arXiv subjects

F. Dai

Publications and source records attributed to F. Dai.

At least 37 records · Page 2Linked to original sources

arXiv2021

Sampling discretization of integral norms and its application

The paper addresses the problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under two standard kinds of assumptions -- conditions on the entropy numbers and conditions in terms of the Nikol'skii-type inequalities. We prove some upper bounds on the number of sample points sufficient for good discretization and show that these upper bounds are sharp in a certain sense. Then we apply our general conditional results to subspaces with special structures, namely, subspaces with the tensor product structure. We demonstrate that applications of results based on the Nikol'skii-type inequalities provide somewhat better results than applications of results based on the entropy numbers conditions. Finally, we apply discretization results to the problem of sampling recovery.

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arXiv2021

37 New Validated Planets in Overlapping K2 Campaigns

We analysed 68 candidate planetary systems first identified during Campaigns 5 and 6 (C5 and C6) of the NASA \textit{K2} mission. We set out to validate these systems by using a suite of follow-up observations, including adaptive optics, speckle imaging, and reconnaissance spectroscopy. The overlap between C5 with C16 and C18, and C6 with C17, yields lightcurves with long baselines that allow us to measure the transit ephemeris very precisely, revisit single transit candidates identified in earlier campaigns, and search for additional transiting planets with longer periods not detectable in previous works. Using \texttt{vespa}, we compute false positive probabilities of less than 1\% for 37 candidates orbiting 29 unique host stars and hence statistically validate them as planets. These planets have a typical size of $2.2R_{\oplus}$ and orbital periods between 1.99 and 52.71 days. We highlight interesting systems including a sub-Neptune with the longest period detected by \textit{K2}, sub-Saturns around F stars, several multi-planetary systems in a variety of architectures. These results show that a wealth of planetary systems still remains in the \textit{K2} data, some of which can be validated using minimal follow-up observations and taking advantage of analyses presented in previous catalogs.

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arXiv2021

Masses and compositions of three small planets orbiting the nearby M dwarf L231-32 (TOI-270) and the M dwarf radius valley

We report on precise Doppler measurements of L231-32 (TOI-270), a nearby M dwarf ($d=22$ pc, $M_\star = 0.39$ M$_\odot$, $R_\star = 0.38$ R$_\odot$), which hosts three transiting planets that were recently discovered using data from the Transiting Exoplanet Survey Satellite (TESS). The three planets are 1.2, 2.4, and 2.1 times the size of Earth and have orbital periods of 3.4, 5.7, and 11.4 days. We obtained 29 high-resolution optical spectra with the newly commissioned Echelle Spectrograph for Rocky Exoplanet and Stable Spectroscopic Observations (ESPRESSO) and 58 spectra using the High Accuracy Radial velocity Planet Searcher (HARPS). From these observations, we find the masses of the planets to be $1.58 \pm 0.26$, $6.15 \pm 0.37$, and $4.78 \pm 0.43$ M$_\oplus$, respectively. The combination of radius and mass measurements suggests that the innermost planet has a rocky composition similar to that of Earth, while the outer two planets have lower densities. Thus, the inner planet and the outer planets are on opposite sides of the `radius valley' -- a region in the radius-period diagram with relatively few members, which has been interpreted as a consequence of atmospheric photo-evaporation. We place these findings into the context of other small close-in planets orbiting M dwarf stars, and use support vector machines to determine the location and slope of the M dwarf ($T_\mathrm{eff} < 4000$ K) radius valley as a function of orbital period. We compare the location of the M dwarf radius valley to the radius valley observed for FGK stars, and find that its location is a good match to photo-evaporation and core-powered mass loss models. Finally, we show that planets below the M dwarf radius valley have compositions consistent with stripped rocky cores, whereas most planets above have a lower density consistent with the presence of a H-He atmosphere.

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arXiv2020

A planetary system with two transiting mini-Neptunes near the radius valley transition around the bright M dwarf TOI-776

We report the discovery and characterization of two transiting planets around the bright M1 V star LP 961-53 (TOI-776, J = 8.5 mag, M = 0.54+-0.03 Msun) detected during Sector 10 observations of the Transiting Exoplanet Survey Satellite (TESS). Combining the TESS photometry with HARPS radial velocities, as well as ground-based follow-up transit observations from MEarth and LCOGT telescopes, we measured for the inner planet, TOI-776 b, a period of 8.25 d, a radius of 1.85+-0.13 Re, and a mass of 4.0+-0.9 Me; and for the outer planet, TOI-776 c, a period of 15.66 d, a radius of 2.02+-0.14 Re, and a mass of 5.3+-1.8 Me. The Doppler data shows one additional signal, with a period of 34 d, associated with the rotational period of the star. The analysis of fifteen years of ground-based photometric monitoring data and the inspection of different spectral line indicators confirm this assumption. The bulk densities of TOI-776 b and c allow for a wide range of possible interior and atmospheric compositions. However, both planets have retained a significant atmosphere, with slightly different envelope mass fractions. Thanks to their location near the radius gap for M dwarfs, we can start to explore the mechanism(s) responsible for the radius valley emergence around low-mass stars as compared to solar-like stars. While a larger sample of well-characterized planets in this parameter space is still needed to draw firm conclusions, we tentatively estimate that the stellar mass below which thermally-driven mass loss is no longer the main formation pathway for sculpting the radius valley is between 0.63 and 0.54 Msun. Due to the brightness of the star, the TOI-776 system is also an excellent target for the James Webb Space Telescope, providing a remarkable laboratory to break the degeneracy in planetary interior models and to test formation and evolution theories of small planets around low-mass stars.

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arXiv2020

A super-Earth and a sub-Neptune orbiting the bright, quiet M3 dwarf TOI-1266

We report the discovery and characterisation of a super-Earth and a sub-Neptune transiting the bright ($K=8.8$), quiet, and nearby (37 pc) M3V dwarf TOI-1266. We validate the planetary nature of TOI-1266 b and c using four sectors of TESS photometry and data from the newly-commissioned 1-m SAINT-EX telescope located in San Pedro Mártir (Mexico). We also include additional ground-based follow-up photometry as well as high-resolution spectroscopy and high-angular imaging observations. The inner, larger planet has a radius of $R=2.37_{-0.12}^{+0.16}$ R$_{\oplus}$ and an orbital period of 10.9 days. The outer, smaller planet has a radius of $R=1.56_{-0.13}^{+0.15}$ R$_{\oplus}$ on an 18.8-day orbit. The data are found to be consistent with circular, co-planar and stable orbits that are weakly influenced by the 2:1 mean motion resonance. Our TTV analysis of the combined dataset enables model-independent constraints on the masses and eccentricities of the planets. We find planetary masses of $M_\mathrm{p}$ = $13.5_{-9.0}^{+11.0}$ $\mathrm{M_{\oplus}}$ ($<36.8$ $\mathrm{M_{\oplus}}$ at 2-$σ$) for TOI-1266 b and $2.2_{-1.5}^{+2.0}$ $\mathrm{M_{\oplus}}$ ($<5.7$ $\mathrm{M_{\oplus}}$ at 2-$σ$) for TOI-1266 c. We find small but non-zero orbital eccentricities of $0.09_{-0.05}^{+0.06}$ ($<0.21$ at 2-$σ$) for TOI-1266 b and $0.04\pm0.03$ ($<0.10$ at 2-$σ$) for TOI-1266 c. The equilibrium temperatures of both planets are of $413\pm20$ K and $344\pm16$ K, respectively, assuming a null Bond albedo and uniform heat redistribution from the day-side to the night-side hemisphere. The host brightness and negligible activity combined with the planetary system architecture and favourable planet-to-star radii ratios makes TOI-1266 an exquisite system for a detailed characterisation.

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arXiv2020

The TOI-763 system: sub-Neptunes orbiting a Sun-like star

We report the discovery of a planetary system orbiting TOI-763 (aka CD-39 7945), a $V=10.2$, high proper motion G-type dwarf star that was photometrically monitored by the TESS space mission in Sector 10. We obtain and model the stellar spectrum and find an object slightly smaller than the Sun, and somewhat older, but with a similar metallicity. Two planet candidates were found in the light curve to be transiting the star. Combining TESS transit photometry with HARPS high-precision radial velocity follow-up measurements confirm the planetary nature of these transit signals. We determine masses, radii, and bulk densities of these two planets. A third planet candidate was discovered serendipitously in the radial velocity data. The inner transiting planet,TOI-763 b, has an orbital period of $P_\mathrm{b}$ = 5.6~days, a mass of $M_\mathrm{b}$ = $9.8\pm0.8$ $M_\oplus$, and a radius of $R_\mathrm{b}$ = $2.37\pm0.10$ $R_\oplus$. The second transiting planet,TOI-763 c, has an orbital period of $P_\mathrm{c}$ = 12.3~days, a mass of $M_\mathrm{c}$ = $9.3\pm1.0$ $M_\oplus$, and a radius of $R_\mathrm{c}$ = $2.87\pm0.11$ $R_\oplus$. We find the outermost planet candidate to orbit the star with a period of $\sim$48~days. If confirmed as a planet it would have a minimum mass of $M_\mathrm{d}$ = $9.5\pm1.6$ $M_\oplus$. We investigated the TESS light curve in order to search for a mono transit by planet~d without success. We discuss the importance and implications of this planetary system in terms of the geometrical arrangements of planets orbiting G-type stars.

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arXiv2020

Three planets transiting the evolved star EPIC 249893012: a hot 8.8-M$_\oplus$ super-Earth and two warm 14.7 and 10.2-M$_\oplus$ sub-Neptunes

We report the discovery of a new planetary system with three transiting planets, one super-Earth and two sub-Neptunes, that orbit EPIC\,249893012, a G8\,IV-V evolved star ($M_\star$\,=\,1.05\,$\pm$\,0.05\,$M_\odot$, $R_\star$\,=\,1.71\,$\pm$\,0.04\,$R_\odot$, $T_\mathrm{eff}$\,=5430\,$\pm$\,85\,K). The star is just leaving the main sequence. We combined \ktwo \ photometry with IRCS adaptive-optics imaging and HARPS, HARPS-N, and CARMENES high-precision radial velocity measurements to confirm the planetary system, determine the stellar parameters, and measure radii, masses, and densities of the three planets. With an orbital period of $3.5949^{+0.0007}_{-0.0007}$ days, a mass of $8.75^{+1.09}_{-1.08}\ M_{\oplus}$ , and a radius of $1.95^{+0.09}_{-0.08}\ R_{\oplus}$, the inner planet b is compatible with nickel-iron core and a silicate mantle ($ρ_b= 6.39^{+1.19}_{-1.04}$ g cm$^{-3}$). Planets c and d with orbital periods of $15.624^{+0.001}_{-0.001}$ and $35.747^{+0.005}_{-0.005}$ days, respectively, have masses and radii of $14.67^{+1,84}_{-1.89}\ M_{\oplus}$ and $3.67^{+0.17}_{-0.14}\ R_{\oplus}$ and $10.18^{+2.46}_{-2.42}\ M_{\oplus}$ and $3.94^{+0.13}_{-0.12}\ R_{\oplus}$, respectively, yielding a mean density of $1.62^{+0.30}_{-0.29}$ and $0.91^{+0.25}_{-0.23}$ g cm$^{-3}$, respectively. The radius of planet b lies in the transition region between rocky and gaseous planets, but its density is consistent with a rocky composition. Its semimajor axis and the corresponding photoevaporation levels to which the planet has been exposed might explain its measured density today. In contrast, the densities and semimajor axes of planets c and d suggest a very thick atmosphere. The singularity of this system, which orbits a slightly evolved star that is just leaving the main sequence, makes it a good candidate for a deeper study from a dynamical point of view.

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arXiv2020

Entropy numbers and Marcinkiewicz-type discretization theorem

This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied to establish a Marcinkiewicz type discretization theorem for integral norms of functions from a given finite dimensional subspace.

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arXiv2020

Sampling discretization of integral norms

The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. Even though this problem is extremely important in applications, its systematic study has begun recently. In this paper we obtain a conditional theorem for all integral norms $L_q$, $1\le q<\infty$, which is an extension of known results for $q=1$. To discretize the integral norms successfully, we introduce a new technique, which is a combination of probabilistic technique with results on the entropy numbers in the uniform norm. As an application of the general conditional theorem, we derive a new Marcinkiewicz type discretization for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses.

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arXiv2020

Mass determinations of the three mini-Neptunes transiting TOI-125

The Transiting Exoplanet Survey Satellite, TESS, is currently carrying out an all-sky search for small planets transiting bright stars. In the first year of the TESS survey, steady progress was made in achieving the mission's primary science goal of establishing bulk densities for 50 planets smaller than Neptune. During that year, TESS's observations were focused on the southern ecliptic hemisphere, resulting in the discovery of three mini-Neptunes orbiting the star TOI-125, a V=11.0 K0 dwarf. We present intensive HARPS radial velocity observations, yielding precise mass measurements for TOI-125b, TOI-125c and TOI-125d. TOI-125b has an orbital period of 4.65 days, a radius of $2.726 \pm 0.075 ~\mathrm{R_{\rm E}}$, a mass of $ 9.50 \pm 0.88 ~\mathrm{M_{\rm E}}$ and is near the 2:1 mean motion resonance with TOI-125c at 9.15 days. TOI-125c has a similar radius of $2.759 \pm 0.10 ~\mathrm{R_{\rm E}}$ and a mass of $ 6.63 \pm 0.99 ~\mathrm{M_{\rm E}}$, being the puffiest of the three planets. TOI-125d, has an orbital period of 19.98 days and a radius of $2.93 \pm 0.17~\mathrm{R_{\rm E}}$ and mass $13.6 \pm 1.2 ~\mathrm{M_{\rm E}}$. For TOI-125b and TOI-125d we find unusual high eccentricities of $0.19\pm 0.04$ and $0.17^{+0.08}_{-0.06}$, respectively. Our analysis also provides upper mass limits for the two low-SNR planet candidates in the system; for TOI-125.04 ($R_P=1.36 ~\mathrm{R_{\rm E}}$, $P=$0.53 days) we find a $2σ$ upper mass limit of $1.6~\mathrm{M_{\rm E}}$, whereas TOI-125.05 ( $R_P=4.2^{+2.4}_{-1.4} ~\mathrm{R_{\rm E}}$, $P=$ 13.28 days) is unlikely a viable planet candidate with upper mass limit $2.7~\mathrm{M_{\rm E}}$. We discuss the internal structure of the three confirmed planets, as well as dynamical stability and system architecture for this intriguing exoplanet system.

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arXiv2019

An extremely low-density and temperate giant exoplanet

Transiting extrasolar planets are key objects in the study of the formation, migration, and evolution of planetary systems. In particular, the exploration of the atmospheres of giant planets, through transmission spectroscopy or direct imaging, has revealed a large diversity in their chemical composition and physical properties. Studying these giant planets allows one to test the global climate models that are used for the Earth and other solar system planets. However, these studies are mostly limited either to highly-irradiated transiting giant planets or directly-imaged giant planets at large separations. Here we report the physical characterisation of the planets in a bright multi-planetary system (HIP41378) in which the outer planet, HIP41378 f is a Saturn-sized planet (9.2 $\pm$ 0.1 R$_\oplus$) with an anomalously low density of 0.09 $\pm$ 0.02 g cm$^{-3}$ that is not yet understood. Its equilibrium temperature is about 300 K. Therefore, it represents a planet with a mild temperature, in between the hot Jupiters and the colder giant planets of the Solar System. It opens a new window for atmospheric characterisation of giant exoplanets with a moderate irradiation, with the next-generation space telescopes such as JWST and ARIEL as well as the extremely-large ground-based telescopes. HIP41378 f is thus an important laboratory to understand the effect of the irradiation on the physical properties and chemical composition of the atmosphere of planets.

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arXiv2019

The Random Transiter -- EPIC 249706694/HD 139139

We have identified a star, EPIC 249706694 (HD 139139), that was observed during K2 Campaign 15 with the Kepler extended mission that appears to exhibit 28 transit-like events over the course of the 87-day observation. The unusual aspect of these dips, all but two of which have depths of $200 \pm 80$ ppm, is that they exhibit no periodicity, and their arrival times could just as well have been produced by a random number generator. We show that no more than four of the events can be part of a periodic sequence. We have done a number of data quality tests to ascertain that these dips are of astrophysical origin, and while we cannot be absolutely certain that this is so, they have all the hallmarks of astrophysical variability on one of two possible host stars (a likely bound pair) in the photometric aperture. We explore a number of ideas for the origin of these dips, including actual planet transits due to multiple or dust emitting planets, anomalously large TTVs, S- and P-type transits in binary systems, a collection of dust-emitting asteroids, `dipper-star' activity, and short-lived starspots. All transit scenarios that we have been able to conjure up appear to fail, while the intrinsic stellar variability hypothesis would be novel and untested.

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arXiv2019

Integral norm discretization and related problems

The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite dimensional spaces. Also, discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of the multivariate trigonometric polynomials with frequencies from a finite set with fixed cardinality. Both new results and a survey of known results are presented.

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arXiv2019

K2-295 b and K2-237 b: two transiting hot Jupiters

We report the discovery from K2 of two transiting hot Jupiter systems. K2-295 (observed in Campaign 8) is a K5 dwarf which hosts a planet slightly smaller than Jupiter, orbiting with a period of 4.0 d. We have made an independent discovery of K2-237 b (Campaign 11), which orbits an F6 dwarf every 2.2 d and has an inflated radius 50 - 60 per cent larger than that of Jupiter. We use high-precision radial velocity measurements, obtained using the HARPS and FIES spectrographs, to measure the planetary masses. We find that K2-295 b has a similar mass to Saturn, while K2-237 b is a little more massive than Jupiter.

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arXiv2019

WASP-4b Arrived Early for the TESS Mission

The Transiting Exoplanet Survey Satellite (TESS) recently observed 18 transits of the hot Jupiter WASP-4b. The sequence of transits occurred 81.6 $\pm$ 11.7 seconds earlier than had been predicted, based on data stretching back to 2007. This is unlikely to be the result of a clock error, because TESS observations of other hot Jupiters (WASP-6b, 18b, and 46b) are compatible with a constant period, ruling out an 81.6-second offset at the 6.4$σ$ level. The 1.3-day orbital period of WASP-4b appears to be decreasing at a rate of $\dot{P} = -12.6 \pm 1.2$ milliseconds per year. The apparent period change might be caused by tidal orbital decay or apsidal precession, although both interpretations have shortcomings. The gravitational influence of a third body is another possibility, though at present there is minimal evidence for such a body. Further observations are needed to confirm and understand the timing variation.

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arXiv2019

Complex Rotational Modulation of Rapidly Rotating M-Stars Observed with TESS

We have searched for short periodicities in the light curves of stars with $T_{\rm eff}$ cooler than 4000 K made from 2-minute cadence data obtained in TESS sectors 1 and 2. Herein we report the discovery of 10 rapidly rotating M-dwarfs with highly structured rotational modulation patterns among 10 M dwarfs found to have rotation periods less than 1 day. Star-spot models cannot explain the highly structured periodic variations which typically exhibit between 10 and 40 Fourier harmonics. A similar set of objects was previously reported following K2 observations of the Upper Scorpius association (Stauffer et al. 2017). We examine the possibility that the unusual structured light-curves could stem from absorption by charged dust particles that are trapped in or near the stellar magnetosphere. We also briefly explore the possibilities that the sharp structured features in the lightcurves are produced by extinction by coronal gas, by beaming of the radiation emitted from the stellar surface, or by occultations of spots by a dusty ring that surrounds the star. The latter is perhaps the most promising of these scenarios. Most of the structured rotators display flaring activity, and we investigate changes in the modulation pattern following the largest flares. As part of this study, we also report the discovery of 371 rapidly rotating M-dwarfs with rotational periods below 4 hr, of which the shortest period is 1.63 hr.

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arXiv2019

HD219666b: A hot-Neptune from TESS Sector 1

We report on the confirmation and mass determination of a transiting planet orbiting the old and inactive G7 dwarf star HD219666 (Mstar = 0.92 +/- 0.03 MSun, Rstar = 1.03 +/- 0.03 RSun, tau_star = 10 +/- 2 Gyr). With a mass of Mb = 16.6 +/- 1.3 MEarth, a radius of Rb = 4.71 +/- 0.17 REarth, and an orbital period of P ~ 6 days, HD219666b is a new member of a rare class of exoplanets: the hot-Neptunes. The Transiting Exoplanet Survey Satellite (TESS) observed HD219666 (also known as TOI-118) in its Sector 1 and the light curve shows four transit-like events, equally spaced in time. We confirmed the planetary nature of the candidate by gathering precise radial-velocity measurements with HARPS@ESO3.6m. We used the co-added HARPS spectrum to derive the host star fundamental parameters (Teff = 5527 +/- 65 K, log g = 4.40 +/- 0.11 (cgs), [Fe/H]= 0.04 +/- 0.04 dex, log R'HK = -5.07 +/- 0.03), as well as the abundances of many volatile and refractory elements. The host star brightness (V = 9.9) makes it suitable for further characterisation by means of in-transit spectroscopy. The determination of the planet orbital obliquity, along with the atmospheric metal-to-hydrogen content and thermal structure could provide us with important clues on the formation mechanisms of this class of objects.

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arXiv2019

K2-290: a warm Jupiter and a mini-Neptune in a triple-star system

We report the discovery of two transiting planets orbiting K2-290 (EPIC 249624646), a bright (V=11.11) late F-type star residing in a triple-star system. It was observed during Campaign 15 of the K2 mission, and in order to confirm and characterise the system, follow-up spectroscopy and AO imaging were carried out using the FIES, HARPS, HARPS-N, and IRCS instruments. From AO imaging and Gaia data we identify two M-dwarf companions at a separation of $113 \pm 2$ AU and $2467_{-155}^{+177}$ AU. From radial velocities, K2 photometry, and stellar characterisation of the host star, we find the inner planet to be a mini-Neptune with a radius of $3.06 \pm 0.16 R_{\oplus}$ and an orbital period of $P = 9.2$ days. The radius of the mini-Neptune suggests that the planet is located above the radius valley, and with an incident flux of $F\sim 400 F_{\oplus}$, it lies safely outside the super-Earth desert. The outer warm Jupiter has a mass of $0.774\pm 0.047 M_{\rm J}$ and a radius of $1.006\pm 0.050R_{\rm J}$, and orbits the host star every 48.4 days on an orbit with an eccentricity $e<0.241$. Its mild eccentricity and mini-Neptune sibling suggest that the warm Jupiter originates from in situ formation or disk migration.

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