Remnants of massive metal-poor stars: viable engines for ultra-luminous X-ray sources

Abstract

Massive metal-poor stars might end their life by directly collapsing into massive (~25-80 Msun) black holes (BHs). We derive the number of massive BHs (N_BH) that are expected to form per galaxy via this mechanism. We select a sample of 66 galaxies with X-ray coverage, measurements of the star formation rate (SFR) and of the metallicity. We find that N_BH correlates with the number of observed ultra-luminous X-ray sources (ULXs) per galaxy (N_ULX) in this sample. We discuss the dependence of N_ULX and of N_BH on the SFR and on the metallicity. Comment: 4 pages, 3 figures, accepted for publication in the Astronomische Nachrichten, to appear in the proceedings of the conference "Ultra-luminous X-ray sources and Middle Weight Black Holes" (Madrid, May 24-26, 2010)

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arXiv:1009.5706v1 [astro-ph.CO] 28 Sep 2010
Astron. Nachr. / AN ????, No.????, 1–4 (????) / DOI please set DOI!
Remnants of massive metal-poor stars: viable engines for ultra-
luminous X-ray sources
M. Mapelli1,⋆, E. Ripamonti1, L. Zampieri2, and M. Colpi1
1Physics Department ‘G. Occhialini’, University of Milano-Bicocca, Piazza della Scienza 3, I–20126 Milan, Italy
2INAF-Osservatorio astronomico di Padova, Vicolo dell’Osservatorio 5, I–35122, Padova, Italy
Received 31 August 2010, accepted ???
Published online later
Key words
black hole physics – X-rays: binaries – X-rays: galaxies – galaxies: starburst
Massive metal-poor stars might end their life by directly collapsing into massive (≈ 25− 80 M⊙) black holes (BHs). We
derive the number of massive BHs (NBH) that are expected to form per galaxy via this mechanism. We select a sample
of 66 galaxies with X-ray coverage, measurements of the star formation rate (SFR) and of the metallicity. We find that
NBHcorrelates with the number of observed ultra-luminous X-ray sources (ULXs) per galaxy (NULX) in this sample. We
discuss the dependence of NULXand of NBHon the SFR and on the metallicity.
c ? ???? WILEY-VCH Verlag GmbH&Co.KGaA, Weinheim
1 Introduction
Most ultra-luminous X-ray sources (ULXs) are located in
galaxies with a high star formation rate (SFR, e.g. Irwin,
Bregman & Athey 2004). The ULXs match the correlation
betweenX-rayluminosityandSFRreportedbyvariousstud-
ies (Grimm,Gilfanov&Sunyaev2003;Ranalli,Comastri&
Setti 2003; Gilfanov, Grimm & Sunyaev 2004a,b,c; Kaaret
& Alonso-Herrero2008; Mineo & Gilfanov 2010).Further-
more, the same studies indicate that the luminosity function
of ULXs is the direct extension of the function for high-
massX-raybinaries(HMXBs).Recentpaperssuggestacor-
relation between ULXs and low-metallicity environments,
andproposethatthismaybeconnectedwiththeinfluenceof
metallicity on the evolutionof massive stars (Pakull& Miri-
oni 2002; Zampieri et al. 2004; Soria et al. 2005; Swartz,
Soria & Tennant 2008). This scenario has been explored in
detail by Mapelli, Colpi & Zampieri (2009, hereafter M09),
by Zampieri & Roberts (2009) and by Mapelli et al. (2010,
hereafter M10), highlighting that a large fraction of ULXs
may actually host massive (∼ 30 − 80M⊙) stellar black
holes (BHs) formed in a low-metallicity environment. In
fact, low-metallicity (Z<∼0.4Z⊙) massive stars lose only
a small fraction of their mass due to stellar winds (Maeder
1992,hereafterM92;Heger&Woosley2002,hereafterHW02;
Heger et al. 2003, hereafter H03; Belczynski et al. 2010,
hereafter B10) and can directly collapse (Fryer 1999; B10)
into massive BHs (25M⊙≤ mBH≤ 80M⊙). These mas-
sive BHs can power most of the known ULXs without re-
quiring super-Eddington accretion or anisotropic emission.
Furthermore, their formation mechanism can explain the
⋆Corresponding authors: e-mail: michela.mapelli@mib.infn.it
correlation between ULXs and SFR, and the fact that ULXs
are preferentially found in low-metallicity regions.
2 Sample of galaxies
In this proceeding, we consider a sample of 66 galaxies.
All of them have X-ray coverage, at least one measurement
of the star formation rate (SFR) and of the metallicity (Z).
64 galaxies are taken from the sample listed in Table 1 of
M10. The remaining two are I Zw 18 and the interacting
pair SBS 0335052/SBS 0335052W1. These two objects are
extremely metal-poor galaxies (XMDs, Moiseev, Pustilnik
& Kniazev 2010, and references therein) and are impor-
tant, because they are the only galaxies with Z < 0.03Z⊙
and with X-rayobservations.Their propertiesand the corre-
sponding references are listed in Table 1. For details about
thedataandthepropertiesoftheother64galaxies,see M10.
For all the galaxies in the sample, we derive a fidu-
cial value for the SFR (when there is more than one mea-
surement, we take, in general, the average value), for the
metallicity (we adopt an uniform calibration, see Pilyugin
& Thuan 2005; when a metallicity gradient is available, we
take the value of Z at 0.7 Holmberg radii, see M10) and we
estimate the number of ULXs NULXafter subtracting the
background contamination (see M10 for details).
3 Observational results
The data collectedfrom the literature were analyzedfollow-
ing the same procedure as described in M10. In particular,
we adopt the χ2analysis (although such method might not
1Inthis proceeding, weconsider the interacting pairs asa unique object,
for consistency with M10.
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2Mapelli et al.: Remnants of massive metal-poor stars and ULXs
Table 1
Properties of the two XMDs in the sample.
Galaxy
I Zw 18
SBS 0335-052
SFR [M⊙yr−1]a
0.07
1.1
Z [Z⊙]b
0.02
0.025
NULXc
1
2.83
aSFR from Wu et al. (2007) for I Zw 18 and from Thuan, Izotov &
Lipovetsky (1997), Pustilnik, Pramskij & Kniazev (2004) and Johnson,
Hunt, Reines (2009) for SBS 0335-052.bMetallicity from Thuan et al.
(2004) for both galaxies.cNULXis the number of ULXs per galaxy after
subtracting the background contamination. Thuan et al. (2004) find 1
ULX in I Zw 18 and 3 ULXs in SBS 0335-052/SBS 0335-052W. The
estimated contamination is 0.00 in I Zw 18 and 0.17 (upper limit) in
SBS 0335-052/SBS 0335-052W.
Fig.1
circles: galaxies with metallicity ≤ 0.2Z⊙; open circles
(red on the web): galaxies with metallicity > 0.2Z⊙. Solid
line: power-law fit for the entire sample; dashed line (red
on the web): power-law fit obtained assuming that the index
of the power law is equal to 1. Central panel: NULXversus
Z. Filled black circles: entire sample; solid line: power-law
fit. Lower panel: NULX/SFR versus Z. Filled black circles:
entire sample.Solid line: power-lawfit. Inall the panels:the
error bars on both the x− and the y− axis are 1σ errors.
Upper panel: NULXversus the SFR. Filled black
be completely suitable for small samples, see M10), per-
form the power-law fits and calculate the correlation co-
efficients (see Table 2). From the upper panel of Fig. 1 it
appears that there is a strong correlation between NULX
and the SFR in our sample. Such correlation is consistent
with a linear relation (see the best-fitting values reported
in Table 2), in agreement with previous studies (see e.g.
Grimm, Gilfanov & Sunyaev 2003). Instead, no significant
correlation appears between NULXand Z (central panel of
Fig. 1). However, a marginally significant correlation ex-
ists between the number of ULXs normalized to the SFR
(NULX/SFR)andthemetallicity.Thissuggeststhatthemetal-
licity affects the formation of ULXs, but its contribution is
less important than that of the SFR. The idea that metal-
licity plays a role in the origin of ULXs is consistent with
previous observations (see e.g. Swartz et al. 2008 and ref-
erences therein) and with some recent theoretical models
(M09; Zampieri & Roberts 2009; Linden et al. 2010; M10).
Finally, the presence of the two XMDs in our sample does
notsignificantlychangethebest-fittingvalues(Table2)with
respect to those derived in M10.
4 Comparison of the data with the
theoretical model
In this Section, we analyze the observational data collected
from the literature on the light of the theoretical model re-
cently proposed by M09 and M10. First, we briefly summa-
rize such model.
4.1 Theoretical model
According to numerical calculations (Fryer 1999; HW02;
H03), a star that, at the end of its life, has a final mass
mfin ≥ 40M⊙is expected to directly collapse into a BH.
In this case, the mass of the remnant BH is likely more
than half of the final mass of the progenitor star, as rela-
tively small mass ejection is expected in the direct collapse.
Thus, stars that at the end of their lives have mfin≥ 40M⊙
are likely to produce massive BHs (B10). The final masses
of the stars strongly depend on their metallicity. Massive
stars with metallicity close to solar cannot havefinal masses
largerthanmfin∼ 10−15M⊙,eveniftheirinitialmasswas
very large, as they are expected to lose a lot of mass due to
stellarwinds(H03).Instead,massivestars withlowermetal-
licity are less affected by stellar winds, and retain a larger
fraction of their initial mass. If its metallicity is sufficiently
low, a star can have a final mass mfin ≥ 40M⊙and can
directly collapse into a massive BH with a mass 25M⊙≤
mBH ≤ 80M⊙(HW02; H03; B10). The recent model by
B10 accounts for the fact that stars with mfin≥ 40M⊙can
directly collapse into BHs. For this reason, in this model
BHs with mass as large as 80M⊙are allowed to form.
On the basis of this scenario, we can derivethe expected
number of massive BHs per galaxy (NBH) as a function of
the star formation rate (SFR) and of the metallicity Z (see
M09, M10):
NBH(SFR, Z) = A(SFR)
?mmax
mprog(Z)
m−αdm,
(1)
wheremmaxisthemaximumstellarmass(weassumemmax=
120M⊙) and α is the slope of the initial mass function
(IMF). Here, we adopt the Kroupa IMF, for which α = 1.3
if m ≤ 0.5M⊙and α = 2.3 for larger masses (Kroupa
2001).mprog(Z) is theminimuminitial stellarmass (i.e.the
mass at zero-age main sequence) for which a star is the pro-
genitor of a massive BH. As we discussed above,mprog(Z)
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Astron. Nachr. / AN (????)3
Fig.2
B10) versus the SFR. Central panel: NBHversus Z. Lower
panel: NBH/SFR versus Z. In all the panels, filled black
circles: entire sample; solid line: power-law fit for the entire
sample; the error bars on both the x− and the y− axis are
1σ errors.
Upper panel: NBH(derived using the model from
strongly depends on the metallicity. In our calculations, we
assume mprog(Z) to be the initial stellar mass for which
the mass of the remnant is mBH
model by B102.
Finally, A(SFR), the normalization constant in equa-
tion (1), can be estimated as
SFR tco
?mmax
wheremministheminimumstellarmass(weassumemmin=
0.08 M⊙), SFR is the current star formation rate and tcois
the characteristic lifetime of a possible companion of the
massive BH. In fact, we are not interested in all the massive
BHs, but only in those that could acquire massive stellar
companions and power observable ULXs. In this proceed-
ing, we adopt a constant value tco = 107yr, which is the
lifetime of a ∼ 15M⊙star.
>∼25M⊙, according to the
A(SFR) =
mminm1−αdm,
(2)
4.2Results
Fig. 2 shows the behaviour of the theoretical model when
applied to the observed SFR and metallicity. As assumed
in the model, NBHscales linearly with the SFR. The cen-
tral panel of Fig. 2 shows that there is no significant cor-
relation between NBHand Z, although we imposed, in the
2M10 also consider an alternative model byPortinari, Chiosi & Bressan
1998.
Fig.3
sus the number of expected massive BHs per galaxy NBH,
derived using the model from B10. The solid line is the
power-law fit for the entire sample. The dashed line (red
on the web) is the power-law fit obtained assuming that the
index of the power law is = 1. The error bars on both the
x− and the y− axis are 1σ errors.
Number of observed ULXs per galaxy NULXver-
model,thatNBHdoesdependonZ.Thisabsenceofcorrela-
tion agrees with what we found for NULXversus Z (central
panel of Fig. 1). Finally, only when the effect of the SFR
is subtracted (by normalizing NBHto the SFR, lower panel
of Fig. 3), it is possible to see the dependence of NBHon
the metallicity. The behaviour of NBH/SFR versus Z in the
model is consistent with that of NULX/SFR versus Z in the
data.
Fig. 3 and Table 2 indicate that there is a correlation
between NBHand NULX. This correlation is slightly more
significant than that between NULXand SFR, when consid-
ering both the χ2analysis and the correlation coefficient.
Recently,Lindenetal.(2010)proposedadifferentmodel
to explain the connection between low-metallicity environ-
ments and ULXs. They indicate that the number, the life-
time and (less significantly) the luminosity of HMXBs are
enhanced by low metallicity. Linden et al. (2010) also point
out a possible problem of M10’s model: massive BHs born
via direct collapse likely do not receive a natal kick and
this fact excludes, in the model by Linden et al. (2010), the
possibility of forming a HMXB via Roche lobe overflow
(RLO).
On the other hand, Linden et al. (2010) always require
super-Eddington emission, to explain the ULXs. Further-
more, the process of the direct collapse and the physics of
thebinarieswhichincludemassiveBHs bornfromitarestill
far from being understood. For example, natal kicks might
still be present, due to asymmetries induced by sterile neu-
trinos(e.g.Kusenko2006).Inalternative,kicks mightoccur
for different reasons, e.g. due to three-body encounters in
the parent cluster (Mapelli et al., in preparation). Such sce-
nario might also explain why ULXs are often found to be
displaced with respect to star-forming regions (e.g. Swartz,
Tennant & Soria 2009).
5 Conclusions
In this proceeding, we considered a sample of 66 galaxies.
All of them have X-ray coverage, at least one measurement
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4Mapelli et al.: Remnants of massive metal-poor stars and ULXs
Table 2
Parameters of the power-law fits and χ2.
xy
Indexa
Normalization
χ2 b
rc
0.92
0.92
NBH
NULX
0.82+0.18
−0.12
1.00
-2.63+0.48
−0.72
-3.35+0.06
−0.06
12.0
13.0
NBH
NULX
SFR
SFR
NULX
0.86+0.22
−0.14
1.00
0.16+0.09
−0.12
0.09+0.06
−0.06
19.3
19.8
0.88
0.88
NULX
ZNULX
-0.16+0.28
−0.28
-0.55+0.21
−0.19
0.12+0.20
−0.20
-0.37+0.16
−0.16
86.5
11.0
-0.15
-0.38
ZNULX/SFR
The SFR and the Z used by the fitting procedure are in units of M⊙yr−1
and of Z⊙, respectively.aWhen the index is equal to 1.00 or to 0.00,
without error, it means that it has been fixed to such value.bχ2is the
non-reduced χ2. The number of degrees of freedom (dof) is 65 when the
index has been fixed, 64 in the other cases.cr is the Pearson correlation
coefficient.
of the SFR and of Z. This sample includes two XMDs,
which have extremely low metallicity and host a relatively
high number of ULXs, when compared to their SFR.
We find that there is a strong correlation between the
number of ULXs per galaxy (NULX) and the SFR. This is
consistent with previous studies (e.g. Grimm, Gilfanov &
Sunyaev 2003). We also find a marginally significant anti-
correlation between NULX/SFR and the metallicity. This
might indicate that the metallicity is the missing ingredi-
ent,tounderstandtheformationofULXs,althoughtheerror
bars are still very large and the sample of galaxies is quite
small.
Recently, M09 and M10 suggested that ULXs might
be connected with massive BHs (25 − 80M⊙) formed by
the direct collapse of massive metal-poor stars (Fryer 1999;
B10). We derive the number of BHs per galaxy (NBH) pre-
dicted by M10 and compare it with the observed NULXin
our sample. We find a strong correlation between NBHand
NULX.
We note that the model by B10 derives the mass of the
remnant for single stars only, without considering stars in
binaries. Stars in close binaries likely have a different mass-
losshistory.Accountingforbinaryprogenitorsmightstrengthen
the dependence of the BH mass on metallicity. Therefore, it
will be necessary to account for binary evolution, to refine
the model of massive BH formation.
Furthermore, the physics of the direct collapse and the
propertiesofmassiveBHsbornfromitareonlypoorlyknown.
These need to be investigated, in order to understand the
process of mass transfer (and of X-ray emission) in binaries
including massive BHs.
Finally,weneedmoreobservationaldata,especiallymea-
surements of the metallicity, to strengthen our conclusions.
XMDs are particularly interesting, because of their pecu-
liarly low metallicity.
Acknowledgements. WethankM. Gomitoni,V.Andreoni, A.Bres-
san, P. Marigo, the organizers and the participants to the confer-
ence “Ultra-Luminous X-ray sources and Middle Weight Black
Holes” (Madrid, 24th-26th May 2010) for useful discussions. LZ
and MC acknowledge financial support through INAFgrant PRIN-
2007-26.
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