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We present a catalog of binary companions to $\delta$ Scuti stars, detected through phase modulations of their pulsations in TESS data. Pulsation timing has provided orbits for hundreds of pulsating stars in binaries from space-based photometry. We have applied this technique to $\delta$ Sct stars observed in the first four years of TESS Mission photometry. We searched the 2-min cadence light curves of 1161 short-period instability strip pulsators for variations in pulsation phase caused by the dynamical influence of an unseen companion. We discovered 53 new binaries and we present orbital parameters and mass functions for the 24 systems with solvable orbits. For the brightest star in our sample $\alpha$ Pictoris, we perform a joint fit of the pulsation timing and Hipparcos astrometry. We present the first orbit for the $\alpha$ Pictoris system, obtaining an orbital period of 1316$\pm$2 days and a mass for $\alpha$ Pic b of 1.05$\pm$0.05 M$_\odot$. We revisit pulsation timing binaries from Kepler with Gaia kinematics, finding four systems that are members of the Galatic thick disk or halo. This suggests that they have been rejuvenated by mass transfer, and their companions are now white dwarfs. Further follow up of these systems may yield valuable constraints of the galactic blue straggler population., Comment: Accepted for publication in MNRAS, 12 pages, 11 figures

Increasingly precise space-based photometry uncovers higher-order effects in transits, eclipses and phase curves which can be used to characterize exoplanets in novel ways. The subtle signature induced by a rotationally deformed exoplanet is determined by the planet's oblateness and rotational obliquity, which provide a wealth of information about a planet's formation, internal structure, and dynamical history. However, these quantities are often strongly degenerate and require sophisticated methods to convincingly constrain. We develop a new semi-analytic model for an ellipsoidal object occulting a spherical body with arbitrary surface maps expressed in terms of spherical harmonics. We implement this model in an open-source Jax-based Python package eclipsoid, allowing just-in-time compilation and automatic differentiation. We then estimate the precision obtainable with JWST observations of the long period planet population and demonstrate the best current candidates for studies of oblateness and obliquity. We test our method on the JWST NIRSpec transit of the inflated warm Neptune WASP-107 b and place an upper bound on its projected oblateness $f<0.23$, which corresponds to a rotation period of $P_{\mathrm{rot}}>13$h if the planet is not inclined to our line of sight. Further studies of long-period exoplanets will necessitate discarding the assumption of planets as spherical bodies. Eclipsoid provides a general framework allowing rotational deformation to be modelled in transits, occultations, phase curves, transmission spectra and more., Comment: 14 pages, 8 figures. Submitted to ApJ. Code available open-source at https://github.com/shishirdholakia/eclipsoid/tree/main

We report on the discovery of Gliese 12 b, the nearest transiting temperate, Earth-sized planet found to date. Gliese 12 is a bright ($V=12.6$ mag, $K=7.8$ mag) metal-poor M4V star only $12.162\pm0.005$ pc away from the Solar System with one of the lowest stellar activity levels known for an M-dwarf. A planet candidate was detected by TESS based on only 3 transits in sectors 42, 43, and 57, with an ambiguity in the orbital period due to observational gaps. We performed follow-up transit observations with CHEOPS and ground-based photometry with MINERVA-Australis, SPECULOOS, and Purple Mountain Observatory, as well as further TESS observations in sector 70. We statistically validate Gliese 12 b as a planet with an orbital period of $12.76144\pm0.00006$ days and a radius of $1.0\pm{0.1}$ R$_\oplus$, resulting in an equilibrium temperature of $\sim$315K. Gliese 12 b has excellent future prospects for precise mass measurement, which may inform how planetary internal structure is affected by the stellar compositional environment. Gliese 12 b also represents one of the best targets to study whether Earth-like planets orbiting cool stars can retain their atmospheres, a crucial step to advance our understanding of habitability on Earth and across the Galaxy., Comment: 19 pages, 7 figures, Accepted for publication in MNRAS, Authors Shishir Dholakia and Larissa Palethorpe contributed equally

There are more than 5000 confirmed and validated planets beyond the solar system to date, more than half of which were discovered by NASA's Kepler mission. The catalog of Kepler's exoplanet candidates has only been extensively analyzed under the assumption of white noise (i.i.d. Gaussian), which breaks down on timescales longer than a day due to correlated noise (point-to-point correlation) from stellar variability and instrumental effects. Statistical validation of candidate transit events becomes increasingly difficult when they are contaminated by this form of correlated noise, especially in the low-signal-to-noise (S/N) regimes occupied by Earth--Sun and Venus--Sun analogs. To diagnose small long-period, low-S/N putative transit signatures with few (roughly 3--9) observed transit-like events (e.g., Earth--Sun analogs), we model Kepler's photometric data as noise, treated as a Gaussian process, with and without the inclusion of a transit model. Nested sampling algorithms from the Python UltraNest package recover model evidences and maximum a posteriori parameter sets, allowing us to disposition transit signatures as either planet candidates or false alarms within a Bayesian framework., Comment: 15 pages, 9 figures, 2 tables, uses AASTeX631

We derive solutions to transit light curves of exoplanets orbiting rapidly-rotating stars. These stars exhibit significant oblateness and gravity darkening, a phenomenon where the poles of the star have a higher temperature and luminosity than the equator. Light curves for exoplanets transiting these stars can exhibit deviations from those of slowly-rotating stars, even displaying significantly asymmetric transits depending on the system's spin-orbit angle. As such, these phenomena can be used as a protractor to measure the spin-orbit alignment of the system. In this paper, we introduce a novel semi-analytic method for generating model light curves for gravity-darkened and oblate stars with transiting exoplanets. We implement the model within the code package starry and demonstrate several orders of magnitude improvement in speed and precision over existing methods. We test the model on a TESS light curve of WASP-33, whose host star displays rapid rotation ($v \sin i_* = 86.4$ km/s). We subtract the host's $\delta$-Scuti pulsations from the light curve, finding an asymmetric transit characteristic of gravity darkening. We find the projected spin orbit angle is consistent with Doppler tomography and constrain the true spin-orbit angle of the system as $\varphi=108.3^{+19.0}_{-15.4}$~$^{\circ}$. We demonstrate the method's uses in constraining spin-orbit inclinations of such systems photometrically with posterior inference. Lastly, we note the use of such a method for inferring the dynamical history of thousands of such systems discovered by TESS., Comment: 33 pages, 9 figures. Submitted to AAS Journals