Accretion disk onto boson stars: A way to supplant black hole candidates

The emission spectrum from a simple accretion disk model around a compact object is compared for the cases of a black hole (BH) and a boson star (BS) playing the role of the central object. It was found in the past that such a spectrum presents a hardening at high frequencies; however, here it is shown that the self-interaction and compactness of the BS have the effect of softening the spectrum; the less compact the star is, the softer the emission spectrum at high frequencies. Because the mass of the boson fixes the mass of the star and the self-interaction the compactness of the star, we find that, for certain values of the BS parameters, it is possible to produce similar spectra to those generated when the central object is a BH. This result presents two important implications: (i) Using this simple accretion model, a BS can supplant a BH in the role of compact object accreting matter, and (ii) within the assumptions of the present accretion disk model, we do not find a prediction that could help distinguish a BH from a BS with appropriate parameters of mass and self-interaction.

Figure 1

(a) Sequences of equilibrium configurations for different values of $\Lambda$ are shown as a function of the central value of the scalar field ${\varphi }_0(0)$. The circles indicate the critical point that divides the stable from the unstable solutions. The inverted triangles indicate the point at which the binding energy is zero. Those configurations between the circles and the triangles (along each sequence) collapse into black holes even under infinitesimal perturbations (see 27 for the full tracking of the formation of an event horizon out of an unstable boson star). Configurations to the right of the triangles disperse away. (b) The compactness of each solution is shown. The critical point is also marked, since the interesting configurations would be those boson stars that are stable (to the left of the circles). In both plots, the transparent circles indicate the special set of configurations we calculate the emission spectrum for in what follows; in the case of $\Lambda =0$, such a configuration is very close to the critical point and it is difficult to see, but it is in there. The configuration marked with a square corresponds to a configuration with $\Lambda =0$, $M=0.499$, and compactness 0.063 32; this compactness is the same as that of the configuration with $\Lambda =20$ and $M=0.633$; see text to take advantage of this remark.

Figure 2

Here it is shown the effective potential that a particle with $L^2=12M^2$ “feels” for two configurations of the same mass $M=0.633$ and $\Lambda =0,20$ and for a black hole of the same mass. At $r=6M$, it is possible to see the ISCO for a test particle on a BH space-time. The interesting result is that, for the more compact stars, test particles can travel deeper inside the star. What is possible to infer is that freely falling observers cannot distinguish whether there is a BH or a BS from $r=30M$ on.

Figure 3

(a) The squared denominator of $E$ and $L$ in (5); the star chosen is the one with $\Lambda =0$, central field $\varphi (0)=0.271$, and mass $M=0.633(M_{\mathrm{pl}}^2/m)$. (b) Physical quantities used for the calculation of $D(r)$ (see text); the solid line indicates these quantities for a black hole of the same mass as the star. The results in this plot coincide with those obtained in Ref. 8.

Figure 4

The emission spectrum from a central star with mass $M=0.633(M_{\mathrm{pl}}^2/m)$ and different values of $\Lambda$. The solid line is obtained when a black hole is considered as the central object. The curve for $\Lambda =0$ is the one obtained in Ref. 8 and shows the hardening of the spectrum at high frequencies. The case $\Lambda =20$ is particularly interesting, because it seems to match the spectrum obtained with the BH.

Figure 5

The emission spectrum from a disk with a central star with mass $M=0.499(M_{\mathrm{pl}}^2/m)$ and $\Lambda =0$. In order to keep $M$ equal to that of the configurations in Fig. 4, it is necessary to set $m=0.499/0.633\times 1.2\times {10}^{-25}\mathrm{GeV}$; otherwise, we could construct a correct spectrum with the incorrect gravitational mass. The similarity between the spectrum due to the BS and to the BH is not as impressive as that of star $Y$, but the hardening of the spectrum is not as strong as that of $\Lambda =0$ in the previous plot. We simply used a star with no self-interaction and compactness $2N_{99}/R_{99}=0.06332$ as that of star $Y$.