Final stages of accretion onto non-Kerr compact objects

The $5–20M_{\odot }$ dark objects in x-ray binary systems and the ${10}^5–{10}^9{M}_{\odot }$ dark objects in galactic nuclei are currently thought to be the Kerr black holes predicted by general relativity. However, direct observational evidence for this identification is still elusive, and the only viable approach to confirm the Kerr black hole hypothesis is to explore and rule out any other possibility. Here we investigate the final stages of the accretion process onto generic compact objects. While for Kerr black holes and for more oblate bodies the accreting gas reaches the innermost stable circular orbit (ISCO) and plunges into the compact object, we find that for more prolate bodies several scenarios are possible, depending on the spacetime geometry. In particular, we find examples in which the gas reaches the ISCO but then gets trapped between the ISCO and the compact object. In this situation, accretion onto the compact object is possible only if the gas loses additional angular momentum, forming toruslike structures inside the ISCO.

Figure 1

The character of the effective ISCO for MN spacetimes with spin parameter $a$ and anomalous quadrupole moment $q$. Compact objects to the right (left) of the solid red line have ISCOs determined by the instability in the radial (vertical) direction. Compact objects to the right (left) of the dotted blue line are oblate (prolate) bodies, while they are more oblate (prolate) than a BH if $q>0$ ($q<0$).

Figure 2

Accretion in Manko-Novikov spacetimes with $a=0.1$ and $q=0.2$, $-0.5$, $-0.6$, and $q=-4$. The solid black line at small radii is the partial horizon $x=1$, the region where closed timelike curves exist (i.e. the region where $g_{\varphi \varphi }<0$) is shown in green/light gray, the red dashed line is the boundary of the ergoregion (i.e. $g_{tt}=0$ on that line), while the red dot on the equatorial plane marks the position of the ISCO, i.e. the inner edge of the thin accretion disk. The thick disk, if it forms, sheds from the ISCO and is denoted by concentric contours, whose label is an upper limit to the ${log}_{10}$ of the gas temperature in $K$ (see text for details). In blue/dark grey is the region accessible to the gas shedding from the inner edges of the thick disk [i.e. the region where $V_{\mathrm{eff}}(E_{\mathrm{inner}},L_{\mathrm{inner}},r,\theta )\ge 0$, $E_{\mathrm{inner}}$, and $L_{\mathrm{inner}}$ being the energy and angular momentum of the gas at the inner edges of the thick disk]. If no thick disk is present, in blue/dark grey is the region accessible to the gas shedding from the inner edge of the thin disk [i.e. the region where $V_{\mathrm{eff}}(E_{\mathrm{ISCO}},L_{\mathrm{ISCO}},r,\theta )\ge 0$]: if this plunge region does not reach the ISCO, we also show (with solid black lines around the ISCO) the contours $V_{\mathrm{eff}}(E_{\mathrm{ISCO}},L_{\mathrm{ISCO}},r,\theta )=-{10}^{-4}$ and $V_{\mathrm{eff}}(E_{\mathrm{ISCO}},L_{\mathrm{ISCO}},r,\theta )=-{10}^{-3}$, which represent the region where the gas reaching the ISCO can shed if subject to a small perturbation. For $q=0.2$ the ISCO is radially unstable, and the gas plunges directly into the compact object remaining roughly on the equatorial plane, as in the Kerr case [scenario (1a)]. For $q=-0.5$ the ISCO is radially unstable and the gas plunges, but does not reach the compact object; instead, it gets trapped between the object and the ISCO and forms a thick disk [scenario (1b)]. For $q=-0.6$ the ISCO is vertically unstable, and the gas plunges directly into the compact object outside the equatorial plane [scenario (2a)]. For $q=-4$ the ISCO is vertically unstable, and the gas does not plunge directly but remains trapped in the vicinities of the ISCO [because $V_{\mathrm{eff}}(E_{\mathrm{ISCO}},L_{\mathrm{ISCO}},r,\theta )<0$ near the ISCO]. However, the potential barrier is not tall enough to allow a thick disk to form, and a small perturbation is enough to cause the gas to fall into the central object [scenario (2b)].

Figure 3

Same notation as in Fig. 2, but for $a=0.5$ and $q=0.2$, $-0.2$, $-0.5$, and $-2$. The accretion properties too are qualitatively similar, case by case, to those displayed for $a=0.1$ in Fig. 2.

Figure 4

Same notation as in Fig. 2, but for $a=0.9$ and $q=0.2$, $-0.015$, $-0.02$, and $-0.12$. The accretion properties are qualitatively similar to those displayed for $a=0.1$ in Fig. 2 and for $a=0.5$ in Fig. 3, except for $q=-0.12$. In that case, the ISCO is vertically unstable, and the gas does not plunge directly but remains trapped in the vicinities of the ISCO [because $V_{\mathrm{eff}}(E_{\mathrm{ISCO}},L_{\mathrm{ISCO}},r,\theta )<0$ near the ISCO]. However, the potential barrier is tall enough to allow the formation of two thick disks, above and below the equatorial plane [scenario (2c)]. This contrasts with the cases $a=0.1$, $q=-4$ (Fig. 2) and $a=0.2$, $q=-2$ (Fig. 3), where the potential barrier is smaller and can be easily overcome if the gas is slightly perturbed.