Primordial black hole formation in matter domination

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "Primordial black hole formation in matter domination".

Jocelyn: This scientific paper investigates the formation threshold and properties of Primordial Black Holes (PBHs) during an early period of Matter Domination,

Vera: First, who's behind it and why it matters.

Title and authors: Vera: So, let's talk about the title and who wrote this paper. "Primordial black hole formation in matter domination" tells us exactly what the focus is: PBHs collapsing specifically during a matter-dominated epoch. The authors are Ebrahimiana, Abolhasanib, and Mirbabayia from the Abdus Salam ICTP and Sharif University of Technology.

Jocelyn: It’s interesting that they're focusing on the matter domination phase because that’s where certain collapse dynamics might behave differently than during inflation or radiation domination, Vera. What do you think about the title itself?

Subrahmanyan: The authors are clearly grounding their theoretical work in a specific cosmological context, which is necessary when you want to connect abstract fluctuation physics to observable outcomes like PBH abundance.

Vera: Exactly. It sets the stage for understanding how the shape of those initial density fluctuations dictates whether we end up with a black hole or something else entirely, which is what this paper is really investigating.

Jocelyn: I wonder if the title implies that they are challenging older assumptions about when these black holes could have formed compared to other epochs.

Subrahmanyan: That’s precisely the implication. The paper suggests that for a cosmologically relevant abundance of PBHs, the effective formation threshold is larger than some previous models suggested in a dust-dominated universe.

Vera: So, essentially, they are refining our understanding of the conditions needed for these black holes to appear during that specific matter-dominated era.

Jocelyn: It sounds like the authors are setting up a comparison between what we see in the CMB and what might be happening at smaller scales during this early epoch.

The paper's summary: Vera: Now, let's get into the actual summary of "Primordial black hole formation in matter domination." The core finding here is that the collapse threshold isn't fixed; it strongly depends on the shape of those initial peaks, and this dependence actually makes them rarer as those peaks become flatter.

Jocelyn: That’s a key point, Vera. So, if you have a slightly flatter fluctuation, it becomes harder for it to collapse into a black hole compared to a very sharp peak. What does that mean for the overall population?

Subrahmanyan: It means that the statistical distribution of peaks plays a huge role; because typical cosmic overdensities aren't perfect top-hats, we have to account for this shape dependence when calculating how many PBHs form.

Vera: And the paper points out that in the extreme case of a top-hat perturbation, Harada et al. argued that velocity dispersion prevents collapse unless the initial peak is larger than a threshold of zeta th ∼ zeta two/five rms.

Jocelyn: But then they immediately narrow that down by including the shape distribution, finding a more realistic effective threshold of zeta th ∼ zeta one/ten rms. That's a significant refinement.

Subrahmanyan: That smaller threshold means that for most peaks to collapse, we need an initial fluctuation level of zeta rms ∼ ten-one which the authors note is much larger than what we observe at the CMB scales.

Vera: So, the implication is that PBH formation during Matter Domination is barely more efficient than what we expect from Radiation Domination. It’s a subtle point about timing and efficiency.

Jocelyn: That suggests that if we are searching for PBHs in the early universe, this paper puts a constraint on how much they could have formed during this specific era compared to other scenarios.

The paper's improvements: Vera: Moving on to the improvements suggested by the authors of "Primordial black hole formation in matter domination," they focus heavily on how typical overdensities, which aren't top-hats, interact with that lower collapse threshold. They find that for a given cosmic abundance, we need zeta rms ∼ zero point one for most PBHs to form from peaks with significantly small second derivatives.

Subrahmanyan: The paper establishes the effective threshold as zeta th ∼ zeta one/ten rms, or log beta ∼ −zeta-one point eight rms, which is a direct consequence of accounting for these typical higher-order derivatives.

Jocelyn: The paper makes a distinction between the dust and w → zero limits, saying that black hole formation in the dust scenario is very sensitive to the profile shape, while in a fluid with constant w, most spherically symmetric peaks collapse into black holes when w → zero.

Vera: That distinction is important because it highlights that velocity dispersion and profile flatness are the deciding factors in the dust scenario, whereas they are more robust in a constant-w fluid model.

Subrahmanyan: The authors also show that numerical N-body simulations confirm this halting mechanism, demonstrating that for a typical profile with A2 = O(one), the threshold for black hole formation is around delta m = O(one).

Jocelyn: It’s interesting how they use these simulations to back up the analytical findings about shell-crossing and velocity dispersion preventing small perturbations from collapsing into black holes.

Conclusion: Vera: So, to wrap up this discussion on "Primordial black hole formation in matter domination," the paper suggests that despite the dynamics of matter domination, PBH formation is constrained by a relatively high effective threshold compared to what some earlier analytical results suggested.

Jocelyn: The main implication for us as observers is that unless we find evidence for these specific fluctuation scales, the abundance of PBHs formed in this era might be much lower than initially estimated.

Subrahmanyan: Theoretically, the finding about spin parameter estimation is also significant; they conclude that the dimensionless spin is typically small when zeta rms is less than one because velocity dispersion plays a more dominant role in preventing collapse than angular momentum.

Vera: That ties it all together: the shape of the peak and velocity dispersion are the primary suppressors for these black holes during this matter-dominated era, which informs our search strategies for gravitational wave signals or other signatures.

Jocelyn: It’s a lot of detail about how initial conditions translate into final black hole properties, and it gives us clearer boundaries for where these objects could have originated.

Subrahmanyan: This paper provides a detailed framework connecting the statistical properties of primordial fluctuations to the physical outcome of collapse during matter domination, which is essential groundwork for future theoretical modeling.