The first million years of the Sun: A calculation of formation and early evolution of a solar-mass star

We present the first coherent dynamical study of the cloud fragmentation-phase, collapse and early stellar evolution of a solar mass star. We determine young star properties as the consequence of the parent cloud evolution. Mass, luminosity and effective temperature in the first million years of the proto-Sun result from gravitational fragmentation of a molecular cloud region that produces a cluster of prestellar clumps. We calculate the global dynamical behavior of the cloud using isothermal 3D hydrodynamics and follow the evolution of individual protostars in detail using a 1D radiation-fluid-dynamic system of equations that comprises a correct standard solar model solution, as a limiting case. We calculate the pre-main sequence (PMS) evolutionary tracks of a solar mass star in a dense stellar cluster environment and compare it to one that forms in isolation. Up to an age of 950.000 years differences in the accretion history lead to significantly different temperature and luminosity evolution. As accretion fades and the stars approach their final masses the two dynamic PMS tracks converge. After that the contraction of the quasi-hydrostatic stellar interiors dominate the overall stellar properties and proceed in very similar ways. Hence the position of a star in the Hertzsprung-Russell diagram becomes a function of age and mass only. However, our quantitative description of cloud fragmentation, star formation and early stellar evolution predicts substantial corrections to the classical, i.e. hydrostatic and initially fully convective models: At an age of 1 million years the proto-Sun is twice as bright and 500 Kelvin hotter than according to calculations that neglect the star formation process.Comment: Four pages, accepted for publication in ApJ Letter

Planetary migration in evolving planetesimals discs

In the current paper, we further improved the model for the migration of planets introduced in Del Popolo et al. (2001) and extended to time-dependent planetesimal accretion disks in Del Popolo and Eksi (2002). In the current study, the assumption of Del Popolo and Eksi (2002), that the surface density in planetesimals is proportional to that of gas, is released. In order to obtain the evolution of planetesimal density, we use a method developed in Stepinski and Valageas (1997) which is able to simultaneously follow the evolution of gas and solid particles for up to 10^7 yrs. Then, the disk model is coupled to migration model introduced in Del Popolo et al. (2001) in order to obtain the migration rate of the planet in the planetesimal. We find that the properties of solids known to exist in protoplanetary systems, together with reasonable density profiles for the disk, lead to a characteristic radius in the range 0.03-0.2 AU for the final semi-major axis of the giant planet.Comment: IJMP A in prin

Orbital migration and the period distribution of exoplanets

We use the model for the migration of planets introduced in Del Popolo, Yesilyurt & Ercan (2003) to calculate the observed mass and semimajor axis distribution of extra-solar planets. The assumption that the surface density in planetesimals is proportional to that of gas is relaxed, and in order to describe disc evolution we use a method which, using a series of simplifying assumptions, is able to simultaneously follow the evolution of gas and solid particles for up to $10^7 {\rm yr}$. The distribution of planetesimals obtained after $10^7 {\rm yr}$ is used to study the migration rate of a giant planet through the model of this paper. The disk and migration models are used to calculate the distribution of planets as function of mass and semimajor axis. The results show that the model can give a reasonable prediction of planets' semi-major axes and mass distribution. In particular there is a pile-up of planets at $a \simeq 0.05$ AU, a minimum near 0.3 AU, indicating a paucity of planets at that distance, and a rise for semi-major axes larger than 0.3 AU, out to 3 AU. The semi-major axis distribution shows that the more massive planets (typically, masses larger than $4 M_{\rm J}$) form preferentially in the outer regions and do not migrate much. Intermediate-mass objects migrate more easily whatever the distance they form, and that the lighter planets (masses from sub-Saturnian to Jovian) migrate easily.Comment: published in A&

Revisiting the transits of CoRoT-7b at a lower activity level

CoRoT-7b, the first super-Earth with measured radius discovered, has opened the new field of rocky exoplanets characterisation. To better understand this interesting system, new observations were taken with the CoRoT satellite. During this run 90 new transits were obtained in the imagette mode. These were analysed together with the previous 151 transits obtained in the discovery run and HARPS radial velocity observations to derive accurate system parameters. A difference is found in the posterior probability distribution of the transit parameters between the previous CoRoT run (LRa01) and the new run (LRa06). We propose this is due to an extra noise component in the previous CoRoT run suspected to be transit spot occultation events. These lead to the mean transit shape becoming V-shaped. We show that the extra noise component is dominant at low stellar flux levels and reject these transits in the final analysis. We obtained a planetary radius, $R_p= 1.585\pm0.064\,R_{\oplus}$, in agreement with previous estimates. Combining the planetary radius with the new mass estimates results in a planetary density of $1.19 \pm 0.27\, \rho_{\oplus}$ which is consistent with a rocky composition. The CoRoT-7 system remains an excellent test bed for the effects of activity in the derivation of planetary parameters in the shallow transit regime.Comment: 13 pages, 13 figures, accepted to A&

Critical Protoplanetary Core Masses in Protoplanetary Disks and the Formation of Short-Period Giant Planets

We study a solid protoplanetary core of 1-10 earth masses migrating through a disk. We suppose the core luminosity is generated as a result of planetesimal accretion and calculate the structure of the gaseous envelope assuming equilibrium. This is a good approximation when the core mass is less than the critical value, M_{crit}, above which rapid gas accretion begins. We model the structure of the protoplanetary nebula as an accretion disk with constant \alpha. We present analytic fits for the steady state relation between disk surface density and mass accretion rate as a function of radius r. We calculate M_{crit} as a function of r, gas accretion rate through the disk, and planetesimal accretion rate onto the core \dot{M}. For a fixed \dot{M}, M_{crit} increases inwards, and it decreases with \dot{M}. We find that \dot{M} onto cores migrating inwards in a time 10^3-10^5 yr at 1 AU is sufficient to prevent the attainment of M_{crit} during the migration process. Only at small radii where planetesimals no longer exist can M_{crit} be attained. At small radii, the runaway gas accretion phase may become longer than the disk lifetime if the core mass is too small. However, massive cores can be built-up through the merger of additional incoming cores on a timescale shorter than for in situ formation. Therefore, feeding zone depletion in the neighborhood of a fixed orbit may be avoided. Accordingly, we suggest that giant planets may begin to form early in the life of the protostellar disk at small radii, on a timescale that may be significantly shorter than for in situ formation. (abridged)Comment: 24 pages (including 9 figures), LaTeX, uses emulateapj.sty, to be published in ApJ, also available at http://www.ucolick.org/~ct/home.htm

Three-dimensional Calculations of High and Low-mass Planets Embedded in Protoplanetary Discs

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from one Earth mass (1 M$_e$) to one Jupiter mass (1 M$_J$) by using the ZEUS hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses M \gsim 0.1 M$_J$ produce significant perturbations in the disc's surface density. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc midplane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the planet's orbit. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 M$_J$ and is highly efficient, occurring at the local viscous rate. The migration timescales for planets of mass less than 0.1 M$_J$, based on torques from disc material outside the planets' Roche lobes, are in excellent agreement with the linear theory of Type I (non-gap) migration for three-dimensional discs. The transition from Type I to Type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few M$_J$ with little migration. Planets with final masses of order 10 M$_J$ would undergo large migration, which makes formation and survival difficult.Comment: Accepted by MNRAS, 18 pages, 13 figures (6 degraded resolution). Paper with high-resolution figures available at http://www.astro.ex.ac.uk/people/mbate

Protostellar mass accretion rates from gravoturbulent fragmentation

We analyse protostellar mass accretion rates from numerical models of star formation based on gravoturbulent fragmentation, considering a large number of different environments. To within one order of magnitude, the mass accretion rate is approximately given by the mean thermal Jeans mass divided by the corresponding free-fall time. However, mass accretion rates are highly time-variant, with a sharp peak shortly after the formation of the protostellar core. We present an empirical exponential fit formula to describe the time evolution of the mass accretion and discuss the resulting fit parameters. There is a positive correlation between the peak accretion rate and the final mass of the protostar. We also investigate the relation of the accretion rate with the turbulent flow velocity as well as with the driving wavenumbers in different environments. We then compare our results with other theoretical models of star formation and with observational data.Comment: 13 pages, 6 figures; accepted by A&

Variable Accretion Rates and Fluffy First Stars

We combine the output of hydrodynamical simulations of Population III star cluster formation with stellar evolution models, and calculate the evolution of protostars experiencing variable mass accretion rates due to interactions within a massive disk. We find that the primordial protostars are extended 'fluffy' objects for the bulk of their pre-main-sequence lifetimes. Accretion luminosity feedback from such objects is high, but as shown in previous work, has a minimal effect on the star cluster. The extended radii of the protostars, combined with the observation of close encounters in the simulations, suggests that mergers will occur in such systems. Furthermore, mass transfer between close protostellar binaries with extended radii could lead to massive tight binaries, which are a possible progenitor of gamma ray bursts.Comment: 7 pages, 6 figures, 2 tables. To be published in MNRA

CoRoT-22 b: a validated 4.9 RE exoplanet in 10-day orbit

The CoRoT satellite has provided high-precision photometric light curves for more than 163,000 stars and found several hundreds of transiting systems compatible with a planetary scenario. If ground-based velocimetric observations are the best way to identify the actual planets among many possible configurations of eclipsing binary systems, recent transit surveys have shown that it is not always within reach of the radial-velocity detection limits. In this paper, we present a transiting exoplanet candidate discovered by CoRoT whose nature cannot be established from ground-based observations, and where extensive analyses are used to validate the planet scenario. They are based on observing constraints from radial-velocity spectroscopy, adaptive optics imaging and the CoRoT transit shape, as well as from priors on stellar populations, planet and multiple stellar systems frequency. We use the fully Bayesian approach developed in the PASTIS analysis software, and conclude that the planet scenario is at least 1400 times more probable than any other false positive scenario. The primary star is a metallic solar-like dwarf, with Ms = 1.099+-0.049 Msun and Rs = 1.136 (+0.038,-0.090) Rsun . The validated planet has a radius of Rp = 4.88 (+0.17,-0.39) RE and mass less than 49 ME. Its mean density is smaller than 2.56 g/cm^3 and orbital period is 9.7566+-0.0012 days. This object, called CoRoT-22 b, adds to a large number of validated Kepler planets. These planets do not have a proper measurement of the mass but allow statistical characterization of the exoplanet population