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Searching for quantum-gravity footprint around stellar-mass black holes

Luigi Foschini, Alberto Vecchiato, Alfio Bonanno

TL;DR

The study investigates whether asymptotically safe gravity imprints can be detected around stellar-mass black holes by examining the inner edge of the accretion disk. Using a literature survey of high/soft state observations, the authors homogenize $r_{ m in}$ measurements and compare them to Kerr GR predictions, accounting for corrections and biases from Comptonization and instrumentation. Across six black-hole binaries, the inner radii are consistent with Kerr expectations, yielding the strongest constraint to date on the ASG parameter, with $ ilde{\xi}= ilde{\xi} \, ext{less than about }0.24$ (equivalently $\xi \, ext{less than about }2.3\times10^{12}$ cm$^2$ for Cygnus X-1). The results reinforce GR in the strong-field regime and highlight the importance of precise spin, distance, and inclination measurements, as well as advanced X-ray capabilities for probing quantum gravity effects.

Abstract

According to the asymptotically safe gravity, black holes may have characteristics different from those described according to general relativity if the running of the gravitational constant coupling happens at low energies. Particularly, they should be more compact, with a smaller event horizon, which in turn affects the other quantities dependent on it, like the photon ring and the size of the innermost stable circular orbit. We decided to test the latter hypothesis by searching in the literature for observational measurements of the inner radius of the accretion disk around stellar-mass black holes. We selected the smallest values measured when the disk was in high/soft state, made them homogeneous by taking into account the most recent and more reliable values of mass, spin, viewing angle, and distance from the Earth, and compared with the expectations of the Kerr metric. We do not find any significant deviation. Some doubtful cases can be easily understood as due to specific states of the object during the observation or instrumental biases. We set the tightest constraint on the parameter $ξ$ obtained to date.

Searching for quantum-gravity footprint around stellar-mass black holes

TL;DR

The study investigates whether asymptotically safe gravity imprints can be detected around stellar-mass black holes by examining the inner edge of the accretion disk. Using a literature survey of high/soft state observations, the authors homogenize measurements and compare them to Kerr GR predictions, accounting for corrections and biases from Comptonization and instrumentation. Across six black-hole binaries, the inner radii are consistent with Kerr expectations, yielding the strongest constraint to date on the ASG parameter, with (equivalently cm for Cygnus X-1). The results reinforce GR in the strong-field regime and highlight the importance of precise spin, distance, and inclination measurements, as well as advanced X-ray capabilities for probing quantum gravity effects.

Abstract

According to the asymptotically safe gravity, black holes may have characteristics different from those described according to general relativity if the running of the gravitational constant coupling happens at low energies. Particularly, they should be more compact, with a smaller event horizon, which in turn affects the other quantities dependent on it, like the photon ring and the size of the innermost stable circular orbit. We decided to test the latter hypothesis by searching in the literature for observational measurements of the inner radius of the accretion disk around stellar-mass black holes. We selected the smallest values measured when the disk was in high/soft state, made them homogeneous by taking into account the most recent and more reliable values of mass, spin, viewing angle, and distance from the Earth, and compared with the expectations of the Kerr metric. We do not find any significant deviation. Some doubtful cases can be easily understood as due to specific states of the object during the observation or instrumental biases. We set the tightest constraint on the parameter obtained to date.

Paper Structure

This paper contains 11 sections, 9 equations, 5 figures.

Table of Contents

  1. Introduction
  2. A short summary of the accretion disk theory and models
  3. Gathering data
  4. Results
  5. Cygnus X-1
  6. GRS 1915+105
  7. XTE J1550-564
  8. GX 339-4
  9. XTE J1650-500
  10. GRO J0422+32
  11. Conclusions

Figures (5)

  • Figure 1: Unfolded spectrum of the diskbb model with $T_{\rm col}=0.4$ keV, and assuming a typical Galactic hydrogen column $N_{\rm H}=10^{21}$ cm$^{-2}$. The vertical dashed line represents the $2$ keV low-energy threshold of RXTE/PCA. The flux is in arbitrary units (diskbb normalization set to 1).
  • Figure 2: Cygnus X-1: inner radius of the accretion disk in units of [$r_{\rm g}$]. The two dashed grey lines represent the range of $r_{\rm isco}$ as expected from GR, while the continuous line represents the $r_{\rm isco}$ with the maximum allowable spin of $a=0.99$ according to MUMMERY25. Reference number refers to the source of data: 1: DOTANI1997; 2: POUTANEN1997; 3-4: CUI1998; 5: FRONTERA2001; 6: TOMSICK2014; 7: SUGIMOTO2016; 8-11: WALTON2016; 12-13 KUSHWAHA2021; 14: YAN2021.
  • Figure 3: GRS 1915+105: inner radius of the accretion disk in units of [$r_{\rm g}$]. The two dashed grey lines represent the range of $r_{\rm isco}$ as expected from GR, while the continuous line represents the $r_{\rm isco}$ with the maximum allowable spin of $a=0.99$ according to MUMMERY25. The arrows indicate upper limits. Reference number refers to the source of data: 1-2: TAAM1997; 3: MUNO1999; 4-7: FEROCI1999; 8-10: RAO2000; 11: BELLONI2000; 12: ZDIARSKI2001; 13-22: VADAWALE2001; 23-27: UEDA2002; 28-29: NAIK2002; 30-32: DONE2004; 33-36: OHKAWA2005; 37-46: RODRIGUEZ2008; 47-50: VIERDAYANTI2010; 51-54: UEDA2010; 55-60: RAHOUI2010; 61: NEILSEN2011; 62: MILLER2016; 63-68: MINEO2017; 69: HESS2018.
  • Figure 4: XTE J1550-564: inner radius of the accretion disk in units of [$r_{\rm g}$]. The two dashed grey lines represent the range of $r_{\rm isco}$ as expected from GR, while the continuous line represents the $r_{\rm isco}$ with the maximum allowable spin of $a=0.99$ according to MUMMERY25. Reference number refers to the source of data: 1: SOBCZAK1999; 2-13: SOBCZAK2000; 14-15: RODRIGUEZ2003; 16: MILLER2003; 17: KUBOTA2004A; 18-20: KUBOTA2004B; 21: SRIRAM2016; 22: CONNORS2019; 23-27: CONNORS2020.
  • Figure 5: GX 339-4: inner radius of the accretion disk in units of [$r_{\rm g}$]. The two dashed grey lines represent the range of $r_{\rm isco}$ as expected from GR, while the continuous line represents the $r_{\rm isco}$ with the maximum allowable spin of $a=0.99$ according to MUMMERY25. Reference number refers to the source of data: 1-2: MILLER2004A; 3: MILLER2004B; 4-5: BELLONI2006; 6: REIS2008; 7: MILLER2008; 8-10: DELSANTO2008; 11-13: MOTTA2009; 14-18: CABALLERO2009; 19: SHIDATSU2011; 20: MOTTA2011; 21: TAMURA2012; 22: RAHOUI2012; 23: PLANT2014; 24-25: LUDLAM2015; 26: KUBOTA2016; 27-29: STIELE2017; 30-33: SRIDHAR2020; 34-36: SHUI2021; 38-40: YANG2023; 41: PEIRANO2023; 42: LIU2023; 43: JANA2024.