Signatures of Einstein-Maxwell dilaton-axion gravity from the observed quasi-periodic oscillations in black holes

TL;DR

This work probes Einstein-Maxwell dilaton-axion (EMDA) gravity, via Kerr-Sen black holes, as a potential extension to General Relativity in the strong gravity regime by analyzing HFQPOs in five black holes. It computes orbital and epicyclic frequencies in Kerr-Sen spacetime and tests eleven QPO models (kinematic and resonant) against HFQPO data, constraining the dilaton charge $r_2$ and spin $a$ through chi-squared and Bayesian (MCMC) analyses. The results show EMDA is not ruled out by current HFQPO data; however, constraints on $r_2$ are model- and source-dependent, with some models favoring Kerr ($r_2 o0$) and others permitting nonzero $r_2$ within sizable uncertainties. The study highlights a need for higher-quality HFQPO measurements to delineate between Kerr and Kerr-Sen spacetimes and to uncover possible additional black hole hairs beyond GR.

Abstract

String-inspired models are often believed to provide an interesting framework for quantum gravity and force unification with promising prospects to resolve issues like dark matter and dark energy which cannot be satisfactorily incorporated within the framework of general relativity (GR). The goal of the present work is to investigate the role of the Einstein-Maxwell dilaton-axion (EMDA) gravity arising in the low energy effective action of the heterotic string theory in explaining astrophysical observations, in particular, the high-frequency quasi-periodic oscillations (HFQPOs) observed in the power spectrum of black holes. EMDA gravity has interesting cosmological implications and hence it is worthwhile to explore the footprints of such a theory in available astrophysical observations. This requires one to study the stationary, axi-symmetric black hole solution in EMDA gravity, which corresponds to the Kerr-Sen spacetime. Such black holes are endowed with a dilatonic charge while the rotation is sourced from the axionic field. We investigate the orbital and epicyclic frequencies of matter rotating in the Kerr-Sen spacetime and consider eleven well-studied QPO models in this work. We compare the model dependent QPO frequencies with the available observations of five BH sources, namely, XTE J1550-564, GRS 1915+105, H 143+322, GRO J1655-40 and Sgr A*. Our analysis provides constrains on the spins of the aforesaid black holes which when compared with previous estimates enables us to understand the observationally favored QPO models for each of these sources. Further, from the current data the EMDA scenario cannot be ruled out in favor of general relativity. We comment on the implications and limitations of our finding and how the present constrains compare with the existing literature.

Figures (36)

• Figure 1: In the above figure, the red shaded region depicts the allowed range of spin corresponding to a given $r_2$ for the Kerr-Sen metric to represent a black hole.
• Figure 2: The above figure shows the radial variation of $f_{\phi}$ for (a) $r_2=0$, (b) $r_2=0.6$ and (c) $r_2= 1.2$ for a $M=10 M_\odot$ BH and (d) $r_2=0$, (e) $r_2=0.6$ and (f) $r_2= 1.2$ for a $M=10^6 M_\odot$ BH. In each sub-figure, the radial variation of $f_{\phi}$ is elucidated for three choices of spin, $a=0$ (the non-rotating case denoted by the red curve), $a=0.8$ for $r_2=0$ (denoted by the orange curve) and $a=\frac{1}{2}(1-\frac{r_2}{2})$ for non-zero $r_2$ (denoted by the orange curve), and $a \approx a_{max}=1-\frac{r_2}{2}$ (the maximal spin denoted by the blue curve).
• Figure 3: The above figure shows the radial variation of $f_{r}$ for (a) $r_2=0$, (b) $r_2=0.6$ and (c) $r_2= 1.2$ for a $M=10 M_\odot$ BH and (d) $r_2=0$, (e) $r_2=0.6$ and (f) $r_2= 1.2$ for a $M=10^6 M_\odot$ BH. In each sub-figure, the radial variation of $f_{r}$ is elucidated for three choices of spin, $a=0$ (the non-rotating case denoted by the red curve), $a=0.8$ for $r_2=0$ (denoted by the orange curve) and $a=\frac{1}{2}(1-\frac{r_2}{2})$ for non-zero $r_2$ (denoted by the orange curve), $a \approx a_{max}=1-\frac{r_2}{2}$ (the maximal spin denoted by the blue curve).
• Figure 4: The above figure shows the radial variation of $f_{\theta}$ for (a) $r_2=0$, (b) $r_2=0.6$ and (c) $r_2= 1.2$ for a $M=10 M_\odot$ BH and (d) $r_2=0$, (e) $r_2=0.6$ and (f) $r_2= 1.2$ for a $M=10^6 M_\odot$ BH. In each sub-figure, the radial variation of $f_{\theta}$ is elucidated for three choices of spin, $a=0$ (the non-rotating case denoted by the red curve), $a=0.8$ for $r_2=0$ (denoted by the orange curve) and $a=\frac{1}{2}(1-\frac{r_2}{2})$ for non-zero $r_2$ (denoted by the orange curve), $a \approx a_{max}=1-\frac{r_2}{2}$ (the maximal spin denoted by the blue curve).
• Figure 5: The above figure (a) demonstrates the variation of $\chi^2$ with the dilaton charge $r_2$ for the five black hole sources in \ref{['Tab2']} assuming RPM. Figure (b) plots the the variation of $\chi^2$ with $r_2$ (assuming the same model) but for a subset of those five BHs where the $\chi^2$ values are large and the variation with $r_2$ is also substantial such that the confidence lines can be drawn. The grey dotted line corresponds to the 1-$\sigma$ contour, the grey short-dashed line corresponds to the 2-$\sigma$ contour and the grey long-dashed line is associated with the 3-$\sigma$ contour for XTE J1550-564, GRS 1915+105 and H1743-322. The red long-dashed line is the 3-$\sigma$ contour corresponding to the source GRO J1655-40.