Studies of planetary atmospheric composition, variability, and evolution require appropriate theoretical and numerical tools to estimate key atmospheric parameters, among which the mass-loss rate is ...often the most important. In evolutionary studies, it is common to use the energy-limited formula, which is attractive for its simplicity but ignores important physical effects and can be inaccurate in many cases. To overcome this problem, we consider a recently developed grid of about 7000 one-dimensional upper-atmosphere hydrodynamic models computed for a wide range of planets with hydrogen-dominated atmospheres from which we extract the mass-loss rates. The grid boundaries are 1:39 in planetary mass, 1:10 in planetary radius, 300:2000 K in equilibrium temperature, 0.4:1.3 in host star's mass, 0.002:1.3 au in orbital separation, and about 1026:5×1030 erg s−1 in stellar X-ray and extreme ultraviolet luminosity. We then derive an analytical expression for the atmospheric mass-loss rates based on a fit to the values obtained from the grid. The expression provides the mass-loss rates as a function of planetary mass, planetary radius, orbital separation, and incident stellar high-energy flux. We show that this expression is a significant improvement to the energy-limited approximation for a wide range of planets. The analytical expression presented here enables significantly more accurate planetary evolution computations without increasing computing time.
There is growing observational and theoretical evidence suggesting that atmospheric escape is a key driver of planetary evolution. Commonly, planetary evolution models employ simple analytic formulae ...(e.g. energy limited escape) that are often inaccurate, and more detailed physical models of atmospheric loss usually only give snapshots of an atmosphere’s structure and are difficult to use for evolutionary studies. To overcome this problem, we have upgraded and employed an existing upper atmosphere hydrodynamic code to produce a large grid of about 7000 models covering planets with masses 1–39 M⊕ with hydrogen-dominated atmospheres and orbiting late-type stars. The modelled planets have equilibrium temperatures ranging between 300 and 2000 K. For each considered stellar mass, we account for three different values of the high-energy stellar flux (i.e. low, moderate, and high activity). For each computed model, we derived the atmospheric temperature, number density, bulk velocity, X-ray and EUV (XUV) volume heating rates, and abundance of the considered species as a function of distance from the planetary centre. From these quantities, we estimate the positions of the maximum dissociation and ionisation, the mass-loss rate, and the effective radius of the XUV absorption. We show that our results are in good agreement with previously published studies employing similar codes. We further present an interpolation routine capable to extract the modelling output parameters for any planet lying within the grid boundaries. We used the grid to identify the connection between the system parameters and the resulting atmospheric properties. We finally applied the grid and the interpolation routine to estimate atmospheric evolutionary tracks for the close-in, high-density planets CoRoT-7 b and HD 219134 b,c. Assuming that the planets ever accreted primary, hydrogen-dominated atmospheres, we find that the three planets must have lost them within a few Myr.
Context. Transmission spectroscopy has become a prominent tool for characterizing the atmospheric properties on close-in transiting planets. Recent observations have revealed a remarkable diversity ...in exoplanet spectra, which show absorption signatures of Na, K and H2O, in some cases partially or fully attenuated by atmospheric aerosols. Aerosols (clouds and hazes) themselves have been detected in the transmission spectra of several planets thanks to wavelength-dependent slopes caused by the particles’ scattering properties. Aims. We present an optical 550–960 nm transmission spectrum of the extremely irradiated hot Jupiter WASP-103b, one of the hottest (2500 K) and most massive (1.5 MJ) planets yet to be studied with this technique. WASP-103b orbits its star at a separation of less than 1.2 times the Roche limit and is predicted to be strongly tidally distorted. Methods. We have used Gemini/GMOS to obtain multi-object spectroscopy throughout three transits of WASP-103b. We used relative spectrophotometry and bin sizes between 20 and 2 nm to infer the planet’s transmission spectrum. Results. We find that WASP-103b shows increased absorption in the cores of the alkali (Na, K) line features. We do not confirm the presence of any strong scattering slope as previously suggested, pointing towards a clear atmosphere for the highly irradiated, massive exoplanet WASP-103b. We constrain the upper boundary of any potential cloud deck to reside at pressure levels above 0.01 bar. This finding is in line with previous studies on cloud occurrence on exoplanets which find that clouds dominate the transmission spectra of cool, low surface gravity planets while hot, high surface gravity planets are either cloud-free, or possess clouds located below the altitudes probed by transmission spectra.
We compare the effects of Nordic walking training (NW) and Free walk (FW) on functional parameters (motor symptoms, balance) and functional mobility (Timed Up and Go at Self‐selected Speed – TUGSS, ...and at forced speed, TUGFS; Self‐selected Walking Speed, SSW; locomotor rehabilitation index, LRI) of Parkinson's disease (PD) patients. The study included 33 patients with clinical diagnosis of idiopathic PD, and staging between 1 and 4 in the Hoehn and Yahr scale (H&Y) randomized into two groups: NW (N = 16) and FW (N = 17) for 6 weeks. Baseline characteristics were compared trough a one‐way ANOVA. Outcomes were analyzed using the Generalized Estimation Equations (GEE) with a Bonferroni post‐hoc. Data were analyzed using SPSS v.20.0. Improvements in UPDRS III (P < 0.001), balance scores (P < 0.035), TUGSS distance (P < 0.001), TUGFS distance (P < 0.001), SSW (P < 0.001), and LRI (P < 0.001) were found for both groups. However, the NW group showed significant differences (P < 0.001) when compared to the FW group for the functional mobility. We conclude the NW improves functional parameters and walking mobility demonstrating that NW is as effective as the FW, including benefits for FW on the functional mobility of people with PD.
Context.
Several observational and theoretical results indicate that the atmospheric temperature of the ultra-hot Jupiter KELT-9b in the main line formation region is a few thousand degrees higher ...than predicted by self-consistent models.
Aims.
Our aim was to test whether non-local thermodynamic equilibrium (NLTE) effects are responsible for the presumably higher temperature.
Methods.
We employed the Cloudy NLTE radiative transfer code to self-consistently compute the upper atmospheric temperature-pressure (TP) profile of KELT-9b, assuming solar metallicity and accounting for Roche potential. In the lower atmosphere, we used an updated version of the HELIOS radiative-convective equilibrium code to constrain the Cloudy model.
Results.
The Cloudy NLTE TP profile is ≈2000 K hotter than that obtained with previous models assuming LTE. In particular, in the 1–10
−7
bar range the temperature increases from ≈4000 to ≈8500 K, remaining roughly constant at lower pressures. We find that the high temperature in the upper atmosphere of KELT-9b is driven principally by NLTE effects modifying the Fe and Mg level populations, which strongly influence the atmospheric thermal balance. We employed Cloudy to compute LTE and NLTE synthetic transmission spectra on the basis of the TP profiles computed in LTE and NLTE, respectively, finding that the NLTE model generally produces stronger absorption lines, particularly in the ultraviolet, than the LTE model (up to 30%). We compared the NLTE synthetic transmission spectrum with the observed H
α
and H
β
line profiles obtaining an excellent match, thus supporting our results.
Conclusions.
The NLTE synthetic transmission spectrum can be used to guide future observations aiming at detecting features in the KELT-9b transmission spectrum. Metals, such as Mg and Fe, and NLTE effects shape the upper atmospheric temperature structure of KELT-9b, and thus affect the mass-loss rates derived from it. Finally, our results call for checking whether this is the case also for cooler planets.
The atmospheres of close-in planets are strongly influenced by mass loss driven by the high-energy (X-ray and extreme ultraviolet, EUV) irradiation of the host star, particularly during the early ...stages of evolution. We recently developed a framework to exploit this connection and enable us to recover the past evolution of the stellar high-energy emission from the present-day properties of its planets, if the latter retain some remnants of their primordial hydrogen-dominated atmospheres. Furthermore, the framework can also provide constraints on planetary initial atmospheric mass fractions. The constraints on the output parameters improve when more planets can be simultaneously analysed. This makes the Kepler-11 system, which hosts six planets with bulk densities between 0.66 and 2.45 g cm−3, an ideal target. Our results indicate that the star has likely evolved as a slow rotator (slower than 85% of the stars with similar masses), corresponding to a high-energy emission at 150 Myr of between 1 and 10 times that of the current Sun. We also constrain the initial atmospheric mass fractions for the planets, obtaining a lower limit of 4.1% for planet c, a range of 3.7–5.3% for planet d, a range of 11.1–14% for planet e, a range of 1–15.6% for planet f, and a range of 4.7–8.7% for planet g assuming a disc dispersal time of 1 Myr. For planet b, the range remains poorly constrained. Our framework also suggests slightly higher masses for planets b, c, and f than have been suggested based on transit timing variation measurements. We coupled our results with published planet atmosphere accretion models to obtain a temperature (at 0.25 AU, the location of planet f) and dispersal time of the protoplanetary disc of 550 K and 1 Myr, although these results may be affected by inconsistencies in the adopted system parameters. This work shows that our framework is capable of constraining important properties of planet formation models.
Context.
Planetary atmospheric evolution modelling is a prime tool for understanding the observed exoplanet population and constraining formation and migration mechanisms, but it can also be used to ...study the evolution of the activity level of planet hosts.
Aims.
We constrain the planetary atmospheric mass fraction at the time of the dispersal of the protoplanetary disk and the evolution of the stellar rotation rate for a dozen multi-planet systems that host sub-Neptunes and/or super-Earths.
Methods.
We employ a custom-developed P
YTHON
code that we have dubbed P
ASTA
(Planetary Atmospheres and Stellar RoTation RAtes), which runs within a Bayesian framework to model the atmospheric evolution of exoplanets. The code combines MESA stellar evolutionary tracks, a model describing planetary structures, a model relating stellar rotation and activity level, and a model predicting planetary atmospheric mass-loss rates based on the results of hydrodynamic simulations.
Results.
Through a Markov chain Monte Carlo scheme, we retrieved the posterior probability density functions of all considered parameters. For ages older than about 2 Gyr, we find a median spin-down (i.e.
P
(
t
)∝
t
y
) of
ȳ
= 0.38
−0.27
+0.38
, indicating a rotation decay slightly slower than classical literature values (≈0.5), though still within 1
σ
. At younger ages, we find a median spin-down (i.e.
P
(
t
)∝
t
x
) of
x̄
= 0.26
−0.19
+0.42
, which is below what is observed in young open clusters, though within 1
σ
. Furthermore, we find that the
x
probability distribution we derived is skewed towards lower spin-down rates. However, these two results are likely due to a selection bias as the systems suitable to be analysed by P
ASTA
contain at least one planet with a hydrogen-dominated atmosphere, implying that the host star has more likely evolved as a slow rotator. We further look for correlations between the initial atmospheric mass fraction of the considered planets and system parameters (i.e. semi-major axis, stellar mass, and planetary mass) that would constrain planetary atmospheric accretion models, but without finding any.
Conclusions.
P
ASTA
has the potential to provide constraints to planetary atmospheric accretion models, particularly when considering warm sub-Neptunes that are less susceptible to mass loss compared to hotter and/or lower-mass planets. The TESS, CHEOPS, and PLATO missions are going to be instrumental in identifying and precisely measuring systems amenable to P
ASTA
’s analysis and can thus potentially constrain planet formation and stellar evolution.
Stimulated by the discovery of a number of close-in low-density planets, we generalise the Jeans escape parameter taking hydrodynamic and Roche lobe effects into account. We furthermore define Λ as ...the value of the Jeans escape parameter calculated at the observed planetary radius and mass for the planet’s equilibrium temperature and considering atomic hydrogen, independently of the atmospheric temperature profile. We consider 5 and 10 M⊕ planets with an equilibrium temperature of 500 and 1000 K, orbiting early G-, K-, and M-type stars. Assuming a clear atmosphere and by comparing escape rates obtained from the energy-limited formula, which only accounts for the heating induced by the absorption of the high-energy stellar radiation, and from a hydrodynamic atmosphere code, which also accounts for the bolometric heating, we find that planets whose Λ is smaller than 15–35 lie in the “boil-off” regime, where the escape is driven by the atmospheric thermal energy and low planetary gravity. We find that the atmosphere of hot (i.e. Teq ⪆ 1000 K) low-mass (Mpl ⪅ 5 M⊕) planets with Λ< 15–35 shrinks to smaller radii so that their Λ evolves to values higher than 15–35, hence out of the boil-off regime, in less than ≈500 Myr. Because of their small Roche lobe radius, we find the same result also for hot (i.e. Teq⪆ 1000 K) higher mass (Mpl ⪅ 10 M⊕) planets with Λ< 15–35, when they orbit M-dwarfs. For old, hydrogen-dominated planets in this range of parameters, Λ should therefore be ≥15–35, which provides a strong constraint on the planetary minimum mass and maximum radius and can be used to predict the presence of aerosols and/or constrain planetary masses, for example.
Planet atmospheric escape induced by high-energy stellar irradiation is a key phenomenon shaping the structure and evolution of planetary atmospheres. Therefore, the present-day properties of a ...planetary atmosphere are intimately connected with the amount of stellar flux received by a planet during its lifetime, thus with the evolutionary path of its host star. Using a recently developed analytic approximation based on hydrodynamic simulations for atmospheric escape rates, we track within a Bayesian framework the evolution of a planet as a function of stellar flux evolution history, constrained by the measured planetary radius. We find that the ideal objects for this type of study are close-in sub-Neptune-like planets, as they are highly affected by atmospheric escape, and yet retain a significant fraction of their primordial hydrogen-dominated atmospheres. Furthermore, we apply this analysis to the HD 3167 and K2-32 planetary systems. For HD 3167, we find that the most probable irradiation level at 150 Myr was between 40 and 130 times solar, corresponding to a rotation period of days. For K2-32, we find a surprisingly low irradiation level ranging between half and four times solar at 150 Myr. Finally, we show that for multi-planet systems, our framework enables one to constrain poorly known properties of individual planets.
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