The Mega-MUSCLES Spectral Energy Distribution Of TRAPPIST-1
David J. Wilson, Cynthia S. Froning, Girish M. Duvvuri, Kevin France, Allison Youngblood, P. Christian Schneider, Zachory Berta-Thompson, Alexander Brown, Andrea P. Buccino, Suzanne Hawley, Jonathan Irwin, Lisa Kaltenegger, Adam Kowalski, Jeffrey Linsky, R. O. Parke Loyd, Yamila Miguel, J. Sebastian Pineda, Seth Redfield, Aki Roberge, Sarah Rugheimer, Feng Tian, Mariela Vieytes
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Draft version February 24, 2021
Typeset using L A TEX default style in AASTeX62
The Mega-MUSCLES Spectral Energy Distribution Of TRAPPIST-1
David J. Wilson, Cynthia S. Froning, Girish M. Duvvuri, Kevin France,
2, 3
Allison Youngblood,
4, 3
P. Christian Schneider, Zachory Berta-Thompson, Alexander Brown, Andrea P. Buccino, Suzanne Hawley, Jonathan Irwin, Lisa Kaltenegger, Adam Kowalski,
2, 3, 10
Jeffrey Linsky, R. O. Parke Loyd, Yamila Miguel, J. Sebastian Pineda, Seth Redfield, Aki Roberge, Sarah Rugheimer, Feng Tian, and Mariela Vieytes McDonald Observatory, University of Texas at Austin, Austin, TX 78712 Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA Laboratory for Atmospheric and Space Physics, University of Colorado, 600 UCB, Boulder, CO 80309 Goddard Space Flight Center, Greenbelt, MD 20771 Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg Dpto. de F´ısica, Facultad de Ciencias Exactas y Naturales (FCEN), Universidad de Buenos Aires (UBA), Buenos Aires, Argentina Astronomy Department, University of Washington, Seattle, WA 98195, USA Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, US Astronomy Department, Cornell University, Ithaca, NY 14853, USA National Solar Observatory, University of Colorado at Boulder, 3665 Discovery Drive, Boulder, CO 80303 JILA, University of Colorado and NIST, Boulder, CO 80309-0440 USA School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287 Leiden Observatory, P.O. Box 9500, 2300 RA Leiden, The Netherlands Wesleyan University, Department of Astronomy and Van Vleck Observatory, 96 Foss Hill Dr., Middletown, CT 06459, USA University of Oxford, Clarendon Laboratory, AOPP, Sherrington Road, Oxford, OX1 3PU, UK State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau, China Instituto de Astronom´ıa y F´ısica del Espacio (CONICET-UBA), Buenos Aires, Argentina. (Received Nov, 2019; Revised Nov, 2019; Accepted February 24, 2021)
Submitted to ApJABSTRACTWe present a 5 ˚A–100 µ m Spectral Energy Distribution (SED) of the ultracool dwarf star TRAPPIST-1, obtained as part of the Mega-MUSCLES Treasury Survey. The SED combines ultraviolet andblue-optical spectroscopy obtained with the Hubble Space Telescope , X-ray spectroscopy obtained with
XMM-Newton , and models of the stellar photosphere, chromosphere, transition region and corona. Anew Differential Emission Measure model of the unobserved extreme-ultraviolet spectrum is provided,improving on the Lyman α –EUV relations often used to estimate the 100–911 ˚A flux from low-massstars. We describe the observations and models used, as well as the recipe for combining them into anSED. We also provide a semi-empirical, noise-free model of the stellar ultraviolet spectrum based onour observations for use in atmospheric modelling of the TRAPPIST-1 planets. INTRODUCTIONAmong the thousands of planetary systems that have been discovered over the past two and a half decades,TRAPPIST-1 is a standout case. Discovered by the TRansiting Planets and PlanestIsimals Small Telescope(TRAPPIST) survey in 2015 (Gillon et al. 2016), the system is comprised of an M8 ultracool dwarf star orbitedby seven planets, all of which have similar masses and radii to Earth and Venus (Gillon et al. 2017; Wang et al.2017). The planets are almost exactly coplanar, have orbital periods ranging between 1.5 and 18.8 days, and are
Corresponding author: David J. Wilsondjwilson394gmail.com a r X i v : . [ a s t r o - ph . S R ] F e b Wilson et al. Wavelength ( ˚A)0 . . . . . F l ux ( e r g s − c m − ˚ A − ) × − XMM APEC DEM HST PHOENIX
Figure 1.
SED of TRAPPIST-1 with all data and models at native resolutions. The sources for each section of the spectrumare labeled above it. all in an orbital resonance with at least one other planet (Luger et al. 2017). At a distance of 12 . ± .
02 pc and r mag = 17 . ± .
01 (Chambers et al. 2016), the system presents a challenging but achievable target for transit spec-troscopy observations of the planets, both now with the Hubble Space Telescope (HST) (de Wit et al. 2016) and in thefuture with JWST (Barstow & Irwin 2016; Morley et al. 2017). Three or four of the planets orbit at distances wherethe energy received from the star is such that liquid water might persist on their surfaces. The TRAPPIST-1 systemtherefore offers opportunities for comparative planetology to test models of planetary habitability, biosignatures andeven, given the small orbital separations between the planets, transfer of material and/or life between the planets(Veras et al. 2018).A complete evaluation of the potential habitability of the TRAPPIST-1 planets requires comprehensive knowledge ofthe parent star. This has proven challenging, with uncertainties remaining over, for example, the star’s age (Burgasser& Mamajek 2017; Gonzales et al. 2019), activity (Vida et al. 2017), and rotation period (Roettenbacher & Kane 2017).Of particular importance, given the close proximity of the planets to the star, is the stellar magnetic activity and theresulting X-ray and ultraviolet emission. High-energy radiation can influence the retention and chemistry of planetaryatmospheres as well as surface survival conditions (Rugheimer et al. 2015; Miguel et al. 2015; O’Malley-James &Kaltenegger 2017). However, TRAPPIST-1 is extremely faint at short wavelengths, making detailed characterisationof the high-energy environment in the system challenging. Wheatley et al. (2017) observed TRAPPIST-1 with
XMM-Newton ( XMM ), finding variable X-ray luminosity with intensity similar to the modern quiescent Sun. Because oftheir proximity to the host stars, the planets would therefore experience XUV intensities much higher than the Earth,sufficient to significantly alter their atmospheres and strip away hydrogen from water in their atmospheres and (ifpresent) oceans (Ribas et al. 2016; Airapetian et al. 2017). Bourrier et al. (2017a,b) obtained time series observationsof the 1215.67˚A Lyman α hydrogen emission line with HST , finding that it evolved over a three-month timescale butwith no evidence for hydrogen (and thus water) escape from TRAPPIST-1c, which transited during their observations.Peacock et al. (2019) used the PHOENIX stellar atmosphere code to model the chromosphere and transition regionof TRAPPIST-1, scaling it to the Bourrier et al. (2017a) Lyman α measurement and to distance-adjusted GALEX observations of stars with a similar spectral type. They found that the flux emitted between 100–912 ˚A varies by anorder of magnitude depending on which calibrator was used. These studies demonstrate that accurately accounting forthe effects of high-energy radiation on the TRAPPIST-1 planets requires spectroscopic observations at all accessiblewavelengths. igh-energy SED of TRAPPIST-1 Table 1.
Summary of observations from. Dataset numbers are given for retrieval from MAST (https://archive.stsci.edu/hst/)or the XMM-Newton Science Archive (http://nxsa.esac.esa.int/nxsa-web/
HST
XMM
Mega-MUSCLES (Measurements of the Ultraviolet Spectral Characteristics of Low-Mass Exoplanetary Systems) isan
HST
Treasury program obtaining 5 ˚A–100 µ m spectral energy distributions (SEDs) of a representative sample of12 M dwarfs, covering a wide range of stellar mass, age, and planetary system architecture and extending the original11-star MUSCLES program (France et al. 2016; Youngblood et al. 2016; Loyd et al. 2016) to stars with lower masses,higher activity and/or faster rotation rates. Here we present the Mega-MUSCLES SED of TRAPPIST-1 (Figure 1),comprised of ultraviolet and X-ray spectroscopy with HST and
XMM , along with state-of-the-art model spectra. Wediscuss the changes made to the data processing and stellar emission modelling implemented for Mega-MUSCLEScompared with MUSCLES, present a semi-empirical model for use in model atmosphere simulations, and compare theobserved SED to the Peacock et al. (2019) models. OBSERVATIONSWe observed TRAPPIST-1 with the Cosmic Origins Spectrograph (COS, Green et al. 2012) and the Space TelescopeImaging Spectrograph (STIS, Woodgate et al. 1998) onboard the
Hubble Space Telescope ( HST ) on 2017 December 15,2018 December 08–12 and 2019 June–08, for a total exposure time of 36379 s. The COS gratings used were G160M(8608 s), G130M (12404 s) and G230L (2731 s), and the STIS gratings were G430L (1795 s) and G140M (10841 s).Combined, these spectra cover the wavelength range 1130–5700 ˚A except for a gap between 2080–2790 ˚A which is notcovered by the COS NUV detector and is too faint for STIS NUV observations. The HST observations are summarisedin Table 1. With the exception of the STIS/G430L exposure, the observations were obtained using photon-countingdetectors in TIME-TAG mode. We extracted light curves from each spectrum to search for and potentially removecontributions from flares or other stellar activity, but found no significant variation.For the COS G160M and G130M observations, variations in target position in the aperture between each orbitinduce slight differences in wavelength calibration. To remove this effect we cross-correlated known emission lines ineach x1d spectrum to shift each spectrum onto a single wavelength scale before coadding. Doing so provides a smallincrease in S/N and resolution compared with the x1dsum files produced by the
CalCOS pipeline.Four spectra were obtained with the STIS G140M grating, covering the Lyman α hydrogen line with a spectral rangeof 1195–1249 ˚A and R ∼ stistools x1d routine, fixing the “a2center” keyword to the identified spectrum position. In one spectrum the trace could not bevisually identified. Lyman α line fluxes in the spectra obtained immediately before and after the non-detection weresimilar, so the non-detection is unlikely to be due to intrinsic variability and probably an instrumental effect such asinaccurate slit positioning. The non-detection was therefore discarded, and the remaining three spectra coadded intothe final G140M spectrum used hereafter.TRAPPIST-1 has been observed multiple additional times with the STIS G140M grating both prior to and sinceour observations (Bourrier et al. 2017a,b). We initially intended to combine all of the available spectra, but we found Wilson et al. . . . C oun t s ( s − )
20 30 40 50Wavelength ( ˚A)0 . . . . C oun t s ( s − c m − ˚ A − ) × − − − − F l ux ( e r g s − c m − ˚ A − ) APEC modelFlux w/o RMF correctionCorrected Flux
Figure 2.
Top: X-ray light curve of TRAPPIST-1 observed on 2018 December 10. Middle:
XMM spectrum of TRAPPIST-1(blue) compared with the APEC model (orange). The model has been binned into the same bins as the spectrum. Bottom:Full APEC model used to correct the x-ray spectrum and provide the 50–120 ˚A range of the SED, along with the raw andRMF-corrected flux conversions described in the text. the detected Lyman α flux to be variable, with the final coadded spectrum highly dependent on which subspectra werechosen for inclusion. Epoch-to-epoch changes are somewhat beyond the scope of this paper and we do not wish topreempt the teams leading the ongoing G140M observations, so we decided to use only the data obtained as part of theMega-MUSCLES program. This has the advantage of ensuring that all of the data in the SED is contemporaneous,at the cost of improved S/N for the Lyman α measurement. We will reevaluate this decision when a full analysis ofthe G140M data is available and update the Mega-MUSCLES High-Level Science Products accordingly.We further observed TRAPPIST-1 with XMM-Newton ( XMM ) using the EPIC instrument with thin filters for 23 kson 2018 December 10, overlapping in time with the COS G130M observations. TRAPPIST-1 was detected with anaverage count rate of 3 counts ks − , less than the average count rate of ≈ −
20 counts ks − found by Wheatleyet al. (2017). Analysis of all available archival data suggested that the Wheatley et al. (2017) result was dominatedby a strong flare(s), thus we take our observation to represent the “typical” or quiescent X-ray flux. SED igh-energy SED of TRAPPIST-1 µ m.3.1. Variability
Late-type M dwarfs are notably active stars, with regular flares and high photometric variability (Paudel et al. 2018).Even stars that appear photometrically quiet in optical surveys have been shown to be active in the ultraviolet (Loydet al. 2018; France et al. 2020). Vida et al. (2017) identified 42 white-light flaring events in the K2 light curve ofTRAPPIST-1, approximately 0.5 d − , although Gillon et al. (2017) only detected two flares in 20 days of infrared Spitzer observations taken at a different epoch, indicating that the flare rate is time and/or wavelength dependent.We must therefore consider activity when assessing the validity of the SED presented here. We detected no flares inany of our ultraviolet and x-ray observations and thus consider the SED to represent TRAPPIST-1 in a “quiescent”,non-flaring state. Flares have been detected in previous x-ray observations by Wheatley et al. (2017), and potentiallyin broadband NUV
Swift photometry by Becker et al. (2020). Determining how representative the ultraviolet spectrapresented here are of the the time-averaged emission of TRAPPIST-1 will require sustained monitoring at multiplewavelengths, a significant challenge considering the limitations of current ultraviolet observatories. Therefore, althoughwe are confident that the Mega-MUSCLES SED is an accurate measurement of the quiescent emission of TRAPPIST-1, efforts to model the atmospheres of the TRAPPIST-1 planets should acknowledge that we have poor constraints onhow that emission changes during a flare, and how often such flares occur.3.2.
X-ray
The
XMM spectrum was fit using the
XSPEC v12.10 package (Arnaud 1996) with models generated using theAstrophysical Plasma Emission Code v3.0.9 (APEC, Smith et al. 2001; Foster et al. 2012), with the data binnedin variable energy bin widths such that each bin contained the same number of counts. The data were fit using atwo-temperature model ( k T = 0.2, 0.4) and a metallicity of 0.4 Solar. Due to the low number of photons, the only freeparameters used were the normalisation of the two temperature components. We used the standard
XSPEC backgroundsubtractions, although we found that ignoring the background changed the derived flux by less than 0.1 dex.Ordinarily, the data could be converted from counts N into physical units F by dividing by the the effective area A of the instrument as a function of energy E , i.e.: F ( E ) ∝ N ( E ) A ( e ) T exp (1)However, for cool spectra such as TRAPPIST-1, issues arise at the low energy boundary (0 . F ( E ) ∝ N ( E ) A ( e ) T exp C ( E ) (2)Where the correction C captures the asymmetry of the spectrum and the RMF. For a symmetric RMF and a flatspectrum, C ( E ) would be 1.0. Consider a spectrum consisting of single emission line at 0.3 keV and low energy cutofffor the spectrum of 0.2 keV: The recorded photon rate will be lower than expected, because a sizable fraction of thephotons will have reconstructed energies below 0.2 keV and will thus be missing from the spectrum. This is not aneffective area but an RMF effect. In fact, the shape of the XMM-Newton RMF at low energies (0.1–0.3 keV) is suchthat more photons will be detected below their nominal energy than above, so that even for a flat spectrum, one wouldneed to correct for the RMF effect. In essence, this procedure ensures that the corrected spectrum reproduces themodel flux, which would not be the case when using Equation 1. However, we caution that this “corrected” spectrum Wilson et al. still includes RMF effects and is meant for illustrative purposes in physical units while the best-fit model spectrumcaptures the emitted spectrum much better.3.3.
Extreme-Ultraviolet and DEM modelling
The most significant departure from the MUSCLES procedure is in the Extreme-Ultraviolet (EUV), where we havereplaced the Linsky et al. (2014) empirical scaling relations with a Differential Emission Measurement (DEM) model,which estimates the chromospheric, transition region and coronal emission based on the strength of the detectedlines in the FUV spectrum and the X-ray flux. A model spectrum is required as the region spanning 120–1100 ˚A isunobservable, both physically due to absorption from interstellar hydrogen between 400-900 ˚A, and a lack of currentlyoperating instruments that can observe the ranges 120–400 ˚A and 900–1100 ˚A (
HST /COS and
Chandra do have somemodes that extend down to 900 ˚A and up to 175 ˚A respectively, but these were not sensitive enough to be practical forthis program). The DEM model is described in detail in Section 5.3.4.
Far- and Near- Ultraviolet
Lyman α reconstruction The H I α line is clearly visible in our coadded STIS G140M spectrum, but is heavily affectedby both interstellar absorption and terrestrial airglow. We reconstructed the full Lyman α profile with a techniquederived from Youngblood et al. (2016), where we simultaneously fit a model of the interstellar absorption and a modelof the intrinsic stellar emission with a Markov Chain Monte Carlo method ( emcee ; Foreman-Mackey et al. 2013).In order to benefit from the increased S/N offered by spectra taken before the Mega-MUSCLES observation whilesimultaneously accounting for possible intrinsic stellar variability, we fit both the new Mega-MUSCLES observationand the observation from Bourrier et al. (2017a) simultaneously. We use a Voigt profile for the stellar emission aswell as for the ISM absorption, but require the ISM absorption to be the same for both observations. To account forwavelength solution errors between the two observations, we do not fix the radial velocities to the same value, butrather require the radial velocity offset between the emission and ISM absorption to be the same between the twoobservations. Based on the measured stellar radial velocity -56.3 ± − (Reiners & Basri 2009a) and the predictedISM radial velocity along TRAPPIST-1’s sightline (-1.25 ± − , Redfield & Linsky 2008), we give the radialvelocity offset parameter a Gaussian prior with mean +55.05 ± − , obtained by adding the stellar and ISMradial velocities and adding their uncertainties in quadrature. We fix the Doppler b value of the ISM absorption profileto 11.5 km s − and D/H= 1 . × − , both standard values for the local ISM (Wood 2004). All other parameters werevaried with uniform priors.Figure 3 shows the spectrum and reconstructed line profile. We report the median and the 68 per cent confidenceinterval as our best fit values and 1 σ error bars. We found an integrated flux of F Ly α = (1 . +0 . − . ) × − erg s − cm − for the Mega-MUSCLES observation, and F Ly α = (1 . +0 . − . ) × − erg s − cm − for the Bourrier et al. (2017a)observation. This value is larger but within 1 σ of the flux ((8 . +1 . − . ) × − erg s − cm − ) found by Bourrier et al.(2017a), and is explained by our fit’s larger column density (log N(HI) = 18.4 ± ± COS spectra
The COS FUV spectrum was contaminated by airglow from Lyman α and O I over the wavelength ranges 1214–1217 ˚A and 1301–1307 ˚A respectively. Both ranges were removed and replaced by the reconstructed Lyman α profile inthe first case and by a polynomial fit to the spectrum on either side in the second. As we therefore have no informationat these wavelengths, for the rest of this paper we assume that there is zero flux from O I at TRAPPIST-1.The COS NUV observations covered the wavelength ranges 1700–2100 ˚A and 2800–3200 ˚A leaving a 700 ˚A gap. Thisgap is partially covered by a second order spectrum spanning 1950–2150 ˚A, but the signal was so weak that we chosenot to include it. The gap was filled with a polynomial fit to the two wavelength regions, with the range 2790–2805 ˚Amasked out to remove contributions from the Mg II Optical to infrared
STIS G430L igh-energy SED of TRAPPIST-1 . . . . . . . − Mega-MUSCLES . . . . . . . − . − . . . . . . . . . . . . . Wavelength (˚A) − . . . R e s i du a l s χ ν = 1.47 . . . . . . . − Bourrier+ 2017 . . . . . . . − . − . . . . . . . . . . . . . Wavelength (˚A) − χ ν = 0.53 F l u x D e n s i t y ( − e r g c m − s − ˚A − ) TRAPPIST-1
Figure 3.
Best-fit models and intrinsic Lyman alpha profiles are shown from a simultaneous fit to the new spectrum presentedin this work and the spectrum presented in Bourrier et al. (2017a). The ISM properties were forced to be the same for the twospectra, but the intrinsic emission profiles were allowed to vary, to account for either intrinsic stellar variability or differences inthe flux calibration between the two datasets. The solid pink lines show the best fits to the data (black lines with error bars),with the dark and light shaded regions corresponding to the 68% and 95% confidence intervals, respectively. The dashed bluelines show the intrinsic emission profiles corresponding to the best fit models, and the dark blue and light blue shaded regionsrepresent the 68% and 95% confidence intervals, respectively. The bottom panels show the residuals of the fit, or the best fitmodels subtracted from the data and divided by the data uncertainty. The reduced chi-squared values are printed in the samepanels.
Figure 4 shows the STIS G430L spectrum of TRAPPIST-1. The spectrum was obtained with a single exposure on aCCD detector, and thus has a slightly different treatment to the rest of the HST data obtained with photon-countingdetectors. Although the spectrum in principle covers the wavelength range 2900–5700 ˚A, in practice the combinationof low detector throughput and the decreasing flux from the target at short wavelengths results in an effective non-detection of the blue end of this range, with almost half of the pixel bins containing negative flux values. We thereforeremoved all points where the mean flux/flux error ratio of the 30 surrounding bins was less than one. This results ina cutoff at 3872 ˚A, similar to the fixed 3850 ˚A cutoff used by Loyd et al. (2016) for the MUSCLES SEDS.Loyd et al. (2016) also found that the STIS G430L spectra obtained for the MUSCLES program had systematicallylower integrated fluxes than photometric measurements of their respective stars, which they suggested was due toimperfect alignment on the STIS slit. In an attempt to correct this, the Mega-MUSCLES G430L spectra were obtainedwith the slit width set to 0.2”, twice that used for MUSCLES. To validate that the fluxes of the Mega-MUSCLES G430Lspectra are correct, we have obtained extensive flux-calibrated spectroscopy with various ground-based instruments,
Wilson et al. F l ux ( e r g s − c m − ˚ A − ) × − STIS G430LPHOENIXPhotometry 3900 3950 4000Wavelength ( ˚A)0246 × − Ca II Figure 4.
Left: STIS G140L spectrum (blue) compared with Pan-STARSS g and Gaia B p photometry (Gonzales et al. 2019)and the PHOENIX model (orange). The spectrum has been smoothed by a factor 2 for clarity, and the PHOENIX model beenconvolved to the resolution of the observed spectrum. Right: Enlarged view of the region in the red box showing Ca II H&Kemission lines, along with the Gaussian fits (orange) used to measure the emission line fluxes (Table 2). Wavelength ( ˚A)10 − − − − − − F l ux ( e r g s − c m − ˚ A − ) PHOENIXPHOENIX (R=1000)Photometry
Figure 5.
PHOENIX model compared with the photometry from Table 1 of Gonzales et al. (2019). The model in green hasbeen convolved to a resolution of R=1000 for easier comparison with the photometry. igh-energy SED of TRAPPIST-1 g and B filtershave band passes that fall nearly entirely in the G430L range. We retrieved B , SDSS g and PanSTARS g magnitudesfrom Vizier and compared them with synthetic photometry calculated by integrating the spectrum over the respectiveband passes. We found that the spectrum underpredicted the photometry by ratios of 0 . ± .
1, 0 . ± .
02 and0 . ± .
01 for B , SDSS g and PanSTARS g respectively. Given that the differences are small and that photometry atshort optical wavelengths is more likely to be affected by stellar activity than at longer wavelengths (Paudel et al. 2018)we chose not to scale the spectra based on the photometry. An additional test is provided by the PHOENIX model,described in more detail below. As Figure 4 shows, the PHOENIX model is in good agreement with the TRAPPIST-1data at regions of relatively low flux, but over-predicts the regions of higher flux. We speculate that this is due to anincomplete treatment of opacity at these wavelengths in the model. Lan¸con et al. (2020) reported similar discrepanciesbetween PHOENIX models and blue spectra of cool stars. For our purposes here the disagreement cannot be fixed byscaling the spectrum, so we leave the flux calibration as is.The G430L spectrum also contains features consistent with emission from the Ca II H&K lines at 3968.4673 and3933.6614 ˚A. The Ca H line is blended with emission from the H (cid:15) line so is given as an upper limit in Table 2.3.5.2.
PHOENIX
Wavelengths from 5700˚A to 100 µ m are filled with a PHOENIX photospheric model spectrum from the Lyon BT-Settl [DIR] CIFIST2011 2015 grid (Allard 2016; Baraffe et al. 2015) as no ground-based spectroscopy of TRAPPIST-1contemporaneous with our HST and
XMM observations is available. Gonzales et al. (2019) used distance-calibratedspectra and photometry to obtain atmospheric parameters of TRAPPIST-1 of T eff = 2628 ±
42 K and log g = 5 . ± .
06 dex. We obtained the four closest models ( T eff , log g = 2600, 5.0; 2700, 5.0; 2600, 5.5; 2700, 5.5) and linearlyinterpolated them onto the measured parameters using the scipy griddata routine. The model flux is then scaled bythe square of the ratio of the measured radius and distance of TRAPPIST-1 (1 . ± . R Jup and 12 . ± .
02 pcrespectively, Gonzales et al. 2019). The BT-Settl models extend to 1000 µ m, but to avoid the SED file size becomingtoo large we truncated the model at 100 µ m. The removed flux contributed less than one per cent of the total integratedflux of the model. Figure 5 compares the PHOENIX model with the data from Gonzales et al. (2019) used to measurethe atmospheric parameters. EMISSION LINE FLUX MEASUREMENTSProducing the DEM and semi-empirical models discussed below required identifying and measuring the fluxes ofemission lines in the COS spectra. Table 2 provides fluxes for all of the lines in the lists compiled by Linsky (2017)and Peacock et al. (2019) that are covered by our spectra. Where lines from the list were detected, we fit themusing a Gaussian profile combined with a linear fit to the surrounding continuum to account for incorrect backgroundsubtraction (Figure 6). The Gaussian profile does not always exactly recreate the apparent shape of the line profiles(for example the C II lines), but, given the low S/N ratio, we cannot be confident that using more complex profileswould not lead to overfitting. We therefore do not claim to recover the shape of the line profile, but provide a reasonablemeasurement of the integrated flux. The flux is given as the integral of the Gaussian adjusted by the y-value of thelinear fit, along with the propagated statistical error of the fit. Where the fit was unsuccessful we computed a 3 σ upper limit by treating the line as a Gaussian with a width fixed to the average of nearby lines and an amplitude equalto three times the error on the linear fit, adjusted by the linear fit as before. The Al II III DIFFERENTIAL EMISSION MEASUREThe differential emission measure (DEM) describes the amount of emitting plasma as a function of temperaturefor an optically thin plasma in coronal equilibrium (Warren et al. 1998; Louden et al. 2017), allowing us to predict https://phoenix.ens-lyon.fr/Grids/BT-Settl/ Wilson et al. . . . . . . F l ux ( e r g s − c m − ˚ A − ) × − C III . . . . × − Si III . . . . . F l ux ( e r g s − c m − ˚ A − ) × − N V N V . . . . . . × − C II C II − . . . . . . . F l ux ( e r g s − c m − ˚ A − ) × − Si IV − . . . . . . × − Si IV F l ux ( e r g s − c m − ˚ A − ) × − C IV C IV . . . . . . . × − Mg II Figure 6.
Detected emission lines in COS spectra of TRAPPIST-1 (blue) and the fit used to measure the integrated fluxes(orange). Example error bars on the flux values are shown in green. The data were smoothed with a 10-point boxcar for clarity,with the exception of the region around the Mg II lines. Line positions were taken from NIST and shifted by the − . − radial velocity of TRAPPIST-1 (Reiners & Basri 2009b). the fluxes of emission lines formed in the coronal atmosphere if we have a functional form to describe the DEM. TheDEM combined with the emissivity of a particular emission line determines the emission flux in that line emitted by astar. By measuring the flux of FUV emission lines formed at ∼ K and the X-ray flux formed at (cid:38) K, we canconstrain the DEM by assuming it is well-described by a smooth low-order polynomial across the temperature rangerelevant to the chromosphere, transition region, and corona. This operates under the same principle as the Linsky igh-energy SED of TRAPPIST-1 Species λ rest (˚A) Flux (10 − erg s − cm − )C III m ± III . ± . I (Ly α ) 1215,67 1 . +0 . − . × N V ± . V ± . II ≤ . II . ± . II . ± . II ± II ± I ≤ . I ] 1355.598 ≤ . V ≤ . II ≤ . IV ± IV ] 1401.156 ≤ . IV . ± . II ≤ . II ≤ . IV ± IV ± I ≤ . II m ≤ . III ] 1666.153 ≤ . II ≤ I ≤ II ± II ≤ II ± II ≤ ∗ Table 2.
Integrated fluxes for ultraviolet emission line lists compiled by Linsky (2017) and Peacock et al. (2019). Lines atwavelengths not covered by our observations were omitted. ∗ Detected, but blended with H (cid:15) . m Multiplet. Wavelength ( ˚A)10 − − − F l ux ( e r g s − c m − ˚ A − ) DEML+14 Lyman α scalingXMM Figure 7.
Comparison of the DEM model with the EUV/Lyman α relationships of Linsky et al. (2014), and the XMM spectrum. Wilson et al. − − F l ux a u ( e r g s − c m − ˚ A − ) Wavelength ( ˚A) − − − − F l ux ( e r g s − c m − ˚ A − ) APEC DEM Semi-EmpiricalModel PHOENIX Sun (scaled)
Figure 8.
Semi-empirical model spectrum of TRAPPIST-1. The four different models components used are labeled abovethe spectrum, and the PHOENIX model has been rebinned to 1 ˚A for clarity. The spectrum is compared with the quiet Solarspectrum Woods et al. (2009), scaled to have the same blackbody photospheric flux as TRAPPIST-1. The left axis shows theflux received from TRAPPIST-1 at Earth, whereas the right shows the flux received at at the 1 au equivalent distance, i.e. thespectrum of TRAPPIST-1 at a distance receiving the same photospheric flux as at 1 au from the Sun et al. (2014) empirical scaling relations, but is tailored more specifically to the star by using more lines to resolve thestructure of the star’s upper atmosphere at a finer temperature resolution. Combining the differential emission measurewith atomic data from
CHIANTI v8.0 (Dere et al. 1997; Del Zanna et al. 2015), we estimate the EUV spectrum ofTRAPPIST-1 between 10 to 912 ˚A, incorporating the errors in fitting the differential emission measure forward to thepredicted EUV spectrum. Full detailed of our DEM prescription are provided in Duvvuri et al. (2021). SEMI-EMPIRICAL MODELGiven the unavoidable low signal-to-noise of ultraviolet observations of late M-dwarfs in general and TRAPPIST-1 inparticular, the Mega-MUSCLES data products will also include semi-empirical models constructed from the observedspectra, which we recommend as inputs for model planetary atmosphere studies as they avoid potentially biasing themodels with the large amount of noise in the observed spectra. The semi-empirical model for TRAPPIST-1 is shownin Figure 8. Four models are used, including the APEC, DEM and PHOENIX models already discussed. The fourthmodel replaces the
HST spectra covering 1100–4200 ˚A. The model is constructed by first fitting a polynomial to theDEM model and the blue end ( λ < α line and thefits to the emission lines shown in Figure 6, as well as the PHOENIX spectrum at those wavelengths, to produce thefinal spectrum section.Figure 8 compares our final semi-empirical model SED with the quiet Solar spectrum (Woods et al. 2009). TheSolar spectrum is scaled by the ratio of the blackbody luminosities of the photospheres of the two stars, such that thephotospheric flux for each spectrum is the same as the irradiation Earth receives. The comparison clearly demonstratesthe relative difference in high-energy flux between TRAPPIST-1 and the Sun, implying that any planet receiving thesame photospheric flux from TRAPPIST-1 as (for example) the Earth receives from the Sun, is experiencing high-energy flux levels that are several orders of magnitude higher (Figure 9), even when the star is not flaring. igh-energy SED of TRAPPIST-1 .
01 0 .
02 0 .
03 0 .
04 0 .
05 0 . − − F T R A PP I S T − [ x ] / F E a r t h b c d e f g h λ = λ = λ = T eq (K) Figure 9.
Fluxes at different wavebands experienced by the TRAPPIST-1 planets compared with the Earth. [x] in the y-axis label refers to planet b, c, etc.. The dashed lines show empirical (including TRAPPIST-1 d) and conservative (excludingTRAPPIST-1 d) edges of the temperate zone for 1 M (cid:76) planets as modelled by Kopparapu et al. (2014). The equilibriumtemperature as a function of distance from the star is shown on the top axis. − − − F m od / F ob s Model 1AModel 2AModel 2B 2 × × × Wavelength ( ˚A)10 − − − Figure 10.
Comparison of the integrated flux of detected emission lines with predicted fluxes given in Table 5 of Peacocket al. (2019) as function of formation temperature (left) and wavelength (right). We were unable to find a measured formationtemperature for Fe II COMPARISON WITH MODEL SPECTRAPeacock et al. (2019) extended the PHOENIX stellar atmosphere code into the ultraviolet by adding contributionsfrom the chromosphere and transition regions, providing model SEDs of the TRAPPIST-1 ultraviolet regions againstwhich we can compare our observations. The three PHOENIX models were calibrated to the Bourrier et al. (2017a)4
Wilson et al.
Lyman α flux (model 1A) and distance-adjusted GALEX photometry of stars with similar spectral types (models 2Aand 2B).Figure 10 compares the predicted line strengths given in Table 5 of Peacock et al. (2019) with the line fluxesmeasured from our COS data (Table 2) as a function of formation temperature and wavelength. For all three models,the agreement between the predicted and measured line fluxes is in general poor. The Lyman α -scaled model 1Aaccurately predicts the measured fluxes of the C II and Ca II lines, but predicts multiple lines at values ∼
10 timeshigher than the upper limits placed on their fluxes here. We find no trend between the accuracy of the predicted fluxesand either formation temperature or wavelength. SWIFT PHOTOMETRYAs this paper was under review, Becker et al. (2020) presented a deep Swift uvm2 observation of TRAPPIST-1,finding a flux of 8 . ± . × − erg s − cm − around 1900 ˚A. As a large fraction of the uvm2 waveband is covered bythe gap in the COS G230L detector, an exact comparison between the SED and the Swift measurement is challenging.Integrating the semi-empirical model over the uvm2 waveband, we find a flux of 1 . × − erg s − cm − , suggestingthat the model may underpredict the flux in the NUV, although there is no way to further test this with the availabledata. We note that, although the uvm2 peaks at ≈ ≈
10 percent of maximum aroundthe Mg II HIGH-LEVEL SCIENCE PRODUCTSThe TRAPPIST-1 SED will be made available at or before publication of this paper on the MUSCLES Trea-sury Survey Page at the Mikulski Archive for Space Telescopes (MAST): https://archive.stsci.edu/prepds/muscles/,https://doi.org/doi:10.17909/T9DG6F. Available products will include the standard data products provided by theMUSCLES survey (i.e., the SED at native and 1 ˚A resolutions along with the component observations and models),along with the new Semi-empirical model SED at native and 1 ˚A resolutions. The remainder of the Mega-MUSCLEStargets, listed at http://cos.colorado.edu/ ∼ kevinf/muscles.html, will be added to the database in the coming months. CONCLUSIONWe have constructed a panchromatic SED of the M8 star TRAPPIST-1, the first data product from the Mega-MUSCLES survey.TRAPPIST-1 is the faintest target in the Mega-MUSCLES survey, and the SED presented here both represents thestate-of-the-art for observation of the high-energy flux of low-mass stars and demonstrates the limits of our currentobserving facilities. Obtaining the ultraviolet spectroscopy pushed the capabilities of COS to their limits, with manyexpected emission lines remaining below the noise limit. The EUV spectrum cannot be observed with any currentlyoperating facility. Improving on these observations, which is desirable given the continued importance of low-massstars for exoplanet science, will require the launch of large-aperture space telescopes with ultraviolet capabilities anda dedicated EUV observatory (Youngblood et al. 2019).We thank S. Peacock for providing the PHOENIX EUV models and E. Gonzales for providing the optical spectraand photometry. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the DataArchive at the Space Telescope Science Institute, which is operated by the Association of Universities for Researchin Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program
HST data presented in this paper were obtained from the Mikulski Archive for Space Telescopes(MAST). AY acknowledges support by an appointment to the NASA Postdoctoral Program at Goddard Space FlightCenter, administered by USRA through a contract with NASA. PCS acknowledges support by DLR under grant 50OR 1901. ArXiv copy note: Due the first author living in Texas in February 2021, the HLSP products will not be available when this paper goeson arXiv. For now, the semi-empirical SEDs can be found here: https://github.com/davidjwilson/Trappist-1 MM. igh-energy SED of TRAPPIST-1 Facilities:
HST (STIS and COS),
XMM-Newton