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| Paper: |
Testing General Relativity with Galactic-Centre Stars |
| Volume: |
439, The Galactic Center: a Window to the Nuclear Environment of Disk Galaxies |
| Page: |
242 |
| Authors: |
Angélil, R.; Saha, P. |
| Abstract: |
The Galactic Centre S-stars orbiting the central supermassive black
hole reach velocities of a few percent of the speed of light. The
GR-induced perturbations to the redshift enter the dynamics via two
distinct channels. The post-Newtonian regime perturbs the orbit from
the Keplerian (Zucker et al., 2006, Kannan & Saha 2009), and the
photons from the Minkowski (Angélil & Saha 2010). The inclusion
of gravitational time dilation at O (v2) marks the first departure of the redshift from the line-of-sight
velocities. The leading-order Schwarzschild terms curve space, and
enter at O(v3). The classical Keplerian
phenomenology dominates the total redshift. Spectral measurements of
sufficient resolution will allow for the detection of these
post-Newtonian effects. We estimate the spectral resolution required
to detect each of these effects by fitting the redshift curve via
the five Keplerian elements plus black hole mass to mock data. We
play with an exaggerated S2 orbit - one with a semi-major axis a
fraction of that of the real S2. This amplifies the relativistic
effects, and allows clear visual distinctions between the
relativistic terms. We argue that spectral data of S2 with a
dispersion ∼ 10 km s–1 would allow for a clear detection of
gravitational redshift, and ∼ 1 km s–1 would suffice for
leading-order space curvature detection. |
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