arXiv subjects

F. Dai

Publications and source records attributed to F. Dai.

At least 19 recordsLinked to original sources

arXiv2026

A decade of monitoring the HIP 41378's planetary system

Multi-planetary systems provide key constraints on planet formation and evolution, as their architecture encodes the dynamical history of planets formed within a common protoplanetary disk. However, the current population remains strongly biased toward compact, short-period systems, and only a limited number of such systems with measured masses and radii are known. HIP 41378 is an exceptional system hosting five transiting planets with orbital periods up to 1.5 years, including an ultra-low density planet HIP 41378 f. The outer transiting planets d and e remained poorly constrained with unknown periods and masses, leaving the system architecture only partially characterised. We present long-term monitoring of this target with high-precision radial-velocity (RV) instruments (HARPS, HARPS-N, HIRES, and ESPRESSO) and space-based photometry spanning 2015-2024. We detect RV signals for all the planets, confirming their orbital periods and constraining their masses. In particular, the RV data strongly favour an orbital period of Pd = 278 days for planet d and refine the orbital period of planet e to Pe = 393+3-5 days. We measure a new mass of Mf = 25 \pm 5 earth masses for HIP 41378 f, confirming its super-puff nature with a bulk density of 0.166+0.033-0.036 g cm3. We also confirm the planetary nature of HIP 41378 g, a non-transiting planet with a 63-day period, and determine its minimum mass. In addition, the RVs reveal a long-period signal, with P = 2602+468-433 days, which we attribute to the candidate planet HIP 41378 h, although a stellar magnetic cycle cannot be excluded. Finally, we investigate the system's dynamical architecture and resonant structure, assess its completeness by constraining additional undetected planets, and discuss the implications for the origin and internal structure of the remarkable planet HIP 41378 f.

astro-ph.EP↗

arXiv2026

A survey of sampling discretization of integral and uniform norms

This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for trigonometric and algebraic polynomials, which play a crucial role in Fourier analysis, interpolation, and approximation theory. We focus on the problem in the broad context of finite-dimensional subspaces, where norms defined by general probability measures are approximated by their discrete counterparts. The primary emphasis is on results closely related to the authors' recent research. A key objective is to highlight the main ideas and techniques that form the foundation of the proofs in this area. This survey serves as a complement to three recently published survey papers on sampling discretization \cite{DPTT, KKLT, LMT}.

math.NA↗

arXiv2026

A survey on sampling recovery

The reconstruction of unknown functions from a finite number of samples is a fundamental challenge in pure and applied mathematics. This survey provides a comprehensive overview of recent developments in sampling recovery, focusing on the accuracy of various algorithms and the relationship between optimal recovery errors, nonlinear approximation, and the Kolmogorov widths of function classes. A central theme is the synergy between the theory of universal sampling discretization and Lebesgue-type inequalities for greedy algorithms. We discuss three primary algorithmic frameworks: weighted least squares and $\ell_p$ minimization, sparse approximation methods, and greedy algorithms such as the Weak Orthogonal Matching Pursuit (WOMP) in Hilbert spaces and the Weak Tchebychev Greedy Algorithm (WCGA) in Banach spaces. These methods are applied to function classes defined by structural conditions, like the $A_\beta^r$ and Wiener-type classes, as well as classical Sobolev-type classes with dominated mixed derivatives. Notably, we highlight recent findings showing that nonlinear sampling recovery can provide superior error guarantees compared to linear methods for certain multivariate function classes.

math.NA↗

arXiv2024

The MOPYS project: A survey of 70 planets in search of extended He I and H atmospheres. No evidence of enhanced evaporation in young planets

During the first Gyr of their life, exoplanet atmospheres suffer from different atmospheric escape phenomena that can strongly affect the shape and morphology of the exoplanet itself. These processes can be studied with Ly$\alpha$, H$\alpha$ and/or He I triplet observations. We present high-resolution spectroscopy observations from CARMENES and GIARPS checking for He I and H$\alpha$ signals in 20 exoplanetary atmospheres: V1298Tau c, K2-100b, HD63433b, HD63433c, HD73583b, HD73583c, K2-77b, TOI-2076b, TOI-2048b, HD235088b, TOI-1807b, TOI-1136d, TOI-1268b, TOI-1683b, TOI-2018b, MASCARA-2b, WASP-189b, TOI-2046b, TOI-1431b, and HAT-P-57b. We report two new high-resolution spectroscopy He I detections for TOI-1268b and TOI-2018b, and an H$\alpha$ detection for TOI-1136d. The MOPYS (Measuring Out-flows in Planets orbiting Young Stars) project aims to understand the evaporating phenomena and test their predictions from the current observations. We compiled a list of 70 exoplanets with He I and/or H$\alpha$ observations, from this work and the literature, and we considered the He I and H$\alpha$ results as proxy for atmospheric escape. Our principal results are that 0.1-1Gyr-old planets do not exhibit more He I or H$\alpha$ detections than older planets, and evaporation signals are more frequent for planets orbiting $\sim$1-3Gyr-old stars. We provide new constrains to the cosmic shoreline, the empirical division between rocky planets and planets with atmosphere, by using the evaporation detections and explore the capabilities of a new dimensionless parameter, $R_{\rm He}/R_{\rm Hill}$, to explain the He I triplet detections. Furthermore, we present a statistically significant upper boundary for the He I triplet detections in the $T_{\rm eq}$ vs $\rho_{\rm p}$ parameter space. Planets located above that boundary are unlikely to show He I absorption signals.

astro-ph.EP↗

arXiv2023

A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067

Planets with radii between that of the Earth and Neptune (hereafter referred to as sub-Neptunes) are found in close-in orbits around more than half of all Sun-like stars. Yet, their composition, formation, and evolution remain poorly understood. The study of multi-planetary systems offers an opportunity to investigate the outcomes of planet formation and evolution while controlling for initial conditions and environment. Those in resonance (with their orbital periods related by a ratio of small integers) are particularly valuable because they imply a system architecture practically unchanged since its birth. Here, we present the observations of six transiting planets around the bright nearby star HD 110067. We find that the planets follow a chain of resonant orbits. A dynamical study of the innermost planet triplet allowed the prediction and later confirmation of the orbits of the rest of the planets in the system. The six planets are found to be sub-Neptunes with radii ranging from 1.94 to 2.85 Re. Three of the planets have measured masses, yielding low bulk densities that suggest the presence of large hydrogen-dominated atmospheres.

astro-ph.EP↗

arXiv2023

TOI-1801 b: A temperate mini-Neptune around a young M0.5 dwarf

We report the discovery, mass, and radius determination of TOI-1801 b, a temperate mini-Neptune around a young M dwarf. TOI-1801 b was observed in TESS sectors 22 and 49, and the alert that this was a TESS planet candidate with a period of 21.3 days went out in April 2020. However, ground-based follow-up observations, including seeing-limited photometry in and outside transit together with precise radial velocity (RV) measurements with CARMENES and HIRES revealed that the true period of the planet is 10.6 days. These observations also allowed us to retrieve a mass of 5.74 $\pm$ 1.46 $M_\oplus$, which together with a radius of 2.08 $\pm$ 0.12 $R_\oplus$, means that TOI-1801 b is most probably composed of water and rock, with an upper limit of 2\% by mass of H$_{2}$ in its atmosphere. The stellar rotation period of 16 days is readily detectable in our RV time series and in the ground-based photometry. We derived a likely age of 600--800 Myr for the parent star TOI-1801, which means that TOI-1801 b is the least massive young mini-Neptune with precise mass and radius determinations. Our results suggest that if TOI-1801 b had a larger atmosphere in the past, it must have been removed by some evolutionary mechanism on timescales shorter than 1 Gyr.

astro-ph.EP↗

arXiv2023

Lebesgue-type inequalities in sparse sampling recovery

Recently, it has been discovered that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error being measured in the square norm. It was established that a simple greedy type algorithm -- Weak Orthogonal Matching Pursuit -- based on good points for universal discretization provides effective recovery in the square norm. In this paper we extend those results by replacing the square norm with other integral norms. In this case we need to conduct our analysis in a Banach space rather than in a Hilbert space, making the techniques more involved. In particular, we establish that a greedy type algorithm -- Weak Chebyshev Greedy Algorithm -- based on good points for the $L_p$-universal discretization provides good recovery in the $L_p$ norm for $2\le p<\infty$. Furthermore, we discuss the problem of stable recovery and demonstrate its close relationship with sampling discretization.

math.NA↗

arXiv2023

TOI-1416: A system with a super-Earth planet with a 1.07d period

TOI 1416 (BD+42 2504, HIP 70705) is a V=10 late G or early K-type dwarf star with transits detected by TESS. Radial velocities verify the presence of the transiting planet TOI-1416 b, with a period of 1.07d, a mass of $3.48 M_{Earth}$ and a radius of $1.62 R_{Earth}$, implying a slightly sub-Earth density of $4.50$ g cm$^{-3}$. The RV data also further indicate a tentative planet c with a period of 27.4 or 29.5 days, whose nature cannot be verified due to strong suspicions about contamination by a signal related to the Moon's synodic period of 29.53 days. The near-USP (Ultra Short Period) planet TOI-1416 b is a typical representative of a short-period and hot ($T_{eq} \approx$ 1570 K) super-Earth like planet. A planet model of an interior of molten magma containing a significant fraction of dissolved water provides a plausible explanation for its composition, and its atmosphere could be suitable for transmission spectroscopy with JWST. The position of TOI-1416 b within the radius-period distribution corroborates that USPs with periods of less than one day do not form any special group of planets. Rather, this implies that USPs belong to a continuous distribution of super-Earth like planets with periods ranging from the shortest known ones up to ~ 30 days, whose period-radius distribution is delimitated against larger radii by the Neptune desert and by the period-radius valley that separates super-Earths from sub-Neptune planets. In the abundance of small-short periodic planets against period, a plateau between periods of 0.6 to 1.4 days has however become notable that is compatible with the low-eccentricity formation channel. For the Neptune desert, its lower limits required a revision due to the increasing population of short period planets and new limits are provided. These limits are also given in terms of the planets' insolation and effective temperatures.

astro-ph.EP↗

arXiv2023

TOI-1130: A photodynamical analysis of a hot Jupiter in resonance with an inner low-mass planet

The TOI-1130 is a known planetary system around a K-dwarf consisting of a gas giant planet, TOI-1130 c, on an 8.4-day orbit, accompanied by an inner Neptune-sized planet, TOI-1130 b, with an orbital period of 4.1 days. We collected precise radial velocity (RV) measurements of TOI-1130 with the HARPS and PFS spectrographs as part of our ongoing RV follow-up program. We perform a photodynamical modeling of the HARPS and PFS RVs, and transit photometry from the Transiting Exoplanet Survey Satellite (TESS) and the TESS Follow-up Observing Program. We determine the planet masses and radii of TOI-1130 b and TOI-1130 c to be Mb = 19.28 $\pm$ 0.97 M$_\oplus$ and Rb = 3.56 $\pm$ 0.13 R$_\oplus$, and Mc = 325.59 $\pm$ 5.59 M$_\oplus$ and Rc = 13.32+1.55-1.41 R$_\oplus$, respectively. We spectroscopically confirm TOI-1130 b that was previously only validated. We find that the two planets orbit with small eccentricities in a 2:1 resonant configuration. This is the first known system with a hot Jupiter and an inner lower mass planet locked in a mean-motion resonance. TOI-1130 belongs to the small yet increasing population of hot Jupiters with an inner low-mass planet that challenges the pathway for hot Jupiter formation. We also detect a linear RV trend possibly due to the presence of an outer massive companion.

astro-ph.EP↗

arXiv2023

Random points are good for universal discretization

There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling discretization results turn out to be very useful in various applications, particularly in sampling recovery. Recent sampling discretization results typically provide existence of good sampling points for discretization. In this paper, we show that independent and identically distributed random points provide good universal discretization with high probability. Furthermore, we demonstrate that a simple greedy algorithm based on those points that are good for universal discretization provides excellent sparse recovery results in the square norm.

math.FA↗

arXiv2023

Universal discretization and sparse sampling recovery

Recently, it was discovered that for a given function class $\mathbf{F}$ the error of best linear recovery in the square norm can be bounded above by the Kolmogorov width of $\mathbf{F}$ in the uniform norm. That analysis is based on deep results in discretization of the square norm of functions from finite dimensional subspaces. In this paper we show how very recent results on universal discretization of the square norm of functions from a collection of finite dimensional subspaces lead to an inequality between optimal sparse recovery in the square norm and best sparse approximations in the uniform norm with respect to appropriate dictionaries.

math.NA↗

arXiv2022

Radial velocity confirmation of a hot super-Neptune discovered by TESS with a warm Saturn-mass companion

We report the discovery and confirmation of the planetary system TOI-1288. This late G dwarf harbours two planets: TOI-1288 b and TOI-1288 c. We combine TESS space-borne and ground-based transit photometry with HARPS-N and HIRES high-precision Doppler measurements, which we use to constrain the masses of both planets in the system and the radius of planet b. TOI-1288~b has a period of $2.699835^{+0.000004}_{-0.000003}$ d, a radius of $5.24 \pm 0.09$ R$_\oplus$, and a mass of $42 \pm 3$ M$_\oplus$, making this planet a hot transiting super-Neptune situated right in the Neptunian desert. This desert refers to a paucity of Neptune-sized planets on short period orbits. Our 2.4-year-long Doppler monitoring of TOI-1288 revealed the presence of a Saturn-mass planet on a moderately eccentric orbit ($0.13^{+0.07}_{-0.09}$) with a minimum mass of $84 \pm 7$ M$_\oplus$ and a period of $443^{+11}_{-13}$ d. The 5 sectors worth of TESS data do not cover our expected mid-transit time for TOI-1288 c, and we do not detect a transit for this planet in these sectors.

astro-ph.EP↗

arXiv2022

Some improved bounds in sampling discretization of integral norms

The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of the Nikol'skii-type inequality. {In particular, we obtain} some upper bounds on the number of sample points sufficient for good discretization of the integral $L_p$ norms, $1\le p<2$, of functions from finite-dimensional subspaces of continuous functions. Our new results improve upon the known results in this direction. We use a new technique based on deep results of Talagrand from functional analysis.

math.FA↗

arXiv2022

On the cardinality of lower sets and universal discretization

A set $Q$ in $\mathbb{Z}_+^d$ is a lower set if $(k_1,\dots,k_d)\in Q$ implies $(l_1,\dots,l_d)\in Q$ whenever $0\le l_i\le k_i$ for all $i$. We derive new and refine known results regarding the cardinality of the lower sets of size $n$ in $\mathbb{Z}_+^d$. Next we apply these results for universal discretization of the $L_2$-norm of elements from $n$-dimensional subspaces of trigonometric polynomials generated by lower sets.

math.NA↗

arXiv2021

K2-99 revisited: a non-inflated warm Jupiter, and a temperate giant planet on a 522-d orbit around a subgiant

We report new photometric and spectroscopic observations of the K2-99 planetary system. Asteroseismic analysis of the short-cadence light curve from K2's Campaign 17 allows us to refine the stellar properties. We find K2-99 to be significantly smaller than previously thought, with $R_{\star} = 2.55\pm0.02$ $\mathrm{R_\odot}$. The new light curve also contains four transits of K2-99b, which we use to improve our knowledge of the planetary properties. We find the planet to be a non-inflated warm Jupiter, with $R_\mathrm{b} = 1.06 \pm 0.01$ $\mathrm{R_{Jup}}$. Sixty new radial velocity measurements from HARPS, HARPS-N, and HIRES enable the determination of the orbital parameters of K2-99c, which were previously poorly constrained. We find that this outer planet has a minimum mass $M_\mathrm{c} \sin i_\mathrm{c} = 8.4\pm0.2$ $\mathrm{M_{Jup}}$, and an eccentric orbit ($e_\mathrm{c} = 0.210 \pm 0.009$) with a period of $522.2\pm1.4$ d. Upcoming TESS observations in 2022 have a good chance of detecting the transit of this planet, if the mutual inclination between the two planetary orbits is small.

astro-ph.EP↗

arXiv2021

The young HD 73583 (TOI-560) planetary system: Two 10-M$_\oplus$ mini-Neptunes transiting a 500-Myr-old, bright, and active K dwarf

We present the discovery and characterisation of two transiting planets observed by \textit{TESS} in the light curves of the young and bright (V=9.67) star HD73583 (TOI-560). We perform an intensive spectroscopic and photometric space- and ground-based follow-up in order to confirm and characterise the system. We found that HD73583 is a young ($\sim 500$~Myr) active star with a rotational period of $12.08 \pm 0.11 $\,d, and a mass and radius of $ 0.73 \pm 0.02 M_\odot$ and $0.65 \pm 0.02 R_\odot$, respectively. HD73583 b ($P_b=6.3980420 _{ - 0.0000062 }^{+0.0000067}$ d) has a mass and radius of $10.2 _{-3.1}^{+3.4} M_\oplus$ and$2.79 \pm 0.10 R_\oplus$, respectively, that gives a density of $2.58 _{-0.81}^{ 0.95} {\rm g\,cm^{-3}}$. HD73583 c ($P_c= 18.87974 _{-0.00074 }^{+0.00086}$) has a mass and radius of $9.7_{-1.7} ^ {+1.8} M_\oplus$ and $2.39_{-0.09}^{+0.10} R_\oplus$, respectively, this translates to a density of $3.88 _{-0.80}^{+0.91} {\rm g\,cm^{-3}}$. Both planets are consistent with worlds made of a solid core surrounded by a volatile envelope. Because of their youth and host star brightness, they both are excellent candidates to perform transmission spectroscopy studies. We expect ongoing atmospheric mass-loss for both planets caused by stellar irradiation. We estimate that the detection of evaporating signatures on H and He would be challenging, but doable with present and future instruments.

astro-ph.EP↗

arXiv2021

HD207897 b: A dense sub-Neptune transiting a nearby and bright K-type star

We present the discovery and characterization of a transiting sub-Neptune orbiting with a 16.20 day period around a nearby (28 pc) and bright(V=8.37) K0V star HD207897 (TOI-1611). This discovery is based on photometric measurements from the Transiting Exoplanet Survey Satellite(TESS) mission and radial velocity (RV) observations from the SOPHIE, Automated Planet Finder (APF) and HIRES high precision spectrographs. We used EXOFASTv2 for simultaneously modeling the parameters of the planet and its host star, combining photometric and RV data to determine the planetary system parameters. We show that the planet has a radius of 2.50+/-0.08 RE and a mass of either 14.4+/-1.6 ME or 15.9+/-1.6 ME with nearly equal probability; the two solutions correspond to two possibilities for the stellar activity period. Hence, the density is either 5.1+/-0.7 g cm^-3 or 5.5^{+0.8}_{-0.7} g cm^-3, making it one of the relatively rare dense sub-Neptunes. The existence of such a dense planet at only 0.12 AU from its host star is unusual in the currently observed sub-Neptune (2<RE<4) population. The most likely scenario is that this planet has migrated to its current position.

astro-ph.EP↗

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.

math.NA↗