A&A 368, 451-463 (2001)
DOI: 10.1051/0004-6361:20000558
L. Sidoli1 - A. N. Parmar1 - T. Oosterbroek1 - L. Stella2 - F. Verbunt3 - N. Masetti4 - D. Dal Fiume4
1 -
Astrophysics Division, Space Science Department of ESA, ESTEC,
Postbus 299, 2200 AG Noordwijk,
The Netherlands
2 -
Osservatorio Astronomico di Roma, Via Frascati 33,
Monteporzio Catone, 00040 Roma, Italy
3 -
Astronomical Institute, Utrecht University,
PO Box 80000, 3508 TA Utrecht, The Netherlands
4 -
Istituto Tecnologie e Studio Radiazioni Extraterrestri, CNR,
Via Gobetti 101, 40129 Bologna, Italy
Received 16 October 2000 / Accepted 12 December 2000
Abstract
We have performed a detailed study of the broadband spectra of
the luminous (
1036 erg s-1) globular cluster
X-ray sources using BeppoSAX. With the
exception of X 2127+119, located in NGC 7078, all the
other spectra are well represented by a two component model consisting
of a disk-blackbody and Comptonized emission. The measured low-energy
absorptions are in good agreement with those predicted from optical
measurements of the host globular clusters. This implies that there is
little intrinsic X-ray absorption within the binaries themselves, and that
the above spectral model provides a good representation of the low-energy
continua. The sources can be divided into two groups.
In the first group, composed of
3 ultra-compact (orbital period <1 hr) sources, the disk-blackbody
temperatures and inner-radii appear physically realistic
and the Comptonization seed photons temperatures and radii
of the emission areas
are consistent with the disk temperatures
and inner radii.
For all the other sources, the disk-blackbody parameters appear not to be
physically realistic and the Comptonization parameters are unrelated
to those of the disk-blackbody emission.
If this is a spectral signature of ultra-compact binaries,
this implies that no other ultra-compact binaries are
present among those studied here.
It is unclear why this difference between the two types of binaries
should exist.
One possibility may be related to the mass ratio, which is similar
in the ultracompact systems and binaries containing black holes.
In the latter systems the soft components are also well-fit with disk-blackbody
models, which appear to have physically realistic parameters.
Key words: accretion, accretion disks - stars: neutron - globular clusters - X-rays: general
LMXB X-ray spectra are generally modeled by
combining one or more spectral components. At
luminosities 1037 erg s-1 these often consist
of a modified blackbody and some form of power-law like
component thought to result from the Comptonization of
cooler photons. At lower luminosities, the
spectra appear to simplify and are often fit with a power-law with an
exponential cut-off at high energies (White et al. 1988).
In this paper we present the results of a systematic survey of the luminous globular cluster X-ray sources undertaken as part of the BeppoSAX Core Program. We pay particular attention to the spectral properties of the persistent emission. A long-term goal of such studies is to understand how the spectral shape may be used to derive information on physically interesting parameters such as the mass accretion rate, the neutron star mass, radius and spin-rate, the system inclination and the viscosity of the material in the accretion disk. For surveys of LMXBs, the study of those located in globular clusters provides a number of advantanges: (1) the distances to the many globular clusters have been independently determined through main-sequence modeling and other methods (see e.g., Carretta et al. 2000). This allows more accurate estimates of luminosity than is typical for galactic LMXBs. (2) The mean cluster abundances have been determined, allowing any dependence of X-ray properties on abundance to be examined. (3) The cluster reddenings have been measured so providing an independent estimate of low-energy absorption. For a number of clusters the reddening is significantly less than typical for galactic LMXBs.
Results of the BeppoSAX observations of Terzan 1, Terzan 2, NGC 6441, and NGC 7078 are to be found in Guainazzi et al. (1999, 1998), Parmar et al. (1999) and Sidoli et al. (2000), respectively. In addition, NGC 6440, Terzan 6, and Liller 1 were observed by BeppoSAX in other programs. Results are reported in in't Zand et al. (1999, 2000) and Masetti et al. (2000), respectively. For these sources data were extracted from the SSD BeppoSAX archive and reprocessed using the SAX Data Analysis System (SAXDAS).
Table 1 includes informations on the globular clusters which are known to contain luminous X-ray sources and have been analysed here. Most of the cluster distances, metallicities and extinctions are taken from Djorgovski (1993). In the case of Terzan 1 more recent estimates of the distance and extinction obtained using HST are used (Ortolani et al. 1999). For the highly absorbed globular cluster Terzan 6 the results of Barbuy et al. (1997) are used, while the metallicity of Liller 1 is taken from the infrared measurements of Frogal et al. (1995).
The metallicities of the studied globular clusters range from strongly underabundant compared to solar (NGC 7078, [Fe/H] = -2.17), to around solar (Liller 1, [Fe/H] = +0.25). Such a wide range of metallicity should allow any dependence of the X-ray properties on this parameter to be probed. However, we caution that the material being accreted does not necessarily have the same metallicity as the host globular cluster since the companion star may have undergone a non-standard evolution during which its envelope composition was altered.
The extinctions to the studied globular clusters range from low
(
,
NGC 1851) to strongly absorbed
(
,
Liller 1). The amount of extinction
strongly affects the low-energy cut-off of the X-ray data and so the
sensitivity to any low-energy spectral components. As an example,
the X-ray source in NGC 1851 is visible using BeppoSAX
down to 0.1 keV, while that in Liller 1 is only detected
above 1 keV.
A summary of all previous observations of the
Globular Clusters luminous X-ray sources
can be found in Sidoli et al. (2000b).
Results from the Low-Energy Concentrator Spectrometer (LECS;
0.1-10 keV; Parmar et al. 1997), Medium-Energy Concentrator
Spectrometer (MECS; 1.8-10 keV; Boella et al. 1997),
High Pressure Gas Scintillation Proportional Counter
(HPGSPC; 5-120 keV; Manzo et al. 1997) and Phoswich
Detection System (PDS; 15-300 keV; Frontera et al. 1997) on-board
BeppoSAX are presented. All these instruments are coaligned and collectively referred
to as the Narrow Field Instruments (NFI).
The MECS and the LECS are grazing incidence
telescopes with imaging gas scintillation proportional counters in
their focal planes. The non-imaging HPGSPC consists of a single unit with a collimator
that was alternatively rocked on- and 180
off-source
every 96 s during most of the observations. During the observations
in the year 2000 th collimator remained on-source.
The PDS consists of four independent non-imaging
units arranged in pairs each having a separate collimator. Each collimator was alternatively
rocked on- and 210
off-source every 96 s during
the observations.
Globular | X-ray |
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BeppoSAX Observation | T | R | Inst. | d | Cluster | ![]() |
|
Cluster | Source | (hr) | Start | Stop | (ks) | (keV) | (kpc) | [Fe/H] | ||
NGC 1851 | X 0512-401 | <0.85 | 2000 Feb. 23 12:44 | Feb. 25 07:44 | 72.2 | 0.1-25 | LM-P | 12.2 | -1.29 | 0.1 |
Terzan 2 | X 1724-304 | 1996 Aug. 17 04:29 | Aug. 18 05:05 | 37.1 | 0.3-100 | LMHP | 10.0 | -0.25 | 4.0 | |
Liller 1 | X 1730-335 | 1998 Feb. 27 03:30 | Feb. 27 19:22 | 16.2 | 1.0-10 | LM- | 7.9 | +0.25 | ![]() |
|
1998 Mar. 02 19:57 | Mar. 03 12:35 | 29.8 | 1.0-10 | LM- | ||||||
Terzan 1 | X 1732-304 | 1999 Apr. 03 12:52 | Apr. 04 15:29 | 47.1 | 2.0-10 | -M- | 5.2 | -0.71 | 6.8 | |
NGC 6440 | X 1745-203 | 1998 Aug. 26 02:11 | Aug. 26 14:36 | 21.6 | 0.4-100 | LMHP | 7.0 | -0.34 | 3.5 | |
NGC 6441 | X 1746-370 | 5.7 | 1999 Apr. 04 18:07 | Apr. 05 20:23 | 49.9 | 0.25-30 | LMHP | 10.7 | -0.53 | 1.3 |
Terzan 6 | X 1747-313 | 12.4 | 1998 Sep. 06 06:16 | Sep. 06 19:02 | 28.9 | 0.5-50 | LMHP | 7.0 | -0.61 | 7.4 |
NGC 6624 | X 1820-303 | 0.2 | 1997 Oct. 02 06:45 | Oct. 02 19:90 | 22.3 | 0.3-30 | LMHP | 8.1 | -0.37 | 0.9 |
1998 Apr. 17 04:14 | Apr. 18 03:12 | 37.5 | 0.3-30 | LMHP | ||||||
1998 Sep. 23 12:44 | Sep. 24 15:30 | 48.3 | 0.3-30 | LMHP | ||||||
NGC 6712 | X 1850-087 | 0.3 | 1997 Apr. 24 11:47 | Apr. 25 11:09 | 42.0 | 0.3-50 | LMHP | 6.8 | -1.01 | 1.4 |
NGC 7078 | X 2127+119 | 17.1 | 1999 Nov. 16 01:15 | Nov. 17 00:50 | 35.5 | 0.1-100 | LM-P | 10.5 | -2.17 | 0.2 |
Table 1 lists the BeppoSAX observations used in this survey together with some basic information about each globular cluster (see Sect. 2). The observations of Terzan 2 and NGC 6712 were made prior to the failure of one of the MECS units. Data from the entire observations were accumulated, except for the following sources: (1) X 1730-335 (the Rapid Burster, hereafter RB). BeppoSAX carried out a total of 7 observations, partly analysed by Masetti et al. (2000), which were extracted from the archive and examined for the presence of bursts. Only two observations included sufficiently long quiescent intervals for this study (see Table 1). (2) For the 5.7 hour dip source X 1746-371 the dipping and bursting intervals discussed in Parmar et al. (1999) were excluded. (3) The eclipse observed from the 12.4 hr eclipsing system X 1747-313 (In't Zand et al. 2000) was excluded. (4) The bursts seen from X 0512-401, X 1724-304, and X 1745-203 were excluded. Table 1 also indicates the instruments that were used in the spectral analysis of each source. In the case of the faintest source studied (Terzan 1, 0.014 MECS counts s-1) only the MECS was used, while for the slightly brighter Liller 1 observations the LECS and MECS were used. If available, all the NFI were used for the brightest sources.
Since previous analyses used different software and calibration
releases, all relevant data were re-extracted.
As usual, good data were selected from intervals when the
elevation angle above the Earth's limb was >
for the LECS and
>
for other instruments and when the instrument
configurations were nominal. This was done by using the SAXDAS 2.0.0 data analysis package.
LECS and MECS data were extracted centered on the source positions
using radii of 8
and 4
,
respectively,
corresponding to about 95% of the total source photons.
In the case of the RB extraction radii of 4
and
2
were used in order to minimize the contribution from the
32
distant bright X-ray source 4U 1728-337.
Similarly, data from the non-imaging instruments were not included
in the RB fits. Background subtraction for the imaging instruments
was performed using standard files; this is not a critical procedure for the
bright sources studied here (with the exception of Terzan 1).
Background subtraction for the non-imaging instruments was carried out
using the offset pointing intervals.
In the case of observations were the HPGSPC remained
coaligned, background subtraction was
performed using data obtained when the instrument
was looking at the dark Earth.
The overall spectra extracted as described above
were first investigated by simultaneously
fitting data from as broad a band as possible.
The LECS and MECS spectra were rebinned to oversample the full
width half maximum of the energy resolution by
a factor 3 and to have additionally a minimum of 20 counts
per bin to allow use of
statistics.
The HPGSPC and PDS spectra were rebinned using the standard techniques in SAXDAS.
Data were selected from within the energy ranges
0.1-8.0 keV (LECS), 1.8-10 keV (MECS), 8.0-20 keV (HPGSPC),
and 15-100 keV (PDS) whenever a sufficient number of
counts were obtained (see Table 1).
The photo-electric absorption
cross sections of Morrison & McCammon (1983)
and the solar abundances of Anders & Grevesse (1989)
are used throughout. Factors were included in the spectral fitting to allow for normalization
uncertainties between the instruments. These factors were constrained
to be within their usual ranges during the fitting (Fiore et al. 1999).
An additional uncertainty of 1% was added quadratically to the uncertainties to account for systematic uncertainties in instrumental responses.
Since we wish to investigate the spectral properties of the sources,
we first attempted to find a general spectral model that could be successfully
applied to all the sources. Many luminous LMXB are fit with a two component
model consisting of a blackbody, or blackbody-like component which might
represent emission from an optically thick accretion disk or from the
neutron star surface, together with a Comptonized component
which may be interpreted as emission
from a hot inner disk region or a boundary layer between the disk and the neutron star.
For the soft component we tried both a single blackbody model and
a disk-blackbody component, in the formulation of
Mitsuda et al. (1984) and Makishima et al. (1986).
The disk-blackbody model assumes that the gravitational energy
released by the accreting material is locally dissipated into
blackbody radiation, that the accretion flow is continuous throughout
the disk, and that the effects of electron scattering are negligible.
There are only two parameters in this model,
where
is the innermost
radius of the disk, i is the inclination angle of the disk and
the blackbody effective temperature at
.
Some limitations of this model are discussed in
Merloni et al. (2000).
For the Comptonized component the XSPEC model
COMPTT (Titarchuk 1994;
Hua & Titarchuk 1995; Titarchuk & Lyubarskij 1995),
which self-consistently calculates the spectrum produced
by the Comptonization of soft photons in a hot plasma,
was used. This model contains as free parameters the temperature of the Comptonizing
electrons,
,
the plasma optical depth with respect to
electron scattering
and the input
temperature of the soft photon (Wien) distribution (
). A
spherical geometry was assumed for the comptonizing region.
Fit result to the broad-band spectra with the single blackbody plus Comptonization and disk-blackbody plus Comptonization are reported in Tables 2 and 3 respectively. A single temperature blackbody plus a cut-off power-law model was also tried, but with unacceptable results in the majority of the sources. Since the disk-blackbody plus Comptonization emission (Table 3) always gives a better (or equally good) fit than single blackbody plus Comptonization emission (Table 2), we will refer to it as the "standard'' model.
Globular | L | ![]() |
kT0 |
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Cluster | (keV) | (keV) | (keV) | (km) | |||||
NGC 1851 | 43 |
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0.14 | 153.2/97 |
Terzan 2 | 200 |
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0.15 | 197.1/178 |
Liller 1 | 8.7 |
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<4.2 |
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<1.5 | <4.0 | <0.14 | 100.7/90 |
2.5 |
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... | ... | ... | 71.0/57 | |
Terzan 1 | 0.059 | <0.66 | <0.48 | >2.2 | <20 | ... | ... | ... | 18.4/11 |
NGC 6440 | 66 |
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0.05 | 101.5/107 |
NGC 6441 | 140 |
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0.04 | 117.6/106 |
Terzan 6 | 59 |
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0.29 | 144.5/119 |
NGC 6624 | 420 |
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0.05 | 268.2/120 |
500 | <0.015 |
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0.05 | 232.5/117 | |
560 |
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0.09 | 588.4/134 | |
NGC 6712 | 13 |
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0.34 | 181.1/154 |
NGC 7078 | 90 |
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0.24 | 375.5/124 |
Globular | L | ![]() |
kT0 |
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f | ![]() |
Cluster | (keV) | (keV) | (keV) | (km) | |||||
NGC 1851 | 47 |
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0.14 | 126.1/97 |
Terzan 2 | 220 |
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0.12 | 191.5/178 |
Liller 1 | 9.6 |
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<0.50 | <37000 | <0.05 | 100.6/90 |
2.5 |
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... | ... | ... | 71.0/57 | |
Terzan 1 | 0.059 | <0.66 | <0.48 | >2.2 | <20 | ... | ... | ... | 18.4/11 |
NGC 6440 | 71 |
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0.14 | 84.8/107 |
NGC 6441 | 140 |
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10 | 107.3/106 |
Terzan 6 | 67 |
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2.16 | 136.5/119 |
NGC 6624 | 480 |
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2.72 0.01 0.01 |
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0.36 | 152.1/120 |
570 |
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0.18 | 182.2/117 | |
660 |
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0.12 | 627.7/134 | |
NGC 6712 | 19 |
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0.76 | 160.0/154 |
NGC 7078 | 65 |
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2.0 | 284.8/124 |
The results of fitting the standard model to all of the extracted spectra
are given in Table 3.
All spectral uncertainties and upper-limits are given at 90% confidence.
The fits to all the spectra are acceptable with the exception of NGC 7078 where the
is 284.8 for 124 degrees of freedom (dof), and the second and third observation
of the source in NGC 6624. Since a different model is
a better representation of the NGC 7078 X-ray spectrum, probably
due to the ADC nature of this source (see Sidoli et al. 2000), we
exclude it from the discussion, though the results of the fitting
procedures have been included in Tables 2 and 3,
for completeness. We note that an acceptable
fit (a
of 100.0 for 109 dof) can also be obtained without the
disk-blackbody component for NGC 6440.
In the case of Liller 1 and Terzan 1 the sources are too faint to derive accurate
spectral parameters. Moreover Liller 1 was not sampled at
energies greater than 10 keV due to the reasons explained in Sect. 3.
We include results from these sources in Tables 2 and 3 for completeness, but do not consider them further.
Figure 1 shows the photon spectra of the remaining sources derived using the standard model. This figure clearly
illustrates the importance of the broad-band coverage afforded by
BeppoSAX in clearly separating the two components. Bolometric
luminosities have been calculated using the energy range 0.1-100 keV
and assuming that the observed
is interstellar.
The results in Sect. 4.1 indicate that for the majority
of sources this assumption is valid.
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Figure 1: The BeppoSAX spectra of each of the globular cluster X-ray sources obtained using the standard model, in order of increasing 0.1-100 keV luminosity. The contributions of the two components (where evident) are shown separately. Except for NGC6441 the COMPTT is the one extending to higher energies |
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We first compared the fitted values of low-energy absorption, ,
with the values predicted using the relation between the optical extinction,
,
and absorption of
derived by
Predehl & Schmitt (1995). If there is no additional absorption
present in the X-ray binaries themselves,
and their low-energy X-ray continua have been properly characterized,
then a good agreement is expected between the
values derived from the globular cluster
measurements,
and those from the LMXB X-ray spectra.
Figure 2 shows the measured values of
taken from
Table 3 plotted against the optically
derived values of
.
The straight line shows the locus
of points with equal optical and X-ray derived
values.
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Figure 2:
The measured values of ![]() ![]() ![]() ![]() ![]() |
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In general, there is good agreement between the two absorption measurements.
In the case of X 1745-203, located in NGC 6440
the X-ray derived
is
0.75 that expected (a difference
of
1.5 1021 atom cm-2). This may suggest the presence
of an additional soft X-ray component that, not being included
in the spectral model, leads to an underestimate of the absorbing column.
Alternatively, the overall X-ray continuum model might be incorrect.
We note that also the blackbody plus COMPTT model does not provide a good
estimate of the column density, being even much lower.
In't Zand et al. (1999) find that the spectrum of
X 1745-203 may also be modeled using either a broken power-law
and blackbody, or a high-energy cut-off power-law, or a bremsstrahlung
and blackbody. In these 3 cases, the derived values of
are in the range 6.7-9.0 1021 atom cm-2,
similar to that predicted from the
measurement of
6.2 1021 atom cm-2. In the case of X 1850-087
located in NGC 6712 the X-ray derived
,
of
3.9 1021 atom cm-2, is
significantly higher than that derived from the optical of
2.5 1021 atom cm-2.
This may suggest the presence of extra absorbing material in this system.
However, when fitting this spectrum with a single blackbody plus Comptonization,
a much lower column density is found (
1.7 1021 atom cm-2).
The soft emission from luminous globular cluster sources
is succesfully fit with a multicolor disk-blackbody component.
If we interprete this model "literally", its
normalization translates into a lower limit for the innermost radius
of
the accretion disk,
.
Except for NGC 1851 and NGC 6624
(where the inclination cannot be constrained),
the values observed are generally low,
thus requiring a quite high inclination angle of the binary
systems, for
to be larger than
the last stable orbit for an accretion disk around a neutron star (
(
) km). We note that still higher inclinations would be derived if the Merloni et al. (2000) correction to the disk-blackbody model were taken into account.
For several globular cluster sources, a confirmation
of their high inclination angles comes from X-ray and optical observations.
In particular, the presence of strong sinusoidal-like modulations in the X-ray flux
(as in the case of the ADC source NGC 7078), partial X-ray eclipses
of the central source by the companion star (Terzan 6), X-ray dips (NGC 6441)
are all indicative of inclination angles >60-70
(Frank et al. 1987).
The temperature
at the inner disk radius is 0.5-3.5 keV,
with the three ultra-compact binaries (NGC 1851, NGC 6712, NGC 6624;
hr) displaying significantly lower
temperatures (<1 keV) compared to all other sources (1.5-3.5 keV).
The variation of
and inner radius of the
accretion disk is displayed in Fig. 3, while the variation
with the disk luminosity, measured in the 0.1-100 keV energy range,
is shown in Figs. 4 and 5.
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Figure 3:
Variation of the disk-blackbody temperature
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Figure 4: Variation of the lower limit to the inner radius of the accretion disk and the luminosity of the disk-blackbody component, in the 0.1-100 keV band (in units of 1035 erg s-1) |
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In the disk-blackbody model, the bolometric luminosity,
,
of the accretion disk can be related to the temperature
and the mass M
of the compact object (see e.g., Eqs. (9) and (11) in Makishima et al. 2000) as
.
A summary of the parameters derived from the disk-blackbody component is
shown in Fig. 5, where the globular cluster sources
appear to be divided into two groups: the ultra-compact binaries,
with
1 keV, the inferred masses of which are compatible with that of a neutron star, and sources with
1 keV,
located on grids with much lower inferred masses for the compact object.
Since all these X-ray binaries (except Terzan 6)
are known to harbor a neutron star, due to their Type I X-ray bursting activity,
either the multi-colour disk-blackbody is not an accurate model for the soft part of the spectrum, or their luminosity has been underestimated, possibly due to a very high inclination
angle of the binary systems. Another explanation may be that the parameters
derived in the framework of the disk-blackbody
model cannot be related directly to physical quantities
(see Merloni et al. 2000).
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Figure 5:
Relation between the disk-blackbody luminosity
measured in the 0.1-100 keV energy range (in units of 1035 erg s-1) and the
temperature
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Thermal Comptonization (Titarchuk 1994)
provides a good fit to the high energy region
of the globular cluster sources spectra.
The relations between the different parameters derived from the spectral analysis are shown in
Figs. 6-11. The Comptonizing plasma
has temperatures
ranging from few keV up to the extremely high value of
92 keV
in the case of the ADC source in NGC 7078.
The seed photons in all sources have temperatures kT0<1 keV
while the Comptonization parameter y,
defined as
,
is in the range
1-7, except for the very low value of
0.03 for the source in
NGC 6441, that might be not in the right regime, since y
1 and
<1.
The trend of y with the luminosity
is shown in Fig. 6,
suggesting that at least for some sources
a correlation exists.The dependence of the plasma optical depths
and of the
electron temperatures
from the total luminosities are shown in Figs. 7 and 8.
Following in't Zand et al. (1999), an equivalent spherical
radius
of the emission area
of the seed photons can be defined as
km,
where d is the distance (in kpc),
is the comptonized flux
(in erg cm-2 s-1, corrected for the
interstellar absorption, 0.1-100 keV band) and kT0 is the seed temperature in keV.
ranges from few km
up to
1300 km (NGC 7078) and seems to correlate
with the total luminosity (see Fig. 9),
as
L0.5 .
This might suggest that the seed photons originate
from the boundary layer (the radial extent and height of which
become larger with increasing accretion rates;
e.g. Popham & Sunyaev 2000)
rather than from the accretion disk.
The comparison between
and the lower limit
to the
inner radius of the accretion disk is shown in Fig. 10.
In this respect, the comparison between the temperatures
of the seed photons and the temperature
is interesting
(see Fig. 11): among the globular cluster
sources, only the ultra-compact binaries
(located in NGC 1851, NGC 6624 and NGC 6712)
display temperatures
consistent with
the temperature of the inner regions
of the accretion disk.
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Figure 6: The Comptonization parameter y versus the total luminosity in the 0.1-100 keV band (in units of 1035 erg s-1) |
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Figure 7:
The optical depth ![]() |
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Figure 8:
The electron temperature
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Figure 9:
The radius ![]() |
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Figure 10:
Plot of the ratio between the lower limit
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Figure 11:
Comparison between the temperature of the seed photons, as estimated from the
Comptonization model, and the temperature
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The galactic globular clusters hosting bright LMXBs are found to be both denser (except NGC 6712) and more metal-rich (except NGC 7078) (see Fig. 12), indicative of the fact that both the high density stellar environment and the metallicity could play a role in the formation mechanism of LMXBs, thought to be via tidal captures or "two plus one" stellar encounters (see Bellazzini et al. 1995).
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Figure 12:
Globular clusters
concentrations "c''
(
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Besides the formation mechanism, it is interesting to investigate if
the metallicity of the accreting matter (assumed to be the same of the
hosting globular cluster) plays a role in the LMXBs spectral properties.
In Figs. 13-19 several parameters derived from the spectral analysis are plotted versus the metallicity ([Fe/H]) of the hosting globular cluster.
The positive correlation between disk temperature
and
the metallicity displayed in Fig. 13 is opposite to
the results of Irwin & Bregman (1999),
who studied in the ROSAT energy band the
dependence of the X-ray properties of LMXBs on
the metallicity of their environment, and found that
the spectra of LMXBs become softer as the metallicity
of their environment increases.
However, we note that our correlation has a quite large
probability of 11% to be obtained by chance; moreover, it might be spurious also
for the reason that the three ultra-compact binaries, where
the accreting matter should be essentially helium, are not expected
to show a trend with the metallicity of the hosting globular cluster.
Note that the same effect may be present when considering the
apparent correlation between the total X-ray luminosity and the metallicity
(see Fig. 15, probability of chance correlation
of 20%). Moreover, no correlation is evident within the much more numerous
X-ray sources residing in the M 31 globular clusters
(Verbunt et al. 1984), in the same range of metallicity.
An apparent anticorrelation of the temperature of the seed photons kT0 with
the metallicity is present, for sources in globular clusters more metallic than 0.1 solar
(see Fig. 17).
For the electron temperature
and the
optical depth of the comptonizing plasma
there are
no obvious correlations with the metallicity
of the accreting matter.
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Figure 13:
Variation of the disk-blackbody temperature
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Figure 14: Variation of the lower limit to the disk-blackbody inner radius with the globular cluster metallicity ([Fe/H]) |
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Figure 15:
Total luminosity
(0.1-100 keV, in units of 1035 erg s-1)
versus globular clusters metallicity ([Fe/H]).
A possible correlation exists,
with higher luminosities as the metallicity increases.
However the same caution as for the
possible correlation of
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Figure 16:
The electron temperature
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Figure 17: The temperature kT0 of the seed photons in the Comptonization model, versus the globular cluster metallicity ([Fe/H]). An anticorrelation exists for globular clusters more metallic than about 0.1 solar |
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Figure 18:
The plasma optical depth ![]() |
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Figure 19:
The radius ![]() |
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All the sources analysed here do not display significant iron line emission, except
for the source in NGC 6624, where a very weak narrow line is detected.
The addition of a narrow
iron line to the standard model,
resulted in the upper limits to the EWreported in Table 4.
Cluster | EW (eV) |
NGC 1851 | <11 |
Terzan 2 | <25 |
Liller 1 | <105 |
Terzan 1 | <2200 |
NGC 6440 | <45 |
NGC 6441 | <15 |
Terzan 6 | <25 |
NGC 6624 | 13
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NGC 6712 | <13 |
NGC 7078 | <33 |
We have performed a systematic survey of the properties of the luminous X-ray sources located in globular clusters. A remarkable property of this sample of LMXBs containing neutron stars is their well known distance and interstellar absorption. This, together with the broad-band capabilities of the BeppoSAX Narrow Field Instruments, allowed us to properly model the 0.1-100 keV spectra, to accurately determine the X-ray luminosity for these sources and to study their general spectral properties in a range of luminosity spanning more than two order of magnitudes.
The spectral fitting gave satisfactory results with our spectral "standard" model, consisting of a disk-blackbody plus a Comptonized emission. Other two-component models, such as a cut-off power-law plus a single-blackbody or a single-blackbody plus Comptonization emission, almost always resulted in poorer quality fits.
However, although our standard model provides a good fit to the spectra of almost all the LMXBs studied, several problems arise with the physical interpretation of the resulting spectral parameters, especially when dealing with the disk-blackbody component.
Indeed, the resulting inner disk radii are too small,
even for extreme inclination
angles of the accretion disks, and, on the other hand,
the inner disk temperature
are high compared with other systems in the galactic plane,
for which
1.5 is usually found
(e.g. Tanaka & Lewin 1995).
For comparison, this same spectral model has been applied
to the BeppoSAX data of two X-ray bursters,
Ser X-1 and GX 3+1, finding a
of
km and
km, respectively,
and a disk temperature,
,
of 1.46 and 1.95 keV
(Oosterbroek et al. 2000).
The only globular cluster sources for which the
multicolor disk-blackbody model seems to reasonably represent the likely
physical parameters of the disk are the ultra-compact binaries, located in NGC 1851,
NGC 6712 and NGC 6624. In these three sources the disk-blackbody provides
reasonable disk radii, and lower
inner disk temperatures. Moreover, since in these three sources the
temperature of the seed photons
kT0 and the radius are in agreement with
and
respectively,
it is tempting to identify the inner disk as the region for the seed photons of
the Comptonization emission. However, we note that the finding of a lower disk temperature
for the ultra-compact binaries
could be partly due to the low interstellar absorption (as estimated
from optical observations) towards these sources,
with respect to other globular cluster sources (see Fig. 20).
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Figure 20:
The inner disk temperature
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For sources where temperatures kT0 were significantly
different from
(NGC 6440, NGC 6441, Terzan 2 and Terzan 6),
we tried also to fit their spectra with the "standard" model
linking the temperatures kT0 and
together.
The main result of this fit with respect to
those reported in Table 3 is the values of the
disk-blackbody parameters: the temperatures
were in the range 0.5-0.8 keV, the ratio f was less than 0.15 for
all the three sources (remarkable, since previous analysis of the NGC 6441 spectrum
resulted in a ratio f=10) and the disk-blackbody radii became 1-8.5 km.
However, this alternative fit resulted
in worse
except for NGC 6440, for which an equally good
was
obtained.
Another problem with the standard model arises
from the relative contribution of the
disk to the Comptonized component.
Indeed, the ratio f of the disk-blackbody 0.1-100 keV
luminosity to the Comptonized one,
should be 1 (Sunyaev & Shakura 1986).
But we find f>1 for the sources NGC 7078 (the ADC source;
),
Terzan 6 (
)
up to the very
high value of NGC 6441 (f=10).
On the other hand, when a single-blackbody is used instead of the disk-blackbody,
the ratio
is always less than 1 (see Table 2).
NGC 6441 is an intriguing source: if a blackbody is used instead of
the disk-blackbody, the Comptonization dominates
the emission and the high energy region of the spectrum, whereas when a disk-blackbody model is used, the opposite is valid.
For the LMXBs where the interpretation of the soft component as
contributed by the inner disk is reasonable, it is possible to estimate
the strength of the neutron star magnetic field.
The total luminosity
of an accreting neutron star can
be expressed as the sum of the luminosity liberated
in the accretion disk
and the remaining luminosity dissipated
at the neutron star radius
,
where
and
(e.g., Priedhorsky 1986).
is the magnetospheric radius
km, where
G is the magnetic field,
10 km,
is the neutron star mass,
erg s-1 and the parameter
accounts
for the disk geometry of the accretion and is
,
(Ghosh & Lamb 1979, 1992).
Thus, the magnetic field strength of a neutron star
can be estimated from the luminosity of the disk.
In Fig. 21 a grid with different neutron star
magnetic fields, calculated assuming R6=1, M2=1 and
=1, is superimposed on a plot of the ratio of disk to total
luminosity, versus the total luminosity (0.1-100 keV).
The ratio of
to
is a measure of
(Priedhorsky 1986):
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(1) |
The magnetic field estimated in this way for the
source X 1820-30 in NGC 6624 (2.1 108 G)
is in agreement with the value derived from the saturation
of the kHz QPO frequencies (Campana 2000).
In the case of the RB, we find a magnetic field (8 108 G)
consistent, within a factor of 2, with that
estimated by Masetti et al. (2000) using the propeller effect model.
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Figure 21:
An estimate of the neutron star magnetic field strength
depending on the disk and total luminosities in the 0.1-100 keV,
in units of 1037 erg s-1.
Straight lines are loci of constant magnetic field
(0.1, 0.5, 1, 2, 5 and 10 108 G, increasing from top to bottom),
assuming a 2![]() |
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We performed broad-band spectroscopy of the luminous X-ray sources located in a number of galactic globular clusters with BeppoSAX. The results can be summarized as follows:
On the other hand, problems exist with a physical interpretation of the spectral parameters of the disk-blackbody component, since we obtained resonable values for the radii of the inner disks only in the case of the ultra-compact binaries. From the similarities between radii and temperatures of the inner accretion disk and the parameters of the "seed" photons in the Comptonization emission, we propose that in the ultra-compact binaries in NGC 1851, NGC 6712 and NGC 6624 the Componization is fed by the inner regions of the accretion disk, while this is not the case for all other sources (in NGC 6440, NGC 6441, Terzan 2 and Terzan 6). It is unclear why the disk-blackbody model gives physically reasonable results only in the case of the ultra-compact binaries. A possibility may be related to the mass ratio which is similar in the ultracompact binaries and binary systems containing black holes. Indeed, physically reasonable parameters are usually obtained from disk-blackbody fits to the soft emission from black hole X-ray binaries (see, e.g., Tanaka & Lewin 1995).
Acknowledgements
The BeppoSAX satellite is a joint Italian-Dutch programme. We thank the staffs of the BeppoSAX Science Data and Operations Control Centers for help with these observations. L. Sidoli acknowledges an ESA Fellowship.