arXiv subjects

Leslie Hebb

Publications and source records attributed to Leslie Hebb.

At least 37 records · Page 2Linked to original sources

arXiv2022

Transit Timing Variations for AU Microscopii b & c

We explore the transit timing variations (TTVs) of the young (22 Myr) nearby AU Mic planetary system. For AU Mic b, we introduce three Spitzer (4.5 $μ$m) transits, five TESS transits, 11 LCO transits, one PEST transit, one Brierfield transit, and two transit timing measurements from Rossiter-McLaughlin observations; for AU Mic c, we introduce three TESS transits. We present two independent TTV analyses. First, we use EXOFASTv2 to jointly model the Spitzer and ground-based transits and to obtain the midpoint transit times. We then construct an O--C diagram and model the TTVs with Exo-Striker. Second, we reproduce our results with an independent photodynamical analysis. We recover a TTV mass for AU Mic c of 10.8$^{+2.3}_{-2.2}$ M$_{E}$. We compare the TTV-derived constraints to a recent radial-velocity (RV) mass determination. We also observe excess TTVs that do not appear to be consistent with the dynamical interactions of b and c alone, and do not appear to be due to spots or flares. Thus, we present a hypothetical non-transiting "middle-d" candidate exoplanet that is consistent with the observed TTVs, the candidate RV signal, and would establish the AU Mic system as a compact resonant multi-planet chain in a 4:6:9 period commensurability. These results demonstrate that the AU Mic planetary system is dynamically interacting producing detectable TTVs, and the implied orbital dynamics may inform the formation mechanisms for this young system. We recommend future RV and TTV observations of AU Mic b and c to further constrain the masses and to confirm the existence of possible additional planet(s).

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arXiv2022

TOI-1696 and TOI-2136: Constraining the Masses of Two Mini-Neptunes with HPF

We present the validation of two planets orbiting M dwarfs, TOI-1696b and TOI-2136b. Both planets are mini-Neptunes orbiting nearby stars, making them promising prospects for atmospheric characterization with the James Webb Space Telescope. We validated the planetary nature of both candidates using high contrast imaging, ground-based photometry, and near-infrared radial velocities. Adaptive Optics images were taken using the ShARCS camera on the 3 m Shane Telescope. Speckle images were taken using the NN-Explore Exoplanet Stellar Speckle Imager on the WIYN 3.5 m telescope. Radii and orbital ephemerides were refined using a combination of TESS, the diffuser-assisted ARCTIC imager on the 3.5m ARC telescope at Apache Point Observatory, and the 0.6 m telescope at Red Buttes Observatory. We obtained radial velocities using the Habitable-Zone Planet Finder on the 10 m Hobby-Eberly Telescope, which enabled us to place upper limits on the masses of both transiting planets. TOI-1696b (P = 2.5 days; R$_{p}$ = 3.24 R$_{\oplus}$; M$_{p}$ $<$ 56.6 M$_{\oplus}$) falls into a sparsely-populated region of parameter space considering its host star's temperature (T$_{\rm{eff}}$ = 3168 K, M4.5), as planets of its size are quite rare around mid to late M dwarfs. On the other hand, TOI-2136b (P = 7.85 days; R$_{p}$ = 2.09 R$_{\oplus}$; M$_{p}$ $<$ 15.0 M$_{\oplus}$) is an excellent candidate for atmospheric follow-up with JWST.

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arXiv2021

TOI-532b: The Habitable-zone Planet Finder confirms a Large Super Neptune in the Neptune Desert orbiting a metal-rich M dwarf host

We confirm the planetary nature of TOI-532b, using a combination of precise near-infrared radial velocities with the Habitable-zone Planet Finder, TESS light curves, ground based photometric follow-up, and high-contrast imaging. TOI-532 is a faint (J$\sim 11.5$) metal-rich M dwarf with Teff = $3957\pm69$ K and [Fe/H] = $0.38\pm0.04$; it hosts a transiting gaseous planet with a period of $\sim 2.3$ days. Joint fitting of the radial velocities with the TESS and ground-based transits reveal a planet with radius of $5.82\pm0.19$ R$_{\oplus}$, and a mass of $61.5_{-9.3}^{+9.7}$ M$_{\oplus}$. TOI-532b is the largest and most massive super Neptune detected around an M dwarf with both mass and radius measurements, and it bridges the gap between the Neptune-sized planets and the heavier Jovian planets known to orbit M dwarfs. It also follows the previously noted trend between gas giants and host star metallicity for M dwarf planets. In addition, it is situated at the edge of the Neptune desert in the Radius--Insolation plane, helping place constraints on the mechanisms responsible for sculpting this region of planetary parameter space.

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arXiv2021

A Search for Planetary Metastable Helium Absorption in the V1298 Tau System

Early in their lives, planets endure extreme amounts of ionizing radiation from their host stars. For planets with primordial hydrogen and helium-rich envelopes, this can lead to substantial mass loss. Direct observations of atmospheric escape in young planetary systems can help elucidate this critical stage of planetary evolution. In this work, we search for metastable helium absorption---a tracer of tenuous gas in escaping atmospheres---during transits of three planets orbiting the young solar analogue V1298 Tau. We characterize the stellar helium line using HET/HPF, and find that it evolves substantially on timescales of days to months. The line is stable on hour-long timescales except for one set of spectra taken during the decay phase of a stellar flare, where absoprtion increased with time. Utilizing a beam-shaping diffuser and a narrowband filter centered on the helium feature, we observe four transits with Palomar/WIRC: two partial transits of planet d ($P = 12.4$ days), one partial transit of planet b ($P = 24.1$ days), and one full transit of planet c ($P = 8.2$ days). We do not detect the transit of planet c, and we find no evidence of excess absorption for planet b, with $ΔR_\mathrm{b}/R_\star<0.019$ in our bandpass. We find a tentative absorption signal for planet d with $ΔR_\mathrm{d}/R_\star = 0.0205\pm0.054$, but the best-fit model requires a substantial (-100$\pm$14 min) transit-timing offset on a two-month timescale. Nevertheless, our data suggest that V1298 Tau d may have a high present-day mass-loss rate, making it a priority target for follow-up observations.

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arXiv2021

Non-detection of Helium in the upper atmospheres of TRAPPIST-1b, e and f

We obtained high-resolution spectra of the ultra-cool M-dwarf TRAPPIST-1 during the transit of its planet `b' using two high dispersion near-infrared spectrographs, IRD instrument on the Subaru 8.2m telescope and HPF instrument on the 10m Hobby-Eberly Telescope. These spectroscopic observations are complemented by a photometric transit observation for planet `b' using the APO/ARCTIC, which assisted us to capture the correct transit times for our transit spectroscopy. Using the data obtained by the new IRD and HPF observations, as well as the prior transit observations of planets `b', `e' and `f' from IRD, we attempt to constrain the atmospheric escape of the planet using the He I triplet 10830 Å absorption line. We do not detect evidence for any primordial extended H-He atmospheres in all three planets. To limit any planet related absorption, we place an upper limit on the equivalent widths of <7.754 mÅ for planet `b', <10.458 mÅ for planet `e', and <4.143 mÅ for planet `f' at 95% confidence from the IRD data, and <3.467 mÅ for planet `b' at 95% confidence from HPF data. Using these limits along with a solar-like composition isothermal Parker wind model, we attempt to constrain the mass-loss rates for the three planets. For TRAPPIST-1b, our models exclude the highest possible energy-limited rate for a wind temperature <5000 K. This non-detection of extended atmospheres having low mean-molecular weight in all three planets aids in further constraining their atmospheric composition by steering the focus towards the search of high molecular weight species in their atmospheres.

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arXiv2020

A warm Jupiter transiting an M dwarf: A TESS single transit event confirmed with the Habitable-zone Planet Finder

We confirm the planetary nature of a warm Jupiter transiting the early M dwarf TOI-1899, using a combination of available TESS photometry; high-precision, near-infrared spectroscopy with the Habitable-zone Planet Finder; and speckle and adaptive optics imaging. The data reveal a transiting companion on an $\sim29$-day orbit with a mass and radius of $0.66\pm0.07\ \mathrm{M_{J}}$ and $1.15_{-0.05}^{+0.04}\ \mathrm{R_{J}}$, respectively. The star TOI-1899 is the lowest-mass star known to host a transiting warm Jupiter, and we discuss the follow-up opportunities afforded by a warm ($\mathrm{T_{eq}}\sim362$ K) gas giant orbiting an M0 star. Our observations reveal that TOI-1899.01 is a puffy warm Jupiter, and we suggest additional transit observations to both refine the orbit and constrain the true dilution observed in TESS.

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arXiv2020

The Habitable-zone Planet Finder Reveals A High Mass and a Low Obliquity for the Young Neptune K2-25b

Using radial-velocity data from the Habitable-zone Planet Finder, we have measured the mass of the Neptune-sized planet K2-25b, as well as the obliquity of its M4.5-dwarf host star in the 600-800MYr Hyades cluster. This is one of the youngest planetary systems for which both of these quantities have been measured, and one of the very few M dwarfs with a measured obliquity. Based on a joint analysis of the radial velocity data, time-series photometry from the K2 mission, and new transit light curves obtained with diffuser-assisted photometry, the planet's radius and mass are $3.44\pm 0.12 \mathrm{R_\oplus}$ and $24.5_{-5.2}^{+5.7} \mathrm{M_\oplus}$. These properties are compatible with a rocky core enshrouded by a thin hydrogen-helium atmosphere (5% by mass). We measure an orbital eccentricity of $e=0.43 \pm 0.05$. The sky-projected stellar obliquity is $λ=3 \pm 16^{\circ}$, compatible with spin-orbit alignment, in contrast to other "hot Neptunes" that have been studied around older stars.

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arXiv2020

TOI-1728b: The Habitable-zone Planet Finder confirms a warm super Neptune orbiting an M dwarf host

We confirm the planetary nature of TOI-1728b using a combination of ground-based photometry, near-infrared Doppler velocimetry and spectroscopy with the Habitable-zone Planet Finder.TOI-1728 is an old, inactive M0 star with \teff{} $= 3980^{+31}_{-32}$ K, which hosts a transiting super Neptune at an orbital period of $\sim$ 3.49 days. Joint fitting of the radial velocities and TESS and ground-based transits yields a planetary radius of $5.05_{-0.17}^{+0.16}$ R$_{\oplus}$, mass $26.78_{-5.13}^{+5.43}$ M$_{\oplus}$ and eccentricity $0.057_{-0.039}^{+0.054}$. We estimate the stellar properties, and perform a search for He 10830 Åabsorption during the transit of this planet and claim a null detection with an upper limit of 1.1$\%$ with 90\% confidence. A deeper level of He 10830 Å~ absorption has been detected in the planet atmosphere of GJ 3470b, a comparable gaseous planet. TOI-1728b is the largest super Neptune -- the intermediate subclass of planets between Neptune and the more massive gas-giant planets -- discovered around an M dwarf. With its relatively large mass and radius, TOI-1728 represents a valuable datapoint in the M-dwarf exoplanet mass-radius diagram, bridging the gap between the lighter Neptune-sized planets and the heavier Jovian planets known to orbit M-dwarfs. With a low bulk density of $1.14_{-0.24}^{+0.26}$ g/cm$^3$, and orbiting a bright host star (J $\sim 9.6$, V $\sim 12.4$), TOI-1728b is also a promising candidate for transmission spectroscopy both from the ground and from space, which can be used to constrain planet formation and evolutionary models.

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arXiv2020

A Mini-Neptune and a Venus-Zone Planet in the Radius Valley Orbiting the Nearby M2-dwarf TOI-1266: Validation with the Habitable-zone Planet Finder

We report on the validation of two planets orbiting the nearby (36pc) M2 dwarf TOI-1266 observed by the TESS mission. The inner planet is sub-Neptune-sized ($R=2.46 \pm 0.08 R_\oplus$) with an orbital period of 10.9 days. The outer planet has a radius of $1.67_{-0.11}^{+0.09} R_\oplus$ and resides in the exoplanet Radius Valley---the transition region between rocky and gaseous planets. With an orbital period of 18.8 days, the outer planet receives an insolation flux of 2.4 times that of Earth, similar to the insolation of Venus. Using precision near-infrared radial velocities with the Habitable-zone Planet Finder Spectrograph, we place upper mass limits of $15.9 M_\oplus$ and $6.4 M_\oplus$ at 95% confidence for the inner and outer planet, respectively. A more precise mass constraint of planet c, achievable with current RV instruments given the host star brightness (V=12.9, J=9.7), will yield further insights into the dominant processes sculpting the exoplanet Radius Valley.

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arXiv2020

The SDSS-HET Survey of Kepler Eclipsing Binaries. Description of the Survey and First Results

The Kepler mission has provided a treasure trove of eclipsing binaries (EBs), observed at extremely high photometric precision, nearly continuously for several years. We are carrying out a survey of ~100 of these EBs to derive dynamical masses and radii with precisions of 3% or better. We use multiplexed near-infrared H band spectroscopy from the SDSS-III and -IV APOGEE instrument and optical spectroscopy from the HET High-Resolution Spectrograph to derive double-lined spectroscopic orbits and dynamical mass-ratios for the EB sample. This information is combined with Kepler photometry to derive orbital inclination, dynamical masses of the components, radii and temperatures. These measurements are directly applicable for benchmarking stellar models that are integrating the next generation of improvements, such as the magnetic suppression of convection efficiency, updated opacity tables, and fine-tuned equations of state. We selected our EB sample to include systems with low-mass ($M \lt 0.8 \; M_{\odot}$) primary or secondary components, many expected to populate the relatively sparse parameter space below $0.5 \; M_{\odot}$. In this paper, we describe our EB sample and the analysis techniques we are utilizing, and present masses and radii for two systems that inhabit particularly underpopulated regions of mass-radius-period space: KIC 2445134 and KIC 3003991. Our analysis of KIC 2445134 ($q=0.411 \pm 0.001$) yields masses and radii of $M_A = 1.29 \pm 0.03 \; M_{\odot}$, $M_B = 0.53 \pm 0.01 \; M_{\odot}$, $R_A = 1.42 \pm 0.01 \; R_{\odot}$, $R_B = 0.510 \pm 0.004 \; R_{\odot}$, and a temperature ratio of $T_B/T_A = 0.635 \pm 0.001$; our analysis of KIC 3003991 ($q=0.298 \pm 0.006$) yields $M_A = 0.74 \pm \; 0.04 M_{\odot}$, $M_B = 0.222 \pm \; 0.007 M_{\odot}$, $R_A = 0.84 \pm 0.01 \; R_{\odot}$, $R_B = 0.250 \pm 0.004 \; R_{\odot}$, and a temperature ratio of $T_B/T_A= 0.662 \pm 0.001$.

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arXiv2019

A sub-Neptune sized planet transiting the M2.5-dwarf G 9-40: Validation with the Habitable-zone Planet Finder

We validate the discovery of a 2 Earth radii sub-Neptune-size planet around the nearby high proper motion M2.5-dwarf G 9-40 (EPIC 212048748), using high-precision near-infrared (NIR) radial velocity (RV) observations with the Habitable-zone Planet Finder (HPF), precision diffuser-assisted ground-based photometry with a custom narrow-band photometric filter, and adaptive optics imaging. At a distance of $d=27.9\mathrm{pc}$, G 9-40b is the second closest transiting planet discovered by K2 to date. The planet's large transit depth ($\sim$3500ppm), combined with the proximity and brightness of the host star at NIR wavelengths (J=10, K=9.2) makes G 9-40b one of the most favorable sub-Neptune-sized planet orbiting an M-dwarf for transmission spectroscopy with JWST, ARIEL, and the upcoming Extremely Large Telescopes. The star is relatively inactive with a rotation period of $\sim$29 days determined from the K2 photometry. To estimate spectroscopic stellar parameters, we describe our implementation of an empirical spectral matching algorithm using the high-resolution NIR HPF spectra. Using this algorithm, we obtain an effective temperature of $T_{\mathrm{eff}}=3404\pm73$K, and metallicity of $\mathrm{[Fe/H]}=-0.08\pm0.13$. Our RVs, when coupled with the orbital parameters derived from the transit photometry, exclude planet masses above $11.7 M_\oplus$ with 99.7% confidence assuming a circular orbit. From its radius, we predict a mass of $M=5.0^{+3.8}_{-1.9} M_\oplus$ and an RV semi-amplitude of $K=4.1^{+3.1}_{-1.6}\mathrm{m\:s^{-1}}$, making its mass measurable with current RV facilities. We urge further RV follow-up observations to precisely measure its mass, to enable precise transmission spectroscopic measurements in the future.

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arXiv2019

High Fidelity Imaging of the Inner AU Mic Debris Disk: Evidence of Differential Wind Sculpting?

We present new high fidelity optical coronagraphic imagery of the inner $\sim$50 au of AU Mic's edge-on debris disk using the BAR5 occulter of the Hubble Space Telescope Imaging Spectrograph (HST/STIS) obtained on 26-27 July 2018. This new imagery reveals that "feature A", residing at a projected stellocentric separation of 14.2 au on SE-side of the disk, exhibits an apparent "loop-like" morphology at the time of our observations. The loop has a projected width of 1.5 au and rises 2.3 au above the disk midplane. We also explored TESS photometric observations of AU Mic that are consistent with evidence of two starspot complexes in the system. The likely co-alignment of the stellar and disk rotational axes breaks degeneracies in detailed spot modeling, indicating that AU Mic's projected magnetic field axis is offset from its rotational axis. We speculate that small grains in AU Mic's disk could be sculpted by a time-dependent wind that is influenced by this offset magnetic field axis, analogous to co-rotating Solar interaction regions that sculpt and influence the inner and outer regions of our own Heliosphere. Alternatively, if the observed spot modulation is indicative of a significant mis-alignment of the stellar and disk rotational axes, we suggest the disk could still be sculpted by the differential equatorial versus polar wind that it sees with every stellar rotation.

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arXiv2019

2020 Vision: Towards a Sustainable OIR System

Open-access telescopes of all apertures are needed to operate a competitive and efficient national science program. While larger facilities contribute light-gathering power and angular resolution, smaller ones dominate for field of view, time-resolution, and especially, total available observing time, thereby enabling our entire, diversely-expert community. Smaller aperture telescopes therefore play a critical and indispensable role in advancing science. Thus, the divestment of NSF support for modest-aperture (1 - 4 m) public telescopes poses a serious threat to U.S. scientific leadership, which is compounded by the unknown consequences of the shift from observations driven by individual investigators to survey-driven science. Given the much higher cost efficiency and dramatic science returns for investments in modest aperture telescopes, it is hard to justify funding only the most expensive facilities. We therefore urge the Astro2020 panel to explicitly make the case for modest aperture facilities, and to recommend enhancing this funding stream to support and grow this critical component of the OIR System. Further study is urgently needed to prioritize the numerous exciting potential capabilities of smaller facilities,and to establish sustainable, long-term planning for the System.

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arXiv2019

The EBLM Project V. Physical properties of ten fully convective, very-low-mass stars

Measurements of the physical properties of stars at the lower end of the main sequence are scarce. In this context we report masses, radii and surface gravities of ten very-low-mass stars in eclipsing binary systems, with orbital periods of the order of several days. The objects probe the stellar mass-radius relation in the fully convective regime, $M_\star \lesssim 0.35$ M$_\odot$, down to the hydrogen burning mass-limit, $M_{\mathrm{HB}} \sim 0.07$ M$_\odot$. The stars were detected by the WASP survey for transiting extra-solar planets, as low-mass, eclipsing companions orbiting more massive, F- and G-type host stars. We use eclipse observations of the host stars (TRAPPIST, Leonhard Euler, SPECULOOS telescopes), and radial velocities of the host stars (CORALIE spectrograph), to determine physical properties of the low-mass companions. Companion surface gravities are derived from the eclipse and orbital parameters of each system. Spectroscopic measurements of the host star effective temperature and metallicity are used to infer the host star mass and age from stellar evolution models. Masses and radii of the low-mass companions are then derived from the eclipse and orbital parameters of each system. The objects are compared to stellar evolution models for low-mass stars, to test for an effect of the stellar metallicity and orbital period on the radius of low-mass stars in close binary systems. Measurements are in good agreement with stellar models; an inflation of the radii of low-mass stars with respect to model predictions is limited to 1.6 $\pm$ 1.2% in the fully convective regime. The sample of ten objects indicates a scaling of the radius of low-mass stars with the host star metallicity. No correlation between stellar radii and orbital periods of the binary systems is determined. A combined analysis with comparable objects from the literature is consistent with this result.

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arXiv2019

The Solar Benchmark: Rotational Modulation of the Sun Reconstructed from Archival Sunspot Records

We use archival daily spot coverage measurements from Howard et al. (1984) to study the rotational modulation of the Sun as though it were a distant star. A quasi-periodic Gaussian process measures the solar rotation period $P_\mathrm{rot} = 26.3 \pm 0.1$ days, and activity cycle period $P_\mathrm{cyc} = 10.7 \pm 0.3$ years. We attempt to search for evidence of differential rotation in variations of the apparent rotation period throughout the activity cycle and do not detect a clear signal of differential rotation, consistent with the null results of the hare-and-hounds exercise of Aigrain et al. (2015). The full reconstructed solar light curve is available online.

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arXiv2018

Non-detection of Contamination by Stellar Activity in the Spitzer Transit Light Curves of TRAPPIST-1

We apply the transit light curve self-contamination technique of Morris et al. (2018) to search for the effect of stellar activity on the transits of the ultracool dwarf TRAPPIST-1 with 2018 Spitzer photometry. The self-contamination method fits the transit light curves of planets orbiting spotted stars, allowing the host star to be a source of contaminating positive or negative flux which influences the transit depths but not the ingress/egress durations. We find that none of the planets show statistically significant evidence for self-contamination by bright or dark regions of the stellar photosphere. However, we show that small-scale magnetic activity, analogous in size to the smallest sunspots, could still be lurking in the transit photometry undetected.

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arXiv2018

Extreme precision photometry from the ground with beam-shaping diffusers for K2, TESS and beyond

The Transiting Exoplanet Survey Satellite (TESS, launched early 2018) is expected to find a multitude of new transiting planet candidates around the nearest and brightest stars. Timely high-precision follow-up observations from the ground are essential in confirming and further characterizing the planet candidates that TESS will find. However, achieving extreme photometric precisions from the ground is challenging, as ground-based telescopes are subject to numerous deleterious atmospheric effects. Beam-shaping diffusers are emerging as a low-cost technology to achieve hitherto unachievable differential photometric precisions from the ground. These diffusers mold the focal plane image of a star into a broad and stable top-hat shape, minimizing photometric errors due to non-uniform pixel response, atmospheric seeing effects, imperfect guiding, and telescope-induced variable aberrations seen in defocusing. In this paper, we expand on our previous work (Stefansson et al. 2017; Stefansson et al. 2018 [submitted]), providing a further detailed discussion of key guidelines when sizing a diffuser for use on a telescope. Furthermore, we present our open source Python package iDiffuse which can calculate the expected PSF size of a diffuser in a telescope system, along with its expected on-sky diffuser-assisted photometric precision for a host star of a given magnitude. We use iDiffuse to show that most ($\sim$80\%) of the planet hosts that TESS will find will be scintillation limited in transit observations from the ground. Although iDiffuse has primarily been developed to plan challenging transit observations using the diffuser on the ARCTIC imager on the ARC 3.5m Telescope at Apache Point observatory, iDiffuse is modular and can be easily extended to calculate the expected diffuser-assisted photometric precisions on other telescopes.

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arXiv2018

Robust Transiting Exoplanet Radii in the Presence of Starspots from Ingress and Egress Durations

We typically measure the radii of transiting exoplanets from the transit depth, which is given by the ratio of cross-sectional areas of the planet and star. However, if a star has dark starspots (or bright regions) distributed throughout the transit chord, the transit depth will be biased towards smaller (larger) values, and thus the inferred planet radius will be smaller (larger) if unaccounted for. We reparameterize the transit light curve to account for "self-contamination" by photospheric inhomogeneities by splitting the parameter $R_p/R_\star$ into two parameters: one for the radius ratio -- which controls the duration of ingress and egress -- and another which measures the possibly contaminated transit depth. We show that this is equivalent to the formulation for contamination by a second star (with positive or negative flux), and that it is sensitive to time-steady inhomogeneity of the stellar photosphere. We use synthetic light curves of spotted stars at high signal-to-noise to show that the radius recovered from measurement of the ingress/egress duration can recover the true radii of planets transiting spotted stars with axisymmetric spot distributions if the limb-darkening parameters are precisely known. We fit time-averaged high signal-to-noise transit light curves from Kepler and Spitzer of ten planets to measure the planet radii and search for evidence of spot distributions. We find that this sample has a range of measured depths and ingress durations which are self-consistent, providing no strong evidence for contamination by spots. However, there is suggestive evidence for occultation of starspots on Kepler-17, and that relatively bright regions are occulted by the planets of Kepler-412 and HD 80606. Future observations with the James Webb Space Telescope may enable this technique to yield accurate planetary radii in the presence of stellar inhomogeneities.

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