Primordial black holes and uncertainties in the choice of the window function

Primordial black holes (PBHs) can be produced by the perturbations that exit the horizon during the inflationary phase. While inflation models predict the power spectrum of the perturbations in Fourier space, the PBH abundance depends on the probability distribution function of density perturbations in real space. To estimate the PBH abundance in a given inflation model, we must relate the power spectrum in Fourier space to the probability density function in real space by coarse graining the perturbations with a window function. However, there are uncertainties on what window function should be used, which could change the relation between the PBH abundance and the power spectrum. This is particularly important in considering PBHs with mass 30 M⊙, which account for the LIGO events because the required power spectrum is severely constrained by the observations. In this paper, we investigate how large an influence the uncertainties on the choice of a window function has over the power spectrum required for LIGO PBHs. As a result, it is found that the uncertainties significantly affect the prediction for the stochastic gravitational waves induced by the second-order effect of the perturbations. In particular, the pulsar timing array constraints on the produced gravitational waves could disappear for the real-space top-hat window function.

Note:

9 pages, 4 figures, title revised, PRD accepted version

black hole: primordial
inflation: model
power spectrum: perturbation
density: perturbation
perturbation: effect
gravitational radiation detector
gravitational radiation: emission
gravitational radiation
gravitational radiation: stochastic
LIGO

References(64)

Figures(8)

[1]

Observation of Gravitational Waves from a Binary Black Hole Merger

LIGO Scientific and
Virgo

Collaborations

•

B.P. Abbott
(
- Caltech
)

et al.

- Phys.Rev.Lett. 116 (2016) 6, 061102
•
e-Print:
- 1602.03837
•
DOI:
- 10.1103/PhysRevLett.116.061102

[2]

GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence

LIGO Scientific and
Virgo

Collaborations

•

B. P. Abbott
(
- LIGO Lab., Caltech
)

et al.

- Phys.Rev.Lett. 116 (2016) 24, 241103
•
e-Print:
- 1606.04855
•
DOI:
- 10.1103/PhysRevLett.116.241103

[3]

GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2

LIGO Scientific and
VIRGO

Collaborations

•

Benjamin P. Abbott
(
- LIGO Lab., Caltech
)

et al.

- Phys.Rev.Lett. 118 (2017) 22, 221101,
- Phys.Rev.Lett. 121 (2018) 12, 129901 (erratum)
•
e-Print:
- 1706.01812
•
DOI:
- 10.1103/PhysRevLett.118.221101

[4]

GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence

LIGO Scientific and
Virgo

Collaborations

•

B.P. Abbott
(
- LIGO Lab., Caltech
)

et al.

- Phys.Rev.Lett. 119 (2017) 14, 141101
•
e-Print:
- 1709.09660
•
DOI:
- 10.1103/PhysRevLett.119.141101

[5]

GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral

LIGO Scientific and
Virgo

Collaborations

•

B.P. Abbott
(
- LIGO Lab., Caltech
)

et al.

- Phys.Rev.Lett. 119 (2017) 16, 161101
•
e-Print:
- 1710.05832
•
DOI:
- 10.1103/PhysRevLett.119.161101

[6]

GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence

LIGO Scientific and
Virgo

Collaborations

•

B.. P.. Abbott
(
- LIGO Lab., Caltech
)

et al.

- Astrophys.J.Lett. 851 (2017) L35
•
e-Print:
- 1711.05578
•
DOI:
- 10.3847/2041-8213/aa9f0c

[7]

Astrophysical Implications of the Binary Black-Hole Merger GW150914

LIGO Scientific and
Virgo

Collaborations

•

B.P. Abbott
(
- Caltech
)

et al.

- Astrophys.J.Lett. 818 (2016) 2, L22
•
e-Print:
- 1602.03846
•
DOI:
- 10.3847/2041-8205/818/2/L22

[8]

On The Maximum Mass of Stellar Black Holes

et al.

- Astrophys.J. 714 (2010) 1217-1226
•
e-Print:
- 0904.2784
•
DOI:
- 10.1088/0004-637X/714/2/1217

[9]

The mass spectrum of compact remnants from the PARSEC stellar evolution tracks

Mario Spera
(
- Padua Observ.
)
,
Michela Mapelli
(
- Padua Observ. and
- INFN, Milan Bicocca
)
,
Alessandro Bressan
(
- SISSA, Trieste and
- Padua Observ.
)

- Mon.Not.Roy.Astron.Soc. 451 (2015) 4, 4086-4103
•
e-Print:
- 1505.05201
•
DOI:
- 10.1093/mnras/stv1161

[10]

Possible Indirect Confirmation of the Existence of Pop III Massive Stars by Gravitational Wave

- Mon.Not.Roy.Astron.Soc. 442 (2014) 4, 2963-2992
•
e-Print:
- 1402.6672
•
DOI:
- 10.1093/mnras/stu1022

[11]

Gravitationally collapsed objects of very low mass

Stephen Hawking
(
- Cambridge U.
)

- Mon.Not.Roy.Astron.Soc. 152 (1971) 75
•
DOI:
- 10.1093/mnras/152.1.75

[12]

Black holes in the early Universe

- Mon.Not.Roy.Astron.Soc. 168 (1974) 399-415
•
DOI:
- 10.1093/mnras/168.2.399

[13]

The Primordial black hole mass spectrum

Bernard J. Carr
(
- Cambridge U., DAMTP and
- Caltech
)

- Astrophys.J. 201 (1975) 1-19
•
DOI:
- 10.1086/153853

[14]

Did LIGO detect dark matter?

Simeon Bird
(
- Johns Hopkins U.
)
,
Ilias Cholis
(
- Johns Hopkins U.
)
,
Julian B. Muñoz
(
- Johns Hopkins U.
)
,
Yacine Ali-Haïmoud
(
- Johns Hopkins U.
)
,
Marc Kamionkowski
(
- Johns Hopkins U.
)

et al.

- Phys.Rev.Lett. 116 (2016) 20, 201301
•
e-Print:
- 1603.00464
•
DOI:
- 10.1103/PhysRevLett.116.201301

[15]

The clustering of massive Primordial Black Holes as Dark Matter: measuring their mass distribution with Advanced LIGO

Sebastien Clesse
(
- RWTH Aachen U.
)
,
Juan García-Bellido
(
- Madrid, IFT
)

- Phys.Dark Univ. 15 (2017) 142-147
•
e-Print:
- 1603.05234
•
DOI:
- 10.1016/j.dark.2016.10.002

[16]

Primordial Black Hole Scenario for the Gravitational-Wave Event GW150914

Misao Sasaki
(
- Kyoto U., Yukawa Inst., Kyoto
)
,
Teruaki Suyama
(
- Tokyo U., RESCEU
)
,
Takahiro Tanaka
(
- Kyoto U.
)
,
Shuichiro Yokoyama
(
- Rikkyo U.
)

- Phys.Rev.Lett. 117 (2016) 6, 061101,
- Phys.Rev.Lett. 121 (2018) 5, 059901 (erratum)
•
e-Print:
- 1603.08338
•
DOI:
- 10.1103/PhysRevLett.117.061101