KEPLER OBSERVATIONS OF TRANSITING HOT COMPACT OBJECTS

The Kepler Mission was designed to find transiting Earth-like planets in the habitable zones of other stars (Borucki et al. 2010a). To accomplish this feat, Kepler was launched into a heliocentric, Earth-trailing orbit allowing stars to be continuously monitored for the lifetime of the mission. A natural product of the mission is that other objects that are Earth-sized or larger that transit the host star can be detected. This includes stellar companions such as M-dwarfs and non-stellar companions such as brown dwarfs (BDs) and white dwarfs (WDs).

Observations of a stellar system with a smaller companion that orbits along our line of sight will be seen to move in front (transit) and behind (occultation) the host star. The transit light curve will have a curved "U" shape due to limb darkening of the stellar surface. The occultation will have a flat bottom and sharp egress and ingress as the flux contribution from the companion is completely obscured. From the shape of the stellar transit, the ratio of the companion and stellar radii and the scaled semimajor axis (a/R_⋆) can be determined. The term a/R_⋆ is related to the mean stellar density. The depth of the occultation gives the ratio of the surface brightness of the companion and stellar host integrated over the observed bandpass.

We present 43 days of high duty cycle, ultra-precise photometry of two transiting objects that have radii similar to Jupiter and effective temperatures >10,000 K. KOI-74b may have properties similar to a low-mass WD, in that it is compact and hot and its radius combined with a rough estimate of its mass is consistent with an internal structure dominated by electron degeneracy. KOI-81b has a radius consistent with either a late M-dwarf, BD, or Jupiter-sized planet, but this picture is inconsistent with its observed temperature and is also likely a WD.

The top panels of Figures 1 and 2 show 43 days of photometry from the Kepler instrument with 1σ error bars. The observations have a cadence of 30 minutes. The gap seen near HJD 2454965 is due to the transmission of data to the Earth and marks the gap between Q0 and Q1 observations (Koch et al. 2010a). The light curve for KOI-81 shows periodicity at 0.72 d. This signal was removed prior to the transit fits by masking off the transit and eclipsing and fitting a sinusoidal curve to the light curve.

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The bottom panels of Figures 1 and 2 show the observations phased with the orbital period. The bottom curve and data are centered on the transit, whereas the upper curve and data are centered on the occultation. The points near the transit are shown with stars and pluses where the different symbols indicate odd and even transits, respectively. Measurements taken during the occultation are shown with open circles.

The data were filtered with a running median boxcar with a width of 10 days. Transit models are computed using the analytic formulas of Mandel & Agol (2002) with nonlinear limb darkening. The data are fit for the center of transit time, period, impact parameter (b), the scaled planetary radius (R/R_⋆), and ζ/R_⋆. The last term, ζ/R_⋆, is related to the transit duration (T_d = 2(ζ/R_⋆)⁻¹) and the mean stellar density (Pál et al. 2009). The transit models are shown in Figures 1 and 2 by the red (lower) line. The occultation is modeled by assuming no limb darkening for the occulted object and shown by the green (upper) line. The transit model assumes that the companion does not emit. While not true, this is a good approximation as the companions KOI-74b and KOI-81b are 800 and 200 times less luminous than the host stars; thus, the dilution only alters the companion radius at the 1% level. We also assumed a circular orbit in our model fits.

Optical spectroscopy obtained at the Kitt Peak 2.1 m was used to estimate KOI-74 as spectral type A1V with T_eff = 9400 ± 150 K and KOI-81 as B9-A0V with T_eff = 10000 ± 150 K. With the stellar density from the transit light curve and T_eff from spectroscopy, the stellar mass and radius were estimated using the ρ_⋆ method as described in Borucki et al. (2010b). This allows us to model the companion radii, orbital period, inclination angle, and occultation depth, which we list in Table 1 as described in Koch et al. (2010b).

2.1. Temperatures of the Companions

2.2. Mass Estimation

KOI-74 and KOI-81 exhibit variations with a periodicity equal to one-half the orbital period and presenting amplitudes of ∼193 ppm and ∼50 ppm, respectively. The KOI-74 light curve also exhibits variability with an amplitude of ∼116 ppm with a period equal to the orbital period. There are various ways to interpret these variations. We could be seeing spot activity induced on the stellar surface from a magnetic interaction between the star and companion. This would be similar to activity seen in the planet hosting system HD179949 (Shkolnik et al. 2004) or τ Bootis (Walker et al. 2008). The variations could also be phase locked due to tidal distortions of the host star. In the later scenario, we can attempt to estimate the mass of the companion.

Ellipsoidal variations show two maxima and minima per orbital revolution. This variability is due the changing observed stellar cross section, reflection effects due to emission and absorption from each component, and gravity darkening. Morris (1985) found from a cosine expansion of the double wave characteristic of the variations that the amplitude of the light variations is given by ΔM = f(τ, U₁)qR³_⋆sin³(i)/a³, where q is the mass ratio of the companion and star, and τ and U₁ express the gravity and limb-darkening terms that describe the surface profile of the distorted star with a radius of R_⋆ with a companion in an orbit with inclination i with a semimajor axis a. Adopting gravity and limb-darkening coefficients from Table II of Beech (1989), we estimate the mass of KOI-74b ∼0.08 M_☉ and KOI-81b ∼0.19 M_☉. These relations are valid when the tidally perturbed stellar surface is in hydrostatic equilibrium. An important issue is addressed below.

The ratio of the tidal acceleration to the star's surface gravity is given by

$$\begin{equation} \epsilon \equiv \frac{M_p}{M_{\star }} \left(\frac{R_{\star }}{a} \right) ^3, \end{equation} \tag{ 1 }$$

where M_⋆ and M_p are the mass of the star and companion, respectively, R_⋆ is the stellar radius, and a is the semimajor axis. This gives a rough measure of the amplitude of the ellipsoidal variability. Assuming that the system is in tidal equilibrium, Equation (16) of Pfahl et al. (2008) can also be used to estimate the mass of the system. Adding this prescription to our transit model allows us to fit for the companion mass. We find that KOI-74b has a mass of ∼0.11 M_☉ and KOI-81b has a mass of ∼0.21 M_☉.

The assumption of tidal equilibrium works well for short period binaries where both members have similar masses. Tidal dissipation circularizes the orbit and synchronizes the stellar rotation period to the orbital period. When the masses are not similar there is no reason to expect the rotation and orbital periods to synchronize, thus the assumption of tidal equilibrium may be invalid.

As shown by Pfahl et al. (2008), the tidal-equilibrium model works well for stars with deep convective atmospheres where flux perturbations arise from changes in the local effective gravity. This is not the case for stars such as KOI-74 and KOI-81 with radiative atmospheres. Tidal forcing of radiative regions could produce significant deviations from hydrostatic balance as gravity waves can penetrate the interiors. Simulations indicate that the observed oscillations can be greater than 10 for stars with M_⋆ > 1.4 M_☉.

If the companion is the remnant of a much larger star and has experienced an episode of mass loss, then the rotational and orbital periods may have already been synchronized. In this case, the companions likely have significant mass. We plan to obtain follow-up spectroscopic observations to search for radial velocity changes. Such observations will place firm limits on the mass of the companions. Until then, we allow to be up to 10 times larger in our estimate for the masses of the companions listed in Table 1 to account for the possibility that the flux variations are produced by g-modes propagating to the surface of the star induced by a less massive companion.

The temperatures of the companions are high. If these objects are planets then we can investigate their thermal properties when the only energy source is irradiation from the star. Assuming a Bond Albedo of zero and complete redistribution of heat for reradiation, we can calculate the equilibrium temperature (T_eq) assuming the companions are blackbodies. The light curve does not show any indication of variability at the orbital period that might indicate a day–night temperature gradient for a tidally locked companion. The calculation of T_eq estimates the temperature of the planet assuming the only energy input is flux from the host star. For KOI-74b this gives an equilibrium temperature of 2250 ± 50 K, and 1715 ± 50 K for KOI-81b. Comparing these values to the measured effective temperatures allows us to conclude that the objects require an additional energy source. This could indicate prior evolution of the companions and we are watching them slowly cool.

Figure 3 shows the positions of the host stars and companions relative to stars, planets, and WDs. The green and cyan points are previously known transiting extrasolar planets¹⁶ and their host stars. The dark blue points show the first five Kepler extrasolar planets (Borucki et al. 2010a). The red diamonds indicate the Earth, Uranus, Neptune, Saturn, and Jupiter. The magenta points mark low-mass stars from Lopez-Morales (2007). The black circles clustered near 1 M_☉ are WDs observed by Hipparcos (Provencal et al. 1998) and those near 0.2 M_☉ are a sample of extremely low-mass WDs (Edmonds et al. 2001; Bassa et al. 2006; Liebert et al. 2004; Kawka & Vennes 2009; van Kerkwijk et al. 1996) that have degenerate companions. The orange lines, from top to bottom, show zero-temperature WD models of Zapolsky & Salpeter (1969) with compositions of H, He, Mg, C, and Fe. The red vertical line is the cooling curve for a 0.2026 M_☉ He-WD from Panei et al. (2007). The red vertical line shows the cooling model for a He-WD with a mass of 0.2026 M_☉ formed through mass transfer (Panei et al. 2007). The stars KOI-74 and KOI-81 are denoted in the upper right portion of the diagram by black stars and the positions of the companion KOI-74b and KOI-81b are labeled.

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The position of KOI-81b in the mass–radius diagram is similar to low-mass stars at the hydrogen burning limit but its inferred temperature is much higher. It has similar physical properties to the cooling He-WD discovered in the globular cluster 47 Tuc by Edmonds et al. (2001). Stellar modeling from the ρ_⋆ (Borucki et al. 2010b) method puts the age of the host star at 340 ± 67 Myr. The observed mass and radius of the companion estimate ∼155 Myr since its creation from the cooling curves of Panei et al. (2007). KOI-74b and KOI-81b orbit at distances of 16 R_☉ and 49 R_☉, respectively. When the hot stars begin shell burning of hydrogen in their interiors, their radii will dramatically increase and will likely result in mass transfer to the companions. That these objects are both found around hot stars is intriguing. The companions are inundated with UV radiation from the host star and are likely suffering from substantial evaporation and ionization.

The light curve for KOI-81 shows significant power near 0.72 c day⁻¹. There may be stellar pulsations induced by tidal interactions with the companion similar to the activity has been seen in the F-type binary star system HD 209295 (Handler et al. 2002). Observations of stellar oscillations offer the opportunity to refine the stellar parameters through asteroseismology.

KOI-74 and KOI-81 are interesting astrophysical systems. Confirmation of the companion masses with spectroscopic radial velocities will help confirm the physical properties of these objects. Follow-up observations are planned as well as continued with the Kepler instrument to help unravel their nature.

Funding for this Discovery mission is provided by NASA's Science Mission Directorate. We are indebted to the entire Kepler team for all the hard work and dedication that made such discoveries possible.

Facilities: Kepler - The Kepler Mission