Probing supermassive black hole seed scenarios with gravitational wave measurements

Author(s)

Ellis, John, Fairbairn, Malcolm, Urrutia, Juan, Vaskonen, Ville

Abstract

The process whereby the supermassive black holes populating the centers of galaxies have been assembled remains to be established, with the relative importance of seeds provided by collapsed Population-III stars, black holes formed in nuclear star clusters via repeated mergers, or direct collapses of protogalactic disks yet to be determined. In this paper we study the prospects for casting light on this issue by future measurements of gravitational waves emitted during the inspirals and mergers of pairs of intermediate-mass black holes, discussing in particular the roles of prospective measurements by LISA and the proposed atom interferometers AION and AEDGE. We find that, the expected number of detectable IMBH binaries is $O(100)$ for LISA and AEDGE and $O(10)$ for AION in low-mass seeds scenarios and goes down to $O(10)$ for LISA and below one for AEDGE and AION in high-mass seed scenarios. This allows all of these observatories to probe the parameters of the seed model, in particular if at least a fraction of the SMBHs arise from a low-mass seed population. We also show that the measurement accuracy of the binary parameters is, in general, best for AEDGE that sees very precisely the merger of the binary.

Figures

\emph{Upper panel:} The low-mass cut on the massive BH population for different values of $m_{\rm cut}$, for $w=1$ (solid) and $w=2$ (dashed). \emph{Lower panel:} The halo mass-BH mass relation: The color coding shows the BH occupation fraction $p_{\rm occ}$ as a function of the halo mass $M_v$ and the BH mass $m_{\rm BH}$ for a scenario with $f_1 = f_2 = 0.5$, $w_1 = w_2 = 1$, $m_{{\rm cut},1} = 100\Msun$ and $m_{{\rm cut},2} = 10^5\Msun$.

\emph{Upper panel:} The low-mass cut on the massive BH population for different values of $m_{\rm cut}$, for $w=1$ (solid) and $w=2$ (dashed). \emph{Lower panel:} The halo mass-BH mass relation: The color coding shows the BH occupation fraction $p_{\rm occ}$ as a function of the halo mass $M_v$ and the BH mass $m_{\rm BH}$ for a scenario with $f_1 = f_2 = 0.5$, $w_1 = w_2 = 1$, $m_{{\rm cut},1} = 100\Msun$ and $m_{{\rm cut},2} = 10^5\Msun$.


\emph{Upper panel:} The low-mass cut on the massive BH population for different values of $m_{\rm cut}$, for $w=1$ (solid) and $w=2$ (dashed). \emph{Lower panel:} The halo mass-BH mass relation: The color coding shows the BH occupation fraction $p_{\rm occ}$ as a function of the halo mass $M_v$ and the BH mass $m_{\rm BH}$ for a scenario with $f_1 = f_2 = 0.5$, $w_1 = w_2 = 1$, $m_{{\rm cut},1} = 100\Msun$ and $m_{{\rm cut},2} = 10^5\Msun$.

\emph{Upper panel:} The low-mass cut on the massive BH population for different values of $m_{\rm cut}$, for $w=1$ (solid) and $w=2$ (dashed). \emph{Lower panel:} The halo mass-BH mass relation: The color coding shows the BH occupation fraction $p_{\rm occ}$ as a function of the halo mass $M_v$ and the BH mass $m_{\rm BH}$ for a scenario with $f_1 = f_2 = 0.5$, $w_1 = w_2 = 1$, $m_{{\rm cut},1} = 100\Msun$ and $m_{{\rm cut},2} = 10^5\Msun$.


\textit{Left panel:} The expected numbers of binaries detectable by AION-1km, AEDGE and LISA during a year of observation, as functions of $m_{\rm cut}$. The solid curves show all detectable binaries whereas the dotted curves show only those for which the last 1 minute of the merger is seen. \textit{Middle and right panels:} Explicit examples of the detectable binaries for a light-seed and a heavy-seed scenario. The sizes of the dots are $\propto \ln[ {\rm SNR}^{-1}]$ with the minimum size corresponding to ${\rm SNR}=10^4$ and the maximal to ${\rm SNR}=10$. The darker dots correspond to binaries for which the last 1 minute of the merger is seen.

\textit{Left panel:} The expected numbers of binaries detectable by AION-1km, AEDGE and LISA during a year of observation, as functions of $m_{\rm cut}$. The solid curves show all detectable binaries whereas the dotted curves show only those for which the last 1 minute of the merger is seen. \textit{Middle and right panels:} Explicit examples of the detectable binaries for a light-seed and a heavy-seed scenario. The sizes of the dots are $\propto \ln[ {\rm SNR}^{-1}]$ with the minimum size corresponding to ${\rm SNR}=10^4$ and the maximal to ${\rm SNR}=10$. The darker dots correspond to binaries for which the last 1 minute of the merger is seen.


Measurement accuracies for the binary parameters: The upper and lower panels correspond to two binaries whose component masses are fixed. In the left panels, the binary is observed for the last 1 year and the errors are shown as a function of its redshift. In the right panels, $z=1$ and the errors are shown as a function of the binary coalescence time at the beginning of a one-year observation. The errors for the masses of the both BHs are almost the same.

Measurement accuracies for the binary parameters: The upper and lower panels correspond to two binaries whose component masses are fixed. In the left panels, the binary is observed for the last 1 year and the errors are shown as a function of its redshift. In the right panels, $z=1$ and the errors are shown as a function of the binary coalescence time at the beginning of a one-year observation. The errors for the masses of the both BHs are almost the same.


\textit{Upper panel:} The 95\% CL accuracy with which LISA, AEDGE and AION-1km could measure $m_{\rm cut}$ over the range $[10^2, 10^6] \Msun$. \textit{Lower panel:} The 95\% CL accuracy with which LISA, AEDGE and AION-1km could measure the fraction of light seeds, $f_{\rm 1}$, assuming an input mixture of seeds with masses $10^2$ and $10^5 \Msun$ and $f_2 = 1 - f_1$. The solid and dashed curves in both panels correspond, respectively, to $w=1$ and $w=2$.

\textit{Upper panel:} The 95\% CL accuracy with which LISA, AEDGE and AION-1km could measure $m_{\rm cut}$ over the range $[10^2, 10^6] \Msun$. \textit{Lower panel:} The 95\% CL accuracy with which LISA, AEDGE and AION-1km could measure the fraction of light seeds, $f_{\rm 1}$, assuming an input mixture of seeds with masses $10^2$ and $10^5 \Msun$ and $f_2 = 1 - f_1$. The solid and dashed curves in both panels correspond, respectively, to $w=1$ and $w=2$.


The 1- and 2-dimensional posteriors of the merger rate parameters $\left(f_1, m_{{\rm cut},1}, m_{{\rm cut},2}\right)$ for a two-component seed model with $m_{{\rm cut},1}=10^2\,M_{\odot}$ $m_{{\rm cut},2}=10^5\, M_{\odot}$ and $f_1=0.5$ for AION-1km (top panel), AEDGE (middle panel) and LISA (bottom panel). The contours enclose the 68\%, 95\% and 99\% CL regions and the dashed vertical lines show the 68\% CL ranges in the marginalized posteriors.

The 1- and 2-dimensional posteriors of the merger rate parameters $\left(f_1, m_{{\rm cut},1}, m_{{\rm cut},2}\right)$ for a two-component seed model with $m_{{\rm cut},1}=10^2\,M_{\odot}$ $m_{{\rm cut},2}=10^5\, M_{\odot}$ and $f_1=0.5$ for AION-1km (top panel), AEDGE (middle panel) and LISA (bottom panel). The contours enclose the 68\%, 95\% and 99\% CL regions and the dashed vertical lines show the 68\% CL ranges in the marginalized posteriors.


The 1- and 2-dimensional posteriors of the merger rate parameters $\left(f_1, m_{{\rm cut},1}, m_{{\rm cut},2}\right)$ for a two-component seed model with $m_{{\rm cut},1}=10^2\,M_{\odot}$ $m_{{\rm cut},2}=10^5\, M_{\odot}$ and $f_1=0.5$ for AION-1km (top panel), AEDGE (middle panel) and LISA (bottom panel). The contours enclose the 68\%, 95\% and 99\% CL regions and the dashed vertical lines show the 68\% CL ranges in the marginalized posteriors.

The 1- and 2-dimensional posteriors of the merger rate parameters $\left(f_1, m_{{\rm cut},1}, m_{{\rm cut},2}\right)$ for a two-component seed model with $m_{{\rm cut},1}=10^2\,M_{\odot}$ $m_{{\rm cut},2}=10^5\, M_{\odot}$ and $f_1=0.5$ for AION-1km (top panel), AEDGE (middle panel) and LISA (bottom panel). The contours enclose the 68\%, 95\% and 99\% CL regions and the dashed vertical lines show the 68\% CL ranges in the marginalized posteriors.


The 1- and 2-dimensional posteriors of the merger rate parameters $\left(f_1, m_{{\rm cut},1}, m_{{\rm cut},2}\right)$ for a two-component seed model with $m_{{\rm cut},1}=10^2\,M_{\odot}$ $m_{{\rm cut},2}=10^5\, M_{\odot}$ and $f_1=0.5$ for AION-1km (top panel), AEDGE (middle panel) and LISA (bottom panel). The contours enclose the 68\%, 95\% and 99\% CL regions and the dashed vertical lines show the 68\% CL ranges in the marginalized posteriors.

The 1- and 2-dimensional posteriors of the merger rate parameters $\left(f_1, m_{{\rm cut},1}, m_{{\rm cut},2}\right)$ for a two-component seed model with $m_{{\rm cut},1}=10^2\,M_{\odot}$ $m_{{\rm cut},2}=10^5\, M_{\odot}$ and $f_1=0.5$ for AION-1km (top panel), AEDGE (middle panel) and LISA (bottom panel). The contours enclose the 68\%, 95\% and 99\% CL regions and the dashed vertical lines show the 68\% CL ranges in the marginalized posteriors.


References
  • [1] J. Kormendy and L. C. Ho, Ann. Rev. Astron. Astrophys. 51, 511 (2013), arXiv:1304.7762 [astro-ph.CO].
  • [2] R. A. Remillard and J. E. McClintock, Ann. Rev. Astron. Astrophys. 44, 49 (2006), arXiv:astro-ph/0606352.
  • [3] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. X 9, 031040 (2019), arXiv:1811.12907 [astro-ph.HE].
  • [4] R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. X 11, 021053 (2021), arXiv:2010.14527 [gr-qc].
  • [5] R. Abbott et al. (LIGO Scientific, Virgo and KAGRA Collaborations), (2021), arXiv:2111.03634 [astroph.HE].
  • [6] J. E. Greene, J. Strader, and L. C. Ho, Ann. Rev. Astron. Astrophys. 58, 257 (2020), arXiv:1911.09678 [astroph.GA].
  • [7] A. E. Reines, Nature Astron. 6, 26 (2022), arXiv:2201.10569 [astro-ph.GA].
  • [8] V. Bromm and A. Loeb, Astrophys. J. 596, 34 (2003), arXiv:astro-ph/0212400.
  • [9] S. F. Portegies Zwart, H. Baumgardt, P. Hut, J. Makino, and S. L. W. McMillan, Nature 428, 724 (2004), arXiv:astro-ph/0402622.
  • [10] M. Atakan Gurkan, M. Freitag, and F. A. Rasio, Astrophys. J. 604, 632 (2004), arXiv:astro-ph/0308449.
  • [11] P. Natarajan, Mon. Not. Roy. Astron. Soc. 501, 1413 (2021), arXiv:2009.09156 [astro-ph.GA].
  • [12] A. Sesana, F. Haardt, P. Madau, and M. Volonteri, Astrophys. J. 611, 623 (2004), arXiv:astro-ph/0401543.
  • [13] M. C. Begelman, M. Volonteri, and M. J. Rees, Mon. Not. Roy. Astron. Soc. 370, 289 (2006), arXiv:astroph/0602363.
  • [14] M. Volonteri, G. Lodato, and P. Natarajan, Mon. Not. Roy. Astron. Soc. 383, 1079 (2008), arXiv:0709.0529 [astro-ph].
  • [15] L. Mayer, S. Kazantzidis, P. Madau, M. Colpi, T. R. Quinn, and J. Wadsley, Science 316, 1874 (2007), arXiv:0706.1562 [astro-ph].
  • [16] T. L. Tanaka and M. Li, Mon. Not. Roy. Astron. Soc. 439, 1092 (2014), arXiv:1310.0859 [astro-ph.CO].
  • [17] K. Inayoshi, E. Visbal, and K. Kashiyama, Mon. Not. Roy. Astron. Soc. 453, 1692 (2015), arXiv:1504.00676 [astro-ph.GA].
  • [18] D. Izquierdo-Villalba, M. Colpi, M. Volonteri, D. Spinoso, S. Bonoli, and A. Sesana, Astron. Astrophys. 677, A123 (2023), arXiv:2305.16410 [astro-ph.GA].
  • [19] M. Volonteri, M. Habouzit, and M. Colpi, Nature Rev. Phys. 3, 732 (2021), arXiv:2110.10175 [astro-ph.GA].
  • [20] A. Sesana, J. Gair, E. Berti, and M. Volonteri, Phys. Rev. D 83, 044036 (2011), arXiv:1011.5893 [astroph.CO].
  • [21] T. Hartwig, M. Volonteri, V. Bromm, R. S. Klessen, E. Barausse, M. Magg, and A. Stacy, Mon. Not. Roy. Astron. Soc. 460, L74 (2016), arXiv:1603.05655 [astroph.GA].
  • [22] J. H. Krolik, M. Volonteri, Y. Dubois, and J. Devriendt, Astrophys. J. 879, 110 (2019), arXiv:1905.10450 [astroph.GA].
  • [23] A. Mangiagli, A. Klein, M. Bonetti, M. L. Katz, A. Sesana, M. Volonteri, M. Colpi, S. Marsat, and S. Babak, Phys. Rev. D 102, 084056 (2020), arXiv:2006.12513 [astro-ph.HE].
  • [24] M. Volonteri et al., Mon. Not. Roy. Astron. Soc. 498, 2219 (2020), arXiv:2005.04902 [astro-ph.GA].
  • [25] H. Haidar et al., Mon. Not. Roy. Astron. Soc. 514, 4912 (2022), arXiv:2201.09888 [astro-ph.GA].
  • [26] C. A. Dong-Páez, M. Volonteri, R. S. Beckmann, Y. Dubois, A. Mangiagli, M. Trebitsch, S. Vergani, and N. Webb, Astron. Astrophys. 676, A2 (2023), arXiv:2303.09569 [astro-ph.HE].
  • [27] G. Agazie et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L8 (2023), arXiv:2306.16213 [astro-ph.HE].
  • [28] J. Antoniadis et al. (EPTA Collaboration), (2023), 10.1051/0004-6361/202346841, arXiv:2306.16224 [astroph.HE].
  • [29] A. Zic et al. (Parkes Pulsar Timing Array Collaboration), (2023), arXiv:2306.16230 [astro-ph.HE].
  • [30] H. Xu et al., Res. Astron. Astrophys. 23, 075024 (2023), arXiv:2306.16216 [astro-ph.HE].
  • [31] G. Agazie et al. (NANOGrav Collaboration), Astrophys. J. Lett. 952, L37 (2023), arXiv:2306.16220 [astro-ph.HE].
  • [32] G. Agazie et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L50 (2023), arXiv:2306.16222 [astro-ph.HE].
  • [33] J. Antoniadis et al. (EPTA), (2023), arXiv:2306.16227 [astro-ph.CO].
  • [34] J. Ellis, M. Fairbairn, G. Hütsi, M. Raidal, J. Urrutia, V. Vaskonen, and H. Veermäe, Astron. Astrophys. 676, A38 (2023), arXiv:2301.13854 [astro-ph.CO].
  • [35] J. Ellis, M. Fairbairn, G. Hütsi, J. Raidal, J. Urrutia, V. Vaskonen, and H. Veermäe, (2023), arXiv:2306.17021 [astro-ph.CO].
  • [36] E. Treister, K. Schawinski, M. Volonteri, and P. Natarajan, Astrophys. J. 778, 130 (2013), arXiv:1310.2249 [astro-ph.CO].
  • [37] A. Ricarte and P. Natarajan, Mon. Not. Roy. Astron. Soc. 474, 1995 (2018), arXiv:1710.11532 [astro-ph.HE].
  • [38] A. Ricarte and P. Natarajan, Mon. Not. Roy. Astron. Soc. 481, 3278 (2018), arXiv:1809.01177 [astro-ph.GA].
  • [39] B. C. Kelly and Y. Shen, Astrophys. J. 764, 45 (2013), arXiv:1209.0477 [astro-ph.CO].
  • [40] B. P. Miller, E. Gallo, J. E. Greene, B. C. Kelly, T. Treu, J.-H. Woo, and V. Baldassare, Astrophys. J. 799, 98 (2015), arXiv:1403.4246 [astro-ph.GA].
  • [41] E. Gallo and A. Sesana, Astrophys. J. Lett. 883, L18 (2019), arXiv:1909.02585 [astro-ph.HE].
  • [42] U. Chadayammuri, A. Bogdan, A. Ricarte, and P. Natarajan, Astrophys. J. 946, 51 (2023), arXiv:2212.04693 [astro-ph.GA].
  • [43] P. Amaro-Seoane et al., arXiv e-prints , arXiv:1702.00786 (2017), arXiv:1702.00786 [astro-ph.IM].
  • [43] P. Amaro-Seoane et al., arXiv e-prints , arXiv:1702.00786 (2017), arXiv:1702.00786 [astro-ph.IM].
  • [44] L. Badurina et al., JCAP 05, 011 (2020), arXiv:1911.11755 [astro-ph.CO].
  • [45] L. Badurina, O. Buchmueller, J. Ellis, M. Lewicki, C. McCabe, and V. Vaskonen, Phil. Trans. A. Math. Phys. Eng. Sci. 380, 20210060 (2021), arXiv:2108.02468 [gr-qc].
  • [46] Y. A. El-Neaj et al. (AEDGE), EPJ Quant. Technol. 7, 6 (2020), arXiv:1908.00802 [gr-qc].
  • [47] V. F. Baldassare, C. Dickey, M. Geha, and A. E. Reines, The Astrophysical Journal 898, L3 (2020).
  • [48] F. Fontanot, P. Monaco, and F. Shankar, Monthly Notices of the Royal Astronomical Society 453, 4113–4121 (2015).
  • [49] W. H. Press and P. Schechter, Astrophys. J. 187, 425 (1974).
  • [50] J. R. Bond, S. Cole, G. Efstathiou, and N. Kaiser, Astrophys. J. 379, 440 (1991).
  • [51] C. G. Lacey and S. Cole, Mon. Not. Roy. Astron. Soc. 262, 627 (1993).
  • [52] G. Girelli, L. Pozzetti, M. Bolzonella, C. Giocoli, F. Marulli, and M. Baldi, Astron. Astrophys. 634, A135 (2020), arXiv:2001.02230 [astro-ph.CO].
  • [53] A. E. Reines and M. Volonteri, Astrophys. J. 813, 82 (2015), arXiv:1508.06274 [astro-ph.GA].
  • [54] A. Rasskazov, G. Fragione, and B. Kocsis, Astrophys. J. 899, 149 (2020), arXiv:1912.07681 [astro-ph.GA].
  • [55] G. Fragione, A. Loeb, B. Kocsis, and F. A. Rasio, Astrophys. J. 933, 170 (2022), arXiv:2204.03745 [astroph.HE].
  • [56] L. S. Finn and D. F. Chernoff, Phys. Rev. D 47, 2198 (1993), arXiv:gr-qc/9301003.
  • [57] D. Gerosa, S. Ma, K. W. K. Wong, E. Berti, R. O’Shaughnessy, Y. Chen, and K. Belczynski, Phys. Rev. D 99, 103004 (2019), arXiv:1902.00021 [astroph.HE].
  • [58] I. Mandel, W. M. Farr, and J. R. Gair, Mon. Not. Roy. Astron. Soc. 486, 1086 (2019), arXiv:1809.02063 [physics.data-an].
  • [59] G. Hütsi, M. Raidal, V. Vaskonen, and H. Veermäe, JCAP 03, 068 (2021), arXiv:2012.02786 [astro-ph.CO].
  • [60] E. Poisson and C. M. Will, Phys. Rev. D 52, 848 (1995), arXiv:gr-qc/9502040.
  • [61] P. Ajith et al., Phys. Rev. D 77, 104017 (2008), [Erratum: Phys.Rev.D 79, 129901 (2009)], arXiv:0710.2335 [gr-qc].
  • [61] P. Ajith et al., Phys. Rev. D 77, 104017 (2008), [Erratum: Phys.Rev.D 79, 129901 (2009)], arXiv:0710.2335 [gr-qc].
  • [62] J. M. Hogan et al., Gen. Rel. Grav. 43, 1953 (2011), arXiv:1009.2702 [physics.atom-ph].
  • [63] L. Badurina, V. Gibson, C. McCabe, and J. Mitchell, Phys. Rev. D 107, 055002 (2023), arXiv:2211.01854 [hepph].