REVIEW
Limits on Black Hole Formation from Cosmic String Loops
Astrophysics · Submitted 14 Jul 1997 · 51 references
Pith's verdict: A real correction and a genuinely new Gμ bound, but the abstract's 'remarkable agreement' is partly an artifact of a steep exponent rather than a deep coincidence.
T0 · AI review
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Referee report
The paper
The paper claims
Cosmic string loops that collapse into black holes give a gamma-ray bound on string tension that nearly coincides with the bound from the cosmic microwave background.
The reading
What carries the argument
The load-bearing object is the $M^{-2.5}$ black hole mass spectrum. It is not assumed; it follows from the scaling solution of the string network, in which the loop formation rate per comoving volume goes as $t^{-4}$ and each loop's mass is proportional to its formation time. Because this is precisely the spectral index used to convert a gamma-ray flux measurement into a limit on $Omega_{PBH}$, the string prediction and the observational bound can be matched directly rather than through a model of the emission spectrum. The second piece of machinery is the inversion: the collapse fraction $f(Gmu)$ from loop-fragmentation simulations turns the limit on $f$ into a limit on $Gmu$.
Extended reading notes
Core claim
The paper's central claim is that the extragalactic gamma-ray background, read as a bound on the present-day density of evaporating black holes, independently constrains the cosmic string tension to $Gmu/c^2 lesssim 2.1 (pm 0.7) times 10^{-6}$. The chain runs as follows. Scaling of the string network fixes the rate at which loops form and hence the rate at which black holes form, $dn_{BH}/dt propto t^{-4}$, which redshifts into a present-day mass spectrum $dn_{BH}/dM propto M^{-2.5}$ for black holes heavier than the mass expiring today, $M_* approx 4.4 times 10^{14} h^{-0.3}$ g. That is exactly the spectral shape for which the gamma-ray limit on the black hole density, $Omega_{PBH} lesssim (5.1 pm 1.3) times 10^{-9} h^{-1.95 pm 0.15}$ from the EGRET measurement, was derived. Integrating the string-predicted spectrum against that bound yields an upper limit on the loop collapse fraction $f$ around $10^{-20}$ to $10^{-19}$ for $Gmu/c^2 approx 1.7 times 10^{-6}$, roughly an order of magnitude stronger than the earlier Caldwell-Gates estimate, which the authors attribute to a misapplication of the gamma-ray limit in that work. Inserting the numerically simulated collapse efficiency $f = 10^{4.9 pm 0.2}(Gmu/c^2)^{4.1 pm 0.1}$ and inverting gives the quoted tension bound. The authors also report a comparable bound from the antiproton flux, $Gmu/c^2 lesssim 1.8 (pm 0.5) times 10^{-6}$, and show that stable Planck-scale relics left behind by evaporating holes can only contribute appreciably to dark matter if the relic mass exceeds roughly $10^3 m_{pl}$.
Load-bearing premise
The whole tension bound rests on a power-law fit to the fraction of loops that collapse into black holes, measured in simulations at string tensions between $10^{-3}$ and $3 times 10^{-2}$ and then extrapolated three to four orders of magnitude down to $10^{-6}$ without a direct check.
Editorial extensions
If this is right
- If the gamma-ray bound is taken at face value, the fraction of cosmic string loops that collapse into black holes at $Gmu/c^2 approx 1.7 times 10^{-6}$ cannot exceed roughly $2 times 10^{-18}$.
- Black hole emission from collapsing loops could plausibly supply a significant part of the observed extragalactic gamma-ray background and of the Galactic antiproton, electron and positron fluxes near 100 MeV.
- A future order-of-magnitude improvement in antiproton sensitivity would push the tension bound to about $1.2 times 10^{-6}$, which would sit uncomfortably close to the value strings need for structure formation.
- Stable black hole remnants can only be a significant dark matter component in the string scenario if their residual mass is above about $10^3$ Planck masses.
Reading between the lines
- The near-coincidence of the gamma-ray and microwave-background numbers is only meaningful if the loop collapse efficiency really follows the simulated power law at $10^{-6}$; a direct simulation at that scale would convert an apparent coincidence into a genuine cross-check.
- Because the gamma-ray bound scales as a high power of $Gmu$, the same argument applies, with weaker force, to strings formed at symmetry-breaking scales far below the structure-formation scale, where microwave-background normalization says nothing.
- If black holes from loops do contribute at the level the authors suggest, the diffuse gamma-ray spectrum between 50 and 200 MeV should show a mild excess with the predicted turnover; a spectral search in existing data would test the scenario without any new string physics.
- The remnant bound is essentially a statement about how much mass survives evaporation, so an independent laboratory or astrophysical constraint on the final state of an evaporating black hole would feed straight back into limits on loop collapse.
Original abstract
In theories with cosmic strings, a small fraction of string loops may collapse to form black holes. In this Letter, various constraints on such models involving black holes are considered. Hawking radiation from black holes, gamma and cosmic ray flux limits and constraints from the possible formation of stable black hole remnants are reanalyzed. The constraints which emerge from these considerations are remarkably close to those derived from the normalization of the cosmic string model to the cosmic microwave background anisotropies.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
In theories with cosmic strings, a small fraction of string loops may collapse to form black holes. In this Letter, various constraints on such models involving black holes are considered. Hawking radiation from black holes, gamma and cosmic ray flux limits and constraints from the possible formation of stable black hole remnants are reanalyzed. The constraints which emerge from these considerations are remarkably close to those derived from the normalization of the cosmic string model to the cosmic microwave background anisotropies.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In theories with cosmic strings, a small fraction of string loops may collapse to form black holes. | background 1.00 | 0.06 | 0.05 | hedged possibility 1.00 |
| s1 | In this Letter, various constraints on such models involving black holes are considered. | contribution 0.98 | 0.70 | 0.04 | asserted 0.66 |
| s2 | Hawking radiation from black holes, gamma and cosmic ray flux limits and constraints from the possible formation of stable black hole remnants are reanalyzed. | method 0.54 | 0.79 | 0.06 | asserted 0.90 |
| s3 | The constraints which emerge from these considerations are remarkably close to those derived from the normalization of the cosmic string model to the cosmic microwave background anisotropies. | result 0.87 | 0.78 | 0.73 | asserted 1.00 |
What was examined, and what was not
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References
How the literature uses it
37 arXiv papers cite this in 55 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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The new constraints are remarkably close to those derived from the normalization of the cosmic string model to the cosmic microwave background anisotropies.
Astrophysical Constraints on Primordial Black Hole Formation from Collapsing Cosmic Strings · 1.00
Papers citing it · 19 sentences without a confident label
Uses its method or tool 1 paper
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Here we adopt the calculations in Refs. [ref] to derive the PBH mass function from cosmic string collapse.
Pinning down the primordial black hole formation mechanism with gamma-rays and gravitational waves · PBHs from cosmic strings · 0.94
Compares with it 2 papers
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Secondly we found a loop (and hence PBH) formation rate which is smaller than in Refs. [ref] by a factor of $0.075$.
Constraints on the cosmic string loop collapse fraction from Primordial Black Holes · Summary · 0.96
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In fact, Eq. [ref] has the same power law as the mass spectrum resulting from the collapse of circular loops [ref] , but with a different pre-factor.
Primordial black holes from cusp collapse on cosmic strings · The PBH mass spectrum · 1.00
Cites it as background 27 papers
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However, we are interested in macroscopically-large loops, which lie well above this dispersion regime for any value of $Gμ$ consistent with observational constraints.] and PBH formation from circular loop collapse has remained an active research topic ever since [ref] .
Primordial black holes from cusp collapse on cosmic strings · Introduction · 0.83
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They can be formed due to the collapse of large density fluctuations produced during inflation [ref] , the cosmological phase transitions [ref] , and the collapse of topological defects [ref] and false vacuum bubbles [ref] , etc.
Supermassive black holes triggered by QCD axion bubbles · Introduction · 0.88
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A cosmological scenario that produces an order one density contrast in the early universe, including models with specific inflaton potentials [ref] , first order phase transitions [ref] , the dynamics of scalar condensates [ref] , or the collapse of topological defects [ref] , provides a means to produce PBH from the gravitational collapse of the perturbation.
Correlating Gravitational Wave and Gamma-ray Signals from Primordial Black Holes · Introduction · 0.80
Discussion
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