Abstract
Monitoring the orbits of stars around Sgr A* offers the possibility of detecting the precession of their orbital planes due to frame dragging, of measuring the spin and quadrupole moment of the black hole, and of testing the no-hair theorem. Here we investigate whether the deviations of stellar orbits from test-particle trajectories due to wind mass loss and tidal dissipation of the orbital energy compromise such measurements. We find that the effects of stellar winds are, in general, negligible. On the other hand, for the most eccentric orbits (e>0.96) for which an optical interferometer, such as GRAVITY, will detect orbital plane precession due to frame dragging, the tidal dissipation of orbital energy occurs at timescales comparable to the timescale of precession due to the quadrupole moment of the black hole. As a result, this non-conservative effect is a potential source of systematic uncertainty in testing the no-hair theorem with stellar orbits.
Highlights
Stars in orbit around the black hole in the center of the Milky Way, hereafter Sgr A∗, have been tracked for more than a decade, providing a measure of the black hole mass (Genzel et al 2010; Ghez et al 2012)
We calculate the range of orbital parameters for which orbital perturbations due to the stellar winds and tides do not preclude the measurement of the black-hole spin and quadrupole moment and, testing of the no-hair theorem
We explored whether deviations of the orbits of star around Sgr A∗ from test particle trajectories due to stellar winds and tides may compromise the measurements of relativistic effects
Summary
Stars in orbit around the black hole in the center of the Milky Way, hereafter Sgr A∗, have been tracked for more than a decade, providing a measure of the black hole mass (Genzel et al 2010; Ghez et al 2012). Precise astrometric observations of stars in close orbits around Sgr A∗ may lead to the detection of orbital precession due to general relativistic frame dragging, measuring the spin of the black hole, and testing the no-hair theorem (Will 2008) Such measurements will be complementary to those that will be achieved with the Event Horizon Telescope (Fish & Doeleman 2010; Johannsen & Psaltis 2010) as well as to timing observations of pulsars in orbit around the black hole (Pfahl & Loeb 2004; Liu et al 2012). We calculate the range of orbital parameters for which orbital perturbations due to the stellar winds and tides do not preclude the measurement of the black-hole spin and quadrupole moment and, testing of the no-hair theorem
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