Shadows of Giants: Constraints on Stupendously Large Black Holes from Negative Sources against the Cosmic Microwave Background

Abstract

Stupendously large astrophysical black holes (SLABs) are hypothetical black holes with masses of more than a trillion Suns. Because observable consequences of their existence have only recently been seriously considered, there have been relatively few constraints on their abundance. This work motivates a simple yet powerful constraint on SLABs: their huge shadows are visible against the cosmic microwave background. SLABs could thus appear as negative sources in microwave data. In fact, the shadow of a SLAB with a fixed mass becomes easier to detect with increasing redshifts past $1.6$. The limits are powerful enough to rule out SLABs of mass $\gtrsim 10^{17}\ M_{\odot}$ within the last scattering surface, and imply $Ω_{BH} \lesssim 10^{-5}$ for masses $10^{15}$--$10^{18}\ M_{\odot}$. I also discuss the effects of accretion and their implications for the limits: SLAB growth, positive accretion luminosity, and obscuring material.

Figures (5)

• Figure 1: The evolution of angular diameter distance with redshift in the Planck 2018 cosmology, showing how it falls past $z \sim 1.6$.
• Figure 2: The cumulative comoving volume with an angular diameter distance below a given value. The black line shows the low-redshift late volume, where the angular diameter distance is small simply because the object is nearby. At high redshift, there is an "early" volume where angular diameter distance decreases well below a Gpc, shown in blue, with the solid line showing the total early volume to the Big Bang and the dashed line only including the early volume out to the last scattering surface.
• Figure 3: Chart of whether the luminosity deficit of the shadow or the luminosity from accretion dominates the net bolometric flux from SLABs of various masses, redshifts, and radiative efficiencies in the B85 steady-state accretion model. Black holes above a line have a net flux dominated by the shadow; those below it would have a net bolometric flux dominated by the accretion luminosity. Black holes are assumed to grow as $M_{\rm BH}(z) \propto (1 + z)^{-1}$. There is a change in slope at later times as the baryonic accretion is no longer limited by the Eddington limit. Note the transition between shadow-dominated and accretion-dominated net flux will differ at individual frequencies.
• Figure 4: Limits on SLABs from black hole shadows alone (95% confidence upper limits), ignoring the possible luminosity and obscuration from baryonic accretion flows. These are in terms of comoving number density (left) and fraction of the cosmological critical density (right). The solid lines represent the limits including both the early and late volume for SLABs of constant mass. The dashed lines represent the limits when only including the late comoving volumes. The dotted lines show the limits for black holes growing as $M_{\rm BH} \propto (1 + z)^{-1}$. Three surveys are plotted: the Planck Catalog of Compact Sources 2 (orange), SPT-SZ (green), and SPT-3G (blue). Other basic limits are shown: in the upper shaded region the mass density of black holes exceeds that of all matter in the Universe; the lower grey lines show where $\le 1$ SLAB is expected in a cosmologically relevant volume. The PCCS2 constraints saturate slightly above these incredulity limits only because the 95% confidence upper limits are compatible with up to $\bar{N} = 3$ SLABs existing on average within the volume.
• Figure 5: How the shadow limits on SLABs evolve if only the volume within a particular redshift is included. The solid grey line is the incredulity limit for the comoving volume out to that redshift. The colors and other line styles are the same as their counterparts in Figure \ref{['fig:SLABLimits']}.