Observational evidence for the origin of X-ray sources in globular clusters
ABSTRACT Low-mass X-ray binaries, recycled pulsars, cataclysmic variables and magnetically active binaries are observed as X-ray sources in globular clusters. We discuss the classification of these systems, and find that some presumed active binaries are brighter than expected. We discuss a new statistical method to determine from observations how the formation of X-ray sources depends on the number of stellar encounters and/or on the cluster mass. We show that cluster mass is not a proxy for the encounter number, and that optical identifications are essential in proving the presence of primordial binaries among the low-luminosity X-ray sources. Comment: 10 pages, 7 figures, to appear in IAUS 246, Dynamical evolution of dense stellar systems, ed. E. Vesperini
arXiv:0710.1804v1 [astro-ph] 9 Oct 2007
Dynamical evolution of dense stellar systems
Proceedings IAU Symposium No. 246, 2007
c ? 2007 International Astronomical Union
Observational evidence for the origin of
X-ray sources in globular clusters
Frank Verbunt1,Dave Pooley2
and Cees Bassa3
1Astronomical Institute, Postbox 80.000, 3508 TA Utrecht, the Netherlands
2Dept. of Astronomy, University of Wisconsin-Madison Madison WI 53706-1582, U.S.A.
3Physics Department, McGill University, Montreal, QC H3A 2T8 Canada
Abstract. Low-mass X-ray binaries, recycled pulsars, cataclysmic variables and magnetically
active binaries are observed as X-ray sources in globular clusters. We discuss the classification
of these systems, and find that some presumed active binaries are brighter than expected. We
discuss a new statistical method to determine from observations how the formation of X-ray
sources depends on the number of stellar encounters and/or on the cluster mass. We show
that cluster mass is not a proxy for the encounter number, and that optical identifications are
essential in proving the presence of primordial binaries among the low-luminosity X-ray sources.
Keywords. X-ray sources, globular clusters, stellar encounters
The first celestial maps in X-rays, in the early 1970s, show that globular clusters
harbour more X-ray sources than one would expect from their mass. As a solution to
this puzzle it was suggested that these bright (Lx ∼>1036erg/s) X-ray sources, binaries
in which a neutron star captures mass from a companion star, are formed in close stellar
encounters. A neutron star can be caught by a companion in a tidal capture, or it can
take the place of a star in a pre-existing binary in an exchange encounter. Verbunt & Hut
(1987) showed that the probability of a cluster to harbour a bright X-ray source indeed
scales with the number of stellar encounters occurring in it; whereas a scaling with mass
does not explain the observations.
With the Einstein satellite a dozen less luminous (Lx ∼<1035erg/s) X-ray sources were
discovered in the early 1980. ROSAT enlarged this number to some 55, and now thanks
to Chandra we know hundreds of dim X-ray sources in globular clusters. The nature and
origin of these dim sources is varied. Those containing neutron stars, i.e. the quiescent
low-mass X-ray binaries in which a neutron star accretes mass from its companion at
a low rate and the recycled or millisecond radio pulsars, have all formed in processes
involving close stellar encounters. The magnetically active binaries, on the other hand,
are most likely primordial binaries, with stars that are kept in rapid rotation via tidal
interaction. Cataclysmic variables are binaries in which a white dwarf accretes matter
from a companion. In globular clusters they may arise either via stellar encounters, or
from primordial binaries through ordinary binary evolution – this is expected to depend
on the mass and density of the globular cluster.
In this paper we describe the classification and identification of the dim sources in Sec-
tion2, and make some remarks on the theory of their formation in Section3. In Section4
2 Frank Verbunt, Dave Pooley, Cees Bassa
log10 (F0.5-2 keV / F2-6 keV)
L 0.5-6 keV (erg s-1)
+ 20% PL
+ 50% PL
Figure 1. Left: X-ray hardness-luminosity diagram for dim sources in globular clusters. I: qui-
escent low-mass X-ray binaries, II: cataclysmic variables III: cataclysmic variables and magneti-
cally active binaries. From Pooley & Hut (2006). Right: Colour-magnitude diagram of NGC6752
on the basis of HST-WFPC2 data; objects within X-ray position error circles are marked. Left of
the main sequence we find cataclysmic variables, above it active binaries. Updated from Pooley
et al. (2002a).
we will discuss a new, and in our view more accurate, way to compare the numbers of
these sources with theoretical predictions.
2. Clasification and identification
Work on the dim sources is progressing along various lines. Grindlay and coworkers
study one cluster, 47Tuc, in great detail (Grindlay et al. 2001, Edmonds et al. 2003,
Heinke et al. 2005). Webb and coworkers use XMM to obtain high-quality X-ray spectra
(e.g. Webb et al. 2006, Servillat this meeting). Dim sources are also found in clusters in
which individual sources are the main target, such as Terzan1 and 5, and M28 (Wijnands
et al. 2002, Heinke et al. 2003, Becker et al. 2003). Lewin initiated a large program to
observe clusters with very different central densities and core radii, and thereby to provide
material for tests on the dependence on these properties of the numbers of dim sources.
Further references to all this work may be found in the review by Verbunt & Lewin
(2006); and in the remainder of this Section.
The first classification of the dim sources may be made on the basis of the X-ray prop-
erties only (Fig.1). The brightest sources in the 0.5-2.5keV band, at Lx ∼>1032erg/s,
tend to be quiescent low-mass X-ray binaries. To better use the Chandra range, one
may also select the brightest sources in the 0.5-6.0keV band, and select soft sources,
with a high ratio of fluxes below and above e.g. 2keV: f0.5−2.0keV/f2.0−6.0keV ∼> 1.
Such sources also are mostly quiescent low-mass X-ray binaries. Between 1031and 1032
erg/s most sources are cataclysmic variables, especially when they have hard spectra
f0.5−2.0keV/f2.0−6.0keV< 1. The faintest sources include magnetically active binaries, of-
ten with soft X-ray spectra. For many faint sources the number of counts is too low to
decide on the hardness of the spectrum.
The second step in classification can be made when identification with a source at
other wavelengths is made. Positional coincidence of an X-ray source with the accurate
radio position of a millisecond pulsar provides a reliable identification and classification.
Positional coincidence with optical sources is only significant if the highest possible as-
X-ray sources in globular clusters
Figure 2. Left: X-ray luminosity as a function of absolute visual magnitude for nearby stars
(selected from H¨ unsch et al. 1999, for details see Verbunt 2001) and for RS CVn systems (from
Dempsey et al. 1993). The upper bound Eq.2.3 is indicated with a solid line. We convert the
X-ray fluxes in the 0.1-2.4 keV range (scale on the left) to the 0.5-2.5 keV range by multiplication
with 0.4 (scale on the right). Right: X-ray luminosity as a function of absolute visual magnitude,
for dim X-ray sources in globular clusters. The assumed separatrices Eqs. 2.1,2.2 are indicated
with dotted lines, the upper bound Eq.2.3 with a solid line. It is seen that some X-ray sources
classified as active binaries in globular clusters are well above this bound.
trometric accuracy is used to limit the number of possible counterparts (e.g. Bassa et
al. 2004). The position of these possible counterparts in a colour-magnitude diagram is
then used to select the probable counterparts. Cataclysmic variables are bluer than the
main sequence stars, and magnetically active binaries may lie above the main sequence.
Systems on the main sequence cannot be unambiguously classified: they may either be
cataclysmic variables in which the optical flux is dominated by the donor star, or main-
sequence binaries with unequal masses whose optical light is dominated by the brighter
star. If a periodicity is found in the X-rays that corresponds to a period at another wave-
length, e.g. the pulse period of a pulsar or the orbital period of a binary, identification
and clasification are secured simultaneously (e.g. Ferraro et al. 2001).
A very useful discriminant in X-ray astronomy in general is the X-ray to optical flux
ratio. In the case of globular clusters we can use the known distance to determine the
optical to X-ray luminosity ratio (Fig2). On the basis of in particular the extensive
data on 47Tuc (Edmonds et al. 2003 and references therein) one finds that the lines of
constant optical to X-ray luminosity ratio
logL0.5−2.5keV(erg/s) = 36.2 − 0.4MV
separates the quiescent low-mass X-ray binaries above it from the cataclysmic variables
below. The line
logL0.5−2.5keV(erg/s) = 34.0 − 0.4MV
roughly separates the cataclysmic variables from the magnetically active binaries.
This latter separatrix leads to a surprise when one compares it with the X-ray lumi-
nosities of nearby stars and of known magnetically active binaries, i.e. RS CVn systems,
near the Sun. For main-sequence stars in the solar neighbourhood, the X-ray luminosity
increases with the rotation speed, up to an upper bound given approximately by
logL0.5−2.5keV(erg/s) = 32.3 − 0.27MV
as illustrated in Fig.2 (left). This bound is lower than the separatrix given by Eq.2.2,
especially for brighter stars. This would imply that active binaries in globular clusters
can have higher X-ray luminosities than similar binaries near the Sun. We suggest, how-
4Frank Verbunt, Dave Pooley, Cees Bassa
ever, that the classification must be reinvestigated, and that some of these objects are
cataclysmic variables. The absence of the blue colour expected for a cataclysmic variable
(see Fig.1) then requires explanation – e.g. as a consequence of the non-simultaneous
measurements at different colours combined with source variability.†
3. Some remarks on theory
Binaries in a globular clusters change due to their internal evolution and/or due to
external encounters. To describe the current cluster binary population one must track
the events for each primordial binary and for each binary that is newly formed via tidal
capture, throughout the cluster. The first estimates of the formation of binaries with
a neutron star necessarily made a number of drastic simplifications. The sum of all
encounters (of a neutron star with a single star, or with a binary) was replaced with an
integral over the cluster volume of the encounter rate per unit volume. Four assumptions
followed: the number density n1,n2of each participant in the encounter scales with the
total mass density ρ, the relative velocity between the encounter participants scales with
the velocity dispersion v, the interaction cross section A is dominated by gravitational
focussing so that A ∝ 1/v2, and the encounter rate is dominated by the encounters in
the dense cluster core. Hence one writes the cluster encounter rate Γ′as
n1n2AvdV ∝ ρo2rc3/v (3.1)
where ρo is the central density and rc the core radius. If one further eliminates the
velocity dispersion through the virial theorem, v ∝ rc√ρo, one has
Γ′∝ ρo1.5rc2≡ Γ
where Γ is referred to as the collision number. With a life time τ the expected number
of binaries of a given type is
N = Γ′τ ∝ Γτ(3.3)
A major advantage of these simple estimates is the clear connection between (the
uncertainty in) the input and (the uncertainty of) the output. Thus, if n1,n2 are the
number densities of neutron stars and of binaries, respectively, Eqs.3.1-3.3 indicate that
the uncertainty in the number N of neutron star binaries scales directly with the uncer-
tainties in n1and n2. Similarly, if we overestimate the life time τ of a binary by a factor
10, the estimated number N is overestimated by the same factor.
Thanks to a concerted effort by various groups fairly detailed computations of the
happenings in globular clusters are now undertaken. This is a fortunate and necessary
development, as many details cannot be understood from the simple scalings above. For
example, the wide progenitors of cataclysmic variables are destroyed by close encounters
before they evolve in a dense cluster core (Davies 1997), but evolve undisturbed into
cataclysmic variables in the outer cluster regions, from where they can sink to the dense
core to form a significant part of the current population there (Ivanova et al. 2006).
A disadvantage of complex computations is that they tend to hide the uncertainties.
If the cross sections A are described in paper I of a series, and the life times τ in paper
III, the large uncertainties in them tend to be less than obvious in paper V where the
† In his contribution to this meeting, Christian Knigge shows that the tentative counterpart
of W24 in 47Tuc, a possible active binary according to Edmonds et al. (2003, Sect.4.5), has blue
FUV-U colours, which suggests that it is a cataclysmic variable. At MV = 2.6 and Lx = 8.7×1030
erg/s, it actually lies below the line given by Eq.2.3.
X-ray sources in globular clusters
Figure 3. Optical (*, scale on left) and
X-ray (+, scale on right) lightcurves of the
dwarf nova YZ Cnc through several outburst
cycles: the outburst in the optical luminos-
ity is accompanied by a marked drop in the
X-ray luminosity. After Verbunt et al. (1999)
final computations are described. The confidence expressed in summaries of the results
of such computations is sometimes rather larger than warranted. An uncertainty in A
or τ has an equally large effect in complex computations as in simple estimates. As a
further illustration we discuss two other uncertainties.
The first relates to the question what happens when mass transfer from a giant to its
binary companion is dynamically unstable. It is usually assumed that a spiral-in follows,
in which the companion enters the envelope of the giant and expells it through friction.
The outcome of this process is computed using conservation of energy, which implies a
drastic shrinking of the orbit (Webbink 1984). However, the study of nearby binaries
consisting of two white dwarfs shows that the mass ratios in them are close to unity
(e.g. Maxted et al. 2002). Such binaries can only be explained if the consequences of
dynamically unstable mass transfer are governed by conservation of angular momentum,
rather than by the energy equation. If the mass leaving the binary has roughly the
same specific angular momentum as the binary, the orbital period changes relatively
little during the unstable mass transfer and concomitant mass loss from the binary (Van
der Sluys et al. 2006). The standard prescription of dynamically unstable mass transfer
hitherto implemented in globular cluster computations must be replaced.
The second uncertainty relates to the conversion of the mass transfer rate in a cata-
clysmic variable to the X-ray luminosity. This conversion does not affect the evolution
of the binary but it is important for comparison with observations, as most cataclysmic
variables in globular clusters are discovered as X-ray sources. It is generally assumed that
the X-ray luminosity scales directly with the mass transfer rate: Lx∝ ˙M. Alas, reality
is more complicated, and indeed in most cases the X-ray luminosity goes down when the
mass transfer rate goes up. This is demonstrated unequivocally in dwarf novae whose X-
ray luminosity drops precipitously during outbursts (Fig.3), but there is evidence that it
is true in the more stable nova-like variables as well (Verbunt et al. 1997). But exceptions
are also known: the dwarf nova SS Cyg has higher X-ray flux during outburst than in
quiescence (Ponman et al. 1995). Theoretical predictions of the numbers of cataclysmic
variables in globular clusters that radiate detectable X-ray fluxes, are not believable when
based on proportionality of X-ray flux and mass-transfer rate.
Observational evidence for the numbers of binaries of various types, and of the depen-
dence of these numbers on cluster properties, may be collected and used to constrain the
theories on formation and evolution of various types of binaries in globular clusters (e.g.
Pooley et al. 2003, Heinke et al. 2006, Pooley & Hut 2006).
In the next Section we describe a new, and we hope more accurate, method of analysing
source numbers: this method is based on direct application of Poisson statistics. This topic
brings one of us, FV, to a brief Intermezzo.