Heavy black hole seed survivors in dwarf galaxies: a case study of Leo I

Abstract

The supermassive black holes (SMBHs) with mass $M_\bullet > 10^9 \, \rm M_\odot$ hosted by high-redshift galaxies have challenged our understanding of black hole formation and growth, as several pathways have emerged attempting to explain their existence. The "heavy-seed" pathway eases the problem with the progenitors of these SMBHs having birth masses up to ${\sim} 10^5~{\rm M_\odot}$. Here, we investigate the possibility that a local dwarf galaxy, Leo I, harbors a heavy-seed descendant. Using Monte-Carlo merger trees to generate the merger histories of 1,000 dark matter halos similar to the Milky Way (MW; with a mass of ${\sim} 10^{12}~{\rm M_\odot}$ at redshift $z{=}0$). We search for Leo-like satellite halos among these merger trees, and investigate the probability that the progenitors of some of these satellites formed a heavy seed. We derive the likelihood of such "heavy seed survivors" (HSSs) across various formation and survival criteria as well as Leo-similarity criteria. We find that the virial temperature for the onset of atomic cooling and rapid gas infall that yields heavy seeds, $T_{\rm act}$, has the largest impact on the number of HSSs. We find HSSs in a fraction $0.7\%$, $18.1\%$, and $96.5\%$ of MW-like halos when $T_{\rm act}$ is set to $9,000$K, $7,000$K, and $5,000$K respectively. This suggests that Leo I could be hosting a heavy seed and could provide an opportunity to disentangle heavy seeds from other SMBH formation mechanisms.

Figures (4)

• Figure 1: We show $\log_{10}(N_{\rm HSS}/N_{\rm trees})$, the frequency of occurence of heavy-seed survivors (HSSs), or a Leo-like satellite halo hosting a DCBH descendant, as a function of the criteria that determine HSS candidacy. This criterion includes the minimum halo mass ratio that determines what constitutes a 'major' merger, $q$, the virial temperature for the onset of atomic cooling, $T_{\rm act}$, and the minimum allowed cooling time ratio to avoid star-formation, $\tau_{\rm cool} = t_{\rm cool}/t_{\rm Hubble}$. An HSS is formed if a Leo-like halo hosts a DCBH (requiring the progenitors of a subhalo at $T_{\rm vir}{=}T_{\rm act}$ to avoid any prior star formation, and that after forming the DCBH, the subhalo experiences one to three 'major' mergers with mass ratio above $q$. Each panel explores two parameters at a time, with the left column showing the value of $\log_{10}(N_{\rm HSS}/N_{\rm trees})$ selected to be the maximum for any value of the third parameter, and the right column showing the median across this third parameter. Lines denote $1\%$, $10\%$, $100\%$, and $300\%$ rates for HSS frequency in our trees. White spaces indicate that no HSS was found among our $N_{\rm trees} = 1,000$ merger trees, so the probability of an HSS existing for a given parameter combination is less than $10^{-3}$. In some cases, there can be three or more HSSs per tree. The HSS frequency has a soft dependence on $\tau_{\rm cool}$, as our halos experience large values of $J_{\rm LW}$ with $\tau_{\rm cool}$ typically greater than 1, so increasing $\tau_{\rm cool}$ does not significantly decrease the number of HSSs. There is a non-linear dependence on $q$, where a large value of $q$ can result in too few major mergers, violating the Leo-like criteria, and a small value of $q$ results in too many mergers. The results have the strongest dependence on $T_{\rm act}$, as decreasing this value increases HSS rates significantly.
• Figure 2: The distribution of the number of HSSs in our 1,000 merger trees. The three cases represent varying degrees of strictness in our three parameters, $q$, $T_{\rm act}$, and $\tau_{\rm cool}$, with the values of these parameters listed in Table \ref{['table1']}. In the least strict case (green), $96.5\%$ of our trees hold at least one HSS, though it is much more common for the trees to have several HSSs. One tree holds as many as 10 HSSs. For the medium case (orange), $18.1\%$ of our trees hold an HSS, with two being the upper limit of HSS per tree. In the strictest case (blue), only $0.7\%$ of our trees have HSSs. This stricter case is the most physically realistic, though future work will be needed to put tighter constraints on the most appropriate $T_{\rm act}$ for rapid gas collapse in atomic-cooling halos.
• Figure 3: We show the HSS frequency as a function of $T_{\rm act}$, the most influential parameter for HSS candidacy. For every tree, we take the median value (dashed) across $q$ and $\tau_{\rm cool}$ for each target $T_{\rm act}$, then average these results across the 1,000 merger trees. We also show the maximum number of HSSs (solid) and the standard deviation (red) across the 1,000 trees. For low values of $T_{\rm act}$, trees typically host three HSS, up to a maximum of 10. This frequency declines rapidly with increasing $T_{\rm act}$, and there are no HSSs for $T_{\rm act} > 9,000$ Kelvin. The plateau in the maximum number of HSSs signals that from $T_{\rm act} {\sim} 7,000$K up to $T_{\rm act} {\sim} 9,000$K, there is no more than one HSS in the median value across $q$ and $\tau_{\rm cool}$.
• Figure 4: Left: The evolution of the masses of black holes born as heavy seeds in our models. We show the median black hole mass (black), a few randomly sampled branches of the merger tree of a Milky-Way-like halo (gray) and the black hole mass standard deviation vs. redshift (red). The median black hole mass near redshift $z{=}0$ is $M_\bullet{\sim}4{\times} 10^6 {\rm M}_\odot$, comparable to the estimate by Bustamante_2021. The earliest heavy-seed survivors (HSSs) at high redshift have an initial mass of $M_\bullet{\sim} 10^4~{\rm M}_\odot$. Right: The black hole vs. stellar mass for our HSSs. The HSSs are initially overmassive, with $M_\bullet/M_* {\sim} 10$, and terminate with $M_\bullet/M_* {\sim} 1$.