Probability distribution of terrestrial planets in habitable zones around host stars

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton’s code, we calculate the evolution of stars with masses less than 4.00 M _⊙. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 M _⊙, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way.     

Observations of extrasolar planet transits with the automated telescopes of the Pulkovo Astronomical Observatory

Exoplanet observations have been performed on the automated Pulkovo Observatory telescopes. We have obtained 33 transit light curves for 16 known exoplanets and six transit observations for three exoplanet candidates discovered by the Kepler telescope. Based on our observations, we have reliably confirmed the existence of an exoplanet with an extremely large radius, R _pl = 1.83 ± 0.16R _Jup, in the system KOI 256 and detected a strong deviation of its orbital revolution from the theoretically predicted one. During the transit of the exoplanet WASP-12b across the stellar disk, we detected bursts that could be caused by the planet transit across spots on the star or by the presence of a satellite around this exoplanet. We detected possible periodic variations in the duration of the exoplanet transit across the stellar disk with time for HAT-P-12b that could be caused by variations in orbital inclination. The transit duration and depth, the central transit time, and the radius and orbital inclination of the planet have been estimated. The equilibrium temperature and albedo have been estimated for several exoplanets.     

Terrestrial planet formation surrounding close binary stars

Most stars reside in binary/multiple star systems; however, previous models of planet formation have studied growth of bodies orbiting an isolated single star. Disk material has been observed around both components of some young close binary star systems. Additionally, it has been shown that if planets form at the right places within such disks, they can remain dynamically stable for very long times. Herein, we numerically simulate the late stages of terrestrial planet growth in circumbinary disks around ‘close’ binary star systems with stellar separations 0.05 AU?aB?0.4 AU and binary eccentricities 0?eB?0.8. In each simulation, the sum of the masses of the two stars is 1 M_⊙, and giant planets are included. The initial disk of planetary embryos is the same as that used for simulating the late stages of terrestrial planet formation within our Solar System by Chambers [Chambers, J.E., 2001. Icarus 152, 205-224], and around each individual component of the α Centauri AB binary star system by Quintana et al. [Quintana, E.V., Lissauer, J.J., Chambers, J.E., Duncan, M.J., 2002. Astrophys. J. 576, 982-996]. Multiple simulations are performed for each binary star system under study, and our results are statistically compared to a set of planet formation simulations in the Sun-Jupiter-Saturn system that begin with essentially the same initial disk of protoplanets. The planetary systems formed around binaries with apastron distances QB≡aB(1+eB)?0.2 AU are very similar to those around single stars, whereas those with larger maximum separations tend to be sparcer, with fewer planets, especially interior to 1 AU. We also provide formulae that can be used to scale results of planetary accretion simulations to various systems with different total stellar mass, disk sizes, and planetesimal masses and densities.     

Core formation in giant gaseous protoplanets

Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 MSaturn to 10 MJupiter. Giant protoplanets with masses of 5 MJupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼0.25 M_⊕ and ∼0.5 M_⊕, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M_⊕. Saturn's core mass is found to be ∼8 M_⊕.     

Mass-radius curve for extrasolar Earth-like planets and ocean planets

By comparison with the Earth-like planets and the large icy satellites of the Solar System, one can model the internal structure of extrasolar planets. The input parameters are the composition of the star (Fe/Si and Mg/Si), the Mg content of the mantle (Mg# = Mg/[Mg + Fe]), the amount of H₂O and the total mass of the planet. Equation of State (EoS) of the different materials that are likely to be present within such planets have been obtained thanks to recent progress in high-pressure experiments. They are used to compute the planetary radius as a function of the total mass. Based on accretion models and data on planetary differentiation, the internal structure is likely to consist of an iron-rich core, a silicate mantle and an outer silicate crust resulting from magma formation in the mantle. The amount of H₂O and the surface temperature control the possibility for these planets to harbor an ocean. In preparation to the interpretation of the forthcoming data from the CNES led CoRoT (Convection Rotation and Transit) mission and from ground-based observations, this paper investigates the relationship between radius and mass. If H₂O is not an important component (less than 0.1%) of the total mass of the planet, then a relation (R/REarth)=ab(M/MEarth) is calculated with (a,b)=(1,0.306) and (a,b)=(1,0.274) for ¹⁰⁻²MEarth<M<MEarth and MEarth<M<10MEarth, respectively. Calculations for a planet that contains 50% H₂O suggest that the radius would be more than 25% larger than that based on the Earth-like model, with (a,b)=(1.258,0.302) for ¹⁰⁻²MEarth<M<MEarth and (a,b)=(1.262,0.275) for MEarth<M<10MEarth, respectively. For a surface temperature of 300 K, the thickness of the ocean varies from 150 to 50 km for planets 1 to 10 times the Earth's mass, respectively. Application of this algorithm to bodies of the Solar System provides not only a good fit to most terrestrial planets and large icy satellites, but also insights for discussing future observations of exoplanets.     

The stars in the Main Sequence and their dynamical parameters

The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR _eff=R/α given by the stellar radii and the coefficients for the inner structure of the stars. As seen in a previous work (Paper I), during the lifetime in the Main SequenceR _eff(t) remains a near invariant when compared to the variation in the time ofR(t) and α(t). With such an effectiveR _eff one obtains the amounts of actionA _c(M), the effective densities ρ_eff(M)=ρ(M)α³(M), the densities of action and of energy (or mean presures in the stellar interior)a _c(M),e _c(M), and the potential energiesE _p(M). The amounts of action areA _c∝M ^k withk≈1.87 for the M stars,k≈5/3 for the KGF stars, andk≈1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek≈5/3 means a near invariant effective density α_eff for the KGF stars, while for such stars the mean densities and coefficients α present the strongest variations with masses ρ(M)∝M ^?1.81, α(M)∝M^0.6. The cases for the M stars (e _c(M)∝M ^?1) and for the A and earlier stars (betweena _c(M)=constant and α_eff(M)∝M ^?1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M _⊙≤M≤25M _⊙. With all this, one can build ‘dynamical’ HR diagrams withA _c(M), E_p(M), α_eff M ^?p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA _c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs. The comparison of the potential energiesE _p(M)∝M ^?p according to the stellar models used here and the observed frequency function ψ(M∝M _?q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE _p(M)ψ(M) is a constant, but this must be confirmed with further studies of the function ψ(M) and its fine structure. There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA _c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.     

Could we identify hot ocean-planets with CoRoT, Kepler and Doppler velocimetry?

Planets less massive than about 10 MEarth are expected to have no massive H-He atmosphere and a cometary composition (∼50% rocks, 50% water, by mass) provided they formed beyond the snowline of protoplanetary disks. Due to inward migration, such planets could be found at any distance between their formation site and the star. If migration stops within the habitable zone, this may produce a new kind of planets, called ocean-planets. Ocean-planets typically consist in a silicate core, surrounded by a thick ice mantle, itself covered by a 100 km-deep ocean. The possible existence of ocean-planets raises important astrobiological questions: Can life originate on such body, in the absence of continent and ocean-silicate interfaces? What would be the nature of the atmosphere and the geochemical cycles? In this work, we address the fate of hot ocean-planets produced when migration ends at a closer distance. In this case the liquid/gas interface can disappear, and the hot H₂O envelope is made of a supercritical fluid. Although we do not expect these bodies to harbor life, their detection and identification as water-rich planets would give us insight as to the abundance of hot and, by extrapolation, cool ocean-planets. The water reservoir of these planets seems to be weakly affected by gravitational escape, provided that they are located beyond some minimum distance, e.g. 0.04 AU for a 5-Earth-mass planet around a Sun-like star. The swelling of their water atmospheres by the high stellar flux is expected not to significantly increase the planets' radii. We have studied the possibility of detecting and characterizing these hot ocean-planets by measuring their mean densities using transit missions in space—CoRoT (CNES) and Kepler (NASA)—in combination with Doppler velocimetry from the ground—HARPS (ESO) and possible future instruments. We have determined the domain in the [stellar magnitude, orbital distance] plane where discrimination between ocean-planets and rocky planets is possible with these instruments. The brightest stars of the mission target lists and the planets closest to their stars are the most favorable cases. Full advantage of high precision photometry by CoRoT, and particularly Kepler, can be obtained only if a new generation of Doppler instruments is built.     

The photometric method of detecting other planetary systems

The photometric method detects planets orbiting other stars by searching for the reduction in the light flux or the change in the color of the stellar flux that occurs when a planet transits a star. A transit by Jupiter or Saturn would reduce the stellar flux by approximately 1% while a transit by Uranus or Neptune would reduce the stellar flux by 0.1%. A highly characteristic color change with an amplitude approximately 0.1 of that for the flux reduction would also accompany the transit and could be used to verify that the source of the flux reduction was a planetary transit rather than some other phenomenon. Although the precision required to detect major planets is already available with state-of-the-art photometers, the detection of terrestrial-sized planets would require a precision substantially greater than the state-of-the-art and a spaceborne platform to avoid the effects of variations in sky transparency and scintillation. Because the probability is so small of observing a planetary transit during a single observation of a randomly chosen star, the search program must be designed to continuously monitor hundreds or thousands of stars. The most promising approach is to search for large planets with a photometric system that has a single-measurement precision of 0.1%. If it is assumed that large planets will have long-period orbits, and that each star has an average of one large planet, then approximately 10⁴ stars must be monitored continuously. To monitor such a large groups of stars simultaneously while maintaining the required photometric precision, a detector array coupled by a fiber-optic bundle to the focal plane of a moderate aperture (≈ 1 m), wide field of view (≈50°) telescope is required. Based on the stated assumptions, a detection rate of one planet per year of observation appears possible.     

Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of hot Jupiters

In this paper we extend the theory of close encounters of a giant planet on a parabolic orbit with a central star developed in our previous work (Ivanov and Papaloizou in MNRAS 347:437, 2004; MNRAS 376:682, 2007) to include the effects of tides induced on the central star. Stellar rotation and orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment that incorporates first order corrections to normal mode frequencies arising from stellar rotation and numerical treatments that are in satisfactory agreement over the parameter space of interest. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5?C6 stellar radii with tides in the star being much stronger for retrograde orbits compared to prograde orbits. Assuming that combined action of dynamic and quasi-static tides could lead to the total circularisation of orbits this corresponds to observed periods up to 4?C5 days. We use the simple Skumanich law to characterise the rotational history of the star supposing that the star has its rotational period equal to one month at the age of 5 Gyr. The strength of tidal interactions is characterised by circularisation time scale, t _ev , which is defined as a typical time scale of evolution of the planet??s semi-major axis due to tides. This is considered as a function of orbital period P _obs , which the planet obtains after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits, respectively, is of order 1.5?C2 for a planet of one Jupiter mass having P _obs ~ 4 days. The ratio grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same P _orb . Note, however, this result might change for more realistic stellar rotation histories. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet?Cplanet scattering, which favours systems with retrograde orbits. The results reported in the paper may also be applied to the problem of tidal capture of stars in young stellar clusters.     

Obliquity evolution of extrasolar terrestrial planets

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ₀), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ₀∼1) are more likely to be produced than straight ones (sinγ₀∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ₀∼10° or the two-body planar problem in which γ₀=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ₀ (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ₀ space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.     

Graphite grain formation in the atmospheres of R coronae borealis stars

The results of calculations of graphite grain formation in the atmospheres of R CrB stars are given. The parameters for the models wereM=1M _⊙,M _bol=?6 mag. The effective temperature ranged from 5300K to 8300K. The chemical composition corresponded to the hydrogen-deficient carbon rich mixture:X=0,Y=0.9,Z _c=0.1. The results obtained show the existence of a critical mass loss rate which is ranged fromM _*≈10^?6 M _⊙yr^?1 forT _eff=5300 K toM _*≈10^?5 M _⊙ yr^?1 forT _eff=8300 K. As soon as the rate of mass loss exceedsM _* by 3–5 times the degree of condensation of carbon changes from 0 to 0.7. The finite radii of grains are about from 0.01 μm to 0.6 μm depending on the density near the condensation point, the velocity of matter outflow, and the stellar effective temperature. The duration of grain growth should amount to some dozens of days. It is supposed that the most probable explanation of dust-shell formation around R CrB stars is graphite condensation behind a shock wave arising from nonlinear stellar pulsation.     

On the protection of extrasolar Earth-like planets around K/M stars against galactic cosmic rays

Previous studies have shown that extrasolar Earth-like planets in close-in habitable zones around M-stars are weakly protected against galactic cosmic rays (GCRs), leading to a strongly increased particle flux to the top of the planetary atmosphere. Two main effects were held responsible for the weak shielding of such an exoplanet: (a) For a close-in planet, the planetary magnetic moment is strongly reduced by tidal locking. Therefore, such a close-in extrasolar planet is not protected by an extended magnetosphere. (b) The small orbital distance of the planet exposes it to a much denser stellar wind than that prevailing at larger orbital distances. This dense stellar wind leads to additional compression of the magnetosphere, which can further reduce the shielding efficiency against GCRs. In this work, we analyse and compare the effect of (a) and (b), showing that the stellar wind variation with orbital distance has little influence on the cosmic ray shielding. Instead, the weak shielding of M star planets can be attributed to their small magnetic moment. We further analyse how the planetary mass and composition influence the planetary magnetic moment, and thus modify the cosmic ray shielding efficiency. We show that more massive planets are not necessarily better protected against galactic cosmic rays, but that the planetary bulk composition can play an important role.     

Constraints on the location of a putative distant massive body in the Solar System from recent planetary data

We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semi-major axis a, all the other Keplerian osculating orbital elements experience long-term variations which are complicated functions of the orbital configurations of both the planet itself and of X. We infer constraints on the minimum distance d _X at which X may exist by comparing our prediction of the long-term variation of the longitude of the perihelion \({\varpi}\) to the latest empirical determinations of the corrections \({\Delta\dot\varpi}\) to the standard Newtonian/Einsteinian secular precessions of several solar system planets recently estimated by independent teams of astronomers. We obtain the following approximate lower bounds on d _X for the assumed masses of X quoted in brackets: 150–200 au (Mars), 250–450 au \(({0.7 m_{\oplus}})\), 3500–4500 au (4 m _Jup).     

Characteristics and Frequency of Weak Stellar Impulses of the Oort Cloud

We have developed a model of the response of the outer Oort cloud of comets to simultaneous tidal perturbations of the adiabatic galactic force and a stellar impulse. The six-dimensional phase space of near-parabolic comet orbital elements has been subdivided into cells. A mapping of the evolution of these elements from beyond the loss cylinder boundary into the inner planetary region over the course of a single orbit is possible. This is done by treating each perturbation separately, and in combination, during a time interval of 5 Myr. We then obtain the time dependence of a wide range of observable comet flux characteristics, which provides a fingerprint of the dynamics. These include the flux distributions of energy, perihelion distance, major axis orientation, and angular momentum orientation. Correlations between these variables are also determined. We show that substantive errors occur if one superposes the separately obtained flux results of the galactic tide and the stellar impulse rather than superposing the tidal and impulsive perturbations in a single analysis. Detailed illustrations are given for an example case where the stellar mass and relative velocity have the ratio M∗/V_rel=0.043 M⊙/km s⁻¹ and the solar impact parameter is 45,000 AU. This case has features similar to the impending Gliese 710 impulse with the impact parameter selected to be close to the low end of the predicted range. We find that the peak in the observable comet flux exceeds that due to the galactic tide alone by ≈41%. We also present results for the time dependence of the flux enhancements and for the mean encounter frequency of weak stellar impulse events as functions of M∗/V_rel and solar impact parameter.     

Velocity distribution of meteoroids in the vicinity of planets and satellites

Collisions in the Solar System play an important role in its history. Impact processes depend essentially on the velocity distribution of meteoroids colliding with a chosen planet. According to Carleman's theorem it is sufficient to find the set of M _k = mathematical expectation of v ^k , v being the collisional velocity. We suppose that M _k for meteoroids of asteroidal nature differs slightly from that for asteroids themselves. So among all numbered minor planets we select those which may potentially collide with the chosen major planet. Then we calculate v at intersection points and count the average over all such points and all selected asteroids. The gravitation of a body-target may be taken into account or not. Numerical results are collected in four Tables.     

An analytical method to compute comet cloud formation efficiency and its application

A quick analytical method is presented for calculating comet cloud formation efficiency in the case of a single planet or multiple-planet system for planets that are not too eccentric (e _p ≲ 0.3). A method to calculate the fraction of comets that stay under the control of each planet is also presented, as well as a way to determine the efficiency in different star cluster environments. The location of the planet(s) in mass-semi-major axis space to form a comet cloud is constrained based on the conditions developed by Tremaine (1993) together with estimates of the likelyhood of passing comets between planets; and, in the case of a single, eccentric planet, the additional constraint that it is, by itself, able to accelerate material to relative encounter velocity U ~ 0.4 within the age of the stellar system without sweeping up the majority of the material beforehand. For a single planet, it turns out the efficiency is mainly a function of planetary mass and semi-major axis of the planet and density of the stellar environment. The theory has been applied to some extrasolar systems and compared to numerical simulations for both these systems and the Solar System, as well as a diffusion scheme based on the energy kick distribution of Everhart (Astron J 73:1039–1052, 1968). The analytic results are in good agreement with the simulations.     

The internal activity and thermal evolution of Earth-like planets

We model the internal thermal evolution of planets with Earth-like composition and masses ranging from 0.1 to 10 Earth masses over a period of 10 billion years. We also characterize the internal activity of the planets by the velocity of putative tectonic plates, the rate at which mantle material is processed through melting zones, and the time taken to process one mantle mass. The more massive the planet the larger its processing rate (?), which scales approximately as ?∝M0.8-1.0. The processing times for all the planets increase with time as they cool and become less active. As would be expected, the surface heat flow scales with planet mass. All planets have similar declines in mantle temperature except for the largest, in which pressure effects cause a larger decline. The larger planets have higher mantle temperatures over all times. The less massive the planet, the larger the decrease in core temperature with time. The core heat flow is also found to decrease more rapidly for smaller planet masses. Finally, rough predictions are made for the time required to generate an atmosphere from estimates of the time to degas water and carbon dioxide in mantle melting zones. The degassing times depend strongly on the initial temperature of the planet, but for the temperatures used in our model all the planets degas within ∼32 Ma after their formation.     

Searching for proto‐brown dwarfs: Extending near IR spectroscopy of protostars below the hydrogen burning limit

Recent observations of nearby star forming regions have offered evidence that young brown dwarfs undergo a period of mass accretion analogous to the T Tauri phase observed in young stars. Brown dwarf analogs to stellar protostars, however, have yet to be definitively observed. These young, accreting objects would shed light on the nature of the dominant brown dwarf formation process, as well as provide ideal laboratories to investigate the dependence of the accretion mechanism on protostellar mass. Recent near infrared surveys have identified candidate proto‐brown dwarfs and characterized low mass protostars in nearby star forming regions. These techniques allow near infrared spectra to diagnose the effective temperature, accretion luminosity, magnetic field strength and rotation velocity of young low mass stars across the stellar/substellar boundary. The lowest mass proto‐brown dwarfs (M < 40 M_Jup), however, will prove challenging to observe given current near IR observational capabilities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photometry and polarimetry of Jupiter at large phase angles: I. Analysis of imaging data of a prominent belt and a zone from pioneer 10

Limb-darkening curves are derived from Pioneer 10 imaging data for Jupiter's STrZ (?18 to ?21° latitude) and SEBn (?5 to ?8° latitude) in red and blue light at phase angles of 12, 23, 34, 109, 120, 127, and 150°. Inhomogeneous scattering models are computed and compared with the data to constrain the vertical structure and the single-scattering phase functions of the belt and the zone in each color. The very high brightness observed at a 150° phase angle seems to require the presence of at lleast a thin layer of reasonably bright and strongly forward-scattering haze particles at pressure levelsof about 100 mbar or less above both belts and zones. Marginally successful models have been constructed in which a moderate optical thickness (τ ≥ 0.5) of haze particles was uniformly distributed in the upper 25 km-amagats of H₂. Excellent fits to the data were obtained with models having a thin (optical depths of a few tenths) haze conentraated above most of the gas. Following recent spectrospcopicanalyses, we have placed the main “cloud” layer or layers beneath about 25 km-amagats of H₂, although successful fits to our continuum data probably could be achieved also if the clouds were permitted to extend all the way up to the thin haze layer. Similarly, below the haze level our data cannot distinguish between models having two clouds separated by a clear space as suggested by R. E. Danielson and M. G. Tomasko and models with a single extensive diffuse cloud having an H₂ abundance of a few kilometer-amagats per scattering mean free path as described by W. D. Cochran. In either case, the relative brightness of the planet at each phase angle primarily serves to constrain the single-scattering phase functions of the Jovian clouds at the corresponding scattering angles. The clouds in these models are characterized by single-scattering phase functions having strong forward peaks and modest backward-scattering peaks, indicating cloud particles with dimensions larger than about 0.6 μm. In our models, a lower single-scattering albedo of the cloud particles in the belt relative to the zone accounts for the contrast between these regions. If an increased abundance of absorbing dust above uniformly bright clouds is used to explain the contrast between belts and zones at visible wavelengths, the limb darkening is steeper than that observed for the SEBn in blue light at small phase angles. The phase integral for the planet calculated for either the belt or the zone model in either color lies in the range 1.2 to 1.3. If a value of 1.25 is used with D.J. Taylor's bolometric geometric albedo of 0.28, the planet emits 2.25 or 1.7 times the energy it absorbs from the Sun if it effective temperature is 134 or 125°K, respectively—roughly as expected from current theories of the cooling of Jupiter's interior.     

Simulation of energy distributions in optical and IR spectra of late-type M4–M6 dwarfs

Spectral types (M4–M6), effective temperatures T _ef (2700–2900 K), and free fall accelerations logg (4.0–4.5) are determined for five M dwarfs using their energy distributions in the spectral range λλ = 680…840 nm. Stellar spectra with resolutions R = 4000 were obtained using the IMACS spectrograph mounted on the ESO Walter Baade 6.5-m telescope. The spectral types are derived from spectral indices and the effective temperatures of the stars are estimated based on their spectral types. Values of T _ef and logg are also derived from the comparison between the observed and theoretical energy distributions, calculated both for dust-free, standard NextGen model atmospheres of red dwarfs, and for semiempirical models considering the presence of dust in stellar atmospheres according to the technique developed by Pavlenko et al. We determine dust parameters for stellar atmospheres of these stars, and establish that it is necessary to account for the decrease in concentration of TiO molecules due to their condensation on dust grains, when T _ef < 3000 K. We conclude that the radiation scattering by dust grains does not have an appreciable effect on energy distributions in the spectra of the considered stars.