRD moreclosely reproduces the observed line width than the SS-RPM model. The wings of Mg II begin forming around3,000 K, indicating that the lower chromosphere mayhave a shallower slope than predicted in the SSRPMmodel.Above the chromosphere, both models simulate atransition region with a steep temperature gradient gov-erned by matching emission lines in the observed FUV spectrum. In our model, we set the temperature at thebase of the transition region to 8,000 K, based on whenthe dominant cooling agent, neutral hydrogen, becomesfully ionized. In the SSRPM model, the transition re-gion begins at 5,000 K. The likely reason for this dis-crepancy is the inclusion of a corona and ambipolar dif-fusion in the SSRPM tools, which are not yet includedin PHOENIX. Using their solar model, Fontenla et al.(1990) analyzed the energy balance of radiative losseswith the downward flow of conductive heat and hydro-gen ionization energy due to ambipolar diffusion fromthe corona. The authors found that the radiative losseswere mainly due to hydrogen, and that ambipolar dif-fusion is greatly important in determining the hydrogenionization in the lower transition region.Figure 12 shows the PHOENIX and SSRPM syntheticEUV – NUV spectra compared to the MUSCLES SEDfor GJ 832. We find good general agreement betweenall spectra long-ward of 200 ˚A. The SSRPM EUV spec-trum from 100 – 912 ˚A is comprised of 36.4% emis-sion from the chromosphere and lower transition regionmodel, and 63.3% emission from the upper transitionregion and corona model. As compared to the SSRPMmodel, we estimate that the lack of coronal flux in ourPHOENIX model may contribute up to an 80% under-prediction in only the 100 – 200 ˚A range. While themaximum temperature in our model does not extend tothe same ∼ K coronal temperatures, we find that theEUV spectrum from 200 – 1170 ˚A compares well to theSSRPM model, with F( λ × − ergcm − s − for our model compared to F( λ × − erg cm − s − for that from Fontenla et al.(2016).Integrating over 100 – 912 ˚A, we find close agreementbetween our computed EUV luminosity: logL EUV =27.31 erg s − , with the SSRPM model: logL EUV = 27.26erg s − and two other methods described in Fontenlaet al. (2016). Sanz-Forcada et al. (2011) calculated apredicted EUV luminosity for GJ 832 using ROSAT
X-ray observations. These observations give an L X XMM-Newton observations, indicat-ing increased activity during the
ROSAT measurement.Fontenla et al. (2016) scaled the predicted luminosityfrom Sanz-Forcada et al. (2011) by this factor of 3.3 toyield logL
EUV = 27.38 erg s − . Finally, the calculatedEUV luminosity from the F EUV /F Lyα derived spectrumin the MUSCLES SED is logL
EUV = 27.39 erg s − . Thesimilarities of the predicted EUV luminosities for thisstar using a variety of methods and observations givesus confidence that all four techniques can be used to es-timate the broadband EUV flux, however, the semiem-8 Peacock et al.
Figure 12.
Comparison of EUV–NUV spectra for GJ 832. The PHOENIX model spectrum (blue) and Fontenla et al. (2016)SSRPM model spectrum (red) have been degraded to the same 1 ˚A resolution as the MUSCLES SED (black). pirical models will provide the fine spectral resolutionnecessary for detailed studies of exoplanet atmospheres. CONCLUSIONSWe present high resolution EUV – IR synthetic spec-tra of three early M planet hosts: GJ 832, GJ 176, andGJ 436. These synthetic spectra reproduce UV and vis-ible spectral observations and UV, visible, and near-IRphotometric detections and predict EUV fluxes similarto the active Sun. The models do not include absorp-tion from the interstellar medium and can therefore bedirectly applied to investigations of photochemistry andstability of exoplanet atmospheres.The temperature profiles for the models consist of alinear structure in the chromosphere and transition re-gion. We find that nearly the same set of parameters( ∇ T T R = 10 K dyne − cm , m T R = 10 − . g cm − ,m T min (cid:39) − . g cm − ) best reproduces the UV obser-vations for all three stars, suggesting that early M typestars may have similar thermal structures in their upperatmospheres. These similarities, however, could also bea result of the simplified thermal structure averaging outsmall differences between the stars. Cool stars are highlyactive in their upper atmospheric layer with locally ac-tive regions of enhanced or depressed EUV flux. Forexample, spatially varying solar atmospheric features,for which there are high resolution spectra available,are modeled with several different thermal structures(Fontenla et al. 2011). Our simplified models providegeneral approximations of the EUV spectrum.We find that our simplified structure produces simi-lar continuum and line fluxes (for wavelengths greaterthan 200 ˚A) to the GJ 832 spectrum computed with theSSRPM semiempirical stellar atmosphere code, whichincludes a corona (Fontenla et al. 2016). The ther-mal structures in each model are significantly different in the upper-most atmospheric layers, with the onsetof the transition region beginning at a pressure nearly100 × lower and a temperature 3,000 K hotter in thePHOENIX model. To improve our general understand-ing of the upper atmospheric temperature-pressure pro-file and prediction of EUV fluxes, we will extend ourthermal structures to coronal temperatures and quantifythe importance of ambipolar diffusion in future work.Starting in the early 2020s after HST stops UV op-erations, there will be an observation gap for FUV andNUV spectroscopy, in addition to the current gap inEUV observations for any star other than the Sun. Dur-ing this time, there will be no instrument available tofollow up with UV observations of newly discoveredplanet host stars. The expansive database of archival
GALEX
UV photometry for hundreds of M stars rang-ing in age and spectral type can be used to guide upper-atmosphere models such as these. These models pre-dict realistic high resolution spectra across unobserv-able wavelengths and are important for furthering ourunderstanding of the effects of high energy radiation onplanets orbiting M stars.This work was supported by NASA Headquartersunder the NASA Earth and Space Science Fellow-ship Program-Grant NNX15AQ94H. E.S. acknowl-edges support from the NASA Habitable Worlds grantNNX16AB62G. We also gratefully acknowledge sup-port from NASA HST Grant HST-GO-14784.001-A.An allocation of computer time from the UA ResearchComputing High Performance Computing (HPC) atthe University of Arizona is gratefully acknowledged.A portion of the calculations presented here were per-formed at the Hochstleistungs Rechenzentrum Nord(HLRN), and at the National Energy Research Su-
UV-IR Spectrum of GJ 832, GJ 176, GJ 436
Gaia
Gaia
Gaia
Multilateral Agreement.
Software:
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UV-IR Spectrum of GJ 832, GJ 176, GJ 43621