MACHO Project Limits on Black Hole Dark Matter in the 1-30 Solar Mass Range

A.B.Tomaney; A.C.Becker; A.J.Drake; B.A.Peterson; C.A.Nelson; C.W.Stubbs; D.L.Welch; D.Minniti; D.P.Bennett; D.R.Alves

REVIEW

MACHO Project Limits on Black Hole Dark Matter in the 1-30 Solar Mass Range

The Macho collaboration: C.Alcock, R.A.Allsman, D.R.Alves, T.S.Axelrod, A.C.Becker, D.P.Bennett, K.H.Cook, N.Dalal

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A.J.Drake, M.Geha, K.Griest, M.J.Lehner, S.L.Marshall, D.Minniti, C.A.Nelson, B.A.Peterson, P.Popowski, M.R.Pratt, P.J.Quinn, C.W.Stubbs, W.Sutherland, A.B.Tomaney, T.Vandehei, D.L.Welch

Astrophysics · Submitted 28 Nov 2000 · 12 references

Pith's verdict: A clean null-result extension of the MACHO exclusion to 30 solar masses, with the 30 M_sun endpoint the softest number in it — and the paper half-says so.

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arXiv IDastro-ph/0011506 (version 1)

Pith IDH3SABYGU, Pith's permanent record of this paper and its review

CitationA.B.Tomaney, A.C.Becker, A.J.Drake, B.A.Peterson, C.A.Nelson, C.W.Stubbs, D.L.Welch, D.Minniti, D.P.Bennett, D.R.Alves, K.Griest, K.H.Cook, M.Geha, M.J.Lehner, M.R.Pratt, N.Dalal, P.J.Quinn, P.Popowski, R.A.Allsman, S.L.Marshall, The Macho collaboration: C.Alcock, T.S.Axelrod, T.Vandehei, W.Sutherland. "MACHO Project Limits on Black Hole Dark Matter in the 1-30 Solar Mass Range." arXiv:astro-ph/0011506 (2000). https://pith.science/paper/H3SABYGU

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Editor's note

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What's new here is narrow but real: the collaboration takes its published 5.7-year LMC dataset, adds a t_hat > 150 day cut to the set A selection, finds zero long-duration events, and converts that into a 95% c.l. exclusion of 0.3–30 M_sun objects as 100% of a model-S halo. The model-independent form — under 4e11 M_sun in compact objects below 30 M_sun — is the honest way to state it, and they state it. The event 22 exclusion is done properly: spectroscopy, extended source, emission lines, z=0.23. That could have been hand-waved and wasn't. The Poisson argument is standard and correctly applied, and the halo model is taken from prior published work rather than tuned here. No circularity worth worrying about; the efficiency is self-calibrated from the same photometry, which is legitimate for a null search. The soft spot the stress-test points at is real but bounded. Eq. 1 gives ~710 days for a 30 M_sun lens, while §4 says the selection includes a t_hat < 600 day cut against slow variables. So the 30 M_sun endpoint is built from the part of the Fig. 1 efficiency curve where the background is worst and the signal is most attenuated, and the paper doesn't report what fraction of the 30 M_sun duration distribution survives the 600-day cut. The endpoint can't be checked from the text. But the authors already concede in §4 that sensitivity above 30 M_sun is poor and that the 8-year dataset is needed to push higher; the stress-test's mechanism is the same one they name, applied at the boundary rather than beyond it. The 0.3–10 M_sun core and the 4e11 M_sun limit don't depend on it. Two smaller things. The efficiency pipeline is described only by reference to A2000b (submitted) and Vandehei's thesis; since the machinery is the published A2000a analysis with one extra cut, that's acceptable for a letter, but a reader who wants to check the long-duration tail has to go hunting. And 'many sets of selection criteria were explored' is asserted as robust without a table; minor, but a one-line table would have closed it. Who it's for: anyone working on compact halo dark matter or microlensing systematics, and anyone who needs the current bound on 1–30 M_sun black holes. It's a solid, appropriately framed null result. Send it out; the referees will mostly be checking the efficiency curve, which is where I'd put my own attention.

Referee report

Significance

This is a useful and timely extension of the MACHO/EROS MACHO window into the several-to-thirty solar mass range, which is the remaining baryonic window after the earlier short- and intermediate-duration results. The strengths are real: the efficiency is self-calibrated from the same photometry rather than assumed, the null result is converted into a limit with an explicit Poisson threshold (three expected events for 95% c.l.), the model dependence is stated openly and a model-independent form of the limit (4 × 10^11 M_sun below 30 M_sun) is given alongside the fractional one, the scaling of the fractional limit with assumed halo mass is spelled out, and the exclusion of event 22 is supported by spectroscopy rather than by assertion. The paper also makes a falsifiable commitment — that the full 8-year dataset should either push the limit to higher masses or yield long-duration events — which is the right way to close a null-result letter.

Major objections (1)

[§3–§4, Fig. 2] The upper endpoint of the exclusion, 30 M_sun, is set by the long-duration tail of the Fig. 1 efficiency acting together with the t_hat < 600 day background cut stated in §4. Equation 1 gives a mean timescale of about 710 days for a 30 M_sun lens, so a substantial fraction of the model-S duration distribution at that mass falls above the 600-day cut and contributes nothing to the expected count alpha. The convolution itself is done correctly — the efficiency curve already encodes the cut — but the manuscript never reports what fraction of the 30 M_sun signal survives into the 150 < t_hat < 600 day window, so the reader cannot check how close alpha(30 M_sun) sits to the Poisson threshold of three. Please state that surviving fraction explicitly, or show alpha(m) with and without the 600-day cut, and state the full selection window (150 < t_hat < 600 days) in §3 where the cuts are defined rather than only in §4. This does not threaten the 0.3–10 M_sun core of the result or the 4 × 10^11 M_sun model-independent limit, but the 30 M_sun number in the abstract is the one resting on the least-tested part of the efficiency curve, and §4 already concedes that the cuts limit sensitivity there.

Minor objections (9)

[Title vs. abstract] The title says '1–30 Solar Mass Range' while the abstract and §3 state 0.3–30.0 M_sun; the two should be reconciled, since the lower endpoint is part of the quoted exclusion.
[§1, reference list] Carr (1994) is cited in the introduction ('As reviewed by Carr (1994)') but does not appear in the reference list; please add it.
[§1, reference list] The text cites 'Dalcanton et al. 1997' for the quasar microlensing limits, but the reference list gives Dalcanton, Canizares, Granados, & Steidel 1994, ApJ, 424, 500; please check which year is intended and make the citation consistent.
[§3, Fig. 1] The efficiency calculation is described only by reference to Alcock et al. (2000b, submitted) and Vandehei (2000, PhD thesis). A short summary of the validation — for example, the injection-and-recovery tests and the blending treatment — would make Fig. 1 self-contained for a reader of this letter.
[Fig. 1] Please state in the caption whether the solid curve includes the t_hat < 600 day cut, and mark that cut on the figure; as drawn, the reader cannot tell where the efficiency is truncated by the background rejection.
[§3] The text first says the analysis uses criteria 'similar to' set A and then says 'we choose simply selection criteria A'; harmonize the wording so it is unambiguous that set A is used unchanged apart from the duration cut.
[Fig. 2] The 99% c.l. line at N = 4.6 is drawn but never discussed in the text; either add a sentence on the 99% exclusion or drop the line.
[Abstract] The phrasing 'exclude objects ... from contributing more than 4 × 10^11 M_sun to the Galactic halo' reads as a mass budget rather than a halo fraction; consider rephrasing to make clear that this is 100% of the model-S halo mass out to 50 kpc.
[§2] For event 22, the redshift z = 0.23 is quoted without line identifications; a brief note on which lines were detected, or a pointer to where the spectrum is shown in Alcock et al. (2000b), would strengthen an exclusion that matters for this paper.

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The paper

The paper claims

A search for long, slow brightenings in the Large Magellanic Cloud finds none, which caps how much of the Galaxy's dark halo can be locked up in black holes between a third of a solar mass and thirty solar masses.

The reading

The paper asks whether the Milky Way's dark halo could be made of black holes or other compact objects in the range of roughly one to thirty Suns, a window that earlier microlensing searches had left open. If a compact object drifts in front of a background star, the star brightens for a time set mostly by the object's mass, so a halo full of ten-solar-mass black holes would produce brightenings lasting hundreds of days rather than the tens of days seen for lighter lenses. The authors search 5.7 years of MACHO photometry of 11.9 million LMC stars for events longer than 150 days and find none. Converting 'none found' into 'fewer than about three expected' at 95% confidence, they exclude objects from $0.3$ to $30.0$ solar masses from making up the whole halo, and combined with earlier short-duration limits conclude that anything under $10$ solar masses supplies less than 40% of a typical dark halo. The result matters because it closes the last mass window in which baryonic dark matter could plausibly have hidden, and it is stated in a form that survives changes to the halo model: at most $4$-$5$ hundred billion solar masses of compact objects below $30$ solar masses can be present within 50 kpc.

What carries the argument

Two pieces of machinery carry the argument. The first is the mass-duration relation for microlensing, $t_0$ roughly $130$ times the square root of the lens mass in solar masses, in days, which is what makes a search for long events equivalent to a search for heavy lenses. The second is the zero-count Poisson bound: if a model predicts $N$ events, the probability of observing none is $e^{-N}$, so $N=3$ corresponds to a 95% exclusion. The bridge between them is the photometric detection efficiency as a function of event duration, computed for the actual observing history, weather, seeing, telescope slips and blending, and then averaged over the halo model's distribution of lens distances and velocities. The halo model used is a cored isothermal sphere with local density $0.0079$ solar masses per cubic parsec, core radius $5$ kpc, and total mass $4$ times $10^{11}$ solar masses within 50 kpc, with an isotropic Maxwellian velocity distribution.

Extended reading notes

Core claim

The central claim is a null result turned into a mass bound. In 5.7 years of MACHO imaging of the Large Magellanic Cloud, using the conservative event-selection criteria of the collaboration's earlier microlensing analysis plus a requirement that the fitted event duration exceed 150 days, no candidate events survive. Because microlensing events are Poisson distributed, a model predicting $3$ or more events is excluded at 95% confidence by seeing zero. Convolving the measured detection efficiency as a function of duration with the predicted duration distribution of a standard halo model, the authors find that a halo made entirely of objects between $0.3$ and $30.0$ solar masses would have produced more than three such events, and is therefore ruled out. Combined with the collaboration's earlier limits at lower masses, this means compact objects below $30$ solar masses cannot constitute the entire dark halo of typical size, and objects below $10$ solar masses contribute under 40% of it. The authors restate the result in halo-independent units: less than $4$-$5$ hundred billion solar masses in compact objects below $30$ solar masses can be present in the halo, with the corresponding figure for objects below $10$ solar masses about $1.6$ hundred billion.

Load-bearing premise

The whole bound rests on the computed detection efficiency for very long events: if the pipeline underestimates how easily a 150-to-600-day brightening would have been found, then the expected number of events for heavy lenses is too high and the mass limit is too strict.

Editorial extensions

If this is right

Black holes and other compact objects below $30$ solar masses are eliminated as the dominant component of a typical Galactic dark halo, leaving primordial black holes in that range unable to solve the dark matter problem on their own.
The bound is quoted in a form that scales with the assumed halo mass, so a halo twice as massive within 50 kpc weakens the 100% exclusion at $30$ solar masses to roughly a 50% one rather than overturning it.
The remaining allowed window for compact halo dark matter moves above roughly $30$ solar masses, where the collaboration says its current cuts on slow variables and on fitted duration below 600 days have little sensitivity.
Because the exclusion applies to any mass function built only from masses in the excluded range, mixed populations of black holes confined to $0.3$ to $30$ solar masses are excluded along with single-mass halos.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same null result is a statement about the longest timescales the survey could measure, so extending the baseline from 5.7 to 8 years should push the bound upward in mass more through better rejection of slow variable stars than through more exposure.
A single confirmed microlensing event with a fitted duration well above 150 days would not merely weaken the limit; it would be direct evidence for a compact object heavier than roughly ten solar masses in the halo, which is a more interesting outcome than the bound itself.
The technique is symmetric in time: the same efficiency curve that converts zero long events into a heavy-mass bound also constrains any population of slow transients, so the analysis doubles as a constraint on long-duration supernovae and AGN misclassification in the LMC lightcurves.
Because the bound is expressed as a total mass in compact objects rather than a fraction, it transfers to any halo model with a different total mass by simple rescaling, which is the form most useful to anyone testing a specific black-hole dark matter scenario.

Original abstract

We report on a search for long duration microlensing events towards the Large Magellanic Cloud. We find none, and therefore put limits on the contribution of high mass objects to the Galactic dark matter. At 95% confidence level we exclude objects in the mass range 0.3 solar masses to 30.0 solar masses from contributing more than 4 times 10^11 solar masses to the Galactic halo. Combined with earlier results, this means that objects with masses under 30 solar masses cannot make up the entire dark matter halo if the halo is of typical size. For a typical dark halo, objects with masses under 10 solar masses contribute less than 40% of the dark matter.

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.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,259 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.64 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We report on a search for long duration microlensing events towards the Large Magellanic Cloud. We find none, and therefore put limits on the contribution of high mass objects to the Galactic dark matter. At 95% confidence level we exclude objects in the mass range 0.3 solar masses to 30.0 solar masses from contributing more than 4 times 10^11 solar masses to the Galactic halo. Combined with earlier results, this means that objects with masses under 30 solar masses cannot make up the entire dark matter halo if the halo is of typical size. For a typical dark halo, objects with masses under 10 solar masses contribute less than 40% of the dark matter.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We report on a search for long duration microlensing events towards the Large Magellanic Cloud.	contribution 0.98	0.93	0.02	asserted 0.92
s1	We find none, and therefore put limits on the contribution of high mass objects to the Galactic dark matter.	result 0.88	0.96	0.38	asserted 1.00
s2	At 95% confidence level we exclude objects in the mass range 0.3 solar masses to 30.0 solar masses from contributing more than 4 times 10^11 solar masses to the Galactic halo.	result 1.00	0.94	0.53	asserted 1.00
s3	Combined with earlier results, this means that objects with masses under 30 solar masses cannot make up the entire dark matter halo if the halo is of typical size.	interpretation 0.98	0.73	0.52	asserted 0.92
s4	For a typical dark halo, objects with masses under 10 solar masses contribute less than 40% of the dark matter.	result 0.69	0.71	0.18	asserted 0.99

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** — Microlensing detection efficiency for the 5.7-year MACHO data, as a function of event timescale bt. The solid line shows the photometric efficiency computed for cut set A, with the additional constraint that bt > 150 days. The dashed line (from A2000a) is the same but without the additional constraint

**Figure 2.** — Number of long duration events expected vs.

**Figure 3.** — Halo fraction upper limit as a function of

Figures reproduced from arXiv:astro-ph/0011506 by the authors.

References

Works cited (12)

[1]

Alcock, C. et al. 1996, ApJ, 471, 774

View on Pith 1996
[2]

Alcock, C. et al. 1997, ApJ, 486, 697 (A97)

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[3]

Alcock, C. et al. 1998, ApJ, 499, L9

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[4]

Aubourg, E. et al. 1995, A&A, 301, 1

View on Pith 1995
[5]

Carr, B.J., Bond, J.R., and Arnett, W.D. 1984, ApJ, 277, 445

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[6]

Carr, B.J. and Hawking, S.W. 1974, MNRAS, 168, 399

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[7]

Steidel, C.C., 1994, ApJ, 424, 500

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[8]

Griest, K., 1991, ApJ, 366, 412

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[9]

Jedamzik, K., 1997, Phys. Rev. D55, 5871

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[10]

Lasserre, T. et al. 2000, A&A, 355, L39

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[11]

Moore, B., 1993, ApJ, 413, L93 Paczy´ nski, B., 1986, ApJ, 304, 1

View on Pith 1993
[12]

Vandehei, T., 2000, PhD thesis, University of Califor- nia, San Diego This 2-column preprint was prepared with the AAS L ATEX macros v4.0. 5 Fig. 1.— Microlensing detection eﬃciency for the 5.7-year MACHO data, as a function of event timescale ˆt . The solid line shows the photometric eﬃciency computed for cut set A, with the additional constraint that ˆt...

View on Pith 2000

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Two populations of LIGO-Virgo black holes
astro-ph.CO 2020-12 conditional novelty 5.0 of 10

Fitting LIGO-Virgo GWTC-2 mergers with a combined astrophysical plus primordial black hole model disfavours a primordial-only population and tightens the primordial black hole dark matter fraction to below 0.2 percent...
Constraining the primordial black hole scenario with Bayesian inference and machine learning: the GWTC-2 gravitational wave catalog
gr-qc 2020-11 conditional novelty 5.0 of 10

Assuming every GWTC-2 black hole merger is primordial, the authors infer that primordial black holes make up about 0.3 percent of dark matter and that accretion, not formation, supplies the observed spins.
NANOGrav results and LIGO-Virgo primordial black holes in axion-like curvaton model
astro-ph.CO 2020-11 conditional novelty 5.0 of 10

Primordial non-Gaussianity in the axion-like curvaton model suppresses induced gravitational waves enough that stellar-mass primordial black holes and the NANOGrav nanohertz signal can be explained by the same early-u...
NANOGrav Hints to Primordial Black Holes as Dark Matter
astro-ph.CO 2020-09 conditional novelty 5.0 of 10

A flat spectrum of curvature perturbations normalized so that primordial black holes make up all dark matter also yields second-order gravitational waves whose amplitude and flat slope match the NANOGrav 12.5-year signal.
Low Mass Black Holes from Dark Core Collapse
astro-ph.HE 2020-09 conditional novelty 5.0 of 10

Non-annihilating dark matter accumulating in a neutron star can collapse into a small black hole that transmutes the host star into a sub-Chandrasekhar mass black hole, and the redshift dependence of the merger rate c...
Primordial Black Holes Confront LIGO/Virgo data: Current situation
astro-ph.CO 2020-05 conditional novelty 5.0 of 10

Primordial black holes can make up at most a few times 10^-3 of dark matter given current LIGO/Virgo merger data, and the spinning component of GW190412 is incompatible with a non-accreting primordial origin.
INTEGRAL constraints on primordial black holes and particle dark matter
astro-ph.CO 2020-04 conditional novelty 5.0 of 10

Diffuse Galactic gamma rays measured by INTEGRAL exclude primordial black holes below 1.2×10^17 g as all of the dark matter at 95% C.L., and weaken prior MeV dark-matter decay limits by a factor of 3 to 10.
Constraints on Primordial Black Holes: the Importance of Accretion
astro-ph.CO 2020-03 conditional novelty 5.0 of 10

Accounting for gas accretion, which can grow primordial black holes by orders of magnitude, weakens present-day dark-matter fraction limits for black holes above a few solar masses.
Neutrino and Positron Constraints on Spinning Primordial Black Hole Dark Matter
hep-ph 2019-12 conditional novelty 5.0 of 10

Spinning primordial black holes up to about 10^17 g are constrained by Super-Kamiokande diffuse supernova neutrino limits and by the INTEGRAL 511 keV positron line, with the positron bound beating diffuse gamma-ray li...
Aspects of Nonlinear Effect on Black Hole Superradiance
hep-ph 2019-10 conditional novelty 5.0 of 10

Nonlinear self-interactions and particle production can saturate a superradiant boson cloud long before it drains the black hole's spin, weakening superradiance-based constraints on ultralight bosons.
Lower bound on the primordial black hole merger rate
astro-ph.CO 2019-08 conditional novelty 5.0 of 10

Even if nearly all early PBH binaries are disrupted, the re-formed and perturbed binaries merge often enough to rule out PBHs as all of the dark matter in the 1 to 100 solar mass range.
Primordial black holes as a dark matter candidate are severely constrained by the Galactic Center 511 keV gamma-ray line
astro-ph.HE 2019-06 conditional novelty 5.0 of 10

The observed 511 keV line from the Galactic Center caps the fraction of dark matter that can be low-mass evaporating primordial black holes at roughly 1 percent or less over the 10^13 to 10^14 kg range.
Constraining the primordial black hole abundance with 21cm cosmology
astro-ph.CO 2019-06 conditional novelty 5.0 of 10

Future 21cm power spectrum measurements from SKA and HERA could tighten limits on solar-mass primordial black holes as dark matter by roughly an order of magnitude beyond current cosmic microwave background bounds.
Lyman-$\alpha$ forest constraints on Primordial Black Holes as Dark Matter
astro-ph.CO 2019-03 conditional novelty 5.0 of 10

Lyman-alpha forest data plus hydrodynamic simulations constrain the primordial black hole abundance times mass to below about 60 solar masses at 2 sigma, tightening the previous bound by roughly two orders of magnitude.
Effect of nonlinearity between density and curvature perturbations on the primordial black hole formation
astro-ph.CO 2019-03 conditional novelty 5.0 of 10

The nonlinear density-curvature relation makes the density field negatively skewed and suppresses primordial black hole formation by an amount comparable to local non-Gaussianity with f_NL about -1, requiring roughly ...
Resonant multiple peaks in the induced gravitational waves
astro-ph.CO 2019-01 accept novelty 5.0 of 10

Induced gravitational waves from a multi-peaked primordial scalar spectrum show peaks at wave-numbers (k_i + k_j)/sqrt(3), one for each pair of scalar peaks.
Voyager 1 $e^\pm$ Further Constrain Primordial Black Holes as Dark Matter
astro-ph.HE 2018-07 conditional novelty 5.0 of 10

Voyager 1 measurements of low-energy cosmic-ray electrons and positrons limit primordial black holes below 10^16 grams to under 0.1% of the Galactic dark matter.
Primordial Black Hole Production in Inflationary Models of Supergravity with a Single Chiral Superfield
hep-ph 2018-06 conditional novelty 5.0 of 10

A hand-tuned double inflection point in a single-chiral-superfield supergravity potential yields CMB-consistent inflation and a primordial black hole population at 5.5e-14 solar masses that could make up about 11% of ...
Formation of primordial black holes in an axionlike curvaton model
astro-ph.CO 2018-05 conditional novelty 5.0 of 10

An axion-like curvaton with an inflaton coupling produces a peaked curvature spectrum that can yield primordial black holes at 30 solar masses or 10^-12 solar masses without violating current constraints.
Constraining Primordial Black Holes with the EDGES 21-cm Absorption Signal
astro-ph.CO 2018-03 conditional novelty 5.0 of 10

Requiring that gas heated by accreting primordial black holes stays below the temperature implied by the EDGES 21-cm dip limits 10 solar mass black holes to between 1 and 10^-3 of the dark matter, depending on the acc...
Primordial Black Holes for the LIGO Events in the Axion-like Curvaton Model
astro-ph.CO 2017-11 conditional novelty 5.0 of 10

With non-Gaussianity included, the axion-like curvaton model can produce enough roughly 30 solar mass primordial black holes to explain the LIGO merger rate while only marginally satisfying pulsar-timing-array bounds ...
Double inflation as a single origin of primordial black holes for all dark matter and LIGO observations
astro-ph.CO 2017-11 conditional novelty 5.0 of 10

A double-inflation model produces primordial black holes in two mass windows simultaneously, one broad enough to be all dark matter and one sharp enough to source the LIGO black hole mergers.
Primordial Black Holes as Dark Matter: Converting Constraints from Monochromatic to Extended Mass Distributions
astro-ph.CO 2017-09 conditional novelty 5.0 of 10

A single equivalent mass per observable lets published monochromatic primordial-black-hole limits be converted into limits on extended mass distributions, and the converted limits come out stronger.
Primordial black holes and second order gravitational waves from ultra-slow-roll inflation
astro-ph.CO 2017-07 conditional novelty 5.0 of 10

A fifth-degree polynomial inflaton potential with a near-inflection point triggers ultra-slow-roll inflation, amplifying the curvature power spectrum by seven orders of magnitude and yielding primordial black holes as...
Gravitational Waves from Primordial Black Hole Mergers
astro-ph.CO 2017-07 conditional novelty 5.0 of 10

Extending the primordial black hole binary merger rate to a lognormal mass function and clustered initial conditions yields a gravitational-wave background bound on primordial black holes that the authors claim is the...
Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era
astro-ph.CO 2017-06 conditional novelty 5.0 of 10

Primordial black holes formed during an early matter-dominated era can supply the dark matter and constrain the inflaton running and spectator spectral index at levels comparable to Planck.

See all 81 Pith citations

How later papers used it

169 later papers cite it

Evidence: some. 169 of the citing papers share no author with it, and 18 of those carry a confident label from Pith's citation classifier.

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Uses its data or values 1 of 11 papers with this label

Included this paper's MACHO microlensing constraints among the constraints in its Set A.

The Maximal-Density Mass Function for Primordial Black Hole Dark Matter (2018) · 0.92 · paraphrased: the licence does not allow quoting

How the literature uses it

131 arXiv papers cite this in 152 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 120 sentences without a confident label

Uses its data or values 10 papers

Using data from the plot of $ρ_PBH/ρ_DM$ against $M_PBH$ from [ref] (which is in turn collated from constraints due to evaporation [ref] , femto-lensing of gamma-ray bursts [ref] , neutron-star capture [ref] , white dwarf explosions [ref] , microlensing [ref] , Planck results [ref] , survival of stars in Segue I [ref] and Eridanus II [ref] , and distribution of wide binaries [ref] ), it is possible to scale the observed constraints on PBH abundance such that they include a period of evolution in the matter dominated phase.

Extreme scenarios: the tightest possible constraints on the power spectrum due to primordial black holes · PBH formation likelihood and power spectrum constraints · 0.96
The EROS collaboration find a $95%$ upper confidence limit $τ< 0.36 ×10^-7$ which they translate into limits on the halo fraction [ref] : [equation] or [equation] Combined EROS and MACHO collaboration limits on short duration events constrain the abundance of light MACHOs [ref] [equation] while a dedicated search by the MACHO collaboration for long ($> 150$ days) duration events leads to limits on more massive MACHOs [ref] : [equation] or [equation]

Generalised constraints on the curvature perturbation from primordial black holes · Microlensing · 0.96
The MACHO collaboration [ref] excluded the objects in the mass range $0.3 M_⊙$ to $30 M_⊙$, and the latest result of the EROS-1 and EROS-2 [ref] excluded the mass range $0.6 ×10^-7 M_⊙< M < 15 M_⊙$, as the bulk component of the galactic DM.

Primordial Black Holes as All Dark Matter · PBH formation and observational constraints · 0.93

Compares with it 3 papers

This bound is stronger than most of current observational constraints [ref] for $10-300 M_⊙ PBH$ [We do not consider CMB constraints reported by Ricotti et al. (2008) [ref] , which overestimate the effects of PBHs on CMB observables (see [ref] ).].

Implications for Dark Matter Direct Detection in the Presence of LIGO-Motivated Primordial Black Holes · Introduction · 0.95
Also shown in fig:sense are current constraints from microlensing surveys [ref] (blue line), and the CMB [ref] (purple and black lines), where the purple contour denotes the bound derived assuming an identical accretion model to the one adopted here.

Constraining the primordial black hole abundance with 21cm cosmology · Results and conclusions · 0.93
Compared to the lensing constraints from EROS-2 [ref] and MACHO [ref] Collaborations, the lensing of FRBs is sensitive to heavier compact objects ($≳$ 1 $M_⊙$), and thus these constraints can also be viewed as complementary probes of exotic compact objects.

Lensing of fast radio bursts: future constraints on primordial black hole density with an extended mass function and a new probe of exotic compact fermion and boson stars · Fermion stars · 1.00

Cites it as background 19 papers

Further details regarding these PBH constraints which are all associated with various caveats [ref] , can be found in the companion article [ref] .

Complementary probes of inflationary cosmology · Introduction · 0.91
These constraints include searching for capture of PBHs by compact objects [ref] , lensing searches [ref] , dynamical effects on ultra-faint dwarf galaxies [ref] , orbital dynamics [ref] , non-observations of stochastic gravitational waves [ref] , and effects of accretion onto PBHs via cosmic microwave background observations [ref] .

Lensing of fast radio bursts: future constraints on primordial black hole density with an extended mass function and a new probe of exotic compact fermion and boson stars · Introduction · 0.87
These have resulted in a multitude of observational constraints [ref] , along with several future projections [ref] along a broad range of PBH masses.

Near future MeV telescopes can discover asteroid-mass primordial black hole dark matter · Introduction · 0.86

Discussion

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Vandehei, T., 2000, PhD thesis, University of Califor- nia, San Diego This 2-column preprint was prepared with the AAS L ATEX macros v4.0. 5 Fig. 1.— Microlensing detection eﬃciency for the 5.7-year MACHO data, as a function of event timescale ˆt . The solid line shows the photometric eﬃciency computed for cut set A, with the additional constraint that ˆt...

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