Primordial Black Holes Give Rise To Mu-Distortion Which Can Be Detected By Future Observations (Cosmology)

If you are a daily reader, you may have came across several articles on our website based on the formation of primordial black holes (PBHs). But, the most popular and natural scenario is, production of PBHs by the collapse of the clumps. In this scenario, PBHs production takes place by the collapse of large overdense clump which is surrounded by an underdense region. After the black hole is formed, the underdense region expands as a shell (shown as a ring in fig 1 below). The shell consists of an underdense and an overdense layer, which is a typical feature of a spherical sound wave packet. As the shell passes by, the fluid density between the black hole and the shell goes back to FRW. Dissipation of the shell due to photon diffusion during the so-called µ-era can release energy into the background, generating µ-distortion in the background photons, and may be seen in Cosmic Microwave Background (CMB).

FIG. 1: Illustrations of the formation of sound shell around a PBH. © Heling Deng

Now, Heling Deng carried out study on the possible μ-distortion in the CMB spectrum around supermassive primordial black holes (PBHs) and how future observations might impose constraints on the PBH density within the mass range 106–1015 M.

He showed that, if there are more than one PBH with M ≳ 106 M within a Silk region, which is of an angular scale of 0.2°, we can have an average distortion µ’ in CMB. The possible non-observation of average distortion in future missions beyond the ΛCDM model (which predicts µ’ ∼ 10¯8) would then place constraints on these black holes. He also suggested that, a bound of particular interest would be f < 10¯3 for 1010M ≲ M ≲ 1012 M.

“Although, such supermassive PBHs are rare in our universe, it is possible that we can see point like distortions with magnitude µM ≳ 10¯7 on some Silk patches in CMB, as long as the black holes have initial mass M ≳ 1012 M.”

Considering that the resolution of future missions could reach δθ ∼ 1°, such a signal in a pixel would be µ1° ≳ 10¯8. The non-observation would imply that these stupendously large PBHs can only constitute a tiny part of the dark matter, with a fraction f < 10¯9 for M ∼ 1012M.

FIG. 2: Constraints on the fraction of dark matter in monochromatic PBHs within the mass range
102– 1015M . The gray regions have been ruled out by current observations. Colored curves are possible upper bounds for fPBH if future observations find certain upper bounds for the average µ-distortion in CMB: µ’ ≲ 10¯5 (blue), µ’ ≲ 10¯6 (orange), µ’ ≲ 10¯7 (green) and µ’ ≲ 10¯8 (red). The purple line is imposed by condition that there should at least be one black holes within the smallest patch future missions can measure. The cyan line is a possible bound if future observations find µ ≲ 10¯8 at an angular scale ∼ 1°. © Heling Deng

If future observations do not see µ-distortion with µ ≳ 10¯8, the shaded regions in the figure 2 (given above), including that with (brown) tilted lines and that with (cyan) dots, should all be excluded. An exciting possibility is that we do see local distortions in CMB, which would be a hint of the existence of stupendously large PBHs, and we will be able to estimate their population.

Finally, although he focused totally on the µ-distortion generated by the Silk damping of the sound shell, he mentioned that the shell itself can be a source of temperature perturbations in CMB. At the time of recombination (t ∼ 1013 s), the shell’s radius (∼ sound horizon) is of an angular size ∼ 1° on the CMB sky, and its thickness is the Silk damping scale ∼ 0.2° (S ∼ Λ), which is comparable to the thickness of the last scattering surface. Therefore, the underdensity and overdensity on the shell (fig. 3) can induce a ring-like feature in CMB and this ring’s radius depends on the black hole’s position relative to the last scattering surface. They estimated the temperature perturbation and found that, PBHs with larger initial masses should be rare on the last scattering surface.

FIG. 3: Sketch of the radiation fluid’s density profile along the radius near the shell at two moments t and t+ ∆t. The shell consists of an underdense and an overdense layer, which is a typical feature of a spherical sound wave packet. The shell’s physical radius is ∼ 2cst, and its thickness increases from S(t) to S(t + ∆t) due to cosmic expansion and the viscosity in fluid. The time it takes for the shell to completely pass through a sphere at the wave front is ∆t ∼ S(t)/cs. During this time, the shell’s wave energy gets dissipated, and the resulting heat is dumped behind the shell (shown as a red line). © Heling Deng

Reference: Heling Deng, “µ-distortion around stupendously large primordial black holes”, Arxiv, pp. 1-21, 2021.

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