Periastron shift of compact stellar orbits from general relativistic and tidal distortion effects near Sgr A*

ABSTRACT The Galactic Centre (Sgr A*), hosting a supermassive black hole, carries sufficient potential for testing gravitational theories. Existing astrometric facilities on Very Large Telescope (VLT) and the Keck Telescope have enabled astronomers to study stellar orbits near Sgr A* and perform new astronomical tests of gravitational theories. These observations have provided strong field tests of gravity (ϕ/c2 ∼ 10−3, which is much greater than ϕ/c2 for the Solar system). In this work, we have estimated magnitudes of various contributions to the periastron shift of compact stellar orbits near Sgr A* for pericentre distance in the range rp = (0.3 – 50)au at a fixed orbital inclination, i = 90°. We take the spin of the black hole as χ = 0.1, 0.44, and 0.9 and eccentricities of the orbit as e = 0.9. The relativistic effects including orders beyond 1PN and spin induced effects are incorporated in the contributions. Effect of tidal distortion on periastron shift has also been added into the estimation by considering gravitational Love numbers for polytropic models of the stars. For the tidal effect, we have considered updated mass–radii relations for low-mass stars and high-mass stars. It has been found that the tidal effect on periastron shift arising from stars represented by polytropes of indices n = 1 and n = 3 terminate above rp ∼ 2 au and rp ∼ 1 au, respectively. The periastron shift angle for the stars has been compared with the astrometric capabilities of existing large telescopes and upcoming extremely large telescopes. Challenges and prospects associated with the estimations are highlighted.

Asteroseismology of tidally distorted sdB stars

ABSTRACT Most subdwarf B stars are located in post-common envelope binaries. Many are in short-period systems subject to tidal influence, and many show pulsations useful for asteroseismic inference. In combination, one must quantify when and how tidal distortion affects the normal modes. We present a method for computing tidal distortion and associated frequency shifts. Validation is by application to polytropes and comparison with previous work. For typical sdB stars, a tidal distortion to the radius of between $0.2\,$ and $2\,$ per cent is generated for orbital periods of 0.1 d. Application to numerical helium core-burning stars identifies the period and mass-ratio domain where tidal frequency shifts become significant and quantifies those shifts in terms of binary properties and pulsation modes. Tidal shifts disrupt the symmetric form of rotationally split multiplets by introducing an asymmetric offset to modes. Tides do not affect the total spread of a rotationally split mode unless the stars are rotating sufficiently slowly that the rotational splitting is smaller than the tidal splitting.

An Investigation of the Small Eccentricity in the Spectroscopic Binary System ζ TrA

The orbital eccentricity of the SB1 system ζ TrA (S.T. F9V, P ∼ 13 d) was found by Skuljan et al. (2004) to be e = 0.01398 ± 0.00019. Lucy (2005) devised a statistical test of the significance of this result, based on the amplitude and phase of the third harmonic in the Fourier analysis of the radial velocity data, and concluded that the non-zero eccentricity measured does not arise from a slightly eccentric Keplerian orbit, but from proximity effects in the binary. He therefore believes a circular orbit should be assigned to this system. In this paper we investigate one possible proximity effect, namely the tidal distortion of the primary star, such that the measured Doppler shift does not accurately indicate the centre of mass radial velocity of the star as a whole. The code of Wilson & Devinney (2003) was used to model the tidal distortion of the measured radial velocities, assuming a range of possible secondary masses, corresponding to M-dwarf companions. The result is that even for the lowest possible mass secondary of 0.09M⊙ with sin i = 1 (this gives the greatest tidal distortion, as it is closest to the primary) there is no significant effect on the radial velocities (the differences are of order 1 m s−1 as a result of the tidal effects). Similar negligible tidal effects arise using a white dwarf companion. We note that the difference between a circular orbit and the observations amounts to as much as 140 m s−1 at some phases, which is essentially the amplitude of the second harmonic in the data. Our conclusion is that this strong and highly significant second harmonic is most probably the result of a small orbital eccentricity as reported by Skuljan et al (2004). We note that the observed third harmonic according to Lucy (2005) has an amplitude of only 5.2 ± 2.0 m s−1, which is just over twice the error bar of its measurement, and that the predicted third harmonic for an eccentric orbit is only 1.6 m s−1.