Homework answers / question archive / You will compose a 800-1000 word article for Carolina Scientific that reports on a recent scientific finding or study at UNC

You will compose a 800-1000 word article for Carolina Scientific that reports on a recent scientific finding or study at UNC

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You will compose a 800-1000 word article for Carolina Scientific that reports on a recent scientific finding or study at UNC. Your article should profile a specific researcher or research lab and draw on a recent scientific article that person/lab has published(linked below). Your goal is to provide an interesting report of that research for an audience of UNC community members.

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Introduction: In this section, you should orient the readers so that they know what topic will be addressed and why it is important for them to know about. You should define the topic and inform the reader about the approach you are taking. What aspects will be covered, and what aspects will not be covered? Indicate what scholarly or professional conversation you are trying to enter.

Body: Include at least three sections here describing different trends, themes, or approaches relevant to your topic. In each section, do not simply summarize research—build a focused discussion of that topic. Rather than moving through each source one at a time, develop comparisons, contrasts, or similarities between articles or studies.

Conclusion: Summarize the major points of the research, and add a final perspective or conclusion. Here, you should refer back to the question or objective set out in the introduction and to the relationships or patterns you developed in the body section. What is the significance of the research you have reviewed? What problems still need to be solved? What research is still needed?

References: Prepare a list of the sources you have cited in your article. Use the citation format used within the discourse community you have chosen, or, if there is no single accepted format, follow the format from a peer-reviewed journal within that discourse community.

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Resources:

• Example of a review article from The Yale Review of Undergraduate Research in Psychology https://campuspress.yale.edu/yrurp/files/2015/11/Smith2013-27rc78t.pdf

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• Examples of review articles from the Journal of Young Investigators:

http://www.jyi.org/issue/literature-review-insights-into-formulating-a-protective-malarial-medicine/

RUBRIC FOR CAROLINA SCIENTIFIC ARTICLE
Criteria and Qualities	Low	Middle	High
Introducing the idea: Research Question	Neither implicit nor explicit reference is made to the topic or purpose of the article.	Readers are aware of the overall problem, challenge, or topic of the article	The topic is introduced, and groundwork is laid as to the direction of the article.
Body: Flow of the review	The summary appears to have no direction, with subtopics appearing disjointed.	There is a basic flow from one section to the next, but not all sections or paragraphs follow in a natural or logical order.	The summary goes from general ideas to specific conclusions. Transitions tie sections together, as well as adjacent paragraphs.
Coverage of content	Major sections of pertinent content have been omitted or greatly run-on. The topic is of little significance to the course.	All major sections of the pertinent content are included, but not covered in as much depth, or as explicit, as expected. Significance to the course is evident.	The appropriate content in consideration is covered in depth without being redundant. Sources are cited when specific statements are made. Significance to the research question is clear.
Clarity of writing and writing technique	It is hard to know what the writer is trying to express. Writing is convoluted. Misspelled words, incorrect grammar, and improper punctuation are evident.	Writing is generally clear, but unnecessary words are occasionally used. Meaning is sometimes hidden. Paragraph or sentence structure is too repetitive. Few (3) spelling, grammar, or punctuation errors are made.	Writing is crisp, clear, and succinct. The writer incorporates the active voice when appropriate and supports ideas with examples. No spelling, grammar, or punctuation errors are made.
Conclusion: A synthesis of ideas and application to library media center program	There is no indication the author tried to synthesize the information or make a conclusion based on the literature under review. No application to library media center program is provided.	The author provides concluding remarks that show an analysis and synthesis of ideas occurred. Some of the conclusions, however, were not supported in the body of the report..	The author was able to make succinct and precise conclusions based on the review. Insights into the problem are appropriate. Conclusions are strongly supported in the review.
Citations/References: Proper CSE format	Citation for the article did not follow CSE format and was missing essential information.	Citation for the article did follow CSE format; however; a few (2) errors in essential information were evident.	Citation for the article did follow CSE format. Essential information was accurate and complete.

 

 

The Astronomical Journal, 161:23 (12pp), 2021 January https://doi.org/10.3847/1538-3881/abbd91 © 2020. The American Astronomical Society. All rights reserved. TOI 540 b: A Planet Smaller than Earth Orbiting a Nearby Rapidly Rotating Lowmass Star Kristo Ment1 , Jonathan Irwin1, David Charbonneau1 , Jennifer G. Winters1 , Amber Medina1 , Ryan Cloutier1 , Matías R. Díaz2 , James S. Jenkins2,3 , Carl Ziegler4 , Nicholas Law5 , Andrew W. Mann5 , George Ricker6,7 , Roland Vanderspek6,7 , David W. Latham1 , Sara Seager6,7,8,9, Joshua N. Winn10 , Jon M. Jenkins11 , Robert F. Goeke7 Alan M. Levine7 , Bárbara Rojas-Ayala12 , Pamela Rowden13 , Eric B. Ting11 , and Joseph D. Twicken11,14 , 1 Center for Astrophysics,?Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA; kristo.ment@cfa.harvard.edu 2 Departamento de Astronomía,Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile 3 Centro de Astrofísica y Tecnologías A?nes (CATA), Casilla 36-D, Santiago, Chile 4 Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada 5 Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA 6 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 7 Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 8 Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA 9 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 10 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA 11 NASA Ames Research Center, Moffett Field, CA 94035, USA 12 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile 13 School of Physical Sciences, The Open University, Milton Keynes MK7 6AA, UK 14 SETI Institute, Mountain View, CA 94043, USA Received 2020 July 16; revised 2020 September 24; accepted 2020 September 25; published 2020 December 11 Abstract We present the discovery of TOI 540 b, a hot planet slightly smaller than Earth orbiting the low-mass star 2MASS J05051443-4756154. The planet has an orbital period of P?=?1.239149 days (±170 ms) and a radius of r = 0.903 ? 0.052RÅ, and is likely terrestrial based on the observed mass–radius distribution of small exoplanets at similar insolations. The star is 14.008 pc away and we estimate its mass and radius to be M = 0.159 ? 0.014 M??and R = 0.1895 ? 0.0079R?, respectively. The star is distinctive in its very short rotational period of Prot = 17.4264 ? 0.0094 hr and correspondingly small Rossby number of 0.007 as well as its high X-ray-tobolometric luminosity ratio of LX L bol = 0.0028 based on a serendipitous XMM-Newton?detection during a slew operation. This is consistent with the X-ray emission being observed at a maximum value of LX L bol ? 10-3 as predicted for the most rapidly rotating M dwarfs. TOI 540 b?may be an alluring target to study atmospheric erosion due to the strong stellar X-ray emission. It is also among the most accessible targets for transmission and emission spectroscopy and eclipse photometry with the James Webb Space Telescope, and may permit Doppler tomography with high-resolution spectroscopy during transit. This discovery is based on precise photometric data from the Transiting Exoplanet Survey Satellite and ground-based follow-up observations by the MEarth team. Uni?ed Astronomy Thesaurus concepts: Transit photometry (1709); Exoplanets (498); Extrasolar rocky planets (511); Stellar rotation (1629) Supporting material: data behind ?gures, machine-readable table signi?cantly degrades in radial velocity (RV) precision, and irregularities of emitted ?ux from starspots and faculae that are rapidly shifting in and out of view across the stellar surface can imprint complicated modulations in the star’s observed ?ux, hampering transit detection. In addition, rapid rotation in M dwarfs also correlates with more frequent ?are emission (Davenport 2016 and references therein), further contaminating the light curve. In particular, the current sample of terrestrial planet hosts within 15 pc of the Sun includes no red dwarfs with rotation periods less than a day, and only one ultracool dwarf with a rotation period below 10 days, TRAPPIST-1, which has an estimated Prot = 1.40 ? 0.05 days (Gillon et al. 2016) or Prot = 3.30 ? 0.14 days (Luger et al. 2017). Transiting planets with radii around or less than 1 RÅ?are of special interest because they are likely to be terrestrial even in the absence of mass constraints from precise RV or transittiming variation (TTV) data. Weiss & Marcy (2014) and Rogers (2015) identi?ed two distinct regimes in the mass– radius relation for small exoplanets: planets below a threshold 1. Introduction Obtaining a representative sample of rotation periods in planet-hosting M dwarfs is important due to the established link between rotation rate and stellar activity. Stars exhibit continual angular momentum loss due to magnetic braking, which subsequently decreases the strength of the stellar magnetic dynamo, leading to a decrease in activity (Skumanich 1972). Consequently, rapidly rotating stars tend to have higher levels of coronal X-ray emission (Wright et al. 2018). Elevated X-ray and UV emission are known tracers of increased magnetic activity (Gronoff et al. 2020) and will have profound consequences on the atmospheric mass loss and potential habitability of any terrestrial planets in the system (e.g., GarciaSage et al. 2017). The vast majority of recent discoveries of terrestrial planets orbiting M dwarfs are in systems with relatively inactive host stars, characterized by stellar rotation periods longer than 100 days. Rapidly rotating stars present observational challenges for planet detection. Rotational broadening of spectral lines 1 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. radius of 1.5 RÅ?tend to have bulk densities consistent with a rocky composition whereas those above that threshold possess a large fraction of volatiles by volume. These results were based on numerous RV studies that had obtained masses for small transiting planets around G and K dwarfs such as Kepler10 (Batalha et al. 2011), Kepler-78 (Howard et al. 2013; Pepe et al. 2013), and Kepler-93 (Dressing et al. 2015). Recent RV measurements have established rocky bulk composition for many small planets orbiting M dwarfs as well, including L 9859 (Cloutier et al. 2019), LHS 1140 (Ment et al. 2019), LTT 3780 (Cloutier et al. 2020a), and TRAPPIST-1 (Grimm et al. 2018). Consistent with the interpretation of two distinct planet populations, Fulton et al. (2017) noticed a de?cit of planets with radii 1.5–2 RÅ?(a radius valley). The radius valley likely arises as a result of photoevaporation (Lopez & Fortney 2013; Owen & Wu 2013, 2017; Lopez & Rice 2018), core-powered mass loss (Ginzburg et al. 2018), or formation in a gas-poor environment (Lee et al. 2014; Lopez & Rice 2018). Its existence was demonstrated speci?cally for K and M dwarfs by Cloutier & Menou (2020) using K2 photometry. Upcoming exo-atmospheric studies with state-of-the-art instruments such as the James Webb Space Telescope (JWST) and ground-based 30 m telescopes will primarily focus on the planets orbiting M dwarfs closest to the solar system. This is due to photon statistics as well as the relative size of the planet compared to the star that make both transmission and emission spectroscopy tractable (Morley et al. 2017). There are currently (as of 2020 April) only 10 stars within 15 pc of the Sun that are known to host transiting planets: the M dwarfs LTT 1445 A (Winters et al. 2019), GJ 357 (Luque et al. 2019), GJ 436 (Butler et al. 2004; Gillon et al. 2007), L 98-59 (Kostov et al. 2019), TRAPPIST-1 (Gillon et al. 2016, 2017b), GJ 1132 (Berta-Thompson et al. 2015; Bon?ls et al. 2018), GJ 1214 (Charbonneau et al. 2009), LHS 3844 (Vanderspek et al. 2019), LHS 1140 (Dittmann et al. 2017; Ment et al. 2019), and the K dwarfs 55 Cnc A (McArthur et al. 2004; Winn et al. 2011) and HD 219134 (Motalebi et al. 2015; Vogt et al. 2015; Gillon et al. 2017a); only two of those systems (L 98-59 and TRAPPIST-1) are known to host planets smaller than 1 RÅ. Four of the planetary systems described above (LTT 1445, GJ 357, L 9859, and LHS 3844) were discovered with the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015). This article presents the discovery of TESS?Object of Interest (TOI) 540 b, a 0.9 RÅ?planet on a 1.24 day orbit discovered by TESS. With a rotation period of 17.4 hr, TOI 540?is rotating more rapidly than TRAPPIST-1, the only other rapidly rotating planet host within 15 pc. We complement TESS?photometry with ground-based follow-up photometry from MEarth, con?rming the planetary nature of the candidate. In addition, we present RV measurements from CHIRON?and the High Accuracy Radial velocity Planet Searcher (HARPS), speckle imaging from the Southern Astrophysical Research (SOAR) Telescope, and X-ray data from XMM-Newton?and ROSAT. from Earth. TOI 540?has a low proper motion for a nearby star (ma = -66.09 ? 0.08 mas yr−1, md = 25.08 ? 0.09 mas yr−1) which likely prevented it from being widely identi?ed as a nearby star before Gaia. The proper motion is also too low to rule out the presence of background stars from archival images (in Section 3.4 we present high-angular-resolution images that rule out the presence of other bright stars in the immediate vicinity). To obtain an estimate for the mass of the star, we use the mass–luminosity relationship for main-sequence M dwarfs in Benedict et al. (2016) and the K-band apparent magnitude of 8.900?±?0.021 from the Two Micron All-Sky Survey (2MASS). This yields a stellar mass of M = 0.159 ? 0.014 M?. We determine the stellar radius using two different mass– radius relations: one determined from optical interferometry of single stars in Boyajian et al. (2012), and another from eclipsing binary measurements in Bayless & Orosz (2006). The former yields R = 0.195 ? 0.011 R? and the latter produces R = 0.182 ? 0.013 R?. We then calculate a weighted average of the two estimates, obtaining R = 0.190 ? 0.008 R?. We note that this is also consistent with the radius–luminosity relation in Mann et al. (2015), which predicts R = 0.197 ? 0.007 R?. Informed by these relationships, we re?ne our estimate of the stellar radius using transit geometry in Section 4 and report the ?nal value in Table 3. In order to determine the color indices of TOI 540, we adopt the J-, H-, and KS-band magnitudes from 2MASS (Skrutskie et al. 2006), and we obtained VJ RKC IKC -photometry from the REsearch Consortium On Nearby Stars (RECONS).15 The VRI photometry was collected on the night of 2019 August 20, with exposure times of 300, 180, and 75 s, respectively. The RECONS ?uxes were extracted using a 4″ radius aperture to minimize contamination from a nearby background star, described in Section 2.1. The VRI magnitudes for TOI 540?are reported in Table 3. The luminosity of TOI 540?can be estimated from bolometric corrections (BC). In particular, interpolating between the BCV values as a function of V - KS in Table 5 of Pecaut & Mamajek (2013) yields a bolometric correction of BCV = -2.938, corresponding to a luminosity of L?=?0.003745 L ?. Alternatively, using the derived third-order polynomial ?t between BCJ and V?−?J in Mann et al. (2015, and its erratum), we obtain BCJ?=?1.951, which gives us a luminosity of L?=?0.003254 L ?. Finally, we use the relationship between BCK and I?−?K in Leggett et al. (2001) to produce BCK?=?2.764 and L?=?0.003383 L ?. We take as our ?nal value the mean and the standard deviation of the three luminosity estimates, L = 0.00346 ? 0.00021 L ?. This allows us to use the Stefan-Boltzmann law to determine the effective stellar temperature via Teff = Teff, ? (L L ?)1 4 (R R?)-1 2 , yielding Teff = 3216 ? 83 K. We adopted the solar values of Mbol, ? = 4.7554 mag and Teff, ? = 5772 K cited in Mamajek (2012). Due to the slow evolution of M dwarfs in their rapid rotation stage, we are unable to place tight constraints on the age of the system. However, we note that TOI 540?is not overluminous (based on the observed color and luminosity), and therefore it is likely to be on the main sequence, implying an age greater than 100 Myr (Baraffe et al. 2002). Based on the galactic space velocity W and established age–velocity relations, and the observed rapid stellar rotation, we can place an upper limit of 2. Properties of the Host Star TOI 540, otherwise known as 2MASS J05051443-4756154 (Skrutskie et al. 2006) and UCAC4 211-005570 (Finch et al. 2014), is a nearby main-sequence M dwarf. Based on the parallax measurement of p = 71.3886 ? 0.0448 mas reported in Gaia DR2 (Gaia Collaboration et al. 2018; Lindegren et al. 2018), we calculate a distance of d = 14.0078 ? 0.0088 pc 15 2 www.recons.org The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. 2 Gyr on the system (Newton et al. 2016). We also estimate the average equivalent width of Hα emission from the four CHIRON?spectra described in Section 3.3 to be 2.8?±?0.1 Å, consistent with TOI 540?not being a pre-main-sequence star. Finally, we use BANYAN Σ (Gagné et al. 2018) to investigate TOI 540’s potential membership of young stellar associations based on its location in XYZUVW space (calculated from the coordinates, proper motion, and RV values), and rule out 27 well-characterized young associations within 150 pc with 99.9% con?dence. TOI 540?is a highly magnetically active star as indicated by the photometric modulation due to stellar spots and the numerous ?ares present in each sector of the TESS data. Measuring how often TOI 540??ares is essential to understanding the environment in which its planet resides. The ?are frequency distribution describes the rate of ?ares as a function of energy and follows the probability distribution N (E ) dE = WE-adE (Lacy et al. 1976, Equation (2)) where α is the slope of the power law and Ω is a normalization constant. Using the methods outlined in Medina et al. (2020), we ?nd a = 1.97 and measure a rate of 0.12 ?ares per day above an energy of E = 3.16 ´ 1031 erg in the TESS bandpass. Medina et al. (2020) ?nd that TOI 540?has a ?are rate that is consistent with other stars of a similar mass and rotation period. bandpass. This leads to an error of 1.6% in the measured transit depth, or 0.8% in the planetary radius. The latter is much smaller than the ?nal uncertainty of 5.8% derived in this work (Table 5). Therefore, we have not corrected the TESS?light curve presented in Section 3.1 for the additional ?ux dilution due to this neighboring source. A planetary candidate with an orbital period of 1.239 days was initially detected by the SPOC in sector 4 data validation reports (DVR; Twicken et al. 2018; Li et al. 2019) with a signal-to-noise ratio of 8.9, based on 16 transits. TESS?ultimately observed 50 transits of TOI 540 b?over the three sectors, with an average transit depth of 2168?±?172 ppm, yielding a signal-to-noise ratio of 15.6. However, the correct spectral type and stellar radius was unde?ned in the TIC (v7) and therefore assumed to be 1 R??during the preparation of the DVR, leading to a substantially overestimated planetary radius of 5 RÅ. We make use of the full PDCSAP light curve from which we remove bright outliers (more than 0.02 mag brighter than the mean ?ux) that constitute 0.099% of the total TESS?data and may be caused by contamination from ?ares. The data clipping is done to ensure consistency between the handling of TESS?and MEarth data sets (see Section 3.2). The ?nal TESS?light curve consists of 48,445 individual data points, and can be seen in Figure 1. We note that per the TESS?data release notes of sector 4,16 an interruption in communications between the instrument and spacecraft resulted in an instrument turn-off for 2.7 days, during which no data were collected. 2.1. A Neighboring Star 6″ Away Our efforts are complicated by a neighboring background star at a distance of 6″ from TOI 540. We ?rst noticed this background source in MEarth follow-up photometry (described in Section 3.2) and subsequently identi?ed it in Gaia DR2. It has a Gaia ID of 4785886975670558336 and is 2.26 mag fainter than the main target in the GBP passband. While both the neighboring star and TOI 540?occupy the same TESS?pixel, we are able to resolve the two stars using MEarth photometry and con?rm that the planet does indeed transit TOI 540. In particular, we extract the light curve of TOI 540?using variable aperture sizes and ?nd that the transit persists with a similar depth down to an aperture of 2 5, a size small enough to exclude the neighboring star. 3.2. MEarth Follow-up Photometry Using the eight 40 cm aperture telescopes of the MEarthSouth telescope array at the Cerro Tololo International Observatory (CTIO) in Chile (Nutzman & Charbonneau 2008; Irwin et al. 2015), we conducted follow-up observations of TOI 540?to con?rm the transits of the terrestrial planet. The MEarthSouth telescopes employ a custom bandpass centered at the red end of the optical spectrum (similar to TESS). We observed 10 transits of TOI 540 b?between 2019 July 27 and 2019 December 8, using an exposure time of 40 s per measurement. However, we discarded the data from the transit on December 8 due to a stellar ?are shortly following the transit egress, which would have led to needless challenges in modeling the out-oftransit ?ux baseline. Therefore, we proceeded by including the data from the ?rst nine transits only. Aperture photometry was carried out in all images using a ?xed aperture radius of 6 pixels, or 5 1. After excluding outliers 0.02 mag brighter than the mean ?ux (0.068% of the data set), the MEarth light curve contains a combined 17,879 data points from all eight telescopes. The individual light curves from each visit are shown in Figure 2. 3. Observations 3.1. TESS?Photometry TESS?collected photometry of TOI 540?in observation sectors 4, 5, and 6, with the observations spanning a nearly three-month period from 2018 October 19 to 2019 January 6. The star was included in the TESS?Input Catalog (TIC) with a TIC ID of 200322593 as well as the TESS?Candidate Target List (CTL; Stassun et al. 2018), and TESS?Guest Investigator programs G011180 (PI: Courtney Dressing) and G011231 (PI: Jennifer Winters). We utilize the two-minute cadence presearch data conditioning (PDCSAP; Smith et al. 2012; Stumpe et al. 2012, 2014) light curve reduced with the NASA Ames Science Processing Operations Center (SPOC) pipeline (Jenkins et al. 2016). The PDCSAP ?uxes have been corrected for instrumental systematic effects as well as crowding: unresolved light from other nearby stars listed in the TIC v7. While the background source from Section 2.1 is listed in version 8 of the TIC, it did not appear in version 7 that was used to reduce the TESS?photometry presented in this work. Based on TIC v8, the background star is 4.46 mag fainter than TOI 540?in the TESS 3.3. CHIRON?and HARPS?Spectroscopy We gathered four reconnaissance spectra of TOI 540?with the CHIRON?spectrograph (Tokovinin et al. 2013) mounted on the CTIO/Small and Moderate Aperture Research Telescope System (SMARTS) 1.5 m telescope at CTIO. The spectra were accumulated as part of a nearly volume-complete spectroscopic survey of nearby mid-to-late M dwarfs. The methods by which we determined the RVs and rotation broadening, below, are described in Winters et al. (2020). The observations were 16 https://archive.stsci.edu/missions/tess/doc/tess_drn/tess_sector_04_ drn05_v04.pdf 3 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. Figure 1. TESS photometry of TOI 540?from sectors 4 (blue), 5 (orange), and 6 (green). The combined transit and stellar rotation model from Section 4 is overplotted as a solid line. (The data used to create this ?gure are available.) carried out between 2018 September and 2019 November in 3?×?20 minutes exposures per observation, employing the image slicer mode for a resolution of R?=?80,000. We obtained multi-order RVs from six spectral orders (see Table 1) as well as an estimated projected rotation velocity of v sin i = 13.98 km s−1. In addition, we collected three spectra using the HARPS?spectrograph (Mayor et al. 2003) mounted on the ESO 3.6 m telescope at La Silla. The HARPS?spectrograph has a measured spectral resolution of R?=?120,000. The observations were carried out in 2019 April (ESO HARPS Program 0103.C0442, PI: Díaz) with a 30 minute exposure time. We estimated the RVs by combining 21 spectral orders and calculated a v sin i of 12.93 km s−1. The RVs are displayed in Figure 3. We adopt the mean of the two rotation velocity estimates as our ?nal value, obtaining v sin i = 13.5 ? 1.5 km s−1. This Prot ¢ 2pR = v sin i = 0.71 ? 0.08 yields a rotation period estimate of sin i days, consistent with the photometrically determined rotation period of 0.72610 day from Section 4 for sin i » 1, suggesting that the inclination of the rotation axis is close to 90°, and that the stellar obliquity is low. The v sin i values for both CHIRON?and HARPS? were generated by applying appropriate rotational broadening to an observed M-dwarf spectrum. We note that our RV measurements have uncertainties greater than 100 m s−1, estimated from theoretical uncertainties for a rotating star (e.g., Bouchy et al. 2001) with in?ation to account for RV scatter in between the spectral orders. The large uncertainties are driven by the low signal-to-noise ratios of the spectra (typically 5–10) due to the star being substantially redder than what is optimal for the spectrographs and settings that were used to collect these spectra. The HARPS?spectra were gathered in the simultaneous reference mode using a Thorium–Argon lamp which signi?cantly degrades the spectrum in the red orders. Rotational broadening of spectral lines also contributes to the degradation of RV precision. The reported errors are on par with the rms of the RVs (163 m s−1). 4 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. Figure 2. Follow-up photometry of TOI 540?from all eight MEarth telescopes by night. The data has been combined and binned to a cadence of 1.44 minutes. The solid line represents the combined transit and baseline model from Section 4. (The data used to create this ?gure are available.) Employing the estimated mass of the planet from Section 5, the RV semi-amplitude for TOI 540 b?corresponding to a circular orbit would be K = 1.4 ? 0.3 m s−1. Therefore, the rapid rotation of the star makes direct mass measurements with RVs currently unfeasible. However, the RVs help rule out a close-in massive companion: the standard deviation of all seven measurements is 167 m s−1, close to the individual uncertainties, and there is no evidence of a trend. In particular, we are able to rule out a companion with a mass of m > 0.73MJup at the orbital period of the transiting planet with 99.7% (3σ) con?dence. This was estimated by ?tting an RV model with the period, epoch, and eccentricity ?xed to the values in Table 3, and calculating the appropriate semi-amplitude for which the cumulative distribution function (CDF) of the c 2 distribution has a p-value below 0.0027. Table 1 RV Data for TOI 540 BJD (TDB) RV (km s−1) Uncertainty (km s−1) Instrument 2458385.8447 2458576.5615 2458578.5499 2458579.5788 2458607.4689 2458801.6815 2458803.5955 18.5791 18.9040 18.4817 18.6201 18.7156 18.3476 18.5508 0.142 0.1886 0.1375 0.1221 0.133 0.195 0.194 CHIRON HARPS HARPS HARPS CHIRON CHIRON CHIRON (This table is available in machine-readable form.) 5 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. Figure 3. RV measurements of TOI 540?from CHIRON?and HARPS?as a function of orbital phase, with phase of zero corresponding to the time of transit. There is no evidence for a signi?cant trend caused by a massive companion. The expected RV semi-amplitude for TOI 540 b?is K = 1.4 ? 0.3 m s−1 (assuming a circular orbit), well below the precision of the currently available data. 3.4. SOAR Speckle Imaging Nearby stars that fall within the same 21″ TESS?pixel as the target can cause photometric contamination or be the source of an astrophysical false positive. We searched for nearby sources to TOI 540?with SOAR speckle imaging (Tokovinin 2018) on 2019 July 14 UT, observing in the visible I bandpass. Details of the observation are available in Ziegler et al. (2020). We detected no nearby sources within 3″ of TOI 540, corresponding to a projected distance of 42 au. The 5σ detection sensitivity and the speckle autocorrelation function (contrast curve) from the SOAR observation are plotted in Figure 4. 3.5. X-Ray Detections by XMM-Newton?and ROSAT A testament to its signi?cant X-ray brightness, TOI 540?was detected by XMM-Newton?during a slew operation on 2004 July 27. The detection appears in the XMM slew 2 catalog with a source ID of XMMSL2 J050514.2-475618 (slew obs. ID 9084800002). The ?ux of the target is listed as (1.43 ? 0.50) ´ 10-12 erg s−1 cm−2 in the soft 0.2–2 keV bandpass and (3.91 ? 1.35) ´ 10-12 erg s−1 cm−2 in the total 0.2–12 keV bandpass. No detection is listed separately in the hard 2–12 keV bandpass. For consistency with Wright et al. (2018), we convert the soft bandpass ?ux into the ROSAT?bandpass of 0.1–2.4 keV. We use the astrophysical plasma emission code (APEC)17 model at solar abundance and a plasma temperature of kT = 0.54 keV . The conversion is done using the portable interactive multi-mission simulator and yields an X-ray ?ux of (PIMMS)18 (1.60 ? 0.56) ´ 10-12 erg s−1 cm−2 in the ROSAT?bandpass. This corresponds to an X-ray-to-bolometric luminosity ratio of LX L bol = 0.0028, consistent with LX L bol ? 10-3 measured by Wright et al. (2018) for rapidly rotating stars. The implications of this are further discussed in Section 5. 17 18 Figure 4. The 5σ detection sensitivity (solid line) and the autocorrelation function (ACF, inset) of TOI 540?from SOAR speckle imaging showing no evidence of nearby light sources. TOI 540?also appears in the second ROSAT all-sky survey source catalog (Boller et al. 2016) with a source name of J050514.2-475625. It was observed by ROSAT?in 1990 August with a count rate of 0.0413?±?0.0176 counts s−1 in the 0.1–2.4 keV energy band. Using the aforementioned APEC model leads to a somewhat lower X-ray ?ux estimate of 3 ´ 10-13 erg s−1 cm−2; however, the error on the count rate is substantial. 4. Modeling of TESS?and MEarth Light Curves We analyze the MEarth and TESS light curve data simultaneously with the Python package exoplanet?(Foreman-Mackey et al. 2019), which is a framework built on the Hamiltonian Monte Carlo methods implemented in PyMC3?(Salvatier et al. 2016) via Theano?(Theano Development Team 2016) for computationally ef?cient sampling. http://www.atomdb.org/ https://heasarc.gsfc.nasa.gov/docs/software/tools/pimms.html 6 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. Table 2 Model Parameters for Light Curve Fitting Parameter Explanation m TESS ln s 2TESS m MEarth ln s 2MEarth M R ln Q0 ln DQ ln Prot ln ? λ ln s 2 ρ t0 ln P r/R b TESS ?ux baseline TESS excess white noise MEarth ?ux baseline MEarth excess white noise Stellar mass Stellar radius Quality parameter Quality parameter Stellar rotation period Covariance amplitude Covariance amp. ratio Covariance amplitude Covariance decay timescale Transit midpoint Orbital period Planet-star radius ratio Impact parameter Prior Value Units ? (0, 10) ? (ln 6.76, 5) ? (0, 10) ? (ln 3.44, 5) ? (0.159, 0.014) ? (0.190, 0.008) ? (1, 10) ? (2, 10) ? (ln 0.7266, 0.01) ? (ln 10.62, 5) ? (0, 1) ? (ln 16.84, 5) ? (0.036, 0.0036) ? (2458411.8264, 0.1) ? (ln 1.23913, 0.01) ? (0.01, 0.4) ? (0, 1 + r R ) −0.025?±?0.025 −8.44?±?2.04 −0.49?±?0.40 1.154?±?0.028 Table 3 Table 3 1.07?±?0.19 7.88?±?0.80 Table 3 0.54?±?0.63 0.54?±?0.25 0.711?±?0.080 0.0463?±?0.0028 Table 3 Table 3 Table 3 Table 3 mmag mmag2 mmag mmag2 M? R? L L days mmag2 L mmag2 days BJD days L L Note.?? (m, s ) denotes a normal distribution. ? (a, b ) denotes a uniform distribution. Importantly, exoplanet?extends the basic support for Gaussian process (GP) modeling in PyMC3?by implementing scalable GPs through celerite?(Foreman-Mackey 2018), which makes the otherwise notoriously slow GP modeling much more tractable. Our model has multiple components that are optimized simultaneously, described in the following sections. We model the rotational modulation in the TESS photometry with a GP employing exoplanet’s Rotation kernel, which has a covariance function that is a sum of two stochastically driven harmonic oscillators (SHO), k TESS (t ; Q0 , DQ , Prot , ? , l) = kSHO (t ; Q1, w1, S1) + kSHO (t ; Q2 , w 2, S2) model a range of complicated rotationally modulated signals (Haywood et al. 2014; Soto et al. 2018; Winters et al. 2019; Cloutier et al. 2020b). The parameters of the kernel are constrained with normal and uniform prior distributions, documented in Table 2. We obtain an initial estimate of 17.4 hr for Prot by ?tting a sum of two sinusoids to the TESS?light curve, and we subsequently constrain Prot with a normal prior distribution centered at that value. The prior for ? is centered at the value corresponding to the variance of the observed TESS light curve. We note that since Q0 will always be positive with this setup, the quality parameters Q1 and Q2 of both SHOs are guaranteed to remain above one-half in Equation (2). The MEarth follow-up photometry is modeled with a separate covariance kernel. This is due to the additional contribution from precipitable water vapor that induces strong nonlinear trends into the individual light curves of each night. The form of the kernel is (1 ) 1 1 + Q0 + DQ Q2 = + Q0 2 2 4pQ1 8pQ2 w1 = w2 = 2 Prot 4Q1 - 1 Prot 4Q22 - 1 Q1 = S1 = l? ? S2 = , w1Q1 w 2 Q2 k MEarth (t ; s , r ) = where the covariance function of a single SHO is given by wt kSHO (t ; Q , w , S ) = SwQe- 2Q ? 1 sinh (hwt ) if 0 < Q < 1 2 ? cosh (hwt ) + 2hQ ? ´ ? 2 (1 + wt ) if Q = 1 2 ? 1 ? cos (hwt ) + sin (hwt ) if Q > 1 2 2hQ ? with h º 1- 1 4Q 2 s 2 ??? 1? ??1 + ?? e-(1 - ? ) 3 t r ? 2 ? ? ? 1? + ?1 - ? e-(1 + ? ) 3 t r ? ? ? ?? (3 ) which, for small values of ò, approximates the well-known Matérn-3/2 kernel (2 ) ? lim k MEarth (t ; s , r ) = s 2 ?1 + ? ?0 ? 3t ? ?e r ? 3 t r. (4 ) Here, ò is ?xed to a standard value of 0.01. The exact form of the Matérn-3/2 kernel (Equation (4)) cannot be implemented within the framework of celerite, and we therefore need to use the approximate form of Equation (3). The timescale parameter r 3 is constrained with a Gaussian prior centered at 30 minutes, which we expect to be the typical minimum timescale for variations in precipitable water vapor in the atmosphere. The prior for σ is centered at the value corresponding to the . Thus, the rotation kernel has ?ve parameters: the quality factors Q0 and DQ, the rotation period Prot , the primary amplitude ? , and the amplitude ratio λ. We note that the two SHO components correspond to the ?rst and second harmonics of the oscillation, with the latter having twice the frequency (or equivalently, half the period) of the former. This type of kernel has been shown to successfully 7 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. model is ?tted simultaneously to TESS and MEarth photometry. While the model presented here does not account for the non-zero exposure times, we did test a model light curve that was oversampled and integrated over the different exposures (also with exoplanet) and found the differences to be negligible. The free parameters in the model are the transit midpoint t0, the orbital period P, the planet-to-star radius ratio r/R, and the impact parameter b. The ?rst two (t0 and P) are constrained relatively tightly with Gaussian priors since they can be pre-determined with good precision from the TESS data alone. The two-dimensionless parameters (r/R and b) have uniform prior distributions. We also include quadratic limbdarkening, with the appropriate coef?cients adopted from Table 5 of Claret (2018) for the spherical PHOENIX-COND limbdarkening model (Husser et al. 2013). In particular, we use a?=?0.1553 and b?=?0.4742, corresponding to a local gravity of log g = 5.0 , an effective temperature of 3200 K, and the TESS bandpass. We separately estimated the limb-darkening coef?cients for the MEarth optical ?lter following the process outlined in Section 6.1 of Irwin et al. (2018). However, due to the similarity between the MEarth and TESS bandpasses, we found no meaningful difference between using either set of limb-darkening coef?cients: the resulting discrepancy in the modeled light curve was orders of magnitude smaller than the measurement uncertainty. Therefore, we decided to simplify the modeling by adopting the TESS limb-darkening coef?cients given above for both data sets. In addition, we allow for a baseline ?ux as well as additional white noise (added in quadrature to each individual ?ux uncertainty) in the TESS and MEarth data as additional model parameters. They are loosely constrained with Gaussian prior distributions. The priors for excess white noise are centered at the values corresponding to the smallest individual ?ux uncertainties in the respective data sets. A comprehensive list of all model parameters is given in Table 2. We note that our reported model assumes a circular orbit (zero eccentricity). Due to the short orbital period of the planet, it is reasonable to expect that tidal dissipation has damped any initial amount of orbital eccentricity to an undetectably small level. Based on the work of Goldreich & Soter (1966), the expected tidal circularization timescale is close to 150,000 yr (assuming the estimated bulk density from Section 5 and a speci?c dissipation function of Q = 100, which is appropriate for terrestrial planets), much shorter than the expected age of the system. Allowing the eccentricity e and the angle of periastron passage ω to ?uctuate produces a posterior probability distribution that is consistent with e?=?0 at the cost of signi?cantly broadening the posterior distributions of several other parameters (such as the impact parameter b) that alter the light curve in a similar way. Since an eccentricity much greater than zero would be inconsistent with the tidal circularization timescale, we keep e ?xed to zero to constrain the other parameters better. We proceed to tune and sample the model posterior distributions with PyMC3. The Markov Chain Monte Carlo (MCMC) sampling is done in parallel in four independent chains. Sampling from each chain begins with a burn-in phase of 1000 steps with an automatically tuned step size such that the acceptance fraction approaches 90%, which facilitates convergence in complicated posterior distributions. We draw 1000 samples from each chain, for a total of 4000 samples. The sample distributions from each chain can be compared to each Table 3 System Parameters for TOI 540 Values for TOI 540 Sourcea (1) (1) (1) Distance (pc) Mass (M? ) Radius (R?) Luminosity (L ? ) Fractional X-ray luminosity LX L bol X-ray ?uxb (erg s−1 cm−2) Effective temperature (K) Age (Gyr) Rotational period (days) Projected rotation velocity (km s−1) 05h 05 min 14.4 s −47° 56′ 15 5 ma = -66.09 ? 0.08 md = 25.08 ? 0.09 VJ = 14.492 ? 0.03 RKC = 13.115 ? 0.03 IKC = 11.402 ? 0.03 J = 9.755 ? 0.022 H = 9.170 ? 0.022 KS = 8.900 ? 0.021 14.0078?±?0.0088 0.159?±?0.014 0.1895?±?0.0079 0.00346?±?0.00021 0.0028 (3) (3) (3) (2) (2) (2) (1) (3) (3) (3) (3) (1.60 ? 0.56) ´ 10-12 3216?±?83 0.1–2 Gyr 0.72610?±?0.00039 13.5?±?1.5 (3) (3) (3) (3) (3) Parameter Values for TOI 540 b Parameter Stellar parameters Right ascension (J2000) Declination (J2000) Proper motion (mas yr−1) Apparent brightness (mag) Modeled transit parameters Orbital period P (days) Eccentricity e Time of mid-transit tT (BJD) Impact parameter b Planet-to-star radius ratio r/R a/R ratio Derived planetary parameters Radius r (RÅ) Semimajor axis a (au) Inclination i (deg) Bolometric incident ?ux S (SÅ) Equilibrium temperaturec Teq (K) 1.2391491?±?0.0000017 0 (?xed) 2458411.82601?±?0.00046 0.772?±?0.029 0.0436?±?0.0012 13.90?±?0.72 0.903?±?0.052 0.01223?±?0.00036 86.80?±?0.28 23.4?±?2.1 611?±?23 Notes. a (1) Gaia Collaboration et al. (2018), (2) Skrutskie et al. (2006), (3) this work. b The X-ray ?ux is given in the ROSAT?bandpass of 0.1–2.4 keV. c The equilibrium temperature assumes a Bond albedo of zero. For an albedo of AB, the reported temperature has to be multiplied by (1 - AB )1 4 . variance of the observed MEarth light curve. We note that due to the estimated stellar rotation period of 17.4 hr, the kernel in Equation (3) is also able to absorb the rotational modulation with the exponential decay timescale being much shorter than the rotation period, whereas a quasi-periodic kernel (such as Equation (1)) would be misled by the nonperiodic changes in the water vapor content. We did experiment with a kernel that combined both a quasi-periodic and a Matérn-3/2 term, but we ultimately found it impossible to decouple the effects of stellar rotation and water vapor variations in a statistically signi?cant way. Thus, the Matérn-3/2 kernel is our preferred model to account for both periodic as well as nonperiodic modulations in the high-cadence but short-baseline MEarth follow-up data. Transits of TOI 540 b?are modeled using the starry module (Luger et al. 2019) included in exoplanet. A single transit 8 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. Figure 5. A phase-folded transit model of TOI 540 b?from Section 4 overlaid on detrended TESS?and MEarth data. Both data sets have been binned to 2.88 minute intervals for visual clarity. The number of transits ?tted is 50 for the TESS data and 9 for MEarth. Figure 6. TESS photometry of TOI 540, phase-folded to the rotation period in Table 3. Solid orange lines overlay the data points, depicting the predicted rotational modulation for each individual observed stellar rotation. The orange curves overlap for the most part, implying that there is no evidence for long-term evolution in the modulation pattern, e.g., due to changes in the starspot coverage. other to detect possible issues related to convergence. We detect no such problems: the resulting parameter distributions from the four chains are all consistent with one another. We report the means and the standard deviations of the modeled transit parameters from the 4000 samples in Table 3 as well as the rest of the parameters (including hyperparameters) in Table 2. The results of the modeling are described in detail in Section 5, and the modeled light curve can be seen overlaid on top of the TESS?and MEarth raw data in Figures 1 and 2, respectively. 5. Discussion and Conclusion TOI 540 b?completes a trip around its rapidly rotating host star once every P?=?1.239149 days (±170 ms). The transits are not grazing with an impact parameter of b = 0.772 ? 0.029, corresponding to an inclination angle of i = 86 ?. 80 ? 0 ?. 28. The planet has a radius of r = 0.903 ? 0.052 RÅ, slightly less than that of Venus. Based on its small radius, the planet is likely to be terrestrial for the reasons outlined in Section 1. Using Earth’s core mass fraction and a semi-empirical mass– radius relation for rocky planets by Zeng et al. (2016) yields an estimated mass of m = 0.69 ? 0.15 MÅ?and a bulk density of r = 5.2 ? 1.4 g cm−3. This corresponds to a surface gravity of g = 8.3 ? 2.0 m s−2. Figure 5 displays the predicted transits 9 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. Figure 7. Estimated ESM and TSM values (Kempton et al. 2018) for the known terrestrial transiting planets within 15 pc of the Sun, highlighting the most promising nearby targets for emission and transmission spectroscopy. Crucially, the two best targets in the top right (55 Cnc e and HD 219134 b) orbit larger K dwarfs and may not be detectable by JWST?once a systematic noise ?oor is taken into account. The color bar represents the equilibrium temperature of the planets assuming zero albedo and full day–night heat redistribution according to Equation (3) of Kempton et al. (2018). The TSM values were calculated with a scale factor of 0.190, calibrated for small planets. The dotted lines accentuate the location of TOI 540 b. The values for all parameters were adopted from the publications listed in Section 1, and masses were estimated from Zeng et al. (2016; with an Earth-like core mass fraction of 0.33) where not available. In addition, we adopted the updated mass measurements for TRAPPIST-1 (T-1) from Grimm et al. (2018). Wherever missing from the publications listed in Section 1, J- and KS-band ?uxes were adopted from Ducati (2002) and Skrutskie et al. (2006). overlaid on detrended and co-added MEarth and TESS?data; the transit depth is consistent within 1σ in either data set, and the residual noise levels are comparable. The mass and radius of the star are not well constrained by the time-series photometry alone and are almost entirely dictated by the prior distributions. The model ?nds a wellde?ned stellar rotation period of Prot = 17.4264 ? 0.0094 hr. Even though the periodicity of the rotation can be established with great precision, the photometric modulation itself has multiple peaks per rotation, pointing to a heterogeneous distribution of spots across the photosphere. The shape of the modulation imprinted onto the TESS?light curve can be seen in Figure 6. However, there is no visual evidence of substantial evolution of the modulated signal over the two and a half months of data collection, facilitating the modeling necessary to isolate the transits of TOI 540 b. The combination of a slowly evolving starspot distribution and a short orbital period that allows for the observation of a large number of transits provides a rare opportunity to make use of TOI 540?to study the atmospheric composition and escape in small planets orbiting active M dwarfs. Out of the known planet systems within 15 pc of the Sun, similar conditions may perhaps be found only in the TRAPPIST-1 system (TRAPPIST-1 has been estimated to spin with a period of 1.4 or 3.3 days; Gillon et al. 2016; Luger et al. 2017)— however, TOI 540?is nearly 2 mag brighter in the J band (and even more so toward the visible). In particular, rapidly rotating M dwarfs have more ?ares and coronal mass ejections, stronger stellar winds, and higher levels of X-ray and UV emission compared to slowly rotating M dwarfs, which likely lead to extensive atmospheric erosion (Vida et al. 2017; Newton et al. 2018 and references therein). Wright et al. (2018) demonstrate a clear relationship between a star’s Rossby number Ro = Prot t (the ratio of the rotation period to the convective turnover time) and its coronal X-ray emission as a fraction of the bolometric luminosity. For stars with Ro > 0.14, this relationship has a power-law slope, with smaller Rossby numbers corresponding to higher X-ray luminosities. Stars with Ro < 0.14 (rapid rotators) have the highest levels of X-ray emission that remains saturated at a constant level of LX L bol ? 10-3. Using an empirically calibrated relation based on the VJ - KS color, we can calculate the convective turnover time of TOI 540?to be close to t = 109 days (Wright et al. 2018, Equation (5)). This corresponds to a Rossby number of Ro = 0.007, suggesting that TOI 540?is in the saturated high X-ray emission regime with an X-ray-to-bolometric luminosity ratio of LX L bol ? 10-3. This hypothesis is consistent with the X-ray detection of TOI 540?by XMM-Newton?that yields LX L bol = 0.0028. Of the transiting planet hosts listed in Section 1, the only other star likely to be in the saturated regime is TRAPPIST-1 with Ro » 0.002 - 0.006. This is based on an estimated convective turnover time of t = 582 days that may be inaccurate as it was derived from stars with VJ - KS < 7.0 (Wright et al. 2018) whereas TRAPPIST-1 is substantially redder with VJ - KS = 8.5 (Gillon et al. 2017b). The bright X-ray ?ux of TOI 540?could present an opportunity to study transits in the X-ray to search for atmospheric loss, although we note that the atmospheric signature would likely be much smaller than the similar detection for HD 189733 b by Poppenhaeger et al. (2013). The planet is likely to be hot: it receives 23.4 times the total radiation from its host star than Earth does from the Sun (and 3.5 times more than Mercury does), equating to a zero-albedo equilibrium temperature of Teq = 611 ? 23 K. The high temperature, however, may make it more amenable to transmission and emission spectroscopy measurements. We calculate the transmission spectroscopy metric (TSM) and emission spectroscopy metric (ESM) from Kempton et al. 10 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. (2018) for all of the nearby transiting terrestrial planets, listed in Section 1. The values are displayed in Figure 7. Crucially, the two best targets in the top right of Figure 7 (55 Cnc e and HD 219134 b) orbit larger K dwarfs and may not be detectable by the James Webb Space Telescope (JWST)?once a systematic noise ?oor is taken into account. Using the scale factors from Kempton et al. (2018), we obtain TSM = 38.9 and ESM = 6.8 for TOI 540 b. The TSM value is above the threshold of 10 suggested by Kempton et al. (2018) and exceeds the TSM values of all but one of the known planets orbiting M dwarfs in Figure 7. Therefore, TOI 540 b?is a prime target for transmission spectroscopy to study a potential high mean molecular weight atmosphere, if indeed such an atmosphere can be retained in close proximity to an active M dwarf. Furthermore, the relatively high ESM value will likely qualify the planet for infrared photometry with JWST?to detect or rule out the presence of an atmosphere in as much as a single secondary eclipse (Koll et al. 2019). Finally, studies of the near-infrared or infrared phase curve could also tell us if TOI 540?has retained an atmosphere. A thermal phase curve study was used by Kreidberg et al. (2019) to rule out the presence of a thick atmosphere on LHS 3844 b, an ultra-short-period terrestrial planet orbiting a more evolved and less active M dwarf that has spun down to a rotation period of 128 days (Vanderspek et al. 2019) but has a mass similar to that estimated for TOI 540. A similar thermal phase curve study for TOI 540?is promising. We also cannot rule out the presence of additional transiting planets in this active system. We carried out a box least-squares analysis (Kovács et al. 2002; Burke et al. 2006) as implemented in Ment et al. (2019) on the TESS light curve, but did not ?nd suf?cient evidence for additional transiting planets, consistent with the results of the SPOC?s search for additional planets. Considering the orbital inclination angle of TOI 540 b, any coplanar transiting planets would be limited to orbital periods of 1.83 days or less, which would likely lead to dynamical instability given the orbital period of TOI 540 b. Therefore, any additional planets around TOI 540?are likely to be nontransiting, or have an inclination substantially closer to 90°?than TOI 540 b. Given the cumulative occurrence rate of 2.5?±?0.2 small planets (1–4 RÅ, P < 200 days) per M dwarf (Dressing & Charbonneau 2015) that was derived from the Kepler population, alternative methods such as TTV (not detected for the 59 transits observed here) or RV studies (provided that enough observations can be accumulated to overcome the signi?cant rotational broadening of spectral lines) may be fruitful to uncover more planets around TOI 540. In addition, high-resolution spectroscopy would allow for a precise modeling of line pro?les during transit, yielding a direct measurement of stellar obliquity from Doppler tomography/the Rossiter–McLaughlin effect. material is based upon work supported by the National Aeronautics and Space Administration under grant No. 80NSSC18K0476 issued through the XRP Program. A.A.M. acknowledges support from the NSF Graduate Research Fellowship under grant No. DGE1745303. R.C. is supported by a grant from the National Aeronautics and Space Administration in support of the TESS science mission. M.R. D. is supported by CONICYT-PFCHA/Doctorado Nacional21140646, Chile. J.S.J. is supported by funding from Fondecyt through grant 1201371 and partial support from CONICYT project Basal AFB-170002. B.R.A. acknowledges the funding support from FONDECYT through grant 11181295. We acknowledge the use of public TESS Alert data from the pipelines at the TESS Science Of?ce and at the TESS Science Processing Operations Center. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. This research was made possible through the use of the AAVSO Photometric All-Sky Survey (APASS), funded by the Robert Martin Ayers Sciences Fund and NSF AST-1412587. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. For securing the VRI photometry reported in this work, we thank RECONS (www. recons.org) members Andrew Couperus, Todd Henry, WeiChun Jao, and Eliot Vrijmoet. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; ?https:// www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has made use of data obtained from XMMSL2, the Second XMM-Newton Slew Survey Catalogue, produced by members of the XMM SOC, the EPIC consortium, and using work carried out in the context of the EXTraS project (“Exploring the X-ray Transient and variable Sky,” funded from the EU’s Seventh Framework Programme under grant agreement No. 607452). This research made use of exoplanet (Foreman-Mackey et al. 2019) and its dependencies (Agol et al. 2020; Astropy Collaboration et al. 2013, 2018; ForemanMackey et al. 2017; Foreman-Mackey 2018; Luger et al. 2019; Salvatier et al. 2016; Theano Development Team 2016). Facilities:?TESS, MEarth, CTIO:1.5 m (CHIRON), ESO:3.6 m (HARPS), SOAR, XMM. ORCID iDs Kristo Ment https://orcid.org/0000-0001-5847-9147 David Charbonneau https://orcid.org/0000-00029003-484X Jennifer G. Winters https://orcid.org/0000-0001-6031-9513 Amber Medina https://orcid.org/0000-0001-8726-3134 Ryan Cloutier https://orcid.org/0000-0001-5383-9393 Matías R. Díaz https://orcid.org/0000-0002-2100-3257 James S. Jenkins https://orcid.org/0000-0003-2733-8725 Carl Ziegler https://orcid.org/0000-0002-0619-7639 Nicholas Law https://orcid.org/0000-0001-9380-6457 Andrew W. Mann https://orcid.org/0000-0003-3654-1602 The MEarth team acknowledges funding from the David and Lucile Packard Fellowship for Science and Engineering (awarded to D.C.). This material is based on work supported by the National Science Foundation under grants AST0807690, AST-1109468, AST-1004488 (Alan T. Waterman Award), and AST-1616624. This publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily re?ect the views of the John Templeton Foundation. This 11 The Astronomical Journal, 161:23 (12pp), 2021 January Ment et al. George Ricker https://orcid.org/0000-0003-2058-6662 Roland Vanderspek https://orcid.org/0000-0001-6763-6562 David W. 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