arXiv subjects

George King

Publications and source records attributed to George King.

8 recordsLinked to original sources

arXiv2026

How Many Reflections Make a Dihedral Set Large?

Given a size-$k$ subset $S$ of a group $G$, how large can the product set $S^n$ be? We study this question, at several layers of refinement, for the infinite dihedral group. First, we give an explicit formula for the maximum size of $S^n$ among all size-$k$ subsets with a prescribed number of reflections. We then determine the optimal number of reflections that a size-$k$ set should contain in order to maximize $|S^n|$. When $k$ is fixed and $n\to\infty$, we obtain a clean asymptotic expression for the maximal size of $S^n$. Moreover, we compute this asymptotic separately for each fixed number of reflections in $S$. We show that the number of reflections influences the asymptotic size of $S^n$ only through a multiplicative coefficient, which admits a direct probabilistic interpretation. Finally, we compute the growth exponent of the maximum of $|S^n|$ when~$k=~n$.

math.GR↗

arXiv2025

The First Dedicated Survey of Atmospheric Escape from Planets Orbiting F Stars

Hydrodynamic escape can strip the envelopes of close-in exoplanets, but most observations of atmospheric mass loss to date have been confined to planets orbiting K and M dwarfs. A growing body of detections of atmospheric escape from planets orbiting early-type stars indicates that they may have significantly stronger and more extended outflows than planets orbiting cooler stars. However, it is unclear whether this limited sample of planets is representative of all gas giants orbiting early-type stars. Motivated by this question, we initiated the first dedicated survey of atmospheric escape from gas giants orbiting F stars in order to understand how their distinct radiation environments shape planetary outflows. We observed ten transits of six planets in an ultra-narrowband filter centered on the metastable helium line using Palomar/WIRC. We report strong ($>3\sigma$) detections of atmospheric escape for WASP-12~b and WASP-180~A~b, tentative ($>2\sigma$) detections for WASP-93~b and HAT-P-8~b, and non-detections for WASP-103~b and KELT-7~b. We fit these measurements with a 1D Parker wind model to derive corresponding mass-loss rates, and combine our results with literature measurements to obtain an updated picture of mass loss from planets orbiting early-type stars. Our results indicate that the observed variation in mass-loss rates can be explained by a combination of Roche filling factor and XUV luminosity, and disfavors NUV-driven escape models.

astro-ph.EP↗

arXiv2025

Why M-dwarf flares have limited impact on the atmospheric evaporation of sub-Neptunes and Earth-sized planets

M-type stars are prime targets for exoplanet searches within their habitable zones (HZs). These stars also exhibit significant magnetic flaring activity, particularly during their first billion years, which can potentially accelerate the evaporation of the hydrogen-helium envelopes of close-in planets. We employ the time-dependent photoionization hydrodynamics code ATES to investigate the impact of flares on atmospheric escape, focusing on an Earth-sized and a sub-Neptune-sized planet orbiting an early M-type star at distances of 0.01, 0.1, and 0.18-0.36 AU-the inner and outer edges of the HZ. Stellar flaring is modeled as a 1 Gyr-long high-activity phase followed by a 4 Gyr-long low-activity phase, each characterized by an appropriate flare frequency distribution. We find that flares have a modest impact-less than a factor of two-on the cumulative atmospheric mass loss, with the greatest absolute enhancement occurring when the planets are at their closest separation. However, the relative enhancement in mass loss between flaring and non-flaring cases is greater at larger orbital separations. This trend arises because, as stellar irradiation fluctuates between quiescent levels and peak flares, the proportion of time that a planet spends in the energy-limited versus recombination-limited mass loss regimes depends on its orbital separation. Additionally, we demonstrate the existence of a characteristic flare energy, intermediate between the minimum and maximum values, that maximizes the fractional contribution to flare-driven mass loss. Our results indicate that the flaring activity of M-dwarfs does not significantly affect the atmospheric retention of close-in planets, including those within the HZ. The potential occurrence of rare super-flares, which current observational campaigns may be biased against, does not alter our conclusions.

astro-ph.EP↗

arXiv2023

Survival in the Neptune desert: LTT 9779 b kept its atmosphere thanks to an unusually X-ray faint host star

The Neptunian desert is a region in period-radius parameter space with very few Neptune-sized planets at short orbital periods. Amongst these, LTT 9779 b is the only known Neptune with a period shorter than one day to retain a significant H-He atmosphere. If the Neptune desert is the result of X-ray/EUV-driven photoevaporation, it is surprising that the atmosphere of LTT 9779 b survived the intense bombardment of high energy photons from its young host star. However, the star has low measured rotational broadening, which points to the possibility of an anomalously slow spin period and hence a faint X-ray emission history that may have failed to evaporate the planet's atmosphere. We observed LTT 9779 with XMM-Newton and measured an upper limit for its X-ray luminosity that is a factor of fifteen lower than expected for its age. We also simulated the evaporation past of LTT 9779 b and found that the survival of its atmosphere to the present day is consistent with an unusually faint XUV irradiation history that matches both the X-ray and rotation velocity measurements. We conclude that the anomalously low X-ray irradiation of the one Neptune seen to survive in Neptunian desert supports the interpretation of the desert as primarily a result of photoevaporation.

astro-ph.EP↗

arXiv2021

The high-energy spectrum of the nearby planet-hosting inactive mid-M dwarf LHS 3844

To fully characterize the atmospheres, or lack thereof, of terrestrial exoplanets we must include the high-energy environments provided by their host stars. The nearby mid-M dwarf LHS 3844 hosts a terrestrial world which lacks a substantial atmosphere. We present a time series UV spectrum of LHS 3844 from 1131-3215A captured by HST/COS. We detect one flare in the FUV, which has an absolute energy of 8.96+/-0.79e28 erg and an equivalent duration of 355+/-31 s. We extract the flare and quiescent UV spectra separately. For each spectrum we estimate the Ly-alpha flux using correlations between UV line strengths. We use Swift-XRT to place an upper limit on the soft X-ray flux and construct a differential emission model (DEM) to estimate flux that is obscured by the interstellar medium. We compare the DEM flux estimates in the XUV to other methods that rely on scaling from the Ly-alpha, Si IV, and N V lines in the UV. The XUV, FUV, and NUV flux of LHS 3844 relative to its bolometric luminosity is log10(Lband/LBol) = -3.65, -4.16, and -4.56, respectively, for the quiescent state. These values agree with trends in high-energy flux as a function of stellar effective temperature found by the MUSCLES survey for a sample of early-M dwarfs. Many of the most spectroscopically accessible terrestrial exoplanets orbit inactive mid- to late-M dwarfs like LHS 3844. Measurements of M dwarf high-energy spectra are preferable for exoplanet characterization, but are not always possible. The spectrum of LHS 3844 is a useful proxy for the current radiation environment for these worlds.

astro-ph.SR↗

arXiv2020

Search for helium in the upper atmosphere of the hot Jupiter WASP-127 b using Gemini/Phoenix

Large-scale exoplanet search surveys have shown evidence that atmospheric escape is a ubiquitous process that shapes the evolution and demographics of planets. However, we lack a detailed understanding of this process because very few exoplanets discovered to date could be probed for signatures of atmospheric escape. Recently, the metastable helium triplet at 1.083 $μ$m has been shown to be a viable window for the presence of He-rich escaping envelopes around short-period exoplanets. Our objective is to use, for the first time, the Phoenix spectrograph to search for helium in the upper atmosphere of the inflated hot Jupiter WASP-127 b. We observed one transit and reduced the data manually since there is no pipeline available. We did not find a significant in-transit absorption signal indicative of the presence of helium around WASP-127 b, and set a 90% confidence upper limit for excess absorption at 0.87% in a 0.075 nm passband covering the He triplet. Given the large scale height of this planet, the lack of a detectable feature is likely due to unfavorable photoionization conditions to populate the metastable He triplet. This conclusion is supported by the inferred low coronal and chromospheric activity of the host star and the old age of the system, which result in a relatively mild high-energy environment around the planet.

astro-ph.EP↗

arXiv2018

NGTS-4b: A sub-Neptune Transiting in the Desert

We report the discovery of NGTS-4b, a sub-Neptune-sized planet transiting a 13th magnitude K-dwarf in a 1.34d orbit. NGTS-4b has a mass M=$20.6\pm3.0$M_E and radius R=$3.18\pm0.26$R_E, which places it well within the so-called "Neptunian Desert". The mean density of the planet ($3.45\pm0.95$g/cm^3) is consistent with a composition of 100% H$_2$O or a rocky core with a volatile envelope. NGTS-4b is likely to suffer significant mass loss due to relatively strong EUV/X-ray irradiation. Its survival in the Neptunian desert may be due to an unusually high core mass, or it may have avoided the most intense X-ray irradiation by migrating after the initial activity of its host star had subsided. With a transit depth of $0.13\pm0.02$%, NGTS-4b represents the shallowest transiting system ever discovered from the ground, and is the smallest planet discovered in a wide-field ground-based photometric survey.

astro-ph.EP↗

arXiv2016

No hydrogen exosphere detected around the super-Earth HD97658 b

The exoplanet HD97658b provides a rare opportunity to probe the atmospheric composition and evolution of moderately irradiated super-Earths. It transits a bright K star at a moderate orbital distance of 0.08 au. Its low density is compatible with a massive steam envelope that could photodissociate at high altitudes and become observable as escaping hydrogen. Our analysis of 3 transits with HST/STIS at Ly-alpha reveals no such signature, suggesting that the thermosphere is not hydrodynamically expanding and is subjected to a low escape of neutral hydrogen (<10^8 g/s at 3 sigma). Using HST Ly-alpha and Chandra & XMM-Newton observations at different epochs, we find that HD97658 is a weak and soft X-ray source with signs of chromospheric variability in the Ly-alpha line core. We determine an average reference for the intrinsic Ly-alpha line and XUV spectrum of the star, and show that HD97658 b is in mild conditions of irradiation compared to other known evaporating exoplanets with an XUV irradiation about 3 times lower than the evaporating warm Neptune GJ436 b. This could be why the thermosphere of HD97658b is not expanding: the low XUV irradiation prevents an efficient photodissociation of any putative steam envelope. Alternatively, it could be linked to a low hydrogen content or inefficient conversion of the stellar energy input. The HD97658 system provides clues for understanding the stability of low-mass planet atmospheres. Our study of HD97658 b can be seen as a control experiment of our methodology, confirming that it does not bias detections of atmospheric escape and underlining its strength and reliability. Our results show that stellar activity can be efficiently discriminated from absorption signatures by a transiting exospheric cloud. They also highlight the potential of observing the upper atmosphere of small transiting planets to probe their physical and chemical properties

astro-ph.EP↗