Constraint on the quadrupole moment of super-massive black hole candidates from the estimate of the mean radiative efficiency of AGN

The super-massive objects at the center of many galaxies are commonly thought to be black holes. In 4-dimensional general relativity, a black hole is completely specified by its mass $M$ and by its spin angular momentum $J$. All the higher multipole moments of the gravitational field depend in a very specific way on these two parameters. For instance, the mass quadrupole moment is $Q = - J^2/M$. If we can estimate $M$, $J$, and $Q$ for the super-massive objects in galactic nuclei, we over-constrain the theory and we can test the black hole hypothesis. While there are many works studying how this can be done with future observations, in this paper a constraint on the quadrupole moment of these objects is obtained by using the current estimate of the mean radiative efficiency of AGN. In terms of the anomalous quadrupole moment $q$, the bound is $-2.01 < q < 0.14$.Comment: 4 pages, 2 figures. v2: refereed versio

Unattainable extended spacetime regions in conformal gravity

The Janis-Newman-Winicour metric is a solution of Einstein's gravity minimally coupled to a real massless scalar field. The $\gamma$-metric is instead a vacuum solution of Einstein's gravity. These spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. In this paper, we reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor. Now curvature invariants remain finite over the whole spacetime. Massive particles never reach the previous singular surface and massless particles can never do it with a finite value of their affine parameter. Our results support the conjecture according to which conformal gravity can fix the singularity problem that plagues Einstein's gravity.Comment: 1+10 pages, 2 figures. v2: refereed versio

Testing the performance and accuracy of the RELXILL model for the relativistic X-ray reflection from accretion disks

The reflection spectroscopic model RELXILL is commonly implemented in studying relativistic X-ray reflection from accretion disks around black holes. We present a systematic study of the model's capability to constrain the dimensionless spin and ionization parameters from $\sim$6,000 NuSTAR simulations of a bright X-ray source employing the lamppost geometry. We employ high count spectra to show the limitations in the model without being confused with limitations in signal-to-noise. We find that both parameters are well-recovered at 90% confidence with improving constraints at higher reflection fraction, high spin, and low source height. We test spectra across a broad range - first at 10$^6-$10$^7$ and then $\sim$10$^5$ total source counts across the effective 3-79 keV band of NuSTAR, and discover a strong dependence of the results on how fits are performed around the starting parameters, owing to the complexity of the model itself. A blind fit chosen over an approach that carries some estimates of the actual parameter values can lead to significantly worse recovery of model parameters. We further stress on the importance to span the space of nonlinear-behaving parameters like $log~\xi$ carefully and thoroughly for the model to avoid misleading results. In light of selecting fitting procedures, we recall the necessity to pay attention to the choice of data binning and fit statistics used to test the goodness of fit by demonstrating the effect on the photon index $\Gamma$. We re-emphasize and implore the need to account for the detector resolution while binning X-ray data and using Poisson fit statistics instead while analyzing Poissonian data.Comment: 9 pages, 6 figures, accepted for publication in Ap

Testing general relativity with the reflection spectrum of the supermassive black hole in 1H0707−-495

Recently, we have extended the X-ray reflection model relxill to test the spacetime metric in the strong gravitational field of astrophysical black holes. In the present Letter, we employ this extended model to analyze XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495 and test deviations from a Kerr metric parametrized by the Johannsen deformation parameter $\alpha_{13}$. Our results are consistent with the hypothesis that the spacetime metric around the black hole in 1H0707-495 is described by the Kerr solution.Comment: 10 pages, 7 figures. v2: refereed versio

Public Release of RELXILL_NK: A Relativistic Reflection Model for Testing Einstein's Gravity

We present the public release version of relxill_nk, an X-ray reflection model for testing the Kerr hypothesis and general relativity. This model extends the relxill model that assumes the black hole spacetime is described by the Kerr metric. We also present relxilllp_nk, the first non-Kerr X-ray reflection model with a lamppost corona configuration, as well as all other models available in the full relxill_nk package. In all models the relevant relativistic effects are calculated through a general relativistic ray-tracing code that can be applied to any well-behaved, stationary, axisymmetric, and asymptotically flat black hole spacetime. We show that the numerical error introduced by using a ray-tracing code is not significant as compared with the observational error present in current X-ray reflection spectrum observations. In addition, we present the reflection spectrum for the Johannsen metric as calculated by relxill_nk.Comment: 15 pages, 8 figures. v2: refereed version. Code and documentation available at http://www.physics.fudan.edu.cn/tps/people/bambi/Site/RELXILL_NK.html and at http://www.tat.physik.uni-tuebingen.de/~nampalliwar/relxill_nk

Towards the use of the most massive black hole candidates in AGN to test the Kerr paradigm

The super-massive objects in galactic nuclei are thought to be the Kerr black holes predicted by General Relativity, although a definite proof of their actual nature is still lacking. The most massive objects in AGN ($M \sim 10^9 M_\odot$) seem to have a high radiative efficiency ($\eta \sim 0.4$) and a moderate mass accretion rate ($L_{\rm bol}/L_{\rm Edd} \sim 0.3$). The high radiative efficiency could suggest they are very rapidly-rotating black holes. The moderate luminosity could indicate that their accretion disk is geometrically thin. If so, these objects could be excellent candidates to test the Kerr black hole hypothesis. An accurate measurement of the radiative efficiency of an individual AGN may probe the geometry of the space-time around the black hole candidate with a precision comparable to the one achievable with future space-based gravitational-wave detectors like LISA. A robust evidence of the existence of a black hole candidate with $\eta > 0.32$ and accreting from a thin disk may be interpreted as an indication of new physics. For the time being, there are several issues to address before using AGN to test the Kerr paradigm, but the approach seems to be promising and capable of providing interesting results before the advent of gravitational wave astronomy.Comment: 12 pages, 6 figures. v2: some typos correcte