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Black Hole and Neutron Star Transients in Quiescence
Kristen Menou, 1;2 Ann A. Esin, 3 Ramesh Narayan, 1
Michael R. Garcia, 1 Jean­Pierre Lasota 2 & Jeffrey E. McClintock 1
ABSTRACT
We consider the X­ray luminosity difference between neutron star and black hole soft X­ray
transients (NS and BH SXTs) in quiescence. We show that the current observational data
clearly suggest that BH SXTs are significantly fainter than NS SXTs. The luminosities of
quiescent BH SXTs are consistent with the predictions of binary evolution models for the mass
transfer rate if (1) accretion occurs via an ADAF in these systems and (2) the accreting compact
objects have event horizons. The luminosities of quiescent NS SXTs are not consistent with
the predictions of binary evolution models, unless most of the mass accreted in the ADAF is
prevented from reaching the neutron star surface. We propose that the discrepancy is because
of an efficient propeller in quiescent NS SXTs and develop a model of the propeller effect that
accounts for the observed luminosities. We argue that modest winds from ADAFs are consistent
with the observations while strong winds are probably not.
Subject headings: X­ray: stars -- binaries: close -- accretion, accretion disks -- black hole physics
-- stars: neutron -- stars: magnetic fields
1. Introduction
Soft X­ray Transients (SXTs) are compact binary systems in which a low­mass secondary (either a
main­sequence star or a subgiant) transfers mass via Roche­lobe overflow onto a black hole (BH) or neutron
star (NS) primary (see reviews by Tanaka & Lewin 1995; van Paradijs & McClintock 1995; White, Nagase
& Parmar 1995). SXTs have highly variable luminosities. They spend most of their lifetimes in a low
luminosity quiescent state, but occasionally undergo dramatic outbursts during which both the optical and
X­ray emission increase by several orders of magnitude (e.g. Chen, Shrader & Livio 1997; Kuulkers 1998).
NS SXT outbursts typically occur every 1­10 years and last for several weeks, while BH SXT outbursts are
typically separated by 10­50 years (or perhaps longer) and last for several months (see Chen et al. 1997).
A variety of observations (see e.g. Tanaka & Shibazaki 1996) indicate that, near the peak of an
outburst, SXTs accrete matter via a standard thin disk (Shakura & Sunyaev 1973), so that there is
little doubt that the accretion is radiatively efficient during this phase. The situation is more complex in
quiescence. The spectra of quiescent BH SXTs do not resemble that of a thin disk, and the accretion rates
inferred from the observed X­ray luminosities disagree by orders of magnitude with the predictions of the
standard disk instability model for quiescent disks (e.g. Lasota 1996).
1 Harvard­Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA.
kmenou@, rnarayan@, mgarcia@, jmcclintock@cfa.harvard.edu
2 UPR 176 du CNRS, DARC, Observatoire de Paris, Section de Meudon, 92195 Meudon C'edex, France.
jpl@orge.obspm.fr
3 Theoretical Astrophysics, Caltech 130­33, Pasadena CA 91125, USA. aidle@tapir.caltech.edu

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Narayan, McClintock & Yi (1996) and Narayan, Barret & McClintock (1997) showed that the
observations of quiescent BH SXTs can be explained by a two­component accretion flow consisting of an
inner hot advection­dominated accretion flow (ADAF, see Narayan, Mahadevan & Quataert 1998 and Kato,
Mineshige & Fukue 1998 for reviews of ADAFs) surrounded by an outer thin disk. In the most recent
version of this model, only the inner ADAF contributes to the observed optical, UV and X­ray emission
of the system. The outer thin disk acts mainly as a reservoir of mass which accumulates until the next
outburst is triggered; the emission of the disk is primarily in the infrared and it is hardly seen as it is
swamped by the emission of the secondary (see Narayan et al. 1996, 1997a and Lasota, Narayan & Yi 1996
for details).
A key feature of the Narayan et al. (1996, 1997a) model of quiescent BH SXTs is the low radiative
efficiency of the ADAF. In these flows, the bulk of the viscously dissipated energy is stored in the gas and
advected with the flow into the black hole (Ichimaru 1977; Narayan & Yi 1995b; Narayan et al. 1996, 1997a).
This explains the unusually low luminosities of BH SXTs. By contrast, in NS SXTs all the advected energy
is expected to be radiated from the neutron star surface, resulting in a much higher radiative efficiency of
the accretion flow even in the presence of an ADAF (Narayan & Yi 1995b). Motivated by this fundamental
distinction between black hole and neutron star systems, Narayan, Garcia & McClintock (1997) and Garcia
et al. (1998) compared the outburst amplitudes of BH SXTs and NS SXTs as a function of their maximum
luminosities and showed that the observations reveal systematically lower relative luminosities in BH SXTs.
They argued that this constitutes a confirmation of the presence of an event horizon in BH SXTs. The
argument has been recently challenged by Chen et al. (1998).
In this paper, we attempt to develop a physical understanding of the difference in quiescent luminosities
between NS and BH SXTs. We first show, in x2, that there is indeed a significant difference in the observed
quiescent luminosities of the two classes of objects, in contrast to the claim of Chen et al. (1998). We then
use binary evolution models in x3 to estimate mass transfer rates in SXTs. We combine these estimates
with the ADAF+thin disk accretion scenario, taking into account the presence of an event horizon in BH
systems and a reradiating surface in NS systems, to determine the expected X­ray luminosities in quiescence
(x4). The model predictions agree well with observations for quiescent BH SXTs. However, the model
substantially overestimates the luminosities of quiescent NS SXTs. In x5 we show that the NS SXT data
can be reconciled with the predictions of the model if we take into account the ``propeller effect'', whereby
the magnetosphere of a rapidly rotating neutron star prevents much of the accreting material from reaching
the surface of the neutron star. In x6 we show that an ADAF model with a moderate wind and a somewhat
less efficient propeller (in NS SXTs), is also consistent with the observed quiescent luminosities of BH and
NS SXTs. Finally, in x7 we discuss possible limitations and extensions of this work and in x8 we summarize
the main results.
2. Observations
In Table 1, we list key parameters of several NS and BH SXTs: the orbital period P orb , the distance D,
the quiescent X­ray luminosity L min in the 0:5 \Gamma 10 keV X­ray band, and the mass m 1 (in solar units) of the
compact primary. Since our main interest is in the quiescent emission, we list only systems for which there
exist reliable measurements of L min . The ratio L min =Lmax (independent of the distance D), where Lmax is
the outburst peak luminosity, had been used in previous investigations of the luminosity difference between
BH and NS SXTs (Narayan et al. 1997b; Garcia et al. 1998). Here, we choose to ignore Lmax (which
depends mainly on the physics of the thin disk in outburst) and concentrate just on the quiescent state of

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SXTs and L min . The values of L min are taken from Narayan et al. (1997b) and Garcia et al. (1998), except
for the BH SXT H1705­250 (see below).
In selecting the systems listed in Table 1, we were careful to avoid any possible confusion between BH
and NS SXTs, since this would make a comparison between the two sets of objects less reliable. Thus,
we limit our sample to the eight BH candidates that have firm dynamical lower limits on the mass of the
primary (McClintock 1998). (Note that this is not true for several so­called BH ``candidates'' of Chen et al.
1998, which seriously weakens their arguments.) Similarly, there is firm evidence that the five systems listed
in Table 1 as NS SXTs contain NS primaries, based on the detection of type I X­ray bursts (e.g. Narayan
et al. 1997b; Chen et al. 1997).
In Figure 1, we plot the quiescent luminosities of the BH and NS systems listed in Table 1 as a function
of their orbital periods P orb . The open circles correspond to NS SXTs and the filled dots correspond to BH
systems. Luminosity upper limits (indicated by downward arrows) are shown for five SXTs, all of which
are BH systems. The orbital period of the NS SXT H1608­52 is uncertain (see Table 1) and its location in
Figure 1 is indicated by dashed circles. Among the undetected SXTs, we choose to include in our sample
only those systems that have been observed for more than 10 ks (see Table 1 herein, and also Table 1 in
Narayan et al. 1997b), which translates to flux levels ! 3 \Theta 10 \Gamma13 ergs s \Gamma1 with current X­ray satellites
(0.5­10 keV; ROSAT/ASCA).
Here we report a new and improved luminosity limit for H1705­250 (=Nova Oph 77) based on the ASCA
observation of 18 September 1996, which we extracted from the HEASARC archive. The exposure time was
31 ks, but unfortunately the target was near the chip boundaries which limits the effective area. The 4oe
upper limit is 0:9 \Theta 10 \Gamma3 c s \Gamma1 , which corresponds to an X­ray flux (1 \Gamma 40 keV) ! 1 \Theta 10 \Gamma13 ergs s \Gamma1 cm \Gamma2 .
Assuming a distance of 8.6 kpc, L x ! 0:9 \Theta 10 33 ergs s \Gamma1 .
To remove the dependence of L min on the mass of the primary, all luminosities are expressed in units
of the Eddington luminosity,
L Edd = 1:4 \Theta 10 38 m 1 erg s \Gamma1 ; (1)
where m 1 , the mass of the compact object in solar units, is listed in Table 1. For a standard radiative
efficiency of 10 %, the Eddington luminosity corresponds to a mass accretion rate of
—
M Edd = 1:39 \Theta 10 18 m 1 g s \Gamma1 : (2)
We use Eddington­scaled luminosities because the mass transfer rates in NS and BH SXTs are likely to
be similar in units of —
M Edd , especially in short orbital period systems (see x3). Thus, any large difference
in L min =L Edd between the two classes of objects would indicate a difference in the radiative efficiencies.
The argument for using P orb along the horizontal axis of Figure 1 is as follows. For any mass transfer
binary system with a low mass secondary, P orb depends primarily on the density of the secondary. At a
given P orb , a BH SXT and a NS SXT will have similar secondaries, so that the mass transfer characteristics
are likely to be similar. Thus a reliable comparison of radiative efficiencies would be possible. In contrast,
if we were to compare the quiescent luminosities of a BH SXT and a NS SXT with quite different P orb ,
a difference in the mass transfer rates (cf x3) could mask actual differences in the radiative efficiencies of
the accretion flows. This point, which is the motivation for the calculations in x3, was first emphasized by
Lasota & Hameury (1998).
Figure 1 strongly suggests that, in Eddington units, BH SXTs are systematically fainter than NS
SXTs. Note that all five of the NS SXTs have been detected in quiescence and have well measured values

-- 4 --
of L min =L Edd while the majority of BH SXTs have only upper limits on L min =L Edd . Further, even if all
the BH SXTs with upper limits end up being detected at their present limiting luminosities (an unlikely
scenario), there would still be a significant difference in the luminosity distributions of BH SXTs and
NS SXTs; almost any trend line one might draw through the BH SXTs in Fig. 1 would correspond to a
substantially lower luminosity than the corresponding line for the NS SXTs.
To make a clearer comparison between BH and NS SXTs with the existing data, we isolate in Figure 2
those systems for which L min and P orb are well determined (see also the very similar Fig. 3 of Lasota
& Hameury 1998). Although there are only a few systems in this figure, we feel that we can conclude
unambiguously that (at least in this small sample) BH SXTs in quiescence are far less luminous than NS
SXTs. The difference is as much as two orders of magnitude for short period systems.
It is important to stress here the excellent upper limit on the quiescent luminosity of the BH SXT
J0422+32. This upper limit is very nearly equal to the very low measured quiescent luminosity of A0620­00.
Thus, there are now two BH SXTs that are two orders of magnitude less luminous, in Eddington units,
than quiescent NS SXTs with comparable P orb .
Narayan et al. (1997b) explained the difference in quiescent luminosities of NS SXTs and BH SXTs
as due to the presence of a hard surface in NS SXTs vs an event horizon in BH SXTs. The presence of a
surface causes the radiative efficiency in NS SXTs to be high, while in BH SXTs most of the dissipated
energy is advected into the event horizon of the BH, without producing observable emission. Narayan et al.
argued that this constitutes observational evidence for event horizons in black holes. In the remainder of
the paper, we expand on this idea and construct a physical model of accretion in NS and BH systems to
explain quantitatively the observations summarized in Figure 2. In x3 we estimate the mass transfer rate in
SXTs, and in x4 and x5 we describe an accretion model that is able to reproduce the observed emission in
the 0:5 \Gamma 10 keV band.
3. Mass Transfer Rates Predicted By Binary Evolution Models
The theory of binary evolution relies on the Roche­lobe model for the description of mass transfer
(Frank, King & Raine 1992). Depending on which mechanism drives the mass transfer, whether it is loss of
orbital angular momentum through gravitational radiation and magnetic braking, or expansion of the donor
as it evolves away from the main­sequence, the binaries are classified as j­driven or n­driven systems. There
is a `bifurcation' orbital period P bif separating the two classes such that for P orb ? P bif we find n­driven
systems whose orbital periods increase with time, and for P orb ! P bif we find j­driven systems whose P orb
decrease with time. The precise value of P bif depends on the history of the system. Estimates range from
0:5 \Gamma 2 days (e.g. Pylyser & Savonije 1988; King, Kolb & Burderi 1996).
The exact form of the magnetic braking law is not well established (see e.g. Kalogera, Kolb & King
1998). Moreover, Menou, Narayan & Lasota (1998) showed that there is strong circumstantial evidence
that magnetic braking (MB) is weak in BH SXTs. In the following, for simplicity, we neglect the influence
of MB in BH and NS SXTs. We will see in x4.2 that any contribution to the mass transfer by MB would
only strengthen the argument that NS SXTs shed mass rather than accrete it.
Following King et al. (1996), the mass transfer rates in j­driven systems with gravitational radiation

-- 5 --
(GR) and n­driven system with secondary expansion (EXP) is given, in Eddington units, by:
—
m T j
—
M T
—
M Edd
ú 9:14 \Theta 10 \Gamma5 m 2
2 (m 1 +m 2 ) \Gamma1=3 (P orb =1d) \Gamma8=3 ; P orb ! P bif (GR); (3)
ú 1:83 \Theta 10 \Gamma2 m \Gamma1
1 m 1:47
2 (P orb =1d) 0:93 ; P orb ? P bif (EXP); (4)
where m 2 is the mass of the secondary in solar units, P orb is scaled in units of 1 day and —
M Edd is defined in
equation (2).
The secondary in j­driven binaries is usually a main­sequence star (see King et al. 1996 for possible
complications) filling its Roche lobe. These stars obey the simple relation m 2 = 0:11(P orb =1 hr) (e.g. Frank
et al. 1992). The prediction for —
m T in case of GR driven mass transfer then becomes
—
m T ú 6:37 \Theta 10 \Gamma4 (m 1 +m 2 ) \Gamma1=3 (P orb =1d) \Gamma2=3 ; P orb ! P bif (GR): (5)
which has only a slight dependence on the mass of the primary m 1 .
Equation (4) for the case of secondary expansion is the linear limit of third­order polynomial fits
(King 1988) to detailed evolutionary tracks computed by Webbink, Rappaport & Savonije (1983). Along
an evolutionary track, the mass m 2 of the expanding secondary decreases as it transfers mass onto the
primary. Since a variety of initial masses and orbital periods (at the onset of mass­transfer) are possible, m 2
is essentially a free parameter in equation (4). However, a careful study of evolutionary tracks 4 shows that
the band of mass transfer rates predicted by equation (4) for values of m 2 in the range 0.5 to 1 reproduces
the mass transfer rates in n­driven accreting binaries for the majority of their lifetime. This band therefore
provides, in a ``population synthesis'' sense, the likely mass transfer rates one can expect in SXTs with
orbital periods larger than the bifurcation period.
We estimate the mass transfer rate expected at a given orbital period by simply adding the contributions
from GR (Eq. [5]) and secondary expansion (a band with m 2 = [0:5; 1] in Eq. [4]). Figure 3 shows that
this results in a relatively short, although plausible, bifurcation period ¸ 10 hr. The estimates of —
M T are
shown separately for BH and NS SXTs, in Eddington units (assuming m 1 = 7 for a BH and m 1 = 1:4 for
a NS). Note that the mass transfer rates are typically similar, in physical units, in BH and NS SXTs with
long orbital periods, and consequently differ by a factor of order five (i.e. the ratio of primary masses) in
Eddington units. However, the mass transfer rates are much closer in Eddington units at short orbital
periods (cf Eq. [5]) where the majority of SXTs are found. This is the motivation behind our use of
Eddington units in Figs. 1 and 2. Note that the comparable values of —
m T predicted for BH SXTs and NS
SXTs contrast with the large luminosity difference of the two classes of objects (Figs. 1 and 2).
Although the estimates shown in Fig. 3 rely on simple considerations that do not take into account
the full complexity of mass transfer (in particular, substantial fluctuations of the mass transfer rates
around the secular values used here may occur; e.g. Warner 1995), they probably provide better than an
order­of­magnitude precision which is sufficient for our discussion. Note, however, that this simple model
is not likely to give an accurate value of —
M T for the BH SXT J1655­40 since this system seems to be in a
special evolutionary state (crossing the Hertzsprung gap, e.g. Kolb 1998).
4 See Verbunt & van den Heuvel (1995) for a semi­analytical model that allows one to compute tracks.

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4. Accretion Models
Following Narayan et al. (1996, 1997a), we assume that the accretion flow is made of two components:
an inner ADAF and an outer thin accretion disk. Since only the ADAF contributes to the emission of
quiescent SXTs in the 0.5­10 keV band, we ignore the thin disk. Further, since the emission of the ADAF is
primarily from regions close to the center, we do not concern ourselves with the precise value of the radius
R tr at which the transition between the ADAF and the thin disk occurs.
Although the ADAF model was initially proposed for quiescent BH SXTs, there is no reason why it
should not apply also to quiescent NS SXTs. In particular, if the transition of the accretion flow from a
thin disk configuration to an ADAF configuration is triggered by the same local physics in the disk, e.g. a
thermal instability in the upper layers of the disk (Meyer & Meyer­Hofmeister 1994; Narayan & Yi 1995b;
Shaviv & Wehrse 1986), the process should occur independently of the nature of the central object. We
note, however, that the presence of a reradiating surface at the center of the ADAF may have significant
effects on the ADAF. For instance, Narayan & Yi (1995b) showed that the critical accretion rate —
m crit in
an ADAF is reduced in the case of a NS (compared to a BH) because the additional supply of soft photons
(from the stellar surface) causes the ADAF to cool more efficiently. This is not an issue here since —
m in all
the quiescent systems we study is well below —
m crit .
We assume conservative mass transfer. Consequently, if —
MADAF is the rate at which mass is accreted
during quiescence via the ADAF and —
M accum is the rate at which mass is accumulated in the outer thin
disk, the mass transfer rate satisfies —
M T = —
MADAF + —
M accum . The proportion of mass accreted vs. mass
accumulated in quiescence is, however, uncertain. Menou et al. (1998) estimated the relative importance
of —
MADAF and —
M accum for most of the BH SXTs listed in Table 1. They estimated —
M accum by taking the
integrated fluences of the outbursts of each source and assuming a radiative efficiency of j = 0:1 (which
provides the total mass accreted in the outburst), and estimated —
MADAF by fitting the quiescent emission
with an ADAF model. Menou et al.'s work indicates that, in quiescent BH SXTs, roughly half the matter
that is transferred from the secondary is accreted via the ADAF and the rest is accumulated in the thin
disk, i.e.
—
MADAF
—
M accum
j g ¸ 1;
—
MADAF
—
M T
= g
1 + g ¸ 1
2 : (6)
In the following models, we treat g as a free parameter, but we expect g to be of order unity in BH SXTs
and, by analogy, also in NS SXTs.
The version of the ADAF model used here is described in detail by Narayan et al. (1998a). It
consistently includes adiabatic compressive heating of electrons in the energy equation (Nakamura et al.
1997) and it uses for the flow dynamics the general relativistic global solutions calculated by Popham &
Gammie (1998).
In previous studies involving ADAFs, most of the model parameters were kept fixed at the following
values (see Narayan et al. 1998b for a discussion): ff ADAF = 0:3 (the viscosity parameter in the ADAF),
fi j P gas =P total = 0:5 (i.e. equipartition between the gas and the magnetic field), fl = 13=9 = 1:44 (adiabatic
index of the gas) and ffi = 10 \Gamma3 (fraction of the viscous dissipation that goes directly into heating the
electrons). We adopt these standard values of ff ADAF , fi and fl in the present models (see x6 for the effect
of varying ffi). We take —
M T to be given by the predictions of binary evolution models (Fig. 3) and obtain
—
MADAF via equation (6) for a given assumed value of g. We calculate the spectral energy distributions of
the models and numerically integrate the spectra to obtain the luminosities in the 0.5­10 keV band. The
results are discussed in the following sections.

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4.1. ADAF models of BH SXTs
Figure 4 shows two bands of luminosities corresponding to ADAF models of BH SXTs. In the upper
band —
MADAF = —
M T , i.e. the entire —
M T is accreted by the black hole via the ADAF, while in the lower band
—
MADAF = —
M T =3 (or g = 1=2). The lower band is in satisfying agreement with the observed luminosities.
The agreement (with a reasonable value of g) shows that the modeling of the quiescent X­ray emission of
BH SXTs with the ADAF model is consistent with the predictions of binary evolution models. The increase
in the luminosity with increasing P orb is also in good agreement.
The bolometric radiative efficiency in the ADAF models constructed here is typically ¸ 10 \Gamma3 compared
to ¸ 10 \Gamma1 for standard thin disk accretion. The X­ray radiative efficiency of these ADAF models is another
two or three orders of magnitude lower since much of the ADAF luminosity comes out as synchrotron
radiation in the optical. Note that these results are sensitive to various details of the ADAF models, and
in particular to the choice of ff ADAF and fi. For instance, we find that, if ff ADAF = 0:1, a fraction ¸ 1=5 of
the mass supplied by the secondary must be accreted via the ADAF in order to obtain agreement with the
observed quiescent luminosities of BH SXTs. The fraction goes down further to ¸ 1=10 if ff ADAF = 0:025.
4.2. ADAF models of NS SXTs
The presence of a hard surface on the accreting star is the key feature of ADAF models of NS SXTs.
The large amount of energy advected in the ADAF, which is lost through the event horizon in BH SXTs,
will be reradiated from the NS surface (Narayan & Yi 1995b). Narayan et al. (1997b) and Garcia et al.
(1998) argued that this additional source of luminosity is the explanation for the systematically larger
luminosity of quiescent NS SXTs as compared to quiescent BH SXTs (Figs 1 and 2). We now investigate
this quantitatively.
In the following, we assume that the thermal energy stored in the ADAF is reradiated as blackbody
emission with a radiative efficiency j ¸ 0:1. The luminosity in the 0.5­10 keV band will be dominated by
the emission coming from the NS surface, so that the additional emission from the ADAF can be ignored
(for simplicity). We also assume that the reradiation occurs from a small fraction f surf of the NS. This is
in agreement with observations of quiescent NS SXTs (e.g. Verbunt et al. 1994; Campana et al. 1998).
For now, we do not seek to justify the small emitting area of the NS. We simply assume for all our NS
models that the area is 10 km 2 . However, our results are not seriously affected even if the radiating area is
increased or decreased by, say, an order of magnitude (i.e as long as most of the blackbody emission is in
the 0.5­10 keV X­ray band). The typical effective temperatures found are T eff ¸ ! 0:5 keV.
The upper band in Fig. 5 shows the luminosities predicted by binary evolution models if g = 1=2, i.e a
third of the mass transferred by the secondary is accreted onto the NS (just as in BH SXTs). We see that
the luminosities predicted are much larger than those observed, by ¸ 3 orders of magnitude (except for the
system EXO 0748­676; see x7 for a discussion of this system). Since any contribution to the mass transfer
by magnetic braking would only increase the mass transfer rates expected (in short orbital period systems),
the discrepancy between the observed and predicted luminosities would be even more serious if magnetic
braking was effective.
One possibility for the discrepancy is that most of the quiescent flux from NS SXTs is emitted outside
the 0.5­10 keV X­ray band. This explanation seems, however, rather unlikely since this emission would
be seen somewhere else in the spectrum, say in hard X­rays or soft fl­rays. Aql X­1 has been observed

-- 8 --
in quiescence in hard X­rays and it is clear that the energy does not come out in the 10­100 keV band
(Campana et al. 1998). In addition, although some theoretical models of boundary layers between an
accretion flow and a NS predict substantial deviations from blackbody emission at higher energies (e.g.
Shapiro & Salpeter 1975, Turolla et al. 1994), there are no models predicting that such a large fraction
(¸ 0:999) of the emission would come out in hard X­rays or fl­rays.
We must therefore consider the possibility that only a small fraction of the mass supplied by the
secondary actually reaches the surface of the NS. The lower band in Fig. 5 shows that the luminosities of
quiescent NS SXTs can be accounted for (except EXO 0748­676) if only a fraction ¸ 10 \Gamma3 of the transferred
mass reaches the NS surface. This is of course a surprisingly small fraction. In the following section, we
argue that the propeller effect can explain the fraction, while in x6 we argue that winds from ADAFs could
further reduce the amount of mass reaching the NS surface.
5. Propeller Effect in Quiescent Neutron Star SXTs
The propeller effect in accreting neutron stars was initially proposed by Illarionov & Sunyaev (1975) to
explain the existence of long­period X­ray pulsars, and it was later developed in more detail by Davies and
Pringle (1981; see also Wang & Robertson 1985). Although the exact details vary, the basic mechanism of
the effect relies on the presence of a centrifugal barrier at the rotating magnetosphere of a rapidly spinning
NS.
Inside the magnetosphere, the accreting gas is forced to follow the magnetic field lines of the NS
since, by definition, in this region magnetic forces dominate the flow dynamics. The fate of the gas is then
determined by the relative magnitudes of the magnetospheric radius, Rm , and the corotation radius, R co ,
defined
by\Omega ? j (GM=R 3
co ) 1=2 ,
where\Omega ? is the angular velocity of the NS (and the magnetosphere). If
R co ! Rm , the magnetosphere rotates so fast that the centrifugal force at Rm is larger than the force
of gravity and hardly any of the gas cannot be accreted onto the NS. This is the propeller effect. The
efficiency of the propeller effect is not well understood (see Davies, Fabian, & Pringle 1979, and Davies &
Pringle 1981). It is also not clear whether the accreting matter is ejected from the system or is merely
accumulated in a boundary layer around the magnetosphere (Wang & Robertson 1985). However, from the
simple physical argument outlined above, it is clear that normal accretion onto the neutron star is inhibited
during the propeller phase.
The first direct observational evidence for the existence of the propeller effect in accreting neutron stars
was reported by Cui (1997) in two X­ray pulsars, GX 1+4 and GRO J1744­28. Cui showed that in both
systems X­ray pulsations ceased during a period of low X­ray flux, which he interpreted as the result of a
decrease in the mass accretion rate and a corresponding increase in the magnetospheric radius to beyond
the corotation radius. Campana et al. (1998) and Zhang et al. (1998) argued that the propeller effect was
also seen in a NS SXT, Aql X­1, during its most recent outburst; the system showed an abrupt decrease of
the X­ray flux, accompanied by considerable hardening of the X­ray spectrum. Both sets of authors propose
that the hard spectrum originates just outside the magnetosphere, where the gas becomes very hot due to
the action of the propeller.
Observations of Aql X­1 show that even in quiescence the blackbody spectral component does not
disappear entirely implying that a small amount of material continues to accrete onto the star, contrary to
simple models of the propeller (Verbunt et al. 1994; Stella et al. 1994). To resolve this problem, Zhang et
al. (1998) propose that accretion in quiescent NS SXTs occurs via a quasi­spherical ADAF, rather than a

-- 9 --
thin disk. This allows some material to accrete near the poles, thereby bypassing the centrifugal barrier. In
this section we develop this idea quantitatively.
5.1. Accretion Geometry in Quiescence
In the following, we assume for simplicity that the NS spin axis is perpendicular to the binary orbital
plane and that the NS spin and magnetic axes are aligned.
5.1.1. Magnetospheric Radius
In the presence of a spherical accretion flow (e.g. Bondi 1952), the magnetospheric (or Alfv`en) radius,
Rm , is usually defined as the radius at which the magnetic pressure, Pmag = B 2 =8ú, due to the neutron
star magnetic field balances the ram pressure, P ram j aev 2
r =2, of the accreting gas, where v r is the radial
infall velocity of the gas (e.g. Frank et al. 1992). The contribution from the thermal pressure of the gas
is generally neglected when considering Bondi­type flows which are highly supersonic (free­falling). An
ADAF, on the other hand, is subsonic down to a few Schwarzschild radii (e.g. Narayan, Kato, & Honma
1997; Chen, Abramowicz & Lasota 1997) and the thermal pressure term must be taken into account.
The polar structure of ADAFs was described by Narayan & Yi (1995a) in the self­similar approximation.
They showed that in the limit of strong advection (f adv ¸ 1), the gas density and temperature (and
therefore the thermal pressure of the gas) are essentially independent of the polar angle `; i.e. these
quantities are nearly constant on spherical shells centered on the accreting object. On the other hand,
the radial infall velocity is smaller than the thermal sound speed in the equatorial plane and decreases
towards the poles. Clearly then, the thermal pressure of the accreting material is the dominant term in
calculating the magnetospheric radius. Since this pressure is constant with `, the magnetosphere will be
nearly spherical.
Despite the difference between a Bondi spherical accretion flow and an ADAF, the value of Rm is
roughly the same in the two cases. In the former, essentially all the gravitational energy released during
accretion goes into bulk kinetic energy of the flow, while in ADAFs, the energy is stored as thermal energy
of the gas. Thus, the ram pressure in Bondi flows must be of the same order as the thermal pressure in
ADAFs. The magnetospheric radius in quiescence then takes the same form (Frank et al. 1992):
Rmq = 6:45 \Theta 10 5 —
m \Gamma2=7 m \Gamma3=7 B 4=7
8 R 12=7
NS;6 cm; (7)
where B 8 is the NS surface magnetic field in units of 10 8 G and RNS;6 is the NS radius in units of 10 6 cm.
For the remainder of the paper, R refers to a radius in physical units and r refers to a radius in
Eddington units.
5.1.2. Accretion in the Propeller Phase
The propeller effect in binary systems is generally discussed in the context of thin disk accretion. In
this model, once the propeller becomes effective, no matter is able to reach the NS surface because the
centrifugal acceleration acts equally against gravity for all the matter located in the disk orbital plane.

-- 10 --
In a spherical flow, however, the centrifugal acceleration at the magnetospheric radius acting on a
parcel of gas, accreting at a polar angle ` from the spin axis, is equal to A c
=\Omega 2
? Rmq sin `,
where\Omega ? is the
angular speed of the magnetic field lines anchored in the NS. The direction of this force is perpendicular
to the spin axis of the NS (and parallel to the orbital plane), so that the component of A c along the
radial direction is simply A c sin `
=\Omega 2
? Rmq sin 2 `. The maximum polar angle below which the gravitational
acceleration (=
Rmq\Omega 2
K (Rmq )) wins over the centrifugal force is given by
sin ` 0
=\Omega K (Rmq )
\Omega ?
: (8)
For ` 0 Ü 1 this simplifies to
` 0
'\Omega K (Rmq )
\Omega ?
: (9)
Note that the residual force acting on all parcels of gas, even those which do not overcome the
centrifugal barrier, tends to direct them toward the orbital plane. In this simple formulation, we do not
consider possible complications due to field line orientation effects.
5.1.3. Fraction of Mass Reaching the NS Surface
Only matter accreting between ` = 0 and ` = ` 0 can overcome the centrifugal barrier and reach the
surface of the NS. The mass accretion rate onto the star is then
—
MNS = \Gamma2
Z `0
0
2úR sin `aev r Rd`; (10)
where ae = ae(R; `) ' ae(R) is the gas density and v r = v r (R; `) ' v r (R) sin 2 ` is the radial infall velocity at
angle ` (positive outward), as given by the self­similar solution of Narayan & Yi (1995a). The factor of 2 in
equation (10) is introduced to account for the two polar caps. The fraction of the total mass accretion rate
—
MADAF in the ADAF that reaches the NS surface is then
f acc j
—
MNS
—
MADAF
' 2
R `0
0 2úR 2 sin `ae(R)v r (R) sin 2 `d`
2
R ú=2
0 2úR 2 sin `ae(R)v r (R) sin 2 `d`
= 2
R `0
0 sin 3 `d`
2
R ú=2
0 sin 3 `d`
' 3
8 ` 4
0 ' 3
8
`\Omega K (Rmq )
\Omega ?
' 4
; (11)
where the last two steps have been calculated in the limit of small ` 0 . For a neutron star with a spin period
of 2 ms, a magnetic field strength of 3 \Theta 10 8 G and accreting at —
mADAF = 10 \Gamma3 , we find f acc ' 0:75 \Theta 10 \Gamma3 .
Note that if the radial velocity does not vary as sin 2 ` but is more nearly constant with ` (as in Bondi
accretion), then f acc would be larger (e.g., if v r (R; `) is independent of `, f acc / ` 2
0 only). On the other
hand, if the accretion flow has a toroidal morphology with empty funnels along the rotation axis, f acc would
be a lot lower than the expression given in equation (11), perhaps even zero. There is thus considerable
uncertainty in the value of f acc .
5.1.4. Fraction of the NS Surface Emitting Radiation
We assume that the gas accreted during the propeller phase follows the magnetic field lines down to
the NS polar caps, where its kinetic and thermal energy is converted to radiation. Dipolar field lines satisfy

-- 11 --
the parametric equation (e.g. Frank et al. 1992):
R = C sin 2 `; (12)
where C is constant for a given field line. Thus, the field lines intersecting the magnetospheric radius at
` = ` 0 , emerge from the NS surface at a polar angle ` S given by:
sin 2 ` S
sin 2 ` 0
= RNS
Rmq : (13)
The accreting material reaches the NS surface at ` Ÿ ` S , and therefore the fraction of the neutron star
surface that re­radiates the accreted energy is
f surf j
2 R `S
0 2ú sin `d`
2 R ú=2
0 2ú sin `d`
' ` 2
S
2 ' ` 2
0
2
RNS
Rmq
; (14)
where we have made use of the fact that ` S ! ` 0 Ü 1. Note the direct dependence of f surf on the NS
magnetic field strength B through Rmq . For a neutron star with a spin period of 2 ms, a magnetic field
strength of 3 \Theta 10 8 G and accreting at —
mADAF = 10 \Gamma3 , we find f surf ' 3 \Theta 10 \Gamma3 .
5.2. Equilibrium Spin Frequency
Equations (11) and (14) demonstrate that in quiescence the mass accretion rate onto a NS and the
emitting area, which determine the total luminosity and spectrum of the system, depend strongly on the
NS angular rotation
speed\Omega ? and the field strength.
Although\Omega ? is not known for most NS SXTs, we
discuss in this section how it can be estimated using our knowledge of the accretion history of an SXT and
of the interaction between the magnetosphere of the NS and the accretion flow.
During the propeller phase, in quiescence, the NS ejects most of the accreting gas that reaches its
magnetosphere. The ejected material leaves the system with higher specific angular momentum than it
had coming in, which results in an effective spin­down of the NS. However, NS SXTs experience outbursts
during which the mass accretion rate onto the NS is orders of magnitude higher than in quiescence. High
—
M causes the magnetosphere to shrink inside the corotation radius so that all the accreting gas is able to
reach the NS surface. The mass and angular momentum of the accreting gas is added to the NS, which
causes it to spin­up. A NS SXT that accretes for a fairly long time is expected to reach an equilibrium spin
frequency\Omega ?;eq such that the spin up during outburst is balanced by the spin down during quiescence.
At the onset of mass transfer, the spin period of the NS in an SXT is likely to be different from the
equilibrium value. In standard Ghosh & Lamb (1979) type models (for steady disks), the timescale Ü eq on
which a typical NS reaches the equilibrium spin period is usually small ( ¸ ? 10 5 yr) compared to the lifetime
of LMXBs (10 8 \Gamma 10 9 yr; see, e.g., Henrichs 1983 for a review). Although Ü eq may be a little larger for
transient accretion, it is reasonable to assume that most of the neutron stars in SXTs have rotation rates
close
to\Omega ?;eq . It is straightforward to show
that\Omega ? is basically unaffected by a single outburst or a single
quiescent phase, because the time spent between two outbursts (¸ a few years) is much shorter than Ü eq .
Therefore, it is not necessary to consider the small jitter
in\Omega ? during the quiescence­outburst cycle. In
the following, we simply assume that once a NS SXT has reached spin equilibrium,
then\Omega ?
=\Omega ?;eq both
during outburst and quiescence.

-- 12 --
5.2.1. Idealized Model for the Spin­up and Spin­down Torques
To determine the equilibrium spin frequency of a NS in a transient binary system we need a theoretical
description of the interaction between the NS and the accretion flow. We begin with the outburst phase
during which accretion occurs via a thin disk and the torque exerted by the accreting gas on the NS is
relatively well understood.
Despite some modifications, current models describing the interaction between a NS and a magnetically
threaded thin accretion disk remain essentially identical to the model initially proposed by Ghosh &
Lamb (1979). In this model, the spin­up torque on the NS results from two contributions. First, the
gas that follows magnetic field lines and reaches the NS surface gives its angular momentum to the NS
(spin­up). Second, the interaction between the magnetic field lines and the threaded thin disk beyond
the magnetospheric radius results in a positive torque on the NS for radii where the field lines rotate
slower than the local Keplerian angular speed of the gas. The lines that thread the disk further out give a
(smaller) negative torque on the NS since these field lines rotate faster than the local Keplerian angular
speed of the gas (Gosh & Lamb 1979). Recent detailed numerical simulations by Daumerie (1996) show
that the overall contribution resulting from the interaction of the accretion flow and the magnetic field lines
beyond the magnetospheric radius is nearly equal to the contribution to the spin­up from the gas reaching
the NS surface. Further, he finds that the torque varies roughly linearly with the fastness parameter
!
j\Omega ?
=\Omega K (Rm ).
Using Daumerie's work as a guide, we propose the following idealized formula for the torque:
—
J = 2 —
MR 2
m\Omega K (Rm )
Ÿ
1 \Gamma
`\Omega ?
\Omega K (Rm )
'–
; (15)
where the factor of 2 appears because of the two nearly equal contributions to the spin­up mentioned above.
Equation (15) assumes that the fastness parameter at equilibrium, ! crit , is exactly unity. This is consistent
with the recent arguments of Wang (1995; see also Wang 1987).
The torque in the propeller regime,
when\Omega ?
?\Omega K (Rm ), is not as well constrained. By analogy with
Ghosh & Lamb type models, we assume that the torque arises from two nearly equal contributions. One
contribution is the negative torque applied to the NS when the propeller expels gas at the magnetosphere
and the other is the negative torque 5 due to the interaction of the magnetic field lines with the accretion
flow beyond the magnetospheric radius. If the gas expelled leaves the magnetosphere with an angular
momentum corresponding to the angular rotation speed of the NS,
viz.\Omega ? (which corresponds to an
efficient propeller), then the negative torque on the NS in the propeller phase is
—
J ¸ \Gamma2 —
MR 2
m\Omega ? ; (16)
where —
M is the rate at which mass reaches the magnetosphere. (The small positive contribution from
the very small fraction of mass accreted on to the NS is neglected.) This expression is in agreement with
equation (15) in the limit
of\Omega ?
AE\Omega K (Rm ). Therefore, we can use the prescription given by equation (15)
to describe the interaction between the NS and the accretion flow throughout the outburst--quiescence
cycle. Since this expression for the torque is a continuous function
of\Omega ? and Rm , it is both realistic and
convenient for calculations.
5 This contribution to the torque is always negative in the propeller regime
because\Omega ?
?\Omega K (R) for all R ? Rmq .

-- 13 --
5.2.2. Spin Equilibrium
We define \DeltaJ o = —
J o \Deltat o to be the integrated spin­up torque over an outburst of duration \Deltat o ,
and \DeltaJ q = —
J q \Deltat q to be the integrated spin­down torque during a propeller phase of duration \Deltat q .
The recurrence time of the SXT is \Deltat o + \Deltat q . We assume, for simplicity, that the two phases can be
approximated as bimodal, with the outburst phase occurring at a typical accretion rate —
M o and the
quiescent phase having a typical lower accretion rate —
M q . These accretion rates define, in turn, the values
of the magnetospheric radius in outburst, 6 Rmo , and in quiescence, Rmq , used in equation (15) to determine
—
J o and —
J q . Since the accretion rate from the peak of the outburst is known to decrease gradually with time,
the value of —
M o used to determine Rmo should be interpreted as a mean over the outburst.
By definition, the NS angular rotation speed at
equilibrium\Omega ?;eq satisfies \DeltaJ o = \DeltaJ q . Using
equation (15), we find
\Omega ?;eq
=\Omega K (Rmq )
`
Rmq
Rmo
' 3=2
Ÿ
1 +
i
Rmq
Rmo
j 1=2
g
–
Ÿ
1 +
i
Rmq
Rmo
j 2
g
– ; (17)
where g is defined in equation (6) and is given by —
M q \Deltat q = —
M o \Deltat o , i.e. the total mass reaching the
magnetosphere during the ADAF­propeller phase divided by the total mass accreted during outburst. Note
that the spin equilibrium period defined by equation (17) differs from the spin equilibrium period defined
for steady accretion onto a NS and usually discussed in the literature (e.g. Henrichs 1983).
5.3. Propeller Regime at Spin Equilibrium
Equation (17) allows us to determine the equilibrium spin period P spin as a function of the parameter
g = —
MADAF = —
M accum . This, in turn, allows us to estimate the quantities f acc (Eq. [11]) and f surf (Eq. [14])
which are relevant for determining the observational properties of quiescent NS SXTs. In the following
calculations, we assume for definiteness that the NS accretes at the Eddington rate ( —
m o = 1) in outburst
and that the mass transfer accretion rate in quiescence is —
m T = 10 \Gamma2:5 (cf Fig. 3). However, our conclusions
do not depend crucially on these assumptions.
Figures 6 and 7 show the variations of —
mNS = —
m T = f acc \Theta g=(1 + g), f surf and P spin with g. As —
mADAF
decreases, the magnetosphere becomes more extended and the propeller effect becomes more efficient. The
solid lines show the results for a NS with a magnetic field strength B = 10 8 G, while the dashed and dotted
lines show the cases B = 10 9 and B = 10 10 G, respectively. Note that recent observations suggest that
accreting neutron stars in low mass binaries have rather low magnetic fields, typically B ¸ ! 10 9 G (e.g.
White & Zhang 1997).
Figure 6 can be related to Fig. 5, where we found that —
mNS= —
m T ¸ 10 \Gamma3 was needed in order to explain
the very low observed luminosities of quiescent NS SXTs. Such a value of —
mNS = —
m T is predicted by the
propeller model if g ¸ 1=5. This value of g is reasonably close to the value g ¸ 1=2 that we obtained for
BH SXTs. Note that the dependence of —
mNS = —
m T on the magnetic field B should cancel out through the
ratios Rmq=Rmo in equation (17). For low magnetic field strengths, however, the inner edge of the disk in
6 Following Frank et al. (1992), we use a value for the magnetospheric radius of the thin disk that is half that used for
spherical accretion (Eq. [7])

-- 14 --
outburst is not given by half the value in equation (7) but is fixed at the last stable orbit at 3 Schwarzschild
radii (for instance, if —
m o – 0:1 and B Ÿ 10 9 G). Consequently, there is a residual dependence of —
mNS = —
m T
on B for small B.
Figure 7a shows that the fraction f surf of the NS surface that emits in quiescence depends much more
strongly on B than f acc does (Fig. 6), as expected from equation (14). For values of g ¸ 1=5 and low
magnetic fields (B ¸ ! 10 9 G), the emitting surface is typically between 1 and 10 km 2 . Observations of
quiescent NS SXTs suggest an emitting surface ¸ 1 km 2 (e.g. Verbunt et al. 1994; Campana et al. 1998).
Given that the surface could very well be underestimated by the standard techniques (e.g. Lewin, Van
Paradijs & Taam 1993), values of ¸ 1 \Gamma 10 km 2 appear in reasonable agreement with the observations.
We note, however, that this result depends quite crucially on the assumed alignment of the NS spin and
magnetic axes. This is a major uncertainty in the calculations.
Figure 7b shows that P spin is even more sensitive to the value of B. For weak magnetic fields (B ¸ ! 10 9
G), the values of the equilibrium spin period are in the range 1 \Gamma 10 ms, which is in agreement with values
recently discussed in the literature for accreting neutron stars in low mass binaries (e.g. White & Zhang
1997).
There are several sources of uncertainty in our simplified model for the propeller, which are discussed
in x6.2 and x7 below. The proximity of the value g ¸ 1=2 required to explain the quiescent luminosities of
BH SXTs to the value g ¸ 1=5 required to explain the luminosities of NS SXTs (with a propeller) suggests,
however, that roughly the same geometry of accretion (outer thin disk and inner ADAF sharing the mass
supplied by the secondary roughly equally) can account for the properties of both classes of objects. The
presence of a hard surface and a magnetic field associated with the spinning neutron star are two major
ingredients of the model. The NS SXTs Aql X­1 (B ¸ 10 8 G, P spin ¸ 2 \Gamma 3 ms, emitting area ¸ 1 km 2 ;
White & Zhang 1997; Zhang et al. 1998; Campana et al. 1998) and SAX J1808.4­3658 (B ! 2 \Theta 10 8
G, P spin = 2:49 ms; Wijnands & van der Klis 1998; Chakrabarty & Morgan 1998) are two interesting
candidates that could allow further testing of the predictions of our ADAF­propeller scenario.
6. Winds from ADAFs and the Efficiency of the Propeller Effect
The gas in an ADAF can in principle escape to infinity via a wind because the Bernoulli parameter in
the accretion flow, a measure of the energy of the gas at infinity, is positive (Narayan & Yi 1994, 1995a).
Blandford & Begelman (1998, hereafter BB98) derived self­similar ADAF solutions that include mass loss
via winds and showed that the Bernoulli parameter can become negative if strong enough winds are present.
They further suggested that the luminosity difference between NS and BH SXTs in quiescence would be
reduced by the combined effect of winds and a smaller value of ff ADAF . This is because for a given rate of
accretion onto the central object, the higher the radiative efficiency of the ADAF (e.g. for smaller ff ADAF ),
the smaller is the difference in luminosity. Similarly, for a given radiative efficiency of the ADAF, the
smaller the accretion rate onto the central object (due to winds), the smaller is the difference in luminosity.
Our results in x4.1 suggest that reducing ff ADAF has only a small effect, so we do not pursue this
option. Quataert & Narayan (1998) showed that the most efficient way of increasing the radiative efficiency
of the ADAF is to include winds and simultaneously increase the value of the parameter ffi, the fraction
of the viscously dissipated energy that directly heats the electrons. They found that models with winds
and high ffi are consistent with the current observations for the BH SXT V404 Cyg in quiescence and the
Galactic Center source Sgr A*. We consider models of this kind for NS SXTs in quiescence.

-- 15 --
In x6.1 and x6.2, we investigate the following two questions. Can winds by themselves, i.e. without any
propeller effect, explain the observed quiescent luminosities of NS SXTs? If not, is a combination of winds
and a propeller consistent with the observations?
6.1. ADAF Models of NS and BH SXTs with Winds
Following BB98, we assume that the accretion rate in the ADAF scales in a self­similar way, i.e.
—
m(r) = —
m(r tr )
`
r
r tr
' p
; (18)
where 0 ! p ! 1 and we assume that the wind is effective over the entire radial extent of the ADAF out to
r out = r tr , the transition radius.
The efficiency of mass loss is not only determined by p, but also by the radial extent of the ADAF
(Eq. [18]). Around a black hole, the ADAF extends from the transition radius (r tr ) down to the event
horizon, and so the accretion rate onto the black hole is —
m in = —
m(r tr )(1=r tr ) p . Around a neutron star,
however, the ADAF has a minimum radius equal to the magnetospheric radius r m , so that the accretion
rate at the magnetosphere is —
m in = —
m(r tr )(r m =r tr ) p . If r m AE 1, as is the case for r mq in quiescent NS
SXTs, then for a given value of p, the presence of a magnetosphere around the NS significantly reduces the
total mass loss relative to the BH case. The value of r m itself depends on the local accretion rate at the
magnetosphere (Eq. [7]). Since the accretion rate at a given radius decreases with increasing p, a larger p
implies both a larger r m and a smaller radial extent for the ADAF.
We solve for the magnetospheric radius by combining equations (7) and (18) and find
r mq =
h
1:35 \Theta —
m(r tr ) \Gamma2 r 2p
tr B 4
8 R 12
NS;6
i 1
7+2p
; (19)
where r mq is expressed in Schwarzschild units for a NS of 1.4 M fi (Eq [19] is the generalization of Eq [7] for
non­zero p). We have confirmed (by combining Eqs. [18] and [19]) that despite the reduction of the radial
extent of the ADAF for larger values of p, increasing p leads to an effective reduction of —
m(rmq ) for any
reasonable values of p, r tr and —
m(r tr ).
For a standard NS with low magnetic field strength (B 8 = 1, RNS;6 = 1) and a typical accretion rate at
the outer boundary of the ADAF —
m(r tr ) = 1=3 \Theta 10 \Gamma2:5 (x4.2; Fig. 3), we find r mq ' 10 in the absence of a
wind (p = 0). For a wind with p = 0:4, r tr = 10 4 (``intermediate'' wind model, ffi = 0:3), we find r mq ' 20
and —
m(rmq )= —
m(r tr ) ' 8 \Theta 10 \Gamma2 , while for a wind with p = 0:8, r tr = 10 4 (``strong'' wind model, ffi = 0:75),
we find r mq ' 35 and —
m(rmq )= —
m(r tr ) ' 1 \Theta 10 \Gamma2 . For these estimates, we have chosen r tr = 10 4 by analogy
with the values usually inferred in quiescent BH SXTs (Narayan et al. 1996; Menou et al. 1998). Were r tr
to be smaller, the overall mass loss in the wind for a given p would be smaller. Note that the ADAF cannot
extend far beyond 10 4 Schwarzschild radii because, for a given —
m ( r tr ), there is a maximum radius out to
which the ADAF can exist (e.g. Esin et al. 1997; Menou et al. 1998).
Figures 8 and 9 show the predicted quiescent luminosities of BH and NS SXTs according to the
intermediate wind model (p = 0:4, r tr = 10 4 , ffi = 0:3), assuming that there is no propeller. Following
Quataert & Narayan (1998), we computed the ADAF models assuming that the dominant effect of the wind
on the structure and the emission properties of the ADAF is to reduce the density in the accretion flow; in
addition, we assume that the emission from the wind itself can be neglected relative to the emission from
the accretion flow.

-- 16 --
Figure 8 shows the quiescent X­ray luminosities (0.5­10 keV) of BH SXTs predicted by this
ADAF+wind model assuming that —
m(r tr ) is equal to 1=3 of the mass supplied by the secondary, and
assuming —
m(r) = —
m(r tr )(r=r tr ) 0:4 . This model gives roughly the same X­ray luminosities as the previous
no­wind ADAF model (x4.1). The actual mass accreting onto the black hole is reduced here, but nevertheless
the luminosities are the same because of the increase in the value of ffi from 10 \Gamma3 to 0:3 (see Quataert &
Narayan 1998).
Figure 9 shows the quiescent X­ray luminosities (0.5­10 keV) of NS SXTs predicted by the same
ADAF+wind model. The magnetospheric radius is r mq = 20 and we have assumed that all the mass
reaching the magnetosphere is accreted onto the NS surface (i.e. no propeller effect). Since the X­ray
luminosity of the ADAF is still much less than the luminosity coming from the NS surface, the main effect
of including the wind is to decrease the luminosity of quiescent NS SXTs in proportion to the reduction of
—
m at the inner edge of the ADAF (Eq. [18]). By comparing figures 5 and 9, it is clear that the luminosity
is descresed by roughly an order of magnitude, which is insufficient to explain the observations. Thus, the
intermediate wind scenario must also invoke a propeller effect, though with a somewhat lower efficiency
than that described in x5. Given the uncertainties in our propeller model (see x6.2), we see no objection to
such a model.
Only for the strongest wind models (p ¸ 1, r tr = 10 4 ) does the luminosity difference between NS SXTs
and BH SXTs predicted by the models reduce to the observed difference. For p = 1 and r tr = 10 4 (B 8 = 1,
RNS;6 = 1), Eq. (18) and (19) predict r mq ' 58 and —
m(rmq )= —
m(r tr ) ' 6 \Theta 10 \Gamma3 , which is basically consistent
with the small accretion rates required to explain the observed quiescent luminosities of NS SXTs (cf.
Fig. 5). But is this a reasonable model? Can the propeller effect be completely ineffective at preventing
mass from reaching the NS surface?
6.2. The Efficiency of the Propeller Effect
If the neutron stars in NS SXTs have spin periods of typically a few ms, as suggested by recent
observations (e.g. White & Zhang 1997; Zhang et al. 1998; Campana et al. 1998; Wijnands & van der Klis
1998), their corotation radii are a few Schwarzschild radii. This is substantially smaller than the few tens
of Schwarzschild radii inferred for r mq in x6.1. The propeller effect is therefore expected to act in these
systems (Illarionov & Sunyaev 1975). Note that the values of r mq quoted in x6.1, which correspond to a
magnetic field strength B of 10 8 G, would be even larger for a larger B (eq. [19]). Can the propeller in such
a system be so ineffective that f acc ¸ 1?
We pointed out in x5.2 that there are large uncertainties in the valus of f acc , which come mainly from
the strong dependence of f acc on the NS rotation speed and the magnetospheric radius: f acc
/\Omega \Gamma4
? R \Gamma6
mq
(the dependence on Rmq also affects the size of the NS emitting area, since f surf / R \Gamma4
mq ). The latter source
of uncertainty is perhaps more important, since
while\Omega ? can be determined by direct observations, Rmq
must be deduced from theoretical arguments.
Although the value of Rmq used in our work (Eq. [7]) is standard, it is based on simple dimensional
arguments. Given the strong dependence of f acc on Rmq , an error, for instance, of only a factor of 1:5 in Rmq
translates to an error of more than an order of magnitude in f acc . Recent work by Psaltis & Chakrabarty
(1998) shows that the standard scaling used for Rmq (for disk­magnetosphere interactions) is not consistent
with observations in at least one weakly magnetized NS SXT (SAX J1808.4­3658). Consequently, we cannot
rule out the possibility that equation (7) overestimates the value of Rmq for an ADAF­magnetosphere

-- 17 --
interaction. The propeller effect would then be significantly less efficient than our previous results suggest
(x5).
If winds alone (p ¸ 1) are to explain the reduced luminosity difference between BH and NS SXTs in
quiescence, we need a highly inefficient propeller. For example, from the no­wind (p = 0) model to the
p = 1 model described in x6.1, r mq increases by a factor ' 5:8 which implies a ¸ 4 \Theta 10 4 times more efficient
propeller according to equation (11). Since the p = 0 model has a propeller with f acc = 10 \Gamma3 , the propeller
would have to be ¸ 10 7 times less efficient in the p = 1 model than we would infer based on the theory
described in x5. In addition, in the presence of a wind, the value of f acc is likely only to be smaller than the
expression in equation (11). This is because the wind flows out preferentially from the polar regions of the
ADAF (Narayan & Yi 1995a), so there is no gas to flow down to the polar caps of the NS. Even allowing
for reasonable uncertainties in the scalings in equation (7), it does not seem likely that the propeller model
could be that wrong. We therefore feel that the p ¸ 1 strong wind model is unlikely.
7. Discussion
Chen et al. (1998; their Fig. 3) argued that the segregation in luminosity swing between outburst and
quiescence previously found by Narayan et al. (1997b) and Garcia et al. (1998) disappears in a large sample.
We point out in this paper that the Chen et al. sample is larger only because they include numerous upper
limits, many of which are based on observations with insufficient sensitivity to detect typical quiescent
SXTs. Unless treated with care, for instance with a ``detection and bounds'' type method (e.g. Avni et
al. 1980; Schmitt 1985), upper limits can obscure a true correlation, and indeed this is the case with the
analysis of Chen et al. (1998).
Our Fig. 2 shows a carefully selected and smaller sample, and we find that there is a clear difference of
luminosity between quiescent BH and NS SXTs. Furthermore, we argue, based on theoretical mass transfer
rates, that it is important to compare quiescent luminosities of NS SXTs and BH SXTs of similar orbital
periods. We find that BH SXTs with short orbital periods are about 2 orders of magnitude fainter in
quiescence (in Eddington units) than NS SXTs with comparable orbital periods. Future observations with
AXAF and XMM will hopefully increase the sample size sufficiently to allow a separate comparison between
long and short period systems. This should help confirm the conclusions of this paper and may solidify the
arguments advanced by Narayan et al. (1997b) and Garcia et al. (1998) for event horizons in black holes.
We find that the luminosities of quiescent NS SXTs are lower than the values predicted by standard
binary evolution models. Following Zhang et al. (1998), we have shown that the propeller effect offers a
plausible explanation for the discrepancy. However, although our model for the propeller effect accounts
for the luminosities and small emitting areas of quiescent NS SXTs, it suffers from several sources of
uncertainty that may affect the results significantly.
The predictions of the model strongly depend on the spin
frequency\Omega ? of the NS and therefore on the
prescription chosen for the torque (Eq. [15]). The magnitude of the torque is not well known, especially in
the propeller regime (e.g. Davies, Fabian & Pringle 1979; Henrichs 1983). The results of our calculations
are also sensitive to the precise values of the magnetospheric radii in quiescence and outburst and to the
assumption ! crit = 1.
If ! crit !
1,\Omega ?;eq is reduced by a factor ! crit (Eq. [17]) and more mass is accreted because f acc is
/ ! \Gamma4
crit . Note, however, that independently of equation [15] and the value of ! crit , spin periods of a few

-- 18 --
milliseconds and low magnetic field strengths (assuming that Eq. [7] is correct) lead to predictions for the
luminosities and surface areas that are consistent with the observations.
Even if the spin periods of neutron stars in NS SXTs are known, the predictions of our propeller
model are still somewhat uncertain because of the strong dependence of the fractions f acc and f surf on the
magnetospheric radius in quiescence Rmq . If the standard expression (Eq. [7]) overestimates the value of
Rmq , then the propeller effect could be less efficient than indicated by our results in x5. In that case, winds
from ADAFs could provide the additional mechanism required to explain the low quiescent luminosities of
NS SXTs.
We have also neglected the likely misalignment between the neutron star spin axis and magnetic axis
and have assumed a dipolar structure for the magnetic field. Relaxing these assumptions could also modify
our results, especially our estimates of the fractions f acc and f surf .
The system EXO 0748­676 appears unusually bright in our sample of quiescent NS SXTs. One possible
explanation is that magnetic braking acts more efficiently in this system because of its rather short P orb ,
giving a larger mass transfer rate. If the mass transfer rate is higher, the propeller effect would also be less
efficient, and would increase the mass falling on the NS even further. Note that EXO 0748­676 is known to
be an unusual binary system, as shown by its unexplained variations of P orb (Hertz, Wood & Cominsky
1997). Another possible explanation is that, for some reason (youth?), this particular system has not yet
reached equilibrium and spins at a relatively slower rate than other NS SXTs. This would result in a less
efficient propeller and a more luminous system in quiescence.
This last point is a general prediction of our propeller model: the propeller effect is less efficient if the
NS in a SXT spins slowly (P spin AE a few ms). It is possible that several such NS SXTs with slowly spinning
NSs exist in our Galaxy. In these NS SXTs, most of the mass accreted via the ADAF would reach the NS in
quiescence. The outbursts of these systems would therefore be of small amplitude (2­3 orders of magnitude
in X­rays rather than 5­6 orders of magnitude) because of their relatively high quiescent luminosities.
In our model, the gas which is stopped by the propeller is neglected and its fate is left unspecified.
This gas could affect both the dynamics and the emission properties of the accretion flow. For instance, it
is unclear how the mass accreted via the ADAF will find its way out of the quasi­spherical accretion flow
after being propelled outward.
In x6, we considered ADAF models with winds assuming that the efficiency p of the wind is the same
for BH and NS SXTs . In principle, p could be different for an ADAF around a BH and around a NS
(because of the presence of the magnetosphere for instance). Having a different value of p for BH and NS
SXTs would not, however, affect our conclusion that winds alone probably cannot explain the observed
quiescent luminosities of NS SXTs.
8. Conclusion
In this paper, we have reconsidered the luminosity difference between black hole and neutron star soft
X­ray transients in quiescence, which has been used to argue for the presence of event horizons in black
holes.
We show that quiescent BH SXTs as a class are fainter than NS SXTs. This result agrees with the
previous work of Narayan et al. (1997b) and Garcia et al. (1998), but it disagrees with the conclusions of

-- 19 --
Chen et al. (1998) who used an inappropriate sample of SXTs for their comparison.
We point out that, for a reliable comparison of the two classes of SXTs, objects with similar orbital
periods P orb should be compared. Otherwise, variations of the mass transfer rate —
M T with P orb can mask
the results.
We find that the observed luminosities of quiescent BH SXTs are consistent with the predictions of
binary evolution models for —
M T if roughly a third of the mass supplied by the secondary is accreted by
the black hole via an ADAF. This estimate is for ff ADAF = 0:3. The fraction goes down to 1=5 and 1=10
for ff ADAF = 0:1 and 0:025 respectively. The observed luminosities of quiescent NS SXTs suggest, on the
other hand, that only a very small fraction of the mass transferred by the secondary reaches the neutron
star surface.
We explain the small fraction in NS SXTs by invoking an efficient propeller. We have constructed a
model for the propeller effect that accounts for the observed luminosities of quiescent NS SXTs and their
small emitting areas. In addition, the model appears to be consistent with the millisecond spin periods
recently inferred from observations of accreting neutron stars in transient low mass binary systems (Aql
X­1, SAX J1808.4­3658).
Winds from ADAFs constitute an alternative explanation (BB98) for the very small fraction of mass
reaching the neutron star surface in quiescence. We argue that an ADAF model with strong winds and
no propeller cannot explain the observed luminosities. However, an ADAF model with a wind of low or
intermediate strength and a somewhat less efficient propeller (but still within the range of uncertainties
of our propeller model) is consistent with the observed quiescent luminosities of BH and NS SXTs. In
this case, the parameter ffi, which measures the fraction of the viscous energy that goes directly into the
electrons, has to be large ¸ 0:3, in agreement with the results of Quataert & Narayan (1998).
Acknowledgments
We are grateful to Josh Grindlay, Mario Livio, Philip Podsiadlowski, Dimitrios Psaltis and Eliot
Quataert for useful discussions. This work was supported in part by NASA grant NAG 5­2837. KM was
supported by a SAO Predoctoral Fellowship and a French Higher Education Ministry Grant. AE was
supported by a National Science Foundation Graduate Research Fellowship.

-- 20 --
Table 1: NEUTRON STAR AND BLACK HOLE SXTs
System P orb (hr) D (kpc) log[L min ] (erg s \Gamma1 ) m 1 (M fi )
(1) (2) (3) (4) (5)
ffi EXO 0748­676 3:82 a 10 e 34:1 1:4 ?
ffi 4U 2129+47 5:2 b 6:3 e 32:8 1:4 ?
ffi 1456­32 (Cen X­4) 15:1 a 1:2 e 32:4 1:4 ?
ffi 1908+005 (Aql X­1) 19 a 2:5 e 32:6 1:4 ?
ffi H1608­52 98:4 c or 5 d 3:6 e 33:3 1:4 ?
ffl GRO J0422+32 (XN Per 92) 5:1 2:6 g ! 31:6 12 k
ffl A0620­00 (XN Mon 75) 7:8 1 h 31:0 6:1 h
ffl GS2000+25 (XN Vul 88) 8:3 2:7 h ! 32:3 8:5 l
ffl GS1124­683 (XN Mus 91) 10:4 5 i ! 32:4 6 i
ffl H1705­250 (XN Oph 77) 12:5 8:6 h ! 33:0 4:9 l
ffl 4U 1543­47 27:0 8 e ! 33:3 n 7 m
ffl J1655­40 (XN Sco 94) 62:9 3:2 j 32:4 7 j
ffl GS2023+338 (V404 Cyg) 155:3 3:5 h 33:2 12 h
NOTE. -- (1) ffi indicates a NS primary and ffl a BH primary. (2) Orbital periods from McClintock (1998),
except where indicated. (3) Distances to the systems. (4) Luminosities in quiescence in the 0.5­10 keV band
(corrected for the revised distances) from Narayan et al. (1997b) and Garcia et al. (1998), except where
indicated. Quiescent luminosities for 4U1543­47 and GRO J1655­40 are based on 20.4 ks and 100 ks ASCA
observations (respectively), and the quiescent luminosity for GRO J0422+32 is based on a 19 ks ROSAT
observation. (5) Primary masses. (a) Van Paradijs (1995). (b) Simbad CDS Catalog. (c) Ritter & Kolb
(1998). (d) Chen et al. (1998). (e) Garcia et al. (1998). (g) Esin et al. (1998). (h) Narayan et al. (1997b).
(i) Esin et al. (1997). (j) Hameury et al. (1997). (k) Beekman et al. (1997). (l) Chen et al. (1997). (m)
This is an arbitrary choice in the range 2:9 \Gamma 7:5 given by Orosz et al. (1998; see also Bailyn et al. 1997).
(n) Orosz et al. (1998). (?) For simplicity, all NS masses are assumed to be 1:4 M fi .

-- 21 --
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-- 24 --
Fig. 1.--- Quiescent luminosities L min (Eddington units) in the 0.5­10 keV band of the NS SXTs (open
circles) and BH SXTs (dots) listed in Table 1. The luminosities are plotted as a function of the orbital
period P orb of each system.

-- 25 --
Fig. 2.--- Same as Fig 1, except that only SXTs with well determined L min and P orb are shown.

-- 26 --
Fig. 3.--- Predictions of binary evolution models for the mass transfer rate —
m T (Eddington units) in NS
and BH SXTs, as a function of the orbital period P orb . GR refers to a phase of mass transfer driven by
gravitational radiation and EXP to mass transfer driven by secondary expansion.

-- 27 --
Fig. 4.--- The upper band shows the quiescent luminosities of BH SXTs in the 0.5­10 keV band predicted
by ADAF models if all the mass transferred by the secondary is accreted via the ADAF. The lower band
corresponds to ¸ 1=3 of the mass transferred being accreted via the ADAF. This model fits the observed
luminosities reasonably well. Both bands have been calculated for ff ADAF = 0:3. The effect of varying ff ADAF
is explained in the text.

-- 28 --
Fig. 5.--- The upper band shows the quiescent luminosities of NS SXTs predicted in the 0.5­10 keV band
if 1/3 of the mass transferred by the secondary reaches the NS surface. The lower band shows that the
luminosities actually observed correspond to a very small fraction (¸ 10 \Gamma3 ) of this mass reaching the NS
surface.

-- 29 --
Fig. 6.--- Fraction of mass transferred by the secondary that reaches the neutron star surface in the propeller
regime, as a function of g = —
mADAF = —
m accum . The solid line shows this fraction for a neutron star with a
surface magnetic field strength of 10 8 G, while the dashed and dotted lines correspond to 10 9 G and 10 10 G,
respectively.

-- 30 --
Fig. 7.--- (a) Fraction f surf of the neutron star surface emitting radiation in the propeller regime, as a
function of g = —
mADAF = —
m accum . The solid line shows f surf for a neutron star with a surface magnetic field
strength of 10 8 G, while the dashed and dotted lines correspond to 10 9 G and 10 10 G, respectively. (b)
Equilibrium spin period P spin as a function of g = —
mADAF = —
m accum for the same magnetic field strengths as
in (a).

-- 31 --
Fig. 8.--- The band shows the quiescent luminosities of BH SXTs in the 0.5­10 keV band predicted by ADAF
models including a wind (p = 0:4, r tr = 10 4 , ffi = 0:3) if 1=3 of the mass transferred by the secondary flows
into the ADAF.

-- 32 --
Fig. 9.--- The band shows the quiescent luminosities of NS SXTs predicted in the 0.5­10 keV band if (1)
1=3 of the mass transferred by the secondary flows into the ADAF, (2) there is a modest wind (p = 0:4,
r tr = 10 4 , ffi = 0:3) and (3) all the mass reaching the NS magnetosphere is accreted onto the surface. For
the same wind parameters as in Fig. 8, the inner radius of the ADAF (= the magnetospheric radius) is at
r mq = 20 (see text). The wind reduces, but only by ¸ one order of magnitude, the accretion rate at the
magnetosphere (compare with Fig. 5).