Polynomial sequences for bond percolation critical thresholds

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4,6,12) and (3^4,6) lattices using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. P03021), implemented as a branching process of lattices. I find the estimates for the bond percolation thresholds, p_c(4,6,12)=0.69377849... and p_c(3^4,6)=0.43437077..., compared with Parviainen's numerical results of p_c \approx 0.69373383 and p_c \approx 0.43430621 . These deviations are of the order 10^{-5}, as is standard for this method, although they are outside Parviainen's typical standard error of 10^{-7}. Deriving thresholds in this way for a given lattice leads to a polynomial with integer coefficients, the root in [0,1] of which gives the estimate for the bond threshold. I show how the method can be refined, leading to a sequence of higher order polynomials making predictions that likely converge to the exact answer. Finally, I discuss how this fact hints that for certain graphs, such as the kagome lattice, the exact bond threshold may not be the root of any polynomial with integer coefficients.Comment: submitted to Journal of Statistical Mechanic

The 3-edge-colouring problem on the 4-8 and 3-12 lattices

We consider the problem of counting the number of 3-colourings of the edges (bonds) of the 4-8 lattice and the 3-12 lattice. These lattices are Archimedean with coordination number 3, and can be regarded as decorated versions of the square and honeycomb lattice, respectively. We solve these edge-colouring problems in the infinite-lattice limit by mapping them to other models whose solution is known. The colouring problem on the 4-8 lattice is mapped to a completely packed loop model with loop fugacity n=3 on the square lattice, which in turn can be mapped to a six-vertex model. The colouring problem on the 3-12 lattice is mapped to the same problem on the honeycomb lattice. The 3-edge-colouring problems on the 4-8 and 3-12 lattices are equivalent to the 3-vertex-colouring problems (and thus to the zero-temperature 3-state antiferromagnetic Potts model) on the "square kagome" ("squagome") and "triangular kagome" lattices, respectively.Comment: 10 pages, 4 figures (2 in colour). Added discussion, 2 refs. in Sec.

The discovery of WASP-151b, WASP-153b, WASP-156b: Insights on giant planet migration and the upper boundary of the Neptunian desert

To investigate the origin of the features discovered in the exoplanet population, the knowledge of exoplanets’ mass and radius with a good precision (≲10%) is essential. To achieve this purpose the discovery of transiting exoplanets around bright stars is of prime interest. In this paper, we report the discovery of three transiting exoplanets by the SuperWASP survey and the SOPHIE spectrograph with mass and radius determined with a precision better than 15%. WASP-151b and WASP-153b are two hot Saturns with masses, radii, densities and equilibrium temperatures of 0.31−0.03+0.04 MJ, 1.13−0.03+0.03 RJ, 0.22−0.02+0.03 ρJ and 1290−10+20 K, and 0.39−0.02+0.02 MJ, 1.55−0.08+0.10 RJ, 0.11−0.02+0.02 ρJ and 1700−40+40 K, respectively. Their host stars are early G type stars (with mag V ~ 13) and their orbital periods are 4.53 and 3.33 days, respectively. WASP-156b is a super-Neptune orbiting a K type star (mag V = 11.6). It has a mass of 0.128−0.009+0.010 MJ, a radius of 0.51−0.02+0.02 RJ, a density of 1.0−0.1+0.1 ρJ, an equilibrium temperature of 970−20+30 K and an orbital period of 3.83 days. The radius of WASP-151b appears to be only slightly inflated, while WASP-153b presents a significant radius anomaly compared to a recently published model. WASP-156b, being one of the few well characterized super-Neptunes, will help to constrain the still debated formation of Neptune size planets and the transition between gas and ice giants. The estimates of the age of these three stars confirms an already observed tendency for some stars to have gyrochronological ages significantly lower than their isochronal ages. We propose that high eccentricity migration could partially explain this behavior for stars hosting a short period planet. Finally, these three planets also lie close to (WASP-151b and WASP-153b) or below (WASP-156b) the upper boundary of the Neptunian desert. Their characteristics support that the ultra-violet irradiation plays an important role in this depletion of planets observed in the exoplanet population

Transit Photometry as an Exoplanet Discovery Method

Photometry with the transit method has arguably been the most successful exoplanet discovery method to date. A short overview about the rise of that method to its present status is given. The method's strength is the rich set of parameters that can be obtained from transiting planets, in particular in combination with radial velocity observations; the basic principles of these parameters are given. The method has however also drawbacks, which are the low probability that transits appear in randomly oriented planet systems, and the presence of astrophysical phenomena that may mimic transits and give rise to false detection positives. In the second part we outline the main factors that determine the design of transit surveys, such as the size of the survey sample, the temporal coverage, the detection precision, the sample brightness and the methods to extract transit events from observed light curves. Lastly, an overview over past, current and future transit surveys is given. For these surveys we indicate their basic instrument configuration and their planet catch, including the ranges of planet sizes and stellar magnitudes that were encountered. Current and future transit detection experiments concentrate primarily on bright or special targets, and we expect that the transit method remains a principal driver of exoplanet science, through new discoveries to be made and through the development of new generations of instruments.Comment: Review chapte

Transiting exoplanets from the CoRoT space mission: XXIX. The hot Jupiters CoRoT-30 b and CoRoT-31 b

We report the discovery as well as the orbital and physical characterizations of two new transiting giant exoplanets, CoRoT-30 b and CoRoT-31 b, with the CoRoT space telescope. Methods. We analyzed two complementary data sets: photometric transit light curves measured by CoRoT, and radial velocity curves measured by the HARPS spectrometer. To derive the absolute masses and radii of the planets, we modeled the stars from available magnitudes and spectra. Results. We find that CoRoT-30 b is a warm Jupiter on a close-to-circular 9.06-day orbit around a G3V star with a semi-major axis of about 0.08 AU. It has a radius of 1.01 \ub1 0.08 RJ, a mass of 2.90 \ub1 0.22 MJ, and therefore a mean density of 3.45 \ub1 0.65 g cm-3. The hot Jupiter CoRoT-31 b is on a close-to-circular 4.63-day orbit around a G2 IV star with a semi-major axis of about 0.05 AU. It has a radius of 1.46 \ub1 0.30 RJ, a mass of 0.84 \ub1 0.34 MJ, and therefore a mean density of 0.33 \ub1 0.18 g cm-3. Conclusions. Neither system seems to support the claim that stars hosting planets are more depleted in lithium. The radii of both planets are close to that of Jupiter, but they differ in mass; CoRoT-30 b is ten times denser than CoRoT-31 b. The core of CoRoT-30 b would weigh between 15 and 75 Earth masses, whereas relatively weak constraints favor no core for CoRoT-31 b. In terms of evolution, the characteristics of CoRoT-31 b appear to be compatible with the high-eccentricity migration scenario, which is not the case for CoRoT-30 b. The angular momentum of CoRoT-31 b is currently too low for the planet to evolve toward synchronization of its orbital revolution with stellar rotation, and the planet will slowly spiral-in while its host star becomes a red giant. CoRoT-30 b is not synchronized either: it looses angular momentum owing to stellar winds and is expected reach steady state in about 2 Gyr. CoRoT-30 and 31, as a pair, are a truly remarkable example of diversity in systems with hot Jupiters

Two super-Earths at the edge of the habitable zone of the nearby M dwarf TOI-2095

The main scientific goal of TESS is to find planets smaller than Neptune around stars bright enough to allow further characterization studies. Given our current instrumentation and detection biases, M dwarfs are prime targets to search for small planets that are in (or nearby) the habitable zone of their host star. Here we use photometric observations and CARMENES radial velocity measurements to validate a pair of transiting planet candidates found by TESS. The data was fitted simultaneously using a Bayesian MCMC procedure taking into account the stellar variability present in the photometric and spectroscopic time series. We confirm the planetary origin of the two transiting candidates orbiting around TOI-2095 (TIC 235678745). The star is a nearby M dwarf ($d = 41.90 \pm 0.03$ pc, $T_{\rm eff} = 3759 \pm 87$ K, $V = 12.6$ mag) with a stellar mass and radius of $M_\star = 0.44 \pm 0.02 \; M_\odot$ and $R_\star = 0.44 \pm 0.02 \; R_\odot$, respectively. The planetary system is composed of two transiting planets: TOI-2095b with an orbital period of $P_b = 17.66484 \pm (7\times 10^{-5})$ days and TOI-2095c with $P_c = 28.17232 \pm (14\times 10^{-5})$ days. Both planets have similar sizes with $R_b = 1.25 \pm 0.07 \; R_\oplus$ and $R_c = 1.33 \pm 0.08 \; R_\oplus$ for planet b and c, respectively. We put upper limits on the masses of these objects with $M_b < 4.1 \; M_\oplus$ for the inner and $M_c < 7.4 \; M_\oplus$ for the outer planet (95\% confidence level). These two planets present equilibrium temperatures in the range of 300 - 350 K and are close to the inner edge of the habitable zone of their star.Comment: Submitted to Astronomy & Astrophysic

Radial velocity confirmation of K2-100b: A young, highly irradiated, and low-density transiting hot Neptune

We present a detailed analysis of HARPS-N radial velocity observations of K2-100, a young and active star in the Praesepe cluster, which hosts a transiting planet with a period of 1.7 d. We model the activity-induced radial velocity variations of the host star with a multidimensional Gaussian Process framework and detect a planetary signal of 10.6 \ub1 3.0 m s−1, which matches the transit ephemeris, and translates to a planet mass of 21.8 \ub1 6.2 M. We perform a suite of validation tests to confirm that our detected signal is genuine. This is the first mass measurement for a transiting planet in a young open cluster. The relatively low density of the planet, 2.04+−006661 g cm−3, implies that K2-100b retains a significant volatile envelope. We estimate that the planet is losing its atmosphere at a rate of 1011–1012 g s−1 due to the high level of radiation it receives from its host star

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.Comment: Published in Nature on November 30, 2023. Supplementary Information can be found in the online version of the paper in the journa