Formation of intermediate-mass black holes as primordial black holes in the inflationary cosmology with running spectral index
Toshihiro Kawaguchi
2
Masahiro Kawasaki
0
1
Tsutomu Takayama
1
Masahide Yamaguchi
2
Jun'ichi Yokoyama
0
3
0
Institute for the Physics and Mathematics of the Universe, The University of Tokyo
,
Kashiwa 277-8582
,
Japan
1
Institute for Cosmic Ray Research (ICRR), The University of Tokyo
,
Kashiwa 277-8582
,
Japan
2
Department of Physics and Mathematics, Aoyama Gakuin University
,
Sagamihara 229-8558
,
Japan
3
Research Centre for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo
,
Tokyo 113-0033
,
Japan
A B S T R A C T Formation of primordial black holes (PBHs) on astrophysical mass scales is a natural consequence of inflationary cosmology, if the primordial perturbation spectrum has a large and negative running of the spectral index as observationally suggested today because double inflation is required to explain it and fluctuations on some astrophysical scales are enhanced in the field-oscillation regime in between. It is argued that PBHs thus produced can serve as intermediate-mass black holes (IMBHs), which act as the observed ultraluminous X-ray sources (ULXs) by choosing appropriate values of the model parameters in their natural ranges. Our scenario can be observationally tested in near future because the mass of PBHs is uniquely determined once we specify the values of the amplitude of the curvature perturbation, spectral index and its running on large scales.
1 I N T R O D U C T I O N
Ultraluminous X-ray sources (ULXs; Makishima et al. 2000)
are characterized by their luminosity greater than 1039 erg s1
(well above the Eddington luminosity of a neutron star) and
offnuclear location in nearby galaxies (Fabbiano 1989; Colbert &
Mushotzky 1999). In addition, X-ray variability on various
timescales are found for some ULXs (Matsumoto & Tsuru 1999; Ptak &
Griffiths 1999; Kaaret et al. 2001; Kubota et al. 2001).
Luminosity, time variability and X-ray spectra of ULXs indicate that ULXs
are accreting black holes, rather than young supernova remnants
(Kaaret et al. 2001). Although association of ULXs with active
starforming regions is clearly shown (Matsushita et al. 2000; Zezas et al.
2002), the physical reason behind the association, and moreover the
origin of ULXs, is still unclear.
The number density of ULXs can be roughly estimated as
follows. Late-type/starburst galaxies hosting numerous compact X-ray
sources (mostly high-mass X-ray binaries) within about 30 Mpc
from the Milky Way are listed in Grimm et al. (2003). The
number of these X-ray sources with each luminosity greater than 2
1038 erg s1 is about 100. Grimm et al. also show that the luminosity
function N(L) of compact X-ray sources, which is defined as a
number of X-ray sources with luminosity greater than L, is universal
for galaxies if it is normalized proportionally to the star-forming
rate (SFR). The normalized luminosity function tells that among
L > 1038.5 erg s1 sources about one-third have L > 1039 erg s1.
Hence, the number of ULXs with L > 1039 erg s1 will be 30
within 30 Mpc. Thus, the number density of ULXs is estimated to
be 103.5 Mpc3.
In spite of observational evidences, theoretical explanations of
ULXs are still in dispute. The most challenging fact is the high
luminosity greater than the Eddington luminosity of a stellar-mass
black hole with mass 10 M . For example, it is argued that
sources of ULXs can be standard stellar-mass black holes with
jets or relativistic beaming (Koerding, Falcke & Markoff 2002).
Another possibility is stellar-mass black holes radiating at
superEddington luminosities due to efficient photon leakage from
accretion discs (e.g. Begelman 2002; Meyer 2004) and/or due to
superEddington accretion rates (slim accretion discs; Abramowicz et al.
1988). Detailed computations of slim accretion discs (Kawaguchi
2003) indeed account for observed X-ray spectra of ULXs
(Ebisawa & Kawaguchi 2006; Foschini et al. 2006; Okajima,
Ebisawa & Kawaguchi 2006; Vierdayanti et al. 2006).
ULXs can also be explained as sub-Eddington accretors by
assuming black holes heavier than stellar-mass black holes (see Miller
& Colbert 2004 and reference therein). Moreover, ULXs exhibit
quasi-periodic oscillations (QPOs) at frequencies lower than the
QPO frequencies of normal black hole binaries by a couple of
orders (Strohmayer & Mushotzky 2003; Strohmayer et al. 2007). A
straightforward interpretation of the longer time-scales is a
heavier black hole mass than 10 M . Hence, intermediate-mass black
holes (IMBHs) with mass 1024 M are considered to be one of
the best candidates of ULXs.
The most challenging problem with such IMBHs is their
formation mechanism. There are several possible mechanisms
discussed so far. For instance, detailed evolution models of stellar
binaries show that the generation rate of IMBHs is very small
(Madhusudhan et al. 2006).
A promising possibility is that IMBHs could be remnants of
Population III stars (e.g. Schneider et al. 2002). It is suggested that
zero-metalicity stars f (...truncated)