A&A 392, 909-920 (2002)
DOI: 10.1051/0004-6361:20021184
J. S. Clark1 - S. P. Goodwin2 - P. A. Crowther1 - L. Kaper3 - M. Fairbairn4 - N. Langer5 - C. Brocksopp6
1 - Department of Physics and Astronomy, University College London,
Gower Street, London, WC1E 6BT, England, UK
2 - Department of Physics and Astronomy, University of Wales, Cardiff,
CF24 3YB, Wales, UK
3 - Astronomical Institute "Anton Pannekoek'', University of Amsterdam and Center for High-Energy
Astrophysics, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
4 - Service de Physique Théorique, CP225,
Université Libre de Bruxelles, 1050 Brussels, Belgium
5 - Astronomical Institute, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands
6 - Astrophysics Research Institute, Liverpool John Moores
University, Liverpool, L41 1LD, UK
Received 22 March 2002 / Accepted 20 June 2002
Abstract
We present the results of a detailed non-LTE analysis of the
ultraviolet and optical spectrum of the O6.5 Iaf+ star
HD 153919 - the mass donor in the high-mass X-ray binary
4U1700-37. We find that the star has a luminosity
log
,
K, radius
,
mass-loss rate
yr-1, and a significant
overabundance of nitrogen (and possibly carbon) relative to solar
values. Given the eclipsing nature of the system these results allow
us to determine the most likely masses of both components of the
binary via Monte Carlo simulations. These suggest a mass for
HD 153919 of
- implying the
initial mass of the companion was rather high
(
60
). The most likely mass for the compact companion
is found to be
,
with only 3.5 per
cent of the trials resulting in a mass less than 2.0
and
none less than 1.65
.
Such a value is significantly in
excess of the upper observational limit to the masses of neutron stars
of 1.45
found by Thorsett & Chakrabarthy
(1999), although a mass of 1.86
has recently
been reported for the Vela X-1 pulsar (Barziv et al. 2001). Our observational data is inconsistent with the
canonical neutron star mass and the lowest black hole mass observed
(
4.4
;
Nova Vel). Significantly changing
observational parameters can force the compact object mass into
either of these regimes but, given the strong proportionality between
and Mx, the O-star mass changes by factors of greater than 2,
well beyond the limits determined from its evolutionary state and
surface gravity. The low mass of the compact object implies that it
is difficult to form high mass black holes through both the Case A &
B mass transfer channels and, if the compact object is a neutron star,
would significantly constrain the high density nuclear equation of
state.
Key words: stars: early-type - stars: individual: HD153919, 4U1700-37 - X-rays: stars - stars: binaries: general
First detected by the Uhuru satellite (Jones et al. 1973) the eclipsing X-ray source 4U 1700-37 was quickly associated with the luminous O6.5 Iaf+ star HD 153919, confirming 4U 1700-37 as a high-mass X-ray binary (henceforth HMXB). HMXBs are systems composed of an OB star and a compact companion (neutron star or black hole), with the X-ray emission resulting from the accretion of material by the compact companion. In the subclass of supergiant HMXB systems material is accreted either via Roche lobe overflow or directly from the powerful stellar wind of the OB primary. Given that HD 153919 slightly underfills its Roche Lobe (e.g. Conti 1978) mass transfer proceeds via the latter mechanism.
Although an orbital period of 3.412 days (Jones et al. 1973) was quickly identified for 4U 1700-37,
extensive searches (e.g. Rubin et al. 1996 and references
therein) have failed to identify any other X-ray periodicities within
the system that might correspond to the pulse period for a possible
neutron star (although Konig & Maisack 1997 claim the
presence of a 13.81 day period in CGRO BATSE & RXTE ASM datasets).
Given the absence of any X-ray pulsations and the unusually hard
nature of the spectrum various authors (e.g. Brown et al. 1996) have suggested that the compact companion could
be a low mass black hole rather than a neutron star. However, Reynolds
et al. (1999) point out that the 2-200 keV spectrum of
4U 1700-37 differs from those commonly observed for black
hole candidates such as Cygnus X-1. Given that the X-ray
spectrum of 4U 1700-37 is qualitatively similar to those of
accreting neutron stars they suggest that the compact object is also a
neutron star, and explain the lack of pulsations as due to either a
weak magnetic field or an alignment of the magnetic field with the
spin axis.
With a spectral type of O6.5 Iaf+, HD 153919 is the
hottest and potentially most massive mass donor of any of the the HMXB
systems. As such, determination of its fundamental parameters (radius,
temperature, mass and chemical composition) is of importance given
that these will potentially provide valuable insights into the
evolution of very massive stars and their ultimate fate. In
particular by determining the masses of the components of HMXB
systems, limits to the progenitor masses for neutron stars and black
holes in such systems can be found while
the chemical composition of the mass donor can shed light on the
pre-supernova (SN) mass transfer mechanisms.
The paper is ordered as follows. Section 2 describes the determination of the physical properties of HD 153919; the complete dataset and the non-Local Thermal Equilibrium (non-LTE) code used to analyse it. Section 3 describes the Monte-Carlo technique used to determine the masses of both components of the binary system. In Sects. 4 and 5 we discuss the implications of our results for the evolution of hot massive stars, limits for the progenitor masses of compact objects and the equation of state for nuclear matter. Finally in Sect. 6 we summarize the main results of the paper.
As will be shown in Sect. 3, determination of the masses of both components in the system is hampered by the considerable uncertainties in the stellar radius of HD 153919. In order to address this problem, and in the light of dramatic advances in the sophistication of non-LTE model atmospheres we have decided to reanalyse both new and published ultraviolet to near-infrared spectroscopic and optical to mid-infrared photometric observations of HD 153919 in order to refine previous estimates of the stellar parameters.
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Figure 1: Plots of selected regions of the optical spectrum of HD 153919 (solid line) and best fit model (dotted line); parameters listed in Table 1. |
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To determine the stellar properties of HD 153919 we have utilised the non-LTE code of Hillier & Miller (1998) which solves the radiative transfer equation subject to the constraints of statistical and radiative equilibrium, in a spherical, extended atmosphere. Line blanketing is incorporated directly through the use of a super-level approach. We use a similar atomic model to that employed by Crowther et al. (2002) in their study of early O supergiants, including H I, He I-II, C III-IV, N III-V, O III-VI, Si IV, P IV-V, S IV-VI and Fe IV-VII. For extreme O supergiants, line blanketing and the strong stellar wind conspire to produce significant differences in stellar parameters relative to the standard plane-parallel hydrostatic results (see Crowther et al. 2002 for further details).
Our procedure is as follows. We adjust the stellar
temperature and mass-loss rate of an individual
model until the "photospheric'' He II
4542 and He
I
4471 lines are reproduced. Simultaneously, we vary the
total mass-loss rate until H
is also matched. The exponent of
the
-law is adjusted until the shape of H
is well
reproduced - for HD 153919 we obtain
.
The
input atmospheric structure, connecting the spherically extended
hydrostatic layers to the
-law wind is achieved via a
parameterized scale height, h (see Hillier et al. 2002
for details), for which h=0.001 yields a reasonable match to
He I and Balmer line wings, consistent with
.
We adopt a terminal wind velocity of
km s-1 (vL01; Howarth et al. 1997).
The formal solution of the radiative transfer equation yielding the
final emergent spectrum is computed separately, and includes standard
Stark broadening tables for H I, He I-II. Except where
noted, these calculations assume a microturbulent velocity
km s-1. Hillier et al. (2002) also
discuss the effect of varying
in O star
models. Additionally, we find good agreement with observations using
km s-1 (Howarth et al. 1997 derived 120 km s-1).
It is extremely difficult to determine accurate He/H abundances in O
supergiants as discussed by Hillier et
al. (2002). Consequently, we adopt
by number,
whilst C and N abundances are varied until diagnostic optical line
profiles are reproduced. In Fig. 1 we present selected optical line
profile fits to FEROS observations of HD 153919. Overall, agreement
for
kK is very good, with the exception of He
II
4686. He I
4471 provides our main
temperature constraint since other blue optical He I lines are
weak or absent. Alternatively, we considered using He I
5876 (or
10830) together with the He II
4686 line. However, this method (followed by Crowther &
Bohannan 1997) yields significantly (
4 kK) lower
stellar temperatures, and suffers from inconsistencies involving the
ionization balance of UV/optical metal lines. Therefore, we have
greater confidence in our adopted diagnostics, which do not suffer
from such problems.
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Figure 2: Plot of the observed (solid line and data points) and theoretical (dotted line) UV-mid-IR spectral energy distribution for HD 153919. |
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Figure 3: Plots of selected regions of the UV spectrum of HD 153919 (solid line) and best fit model (dotted line); parameters listed in Table 1. Note that our model does not take into account the observed Raman-scattered emission lines (which are not of a photospheric origin) in the range 1400-1700 Å. |
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From spectral energy distribution fits to IUE spectrophotometry and
Johnson photometry (Fig. 2), we derive
mag. Alternatively, using the intrinsic colour of
(B-V)0=-0.30from the early O supergiant calibration of Schmidt-Kaler (1982),
we derive
EB-V=0.55 from Johnson photometry of HD 153919
(V=6.54 and B-V=0.25, Bolton & Herbst 1976).
Consequently, we adopt
for the remainder
of this work. We adopt a distance modulus of 11.4 mag to HD 153919
(Ankay et al. 2001), implying
MV=-6.53 mag. Our derived
temperature provides a bolometric correction of -3.3 mag, therefore
we obtain
for HD 153919, and thus R=21.9
.
The derived mass-loss rate is
yr-1, assuming that the H
line-forming region
is not clumped. Moderate clumping would reduce this value by a factor
of
2. Derived parameters are listed in Table 1, and are in
reasonable agreement with those derived by vL01 through the analysis
of ultraviolet resonance lines based on the Sobolev with Exact
Integration (SEI) method.
Our primary nitrogen abundance diagnostics are N III 4634-41 and
4097, which together imply
.
With this value, the
very weak N III
5320-4 feature is well matched, but
other lines in the vicinity of He II
4542 are somewhat
too strong (likely due to an incomplete treatment of N III
quartet states in our models). Carbon is somewhat more difficult to
constrain, with C III
4647-51 well matched for
.
C IV
5801-12 is well reproduced with this value, whilst C
III
5696 is too weak, implying a yet higher abundance. As
discussed elsewhere (e.g. Hillier et al. 1998), oxygen is
exceedingly difficult to constrain in mid-O supergiants due to lack of
suitable optical diagnostics. The high nitrogen overenrichment is not
easily explained via single star evolution, unless carbon (and to a
lesser degree oxygen) is very depleted via the CN (or ON) cycle.
Crowther et al. (2002) discuss similar problems for
Magellanic Cloud O supergiants.
Turning to UV comparisons, we show rectified high resolution IUE
spectroscopy of HD 153919 (phase 0.15) in Fig. 3 together
with synthetic spectra. Overall, agreement for
He II 1640, C IV
1550 and N IV
1718
is reasonable, with predicted Si IV
1393-1402 emission
too weak adopting
.
Since X-rays are not explicitly considered in this study,
the shocked UV N V
1238-42 resonance doublet is
predicted to be too weak. The sole prominent oxygen feature present
in the UV (or optical) region is O IV
1338-43, which
is reasonably well matched with
,
although we do not claim that this represents an accurate
constraint.
Additional, powerful evidence in favour of our derived temperature is
the good match between the synthetic Fe IV-V spectrum and
observations, again with
.
Figure 2 shows good agreement with the dominant Fe V
"forest'' observed between
1300-1600 in HD 153919, plus the
weaker Fe IV in the
1500-1800 region. Fe VI is
not strongly predicted nor observed in the
1200-1400 region
(see Crowther et al. 2002 for further details).
While it is possible to explain the nitrogen enrichment in terms of rotational mixing it is impossible to produce carbon enrichment via this mechanism. Any carbon produced in the helium burning layers of the star has to pass through the hydrogen burning layers before reaching the surface where it will be converted to nitrogen. Therefore, any excess carbon in HD 153919 is therefore likely to result from mass transfer from the more evolved binary component prior to SN - this will be returned to in Sect. 4.
Given the presence of a compact companion for HD 153919, it is reasonable to ask whether the assumption of spherical geometry is justified - does the X-ray flux lead to significant departures from spherical symmetry for the ionisation of the wind (which in turn could lead to modifications in the line driving force)? Hatchett & McCray (1977) suggest that the X-ray emission will lead to a reduction of moderately ionised atoms in the wind (such as Si IV and C IV). Given that the ionised zone will move with the compact object we might expect to see orbital modulation in some of the wind UV resonance lines as the ionised zone passes in front and behind the stellar disc (or from the presence of a photo-ionization wake in the system, cf. Kaper et al. 1994). However, there is no convincing evidence for orbital modulation in the UV resonance line due to the Hatchett-McCray effect (e.g. Kaper et al. 1990, 1993); the small changes in line profiles with orbital phase are instead most likely due to Raman scattering of EUV photons generated by the X-ray source (Kaper et al. 1990, 1993). Additionally, the modeling was performed on the spectrum obtained during the X-ray eclipse to further minimise any possible effects of irradiation on the stellar wind (cf. Sect. 2.1).
Using a modified 2-dimensional Sobolev Exact Integration (SEI) code vL01 analyse the UV line variability and confirm that any Strömgren sphere caused by the presence of the X-ray source is rather small, and will have a negligible effect on the ionization structure and line driving of the wind (since the wind is dense and the ionizing flux low). Equally, the Strömgren zone does not extend to the surface of the star and so should not lead to a significant degree of X-ray heating of the stellar surface.
Phase resolved continuum observations (e.g. vL01; Hammerschlag-Hensberge & Zuiderwijk 1977; van Paradijs et al. 1978) constrain orbital variability to <4 per cent in the UV and 4-8 per cent in the optical, indicating that HD 153919 shows little departure from sphericity (possibly as a result of a large mass ratio). Note that continuum emission from the stellar wind is essentially negligible at wavelengths shorter than a few microns. Therefore, the lack of significant variability cannot be attributed to emission from the outer regions of the stellar wind "shielding'' a heavily perturbed stellar surface and/or inner wind from view.
The photometric variability further constrains any change in stellar temperature due to X-ray heating to less than the uncertainty in the stellar temperature derived from our NLTE modeling. Therefore, we have confidence that deviations from spherical symmetry in HD 153919 and/or the effects of X-ray irradiation are negligible for the purposes of spectroscopic modeling.
Since no X-ray pulsations have been convincingly measured for
4U1700-37 - and hence no determination of axsini is
possible - the orbital solution cannot be uniquely determined. However,
following Heap & Corcoran (1992) and Rubin et
al. (1996) we may estimate the mass of the companion using a
Monte Carlo method. The mass of the companion can be calculated using
a series of equations relating eclipse and orbital parameters.
The Roche lobe filling factor
is defined by
The errors on Mx are significantly smaller than previous work (e.g.
Rubin et al. 1996) due to the far more stringent limits on
,
which constrain the orbital and eclipse parameters far
more strongly. This is not surprising as the eclipse parameters are
used to work out the orbital parameters and the eclipse constraints
rely strongly on the O-star radius.
Parameter | Value |
E(B-V) |
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log(![]() ![]() |
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21.9
+1.3-0.5 ![]() |
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1750 km s-1 |
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3.45-3.55 |
Figure 5 shows the O-star mass distributions around
.
Again the distribution is anti-symmetric with 32 per cent
of trials between 50-60
,
26 per cent between
40-50
and only 2 per cent less than 40
.
Therefore, the mass implied for HD 153919 appears to be
consistent with both that expected from its spectral classification
and relevant evolutionary tracks (see Fig. 6), and that
suggested by its high terminal wind velocity (Sect. 2). Additionally
the
determined from the He I and Balmer line wings
(Sect. 2.2) indicates a minimum mass of 50
(and
maximum of
60
), again fully consistent with the
results of the Monte Carlo simulation. Therefore, given the
consistency between mass estimates based on spectral type,
evolutionary tracks (when compared to the stellar temperature and
luminosity derived from modeling), surface gravity and the Monte Carlo
simulations, we have confidence that the mass of HD 153919
lies in the range 50-60
.
This resolves the problem that the
star is undermassive by a factor of
2.
However, the mass of the compact companion is more problematic given
that it is significantly in excess of the observed mass range
for NS, but apparently considerably lower than those found for BH
candidates (e.g. Fig. 7). If a minimum mass of 50
is
adopted for HD 153919 the minimum value of Mx that may
be obtained is 1.83
,
while for values of Mo between
50-60
only 0.17 per cent of trials
result in
.
This will be returned to in Sect. 5.
Recent reanalysis of spectroscopic data by Hammerschlag-Hensberge et al. (in prep.) suggests that the eccentricity of the orbit is somewhat
uncertain, and that the orbital velocity curve is equally well fit by
an orbit of eccentricity
as it is by a circular
orbit. In order to address this uncertainty we modified the above
equations for the more general case of an elliptical orbit and
repeated the simulations with
.
This resulted in
significantly higher masses for both components, with
and
.
Therefore, the mass of the O star in the case of an elliptical orbit
is significantly higher than expected for
an O6.5 Iaf+ star (only 0.002 per cent of the trials result in a
mass
50
,
and 5 per cent give a mass between
50-60
). Such high values for
are inconsistent with the measured
and we note that 95 per
cent of trials are rejected due to the inclination constraints,
suggesting that a low eccentricity solution is more likely.
If such extreme values for
are adopted, the mass of the
compact object is still less than that observed for the lowest mass
black hole candidate known (
4.4
;
Sect. 5) and
remains significantly greater than any known neutron star. Indeed, the
lowest mass estimates for both components were derived in the case of
a circular orbit; therefore the value of
represents a lower limit for the
mass of the compact object
, and we
suggest that these results favour a low eccentricity solution for the
orbit (we note that the orbital eccentricity of Vela X-1 is
overestimated from optical observations when compared to the value
derived from timing analysis, cf. Barziv et al. 2001).
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Figure 4:
Histogram of the results of the Monte Carlo simulations for
the mass of the compact object in 4U1700-37. The results
indicate a mass in the range of
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The stellar parameters for both primary and compact companion determined via non-LTE modeling and Monte-Carlo simulation raise many important questions regarding the evolution of single and binary massive O stars and their ultimate post-SN fate. However, such questions are complicated by the uncertain evolution of massive stars after leaving the main sequence and the role that binarity and associated - possibly non-conservative - mass transfer plays in modifying this; for instance the time at which the hydrogen rich outer layers are lost exposing the helium core plays a critical role in determining the final pre-SN mass of the star (e.g. Brown et al. 2001 and references therein).
Heap & Corcoran (1992) propose an initial
80
40
binary system with subsequent evolution
via case B mass transfer
after
yrs, proceeding for 104 yrs (via Roche-lobe
overflow; RLOF). After the mass transfer the initially more massive
star has lost enough material due to the combination of wind driven
mass loss and the brief period of non-conservative RLOF to
become a WR star, which subsequently explodes as a SN.
Based on their identification of the Sco OB1 association as the
birthplace of HD 153919, Ankay et al. (2001) propose
a lower initial mass of the SN progenitor
(30
+30-10
)
based on the turnoff mass for the
proposed
Myr age of Sco OB1 at the time of the
supernova. Assuming conservative Case B mass transfer they
derive an initial mass of at least 25
and suggest the
short orbital period Wolf-Rayet (WR) binary
CQ Cep/HD 214419 as a possible example of the progenitor
system. However they note that the assumption of conservative mass
loss might be incorrect and highlight the non-conservative scenario of
Wellstein & Langer (1999). Such a scenario is attractive
since the loss of substantial quantities of mass and angular momentum
naturally lead to short period binaries (assuming both components do
not merge). However, common envelope evolution is poorly understood
and therefore somewhat limits our ability to quantitatively
reconstruct the pre-SN evolution of the binary.
Despite these uncertainties we can address the general evolution of
the binary in some detail. Our present mass estimate for
HD 153919 of
suggests
a mass for the SN progenitor of the order of
60
,
at
the upper range of that proposed by Ankay et al. (2001)
. The
short orbital period of HD 153919/4U1700-37 favours
non conservative evolution probably via case B mass transfer. While
mass loss via the stellar wind of the SN-precursor during the WR phase
will lead to a widening of the orbit, a favourable SN kick may
overcome these problems.
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Figure 5:
Histogram of the results of the Monte Carlo simulations for
the mass of the O6.5Iaf+ primary HD 153919 - the results
indicate a mass in the range of ![]() ![]() |
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Parameter | Value |
![]() |
21.4-23.2 ![]() |
![]() |
0.5-1.0a |
![]() |
0.8-1.0a |
e | 0.0b |
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P |
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Figure 6:
The location of HD 153919 in the Hertzsprung-Russell
diagram. The evolutionary tracks of Lejeune & Schaerer
(2000) for starsof a given initial mass are indicated (up
to the phase of core-helium burning). The numbers along the tracks
show the decrease in ![]() |
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The alternative Case C evolution appears unlikely given that the SN
will occur several thousand years after the end of mass
transfer/loss. This time period appears unrealistically short given
that this will not allow sufficient time for the helium mantle to be
removed to expose the C/O core (i.e. the star will not pass though a
WC phase). Therefore the SN progenitor would have a large mass at the
point of SN; for a SN progenitor with an intial mass of 60 we might expect the mass to be of the order of 30
(the
maxium helium core mass). This implies the loss of a very large
quantity of material in the SN, contradicting the estimate of Ankay et
al. (2001) that only
9
was lost in the SN
(and we might also expect such a scenario to lead to a very high mass
compact object, cf. Brown et al. 2001).
The high mass implied for the SN precursor suggests that such a star
would be likely to evolve through a Luminous Blue Variable (LBV) phase
rather than a Red Supergiant (RSG) phase on its way to becoming a WR
star (stars with initial masses 40
likely avoid the
RSG phase). Such an evolutionary path is likely to prevent mass
transfer onto HD 153919 via RLOF (Wellstein & Langer
1999). Significant accretion of material by
HD 153919 via RLOF seems implausible in any case, as this
would lead to a large orbital separation and period (Wellstein &
Langer 1999). Instead, the formation and subsequent
ejection of a common envelope (despite the SN precursor avoiding
the RSG phase) and simultaneous reduction in orbital period and binary
separation is suggested. Such a scenario therefore implies that the
present day mass of HD 153919 forms a lower limit to the mass
of the SN precursor, subject to the possible accretion of a small
quantity of material directly from the wind of the SN precursor (see
below).
After the ejection of the outer layers of the SN precursor we are left
with a short orbital period WR+O star binary. Support for this
scenario is provided by the possible overabundance of carbon (or
rather the lack of significant C depletion as might be expected for
CNO processed material; Sect. 2.2) in HD 153919. The carbon
rich material must have originated in the SN precursor during a carbon
rich WC stage, independently suggesting a rather high initial mass for
the SN precursor. Subsequent mass transfer would then have to occur
via direct wind fed accretion, with the wind of the WC star impacting
directly on the surface of the O star. Despite the high mass loss rate
of the O star (
yr-1; Table
2) the possibility of such accretion is suggested by hydrodynamical
simulations of colliding wind binaries (Gayley et al.
1997; Dessart, Petrovic & Langer, in prep.).
We may exclude the overabundance in nitrogen originating via direct
wind accretion during the WN phase of the SN precursor. For a
nitrogen overabundance in HD 153919 of 9, the nitrogen mass
fraction,
,
is the same value as is found in the winds of WN
stars which implies that HD 153919 would have to accrete 18
from the SN precursor during the WN phase to produce such
an overabundance. Given that this is unreasonably high, we suggest
that the excess nitrogen probably originated from internal, rotational
mixing (nitrogen overabundances are not unusual for O stars).
Several short period WR+O star binaries are known and could provide
analogues to the precursor of the present binary configuration. At
present CQ Cep does not fit particularly well
(
,
,
P=1.6 days) - in a
few 105 yrs when the WN star has lost mass and has evolved into a
lower mass WC star (and the period has lengthened) it may provide a
better model for the system. However, of the known WC+O binaries,
HD 63099 (
,
,
P=14 days) could evolve into a HD 153919/4U1700-37
like binary if the SN kick is favourable. Other known WR+O star
binaries that could form similar systems are HD 152270
(
,
,
P=8.9 days) and
HD 97152 (
,
,
P=7.9 days); in all three cases the present mass of the WC star is
9
as suggested for the SN precursor by Ankay et al. (2001) on the basis of the present mass of the compact
companion and the current space velocity of the system. Therefore, of
the six WC+O binaries with known masses (van der Hucht 2001)
three are found to have parameters consistent with the presumed pre-SN
stage of 4U 1700-37.
The results of the Monte-Carlo simulations suggest that the SN formed
a compact object (see Sect. 5) with a mass in the range
.
As massive binary models show that Case B
primary stars of larger initial mass evolve to a larger final mass,
and that Case A primaries end up less massive than Case B's (cf.
Wellstein & Langer 1999; Wellstein et al.
2001) we can conclude that the remnants of all Case A/B
primaries initially less massive than about 60
are less
massive than about 2.5
.
Theoretical predictions suggest that a 60
star in a close
binary system is capable of producing either a low or a high mass
compact object depending sensitively on the wind mass loss rate
adopted for such a star during its WR phase; a variation of only a
factor of three in the WR mass loss rate leading to compact object
masses in between 1.2 and 10
(Fryer et al. 2002). This
result shows that given the present uncertainties in WR mass loss
rates, the relatively low mass found for the compact star in 4U1700-37
is not in conflict with the evolutionary scenario proposed above (and
also argues for a relatively high WR mass-loss rate).
Therefore, given the low mass of the compact companion in 4U1700-37, it seems to be difficult to explain any of the (high mass) galactic black hole binaries as being produced through the Case A/B channel (cf., Portegies Zwart et al. 1997) except for those with the most massive SN-progenitors (Brown et al. 2001). Indeed, evolutionary scenarios invoking Case C mass transfer (Brown et al. 1999) seem to be required to explain the high-mass black holes in low-mass X-ray binaries.
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Figure 7:
Mass distribution for neutron stars and black holes (after
Charles 1998). Neutron star masses are from Ash et al. (1999),
Barziv et al. (2001), van Kerkwijk et al. (1995) and Thorsett &
Chakrabarty (1999). Black hole masses provided by Charles
(priv. comm.). Error bars for systems other than 4U1700-37
are 1 sigma errors; see Sect. 3 for a discussion of the errors
associated with the mass of 4U1700-37 but note that the
probability of
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At present mass determinations exist for 36 compact objects, of which
21 are neutron stars and the remainder black hole candidates (Fig. 7).
Thorsett & Chakrabarthy (1999) found that the masses of
neutron stars are clustered in a remarkably narrow range (mean of
1.35
and a standard deviation of
0.04
). However, recent analysis of Vela X-1 by
Barziv et al. (2001) suggests that the pulsar has a mass of
1.87
+0.23-0.17
,
while Orosz & Kuulkers (1999) find a mass of
for Cygnus X-2 (however Titarchuk
& Shaposhnikov 2002 have recently proposed
on the basis of Type-I X-ray bursts).
Based on assumptions about the origin of kilohertz quasi-periodic oscillations
Zhang et al. (1997) suggest that several LMXBs may also
contain massive (2
)
neutron stars, resulting from the
accretion of substantial amounts of material over long (108 yrs)
periods of time. However their putative descendants, radio pulsar+white
dwarf binaries, provide no evidence for massive neutron stars (Barziv et al. 2001). The same is true for the Be/X-ray binaries, which
have evolved from lower mass systems than the OB-supergiant HMXBs.
Only in the latter systems evidence has been found for massive neutron
stars and black hole candidates.
Masses for a number of black hole candidates have also been
determined; lower limits to their masses comfortably exceed
3 .
Indeed several objects appear to have masses
10
(e.g.
for
GRS 1915+105; Greiner et al. 2001),
with most typically
6
.
At present the binary system
with the lowest mass candidate black hole is Nova Vel
(
;
Fillipenko et al. 1999).
Given that the mass of the compact object in 4U1700-37 lies
outside the present observational range for both neutron stars and
candidate black holes, is it possible to increase/decrease the mass of
the compact object such that it is consistent with either type of
object? For the case of a circular orbit we find no solutions
consistent with
.
Very eccentric orbital
solutions do allow values of Mx in this range although we note
there is no physical motivation for them. Such solutions imply values
of
greatly in excess of 100
,
well above current
evolutionary predictions for the mass of an O6.5 Iaf+ star. Stars
with masses in excess of 100
are instead expected to
evolve to H depleted WR stars via a H rich pseudo-WNL phase
where their powerful stellar winds mimic the spectra of more
(chemically) evolved stars of lower masses.
Such a large mass would also be inconsistent with the constraints
imposed by the surface gravity (Sect. 2.2) and the relationship
between stellar mass and the terminal wind velocity. Finally the
result would imply that even very massive stars (given that the
initial mass of the SN progenitor had to be significantly in excess of
the present mass of HD 153919) leave relatively low mass
remnants post supernova, presenting significant problems for the
origin of heavy (>10 )
black holes such as
e.g. Cyg X-1. Therefore we conclude that Mx appears to be
inconsistent with the range of masses of known black hole
candidates.
Given the stringent lower limits derived in Sect. 3 it also appears
difficult to bring the mass of the compact object into line with the
range of masses found by Thorsett & Chakrabarthy (1999).
Inspection of the evolutionary tracks in Fig. 6 suggest that stars
with initial masses of the order of 60
initially evolve
redwards before returning bluewards after undergoing significant mass
loss, most likely during an LBV phase. While we note that the
behaviour of stars in this short lived phase is very uncertain it is
unlikely that we could be observing HD 153919 after such an
excursion, since we would expect significant chemical enrichment - the
H rich mantle having been lost - which is not observed. Likewise, the
mass constraint imposed by the determination of the surface gravity
also appears to exclude this scenario.
Furthermore, such a low value for
and Mx would reintroduce
the problem of HD 153919 being undermassive for its spectral
type by a factor
2. While the primaries in some HMXB systems are
found to be undermassive (e.g. Cen X-3 and LMC X-4;
Kaper 2001) this is attributed to mass loss via RLOF - wind
fed systems do not show this effect (Kaper 2001). Given that
4U1700-37 is currently a wind fed system and is yet to evolve
into a RLOF system this could not explain such a mass discrepancy.
Indeed, given the evolutionary constraints imposed by the present
orbital period it is likely that no significant mass transfer has
occured onto HD 153919 during its lifetime, and it will have
evolved as if it were an isolated star.
If we accept
- as implied by the
simulations - the nature of the compact companion remains
uncertain. Conflicting claims as to the nature of the object have been
made on the basis of the X-ray spectrum of 4U1700-37
(Sect. 1). While we cannot discriminate between the twin possibilities
of massive neutron star or low mass black hole from our present
measurements we note that consideration of the masses of both
components of the binary appear to exclude the possibility that stars
with masses of
60
can produce 5-10
black
holes via case A or B evolution.
If the compact object in 4U1700-37 is a black hole it confirms Brown et al.'s prediction of the existence of "low mass black holes'' (based on their "soft'' equation of state, Brown et al. 1996), while if the object is a neutron star the high mass would severely constrain the equation of state of matter at supra-nuclear densities.
The relationship between the mass of a neutron star and its central density is calculated by integration of the Tolman-Oppenheimer-Volkoff (TOV) equation (Oppenheimer & Volkoff 1939) which is the relativistic expression for hydrostatic equilibrium. In order to perform the integration it is neccesary to understand the equation of state of the degenerate nuclear matter in the star.
Because of their non-perturbative nature, strong interactions between
nuclei are extremely difficult to calculate even under normal conditions.
However, there are several models of the internuclear potential in the
literature which have achieved much success in modelling nuclei e.g.
Stoks et al. (1994), Wiringa et al. (1995) and
Machleidt et al. (1996). One of the most successful
and up to date of these models has been applied to the neutron star
equation of state by Akmal et al. (1998) yielding a maximum
mass of between 2.2 and 2.4
for a neutron star made completely
of normal nuclear matter.
There is also the possibility of a QCD phase transition occuring in
the centre of the neutron star. The large chemical potential has a
similar effect to a large temperature on the QCD coupling constant.
Consequently the interquark coupling can be reduced to the point where
deconfinement occurs and nuclei dissolve into quark matter. The
presence of quark matter has the effect of softening the equation of
state which leads to a lower possible maximum mass for the neutron
star. The energy scale at which deconfinement occurs can be
parameterised by the QCD bag constant B, a phenomenological
parameter representing the difference in energy density between the
vacua of hadronic and quark matter (
-200 MeV fm-3).
Inclusion of a phase transition to such a mixed state reduces the
maximum mass of the neutron star to
2
for B=200MeV fm-3 and
1.9
for B=122 MeV fm-3(Akmal et al. 1998)
.
If the neutron is rotating rapidly, the TOV equation ceases to be a valid approximation and one must drop the assumption of spherical symmetry in the metric. The effect of the rotation will increase the allowed mass of the neutron star as one might expect, but it is shown (Heiselberg & Hjorth-Jensen 1999) that even with rotation one cannot obtain a neutron star with a mass much higher than those listed above without using an equation of state so stiff that the sound speed in the neutron-star interior becomes superluminal.
To summarize this subsection, state of the art models for nuclear
equations of state which include the effects of three nucleon
interactions marginally allow the existence of a 2.4 neutron star. However, the existence of such a star would place
severe constraints upon the onset of new physics at high hadronic
densities.
For instance, in the model where a quark matter core is
expected to develop, the bag constant B would have to be
considerably larger than 200 MeV fm-3 in order for such a star
to be viable.
We have performed a sophisticated NLTE analysis on the O6.5 Iaf+ star
HD 153919, the primary of the HMXB 4U1700-37 and
used the results to constrain the masses of both components of the
system via a Monte Carlo simulation. Our NLTE model atmosphere
analysis leads to parameters for HD 153919 of
log(
,
K,
,
yr-1, and an overabundance
of nitrogen and possibly carbon over solar metallicities. Combined
with the short orbital period of the system this implies a common
envelope phase of pre-SN evolution - despite the mass of the SN
progenitor apparently precluding a RSG phase - leading to the
formation of a close WC+O star binary, with the carbon enrichment of
HD 153919 a result of the impact of the stellar wind of the
WC star on the surface of the O star.
The Monte Carlo simulations result in masses for the O star and
compact object of
and
,
with none of the 106 trials
resulting in
,
while only 3.5 per cent of
the trials result in
.
Given that no
significant mass transfer via RLOF has occured this implies that the
initial mass of the SN precursor must have been
60
.
Thus even very massive stars can effectively
"melt down'' to leave rather low mass post-SN remnants. Equally, the
masses of both components imply that it is impossible for stars of
60
to leave 5-10
remnants via Case A or
B evolution, suggesting that most high mass black holes are instead
formed via Case C mass transfer.
The mass of the compact object is found to lie in between the range of
masses observed for neutron stars and black holes. Given that and Mx are strongly correlated, forcing consistency between Mxand either type of object results in significant discrepancies between
and evolutionary predictions for the mass of
HD 153919.
In order to produce consistency with the range of masses observed for
neutron stars the O star has to be significantly undermassive for its
spectral type and luminosity class. While theoretical evolutionary
tracks for massive (60
)
stars suggest that after a
redwards excursion the star will evolve bluewards again with a
substantially reduced mass, such a star would show significant
chemical enrichment (and H depletion) which is not observed. Equally,
the surface gravity determined from modeling excludes such an
anomolously low mass.
Forcing consistency between Mx and the masses of known black hole
candidates (
)
results in
100
.
Stars of such extreme masses are not expected to
go through an O supergiant phase, rather evolving into H depleted WR
stars via a H-rich pseudo WR phase, where their high mass loss rate
simulates the spectrum of a WR star. Once again, the constraint
implied by the surface gravity also appears to exclude this
possibility.
We are therefore left with the conclusion that no solution is fully consistent with present expectations for stellar evolution and the chemical abundances and surface gravity of HD 153919. If the compact object has a mass consistent with the observed range of neutron star masses, the O star is significantly undermassive, while if it consistent with the lower limit to black hole masses the O star is overmassive by a similar (or larger) factor. Finally if - as the Monte Carlo analysis implies - the probable mass of the O star is consistent with evolutionary predictions and the measured surface gravity, the mass of the compact object lies in between the two alternatives.
While our results do not allow us to distinguish between a massive
neutron star or a low mass black hole, the existence of a neutron star
of mass in the mass range
would significantly
constrain the high density nuclear equation of state and provide
details about the QCD phase transition complementary to information
about the temperature induced transition which will be obtained at
RHIC and LHC. Phenomena which might occur deep in the star such as
the appearance of hyperons or a quark matter core would be strongly
constrained as the existence of these phases might result in an
equation of state too soft to support such a high mass star.
Acknowledgements
This paper is partially based on observations collected at the European Southern Observatory, Chile. The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council. JSC, SPG & CB gratefully acknowledge PPARC funding. LK is supported by a fellowship of the Royal Accademy of Arts and Sciences in The Netherlands. MF is supported by the FNRS and was helped by conversations with Nicolas Borghini; we also thank John Porter, Marten van Kerkwijk and Phil Charles for their helpful comments.