Polarimetry and strong gravity effects from spots orbiting near a black hole

TL;DR

This paper investigates how the orbiting spot model predicts flux and polarization variations in black hole accretion, highlighting the impact of emission region geometry on observable signals.

Contribution

It introduces the influence of emission region shape, such as spiral versus small spot, on flux and polarization modulations near black holes.

Findings

Spiral-shaped emission regions produce distinct lightcurve signatures.

Polarization degree and angle vary predictably with orbiting spots.

Emission geometry can be distinguished through polarization measurements.

Abstract

We study the modulation of the observed radiation flux and the associated changes in the polarization degree and angle that are predicted by the orbiting spot model for flares from accreting black holes. The geometric shape of the emission region influences the resulting model lightcurves, namely, the emission region of a spiral shape can be distinguished from a simpler geometry of a small orbiting spot.

Equations

$$ds^{2}=-\frac{\Delta}{\Sigma}\Big{(}dt-a\sin^{2}\theta\;d\phi\Big{)}^{2}+\frac{\Sigma}{\Delta}\;dr^{2}+\Sigma\;d\theta^{2}+\frac{\sin^{2}\theta}{\Sigma}\Big{[}a\;dt-\big{(}r^{2}+a^{2}\big{)}\;d\phi\Big{]}^{2}$$

Full text

We further explore this scheme for the observed flares from the supermassive black hole in the context of Galactic center (Sgr A*). Our code simulates the lightcurves for a wide range of parameters. The energy dependence of the changing degree and angle of polarization should allow us to discriminate between the cases of a rotating and a non-rotating black hole.

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1 Introduction

Relativistic corrections to a signal from orbiting spots can lead to large rotation in the plane of observed X-ray polarization. When integrated over an extended surface of the source, this can diminish the observed degree of polarization. Such effects are potentially observable and can be used to distinguish among different models of the source geometry and the radiation mechanisms responsible for the origin of the polarized signal. The idea was originally proposed in the 1970s,[4, 5, 17] however, its observational confirmation and practical use in observations are still is a challenging task.

The geometrical effects of strong gravitational fields act on photons independently of their energy. The gravitational field is described by the metric of Kerr black hole [16]

[TABLE]

in Boyer-Lindquist (spheroidal) coordinates $t$, $r$, $\theta$, $\phi$. The metric functions $\Delta(r)$ and $\Sigma(r,\theta)$ are known in an explicit form. The event horizon occurs at the roots of equation $\Delta(r)=0$; the outer solution is found given by $r=R_{+}=1+(1-a^{2})^{1/2}$.

Let us note that there are some similarities as well as differences between the expected manifestation of relativistic effects in polarization changes in X-rays and in other spectral bands (NIR). We show these interrelations in the associated poster and point out that the near-infrared polarization measurements of the radiation flares from the immediate vicinity of the horizon have been studied in detail from the Galactic Center (Sagittarius A*) supermassive black hole.[15, 21, 20]

2 Polarization from an Orbiting Spot

Within the scheme of the spot scenario the spots are considered to represent regions of enhanced emission on the disc surface rather than massive clumps that would decay due to shearing motion in the disc. The observed signal is modulated by relativistic effects. Doppler and gravitational lensing influence the observed radiation flux and this can be computed by GR ray-tracing. Such an approach has been developed to compute also strong gravity effects acting on polarization properties.[11]

Our code (KY) is publicly available.[7] The current version333http://stronggravity.eu/results/models-and-data/ allows the user to include the polarimetric resolution and to compute the observational consequences of strong-gravity effects from a Kerr black hole accretion disc. Within the XSPEC notation, this polarimetric resolution is encoded by a switch defining which of the four Stokes parameters is returned in the photon count array at the moment of the output from the model evaluation. This way one can test and combine various models, and pass the resulting signal through the response matrices of different instruments. As an illustration, figure 1 shows a single time-frame from a simulation of a spot rotating rigidly at constant radius.

The detected polarization degree is expected to decrease mainly in the part of the orbit where the spot moves close to the region where the photons are emitted perpendicularly to the disc and the polarization angle changes rapidly. The drop of the observed polarization degree occurs also in those parts of the orbit where the magnetic field points approximately along light ray (see fig. 2 for a map showing the distribution of the polarization effects within the disk plane of a rapidly rotating Kerr black hole). For the more realistic models the resulting polarization exhibits a very complex behaviour due to, e.g., Faraday rotation effects interfering with strong-gravity.[10] Among generic features is the peak in polarization degree for the spin parameter $a\rightarrow M$ and large inclinations, caused by the lensing effect at a particular position of the spot in the orbit. This effect disappears in the non-rotating $a=0$ case.

To conclude, let us note that the above described modelling has recently gained new impetus in the context of forthcoming X-ray polarimetry satellite missions that have been under active consideration. The enhanced X-ray Timing and Polarimetry (eXTP) mission [22, 9] is the concept of novel Chinese X-ray mission that has currently reached the extended phase A with a possible contribution from Europe and the anticipated launch date by 2025.

The Large Area Detector (LAD) aboard the new mission will be a suitable instrument for performing time-resolved spectroscopy with polarimetric resolution, large effective area, and moderate energy resolution to explore bright flares from accreting black holes, possibly in the connection with the processes of tidal disruption of stars and similarly violent events.[23, 24, 25, 6]

Let us just remind the reader that the revealing role of X-ray polarimetry clearly extends to all scales far away from the central black hole. This has been widely discussed in the context of reflection nebulae surrounding Galactic center.[3, 14] The combination of the polarization signal from the Sgr B and Sgr C complexes strengthens the need for an imaging detector with a fine spatial resolution to resolve the structures as small as the Bridge clouds. Therefore, the X-ray polarimetry is needed to explore variety of physical processes operating near supermassive black hole.

3 Conclusions

We explored the approach based on mapping the Kerr black hole equatorial plane onto the observer’s plane at radial infinity. Orbiting spots are projected onto the disc plane (hence imposing the vertically averaged approximation) and then their image is transported towards a distant observer. The strong gravity effects can be seen as the predicted (time-dependent) direction of polarization is changed by light propagation through the curved spacetime. What can be foreseen in the near future is the tracking of the wobbling image centroid that a spot produces. With the polarimetric resolution, this wobbling can provide the evidence of orbiting features.

In conclusion, the rotating spots are a viable scenario capable to explain the occurrence about once per day of modulated flares from within a few milli-arcseconds of the Sagittarius A* supermassive black hole.[12, 18] However, the astrophysically realistic scenarios have to account not only for the time-scales of gradual dispersion of the orbiting features by tidal effects [1, 19] but also for the effects of plasma influencing the light propagation through a non-vacuum spacetime near the black hole.[2, 13]

Acknowledgments

The authors acknowledge the Czech Ministry of Education, Youth and Sports (MŠMT) project INTER-INFORM (ref. LTI 17018), titled “Promotion and Development of International Scientific Cooperation in Relativistic Astrophysics and Preparation of X-ray Space Missions”.