The Far Ultraviolet M-dwarf Evolution Survey. I. The Rotational Evolution of High-Energy Emissions
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The Far Ultraviolet M-dwarf Evolution Survey. I. The Rotational Evolution of High-Energy Emissions ∗ J. S ebastian P ineda , † A llison Y oungblood , and K evin F rance University of Colorado Boulder, Laboratoy for Atmospheric and Space Physics, 3665 Discovery Drive, Boulder CO, 80303, USA Visiting astronomer, Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universitiesfor Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA
ABSTRACTM-dwarf stars are prime targets for exoplanet searches because of their close proximity and favorable proper-ties for both planet detection and characterization. However, the potential habitability and atmospheric charac-terization of these exoplanetary systems depends critically on the history of high-energy stellar radiation fromX-rays to NUV, which drive atmospheric mass loss and photochemistry in the planetary atmospheres. Withthe Far Ultraviolet M-dwarf Evolution Survey (FUMES) we have assessed the evolution of the FUV radiation,specifically 8 prominent emission lines, including Ly α , of M-dwarf stars with stellar rotation period and age.We demonstrate tight power-law correlations between the spectroscopic FUV features, and measure the intrinsicscatter of the quiescent FUV emissions. The luminosity evolution with rotation of these spectroscopic featuresis well described by a broken power-law, saturated for fast rotators, and decaying with increasing Rossby num-ber, with a typical power-law slope of −
2, although likely shallower for Ly α . Our regression fits enable FUVemission line luminosity estimates relative to bolometric from known rotation periods to within ∼ × more EUV energy relative to modern Earth. Moreover, the bulk of this UV exposure likely takesplace within the first Gyr of the stellar lifetime. INTRODUCTIONThe presence of self-sustained magnetic fields in low-massstars has important consequences for their upper atmosphericstructure and their high-energy radiative environments. Dueto non-thermal magnetic heating processes (see within Lin-sky 1980; Hall 2008), thought to be either wave dissipa-tion (e.g., Narain & Ulmschneider 1996) or Joule heatingfrom magnetic reconnection (e.g., Klimchuk 2006), theselow-mass stars exhibit significant temperature inversions intheir outer atmospheres. These portions of the stellar atmo-sphere, the chromosphere, transition region and corona, arelargely responsible for the entire high-energy spectrum fromthe near ultraviolet (NUV) to the X-rays in low-mass stars(see Linsky 2017, for recent review). While much e ff ort hasbeen devoted to studying stellar chromospheres / coronae, thenature of these structures, the underlying processes that gen- ∗ This research is based on observations made with the NASA / ESA Hub-ble Space Telescope obtained from the Space Telescope Science Institute,which is operated by the Association of Universities for Research in As-tronomy, Inc., under NASA contract NAS 5–26555. † [email protected] erate them, and their evolution remain poorly understood, es-pecially for M-dwarf stars.Addressing these questions has attained renewed urgencygiven the prevalence of terrestrial exoplanets orbiting M-dwarfs, with at least ∼
20% of these stars hosting an Earth-sized planet within their habitable zones (HZ; e.g., Dress-ing & Charbonneau 2015; Vanderburg et al. 2020). More-over, the best systems for detailed atmospheric characteri-zation with the
James Webb Space Telescope will be aroundnearby low-mass M-dwarfs (e.g., Morley et al. 2017). Under-standing the high-energy emissions of these systems is cru-cial because of the role they play in planetary atmosphericmass-loss and photochemistry (e.g., Scalo et al. 2007; Owen& Jackson 2012; Tian & Ida 2015; Luger & Barnes 2015).For example, for a Neptune / Earth-sized planet in the HZ ofan M-dwarf, strong radiation shortward of (cid:46)
911 Å (X-rays + extreme ultraviolet, XUV) can dictate the ultimate watercontent of the planet through atmospheric evaporation (Owen& Jackson 2012). Furthermore, the balance of NUV (1700-3200 Å) to FUV (912-1700 Å) emissions can determine equi-librium levels of abiotically produced O , complicating thesearch for biosignatures (see within Meadows et al. 2018). a r X i v : . [ a s t r o - ph . S R ] F e b P ineda et al .The completion of the MUSCLES Treasury Survey pro-vided the first comprehensive constraints of M-dwarf X-rayand UV luminosities from panchromatic observations of ex-oplanet hosting M-dwarfs (France et al. 2016; Youngbloodet al. 2016; Loyd et al. 2016; Youngblood et al. 2017). Theirwork further showed that the entire XUV and FUV broad-band fluxes could be estimated based on a couple of FUV orNUV spectroscopic features (France et al. 2016; Youngbloodet al. 2017). These measurements have since become impor-tant inputs into models of planetary atmospheres (e.g., Gaoet al. 2015; Ranjan et al. 2017). However, interpreting fu-ture atmospheric observations, potential biosignature detec-tions and the ability of such atmospheres to develop life, alsodepends on the evolution of the planetary atmosphere andhence the evolution of the incident radiation field. The MUS-CLES survey focused on older field objects with confirmedplanet detections, however, at early ages these M-dwarf hostslikely exhibited much stronger high-energy emissions (e.g.,Shkolnik & Barman 2014), capable of desiccating terrestrialworlds early in their lifetimes (Tian & Ida 2015).Understanding this evolution has been challenging becauseof the di ffi culty in determining stellar ages in the M-dwarfregime (Guinan et al. 2016). Although the ages of some ob-jects can be determined through membership in clusters oryoung moving groups (see within Zuckerman & Song 2004),the vast majority of M-dwarfs lack precise age determina-tions. Instead, rotation can be used as a proxy for stellar age,as in gyrochronology (e.g., Skumanich 1972; Barnes 2003;Meibom et al. 2015; van Saders et al. 2016), although un-derstanding the angular momentum evolution of M-dwarfsremains a topic of continued work (Barnes 2010; Reiners &Mohanty 2012; Garra ff o et al. 2015; Guinan et al. 2016; Gar-ra ff o et al. 2018). Nevertheless, there is a fundamental phys-ical interplay between stellar age, rotation and magnetic ac-tivity in low-mass stars (e.g., Skumanich 1972; Noyes et al.1984; Vidotto et al. 2014), a consequence of the feedback be-tween magnetic field generation in the internal dynamo andangular-momentum loss over time through coronally drivenstellar winds.Indeed, rotation-activity correlations have been used ex-tensively as probes of these magnetic processes and theirevolution in M-dwarfs, confirming the strong rotational de-pendence of the magnetic emissions, even across the fullyconvective boundary toward late M-dwarfs, and a saturationof the activity at fast rotation rates and young ages (e.g.,Pizzolato et al. 2003; Stelzer et al. 2013; Wright & Drake2016; Newton et al. 2017; Houdebine et al. 2017; Astudillo-Defru et al. 2017; Shulyak et al. 2017; Wright et al. 2018).These studies have focused predominantly on X-rays or opti-cal emission lines like H α to trace the magnetic activity. Thequiescent UV spectra of active M-dwarfs had been largelyunexplored except for a few well known flare stars (Rutten et al. 1989; Hawley & Pettersen 1991; Ayres et al. 2003;Hawley et al. 2003, 2007), limiting our ability to probe therotational evolution of these features. Understanding theseUV emissions is not only important for the incident radiationfield impacting planetary atmospheres, but the various emis-sion lines spanning a range of formation temperatures in theFUV spectra serve as unique probes throughout the di ff er-ent layers of the transition region ( T f ∼ . − . ), where thetemperature in the outer atmosphere is rising rapidly from thechromosphere to the corona (see within Linsky 2017).These developments motivate the Far Ultraviolet M-dwarfEvolution Survey (FUMES) with the Hubble Space Tele-scope ( HST ) to examine the rotational evolution of the FUVspectral features in early-to-mid M-dwarfs, provide impor-tant benchmarks for their high energy emission over time,and provide constraints to the chromospheric / coronal struc-ture of active low-mass stars. In this paper, the first of several,we focus on the quiescent emissions of our FUMES sampleas a function of rotation / age. In Section 2, we introduce theFUMES sample and assess their stellar properties. In Sec-tion 3, we discuss our HST observations and spectral mea-surements. In Section 4, we examine the rotation-activitycorrelations of UV emission in low-mass stars incorporatingliterature data. In Section 5, we discuss the implications ofour measurements for the temporal evolution of high-energyemissions around low-mass stars. Lastly, in Section 6 weprovide our conclusions and summarize our findings in Sec-tion 7. SAMPLE AND STELLAR PROPERTIESIn contrast to previous samples of M-dwarf stars selectedfor UV observations, either exoplanet hosts (e.g., MUS-CLES, France et al. 2013) or known flare stars (e.g., Haw-ley et al. 2003, 2007), the FUMES target list of 10 objectswas chosen to span a range of rotation periods from ∼ (cid:38)
70 d) objectsin this spectral type range, allowing us to focus on providingthe comparison with more active targets.UMES 3
Table 1.
IR Data Observing LogName UT Date Instrument Airmass A0 Calibrator Seeing Exp. Time (s) SNR a WeatherGJ 4334 2017-11-22 TSPEC 1.08 HD 240290 2” 20 160 Windy, ClearGJ 49 2017-11-22 TSPEC 1.15 HD 5031 2” 8 380 Windy, ClearHIP 112312 2017-11-05 ARCoIRIS 1.17 HD 213044 1.8” 8 280 ClearLP 247-13 2017-11-22 TSPEC 1.02 HD 21038 2” 20 275 Windy, ClearHIP 17695 2017-11-05 ARCoIRIS 1.24 HD 24003 1.8” 8 360 Partly CloudyHIP 23309 2017-11-06 ARCoIRIS 1.38 HD 32507 1.3” 10 500 ClearCD-35 2722 2017-11-06 ARCoIRIS 1.38 HD 42681 1.3” 8 390 Partly CloudyGJ 410 2019-04-30 TSPEC 1.04 HD101060 1.2” 20-25 170 CloudyLP 55-41 2017-11-22 TSPEC 1.28 HD 32781 2” 25 120 Windy, ClearG 249-11 2017-11-22 TSPEC 1.3 HD 32781 2” 25 180 Windy, Clear a This column reflects the typical signal-to-noise ratio in the H-band of each spectrum.
Before delving into the analysis of the UV emissions (Sec-tion 3), it is important to estimate the physical properties ofour targets. To these ends, we obtained infrared spectra ofall 10 stars, which enabled us to consistently determine spec-tral types, measure metallicity indicators and compare esti-mates for e ff ective temperature and bolometric luminosity(e.g., Newton et al. 2015; Terrien et al. 2015). These dataare discussed in Section 2.1. The IR data were most valu-able for estimating spectral types and ruling out the possibleinfluence of cool unknown companions in the photometry.Ultimately, we rely on the results of Pineda et al. ( submit-ted ) for the physical properties of the stars used in this work.Those methods are summarized below in Section 2.3.2.1. IR Data
To measure the NIR spectra of our sample targets weused the TripleSpec (TSPEC) instrument (Wilson et al. 2004)on the ARC 3.5 m telescope at the Apache Point Observa-tory and the similarly designed ARCoIRIS instrument onthe Blanco 4 m telescope at NOAO’s Cerro Tololo Inter-American Observatory. A summary of these observations canbe found in Table 1. Both instruments, with a 1.1” slit, pro-vide R ∼ µ mand the updated ARCoIRIS design covering 0.80-2.47 µ m.For all of our data we took the same observing approach,using an ABBA slit nod sequence with short exposures ( < Instrument info can be found here: ARCoIRIS mass to provide a reference for flux and telluric calibration(Vacca et al. 2003).We reduced the data using modified versions of
Spextool (Cushing et al. 2004), one for TSPEC and a separate one forARCoIRIS. We summarize the data reduction procedure asfollows. We first created the master flatfield for each ob-serving night by median combining several dome lamp ex-posures, and subtracting o ff the median thermal contributionfrom dome exposures taken with the lamps o ff . The thermalcontribution is most significant in the K -band. The wave-length calibration for each target was then determined fromthe median sky spectrum, created from each target’s scienceobservations. Initial sky subtraction was performed fromdi ff erencing AB nod pairs, from which we determined theobject trace in each order. We extracted the spectrum in win-dows centered along the trace, applying the normalized flat-field and wavelength calibration. When variable cloud coverwas evident, we also applied additional sky subtraction, re-moving a linear fit to the residual background. The spectrafrom individual frames were averaged together to increasethe signal-to-noise ratio and then we used the similarly ex-tracted A0 calibrator spectra to correct for telluric absorptionand provide a flux calibration using xtellcorr (Vacca et al.2003). We then merged the di ff erent echelle orders, aver-aging the spectra in overlapping wavelength regions to cre-ate the final spectrum of each target. The IR spectra of theFUMES sample is shown in Figure 1.2.2. Spectral Types For TSPEC see TriplespecTool and for the ARCoIRIS version, developedby Dr. Allers, see TS4 Reduction. Given an AB nod pair the sky contribution can be estimated as S = . A + B ) −| ( A − B ) | ]. For short exposures, one needs to accumulate several framesto produce su ffi cient signal in sky emission. P ineda et al . . . . . . . . . Wavelength ( µ m) − − − N o r m a li z e d λ F λ +O ff s e t HIP23309GJ410CD35-2722GJ49LP247-13HIP17695LP55-41G249-11HIP112312GJ4334
Figure 1.
The NIR spectra, shown here, allow us to provide spec-tral types for our sample in the NIR and assess physical propertiesusing spectroscopic calibrations (see Section 2). The spectra havebeen normalized in the H -band at the median flux between 1.55and 1.75 µ m. Regions of heavy atmospheric absorption have beenremoved, with gray shaded areas denoting wavelengths still influ-enced by some telluric water bands. We determine the NIR spectral type classifications for theFUMES sample using the composite spectral standards com-piled from multiple stars by Newton et al. (2014). TheseNIR spectra, taken with the NASA Infrared Telescope Fa-cility (IRTF) / SpeX, are classified on the KHM system origi-nally defined by Kirkpatrick et al. (1991, 1995, 1999) at redoptical wavelengths. We first computed the H O-K2 indexdefined by Rojas-Ayala et al. (2012) as a K -band feature sen-sitive to spectral type, and used the calibration from Newtonet al. (2014) (their Equation 2) to convert this measurementto an initial type estimate. We then used this classificationto select a range of nearby spectral standards, spanning onetype earlier and later, to compare against our observations toclassify the spectra by eye using features across the entireinfrared spectrum. This holistic approach helped mitigatepotential feature mismatches introduced by metallicity dif- https: // / ∼ ernewton / nirsurvey.html We prefer the conversion from H O-K2 index to NIR spectral type fromNewton et al. (2014) rather than Rojas-Ayala et al. (2012) because the for-mer is based on classifications using the entire NIR spectra. ferences between the targets and the standards by not relyingon any single features in the spectra. We determined a singlebest type for each of the
Y JHK bands and took the medianas our best classification.Our NIR classifications for the FUMES sample are shownin Table 2, and we estimate spectral type uncertainties ofhalf a subtype. We also include the literature optical spectraltypes for comparison, typically from the Palomar / MichiganState University (PMSU) survey (Reid et al. 1995; Hawleyet al. 1996) for the field objects, but from additional sourcesfor the younger stars. As discussed in Rojas-Ayala et al.(2012) and Newton et al. (2014), the literature optical spec-tral types are often dependent on metallicity across the M1-M4 range, and we consider the NIR classifications to be themore consistent metrics. We similarly report the NIR / opticalspectral types for the literature sample in Table 2. These clas-sifications will be important in Section 5.A couple of objects deserve further attention. Since theNewton et al. (2014) standards do not include spectra fortypes earlier than M1, we also used the M0 and K7 standardswithin the IRTF spectral library (Rayner et al. 2009) whenclassifying GJ410 and HIP23309. The M1 star, CD-35 2722,has an L4 companion that is 5 magnitudes fainter across the JHK -bands (Wahhaj et al. 2011) at a separation of ∼
70 AU.This companion is unresolved in our spectroscopic observa-tions, but the ∼
1% contribution to the integrated NIR fluxesdid not meaningfully distort the observed spectra. However,there was evidence for a slightly deeper 0.99 µ m FeH fea-ture than would be expected for an M1 dwarf, perhaps dueto the strength of this feature in L-dwarf spectra (e.g., Kirk-patrick 2005). The young star HIP 112312 has an opticalclassification as a subgiant from Torres et al. (2006). With-out subgiant standards with which to compare in the NIR,we cannot confirm this classification with our observations.For this star we also compared the M-giant IRTF NIR stan-dards (Rayner et al. 2009), finding that the HIP 112312 NIRspectrum largely agrees with the dwarf sequence except fordeeper CO lines in the K -band, which are very prominent inthe M-giant spectra, reflecting the relatively low gravity ofthis young object. The other young FUMES stars (see Ta-ble 2) showed spectra consistent with the dwarf standards.2.3. Stellar Properties
Our aim in this paper is to analyze the relation betweenFUV emissions and the physical properties of low-mass stars.To these ends, we desired self-consistent properties, mass,radius, bolometric luminosity, and e ff ective temperature foreach FUMES target, and any suitable additional targets foundin the literature. Consistently determined properties are cru-cial to mitigate potential systematic e ff ects introduced by re-lying on an assortment of eclectic literature determinationsfor these stellar properties. Although our IR spectra allowedUMES 5 Table 2.
UV Sample a Name SpT L bol Mass Radius T e ff Rot. Period b References c Opt / NIR (10 erg s − ) ( M (cid:12) ) ( R (cid:12) ) (K) (d)G 249-11 M4 d / M4 2 . ± .
07 0 . ± .
006 0 . ± .
010 3277 ± e M4IV / M4.5 16 . ± . . ± . . . ± . . ± . ± .
005 19, 14, 9GJ 4334 M4.5 / M5 3 . ± .
09 0 . ± .
007 0 . ± .
012 3260 ± d / M3 8 . ± .
22 0 . ± .
01 0 . ± .
017 3412 ± f M3 / M4 11 . ± . . ± . . . ± . . ± . ± .
01 1, 14, 9LP 247-13 M2.7 / M3.5 12 . ± .
35 0 . ± .
013 0 . ± .
02 3511 ± / M1 18 . ± . . ± .
015 0 . ± .
023 3713 ± . ± . / M0.5 21 . ± . . ± .
015 0 . ± .
024 3786 ± fg M1 / M1 21 . ± . . ± .
002 0 . ± .
003 3727 ± . ± .
004 19, 14, 9HIP 23309 e M0 / M0 68 . ± . . . ± . . . ± .
014 3886 ± . ± .
07 19, 14, 9Prox. Cen. * M5.5 / - 0 . ± . . . ± .
003 0 . ± .
005 2992 ± / - 0 . ± .
014 0 . ± .
003 0 . ± .
007 2976 ±
133 6, - , 2GJ 1214 M4.5 / M4 1 . ± . . . ± .
005 0 . ± . . ± ± / - 1 . ± .
05 0 . ± .
005 0 . ± .
009 3196 ± / M4 2 . ± .
04 0 . ± .
005 0 . ± .
009 3334 ±
170 15, 11, 2GJ 628 * M3.5 / M3 4 . ± .
04 0 . ± .
007 0 . ± .
007 3307 ± . ± . / M2 4 . ± .
04 0 . ± .
007 0 . ± .
008 3424 ± . ± . / M5 4 . ± . . . ± .
008 0 . ± .
013 3293 ± . ± . / M3 4 . ± .
15 0 . ± .
008 0 . ± .
013 3370 ± . ± . / - 5 . ± .
13 0 . ± .
008 0 . ± .
014 3443 ± . ± . / M3 5 . ± .
04 0 . ± .
007 0 . ± .
004 3201 ± . ± . / - 6 . ± .
09 0 . ± .
009 0 . ± . . ±
107 15, - , 2Gl 436 * M2.5 / M3 9 . ± .
11 0 . ± .
009 0 . ± .
011 3477 ± . ± .
08 15, 11, 3AD Leo M3 / M3 8 . ± . . ± .
010 0 . ± .
02 3425 ± . ± . / - 10 . ± . . ± .
011 0 . ± .
018 3539 ± . ± . / . ± .
22 0 . ± .
01 0 . ± .
008 3672 ±
33 6, - , 2GJ 176 * M2 / M2 13 . ± .
12 0 . ± .
012 0 . ± .
015 3632 ± . ± . e M0 / - 37 . ± . . . ± . . . ± . . ± a Stellar properties are from Pineda et al. ( in prep ), quoting medians and the central 68% confidence interval, see Section 2.3. Thehorizontal division separates the new FUMES ( top ) targets from the literature stars ( bottom ). b Rotation periods are taken from the literature, typically from either photometric variations or long-term monitoring of periodicemission lines. Uncertainties are as reported in the literature if available. c References in order denote source for optical spectral type, infrared spectral type and rotation period. d Optical spectral types were not available in the literature, so we used our NIR classification and Eqn. 3 from Newton et al. (2014)with the metallicity determined from their calibration of the equivalent widths of the Na doublet at 2.2 µ m (their Equation 10). e HIP 23309, HIP112312, and AU Mic are members of β Pic which has a mean age of ∼
24 Myr (Bell et al. 2015). f CD-35 2722, and HIP17695 are members of AB dor which has a mean age of ∼
150 Myr (Bell et al. 2015). g CD-35 2722 is a binary with a substellar L4 companion with separation of ∼
70 AU (Wahhaj et al. 2011). ∗ Star names listed with an asterisk have measured angular diameters from interferometric measurements (von Braun et al. 2011;Boyajian et al. 2012; von Braun et al. 2014; Kane et al. 2017), incorporated in the radius estiamtes, see Pineda et al. ( in prep ). References. – (1) Alonso-Floriano et al. (2015), (2) Astudillo-Defru et al. (2017), (3) Bourrier et al. (2018), (4) Donati et al.(2008), (5) Hartman et al. (2011), (6) Hawley et al. (1996), (7) K¨uker et al. (2019), (8) Mallonn et al. (2018), (9) Messina et al.(2010), (10) Morin et al. (2008), (11) Newton et al. (2014), (12) Newton et al. (2016), (13) Newton et al. (2018), (14) This Work,(15) Reid et al. (1995), (16) Shkolnik et al. (2009), (17) Su´arez Mascare˜no et al. (2015), (18) Su´arez Mascare˜no et al. (2016),(19) Torres et al. (2006). P ineda et al .us to utilize spectroscopic property calibrations (e.g., Mannet al. 2015; Newton et al. 2015; Terrien et al. 2015), such datawere not uniformly available for both the FUMES and liter-ature targets, and we thus rely instead on the largely photo-metric results from our companion paper summarized below(Pineda et al. in prep ). The corresponding stellar propertiesare shown in Table 2. 2.3.1. Field Stars
To determine the properties of low-mass field stars Pinedaet al. ( in prep ) use a Bayesian framework to combine multipleempirical calibrations, largely photometry based, to jointlyconstrain mass, radius, bolometric luminosity, and derive thestellar e ff ective temperature. Their methods fully incorpo-rate measurement uncertainties, and intrinsic scatter withinthe utilized calibrations, and produce well defined joint pos-terior distributions for the full set of physical properties.Pineda et al. ( in prep ) jointly uses the mass-luminosity re-lation of Mann et al. (2019), the bolometric correction cali-bration of Mann et al. (2015), and a new mass-radius relationvalid across 0 . . M (cid:12) with 3.1% uncertainties at fixed massspecifically developed in that work.The Bayesian framework further allowed them to freely in-corporate additional measurements whenever available, suchas bolometric fluxes, or angular diameters from interferome-try. Many of the individual objects in the sample (see Table 2)had these additional measurements which largely improvedthe precision of the physical properties of a given sample ob-ject. Full details on these methods are available in Pineda etal. ( in prep ).As compared to literature estimates of the M-dwarf ensem-ble analyzed in Pineda et al. ( in prep ), their methods yieldeda stellar sequence with less scatter, consistent property esti-mates for objects with interferometric angular diameter mea-surements, and stellar densities consistent with independentdata inferred from exoplanetary transits of low eccentricityplanets. 2.3.2. Young Stars
Of the objects shown in Table 2, five are high probabil-ity members of known young moving groups: HIP 112312,HIP 17695, CD-35 2722, HIP 23309, and AU Mic (Pinedaet al. in prep ). Because the available empirical calibrationsare only applicable to field age stars, these five young objectsrequired a di ff erent approach for estimating their stellar prop-erties. For these stars, Table 2 also quotes the stellar modelbased results from Pineda et al. ( in prep ). We summarizetheir methods as follows.Within a Bayesian framework, Pineda et al. ( in prep ) cou-ple stellar evolutionary models with spectral energy distribu-tion fitting of model spectra using blue optical to far infraredphotometry. Using Monte Carlo sampling, a given mass andage within the evolutionary model defines the corresponding bolometric luminosity and radius, and thus the e ff ective tem-perature and gravity of a sample point. These properties arethen used for interpolation of a model atmosphere grid andgeneration of synthetic photometry for comparison with theobserved data points. The best-fit stellar properties are thosethat best reproduce the photometry consistently within theevolutionary models. This approach self-consistently pro-duces parameter estimates for all of the properties with welldefined posterior distributions for each. For the five youngobjects, Table 2 reproduces the parameter results using mag-netic stellar evolutionary models (Feiden & Chaboyer 2013,2014; Feiden 2016). Full details of these methods and anal-ysis of likely systematic e ff ects in the model choices are ex-plained in Pineda et al. ( in prep ).Those properties most directly constrained by the SED fit-ting, namely L bol , T e ff , and R are consistent within errors toliterature values (Pineda et al. in prep ). The young stars usedin this work are all active M-dwarfs, and we discuss furtherhow their modeling choices and thus the inferred mass im-pact our rotation activity analysis in Section 4.1. FAR ULTRAVIOLET EMISSIONS3.1.
HST Data
We used the Space Telescope Imaging Spectrograph(STIS) on
HST to measure the FUV spectra of our FUMESsample through program HST GO-14640 (PI - Pineda). Weshow a summary of our observations in Table 3. Typicallydata were taken using the G140L grating with the FUV-MAMA detector, providing a typical resolving power of ∼ ∼ spectralPhoton routines from R.O. P. Loyd previously used in the HST -STIS and
HST -COSanalyses of M-dwarf UV spectra (e.g., Loyd & France 2014;Loyd et al. 2018). To summarize, the reduction procedure The codes are available on GitHub: https: // github.com / parkus / spectralPhoton. UMES 7
Wavelength (˚A) − − − − F λ ( e r g s − c m − ˚A − ) Ly α (attenuated)C iii Si iii N v Si iv C iv C ii C i C i O i He ii Si ii Al ii Stellar FluxUncertainty . . . . . × − Figure 2.
The FUV spectra of M-dwarfs show several discrete emission features spanning lines that probe di ff erent temperatures in the transitionregion from C ii to N v . This example illustrates a typical spectrum in the FUMES data set (GJ49, T exp = HST -STIS G140L. The inset figure shows the low-level continuum emission from 1450-1520 Å. sums the photons in a narrow ribbon identified as the stel-lar trace subtracting o ff a background count rate determinedfrom the signal in o ff set regions with the same wavelengths.The reduction then uses the flux calibration from the full ex-posures to convert the photon counts to a calibrated spectrum.The advantage of spectralPhoton over the standard out-put from the STScI pipelines is that it allows for the defini-tion of custom wavelength extraction regions, trace locations,and integrated time intervals. This was important becausewe found for the faint targets LP 55-41 and G 249-11 thatthe standard pipeline products did not correctly identify thestellar trace. Additionally, some of the targets flared duringour observations, which we removed by manually identifyingwhen the flares took place, and defining custom time intervalsduring the exposures for extraction of photons correspondingto the quiescent emission spectra.The majority of our targets were observed in the wider0.2” STIS slit mitigating potential slit-loss e ff ects, a ff ectingthe flux calibration, with poor acquisition, target centering orguiding. For one target, HIP 23309, observed with the nar-rower 0.1” slit for bright object protection considerations, thetime series analysis showed a long-term trend in the photoncounts over the course of the orbit (this e ff ect was not seen inthe data for GJ 410, the other program observation employingthe 0.1” slit). To correct for this we fit a third-order polyno-mial to the trend (in the 10 s binned light curve) to divideit out and scaled to the average peak count rate. The quies-cent spectrum was subsequently extracted from the appropri-ately scaled spectrum. For each target we extracted spectrafrom each exposure (usually 1 per orbit), and then co-addedthem together rebinning onto a constant linear wavelengthgrid. For the echelle spectra we also merged the wavelengthregions in which the echelle orders overlap, averaging fluxpoints falling within the same 0.05 Å bins, and preserving Table 3.
UV Data SummaryName UT Date Grating Aperture a OrbitsGJ 4334 2017-09-20 G140L 0.2” 2GJ 49 2017-09-20 G140L 0.2” 2HIP 112312 2017-08-22 E140M 0.2” 1LP 247-13 2017-09-13 G140L 0.2” 1HIP 17695 2017-12-27 E140M 0.2” 1HIP 23309 2017-11-24 G140L 0.1” 1CD-35 2722 2017-09-26 G140L 0.2” 1GJ 410 2017-12-18 G140L 0.1” 1LP 55-41 2017-09-13 G140L 0.2” 3G 249-11 2017-09-10 G140L 0.2” 3 a Aperature denotes the width of the STIS slit. the integrated flux of the spectral bin. We show an exampleG140L spectrum of one of our targets in Figure 2, and anechelle E140M spectrum in Figure 3.By using STIS, we were able to observe Ly α in all ofour objects, as well as all of the significant FUV emis-sion lines He ii λ . ii λλ . , .
71 Å, C iii λ . iv λλ . , .
78 Å, Si iii λ . iv λλ . , .
77 Å, and N v λλ . , .
806 Å.These lines span mean formation temperatures log T (K) = We focused on these lines as both the The mean formation temperatures listed in Table 7 depend on the di ff eren-tial emission measure and may di ff er (significantly) from the peak forma-tion temperature. P ineda et al . . . . . . . . . . F λ ( − e r g s − c m − ˚A − ) Ly α (attenuated)Si iii Stellar FluxUncertainty1250 1275 1300 1325 1350 1375 14000 . . . . . . . . F λ ( − e r g s − c m − ˚A − ) N v Si iv C ii O i Wavelength (˚A) . . . . . . F λ ( − e r g s − c m − ˚A − ) C iv C i C i He ii − . . . . . Figure 3.
This
HST -STIS E140M data for HIP 17695 (T exp = most prominent in the data, being well measured both in theFUMES targets and the literature sample.3.2. FUV Line Fitting
To measure the target emission line fluxes, we usedPyMC3 to fit the observed line shapes, typically with eithera Voigt or Gaussian profile convolved with the instrumentline spread function. Although we must assume a particu-lar profile shape, these shapes are well motivated physically,and this approach has several advantages to simply summingthe flux in the appropriate region for each line. At high res-olution, we can measure the line widths, compare the emis-sion core to the line wings, and examine centroid o ff sets, in- The LSFs have spectral resolutions of 1.7-1.5 pixels at FWHM for STIS-G140L and 1.4-1.3 pixels at FWHM for E140M. We used the LSFs ob-tained from the STSci STIS instrument documentation. dicative of the stellar radial velocity. We can also simultane-ously fit a continuum level below each line and incorporatethe uncertainty in that estimate to our reported emission linefluxes. This e ff ect was especially important in the G140Ldata, where there appeared to be some continuum level be-low many of the lines. For example in the region aroundN v , some of the low-level extended Ly α wing emission couldbe seen. In the E140M data, no continua were evident. Wequantify continuum levels in Section 3.3. Additionally, theline fitting is robust to potentially badly characterized datapoints because it allows us to include a fit scatter term to thedata to account for underestimated errors.We summarize the model profiles fit to the data in Table 4,where the number in front of the profile shape indicates thatmultiple lines were fit simultaneously, and the continuumcomponent is described by a line with an unknown slope andUMES 9 . . . . . . . . .
020 N V1639 . . . . . . . . . . . F λ ( − e r g s − c m − ˚A − ) He IIHIP 17695 1634 1636 1638 1640 1642 1644 1646 16480 . . . . .
08 He IILP 247-131174 . . . . . . . Wavelength (˚A) − . . . . .
75 C III 1170 1172 1174 1176 1178 1180 1182 1184 1186
Wavelength (˚A) . . . . . .
05 C III
Figure 4.
We show example results displaying our typical line fits for N v ( top ), He ii ( middle ), and C iii ( bottom ), with both E140M highresolution data ( left ), and G140L low resolution data ( right ). Data (black) are from HIP 17695 ( left ) and LP247-13 ( right ), with the shadedregion (blue) denoting the 1 σ confidence interval for the model about its median. Emission lines that are separable at high resolution canbecome blended in the lower resolution data. constant o ff set. When multiple lines are fit simultaneously, asin the C iv doublet, the widths of the Gaussian and Lorentziancomponents in the Voigt profile shape are constrained to beidentical in each line. This reduces the number of free pa-rameters in the fit and is justified because each line comesfrom the same species, forming under similar temperatureconditions with only a small di ff erence in energy levels be-tween the transitions. As priors in our Bayesian regressionanalysis, we used uniform distributions for the line flux, cen-ter, and when necessary the continuum o ff set and slope. Forthe width parameters in the Gaussian and Lorentzian com-ponents we used a weakly informative Half-Cauchy distribu-tion, with a characteristic width of 100 km s − . This choicehad a negligible a ff ect on the parameter posterior distribu- For the non-negative Half-Cauchy distribution, half of the probability massdensity is contained at parameter values less than the characteristic widthwith the distribution tail decaying in a Lorentzian fashion. tion, but greatly improved MCMC sampling e ffi ciency andconvergence relative to a log uniform prior within PyMC3.We show examples of our fit line profiles in Figure 4, withthe results for the total line fluxes shown in Table 5. TheLy α emission is the focus of paper II (Youngblood et al. ac-cepted ), and we reproduce those results here. For the twotargets with E140M data, we fit a single Gaussian line forSi iii , to be consistent with the approach for the G140L data,that required simultaneous fitting with Ly α (Youngblood etal. accepted ). At the higher resolution, the low flux C iii linesare somewhat blended but distinguishable, so we fit six com-ponents to the multiplet, but only a single Gaussian featureat low-resolution. The He ii multiplet, by contrast, remainsunresolved in all the datasets and we fit a single Gaussian forthe combined emission accordingly. In general for the He ii line fits, the best model scatter term was often larger than thefits for other lines of the same star possibly indicating thatthe shape choice was not ideally suited to the data. For this0 P ineda et al . Table 4.
Model Line FittingLine ID G140L E140MLy α a Voigt + ISM Voigt + ISMHe ii Gaussian + Continuum GaussianC ii b Gaussian + Continuum VoigtC iii
Gaussian + Continuum 6x GaussianC iv
2x Voigt + Continuum 2x VoigtN v
2x Voigt + Continuum 2x VoigtSi iii a Gaussian + Ly α GaussianSi iv
2x Voigt + Continuum 2x Voigt a For G140L data the Ly α line is jointly fit, account-ing for ISM absorption, with Si iii (Youngblood etal. accepted ), but for E140M data the Si iii line is fitindependently. b For the E140M data we fit only the single redwardline in the C ii doublet, λ λ ff ected by the ISM; for G140Ldata, these lines are blended, see Table 5. unresolved multiplet, however, our model choice remains thesimplest way to capture the line flux.For the E140M data the C ii doublet is resolved, but at low-resolution the two lines are blended, which impacts the fluxmeasurements since one of the lines is impacted by ISM ab-sorption. We estimated the typical ISM attenuation of theC ii − (0.05 Å) forthe Gaussian component and 20 km s − (0.04 Å) for theLorentzian component based on our E140M spectra of HIP17695’s unattenuated C ii ii ISMparameters identified by Redfield & Linsky (2004) for starsinside 40 pc is 13.1-15.2 for the log column density, 2.9-6.6km / s for the Doppler b value, and a radial velocity of -30 kms − to 30 km s − . We created 10,000 realizations of the atten-uated 1334 Å flux where column density, b value, and radialvelocity of the absorbers relative to the star’s rest frame weredrawn from uniform distributions with the ranges describedpreviously. We found that the median attenuation for the1334 Å line is 14%, with a 68% confidence interval range of4-45%. Assuming the 1334 and 1335 Å C ii lines are equallypopulated (a reasonable assumption for thermal equilibrium),total C ii fluxes derived from the low-resolution spectra wherethe two lines are blended should be corrected upward ∼ σ upper limits for these lines by simply summing the fluxin the region around the expected line center, and comput-ing the associated uncertainty in that flux. For the few linesthat were measurable, C ii , C iv , and N v , we accommodatedthe lower signal-to-noise ratio by only fitting single Gaussianline profiles in each case, one component for the blended C ii ,and two components each for the C iv and N v doublets. Theseresults are included in Table 5.3.3. FUV Continuum Emission
Although the FUV spectra of low-mass stars is dominatedby discrete emission line features, there is a weak under-lying FUV continuum that is likely defined by the recom-bination edges of species like Si (Loyd et al. 2016; Pea-cock et al. 2019). As seen in Figures 2 and 3, continuumemission between the strong line features was evident in thelow-resolution G140L spectra, but unapparent in the high-resolution E140M spectra. This is a consequence of thehigher sensitivity and lower resolution of the G140L grating,making it easier to detect weak continuum levels. Comparedto
HST -COS medium-resolution gratings (G130M, G160M),the
HST -STIS low-resolution grating (G140L) is slightlymore sensitive at detecting faint continuum emission. Forthe full FUMES sample we quantify the FUV continuum lev-els apparent in our spectra following the work of Loyd et al.(2016).As part of the MUSCLES program they defined an ensem-ble of narrow bands (0.7-1 Å in width) interspersed betweenthe prominent FUV emission lines to assess the FUV con-tinuum flux across 1300-1700 Å. We used these same bands(obtained through private communication, Loyd, R. O. P.)transformed to the radial velocity frame of our targets to in-tegrate the FUV continuum. We were able to use the bandsunaltered for the E140M data sets; however, for the lowerresolution G140L data, we visually verified that the bandsdid not overlap with any of the strong emission lines. Thisremoved 6 narrow bands ( ∼ ∼
150 Å cumulative width of thepassbands. For 8 of the 10 targets, including the two ob-served with the E140M grating, we measure a non-zero FUVcontinuum level, all except for G149-11 and LP 55-41. Al-though in each narrow band the integrated flux is usually in- Using the STScI exposure time calculator (http: // etc.stsci.edu), detecting alow-level flat continuum ( F λ = − erg s − cm − Å − at 1350 Å) at asignal-to-noise threshold of 3 would take twice as long with COS G130Mas opposed to STIS G140L (6.1 ks vs. 2.9 ks) when accounting for thefactor of ∼
15 di ff erence in resolution. All the FUMES targets had measured RVs, except G249-11 and LP 55-41,for which we used a 0 km s − frame. The shift is small in general and hasno impact on the result, since these two targets were too faint to detect anycontinuum emission. UMES 11
Table 5.
FUV Line Fluxes a Name Ly α b He ii C ii c C iii C iv N v Si iii d Si iv G 249-11 — < . < . < .
014 0 . ± .
003 0 . ± . < . ± . ± .
48 3 . ± .
18 3 . ± . . . ± . . . ± . . . ± . . . ± . . GJ 4334 7 . ± . . . ± . . . ± .
03 0 . ± .
01 1 . ± . . . ± .
024 0 . ± . . . ± . < .
018 0 . ± . < . < .
034 0 . ± .
004 — < . ± . ± . . . ± .
14 2 . ± . . . ± . . . ± .
11 1 . ± . . . ± . . LP 247-13 442 ± . ± .
13 1 . ± .
07 1 . ± .
081 3 . ± .
11 0 . ± . . . ± . . . ± . ± . ± . . . ± .
09 0 . ± .
035 2 . ± .
07 0 . ± . . . ± . . . ± . ± . ± .
17 2 . ± .
09 0 . ± .
099 2 . ± . . . ± .
051 0 . ± . . . ± . . ± . . . ± .
18 2 . ± . . . ± .
09 4 . ± .
12 0 . ± .
05 1 . ± .
06 1 . ± . . ± . . . ± . . . ± .
09 2 . ± . . . ± .
19 1 . ± .
06 2 . ± . . . ± . a All fluxes are as observed at Earth, in units of 10 − erg s − cm − , and the flux from multiplet lines are added together, unless indicatedotherwise. Uncertainties reflect the central 68% confidence interval about the median. b Ly α fluxes as reconstructed in FUMES paper II (Youngblood et al. accepted ). For G249-11 and LP 55-41, the weak emission precluded aconfident fit. c For HIP112312 and HIP17695 with E140M data we report the flux of just the λ ∼
7% to account for the influence of the ISM (see Section 3.2). d Si iii fluxes are from FUMES paper II (Youngblood et al. accepted ), jointly fit with Ly α in G140L STIS data. Table 6.
FUV Continuum MeasurementsName Obs Flux S / N(erg s − cm − Å − )GJ 4334 5 . ± . × − . ± . × − a . ± . × − . ± . × − a . ± . × − . ± . × − . ± . × − . ± . × − . ± × − —G 249-11 5 ± × − — a The E140M spectra show very little contin-uum if any, leading to likely poorly charac-terized uncertainties, and thus these valuesshould be taken with caution. significant, revealing no clear continuum shape, when addingup the emissions across all of the narrow passbands of thespectra the overall continuum emission is detectable. For thequoted uncertainties of Table 6, we propagated the data un-certainty through the continuum flux summation. Our results are broadly consistent with those of Loyd et al.(2016) accounting for the distance to each target; however,with this broader sample of stars we see evidence for a widearray of continuum levels. Higher signal-to-noise spectra areneeded to verify the detection of these average continua anddetermine what defines their flux levels and spectral compo-sition. 3.4.
Line-Line Correlations
Our FUV emission line measurements are diagnostic of thestellar upper atmospheres and how they change with mag-netic heating. Because they form in similar regions, the linestrengths are strongly correlated, as has been well illustratedin the literature (e..g, Youngblood et al. 2017). We build onthese results by expanding the available UV samples usingour new measurements with the FUMES targets. In additionto the FUMES data we also analyzed the Mg ii NUV data forthe literature sample, as representative of an additional atmo-spheric layer and spectral region of interest.Since C iv is a bright and readily accessible emission fea-ture, we show in Figures 5-6 the correlation of each of theemission lines of Table 5 against C iv . We plot the luminosi-ties of each feature as two-dimensional error ellipses (2 σ contours) representative of the bivariate error distributionsfor the luminosities of each line pair. We further discussthe di ff erence in undertaking this analysis in luminosity ascompared to surface flux in Appendix A. Since each lumi-nosity depends on the known parallax and its uncertainty, the2 P ineda et al . H e II l og L ( e r g s − ) γ = 1 . ± . C = − ± s = 0 . ± . . FUMESLiterature
24 25 26 27 28
C IV log L (erg s − ) − . . R e s i du a l s S i I V l og L ( e r g s − ) γ = 0 . ± . C = 0 . ± . s = 0 . ± . .
24 25 26 27 28
C IV log L (erg s − ) − . . R e s i du a l s NV l og L ( e r g s − ) γ = 0 . ± . C = 2 . ± . s = 0 . ± . .
24 25 26 27 28
C IV log L (erg s − ) − . . . R e s i du a l s C II l og L ( e r g s − ) γ = 1 . ± . C = − ± s = 0 . ± . .
24 25 26 27 28
C IV log L (erg s − ) − . . . R e s i du a l s E ff ec t i v e T e m p e r a t u r e ( K ) Figure 5.
Our FUV emission line correlations for the combined FUMES (black outline) and literature samples show tight power-law fits, L y = CL γ CIV , with scatter s . Each star is shown as a representative error ellipse corresponding to a 2 σ confidence level. Dashed lines show theindividual best fit relations for each line-pair. Any FUV line can be used to predict any other emission line in quiescence. The lower panel ofeach plot shows the central residuals from the power-law fit with the intrinsic scatter s shaded in gray. luminosity determinations have correlated uncertainties, re-vealed by diagonally oriented ellipses. This correlation ismore prominent when the parallax uncertainty dominates theluminosity measurements. Figures 5 and 6 shows these datawith the filled shading of each shape indicating the e ff ectivetemperature of the stars. The emission fluxes are not primar-ily determined by the stellar e ff ective temperature, as bothwarmer and cooler objects in the FUMES and literature sam-ples show high and low FUV luminosities, but instead byeach object’s activity regime, as will be discussed in Sec-tion 4. The correlations shown in Figures 5-6 further demonstratethat the C iv strength can be used to predict the quiescentemission of any of the other prominent transition regionemission lines across four orders of magnitude in luminos-ity. To these data, we fit a power-law relation using C iv asthe predictor variable, within a Bayesian framework (Kelly2007), accounting for uncertainties in both dimensions andincorporating an intrinsic scatter at fixed C iv luminosity. Wedefined the regression model for the line luminosities, L y , aslog L y , i | γ, C , s ∼ N i ( γ log L x , i + log C , s ) , (1)UMES 13 C III l og L ( e r g s − ) γ = 1 . ± . C = − ± s = 0 . ± . . FUMESLiterature
26 27 28
C IV log L (erg s − ) − . . . R e s i du a l s S i III l og L ( e r g s − ) γ = 1 . ± . C = − . ± . s = 0 . ± . .
24 25 26 27 28
C IV log L (erg s − ) − . . R e s i du a l s L y α l og L ( e r g s − ) γ = 0 . ± . C = 9 . ± . . s = 0 . ± . .
24 25 26 27 28
C IV log L (erg s − ) − . . . R e s i du a l s M g II l og L ( e r g s − ) γ = 0 . ± . . log C = 4 ± s = 0 . ± . .
24 25 26 27 28
C IV log L (erg s − ) − . . . R e s i du a l s E ff ec t i v e T e m p e r a t u r e ( K ) Figure 6.
Continued from Figure 5. The correlation for the NUV Mg ii line shows greater scatter than any of the FUV relations. where x corresponds to C iv and y any of the other lines (e.g.,N v , Si iv etc.), N ( µ, σ ) denotes a Normal distribution of mean µ and standard deviation σ , i denotes each star in the dataset,and s is the intrinsic scatter of the power-law relation in log-log space. , The s parameter is fit along with the power-lawmodel, with its marginalized posterior distribution describingthe set of intrinsic scatters consistent with the uncertainty ofthe data, and the posterior distributions on γ and C . The peakof that distribution is our best estimate of the representative The notation of Equation 1, e.g., z | u , w ∼ N ( u , w ), indicates that the ran-dom variable z conditioned on u and w follows the probability density func-tion defined by N . intrinsic scatter in the line-line correlations. As an example,a scatter value, s = .
1, would suggest an individual line lu-minosity could be predicted to within ∼ iv lu-minosity.The probability distribution for each line luminosity pairwere defined, in the case of FUMES targets, by their joint dis-tribution created from the sampled line flux posteriors of themodel fits (see Section 3.2) combined with the parallax mea-surement and its uncertainty. For literature data, we assumedGaussian distributions for the line fluxes and combined withthe parallax measurements to determine the joint luminositydistributions at each datum pair. The likelihood is definedby the product across the sample of stars with Equation 1.4 P ineda et al . Table 7.
Line Correlations with C iv a Line log T f N samp γ log C s Mg ii . ± . . ± . ± . . Ly α . ± .
09 9 . ± . . . ± . . C ii . ± . − ± . ± . . Si iii . ± . − . ± . . ± . . C iii . ± . − ± . ± . . He ii . ± . − ± . ± . . Si iv . ± .
03 0 . ± . . ± . . N v . ± .
03 2 . ± . . ± . . a C iv has log T f = .
0. Reported parameters correspond to themedian of the marginalized posterior distributions with uncer-tainties indicating the central 68% confidence interval.
In log-log space this is a linear model and we used a uniformprior on log C , the o ff set, a Cauchy distribution for the power-law exponent, γ , and a Half-Cauchy distribution with unityshape parameter for the scatter, s . These priors are mini-mally informative, and only marginally a ff ect the posteriordistributions in γ , s , and C , while improving Monte Carloconvergence e ffi ciency. An example of the joint posteriordistributions for these fits is shown in Figure 7. The result ofthese fits are indicated by the dashed lines in Figures 5-6, andwe tabulate the fit parameters in Table 7.The line pair with the smallest intrinsic scatter is C iv -N v ( ∼ ii and Ly α show the greatest scatter values, andcorrespond to the lowest formation temperature lines that westudied. On the contrary, C ii forms at similar temperatures toMg ii and shows as small a scatter as the hotter Si iv transitionregion line. The larger scatter for Mg ii relation could be dueto unaccounted for uncertainty associated with the ISM cor-rection needed for the Mg ii flux estimates (Youngblood et al.2016). This may also a ff ect the Ly α correlation; however,the formation of Ly α , its central profile, and its broad emis-sion (Youngblood et al. accepted ) is likely more complicated(Peacock et al. 2019). Predicting that emission from the tran-sition region C iv luminosity thus may not account for all ofthe processes impacting the Ly α flux. In practice we used a uniform distribution in the angle, θ , which corre-sponds to the angle the line in log-log space makes with the horizontal, andset γ = tan θ . . . . . γ − − − l og C . . γ . . . . s − − − log C .
05 0 .
10 0 .
15 0 . s Figure 7.
The joint posterior distributions for our typical power-lawfits to the line-line correlations (see Section 3.4) illustrate how sam-ples for the power-law slope, γ , and constant, log C , are highly cor-related. The lines in the lower left corner show the 1 σ , 2 σ and 3 σ contours on top of semi-transparent points from our MCMC sam-pling. The diagonal shows the marginalized distributions for eachproperty with the distribution visualized from kernel density estima-tion. Along the diagonal the dashed lines indicate the median andmiddle 68% confidence intervals. The upper right corner visual-izes the detailed shape of the joint posteriors through kernel densityestimation, showing well defined peaks. The rest of the line-line correlations show consistent scat-ters of 0.1-0.2 dex at fixed C iv luminosity. These measure-ments represent the intrinsic scatter of FUV line emissionacross the population, as all of the observations were eithertaken simultaneously or closely spaced in time (France et al.2016). If this is indeed due to intrinsic variation, it may de-fine the limit to which FUV features can be used to predictone another. Additionally, this intrinsic variation may di ff erbetween the ‘inactive’ and ‘active’ subsamples, however, oursamples in each are not large enough to fully investigate. ROTATION-ACTIVITY RELATION4.1.
Regression Model Fitting
Canonical rotation-activity correlations with optical andX-ray emission (e.g., Pizzolato et al. 2003; Wright et al.2011; Astudillo-Defru et al. 2017; Newton et al. 2017) haveillustrated a strong rotational dependence typically charac-terized by a power-law distribution, and a saturated regimeof activity for the fastest rotators. Since Noyes et al. (1984),these relationships have been used to investigate the inter-UMES 15play between the internal convective motions and di ff erentialstellar rotation within an α - Ω magnetic dynamo, thought tooperate in stars with partly convective interiors (e.g., Mon-tesinos et al. 2001; Browning et al. 2006). Mediated by thetachocline interface between the radiative core and convec-tive envelope, the dynamo sustains the magnetic field throughcyclic regeneration of toroidal and poloidal field. Theorysuggests that the magnetic fields, and hence the resulting ac-tivity tracers should thus be mediated by the Rossby number, Ro = P /τ c , the ratio between the rotational period and theconvective turn over time, which characterizes the timescalesfor bulk motions of internal convection. Recent results havefurther extended these studies across the boundary betweenfully convective and partly convective interiors (Newton et al.2017; Wright et al. 2018) with M dwarf samples, illustratinga continued rotational dependence for the activity tracers, de-spite the need for alternative dynamos for the lowest massstars, which lack that tachocline interface.With the FUMES sample, we can now probe these samemechanisms with new indicators of the magnetic activity inthe FUV. To our emission line data, we fit a broken power-law as a function of Ro , L y / L bol = ( L y / L bol ) sat , Ro ≤ Ro c A ( Ro ) η , Ro > Ro c , (2)where ( L y / L bol ) sat denotes the strength of emission line y , inthe saturated regime relative to the star’s bolometric lumi-nosity, η indicates the slope of the unsaturated regime, and Ro c is the critical Rossby number at which the activity tran-sitions between regimes, with A ≡ ( L y / L bol ) sat ( Ro c ) − η to en-sure continuity. To compute the Rossby number, we use theknown rotation periods (see Table 2), and the empirical cal-ibration for the convective turn overtime, τ c , as a functionof mass from Wright et al. (2018). We discuss systematice ff ects in this choice of calibration in Appendix B. Our seg-mented regression fit further includes a scatter term, σ L , de-scribing intrinsic dispersion in the observed luminosities at afixed Rossby number, such thatlog( L y / L bol ) i | { β } ∼ N (log[ L y / L bol ( Ro i )] , σ L ) , (3)where the index i indicates the data for each star, and { β } = { Ro c , ( L y / L bol ) sat , η, σ L } is the set of four model parameters.Within this Bayesian model we employ as priors uniform dis-tributions for log( L y / L bol ) sat and Ro c , a zero centered Cauchydistribution with unity shape parameter for the slope η (seefootnote 13), and Half-Cauchy distribution with unity shapeparameter for σ L .Our fitting process using PyMC3 accounts for random un-certainty in both dimensions (Kelly 2007), and possible errorcorrelations between the assumed mass, and bolometric lu-minosity using the sampled posterior distributions from the Table 8.
Rotation-Activity Correlations a Line N samp η Ro c log( L line / L bol ) sat σ L Ly α − . ± . . . ± . . − . ± . . . ± . . Mg ii − . ± . . . ± . . − . ± . . . ± . . C ii − . ± . . . ± . . − . ± .
16 0 . ± . . Si iii − . ± . . . ± . − . ± .
13 0 . ± . . He ii − . ± . . . ± . − . ± .
11 0 . ± . . Si iv − . ± . . . ± . − . ± .
14 0 . ± . . C iv − . ± . . . ± . . − . ± .
15 0 . ± . . N v − . ± . . . ± . − . ± . . . ± . . a Reported parameters correspond to the median of the marginalized poste-rior distribution with uncertainties indicating the central 68% confidenceinterval. work of Pineda et al. ( in prep ). The error correlations be-tween M and L bol are generally small for the field objects,but can be significant for the young stars (see Pineda et al. inprep ). We also included the scatter in the convective turnovertime calibration from Wright et al. (2018) of 0.055 dex inlog τ c at fixed mass. When using the literature periods, wefurther incorporated the quoted uncertainties in those mea-surements if available or used a 10% Gaussian uncertainty ifnot, see Table 2 (private communication, Newton, E.). Ex-cept for the Ly α measurements of some stars, the randomuncertainties in the rotation-activity data are typically domi-nated by the error on the Rossby number driven by the scatterin the τ c calibration. This careful accounting of the knownsources of random error enabled us to carefully examine sys-tematic e ff ects with this fitting (see Appendix B).We applied these methods to eight UV emission lines, Ly α ,Mg ii , C ii , Si iii , He ii , Si iv , C iv , and N v , for which the sam-ples permitted a detailed rotation-activity fit. We show thebest parameter results in Table 8 from the marginalized pos-teriors, with the fit solutions plotted in Figure 8. We alsoshow an example of the joint posterior distributions for thisfitting in Figure 9, illustrating how the critical Rossby num-ber and unsaturated regime slope are generally correlated inour rotation-activity parameterization of Equation 2.Because this regression analysis relies on stellar mass es-timates for determining Ro , it may be potentially biased byour choice for the young stars to utilize the magnetic modelbased masses, which are larger than the non-magnetic modelmasses (see Pineda et al. in prep ), with a correspondinglylarger implied Ro . This concern applies only to the fiveyoung stars in our sample (see Table 2). However, of thefive, only AU Mic ( Ro = . .
17) appears to be nearthe transition between saturated and unsaturated regimes.HIP 112312, HIP 17695, and CD-35 2722 have Ro val-6 P ineda et al . − − − − − − l og ( L NV / L b o l ) log( L line /L bol ) sat = − . ± . . η = − . ± . . Ro c = 0 . ± . σ L = 0 . ± . . − − − − − − l og ( L C I V / L b o l ) log( L line /L bol ) sat = − . ± . η = − . ± . . Ro c = 0 . ± . . σ L = 0 . ± . . − − − − − − l og ( L S i I V / L b o l ) log( L line /L bol ) sat = − . ± . η = − . ± . . Ro c = 0 . ± . σ L = 0 . ± . . − − − − − − l og ( L H e II / L b o l ) log( L line /L bol ) sat = − . ± . η = − . ± . . Ro c = 0 . ± . σ L = 0 . ± . . − − − − − − l og ( L S i III / L b o l ) log( L line /L bol ) sat = − . ± . η = − . ± . . Ro c = 0 . ± . σ L = 0 . ± . . − − − − − − l og ( L C II / L b o l ) log( L line /L bol ) sat = − . ± . η = − . ± . . Ro c = 0 . ± . . σ L = 0 . ± . . − − log Rossby ( Ro = P/τ c ) − − − − l og ( L M g II / L b o l ) log( L line /L bol ) sat = − . ± . . η = − . ± . . Ro c = 0 . ± . . σ L = 0 . ± . . − − log Rossby ( Ro = P/τ c ) − . − . − . − . − . l og ( L L y α / L b o l ) log( L line /L bol ) sat = − . ± . . η = − . ± . . Ro c = 0 . ± . . σ L = 0 . ± . . E ff ec t i v e T e m p e r a t u r e ( K ) Figure 8.
Rotation-activity correlations are prominent across all of the UV emission features analyzed in this work. Individual data points arerepresented by 1 σ error ellipses, shaded to indicate each star’s e ff ective temperature. The best fit broken power law models (see Section 4) areshown in gray illustrating the 1 σ (dark gray) and 2 σ (light gray) scatters. UMES 17 − . − . − . − . l og ( L li n e / L b o l ) s a t . . . R o c − . − . − . − . η − . − . − . log( L line /L bol ) sat . . . . σ L . . . Ro c − . − . − . − . η . . . . σ L Figure 9.
The He ii joint posterior distributions (displayed as in Fig-ure 7) for the broken power-law fit (see Section 4) of the rotation-activity relation illustrate the correlation of the slope ( η ), and criticalRossby number ( Ro c ). The posterior results for fits to the other fea-tures are qualitatively identical, with results shown in Table 8. ues well below 0.1 regardless of the model choice for themass estimate, and HIP 23309 has a Ro = . .
39, largerthan the literature values of Ro c ∼ . .
20 (Newton et al.2017; Wright et al. 2018). Because horizontal systematicswithin the saturated regime have no influence on the rotation-activity fits, and only one of the stars in a sample of (cid:38) ff ecting the analysis, weconsider this systematic e ff ect in young star masses to mini-mally impact our results. Furthermore, these young stars donot appear to be outliers in our rotation-activity plots (Fig-ure 8). Although the di ff erence in Ro is small, only the re-sult for Mg ii is likely to be impacted by the mass choice forAU Mic, because of the limited target sample for that line.Correspondingly, the rotation-activity fit parameters for Mg ii have larger uncertainties.We further consider the quality of our fits by examiningthe residuals, as illustrated in Figure 10. The data residualsare consistent with being normally distributed about the bestmedian rotation-activity relation, and show no apparent de-pendence on stellar mass. There may be some hints of anexcess of data points below the median fit at large Rossbynumbers ( ∼ − . − . − . − . − . − . − . − . l og ( L NV / L b o l ) − . − . − . − . . . log Rossby ( Ro = P/τ c ) − . . . R e s i du a l s . . . Mass ( M (cid:12) ) Figure 10.
Our rotation-activity model provides a good fit acrossour entire sample for each emission line, with the results for N v shown here again as an example, but now with error ellipses shadedaccording to stellar mass. The residuals are consistent with a normaldistribution, and show no significant correlation with mass (Pearsoncoe ffi cient of − . σ L . rotation periods the single power-law may be overestimatingthe magnetic activity.With these considerations, for all of the emission lines, wedeem the broken power-law to accurately describe the ro-tation dependence of the UV activity indicators across theentire sample, with each line showing slightly di ff erent emis-sions levels in the saturated regime, consistent critical Rossbyvalues of ∼ − . − . L line / L bol ) sat in theC ii , Si iii , N v , and Si iv lines all exceed those measured byFrance et al. (2018) for an ensemble of FGKM stars, whichwere all in the range of − . −
6. In the saturated activ-ity regime, M-dwarf FUV emissions exceed that of warmerstars relative to bolometric. For the power-law decay withdecreasing rotation, all the lines except Ly α are consistentwith a slope of −
2, with Ly α corresponding to the shallow-est slope in the rotation-activity analysis. While the error baris large, because these data rely on model reconstructions ofthe emission flux, we consider if those assumptions may besystematically impacting this result.4.2. Ly α and Evolving Emission Line Ratios ineda et al . − . − . − . − . . . log Ro . . . . . . . . l og ( L L y α / L M g II ) Effective Temperature (K)
Figure 11.
The ratio of Ly α to Mg ii emission, which tracks theFUV / NUV stellar flux ratio, rises with increasing Rossby numberover the course of stellar angular momentum evolution. The shadedarea denotes the central 68% confidence region defined by combin-ing the rotation-activity fits to Ly α and Mg ii , see Section 4.2. Our Ly α reconstructions (Youngblood et al. accepted ) andthose from the literature sample (Youngblood et al. 2016),typically assume a Voigt-like profile for the emission, how-ever, there is some evidence and theory suggesting that theISM obscured Ly α profile peak may show an absorption self-reversal like that observed in other chromospheric lines (e.g.,Linsky et al. 1979; Redfield & Linsky 2002; Guinan et al.2016; Youngblood et al. 2016; Peacock et al. 2019). OurLy α reconstructions do not account for this e ff ect, and wemay thus be overestimating the Ly α flux. However, for thise ff ect to impact the fitted slope in the rotation-activity un-saturated regime, the strength of self-reversals would alsoneed to depend on the Rossby number. Theoretical Ly α lineprofiles from Peacock et al. (2019) for GJ 832, GJ 176, andGJ 436 also show strong core absorption due to non-LTE ef-fects, such that the reconstructed fluxes are greater by a factorof ∼
2. A systematic e ff ect at this level or stronger betweenactive and inactive M-dwarfs is needed to explain the shal-low Ly α slope. However, more data is required to validatewhether these theoretical profiles match those produced bynature. There is currently no evidence for such a systematicdi ff erence in Ly α core profiles between active and inactiveM-dwarfs.If typical Ly α lines only show weak self-reversals in M-dwarfs as suggested empirically by Guinan et al. (2016) andBourrier et al. (2017), then the shallow slope could indicatethe persistence of Ly α emission at slow rotation rates even asother high-energy features decay more rapidly. As the mostprominent emission lines in the FUV and NUV respectively,we consider the evolution of the ratio of Ly α to Mg ii emis-sions. We illustrate this in Figure 11, showing the emission ratio as a function of Rossy number. The shaded region de-notes the ratio of the power-law fits in the two lines fromSection 4.1 consistent with the uncertainties in the parame-ter estimates to the 1 σ level. More data are needed to bet-ter refine rotation-activity relationships in both features, butthe rise in ratio with angular momentum evolution indicatesthat the relative strengths of di ff erent portions of the high-energy spectrum changes over time. Evolutionary changesin the spectral illumination has implications for the preva-lent photochemistry and atmospheric history of any exoplan-etary systems orbiting low-mass hosts. For example, strongerFUV relative to NUV emissions may drive a build-up of pho-tochemical ozone in planetary atmospheres (e.g. Gao et al.2015; Harman et al. 2015). Although a full account of therelative contribution of Mg ii to the total NUV luminosity isnecessary for a complete description, our data suggest thatthis e ff ect may increases as stars spin-down over time. Fur-thermore, such an evolutionary e ff ect may be more prominentfor early M-dwarfs, and not as significant for late M-dwarfs(Schneider & Shkolnik 2018).4.3. Trends with Formation Temperature
Our results across all of the lines (Table 8) reveal that mostof the best fit slopes are around the canonical value of − − ff erent lines, we plotour fit parameters for η and Ro c as a function of line for-mation temperature in Figure 12. The UV lines are plotted atthe temperatures listed in Table 7, to which we also add theH α results of Newton et al. (2017) as representative of thechromosphere, and the X-ray results of Wright et al. (2011,2018) corresponding to the corona using a nominal temper-ature of 10 K, although X-ray flux contributions extend tohigher temperatures. In Figure 12, we show the mean valuerepresentative of the transition region, taking the combinedposteriors across all the lines in each parameter, yielding me-dians and central 68% confidence intervals of η = − . ± . . and Ro c = . ± . . . Our mean result is consistent to withinthe uncertainties with both the chromospheric and coronalresults in the literature.However, there may be a trend in the unsaturated rotation-activity slope as a function of formation temperature. Whilethis is largely a consequence of di ff erent values for the H α and X-ray results, our UV data fall directly in between. Asstars spin down in the unsaturated regime, the coronal X-rayemissions appear to decline rapidly with deeper atmosphericlayers showing a slower decay in their magnetic activity. TheUMES 19 . . . . . . . − . − . − . − . − . η H α , Newton et al. (2017)FUV LinesX-raysTransition Region Mean . . . . . . . log T f (K) . . . . . . . R o c Partly Convective, Wright et al. (2011)Fully Convective, Wright et al. (2018)
Figure 12.
Our new results for the transition region rotation-activityrelationships, unsaturated slope, η ( Top ), and critical Rossby num-ber, Ro c ( bottom ), enable a comparison across features probing dis-tinct regions of the stellar upper atmosphere. As activity declineswith slower rotation, the layers of the atmosphere from the chromo-sphere to the corona may respond di ff erently, see Section 4.3. onset of activity decline with slower rotation begins first inX-rays, and only after some angular momentum evolutionthe transition region and chromospheric features also beginto decline, since the best fit Ro c are greater for the deeperlayers.If these trends hold from analyses of larger UV samples,they will help reveal the role of magnetic heating processes inmediating the relationship between the internal magnetic dy-namo and the emission features. While the rotation-activityrelationships have been used to constrain stellar dynamos,this connection is indirect. The emission is necessarily aconsequence of the non-thermal magnetic heating, and if thedi ff erent layers exhibit distinct power-law slopes, then thise ff ect of the heating processes needs to be accounted for when making dynamo inferences from rotation-activity re-lationships. The trend evident in the top panel of Figure 12for the unsaturated slope suggests that whether the dominantprocess is Alfv´en wave heating or nano-flare reconnection,the decline in non-thermal heating with weaker average fieldstrengths (e.g., Shulyak et al. 2017) as stars spin down takesplace from the outer most layers inward. In other words, themagnetic heating processes persist more strongly in deeperatmospheric layers across angular momentum evolution af-fecting the relative strengths of emission features formed indi ff erent layers of the atmosphere.There are however some important caveats to the compar-isons implicit in Figure 12. Between this work and the stud-ies of Newton et al. (2017) and Wright et al. (2011, 2018), thesamples are not identical. Our work and Newton et al. (2017)use similar mixed age samples of M-dwarfs, whereas the X-ray data of Wright et al. (2018) also includes more massivestars, although normalizing by the bolometric luminosity andexamining the rotation relationship in Ro is designed to ac-count for these possible di ff erences. More significantly, aswe discuss in Appendix B, di ff erences in the Ro calibrationcan impart systematic e ff ects on the rotation-activity analy-ses. Newton et al. (2017) used the calibration of Wright et al.(2011), whereas we used that of Wright et al. (2018). Rela-tive to our work the Newton et al. (2017) results for criticalRossby number and unsaturated slope could be systemati-cally greater than if they used the same calibration. The mag-nitude of this e ff ect however can be small and depends on thestellar sample (see Appendix B). Moreover, there may havebeen issues with the analyses of Wright et al. (2011) lead-ing to a much steeper power-law slope (Reiners et al. 2014).Nevertheless, it appears that in the chromosphere η is likelyshallower than −
2, whereas in the corona it is steeper than −
2, with the transition region value from our work right in themiddle. Consistent methods and calibrations need to be ap-plied across the di ff erent wavebands to discern whether thereare indeed rotation-activity trends as a function of where inthe stellar atmosphere the emission originates.4.4. Alternatives to Rossby Number?
Potential issues with a choice of calibration can be avoidedby circumventing the Rossby number entirely. Reiners et al.(2014) argue for a more general approach in analyzing therotation-activity relationships of low-mass stars, and con-clude that the activity dependence can be well describedby a combination of rotation period and radius, specifically L X / L bol = kP − R − , where k is a scaling constant. We con-sider how this relationship may apply to our UV data. InFigure 13, we show the He ii luminosity normalized by stel-lar bolometric luminosity against the stellar P − R − . Like theRossby scaling, Figure 13 illustrates a potentially power-lawdecay in emission with a scatter of activity at a given ab-0 P ineda et al . − . − . − . − . − . . . . . log( P − R − ) (d − R − (cid:12) ) − . − . − . − . − . − . − . l og ( L H e II / L b o l ) . . . Mass ( M (cid:12) ) Figure 13.
The UV emission of our sample, traced by He ii , plottedas representative 1 σ ellipses against the rotation period and radiusprovides an alternative description for the rotation-activity relation-ship. These data show a possible mass dependence in the activity,see Section 4.4. scissa. Although our sample is much smaller, there are hintsof the mass dependence in activity using this scaling that wasillustrated by Newton et al. (2017) with H α data by whichmore massive stars preferentially lie to the right of the lo-cus of points in Figure 13. The mass dependence appears toincrease the intrinsic scatter at fixed rotation in the activitybeyond the ∼ L HeII / L bol vs. Ro .While it is evident that rotation still plays a key role inthe magnetic emission of fully convective stars, an empiricalRossby number may not be the most appropriate scaling touncover the underlying relationships governing the dynamoaction, and possible di ff erences with partly convective stars.It appears to work su ffi ciently well across the chromosphere,transition region and corona, however, by defining Ro specif-ically to minimize scatter in the rotation-activity diagramsacross this full range of stars, this procedure may be maskingreal di ff erences in the evolution of magnetic activity betweenpartly and fully convective objects (e.g., Magaudda et al.2020). If these two stellar mass regimes did indeed showdistinct rotation-activity correlations, i.e., statistically distin-guishable rotational dependencies of their activity decay, theprocess of defining an empirical Rossby number across bothsamples would be averaging together these possible di ff er-ences, since it presupposes that both samples follow the samepower-law relation. TEMPORAL EVOLUTIONIn Section 4, we used the stellar rotation period as aproxy for examining magnetic activity throughout the life-times of low-mass stars. However, using gyrochronology (e.g., Barnes 2003), we can also compare our FUV activ-ity indicators directly to stellar ages using literature relationsconnecting rotation period and age. While this practice iswell established for solar-like stars (e.g., Angus et al. 2015;Gallet & Bouvier 2015), the process is much more di ffi cultfor M-dwarfs (e.g., Guinan et al. 2016), which lack a mul-titude of targets with well determined ages. Nevertheless,Engle & Guinan (2018) have developed empirical relationsfor M0-M1 and M2.5-M6 dwarfs to estimate ages from mea-sured rotation periods. Although such gyrochronology rela-tions for M-dwarfs remain ongoing work, we use those re-sults in this paper to provide an approximate indication ofthe expected behavior across the low-mass star regime.5.1. UV Emissions Across Time
We thus show the evolution of FUV activity with age inFigure 14, focusing on the N v emission feature as represen-tative of all of the other FUV lines (Sections 3.4 and 4). Wechose the N v line for this analysis as it is tightly correlatedwith C iv , and existing literature relations allow us to also es-timate EUV emission from their measurements, see below.For the five objects with moving group membership (seeTable 2), we used the mean group age with error, and the gy-rochronology relations for the rest of the sample. To assessthe uncertainties on the ages from the gyrochronology cali-bration, we used the reported uncertainties of the parametersof the best-fit relations (Engle & Guinan 2018) and the pe-riod uncertainties as in Section 4.1, sampling each appropri-ately, assuming independently Gaussian distributed variablesin computing the distribution for the age estimate. Becausethe Engle & Guinan (2018) rotation-age relations are definedby two bins of spectral type ranges, for our sample we usedthe appropriate relation corresponding to the optical spectraltypes listed in Table 2. However, some of our objects havespectral types, M1.5-M2, between the defined ranges for therotation-age relations. For these objects we combined the es-timates from both the M0-M1 and M2.5-M6 relations to de-termine the age estimate and its uncertainty. Three of thesestars were rapid rotators without known ages: AD Leo, EVLac, and LP 247-13. Given the large uncertainty in the gy-rochronology ages, especially early on where the rotationalevolution has yet to converge, we plot these age estimates as3 σ upper limits (triangles in Figure 14).In Figure 14, we also shade the points according to their ef-fective temperature. Based on these age estimates, Figure 14illustrates how cooler, later M-dwarfs persist with strong ac- Engle & Guinan (2018) did not report a scatter about their best fit rotation-age relations, so we could not incorporate that uncertainty in these ageestimates. For the M0-M1 bin, we ignored the uncertainty on their power-law exponent, as the results are too sensitive to its value and we cannotproperly account for its correlation with the other parameters that wouldmitigate this e ff ect. UMES 21 − − Age (Gyr) − . − . − . − . − . − . l og ( L NV / L b o l ) GyrochronologyMoving Group3000 3250 3500 3750
Effective Temperature (K)
Figure 14.
The N v luminosity of our sample as a function of age il-lustrates how young M-stars exhibit saturated FUV emissions whichlast for ∼ σ ) are determined from the group agedetermination in the literature, or from the uncertainties in the gy-rochronology relations, with upper limits for the rapid rotation starages indicated as triangles, see Section 5. tivity levels for a longer duration of their early lifetimes.Considering the mean level of log( L NV / L bol ) sat ∼ − .
37 and0.33 dex scatter, some of the cooler objects may display nearsaturation level activity beyond an age of 1 Gyr. In contrast,the warmer M-dwarfs, by this age, appear to have declined intheir magnetic emissions by an order of magnitude relative tothe saturated regime. Using
GALEX photometry, Schneider& Shkolnik (2018) also found this divergence in UV evolu-tion between early and mid-M dwarfs.Because of its importance to exoplanetary atmosphericheating, we also considered what our FUV evolutionary dataimply for the extreme ultraviolet portion of the high-energyspectrum. To estimate the EUV from the FUV data, we usedthe empirical relation of France et al. (2018) between N v emission and the blue portion of the EUV passband, EUVb(90-360 Å). While not the full EUV spectrum, this is the por-tion for which available data and relatively low ISM attenua-tion have permitted any empirical estimates in the low-massstar regime. This EUVb band corresponds to about half ofthe total EUV energy from M-dwarf stars (Fontenla et al.2016; France et al. 2018). In Figure 15, we plot this EUVevolution with the same ages as discussed above, and EUVbluminosities determined from the N v emission, incorporat-ing the parameter uncertainties and 0.24 dex scatter in theFrance et al. (2018) relation. For young active M-dwarf starsthe EUV luminosity is ∼ − . relative to bolometric, withthese emissions lasting for the first several hundreds of Myrsof their lives and perhaps longer. − − Age (Gyr) − − − − − L E UV b / L b o l GyrochronologyMoving Group3000 3250 3500 3750
Effective Temperature (K)
Figure 15.
Based on available scaling relations from the FUV(France et al. 2018), we can estimate the EUVb (90-360 Å) luminos-ity of low-mass stars, similar to Figure 14. The temporal evolutionof EUV emission drops ∼ While these empirical relations for age, and di ffi cult to de-tect portions of the spectrum, like the EUV, provide gen-eral estimates for the evolution of activity and high-energyemission, Figure 15 further illustrates the broad uncertaintyinherent in using these estimates as inputs to exoplanetaryevolution modeling. Refined rotation-age relations in the M-dwarf regime, and expanded samples of stellar EUV detec-tions, from missions like ESCAPE (France et al. 2019), willgreatly expand the utility of these methods for exoplanetaryapplications.Assuming the Rossby parameterization removes a signif-icant mass dependence, we use the rotation-activity correla-tion regression fits together with the assumed rotation evolu-tion to calculate the activity evolution of early and mid M-dwarfs. In Figure 16, we plot separate curves for the evolu-tion of N v emission with stellar age, for a 0.6 M (cid:12) M-dwarf,corresponding to the M0-M1 rotational evolution, and a 0.25 M (cid:12) M-dwarf, corresponding to the M2.5-M6 rotational evo-lution. The top panel of Figure 16, shows the expected me-dian evolution for each mass star with its central 68% confi-dence level. The uncertainties are determined at a given ageby sampling the uncertainty distributions of the rotation-agerelation, the calibration between mass and convective turnover time, and the joint posterior of the rotation-activity fit.The bottom panel of Figure 10 additionally includes the scat-ter at fixed Rossby number (see Section 4), to illustrate therange of likely emission values accounting for intrinsic scat-ter in the observed population. More data are required to as-sess; however, we expect this scatter to include the e ff ects ofrotational variability, activity cycles, and possible metallicityvariations. While the nominal N v emission levels relative to2 P ineda et al . − − − L NV / L b o l Median Evolution M = 0 . M (cid:12) M = 0 . M (cid:12) − − Age (Gyr) − − − L NV / L b o l Instantaneous Emission
Figure 16.
The early and mid M-dwarf FUV temporal evolutionimplied by our rotation-activity correlation in N v , and the empiricalrotation-age relations, show possible di ff erences across time, withranges indicating the central 68% confidence interval about the me-dian. The top panel focuses on just the average evolution, and thebottom panel includes the likely range for emission accounting forthe observed scatter across the populations ( ∼ bolometric are higher for lower mass objects at the same age,there is little di ff erence in the evolution within the uncertain-ties. 5.2. Accumulated UV Evolutionary Histories
With possibly distinct UV luminosity evolution betweenearly and mid M-dwarfs, as shown in Figure 16, we calculatethe typical evolution of the UV illumination for exoplane-tary systems using the median N v rotation-activity relation(Section 4), and the age-rotation evolution from (Engle &Guinan 2018). The average evolution for individual systemsmay vary by up to a factor of two. As a measure of the illumi-nation histories, we assess how much quiescent UV energy agiven exoplanet accumulates over time as E ( t ) = (cid:90) t F UV ( τ ) d τ = (cid:90) t R ( τ ) L bol ( τ )4 π d d τ , (4)where F is the UV flux impinging on the planet at an averagedistance d from the host, and we integrate from 0 to an age t .The UV flux can be rewritten as a combination of the emis- sion ratio evolution, R ( τ ) = L y / L bol , determined from Sec-tion 4, and L bol ( τ ), which accounts for changes in bolometricluminosity with stellar evolution. In evaluating Equation 4,we use evolutionary models (Dotter et al. 2008; Feiden 2016)for the bolometric luminosity, which can evolve substantiallyat young ages (see Figure 17), and allows a self-consistentmetric across several Gyrs. We compared the accumulatedUV energies for planets around a 0.25 M (cid:12) host and a 0.60 M (cid:12) host with that of a planet around a Sun-like star.In order to compare with the lower-mass objects, the UVemission history for Sun-like stars required a di ff erent treat-ment from our approach with M-dwarfs. Using a sample ofG-dwarfs, Ribas et al. (2005) determined the EUV evolution-ary history of Sun-like stars, as a simple power-lay decaywith time across 0.1-6.7 Gyr. Since results from France et al.(2018) suggest that the N v emission and EUV of solar andlower-mass stars are related by a simple multiplicative fac-tor, we consider the Sun-like N v emission to follow the samepower-law defined by Ribas et al. (2005). We thus scaledtheir result to the Sun’s current N v luminosity from Duvvuriet al. ( accepted ) using the solar minimum quiescent Solarirradiance spectrum of Woods et al. (2009): F N v , (cid:12) = . τ − . , erg s − cm − , . < τ < . , (5)where τ is in units of Gyrs. We take the current age of theSun to be 4.6 Gyr, and this flux is evaluated at a distance of1 AU. Although the EUV bands from Ribas et al. (2005) andFrance et al. (2018) are di ff erent, this conversion allows arepresentative evolutionary history for the Sun-like N v emis-sions, which we can compare with the activity-age evolutiondetermined for M-dwarfs in Section 5.1. Since Equation 5 isonly applicable to a particular age interval, to extrapolate toyounger ages we consider the UV emissions at τ = τ < L N v / L bol = − .
75, set by themodel bolometric luminosity at τ = . τ < v emission experienced by a planet at a fixed distance of 1 AUfrom its host, for the 3 planet host cases, 0.25 M (cid:12) , 0.60 M (cid:12) ,and 1.0 M (cid:12) , starting at 1 Myr, the lower limit of the evolu-tionary models. Around the higher-mass objects the absoluteN v illumination is typically higher than around the lower-mass stars. The shaded bands in Figure 18 propagate theuncertainty in the median evolution (as in Figure 16) throughthe integral of Equation 4. We do not include the intrinsicscatter because we focus here on the cumulative average his-tory from the rotation-activity analysis. Our treatment, how-ever, excludes uncertainty from unknown systematics withUMES 23 − − − Age (Gyr) − . − . − . − . − . . . l og [ L b o l ( τ ) ] ( L (cid:12) ) M = 1 . M (cid:12) M = 0 . M (cid:12) M = 0 . M (cid:12) Non-MagneticMagnetic
Figure 17.
The bolometric luminosity evolution in the stellar mod-els used in this work to calculate the history of low-mass star UVillumination. the bolometric luminosity evolution, although at least withregards to the role of magnetism, its contribution may be mi-nor (see Figure 17). Ribas et al. (2005) did not report un-certainties for their EUV evolution in Sun-like stars, and wethus do not include it either.In Figure 19, we also show the ratios ( E . / E (cid:12) , E . / E (cid:12) ,and E . / E . ) of the accumulated UV energies, propagat-ing the uncertainty in the M-dwarf median rotational evolu-tion. The left-side axes give the result for planets at equaldistances around each star, and the right-side axes indicatethe same ratio, but for the respective habitable zones. Thisfurther assumes planets at that distance have remained therethroughout history. The right-axis curves are thus a constantmultiple of the left-axis, as in E a E b (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) HZ = (cid:82) t R a L bol , a d τ (cid:82) t R b L bol , b d τ × d , b d , a , (6)where the habitable zone distances are determined by the 5Gyr bolometric instellations. The right-side axes in Figure 19thus indicate the relative accumulated UV energies for plan-ets in the respective field age habitable zones of each star.In Figure 19, we illustrate in the low-mass star regime thatat a constant distance exoplanets orbiting higher-mass ob-jects experience a greater absolute accumulation of UV en-ergy. However, within the respective habitable zones aroundeach host the planets orbiting the lower-mass star interceptmuch more UV energy. For example, relative to the Eartharound the Sun, the same planet in the habitable zone aroundthe 0.25 M (cid:12) star will accumulate ∼
20 times more UV energyby the time it has reached field age, which is ∼ M (cid:12) star. Within the known uncertainty of the median rotational − − − Age (Gyr) E N V | d = AU ( e r g c m − ) M = 1 . M (cid:12) M = 0 . M (cid:12) M = 0 . M (cid:12) Non-MagneticMagnetic
Figure 18.
The cumulative N v energy experienced by a planetarysystem at a distance of 1 AU from its host star, according to Equa-tion 4, for each of 3 host masses, accounting for rotation-activityand bolometric luminosity evolution. For the M-dwarfs we includetwo lines each to illustrate the evolution with magnetic and non-magnetic models. The absolute high-energy fluxes at other bandscan be scaled from the N v emissions. The shaded bands indicatethe central 68% confidence interval for the median evolution of theUV emissions using non-magnetic models, the corresponding mag-netic model interval (not shown) is similar. evolution these figures can vary by factors of a couple. Thecurves of Figure 19 reflect at early times di ff erential bolomet-ric luminosity evolution modulated by activity-age evolutionat late times, with modulations of the evolution dictated bythe age at which each star begins their power-law decay ofUV activity. The bottom panel of Figure 19 also shows theresults using both magnetic (dashed line) and non-magnetic(solid line) models to illustrate that similarity of the luminos-ity evolution, and the robustness of our results to this poten-tial systematic e ff ect.These results were derived specifically using N v emis-sions; however, the line is broadly representative of the entireFUV band given the strong correlations between emissionlines (Section 3.4). Thus, although the absolute energy levelsdetermined from Equation 4, and shown in Figure 18, willvary between choice of UV feature, the ratios of Figure 19are broadly representative of total FUV emissions. Moreover,to the extent that the N v emission is directly proportional toEUV emissions (France et al. 2018), the ratios of Figure 19translate exactly to the relative exposure of planets to EUVemissions around each stellar host. This is a key result giventhe importance of EUV fluxes for exoplanetary atmosphericheating and escape.In Figure 20, we further show the importance of di ff er-ent epochs in the total accumulated UV exposure for exo-planetary systems. Relative to the cumulative quiescent UV4 P ineda et al . . . . . . . . . E . / E (cid:12) | d = c o n s t . . . . . . . E . / E (cid:12) | d = c o n s t − − − Age (Gyr) . . . . . . . . E . / E . | d = c o n s t Non-MagneticMagnetic E . / E . | H Z . . . . . . . . E . / E (cid:12) | H Z E . / E (cid:12) | H Z Figure 19.
A ratio comparison of the accumulated UV energiesover evolutionary history impacting planets orbiting stars of 0.25,0.60 and 1.0 M (cid:12) , following Equation 4. The left-side axes corre-spond to planets at equal distances around the respective hosts, andthe right-side axes correspond to planet distances at which the 5 Gyrbolometric instellations are equivalent, i.e., comparing the field-agehabitable zones around each host. Top - Early-M dwarf relative toSun-like star, middle - mid-M dwarf relative to Sun-like star, and
Bottom - mid-M dwarf relative to early-M dwarf, using both mag-netic (dashed) and non-magnetic (solid) models for the stellar lumi-nosity evolution, see Section 5.2. In each case, the more massivehosts deliver more UV energy to planets at the same distance, butwithin their respective habitable zones, planets orbiting the lower-mass star experience greater levels of UV emission. The shadedregions of each panel indicate the central 68% confidence regionaccounting for the known uncertainty in the median rotational evo-lution of FUV emissions. − − − Age (Gyr) . . . . . . E / E t = G y r M = 1 . M (cid:12) M = 0 . M (cid:12) M = 0 . M (cid:12) Figure 20.
The UV energy accumulation (see Equation 4) as a func-tion of time (as in Figure 18) relative to the total at t = energy experienced at an age of 5 Gyrs, for planets aroundlow-mass hosts, they reach total energetic exposures exceed-ing ∼
50% by ages of 800, 600, and 250 Myr respectively forhosts of mass 0.25, 0.60, and 1.0 M (cid:12) . These results quantifythe importance of the first Gyr of stellar lifetimes in their to-tal energetic input to exoplanetary systems. These early agesclearly need to be taken into account when considering theevolutionary history of planetary systems, and their responseto high-energy emissions. CONCLUSIONSThe UV data of the FUMES sample presented in this papercombined with the literature data has allowed us to examinehow the far ultraviolet spectroscopic emissions of low-massstars change with angular momentum evolution over time. Atfast rotation rates (Rossby number, Ro (cid:46) . (cid:46)
1) Gyr, the FUV lines exhibit satu-rated emissions at levels of 10 − . -10 − . relative to the stellarbolometric luminosity, depending on the specific line, withLy α being the strongest feature. As the stars spin-down withage, these emission levels drop by ∼ α , which will change the spectroscopic balance ofenergy output (i.e., FUV / NUV ratio) between young and oldM-dwarfs. This evolutionary behavior is evident throughoutthe M-dwarf sample for both early and mid-to-late M-dwarfs.Because these stars show similar FUV luminosities relativeto bolometric, the early M-dwarfs are more UV luminous inabsolute terms, but with potentially di ff erent spin-down be-haviors, the cooler stars may emit at the saturation levels forUMES 25a greater duration of their early lifetimes. This evolutionarybehavior may have several implications across stellar astro-physics and exoplanetary science.6.1. Stellar Atmospheres and Dynamos
The FUV emission lines directly probe the transition re-gion of the stellar coronal atmosphere. Our spectroscopicdata showed how the di ff erent features change with rotation,directly implying how the atmospheric structure changesacross time, between active and inactive low-mass stars.These data can thus be used to directly assess those changesthrough stellar chromospheric and coronal models (e.g.,Fontenla et al. 2016; Peacock et al. 2019). The comparisonof the rotation-activity relationships across H α , the FUV, andX-rays, however, suggests more significant changes in thecorona with spin-down relative to the changes in the deeperlayers of the atmosphere. These di ff erences must be a di-rect consequence of how the non-thermal heating processeschange with rotation rate. Models of the magnetic heatingprocess itself in M-dwarfs must be able to account for theseevolutionary e ff ects, and their significance at di ff erent layersof the atmosphere.This aspect of non-thermal chromospheric / coronal heatingis an important consideration in making dynamo inferences,because the observed rotation-activity relationships in di ff er-ent wavebands, often used for this endeavor, are mediatedby the magnetic heating, and are not directly defined by thedynamo processes. The multi-wavelength rotation-activityrelationships need to be reconciled with more homogeneousmethodologies, including the possibly di ff erent behaviors indi ff erent upper atmospheric layers in order to provide defini-tive conclusions with respect to dynamo theory. Crucially,while our analysis shows that a Rossby scaling works well fornormalizing the rotation-activity relationships in both partlyand fully convective M-dwarfs, the empirical scaling maybe masking real di ff erences in these populations. This ef-fect is potentially evident in alternative scalings, however,larger samples are required to examine these di ff erences inthe UV, to compare with other wavebands (e.g., Magauddaet al. 2020). 6.2. Exoplanets
The stellar high-energy spectrum largely defines the preva-lent photochemistry and mass-loss history of exoplanetarysystems. While these e ff ects have often been investigatedin the context of individual nearby planets around low-massstars, the present day observations of the planetary atmo-sphere have been shaped by the cumulative history of thesestellar emissions. Our spectroscopic FUV data provide its ro-tational evolution for M-dwarfs directly, which can be trans-formed using rotation-age gyrochronology relationships. Al-though the latter remain uncertain for M-dwarfs, their im- provement will greatly improve our assessments of this evo-lutionary history. Employing literature scaling relations us-ing FUV emission features then enables estimates across thehigh-energy spectrum, including the EUV (e.g., France et al.2016, 2018). To understand exoplanetary atmospheres thisstellar emission history needs to be taken into account.Of particular importance is the likely di ff erence betweenearly and mid-to-late M-dwarfs, with regard to how long theypersist in exhibiting near saturation level activity. By oldfield ages, planets in similar orbits around these two di ff erentkinds of hosts will have experienced likely di ff erent historiesin high-energy radiative environments (e.g., Luger & Barnes2015). Moreover, changes in the relative significance of FUVor NUV emissions over time will influence the prevalent ex-oplanetary atmospheric molecules that are observable today.Our results enable a way to account for these e ff ects acrossdi ff erent emission features and wavebands when consideringnew exoplanetary systems.Using our rotation-activity correlation fits (Section 4), as-suming no residual mass dependence, we can predict themost prominent FUV emission features in quiescence froma known rotation period and mass to generally within 0.3dex of intrinsic scatter. This scatter pertains to the samplepopulation and is likely a consequence of the combined ef-fects of activity cycles, rotation variations in visible activeregions, metallicity di ff erences, and / or the stochastic natureof magnetic heating. As an example, we imagine a 0.4 M (cid:12) star with 60 d rotation period, with 3% uncertainty on themass and 5% in the rotation period. Accounting for scatterin the Rossby number calibration and our best fit parameters,our rotation-activity correlations would predict a mean valueof log( L CIV / L bol ) = − . ± .
16. With improved rotation-age relations, our data will enable a more comprehensive as-sessment of the high-energy radiative input to exoplanetarysystems across time. SUMMARYIn this paper, we have examined the far ultraviolet emissionof M-dwarf stars, as probes of the stellar upper atmosphereand non-thermal magnetic heating, their rotational evolu-tion, and possible implications for planetary systems orbitingthese kinds of hosts. Additional FUMES papers will discussthe Ly α reconstructions (Youngblood et. al. accepted ), andtime variability in the UV / optical emissions (Duvvuri et al. in prep ). For this work, our primary findings are summarizedbelow. • We reported emission line-emission line correlationsacross ∼ iv emissions, revealing ∼ ineda et al .one another across the M-dwarf population, see Sec-tion 3.4. • We provided rotation-activity correlations as a func-tion of Rossby number across 8 UV features, includingLy α , with typical power-law slopes of − • The decay of Ly α emission with rotation is likelyweaker than it is for other FUV features, implying evo-lutionary changes in the relative balance of UV spec-troscopic emissions, see Section 4.2. • A possible trend in the rotation-activity correlationsas a function of atmospheric layer points to the im-portance of disentangling magnetic heating e ff ectsthrough the stellar atmosphere when investigating thedynamo dependence on rotation rate, see Section 4.3. • We demonstrated systematic e ff ects in the resultingfit parameters for rotation-activity correlations (power-law slope, critical Rossby number) when utilizing dif-ferent empirical calibrations for the convective turnover time as a function of mass, see Appendix B. • Mid-to-late M-dwarfs may exhibit saturation levelFUV activity for a longer duration of their early life-times relative to early M-dwarfs, with correspond-ingly distinct histories of high-energy emission im-pacting exoplanetary systems around these hosts, seeSection 5. • Planets in the habitable zones around mid-to-late M-dwarfs, at field ages, will have accumulated ∼ × moreEUV exposure than planets around early M-dwarfs,and 20 × more exposure than planets in the habitablezones around Sun-like stars, see Section 5.2. • For planets orbiting low-mass stars, the majority of en-ergetic UV exposure accumulated by the age of 5 Gyrswas experienced during the saturated phase of activityevolution, lasting ∼ Facility:
HST (STIS), Blanco (ARCoIRIS), APO(TSPEC) APPENDIXA.
Concerning the Use of Surface Fluxes
In Section 3.4, we correlated FUV line flux measure-ments, illustrating tight relationships between di ff erent emis-sion features probing distinct temperatures of the transitionregion. In the literature these kinds of correlations have beenexpressed similarly, but instead of luminosity, they have beenexpressed using the surface flux, normalizing the luminosi-ties by the stellar surface area (e.g., Wood et al. 2005; Young-blood et al. 2017). While this attempts to normalize the emis-sions accounting for the area of the emitting region to enablecomparisons across di ff erent kinds of stars, the inclusion ofthe radii introduces additional uncertainty and increases theerror correlations, as the radius uncertainty will dominate theerror budget relative to the parallax and flux measurements. In Figure 21, we illustrate this e ff ect using the same data forC iv and Si iv that comprise the upper right most panel of Fig-ure 5, but transforming the emission measurements to sur-face flux with the radius determinations from Table 2. Therepresentative 2 σ error ellipses now are all highly inclined,revealing the strong correlations between the uncertainties ineach quantity.The power-law slope estimated in such line-line correla-tions using the surface flux should be identical to the lumi-nosity approach used in this work, however, the uncertaintieson such estimates do not accurately reflect the nature of theunderlying data if they do not account for this correlated er-ror, and are less precisely constrained when accounting forthe actual radii uncertainty in the analysis. This additionaluncertainty may obscure intrinsic scatter in the analyzed cor-relations. We therefore recommend luminosity as a currently This e ff ect was less significant in the past when parallaxes were not knownas precisely (pre- Gaia ). UMES 27 . . . . . . . C IV log F (erg s − cm − ) . . . . . . . S i I V l og F ( e r g s − c m − ) FUMESLiterature E ff ec t i v e T e m p e r a t u r e ( K ) Figure 21.
The measured emission strengths of C iv and Si iv as inFigures 5 and 5, but shown as surface flux instead of luminosity uti-lizing our radius determinations from Table 2. Line-line regressionanalyzes not accounting for correlated uncertainties, as shown hereby slanted ellipses, will yield biased results, see Appendix A. more robust choice when defining predictive relations be-tween stellar emission features. However, whenever surfacefluxes are necessary, a careful accounting of possibly corre-lations should be included.B. Systematics with the Convective Turnover Time
In Section 4, we analyzed the rotation-activity relation ofM-dwarfs in FUV emission lines with the FUMES and liter-ature samples. We used the empirical calibration of Wrightet al. (2018) to estimate the convective turn over time fromthe stellar mass in computing the Rossby number, Ro = P /τ c ,for each star. This empirical calibration is based on mini-mizing the scatter in the X-ray rotation-activity correlation oflow-mass stars. Wright et al. (2011) details the typical pro-cedures used in developing this kind of empirical calibration.Since the Ro is generally closely related to the internal dy-namo action (although see Reiners et al. 2014), the use of thiskind of calibration enables a dynamo comparison amongststars with convective interiors, from F to M stars. However,changes in the kind of magnetic dynamo that generates fieldin fully convective stars, for example α instead of α - Ω (e.g.,Browning 2008), suggest that there is no physical reason asingle such calibration should work across that full range.Moreover, with relatively deeper convective zones, a singlerepresentative value for the time scale of convective motionsis likely an increasingly poor approximation with decreasingstellar mass. Accordingly, although the empirical calibrationreduces the X-ray rotation-activity scatter, it may not be rep-resentative of the dynamo behavior in the fully convectiveregime. . . . . . . . . Mass ( M (cid:12) ) τ c ( d ) Wright et al. (2011)N´u˜nez et al. (2015)Wright et al. (2018)
Figure 22. Di ff erent calibrations for the convective turn overtime as a function of mass yield systematic di ff erences in rotation-activity analyses when used to compute a characteristic Rossbynumber, Ro , see Appendix B. Nevertheless, using these relations provides a means tocompare to literature results and test how the X-ray calibratedrelation applies to the activity at other wavelengths, as wehave done in Section 4. As detailed in this Appendix, we fur-ther investigated how those results are impacted by the choiceof empirical calibration for the convective turnover time as afunction of stellar mass. In Figure 22, we plot three such lit-erature calibrations from Wright et al. (2011), N´u˜nez et al.(2015), and Wright et al. (2018), including the scatter aboutthose relationships, reported in those works, or obtained viaprivate communication (0.064 dex, Nu˜nez, A.). The N´u˜nezet al. (2015) calibration uses the same data as Wright et al.(2011), but assumes the canonical value for the best fit slope( −
2) instead of the best fit value from Wright et al. (2011),and the Wright et al. (2018) calibration, which sits in be-tween the other two, updates the Wright et al. (2011) resultwith more fully convective stars and a slightly di ff erent func-tional form.We re-fit the rotation-activity data presented in Section 4,using the same methods, but using the two additional liter-ature calibrations to determine their impact on the best fitparameters. These results are shown in Table 9 for the crit-ical Rossby number, Ro c , and in Table 10 for the slope ofthe unsaturated regime, η . The e ff ect of the di ff erent cali-brations is most readily illustrated by comparing the resultsusing Wright et al. (2011) vs. N´u˜nez et al. (2015), as theyhave a greater separation in τ c - M space (see Figure 22).The N´u˜nez et al. (2015) calibration gives higher convectiveturnover times at a given mass than Wright et al. (2011).Consequently, the best fit Ro c is systematically smaller us-ing N´u˜nez et al. (2015) than it is when using the Wrightet al. (2011) calibration — higher τ c corresponds to smaller8 P ineda et al . Table 9.
Critical Rossby Systematics: Ro c a Line Wright et al. (2011) N´u˜nez et al. (2015) Wright et al. (2018)Ly α . ± . . . ± . . . ± . . Mg ii . ± . . . ± . . . ± . . C ii . ± . . . ± . . . ± . . Si iii . ± .
08 0 . ± . . ± . He ii . ± .
06 0 . ± . . . ± . Si iv . ± .
08 0 . ± . . ± . C iv . ± .
08 0 . ± . . ± . . N v . ± .
09 0 . ± . . ± . a Reported parameters correspond to the median of the marginalized poste-rior distribution with uncertainties indicating the central 68% confidenceinterval. The reference for each column indicates the source used for thecalibration of the mass dependent convective turn over time.
Table 10.
Unsaturated Slope Systematics: η a Line Wright et al. (2011) N´u˜nez et al. (2015) Wright et al. (2018)Ly α − . ± . . − . ± . . − . ± . . Mg ii − . ± . . − . ± . . − . ± . . C ii − . ± . . − . ± . . − . ± . . Si iii − . ± . . − . ± . . − . ± . . He ii − . ± . . − . ± . . − . ± . . Si iv − . ± . . − . ± . . − . ± . . C iv − . ± . . − . ± . . − . ± . . N v − . ± . . − . ± . . − . ± . . a Reported parameters correspond to the median of the marginalized poste-rior distribution with uncertainties indicating the central 68% confidenceinterval. The reference for each column indicates the source used for thecalibration of the mass dependent convective turn over time. Ro . Between the two calibrations as applied to our data, thisyielded a systematic o ff set of ∼ Ro c , see Table 9.This e ff ect on the best fit critical Rossby number is rel-atively intuitive given the direct impact on the convectiveturnover time between calibration choices. However, we alsoobserve a systematic di ff erence in the best fit slope fromthe rotation-activity analysis when changing between empir- ical calibrations. With our data, larger assumed convectivetime scales (smaller Ro ) yielded systematically steeper slopes(more negative) for the unsaturated regime, see Table 10. Al-though small, this e ff ect is generally evident across the eightdi ff erent lines we analyzed. To illustrate this systematic ef-fect, we show representative ellipses for the joint posteriordistributions of Ro c - η across 4 FUV lines in Figure 23. Theerror ellipses for each individual line shift to the left (smaller Ro c ), and down (steeper η ) when changing calibrations fromWright et al. (2011) to N´u˜nez et al. (2015). Because thesefit parameters are correlated, it is perhaps unsurprising thatsystematic e ff ects would appear in both Ro c and η , however,the systematic shift is not in the same direction, as the criticalRossby number and slope posteriors are anti-correlated, notcorrelated.We attribute this systematic e ff ect to the non-linearity ofthe calibrations as applied to individual samples. If thechoice of empirical calibration scaled the assumed Rossbynumbers of all of the stars in the same way, we could ex-pect the best fit slope of the unsaturated regime to remainconstant. A comparison of the calibrations for τ c ( M ) (seeFigure 22), shows that this is generally not the case. Thus,depending on the sample of stars, some objects shift in Ro space more than others. A large number of fully convectivestars in the sample would likely increase the magnitude ofthis systematic e ff ect on the best-fit slopes between the cal-ibrations of Wright et al. (2011) and N´u˜nez et al. (2015), asthat is where those functions largely diverge. It is thereforedi ffi cult to estimate the extent of this systematic e ff ect on theslopes without doing the entirety of the analysis with multi-ple calibrations for τ c for each sample of stars. This makescomparisons somewhat more di ffi cult across the literature asmethods have been updated and evolved over time, with dif-ferent stellar samples. Future comparisons across wavebandsand samples will greatly benefit from homogeneous analysismethodologies. The framework presented in this paper forthe rotation-activity work (Section 4), accounts for knownuncertainties across all available data, possible correlations,and includes a measure of the intrinsic scatter within the re-gression fit. The presence of these systematics e ff ects, espe-cially when using a quantity as uncertain as the convectiveturnover time scale, also supports the argument in favor offinding simpler descriptions that capture the relevant physicsfor characterizing the dependence of activity on stellar phys-ical and rotational properties, as discussed in Reiners et al.(2014). We tested some of those methods in Section 4.4.REFERENCES Alonso-Floriano, F. J., Morales, J. C., Caballero, J. A., et al. 2015,A&A, 577, A128, doi: 10.1051 / / / mnras / stv423 UMES 29 .
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