We present the mass-density relationship (log M - log rho) for objects with masses ranging from planets (M ~ 0.01 M_Jup) through stars (M > 0.08 M_Sun). This relationship shows three distinct regions separated by a change in slope in log M -- log rho
plane. In particular, objects with masses in the range 0.3 M_Jup to 60 M_Jup follow a tight linear relationship with no distinguishing feature to separate the low mass end (giant planets) from the high mass end (brown dwarfs). The distinction between giant planets and brown dwarfs thus seems arbitrary. We propose a new definition of giant planets based simply on changes in the slope of the log $M$ versus log rho relationship. By this criterion, objects with masses less than ~ 0.3 M_Jup are low mass planets, either icy or rocky. Giant planets cover the mass range 0.3 M_Jup to 60 M_Jup. Analogous to the stellar main sequence, objects on the upper end of the giant planet sequence (brown dwarfs) can simply be referred to as high mass giant planets, while planets with masses near that of Jupiter can be considered to be low mass giant planets.
We investigate the nature of the long-period radial velocity variations in Alpha Tau first reported over 20 years ago. We analyzed precise stellar radial velocity measurements for Alpha Tau spanning over 30 years. An examination of the Halpha and Ca
II 8662 spectral lines, and Hipparcos photometry was also done to help discern the nature of the long-period radial velocity variations. Our radial velocity data show that the long-period, low amplitude radial velocity variations are long-lived and coherent. Furthermore, Halpha equivalent width measurements and Hipparcos photometry show no significant variations with this period. Another investigation of this star established that there was no variability in the spectral line shapes with the radial velocity period. An orbital solution results in a period of P = 628.96 +/- 0.90 d, eccentricity, e = 0.10 +/- 0.05, and a radial velocity amplitude, K = 142.1 +/- 7.2 m/s. Evolutionary tracks yield a stellar mass of 1.13 +/- 0.11 M_sun, which corresponds to a minimum companion mass of 6.47 +/- 0.53 M_Jup with an orbital semi-major axis of a = 1.46 +/- 0.27 AU. After removing the orbital motion of the companion, an additional period of ~ 520 d is found in the radial velocity data, but only in some time spans. A similar period is found in the variations in the equivalent width of Halpha and Ca II. Variations at one-third of this period are also found in the spectral line bisector measurements. The 520 d period is interpreted as the rotation modulation by stellar surface structure. Its presence, however, may not be long-lived, and it only appears in epochs of the radial velocity data separated by $sim$ 10 years. This might be due to an activity cycle. The data presented here provide further evidence of a planetary companion to Alpha Tau, as well as activity-related radial velocity variations.
Kepler-78b is a transiting Earth-mass planet in an 8.5 hr orbit discovered by the Kepler Space Mission. We performed an analysis of the published radial velocity measurements for Kepler-78 in order to derive a refined measurement for the planet mass.
Kepler-78 is an active star and radial velocity variations due to activity were removed using a Floating Chunk Offset (FCO) method where an orbital solution was made to the data by allowing the velocity offsets of individual nights to vary. We show that if we had no a priori knowledge of the transit period the FCO method used as a periodogram would still have detected Kepler-78b in the radial velocity data. It can thus be effective at finding unknown short-period signals in the presence of significant activity noise. Using the FCO method while keeping the ephemeris and orbital phase fixed to the photometric values and using only data from nights where 6-10 measurements were taken results in a K-amplitude of 1.34 +/- 0.25 m/s. a planet mass of 1.31 +/- 0.24 M_Earth, and a planet density of rho = 4.5 (-2.0/+2.2) g/cm^3. Allowing the orbital phase to be a free parameter reproduces the transit phase to within the uncertainty. The corresponding density implies that Kepler-78b may have a structure that is deficient in iron and is thus more like the Moon. Although the various approaches that were used to filter out the activity of Kepler 78 produce consistent radial velocity amplitudes to within the errors, these are still too large to constrain the structure of this planet. The uncertainty in the mass for Kepler-78b is large enough to encompass models with structures ranging from Mercury-like (iron enriched) to Moon-like (iron deficient). A more accurate K-amplitude as well as a better determination of the planet radius are needed to distinguish between these models.
We investigate the radial velocity variation of GJ 581 based on measurements from the HARPS and Keck HIRES spectrographs. A Fourier pre-whitening procedure is able to extract four planetary signals in the HARPS data and two from the Keck data. Combin
ing both data sets increases the significance of the four planet signals found by HARPS. This indicates that the Keck data also supports the presence of four planets. A periodogram analysis of the residual radial velocity measurements after removal of the four planetary signals shows several periodic signals that are significant when assessing the false alarm probability via a bootstrap. However, it is demonstrated that these are not due to planetary companions. This analysis is able to confirm the presence of four planets around GJ 581, but not the presence of GJ 581g.
We present an analysis of the publicly available HARPS radial velocity (RV) measurements for Alpha Cen B, a star hosting an Earth-mass planet candidate in a 3.24 day orbit. The goal is to devise robust ways of extracting low-amplitude RV signals of l
ow mass planets in the presence of activity noise. Two approaches were used to remove the stellar activity signal which dominates the RV variations: 1) Fourier component analysis (pre-whitening), and 2) local trend filtering (LTF) of the activity using short time windows of the data. The Fourier procedure results in a signal at P = 3.236 days and K = 0.42 m/s which is consistent with the presence of an Earth-mass planet, but the false alarm probability for this signal is rather high at a few percent. The LTF results in no significant detection of the planet signal, although it is possible to detect a marginal planet signal with this method using a different choice of time windows and fitting functions. However, even in this case the significance of the 3.24-d signal depends on the details of how a time window containing only 10% of the data is filtered. Both methods should have detected the presence of Alpha Cen Bb at a higher significance than is actually seen. We also investigated the influence of random noise with a standard deviation comparable to the HARPS data and sampled in the same way. The distribution of the noise peaks in the period range 2.8 - 3.3 days have a maximum of approximately 3.2 days and amplitudes approximately one-half of the K-amplitude for the planet. The presence of the activity signal may boost the velocity amplitude of these signals to values comparable to the planet. It may be premature to attribute the 3.24 day RV variations to an Earth-mass planet. A better understanding of the noise characteristics in the RV data as well as more measurements with better sampling will be needed to confirm this exoplanet.
We use precise radial velocity measurements and photometric data to derive the frequency spacing of the p-mode oscillation spectrum of the planet-hosting star Beta Gem. This spacing along with the interferometric radius for this star is used to deriv
e an accurate stellar mass. A long time series of over 60 hours of precise stellar radial velocity measurements of Beta Gem were taken with an iodine absorption cell and the echelle spectrograph mounted on the 2m Alfred Jensch Telescope. Complementary photometric data for this star were also taken with the MOST microsatellite spanning 3.6 d. A Fourier analysis of the radial velocity data reveals the presence of up to 17 significant pulsation modes in the frequency interval 10-250 micro-Hz. Most of these fall on a grid of equally-spaced frequencies having a separation of 7.14 +/- 0.12 micro-Hz. An analysis of 3.6 days of high precision photometry taken with the MOST space telescope shows the presence of up to 16 modes, six of which are consistent with modes found in the spectral (radial velocity) data. This frequency spacing is consistent with high overtone radial pulsations; however, until the pulsation modes are identified we cannot be sure if some of these are nonradial modes or even mixed modes. The radial velocity frequency spacing along with angular diameter measurements of Beta Gem via interferometry results in a stellar mass of M = 1.91 +/- 0.09 solar masses. This value confirms the intermediate mass of the star determined using stellar evolutionary tracks. Beta Gem is confirmed to be an intermediate mass star. Stellar pulsations in giant stars along with interferometric radius measurements can provide accurate determinations of the stellar mass of planet hosting giant stars. These can also be used to calibrate stellar evolutionary tracks.
The mass of CoRoT-7b, the first transiting superearth exoplanet, is still a subject of debate. A wide range of masses have been reported in the literature ranging from as high as 8 M_Earth to as low as 2.3 M_Earth. Although most mass determinations g
ive a density consistent with a rocky planet, the lower value permits a bulk composition that can be up to 50% water. We present an analysis of the CoRoT-7b radial velocity measurements that uses very few and simple assumptions in treating the activity signal. By only analyzing those radial velocity data for which multiple measurements were made in a given night we remove the activity related radial velocity contribution without any a priori model. We demonstrate that the contribution of activity to the final radial velocity curve is negligible and that the K-amplitude due to the planet is well constrained. This yields a mass of 7.42 +/- 1.21 M_Earth and a mean density of rho = 10.4 +/- 1.8 gm cm^-3. CoRoT-7b is similar in mass and radius to the second rocky planet to be discovered, Kepler-10b, and within the errors they have identical bulk densities - they are virtual twins. These bulk densities lie close to the density - radius relationship for terrestrial planets similar to what is seen for Mercury. CoRoT-7b and Kepler-10b may have an internal structure more like Mercury than the Earth.
