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How open is the asteroid-mass primordial black hole window?
by Matthew Gorton, Anne M. Green
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Matthew Gorton · Anne Green |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2403.03839v1 (pdf) |
| Date submitted: | 2024-03-11 15:57 |
| Submitted by: | Green, Anne |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Primordial black holes (PBHs) can make up all of the dark matter (DM) if their mass, $m$, is in the so-called 'asteroid-mass window', $10^{17} \, {\rm g} \lesssim m \lesssim 10^{22} \, {\rm g}$. Observational constraints on the abundance of PBHs are usually calculated assuming they all have the same mass, however this is unlikely to be a good approximation. PBHs formed from the collapse of large density perturbations during radiation domination are expected to have an extended mass function (MF), due to the effects of critical collapse. The PBH MF is often assumed to be lognormal, however it has recently been shown that other functions are a better fit to numerically calculated MFs. We recalculate both current and potential future constraints for these improved fitting functions. We find that for current constraints the asteroid-mass window narrows, but remains open (i.e. all of the DM can be in the form of PBHs) unless the PBH MF is wider than expected. Future evaporation and microlensing constraints may together exclude all of the DM being in PBHs, depending on the width of the PBH MF and also the shape of its low and high mass tails.
Current status:
Reports on this Submission
Report
In this paper, I recognize the value in discussing the deviation of the PBH mass function from log-normal, and in putting limits on the time variation to be taken into account shown in Ref.[40] Mosbech and Picker
Before accepting, I give some non-negligible remarks concerning the pioneering works.
1) The discussion of time variation given in arXiv:2307.06467 should also be mentioned in the text, as should Ref.[40] Mesbeck and Picker.
2) In the section discussing the limit from MeV gamma-rays, I encourage the authors to also mention to Ref.[38], which was the first conservative limit on PBHs by the diffuse MeV-gamma-ray background reported by COMPTEL. This was followed by Ref.[23] Korwar and Profumo and others, who additionally obtained the bound by the galactic gamma-ray limits based on their stronger assumptions although it is debatable whether the more stringent limits obtained based on stronger assumptions, as in Ref.[23], make sense. However, it should be discussed more fairly without omitting the independent bound obtaiened by the diffuse MeV gamma-ray background.
Recommendation
Ask for minor revision
Report
This paper updates constraints on primordial black holes (PBHs) in the asteroidal mass range for an extended mass function. This is timely since many researchers argue that such PBHs could provide the dark matter. The constraints are usually presented for a lognormal mass function but more recent studies (in particular, by Gow et al.) have replaced this with a skewed lognormal mass function. As far as I’m aware, this is the first paper to calculate the corresponding modifications for the constraints.
I’m happy to recommend the paper for publication. The authors have done a careful job and they’ve been very thorough in referring to previous work on constraints with an extended mass function. The key results are in Figures 2 & 3, which are very useful. One minor point: the paper is somewhat overladen with acronyms and, while they are all defined, one has to constantly go back to find what they mean. I've have some more detailed comments, which might prompt minor changes.
Requested changes
P2. Some researchers would disagree with the claim that solar-mass PBHs are excluded, so they might wish to modify this remark. This is not crucial to the main point of the paper but citing papers with contrary views might be more balanced.
P5. Perhaps the relationship between Refs. 16 and 35 could be clarified. For example, do eqns (7) and (8) both come from Ref. 16? The latter focusses on stellar-mass PBHs but Ref. 35 is earlier and explicitly refers to constraints.
P6. I think that tau in eqn (10) should have a subscript i to indicate that it’s the lifetime for the PBHs of mass mi.
P7. Although attributed to 2022 papers, the m^3 tail effect goes back to the earliest work on PBH evaporation and is crucial (for example) to the analysis of Ref. [39].
Recommendation
Publish (meets expectations and criteria for this Journal)
Author: Anne Green on 2024-06-27 [id 4588]
(in reply to Report 1 on 2024-05-07)
We are grateful to the referee for their careful reading of the manuscript and helpful comments.
We now write out lognormal, skew-lognormal, critical collapse and generalised critical collapse in full throughout.
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There are modelling uncertainties in the constraints, however we are not aware of any paper that shows that Solar mass PBHs could make up all of the dark matter when all existing constraints are taken into account. In particular, long-duration microlensing surveys (Blaineau et al. (2022) https://inspirehep.net/literature/2040092 and Mroz et al. (2024) https://inspirehep.net/literature/2764863) now place tight constraints on the abundance of compact objects with masses up to 1000 Solar masses. Uncertainties in the distribution of dark matter do not change the excluded mass range by orders of magnitude (see e.g. Alcock et al. (1996) https://ui.adsabs.harvard.edu/abs/1996ApJ...461...84A/abstract, and various subsequent papers). If PBHs formed very compact clusters, so that the cluster as a whole rather than individual PBHs acts as a lens, then the microlensing constraints would be significantly weakened (as in Calcino, Garcia-Bellido and Davis (2018) https://inspirehep.net/literature/1664442). However in this case, as shown in de Luca et al. (2022) (https://inspirehep.net/literature/2131836), other constraints would be tightened such that Solar mass PBHs making up all of the dark matter remains excluded. We have addressed this comment by adding “Under standard assumptions” to the 4th sentence of the introduction, which previously started “PBHs can only account. . . ”
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Ref. 35 calculates mass functions numerically, and the results described in the first two sentences of the paragraph starting “Gow et al. [16, 35]” were found in both papers. The subsequent more detailed results (starting from the sentence “As Delta is increased. . . . . . . skewed towards low masses [16]”) are just from Ref. 16. To make this clearer, in the subsequent sentence we have re- placed “Of the fitting functions they consider” with “Of the fitting functions considered in Ref. [16]”.
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We have added a subscript ‘i’ to the lifetime tau as suggested.
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We have added citations to Ref. 38 (now Ref. 28) and also Page and Hawking (1976) for the m3 factor in the relationship between the initial and present-day mass functions.
Author: Anne Green on 2024-06-27 [id 4589]
(in reply to Report 2 on 2024-06-17)We are grateful to the referee for their helpful comments.
We’ve added a citation to arXiv:2307.06467.
As we tried to explain in the original version of the manuscript (text starting “There are various evaporation constraints, from different particle species and observations, calculated using different assumptions, with different uncertainties...”) we consider two illustrative constraints and aren’t making any statements regarding which constraints are best/most reliable. To address this comment we’ve reworded the aforementioned text and added a citation to Ref. [38] (which is now Ref. [28]) to this paragraph. We’ve also removed “the” from “We calculate the constraints” in the opening sentence of the final paragraph of Sec. 1 and also from “we have explored how the constraints” in the fourth sentence of the first paragraph of Sec. 4.