Evaporation of Jupiter like planets orbiting extreme horizontal branch stars
We study the evaporation of planets orbiting close to hot (extreme) horizontal branch (EHB) stars. These planets survived the common envelope phase inside the envelope of the reg giant star progenitor. We find that Jupiter-like planets orbiting within from an EHB star suffers a non-negligible mass-loss during their evolution on the horizontal branch. The evaporated gas is ionized and becomes a source of Balmer lines. Such planets might be detected by the periodic variation of the Doppler shift of the Balmer lines.
Horizontal branch (HB) stars are core Helium burning stars that have evolved from main sequence (MS) stars through the red giant branch (RGB). During the RGB phase the star loses a non-negligible amount of mass. The amount of mass lost determines the properties of the descendant HB star. Namely, its location on the HR diagram.
HB stars with low mass envelope have small radii and they are hot. They are called extreme HB (EHB) stars (other names are sdO or sdB or hot subdwarfs; in this work we will use all these terms indistinguishably). To become an EHB star, the RGB progenitor must lose most of its envelope. The reason that some RGB stars lose so much mass was a major unsolved issue in stellar evolution. The debate was whether a single star (e.g., Yi 2008) can account for the formation of hot subdwarfs, or whether binary evolution is behind the hot subdwarf phenomenon (e.g., Han et al. 2007). Recent studies suggest the binary interaction is behind the formation of most EHB stars (for a recent paper and more references see Geier et al. 2010a). However, not all EHB stars have stellar companions. It has been suggested that massive planet companions can also influence RGB stars and cause the formation of EHB stars (Soker 1998; by planet we will refer in this paper also to brown dwarfs). This model was confirmed with the discovery of a substellar object in a close orbit to an sdB star (HD 149382, Geier et al. 2009), as well as a planet orbiting a red HB star that lost some of its envelope (Setiawan et al. 2010). The intense UV radiation from the EHB evaporates the outer layers of a surviving close in planet. In this paper we study this process.
The escape of atoms from a planet has been deduced observationally from absorption of atomic hydrogen around the planet HD209458b that orbits a MS star (Vidal-Madjar et al. 2003; Vidal-Madjar & Lecaveleier des Etangs 2004). In early studies several groups (e.g., Lammer et al. 2003; Baraffe et al. 2004, 2005) suggested that hot Jupiters orbiting MS stars can be evaporated down to their bare core.
Many detailed calculations have been made on evaporation of planets in different conditions and circumstances (Dopita & Liebert 1989; Schneider et al. 1998; Schneiter et al. 2007; Soker 1999; Lammer et al. 2003; Baraffe et al. 2006; Erkaev et al. 2007; Jackson et al. 2008; Garcia Munoz 2007; Lammer et al. 2009; Murray-Clay et al. 2009). Villaver & Livio (2007), for example, calculated the outflowing particle flux by equating the energy input and the energy required for hydrogen to escape. Their treatment is not much different from those of others (e.g., Baraffe et al. 2004; Erkaev et al. 2007; Lecavelier des Etangs 2007,Lecavelier des Etangs et al. 2008; Penz et al. 2008a; Lammer et al. 2003, 2009; Valencia et al. 2010a; Sanz-Forcada et al. 2010). Another approach which takes into account the recombination of the evaporated gas is presented by Dopita & Liebert (1989) and McCray & Lin (1994).
Different models predict different mass-loss rates (e.g., Hunten 1982; Sasselov 2003; Vidal-Madjar & Lecavelier des Etangs 2004; Erkaev et al. 2007; Hubbard et al. 2007; Ehrenreich 2008, Ehrenreich et al. 2008; Davis & Wheatley 2009; Lammer et al. 2009 & Linsky et al. 2010). Murray-Clay et al. (2009) comprehensively review the basic “energy - limited” model that is based on channelling heating radiation to mass-loss. In the simplest approach most of the ionizing radiation energy goes into work to expel the envelope. This model is similar to the one used by Lecavelier des Etangs (2007), but the assumption of conversion is unrealistic and overestimate the mass-loss rate. A more realistic approach limits the radiation energy available for mass-loss. In their model Murray-Clay et al. (2009) take a realistic heating efficiency of , since not all the absorbed EUV energy is channelled into heating. Other hydrodynamical models by Yelle (2004), Garcia Munoz (2007), Erkaev et al. (2007) and Lammer et al. (2009) take the same approach. Soker (1999; based on Dopita & Leibert 1989), for example, further took into account the recombination of the outflowing gas. This process causes a decrease in the mass-loss rate. We will use the energy-limited process with efficiency. For example, by considering the effect of recombination of the outflowing gas. This makes the model generally applicable to high and low ionization fluxes for planets around EHB stars.
Lecavelier des Etangs et al. (2004) and Lecavelier des Etangs (2007) concluded based on their detailed calculations that planets with orbital distances of from a MS star will be evaporated unless they are significantly heavier than Jupiter. This approach is strengthened by Davis & Wheatley (2009) who examine the EUV from MS stars (F, G and K), and conclude that planets will not exist at small orbital distances. Let us mention a number of observed cases of planets orbiting MS stars, that motivate our study of planets orbiting HB stars, in particular EHB stars. Valencia et al. (2010a, b) raised the possibility that the super-earth like planet CoRot-7 b (, , , ) is the outcome of evaporation of an Uranus like planet. Baraffe et al. (2004) find that a planet with a mass below a critical mass of orbiting a solar-type star at an orbital separation of , will be completely evaporated in Gyr, unless it has a central rocky core. Jackson et al. (2010) elaborated on the importance of evaporation and calculated two paths. In the first CoRoT-7 b has always been a rocky planet, and in the second CoRoT-7 b is a remnant of a gas giant. Jackson et al. (2010) took into consideration tides, and concluded that it is possible that CoRoT-7 b is a remnant of a gas giant planet. If this finding holds to the cases we study here, it is possible that future observations will reveal many more “earth like planets” around white dwarfs (WDs) or HB stars, that actually started their life as gas giant planets.
We start by studying the evaporation of planets orbiting EHB stars (sec. 2). The gas escaping from the planet will be ionized by the radiation of the HB parent star, and become a source of H emission. This idea has been raised before as an indirect way to search for planets in Planetary Nebulae and Jupiter like planets around WDs (Soker 1999; Chu et al. 2001). We modify this idea and try to search for planets around EHB stars through their H emission. In section 3 we examine the conditions for this emission to be detected. Our short summary is in section 4.
2 Evaporation of a Planet Orbiting an Hb Star
2.1 Basic evaporation processes
We start by considering heating by EUV radiation, a process that was studied in detail for MS and pre-MS central stars (e.g., Chamberlain & Hunten 1987; Yelle 2004; Tian et al. 2005). At this stage we will not consider the role of the magnetic field of the planet, although it can play some role (e.g., Griebmeier et al. 2004; Lammer et al. 2009). We adopt the simple model presented by Lecavelier des Etangs (2007) which represents the blow - off mechanism (Erkaev et al. 2007) and investigate the implications for a planet orbiting an HB star (this model is similar the model purposed by Murray-Clay et al. 2009). The potential energy per unit mass in the atmosphere is
where , , and are the planet mass, planet radius, Jupiter mass, and Jupiter radius respectively and is the escape velocity from the planet. Even for very-hot Jupiters the magnitude of the potential energy is much larger than the kinetic energy of thermal gas particles, and we follow Lecavelier des Etangs (2007) and neglect the kinetic energy of atoms in the planet atmosphere.
The general expression for mass-loss according to Lecavelier des Etangs (2007), is
where is total EUV power in the range of (Lecavelier des Etangs 2007) received by the planet. We took into account that not all the absorbed EUV radiation will be channelled to evaporation by introducing the parameter . Although some studies use (e.g. Lammer et al. 2003; Baraffe et al. 2004; Lecavelier des Etangs 2007), more recent studies found the efficiency to be lower, e.g., Penz et al. (2008b) find for hydrogen rich thermosphere, and Lammer et al. (2009) find . Most significant in reducing the efficiency is L cooling by collisionally excited hydrogen atoms (Murray-Clay et al. 2009).
An appropriate calculated spectrum is required for EHB stars since a black body (BB) radiation does not fit the spectrum below . In Figure 1 we compare the spectrum calculated by Geier et al. (2010b) for HD 149382, an sdB star with an effective temperature of and , where is the gravity on the stellar surface, with a BB radiation at the same temperature. In the case of a BB radiation we have
where is the planck constant, is the speed of light, and is the Boltzmann constant.
Soker (1999, where more details are given) calculates the mass ablation rate of the planet by taking the ionization approach, but including the effect of recombination, following McCray & Lin (1994) who calculated the ablation of the ring around SN1987A. Recombination transfers kinetic energy to radiation that escapes, and reduces the ablation rate. The ionization rate is multiply by the ratio of recombination time to escape time (as long as this ratio is not larger than 1). The expression derived by Soker (1999) is
where is the recombination time, is the total number density of the ablated layer, is the escape time from the planet, is the speed of sound, is the rate of ionizing photons hitting the planet, is the ionization efficiency and is the mean mass per particle. The ionizing rate is given by , where is the number of ionizing photons per unit time emitted by the HB star (Soker 1999). Assuming that the evaporated mass outflows at the sound speed and toward the half hemisphere facing the star, the mass-loss rate is
It must be emphasized that the ionization evaporation rate given by Eq. (6) was used by Soker (1999) for Uranus like planets, that have very low escape energy (Eq. 1). For more massive planets the escape energy is comparable to the energy of the ionizing radiation, and cannot be neglected. Therefore, the evaporation rate given by Eq. (6) becomes inappropriate when it gives value above that given by Eq. (2). In this paper we deal with massive planets and with brown dwarf orbiting close to HB stars. We consider the ionization evaporation rate as a cautionary step, because it takes into account recombination that reduces the efficiency.
Fig. 2 presents the ablation rate based on Lecvelier des Etangs (2007) as given by equation (2), with the ionization model (Dopita & Liebert 1989; Soker 1999) as given here by equation (6), both as function of the orbital separation. These are calculated with the appropriate spectrum as was calculated for HD 149382 (Fig. 1). For comparison we show the evaporation rate for a BB spectrum with the same effective temperature and luminosity (black upper line). The ionization model is presented in figure Fig. 2 only for comparison purposes and it does not apply when the escape velocity exceeds the sound speed.
The properties of the EHB central star and the planet are taken to be those of the HD 149382 system (Geier et al. 2009; see figure caption). The orbital separation of this system is , but in the figure this is an independent variable. On the right axis of Fig. 2 we give the total mass that would be evaporate during a period of , about the duration of the HB, with the same mass-loss rate given on the left axis. For these parameters we find and and we assume an efficiency of , and , where is the outflow velocity. For the ablation rate based on ionization (equation 6) we substitute the following numerical values: (Osterbrock 1989) and . The expanding gas does not reach the escape velocity. It escapes the planet when it leaves the planet’s Roche lobe. The mass-loss curves in Fig. 2 were calculated for , and therefore represent a lower limit. For the evaporation process to be efficient, the orbital separation cannot be too large, i.e., , depending on the exact planet properties (Davis & Wheatley 2009 and references therein). We here show the results up to an orbital separation of .
We now turn to include recombination in the energy-limited process, as this is the more realistic approach. We do it for the parameters of HD 149382 (represented by the blue thin line in Fig. 2).
2.2 Including recombination of the evaporated gas
When the central source is hot a large fraction of the radiation is energetic enough to ionize the evaporated gas. The evaporated gas recombines and emits at a longer wavelength radiation that escapes from the planet’s vicinity. Although recombination is not relevant to planets around solar-like stars, its role becomes more important for hot HB stars and central stars of planetary nebulae. To facilitate a simple calculation we make the following simplifying assumptions.
Most of the evaporated gas flows toward the radiation source, i.e., the parent star. Namely, the evaporated gas escapes to a solid angle of with .
The central star keeps the gas almost fully ionized, such that the rate of recombination equals that of ionization by the radiation of the parent star.
The ionizing photons of the parent star that are absorbed by the evaporated gas are removed from the radiation that heat the star.
Most of the recombination radiation is by gas close to the planet where density is high. Therefore, a half or less of the radiation of the recombining evaporated gas will be absorbed back by the planet and heat it. To put an upper limit on the role of recombination, we assume that all the radiation emitted by the recombining gas escapes.
We assume that the gas outflow velocity is about equal to the sound speed (Gu et al. 2003; Li et al. 2010; Lai et al. 2010; Trammell et al. 2010 and references therein).
The recombination rate is proportional to the density square, hence the square of the mass-loss rate. Therefore, the rate the evaporated gas removes photons from the parent stellar radiation is , where is a constant to be derived below. Instead of equation (2), the new equation reads now
where is the average energy of the ionizing photons, and in the second equality we defined the zeroth order evaporation rate (when recombination is neglected and ) . Equation (7) is a quadratic equation that can be solved analytically. By our assumptions, the density of the evaporated gas is
where is the outflow velocity which is taken as . The recombination rate per unit volume is , where by the assumption of (almost) fully ionized gas can be written as , where is appropriately calculated from for a fully ionized solar composition in case B recombination (Osterbrock 1989). We neglect processes that become more important due to the high collision rate expected in the very dense outflowing gas near the planet. The total recombination rate is obtained by integrating over the entire volume according to our assumptions
Substituting equation (8), and performing the integration gives
The last equality gives the value of that we substitute into equation (7).
Recombination becomes important when the last term in equation (7) becomes non negligible. Taking , this occurs when
Substituting typical values gives the evaporation rate above which recombination is important
In Fig. 2 the energy-limited process is included with recombination (equation 7) and is depicted by the blue thin line. It can be seen that the recombination becomes important when the evaporation rate is as given in equation (12). Namely, it is important in the entire relevant range of parameters here. The evaporation rate we will use in calculating the H emission is the one given by the blue thin line of Fig. 2.
The substellar object (a planet or a BD) mass in HD 149382 is (Geier et al. 2009) at an uncertain orbital separation of . From Fig. 2 we learn that the total evaporated mass of this object during the HB phase will be . This amount is significant, but seems that the substellar object in this system will survive the HB phase of its parent star.
3 H Emission of the Evaporate Material
We consider here hot HB stars such that the evaporated gas of close planets is almost fully ionized. The calculation of the H luminosity from the evaporated gas is done in the following way (e.g. Bhatt 1985 for destructed comets). We start with the following assumptions, some of which were used in section 2.
The evaporation is mainly into a solid angle . If it is toward the parent star , while if it is spherical .
Close to the planet, where most of the recombination occurs, the material flows at the sound speed.
For typical values we find the medium to be optically thin to H.
We assume that the evaporated gas is almost completely ionized. Any recombination that occurs is balanced by the incoming photons from the EHB star.
Most of the recombination and the H source occur at a relatively high density of . At such densities collision between atoms change the amount of energy that is channelled to H. In our simple treatment we neglect the dependence of the recombination coefficient on density. We note that Bhatt (1985) calculates the H emission from a destructed comet. He estimates the density to be and neglects the dependence on density. Korista et al. (1997) found that the dependence of the recombination coefficient to H on density in these densities is negligible.
The H energy released due to recombination is:
Solving the integral yields
The equivalent width of the H emission is calculated for the simulated (accurate) spectrum of HD 149382 (Geier et al. 2010b), where , , . When assuming heating efficiency of , therefore, we get and hence for H emission and for emission. The expected H emission is within the capability of existing telescopes, while the expected H emission seems to be below detection limit. When changing the heating efficiency to ,the mass-loss becomes and we get for H emission and for emission. Although the EWs are not high in both cases, their periodic variation might ease the detection of the line. At an orbital separation of the orbital velocity of the substellar companion is . Therefore, during the orbital period the center of the emission by the evaporated gas might move back and forth over a range of up to and , for the H and H emission lines, respectively. We conclude that it might be possible to identify a planet via the H emission of its ablated envelope.
We estimated the evaporation mass-loss rate from a planet heated by its parent hot sdB/sdO (EHB) star. The hot star ionizes the evaporated gas. We assume that it is almost fully ionized. We reconcile two known evaporation mechanisms (summarized in section 1) by including the effect of recombination in the evaporated gas, and using the energy-limited model. We then calculated the expected emission in the lines of H (equation 14) and H. As the emission comes from the planet vicinity, the Doppler shift will be of tens of over the orbital period. The emission with its periodic Doppler shift can be used to directly detect the planet. We note that Bhatt (1985) proposed to observed the H emission from destructed extra-solar comets.
We found that for the substellar object of the system HD 149382 (Geier et al. 2009) the equivalence widths of the emission of the two lines might be as high as and , respectively, and the Doppler shifts will periodically vary on a range of up to and , respectively (depending on the inclination of the system). The detection of the lines is not simple (in particular H), as the EHB star itself has absorption in those lines. However, the periodic Doppler variations might help recognize the emission lines by the evaporated gas from the planet.
The total evaporated mass along the HB evolution can be non-negligible. However, we can assume (despite the big uncertainties) that the planet in HD 149382 will survive the entire HB evolution of the star.
The ramification of our study is that sdB/sdO (EHB) stars should be a prime target for high spectral resolution observation in the H (equation 14) and H lines. The observation should look for Doppler variations with an amplitude of tens of , with a period of hours to weeks, that hint to the presence of an evaporating planet. The target stars are sdB/sdO stars in the field (disk of the galaxy), where metallicity is higher. EHB stars in globular clusters are less likely to have surviving sub-stellar objects, and they are typically at large distances. Still, some fraction of EHB stars in globular clusters might have surviving substellar objects around them.
We thank Stephan Geier and Uli Heber for helpful discussions and suggestions. We thank the referee for very helpful comments. The Research was supported in part by the N. Haar and R. Zinn Research fund at the Technion, The Israel Science Foundation, and The Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel.
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