Incident Stellar Flux Research Articles

The California-Kepler Survey. II. Precise Physical Properties of 2025 Kepler Planets and Their Host Stars*

Abstract We present stellar and planetary properties for 1305 Kepler Objects of Interest hosting 2025 planet candidates observed as part of the California-Kepler Survey. We combine spectroscopic constraints, presented in Paper I, with stellar interior modeling to estimate stellar masses, radii, and ages. Stellar radii are typically constrained to 11%, compared to 40% when only photometric constraints are used. Stellar masses are constrained to 4%, and ages are constrained to 30%. We verify the integrity of the stellar parameters through comparisons with asteroseismic studies and Gaia parallaxes. We also recompute planetary radii for 2025 planet candidates. Because knowledge of planetary radii is often limited by uncertainties in stellar size, we improve the uncertainties in planet radii from typically 42% to 12%. We also leverage improved knowledge of stellar effective temperature to recompute incident stellar fluxes for the planets, now precise to 21%, compared to a factor of two when derived from photometry.

Atmospheric Circulation of Hot Jupiters: Dayside–Nightside Temperature Differences. II. Comparison with Observations

Abstract The full-phase infrared light curves of low-eccentricity hot Jupiters show a trend of increasing fractional dayside–nightside brightness temperature difference with increasing incident stellar flux, both averaged across the infrared and in each individual wavelength band. The analytic theory of Komacek & Showman shows that this trend is due to the decreasing ability with increasing incident stellar flux of waves to propagate from day to night and erase temperature differences. Here, we compare the predictions of this theory with observations, showing that it explains well the shape of the trend of increasing dayside–nightside temperature difference with increasing equilibrium temperature. Applied to individual planets, the theory matches well with observations at high equilibrium temperatures but, for a fixed photosphere pressure of , systematically underpredicts the dayside–nightside brightness temperature differences at equilibrium temperatures less than . We interpret this as being due to the effects of a process that moves the infrared photospheres of these cooler hot Jupiters to lower pressures. We also utilize general circulation modeling with double-gray radiative transfer to explore how the circulation changes with equilibrium temperature and drag strengths. As expected from our theory, the dayside–nightside temperature differences from our numerical simulations increase with increasing incident stellar flux and drag strengths. We calculate model phase curves using our general circulation models, from which we compare the broadband infrared offset from the substellar point and dayside–nightside brightness temperature differences against observations, finding that strong drag or additional effects (e.g., clouds and/or supersolar metallicities) are necessary to explain many observed phase curves.

THE INNER EDGE OF THE HABITABLE ZONE FOR SYNCHRONOUSLY ROTATING PLANETS AROUND LOW-MASS STARS USING GENERAL CIRCULATION MODELS

ABSTRACT Terrestrial planets at the inner edge of the habitable zone (HZ) of late-K and M-dwarf stars are expected to be in synchronous rotation, as a consequence of strong tidal interactions with their host stars. Previous global climate model (GCM) studies have shown that, for slowly rotating planets, strong convection at the substellar point can create optically thick water clouds, increasing the planetary albedo, and thus stabilizing the climate against a thermal runaway. However these studies did not use self-consistent orbital/rotational periods for synchronously rotating planets placed at different distances from the host star. Here we provide new estimates of the inner edge of the HZ for synchronously rotating terrestrial planets around late-K and M-dwarf stars using a 3D Earth-analog GCM with self-consistent relationships between stellar metallicity, stellar effective temperature, and the planetary orbital/rotational period. We find that both atmospheric dynamics and the efficacy of the substellar cloud deck are sensitive to the precise rotation rate of the planet. Around mid-to-late M-dwarf stars with low metallicity, planetary rotation rates at the inner edge of the HZ become faster, and the inner edge of the HZ is farther away from the host stars than in previous GCM studies. For an Earth-sized planet, the dynamical regime of the substellar clouds begins to transition as the rotation rate approaches ∼10 days. These faster rotation rates produce stronger zonal winds that encircle the planet and smear the substellar clouds around it, lowering the planetary albedo, and causing the onset of the water-vapor greenhouse climatic instability to occur at up to ∼25% lower incident stellar fluxes than found in previous GCM studies. For mid-to-late M-dwarf stars with high metallicity and for mid-K to early-M stars, we agree with previous studies.

Nuclear fusion in the deuterated cores of inflated hot Jupiters

Ouyed et al. (1998) proposed Deuterium (DD) fusion at the core-mantle interface of giant planets as a mechanism to explain their observed heat excess. But rather high interior temperatures (~10^5 K) and a stratified D layer are needed, making such a scenario unlikely. In this paper, we re-examine DD fusion, with the addition of screening effects pertinent to a deuterated core containing ice and some heavy elements. This alleviates the extreme temperature constraint and removes the requirement of a stratified D layer. As an application, we propose that, if their core temperatures are a few times 10^4 K and core composition is chemically inhomogeneous, the observed inflated size of some giant exoplanets ("hot Jupiters") may be linked to screened DD fusion occurring deep in the interior. Application of an analytic evolution model suggests that the amount of inflation from this effect can be important if there is sufficient rock-ice in the core, making DD fusion an effective extra internal energy source for radius inflation. The mechanism of screened DD fusion, operating in the above temperature range, is generally consistent with the trend in radius anomaly with planetary equilibrium temperature $T_{\rm eq}$, and also depends on planetary mass. Although we do not consider the effect of incident stellar flux, we expect that a minimum level of irradiation is necessary to trigger core erosion and subsequent DD fusion inside the planet. Since DD fusion is quite sensitive to the screening potential inferred from laboratory experiments, observations of inflated hot Jupiters may help constrain screening effects in the cores of giant planets.

THE FIVE PLANETS IN THE KEPLER-296 BINARY SYSTEM ALL ORBIT THE PRIMARY: A STATISTICAL AND ANALYTICAL ANALYSIS

Kepler-296 is a binary star system with two M-dwarf components separated by 0.2 arcsec. Five transiting planets have been confirmed to be associated with the Kepler-296 system; given the evidence to date, however, the planets could in principle orbit either star. This ambiguity has made it difficult to constrain both the orbital and physical properties of the planets. Using both statistical and analytical arguments, this paper shows that all five planets are highly likely to orbit the primary star in this system. We performed a Markov-Chain Monte Carlo simulation using a five transiting planet model, leaving the stellar density and dilution with uniform priors. Using importance sampling, we compared the model probabilities under the priors of the planets orbiting either the brighter or the fainter component of the binary. A model where the planets orbit the brighter component, Kepler-296A, is strongly preferred by the data. Combined with our assertion that all five planets orbit the same star, the two outer planets in the system, Kepler-296 Ae and Kepler-296 Af, have radii of 1.53 +/- 0.26 and 1.80 +/- 0.31 R_earth, respectively, and receive incident stellar fluxes of 1.40 +/- 0.23 and 0.62 +/- 0.10 times the incident flux the Earth receives from the Sun. This level of irradiation places both planets within or close to the circumstellar habitable zone of their parent star.

IMPACT OF ATMOSPHERIC REFRACTION: HOW DEEPLY CAN WE PROBE EXO-EARTH'S ATMOSPHERES DURING PRIMARY ECLIPSE OBSERVATIONS?

Most models used to predict or fit exoplanet transmission spectra do not include all the effects of atmospheric refraction. Namely, the angular size of the star with respect to the planet can limit the lowest altitude, or highest density and pressure, probed during primary eclipses, as no rays passing below this critical altitude can reach the observer. We discuss this geometrical effect of refraction for all exoplanets, and tabulate the critical altitude, density and pressure for an exoplanet identical to Earth with a 1 bar N2/O2 atmosphere, as a function of both the incident stellar flux (Venus, Earth, and Mars-like) at the top of the atmosphere, and the spectral type (O5-M9) of the host star. We show that such a habitable exo-Earth can be probed to a surface pressure of 1 bar only around the coolest stars. We present 0.4-5.0 micron model transmission spectra of Earth's atmosphere viewed as a transiting exoplanet, and show how atmospheric refraction modifies the transmission spectrum depending on the spectral type of the host star. We demonstrate that refraction is another phenomenon that can potentially explain flat transmission spectra over some spectral regions.

Occurrence and core-envelope structure of 1-4× Earth-size planets around Sun-like stars.

Small planets, 1-4× the size of Earth, are extremely common around Sun-like stars, and surprisingly so, as they are missing in our solar system. Recent detections have yielded enough information about this class of exoplanets to begin characterizing their occurrence rates, orbits, masses, densities, and internal structures. The Kepler mission finds the smallest planets to be most common, as 26% of Sun-like stars have small, 1-2 R⊕ planets with orbital periods under 100 d, and 11% have 1-2 R⊕ planets that receive 1-4× the incident stellar flux that warms our Earth. These Earth-size planets are sprinkled uniformly with orbital distance (logarithmically) out to 0.4 the Earth-Sun distance, and probably beyond. Mass measurements for 33 transiting planets of 1-4 R⊕ show that the smallest of them, R < 1.5 R⊕, have the density expected for rocky planets. Their densities increase with increasing radius, likely caused by gravitational compression. Including solar system planets yields a relation: ρ = 2:32 + 3:19 R=R ⊕ [g cm(-3)]. Larger planets, in the radius range 1.5-4.0 R⊕, have densities that decline with increasing radius, revealing increasing amounts of low-density material (H and He or ices) in an envelope surrounding a rocky core, befitting the appellation ''mini-Neptunes.'' The gas giant planets occur preferentially around stars that are rich in heavy elements, while rocky planets occur around stars having a range of heavy element abundances. Defining habitable zones remains difficult, without benefit of either detections of life elsewhere or an understanding of life's biochemical origins.

Possible climates on terrestrial exoplanets

What kind of environment may exist on terrestrial planets around other stars? In spite of the lack of direct observations, it may not be premature to speculate on exoplanetary climates, for instance, to optimize future telescopic observations or to assess the probability of habitable worlds. To begin with, climate primarily depends on (i) the atmospheric composition and the volatile inventory; (ii) the incident stellar flux; and (iii) the tidal evolution of the planetary spin, which can notably lock a planet with a permanent night side. The atmospheric composition and mass depends on complex processes, which are difficult to model: origins of volatiles, atmospheric escape, geochemistry, photochemistry, etc. We discuss physical constraints, which can help us to speculate on the possible type of atmosphere, depending on the planet size, its final distance for its star and the star type. Assuming that the atmosphere is known, the possible climates can be explored using global climate models analogous to the ones developed to simulate the Earth as well as the other telluric atmospheres in the solar system. Our experience with Mars, Titan and Venus suggests that realistic climate simulators can be developed by combining components, such as a 'dynamical core', a radiative transfer solver, a parametrization of subgrid-scale turbulence and convection, a thermal ground model and a volatile phase change code. On this basis, we can aspire to build reliable climate predictors for exoplanets. However, whatever the accuracy of the models, predicting the actual climate regime on a specific planet will remain challenging because climate systems are affected by strong positive feedbacks. They can drive planets with very similar forcing and volatile inventory to completely different states. For instance, the coupling among temperature, volatile phase changes and radiative properties results in instabilities, such as runaway glaciations and runaway greenhouse effect.

THE INFLUENCE OF DIFFERENTIAL IRRADIATION AND CIRCULATION ON THE THERMAL EVOLUTION OF GAS GIANT PLANETS. I. UPPER LIMITS FROM RADIATIVE EQUILIBRIUM

As a planet ages, it cools and its radius shrinks at a rate set by the efficiency with which heat is transported from the interior out to space. The bottleneck for this transport is at the boundary between the convective interior and the radiative atmosphere; the opacity there sets the global cooling rate. Models of planetary evolution are often one dimensional (1D), such that the radiative–convective boundary (RCB) is defined by a single temperature, pressure, and opacity. In reality the spatially inhomogeneous stellar heating pattern and circulation in the atmosphere could deform the RCB, allowing heat from the interior to escape more efficiently through regions with lower opacity. We present an analysis of the degree to which the RCB could be deformed and the resultant change in the evolutionary cooling rate. In this initial work we calculate the upper limit for this effect by comparing an atmospheric structure in local radiative equilibrium to its 1D equivalent. We find that the cooling through an uneven RCB could be enhanced over cooling through a uniform RCB by as much as 10%–50%. We also show that the deformation of the RCB (and the enhancement of the cooling rate) increases with a greater incident stellar flux or a lower inner entropy. Our results indicate that this mechanism could significantly change a planet's thermal evolution, causing it to cool and shrink more quickly than would otherwise be expected. This may exacerbate the well-known difficulty in explaining the very large radii observed for some hot Jupiters.

UNDERSTANDING TRENDS ASSOCIATED WITH CLOUDS IN IRRADIATED EXOPLANETS

Unlike previously explored relationships between the properties of hot Jovian atmospheres, the geometric albedo and the incident stellar flux do not exhibit a clear correlation, as revealed by our re-analysis of Q0 to Q14 Kepler data. If the albedo is primarily associated with the presence of clouds in these irradiated atmospheres, a holistic modeling approach needs to relate the following properties: the strength of stellar irradiation (and hence the strength and depth of atmospheric circulation), the geometric albedo (which controls both the fraction of starlight absorbed and the pressure level at which it is predominantly absorbed) and the properties of the embedded cloud particles (which determine the albedo). The anticipated diversity in cloud properties renders any correlation between the geometric albedo and the stellar flux to be weak and characterized by considerable scatter. In the limit of vertically uniform populations of scatterers and absorbers, we use an analytical model and scaling relations to relate the temperature-pressure profile of an irradiated atmosphere and the photon deposition layer and to estimate if a cloud particle will be lofted by atmospheric circulation. We derive an analytical formula for computing the albedo spectrum in terms of the cloud properties, which we compare to the measured albedo spectrum of HD 189733b by Evans et al. (2013). Furthermore, we show that whether an optical phase curve is flat or sinusoidal depends on whether the particles are small or large as defined by the Knudsen number. This may be an explanation for why Kepler-7b exhibits evidence for the longitudinal variation in abundance of condensates, while Kepler-12b shows no evidence for the presence of condensates, despite the incident stellar flux being similar for both exoplanets.

INDICATION OF INSENSITIVITY OF PLANETARY WEATHERING BEHAVIOR AND HABITABLE ZONE TO SURFACE LAND FRACTION

It is likely that unambiguous habitable zone terrestrial planets of unknown water content will soon be discovered. Water content helps determine surface land fraction, which influences planetary weathering behavior. This is important because the silicate weathering feedback determines the width of the habitable zone in space and time. Here a low-order model of weathering and climate, useful for gaining qualitative understanding, is developed to examine climate evolution for planets of various land-ocean fractions. It is pointed out that, if seafloor weathering does not depend directly on surface temperature, there can be no weathering-climate feedback on a waterworld. This would dramatically narrow the habitable zone of a waterworld. Results from our model indicate that weathering behavior does not depend strongly on land fraction for partially ocean-covered planets. This is powerful because it suggests that previous habitable zone theory is robust to changes in land fraction, as long as there is some land. Finally, a mechanism is proposed for a waterworld to prevent complete water loss during a moist greenhouse through rapid weathering of exposed continents. This process is named a "waterworld self-arrest," and it implies that waterworlds can go through a moist greenhouse stage and end up as planets like Earth with partial ocean coverage. This work stresses the importance of surface and geologic effects, in addition to the usual incident stellar flux, for habitability.

DISCOVERY AND ATMOSPHERIC CHARACTERIZATION OF GIANT PLANET KEPLER-12b: AN INFLATED RADIUS OUTLIER

We report the discovery of planet Kepler-12b (KOI-20), which at 1.695\pm0.030 RJ is among the handful of planets with super-inflated radii above 1.65 RJ. Orbiting its slightly evolved G0 host with a 4.438-day period, this 0.431\pm0.041 MJ planet is the least-irradiated within this largest-planet-radius group, which has important implications for planetary physics. The planet's inflated radius and low mass lead to a very low density of 0.111\pm0.010 g cm-3. We detect the occultation of the planet at a significance of 3.7{\sigma} in the Kepler bandpass. This yields a geometric albedo of 0.14\pm0.04; the planetary flux is due to a combination of scattered light and emitted thermal flux. We use multiple observations with Warm Spitzer to detect the occultation at 7{\sigma} and 4{\sigma} in the 3.6 and 4.5 {\mu}m bandpasses, respectively. The occultation photometry timing is consistent with a circular orbit, at e < 0.01 (1{\sigma}), and e < 0.09 (3{\sigma}). The occultation detections across the three bands favor an atmospheric model with no dayside temperature inversion. The Kepler occultation detection provides significant leverage, but conclusions regarding temperature structure are preliminary, given our ignorance of opacity sources at optical wavelengths in hot Jupiter atmospheres. If Kepler-12b and HD 209458b, which intercept similar incident stellar fluxes, have the same heavy element masses, the interior energy source needed to explain the large radius of Kepler-12b is three times larger than that of HD 209458b. This may suggest that more than one radius-inflation mechanism is at work for Kepler-12b, or that it is less heavy-element rich than other transiting planets.

Estimation of the XUV radiation onto close planets and their evaporation

Context: The current distribution of planet mass vs. incident stellar X-ray flux supports the idea that photoevaporation of the atmosphere may take place in close-in planets. Integrated effects have to be accounted for. A proper calculation of the mass loss rate due to photoevaporation requires to estimate the total irradiation from the whole XUV range. Aims: The purpose of this paper is to extend the analysis of the photoevaporation in planetary atmospheres from the accessible X-rays to the mostly unobserved EUV range by using the coronal models of stars to calculate the EUV contribution to the stellar spectra. The mass evolution of planets can be traced assuming that thermal losses dominate the mass loss of their atmospheres. Methods: We determine coronal models for 82 stars with exoplanets that have X-ray observations available. Then a synthetic spectrum is produced for the whole XUV range (~1-912 {\AA}). The determination of the EUV stellar flux, calibrated with real EUV data, allows us to calculate the accumulated effects of the XUV irradiation on the planet atmosphere with time, as well as the mass evolution for planets with known density. Results: We calibrate for the first time a relation of the EUV luminosity with stellar age valid for late-type stars. In a sample of 109 exoplanets, few planets with masses larger than ~1.5 Mj receive high XUV flux, suggesting that intense photoevaporation takes place in a short period of time, as previously found in X-rays. The scenario is also consistent with the observed distribution of planet masses with density. The accumulated effects of photoevaporation over time indicate that HD 209458b may have lost 0.2 Mj since an age of 20 Myr. Conclusions: Coronal radiation produces rapid photoevaporation of the atmospheres of planets close to young late-type stars. More complex models are needed to explain fully the observations.

Titan under a red dwarf star and as a rogue planet: requirements for liquid methane

Titan has a surface temperature of 94 K and a surface pressure of 1.4 atmospheres. These conditions make it possible for liquid methane solutions to be present on the surface. Here, we consider how Titan could have liquid methane while orbiting around an M4 red dwarf star, and a special case of Titan orbiting the red dwarf star Gliese 581. Because light from a red dwarf star has a higher fraction of infrared than the Sun, more of the starlight will reach the surface of Titan because its atmospheric haze is more transparent to infrared wavelengths. If Titan was placed at a distance from a red dwarf star such that it received the same average flux as it receives from the Sun, we calculate the increased infrared fraction, which will warm surface temperatures by an additional ∼10 K. Compared to the Sun, red dwarf stars have less blackbody ultraviolet light but can have more Lyman α and particle radiation associated with flares. Thus depending on the details, the haze production may be much higher or much lower than for the current Titan. With the haze reduced by a factor of 100, Titan would have a surface temperature of 94 K at a distance of 0.23 AU from an M4 star and at a distance of 1.66 AU, for Gliese 581. If the haze is increased by a factor of 100 the distances become 0.08 and 0.6 AU for the M4-star and Gliese 581, respectively. As a rogue planet, with no incident stellar flux, Titan would need 1.6 W/m 2 of geothermal heat to maintain its current surface temperature, or an atmospheric opacity of 20× its present amount with 0.1 W/m 2 of geothermal heat. Thus Titan-like worlds beyond our solar system may provide environment supporting surface liquid methane.

Lessons from detections of the near-infrared thermal emission of hot Jupiters

AbstractThere have recently been a flood of ground-based detections of the near-infrared thermal emission of a number of hot Jupiters. Although these near-infrared detections have revealed a great deal about the atmospheric characteristics of individual hot Jupiters, the question is: what information does this ensemble of near-infrared detections reveal about the atmospheric dynamics and reradiation of all hot Jupiters? I explore whether there is any correlation between how brightly these planets shine in the near-infrared compared to their incident stellar flux, as was theoretically predicted to be the case. Secondly, I look for whether there is any correlation between the host star's activity and the planet's near-infrared emission, like there is in the mid-infrared, where Spitzer observations have revealed a correlation between the host star activity with the presence, or lack thereof, of a temperature inversion and a hot stratosphere.

Erratum to Thermal and hydrostatic structure of the protoplanetary nebula exposed to stellar radiation and stellar wind from the central star

A model for a nebula exposed to the radiation and stellar wind from the central star has been examined. T Tauri stars commonly have disks and stellar wind, though we have no theoretical model on nebular thermal structure under the wind. The aims of this paper are to propose a theoretical nebula model, and to perform mathematical analysis on the geometrical structure and temperature distribution of a passive nebula. Its geometrical surface is determined by the dynamical pressure of the stellar wind. The nebular surface is assumed to be a black body surface, heated by the incident stellar photon flux. We obtain temperature from the equation of energy balance between the stellar radiation upon this nebular surface and the black body radiation from it. The temperature distribution in passive disks is insensitive to the wind strength and is almost identical even if the wind strength changes by five orders of magnitude. The nebula temperature is not expressed by a simple power law function of the distance from the central star. This is an important difference between our results and those of previous works. Since the nebula surrounding a T Tauri star is influenced by stellar wind, our model may be more appropriate than any other simple single power law temperature for passive protoplanetary nebulae.

GROUND-BASED NEAR-INFRARED OBSERVATIONS OF THE SECONDARY ECLIPSE OF CoRoT-2b

We present the results of a ground-based search for the secondary eclipse of the 3.3 Mjup transiting planet CoRoT-2b. We performed near infrared photometry using the LIRIS instrument on the 4.2 m William Herschel Telescope, in the H and K_s filters. We monitored the star around two expected secondary eclipses in two nights under very good observing conditions. For the depth of the secondary eclipse we find in H-band a 3 sigma upper limit of 0.17%, whereas we detected a tentative eclipse with a depth of 0.16+-0.09% in the K_s-band. These depths can be translated into brightness temperatures of T_H<2250 K and T_{K_s} = 1890(+260-350) K, which indicate an inefficient re-distribution of the incident stellar flux from the planet's dayside to its nightside. Our results are in agreement with the CoRoT optical measurement (Alonso et al. 09) and with Spitzer 4.5 and 8 micron results (Gillon et al. 09c).

Thermal Waves in Irradiated Protoplanetary Disks

Protoplanetary disks are mainly heated by radiation from the central star. Since the incident stellar flux at any radius is sensitive to the disk structure near that location, an unstable feedback may be present. Previous investigations show that the disk would be stable to finite-amplitude temperature perturbations if the vertical height of optical surface is everywhere directly proportional to the gas scale height and if the intercepted fraction of stellar radiation is determined from the local grazing angle. We show that these assumptions may not be generally applicable. Instead, we calculate the quasi-static thermal evolution of irradiated disks by directly integrating the global optical depths to determine the optical surface and the total emitting area-filling factor of surface dust. We show that, in disks with modest mass accretion rates, thermal waves are spontaneously and continually excited in the outer disk, propagate inward through the planet-forming domains, and dissipated at small radii where viscous dissipation is dominant. This state is quasi-periodic over several thermal timescales and its pattern does not depend on the details of the opacity law. The viscous dissipation resulting from higher mass accretion stabilizes this instability such that an approximately steady state is realized throughout the disk. In passive protostellar disks, especially transitional disks, these waves induce significant episodic changes in SEDs, on the time scales of years to decades, because the midplane temperatures can vary by a factor of two between the exposed and shadowed regions. The transitory peaks and troughs in the potential vorticity distribution may also lead to baroclinic instability and excite turbulence in theplanet-forming regions.

Thermal and hydrostatic structure of the protoplanetary nebula exposed to stellar radiation and stellar wind from the central star

Abstract A model for a nebula exposed to the radiation and stellar wind from the central star has been examined. T Tauri stars commonly have disks and stellar wind, though we have no theoretical model on nebular thermal structure under the wind. The aims of this paper are to propose a theoretical nebula model, and to perform mathematical analysis on the geometrical structure and temperature distribution of a passive nebula. Its geometrical surface is determined by the dynamical pressure of the stellar wind. The nebular surface is assumed to be a black body surface, heated by the incident stellar photon flux. We obtain temperature from the equation of energy balance between the stellar radiation upon this nebular surface and the black body radiation from it. The temperature distribution in passive disks is insensitive to the wind strength and is almost identical even if the wind strength changes by five orders of magnitude. The nebula temperature is not expressed by a simple power law function of the distance from the central star. This is an important difference between our results and those of previous works. Since the nebula surrounding a T Tauri star is influenced by stellar wind, our model may be more appropriate than any other simple single power law temperature for passive protoplanetary nebulae.

Birth and fate of hot-Neptune planets

This paper presents a consistent description of the formation and the subsequent evolution of gaseous planets, with special attention to short-period, low-mass hot-Neptune planets characteristic of $\mu$ Ara-like systems. We show that core accretion including migration and disk evolution and subsequent evolution taking into account irradiation and evaporation provide a viable formation mechanism for this type of strongly irradiated light planets. At an orbital distance $a \simeq$ 0.1 AU, this revised core accretion model leads to the formation of planets with total masses ranging from $\sim$ 14 $\mearth$ (0.044 $\mjup$) to $\sim$ 400 $\mearth$ (1.25 $\mjup$). The newly born planets have a dense core of $\sim$ 6 $\mearth$, independent of the total mass, and heavy element enrichments in the envelope, $M_{\rm Z,env}/M_{\rm env} $, varying from 10% to 80% from the largest to the smallest planets. We examine the dependence of the evolution of the born planet on the evaporation rate due to the incident XUV stellar flux. In order to reach a $\mu$ Ara-like mass ($\sim$ 14 $\mearth$) after $\sim $ 1 Gyr, the initial planet mass must range from 166 $\mearth$ ($\sim$ 0.52 $\mjup$) to about 20 $\mearth$, for evaporation rates varying by 2 orders of magnitude, corresponding to 90% to 20% mass loss during evolution. The presence of a core and heavy elements in the envelope affects appreciably the structure and the evolution of the planet and yields $\sim 8%-9%$ difference in radius compared to coreless objects of solar composition for Saturn-mass planets. These combinations of evaporation rates and internal compositions translate into different detection probabilities, and thus different statistical distributions for hot-Neptunes and hot-Jupiters.