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Investigating the interaction of a Cosmic String with an Accreting Black Hole

Ishan Swamy, Deobrat Singh

TL;DR

This paper addresses how a one-dimensional cosmic string attached to a rotating black hole can extract rotational energy and alter the spin, thereby shifting the ISCO radius $R_{ISCO}$ that governs accretion-disk dynamics. The authors derive the Kerr-based ISCO expression $R_{ISCO}=M Z_0$ and relate its evolution to mass flow, with a string-induced mass loss $\dot{M}_{str} \approx 10^4 \mu$, linking ISCO changes to the string tension $\mu$. Through numerical analysis for a $10 M_\odot$ black hole in a low-mass X-ray binary and two tension regimes, they show that small tensions yield pronounced transition phases in $R_{ISCO}$ while large tensions slow spin-up and can eliminate these transitions, potentially preserving the disk. The work suggests observable signatures such as wind ejections or altered ISCO positions that could provide evidence for cosmic strings in X-ray binaries, offering an alternative avenue to gravitational-wave and lensing methods for cosmic-string detection.

Abstract

Rotating black holes when attached to a cosmic string have their rotational energy extracted leading to a change in its spin and mass. The spin of a black hole can be measured using various methods for an accreting black hole in an X-ray binary system. Accretion disks around black holes have an innermost stable circular orbit (ISCO) whose location is directly dependent on spin and mass of the black hole. The orbit's location changes as the black hole's spin changes and hence can be a method to detect the presence of cosmic strings. This study investigates this change and suggests the ejection of accretion material as black hole spin approaches maximum for prograde motion and material falling into the black hole for retrograde motion, regardless of the presence of cosmic string. However, in the presence of cosmic string, the spin-up process due to accretion is found out to be slower, even with high accretion rates and is detectable. There is a transition phase that occurs as the black hole approaches maximum spin, where even small changes in spin result in significant changes in the ISCO's position. Accreting black holes attached to a large string never reach this transition phase and this absence serves as potential evidence for the existence of a cosmic string.

Investigating the interaction of a Cosmic String with an Accreting Black Hole

TL;DR

This paper addresses how a one-dimensional cosmic string attached to a rotating black hole can extract rotational energy and alter the spin, thereby shifting the ISCO radius that governs accretion-disk dynamics. The authors derive the Kerr-based ISCO expression and relate its evolution to mass flow, with a string-induced mass loss , linking ISCO changes to the string tension . Through numerical analysis for a black hole in a low-mass X-ray binary and two tension regimes, they show that small tensions yield pronounced transition phases in while large tensions slow spin-up and can eliminate these transitions, potentially preserving the disk. The work suggests observable signatures such as wind ejections or altered ISCO positions that could provide evidence for cosmic strings in X-ray binaries, offering an alternative avenue to gravitational-wave and lensing methods for cosmic-string detection.

Abstract

Rotating black holes when attached to a cosmic string have their rotational energy extracted leading to a change in its spin and mass. The spin of a black hole can be measured using various methods for an accreting black hole in an X-ray binary system. Accretion disks around black holes have an innermost stable circular orbit (ISCO) whose location is directly dependent on spin and mass of the black hole. The orbit's location changes as the black hole's spin changes and hence can be a method to detect the presence of cosmic strings. This study investigates this change and suggests the ejection of accretion material as black hole spin approaches maximum for prograde motion and material falling into the black hole for retrograde motion, regardless of the presence of cosmic string. However, in the presence of cosmic string, the spin-up process due to accretion is found out to be slower, even with high accretion rates and is detectable. There is a transition phase that occurs as the black hole approaches maximum spin, where even small changes in spin result in significant changes in the ISCO's position. Accreting black holes attached to a large string never reach this transition phase and this absence serves as potential evidence for the existence of a cosmic string.

Paper Structure

This paper contains 9 sections, 15 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Radius of Innermost Stable Circular Orbit
  3. Numerical Analysis
  4. Small String tension
  5. Large String tension
  6. Results and Discussion
  7. Conclusions
  8. Acknowledgement
  9. References

Figures (9)

  • Figure 1: Schematic illustration of the Black Hole - Cosmic String system considered.
  • Figure 2: $\dot{R}_{ISCO}$ vs $\alpha$ for $\mu = 10^{-40}$
  • Figure 3: $\dot{R}_{ISCO}$ vs $\alpha$ for $\mu = 10^{-40}$ displaying its transition phase
  • Figure 4: $\dot{R}_{ISCO}$ vs $\alpha$ for $\mu = 10^{-40}$ displaying discontinuity at $\alpha = 0$
  • Figure 5: $R_{ISCO}$ vs $\alpha$ for $0<\alpha<1$ and $\mu = 10^{-40}$
  • ...and 4 more figures