Giant Planets at Small Orbital Distances

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Giant Planets at Small Orbital Distances Giant Planets at Small Orbital Distances T Guillot A Burrows WB Hubbard JI Lunine and D Saumon Received accepted astro-ph/9511109 22 Nov 1995 Department of Planetary Sciences University of Arizona Tucson AZ guillot hubbard jlunine dsaumonlplarizonaedu Departments of Physics and Astronomy University of Arizona Tucson AZ burrowscobaltphysicsarizonaedu Hubble Postdoctoral Fellow ABSTRACT Using Doppler sp ectroscopy to detect the reex motion of the nearby star Pegasi Mayor Queloz claim to have discovered a giant planet in a AU day orbit They estimate its mass to b e in the range M to J M but are not able to determine its nature or origin Including the eects J of the severe stellar insolation implied we extend the theory of giant planets we have recently developed to encompass those at very small orbital distances Our calculations can b e used to help formulate search strategies for luminous planets in tight orbits around other nearby stars We calculate the radii and luminosities of such giants for a variety of comp ositions HHe He H O and olivine evolutionary tracks for solarcomp osition gas giants and the geometry of the Hayashi forbidden zone in the gasgiant mass regime We show that such planets are stable and estimate the magnitude of classical Jeans evaporation and of photo disso ciation and loss due to EUV radiation Even over the lifetime of the primary the companion would not have lost a large fraction of its mass In addition we demonstrate that for the mass range quoted such planets are well within their Ro che lob es We show that the strong comp ositiondep endence of the mo del radii and distinctive sp ectral signatures provide clear diagnostics that might reveal Peg Bs nature should interferometric or adaptiveoptics techniques ever succeed in photometrically separating planet from star Introduction As the search for planets and brown dwarfs around nearby stars accelerates we should exp ect to b e surprised In no instance is this b etter illustrated than in the recent discovery by Mayor Queloz of a planet orbiting a G star Pegasi parsecs away With a day p erio d a semima jor axis of AU an eccentricity less than and an inferred mass b etween and Jupiter masses M this ob ject is surely the most J problematic nd in recent memory As of this writing the telltale p erio dic Doppler shift in the sp ectral lines of the primary had b een conrmed by Marcy Butler and by Noyes et al A go o d case can b e made for the existence of Peg B simply from the absence of signicant photometric variations in V mag Mayor Queloz Burki Burnet Kuenzli or asymmetries in the line proles Mayor Queloz and from the diculty of explaining such a p erio d as pulsation of a nearsolar analog One hundred times closer to its primary than Jupiter itself Peg B thwarts conventional wisdom Boss had argued that the nucleation of a HHerich Jovian planet around a ro ck and ice core could b e achieved in a protostellar disk only at and b eyond the ice p oint at Kelvin exterior to AU Walker et al had surveyed for reex motion Gtype stars over years and seen nothing more massive than M interior to AU Zuckermann Forveille Kastner had measured CO J emissions from a variety of nearT Tauri disks had extrap olated to H and had concluded that there may not b e enough mass or time to form a Jupiter around a ma jority of stars The discovery of Peg B while not strictly inconsistent with any of these pap ers vastly enlarges the parameter space within which we must now search Several scenarios for the origin of Peg B are emerging It could b e a canonical gas giant that formed many AUs from Peg A but through frictional and tidal eects spiraled inward during the protostellar phase Lin Bo denheimer As ab ove it could have formed conventionally but collided with a massive companion and lost of its orbital angular momentum and of its orbital energy It could b e comp osed predominantly of hydrogen and helium accreted from the protostellar disk but have nucleated in situ around a large ro ck core without ice It could b e a giant terrestrial planet formed by the accumulation of planetesimals or It could b e an evaporated ablated or tidally stripp ed brown dwarf or star However whatever the provenance or evolutionary history of Peg B a knowledge of the thermal and structural characteristics of giant planets with a variety of comp ositions and masses M is required to understand it and others like it A chondritic helium p or ice planet with a mass of M has a radius R that is signicantly smaller than J p that of a hydrogenrich Jupiter At a given eective temp erature smaller radii translate into smaller luminosities L Recently we have studied the theoretical evolution of gas giants around nearby stars with masses from through M and of Brown DwarfsM Dwarfs with masses from J through M Saumon et al Burrows et al Saumon et al Burrows J et al Burrows Hubbard Lunine Over these three orders of magnitude in mass the basic input physics is the same Though we had previously considered the eects of stellar insolation we had not explored such eects at separations near those of Peg B In this pap er we present a theory of extrasolar giant planets at small orbital distances D We calculate the radii and luminosities of planets with a variety of comp ositions masses and separations Though we fo cus on the Peg A Peg B system our results can b e extended and scaled to planetary systems with other characteristics and are meant to aid in the formulation of search strategies around nearby stars In addition we explore the p ossibilities of tidal truncation and evaporation and conclude with a discussion on the photometric discriminants of the various theories concerning the nature of Peg B The Radii of Giant Planets as a Function of Comp osition The hydrogenhelium equation of state that we have employed for this study is describ ed in Saumon Chabrier Van Horn and incorp orates stateoftheart prescriptions for the interactions among H H protons and electrons and for the metallization of hydrogenhelium mixtures at high pressures The evolutionary co des that we have employed are a Henyey co de Burrows et al and a co de that treats the quasistatic problem as an implicit twopoint b oundary value problem Guillot Morel The latter was constructed to address the p ossibility that Jupiter and Saturn may have nonadiabatic structures Guillot et al and allows for the existence of large radiative zones We have expanded this more general co de to address the evolution of giant planets very near their primaries for a variety of planet masses For the evolution of the gas giants we used the opacities of Alexander Ferguson At the distance of Jupiter from the Sun the dierence b etween convective and radiativeconvective mo dels is slight However when the orbital distance of a gas giant from a GV star for example is smaller than AU external heating by the star b ecomes imp ortant early in the planets evolution towards its steady state Due to the very small heat diusivities in gas giants at high pressure this radiative zone do es not p enetrate deeply in mass p erhaps encompassing but can p enetrate deeply in radius by as much as in a Hubble time Convective heat transp ort from the inner convective zone continues to co ol it The entropy of the radiative zone at the photosphere is maintained at a higher roughly constant value as the eective temp erature T of the planet stabilizes e Since its interior continues to co ol and lose its thermal pressure supp ort the entire planet continues to shrink Because the planets eective temp erature is stabilizing its luminosity is decreasing though at a progressively lower rate see x b elow For Peg B the predicted radii after Gigayear Gyr are b etween R and R for M s from J J p M to M These are as much as a factor of two smaller that the corresp onding radii J J for fully convective planets After Gyr the estimated age of Peg A the radii for these same planets are b etween R and R The b ehavior of radius versus mass for J J giant planets in the mass range suggested for Peg B is depicted in Figure Radii and b olometric luminosities not including the reected comp onent for various representative mo dels are given in Tables a b We have included on Figure the corresp onding curves for helium H O and olivine Mg SiO planets as well as that for fully convective planets The equations of state for H O and olivine as representative of ro ck were taken from the ANEOS compilation Thompson The large mean molecular weight of giant ro cky planets ensures that thermal eects are small in most of the interior Hubbard so that an olivine or ice planet in close orbit around a star will probably not have a radius signicantly larger than predicted by our calculations Though Peg A has not had enough time to synchronize its spin p erio d with Peg Bs orbital p erio d Peg Bs spin p erio d is surely tidally lo cked with its orbit at days The time for the tidal spindown of the planet is given by R M D p p Q p GM M R p p where Q is the planets tidal dissipation factor is the planets primordial rotation p rate M is the stars mass and G is the gravitational constant Taking Q and s Jupiters values we obtain years For a giant terrestrial p planet R is smaller but Q is also smaller and so would not b e very dierent Therefore p since Peg As age is years Peg B should always present the same face to its primary whatever its comp osition The equilibrium
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