Accretion disks around black holes in scalar-tensor-vector gravity

Scalar-tensor-vector gravity (STVG) is an alternative theory of gravitation that has successfully explained the rotation curves of nearby galaxies, the dynamics of galactic clusters, and cosmological data without dark matter, but has hardly been tested in the strong gravity regime. In this work, we aim at building radiative models of thin accretion disks for both Schwarzschild and Kerr black holes in STVG theory. In particular, we study stable circular equatorial orbits around stellar and supermassive black holes in Schwarzschild and Kerr STVG spacetimes. We also calculate the temperature and luminosity distributions of accretion disks around these objects. We find that accretion disks in STVG around stellar and supermassive black holes are colder and less luminous than in GR. The spectral energy distributions obtained do not contradict current astronomical observations.

Figure 1

Plot of the effective potential as a function of the radial coordinate for different values of the parameter $\alpha$ in the case of a stellar mass black hole in Schwarzschild STVG spacetime. Here, $x_{\mathrm{isco}}=r_{\mathrm{isco}}/r_{\mathrm{g}}$ stands for the location of the innermost stable circular orbit.

Figure 2

Plot of the effective potential as a function of the radial coordinate for different values of the parameter $\alpha$ in the case of a supermassive black hole in Schwarzschild STVG spacetime. Here, $x_{\mathrm{isco}}=r_{\mathrm{isco}}/r_{\mathrm{g}}$ stands for the location of the innermost stable circular orbit.

Figure 3

Plot of the effective potential as a function of the radial coordinate for different values of the parameter $\alpha$ in the case of a stellar mass black hole in Kerr STVG spacetime; the spin of the black hole is $\tilde{a}=0.99$. Here, $x_{\mathrm{isco}}=r_{\mathrm{isco}}/r_{\mathrm{g}}$ stands for the location of the innermost stable circular orbit.

Figure 4

Plot of the effective potential as a function of the radial coordinate for different values of the parameter $\alpha$ in the case of a supermassive black hole in Kerr STVG spacetime; the spin of the black hole is $\tilde{a}=0.99$. Here, $x_{\mathrm{isco}}=r_{\mathrm{isco}}/r_{\mathrm{g}}$ stands for the location of the innermost stable circular orbit.

Figure 5

Plot of the specific angular momentum as a function of the radial coordinate for a test particle in a circular equatorial orbit around a supermassive Kerr STVG black hole of spin $\tilde{a}=0.99$.

Figure 6

Plot of the specific energy as a function of the radial coordinate for a test particle in a circular equatorial orbit around a supermassive Kerr STVG black hole of spin $\tilde{a}=0.99$.

Figure 7

Plot of the angular velocity as a function of the radial coordinate for a test particle in a circular equatorial orbit around a supermassive Kerr STVG black hole of spin $\tilde{a}=0.99$.

Figure 8

Top: Temperature as a function of the radial coordinate for a stellar Schwarzschild-STVG black hole. Bottom: Residual plot of the temperature as a function of the radial coordinate for a stellar Schwarzschild-STVG black hole.

Figure 9

Top: Luminosity as a a function of the energy for a stellar Schwarzschild-STVG black hole. Bottom: Residual plot of the luminosity as a function of the energy for a stellar Schwarzschild-STVG black hole.

Figure 10

Top: Temperature as a function of the radial coordinate for a supermassive Schwarzschild-STVG black hole. Bottom: Residual plot of the temperature as a function of the radial coordinate for a supermassive Schwarzschild-STVG black hole.

Figure 11

Top: Luminosity as a function of the energy for a supermassive Schwarzschild-STVG black hole. Bottom: Residual plot of the luminosity as a function of the energy for a supermassive Schwarzschild-STVG black hole.

Figure 12

Top: Temperature as a function of the radial coordinate for a stellar Kerr-STVG black hole of spin $\tilde{a}=0.99$. Bottom: Residual plot of the temperature as a function of the radial coordinate for a stellar Kerr-STVG black hole of spin $\tilde{a}=0.99$.

Figure 13

Top: Luminosity as a function of the energy for a stellar Kerr-STVG black hole of spin $\tilde{a}=0.99$. Bottom: Residual plot of the luminosity as a function of the energy for a stellar Kerr-STVG black hole of spin $\tilde{a}=0.99$.

Figure 14

Top: Temperature as a function of the radial coordinate for a supermassive Kerr-STVG black hole of spin $\tilde{a}=0.99$. Bottom: Residual plot of the temperature as a function of the radial coordinate for a supermassive Kerr-STVG black hole of spin $\tilde{a}=0.99$.

Figure 15

Top: Luminosity as a function of the energy for a supermassive Kerr-STVG black hole of spin $\tilde{a}=0.99$. Bottom: Residual plot of the luminosity as a function of the energy for a supermassive Kerr-STVG black hole of spin $\tilde{a}=0.99$.