Issue 
A&A
Volume 506, Number 3, November II 2009



Page(s)  1297  1307  
Section  Stellar structure and evolution  
DOI  https://doi.org/10.1051/00046361/200912552  
Published online  27 August 2009 
A&A 506, 12971307 (2009)
Young prelowmass Xray binaries in the propeller phase
Nature of the 6.7h periodic Xray source 1E 1613485055 in RCW 103
H. Bhadkamkar  P. Ghosh
Department of Astronomy & Astrophysics, Tata Institute of Fundamental Research, Mumbai 400 005, India
Received 21 May 2009 / Accepted 23 August 2009
Abstract
Context. Discovery of the 6.7h periodicity in the Xray source
1E 1613485055 in RCW 103 has led to investigations of the nature of
this periodicity.
Aims. To explore a model for 1E 1613485055 wherein a fastspinning neutron star with a magnetic field 10^{12} G
in a young prelowmass Xray Binary (preLMXB) with an eccentric orbit
of period 6.7 h operates in the ``propeller'' phase.
Methods. The 6.7h light curve of 1E 1613485055 is modeled in
terms of orbitallymodulated mass transfer through a viscous accretion
disk and subsequent propeller emission. Formation of eccentric binaries
in supernovae and their subsequent tidal evolution are studied.
Results. The light curve of 1E 1613485055 can be quantitatively
accounted for by models of propeller torques of both IllarionovSunyaev
type and RomanovaLovelace et al. type, and spectral and
other properties are also in agreement. Formation and evolution of
model systems are shown to be in accordance both with standard theories
and with Xray observations of 1E 1613485055.
Conclusions. The preLMXB model for 1E 1613485055 and similar
sources agrees with observation. Distinguishing features between this
model and the recentlyproposed magnetar model need to be explored.
Key words: Xrays: binaries  stars: neutron  stars: evolution  accretion, accretion disks  ISM: supernova remnants  Xrays: general
1 Introduction
The point soft Xray source 1E 1613485055 (henceforth 1E) near the center of the young (2000 y old) supernova remnant (SNR) RCW 103 has attracted much attention lately, following the discovery of a strong 6.67 h periodic modulation in 1E by de Luca et al. (2006, henceforth dL06) from a deep XMMNewton observation of the source in 2005. 1E was discovered in 1980 (Touhy & Garmire 1980) as a soft Einstein Xray source. The original interpretation as an isolated neutron star was found to be untenable in view of subsequent discovery by other Xray satellites (e.g., ROSAT, ASCA, Chandra) of the large variability of 1E on the timesacle of a few years (dL06). A periodicity at 6 h was first hinted at by Chandra observations, but the first clear, strong detection came from the above 2005 observations of dL06, who also showed the existence of this periodicity in the data from earlier 2001 observations of 1E with XMMNewton, when the source luminosity was higher by a factor 6 during the course of its sequence of severalyear timescale outbursts nentioned above, documented by these authors from archival data.
The nature of the above 6.67 h periodicity is an interesting question, on which preliminary discussions were reported in dL06. Recently, Pizzolato et al. (2008, henceforth P08) have proposed a model for the 1E system wherein it is a close binary consisting of a magnetar, i.e., a neutron star with a superstrong magnetic field 10^{15} G, and a lowmass companion. The 6.67 h periodicity is identified in this model with the spin period of the neutron star, to which this young neutron star has been spun down in such a short time by the torques associated with its enormous magnetic field. This period has also been proposed by P08 to be in close synchronism with the orbital period of the binary, in analogy with what is believed to be happening in Polar Cataclysmic Variables or AM Hertype systems. The observed Xray emission from 1E is that from the magnetar in this model.
In this paper, we explore an alternative model for the 1E system wherein it is a close binary system consisting of a young neutron star with a canonical magnetic field 10^{12} G, and a lowmass companion, i.e., a prelowmass Xray Binary (henceforth preLMXB), such as are believed to be the standard progenitors of Lowmass Xray Binaries (henceforth LMXBs). Such preLMXBs are born after the commonenvelope (CE) evolution phase of the original progenitor binary system consisting of a massive star and a lowmass companion, which leads to the formation of a binary consisting of the Hecore of the original massive star and the lowmass companion (Ghosh 2007, and references therein). The Hestar susequently explodes in a supernova, leading to a neutron star in orbit with a lowmass companion, i.e., the preLMXB referred to above. This is the standard Hestar supernova scenario for the formation of LMXBs (Ghosh 2007, and references therein). The 6.67 h periodicity is identified in our model with the orbital period of the binary. In our model the young neutron star is still spinning very rapidly, with a canonical spin period 10100 ms, and is operating in the ``propeller'' regime, wherein any matter approaching the fastrotating magnetosphere of the neutron star is expelled by the energy and angular momentum deposited into it through its interaction with the magnetospheric boundary (Illarionov & Sunyaev 1975, henceforth IS75; Davies & Pringle 1981; Illarionov & Kompaneets 1990; Illarionov et al. 1993; Ghosh 1995; Mineshige et al. 1991; Davies et al. 1979, and references therein, henceforth G95; Lovelace et al. 1999, henceforth LRB99; Romanova et al. 2004,2005, henceforth RUKL05; Ustyugova et al. 2006, henceforth UKRL06).
The observed Xray emission from 1E in our model is that from the propeller: indeed, it is wellknown that soft Xray transients (SXRTs) like Aquila X1 and others (see Sect. 7.1) go through low/quiescent states during the decay of their outbursts, during which their luminosities and spectral properties are very similar to those of 1E, and the neutron stars in them are believed to be in the propeller regime (Campana et al. 1998; Stella et al. 2000). The observed 6.67 h periodicity in our model is due to the orbital modulation of the supersonic propeller, which is caused by the orbital modulation of the masstransfer rate in the eccentric binary orbit of a young system like 1E. It is wellknown that young postSN binaries with lowmass companions like 1E are almost certain to have eccentric orbits, due to the large eccentricities produced in such systems in the SN explosion (see Sect. 6.1) and the duration of the subsequent tidal circularization compared to the ages of systems like 1E (see Sect. 6.2). By contrast, SXRTs are believed to be old LMXB systems with circular orbits, where such modulation will not occur.
We show in this work that the 6.67 h light curve of 1E can be accounted for quantitatively by our model for propeller torques of both IllarionovSunyaev type and RomanovaLovelace et al. type (see Sect. 2), and that the observed spectral and other characteristics are also in general agreement with our overall picture. Thus, further diagnostic features need to be explored in order to distinguish between our model and the magnetar model as a viable description of this and similar sources.
2 Propeller phase in preLMXBs
In a prelowmass Xray Binary (preLMXB: see above), the newborn, fastrotating neutron star is unable at first to accrete the matter that is being transferred from the companion through the inner Lagrangian point L_{1}, because of the fast rotation of the neutron star (IS75, Illarionov et al. 1993; Illarionov & Kompaneets 1990; Davies & Pringle 1981; Mineshige et al. 1991; Davies et al. 1979, G95, LRB99; Romanova et al. 2004, RUKL05, UKRL06). Because of its large angular momentum, this matter forms an accretion disk and reaches the magnetospheric boundary of the magnetized neutron star, whereupon this ionized matter interacts with the fastrotating neutron star's magnetic field, and the energy and angular momentum deposited in it by magnetic stresses associated with this fastrotating magnetic field expel it. This is the propeller phase of the system (IS75), during which the neutron star spins down as it loses angular momentum and rotational energy. During this propeller phase, the disk matter at the magnetospheric boundary is shockheated as the ``vanes'' of the supersonic propeller (IS75) hit it, and the hot matter emits in the soft Xray band. This emission appears unmodulated at the neutronstar spin frequency (as opposed to the Xray emission from canonical accretionpowered pulsars, which comes from the neutronstar surface) to a distant observer, who sees only the total emission from the heated matter at the magnetospheric boundary. Observations of transient lowmass Xray binaries (i.e., the soft Xray transients or SXRTs) like Aquila X1 (Campana et al. 1998) and SXJ1808.43658 (Stella et al. 2000) in quiescence, when the neutron stars in them are thought to be operating in the propeller phase, amply confirm this point.
The propeller luminosity L during the above phase is given by , where N is the propeller torque acting on the neutron star and is its spin angular velocity. The propeller torque N was first estimated by IS75 in their pioneering suggestion of this mechanism, and subsequent work over approximately the next two decades considered variations of this torque under different circumstances, as summarized in G95. These works addressed themselves largely to quasispherical accretion, and we shall call this kind of propeller torque the IllarionovSunyaev type (or IStype for short) torque, which was widely used in that timeframe in propeller spindown calculations. In the 2000s, Romanova, Lovelace and coauthors reported a series of calculations of the propeller effect for diskaccreting magnetic stars based on their numerical MHD simulations (Romanova et al. 2004, RUKL05, UKRL06; also see the analytic estimates in LRB99). We shall call the propeller torque obtained from this line of work the RomanovaLovelace et al. type (or RUKLtype for short) torque. In this work, we shall consider both IStype and RUKLtype propeller torques for the problem at hand.
Consider IStype torques first.
For such fastrotating neutron stars as we are concerned with in this
work, the propeller operates in the supersonic regime, and its
torque is given by (G95 and the references therein),
In Eq. (1), is the Keplerian angular velocity at the magnetospheric radius , is the magnetic moment of neutron star and M_{x} is its mass. Combining this equation with the standard expression for the magnetospheric radius (Ghosh 2007), viz.,
where is the rate at which transferred matter arrives at the magnetospheric boundary, we obtain the following expression for the propeller luminosity:
In Eq. (3), is in units of 10^{14} g s^{1}, L_{35} is L in the units of 10^{35} erg s^{1}, is the neutronstar spin period, is the neutronstar magnetic moment in units of 10^{30} G cm^{3}, and m_{x} is the neutronstar mass in units of solar mass. As neutron stars are thought to have s at birth, and as the propeller phase is thought to end when the spin period is longer than s, we have made the canonical choice for the expected scale of in systems like 1E. Equation (3) clearly shows how the propeller luminosity scales with the massarrival rate , and essential neutronstar properties, namely, its spin period , its magnetic moment , and its mass M_{x}.
Now consider RUKLtype torques. These authors summarized the
results of some of their extensive MHD simulations in RUKL05 and
UKRL06 in terms of powerlaw fits to these results, showing that the
scaling of the total propeller torque N with the magnetic
moment
and the spin rate
of the neutron star was
However, the scaling of N with was not available from the above references, because only the parameters and (and also the turbulence and magnetic diffusivity parameters of the disk: see below) seem to have been varied in the series of simulations reported in these references. In order to estimate the scaling of N with for RUKLtype torques, we proceeded in the following way.
First, we did an analytic estimate in the following manner. In their analytic study, LRB99 argued that the radius of the inner edge of the disk should depend on the stellar rotation rate in addition to the parameters and that (see above) depended upon. The scaling with , , and that these authors derived was revised in UKRL06, the final result being given as . (Note the closeness of the scalings with and with those which apply to , as given above.)
In a simple first approach, if we argue that a reasonable estimate
of the torque scalings may be obtained by replacing
with
in Eq. (1) for disk accretion, we arrive at
the scaling
for RUKLtype torques. Noticing the qualitative similarity of the the scalings with and in Eq. (5) with those of the actual RUKLtype torque given in Eq. (4), and furthermore the quantitative closeness for the scaling with , we argued that the best estimate would be to use the scalings of Eq. (4) for and , and the scaling of Eq. (5) for , thus arriving at a suggested scaling for the RUKLtype torque as
Before proceeding further, we recognized that RUKLtype torques may arise from more complicated interactions than are describable by the above arguments, and so attempted to verify the above scaling by further comparison with RUKL results. To this end, we noted the correlated variations of N and recorded in Fig. 4 of Romanova et al. (2004), and fitted the two prominent peaks in N and at the extreme right of this figure to a power law. This gave an exponent 0.37, coincident with that in Eq. (6) within errors of determination. With this support, we use the scalings of Eq. (6) for the RUKLtype torque in this work, deferring further considerations to future publications.
In order to obtain the dimensional values of the RUKLtype propeller
torques and related variables, we now insert the reference units
for the RUKL simulations given in RUKL05 and UKRL06, thus obtaining
for the torque:
Here, N_{33} is the propeller torque in units of 10^{33} g cm^{2} s^{2}, the units of other variables are as before, and we have kept the values of the turbulence and magnetic diffusivity parameters of the accretion disk in RUKLtype models at the canonical values given in RUKL05 and UKRL06. The RUKL propeller luminosity L is then obtained in a straightforward manner as
In Eq. (8), the units of all variables are as before.
Comparison of Eqs. (3) and (8) immediately leads to the following conclusions about IStype and RUKLtype propeller luminosities. First, the scalings with and are almost identical for the two types. Secondly, the scaling with the neutronstar spin period is stronger (3 instead of 2) for the RUKLtype than for the IStype. Finally, for identical values of the variables , , and , the RUKLtype propeller luminosity is about three orders of magnitude lower than the IStype propeller luminosity. Conversely, at fixed values of and , roughly equal luminosities are given by the two types if the spinrate for the RUKL type is about an order of magnitude higher than that for the IS type.
As indicated earlier, in this work we are exploring the properties of such propellers as described above during the relatively early stages of postsupernova binaries containing preLMXBs, when the binary orbits are expected to be appreciably eccentric, as explained in Sect. 6.1. In such a system, the masstransfer rate through the inner Lagrangian point L_{1} is expected to vary periodically with the orbital phase, as detailed below in Sect. 3. This flow of matter forms an accretion disk because of its large specific angular momentum, as explained above, and slow viscous effects in the disk modify the profile of the above periodic modulation (making it less sharp), and the resultant periodic profile is that which is shown by the massarrival rate at the neutron star. The propeller luminosity then follows suite, showing a periodic modulation, as described by Eq. (3) for the IStype torque or Eq. (8) for the RUKLtype torque. In this scenario, therefore, we identify the 6.67 h period of 1E with the binary period of a young, eccentric preLMXB, which is expected to turn much later into a standard LMXB after passing through further intermediate phases (see Sect. 6.4). In the next section, we give details of the expected nature of the masstransfer modulation at the orbital period.
3 Orbital modulation of mass transfer
The problem of orbital modulation of mass transfer in eccentric orbits
has been studied by a number of authors over almost three decades now,
adopting various approaches appropriate for various aspects of
the problem they have studied. These aspects have covered a
considerable range, from a scrutiny of the concept of the Roche lobe
in an eccentric orbit (Avni 1976), to a study of testparticle motion
through numerical integration of the restricted threebody problem
at or near periastron passage (Lubow & Shu 1975), to explicit calculations of
orbital phasedependent flow through L_{1} from a suitablymodeled
stellar envelope (Joss & Rappaport 1984, and references therein).
For our purposes here, we have adopted the
results of the calculations described by Brown & Boyle (1984,
hereafter BB): these authors described the flow through L_{1} from
the atmosphere of the lobefilling companion with a scale height H
as a sort of nozzle flow through the inner Lagrangian point,
integrating over a Maxwellian distribution of velocities
(characterized by thermal velocity scale )
for the stellar
matter. Their final result for the rate of mass transfer as a function
of the true anomaly
is given by:
In Eq. (9), e is the orbital eccentricity, and the dimensionless function is the ratio of the phasedependent equivalent Rochelobe radius of the companion to the phasedependent orbital distance in the eccentric orbit, being the value of at periastron (). From standard geometry of ellipses, is given by:
where is periastron distance. Finally, is the the dimensionless scaleheight parameter introduced by BB.
It is convenient to work in terms of the ratio as it varies relatively slowly with orbital phase (and is, in fact, independent of this phase for a nonrotating companion: see below). The other properties of the binary system that depends on are (a) the mass ratio , being the mass of the lowmass companion; and (b) the rate of rotation of the companion, usually expressed in units of the orbital angular velocity at periastron as . The scale of the masstransfer rate in Eq. (9) is set by the above velocity scale , the scalesize pH for the effective crosssection of the above ``nozzle'', and the basic density scale in the stellar atmosphere.
Prescriptions for
have been given in the 1970s and '80s;
we use here the generalized JossRappaport (Joss & Rappaport 1984) expressions
adopted by BB, namely,
where the coefficients in are given by:
and the variable K depends on the above rotation parameter and the orbital phase as:
From Eqs. (11)(13), it is clear that, for a nonrotating companion with K=0, is independent of the orbital phase, and depends only on the mass ratio Q. Thus, for a given Q, simply scales with as the eccentric orbit is traversed. It is stellar rotation which modifies the Roche potential in such a way that this simple scaling is broken, and depends on orbital phase. The phasedependent factor in K goes back to the original work of Avni (1976). In our present work, we study the limits of (a) no stellar rotation, , and (b) synchronous stellar rotation, , to cover a range of possibilities (see below). The estimated accuracy in the above prescription for determining equivalent Rochelobe radii is 2%.
Detailed models with the mass transfer profile given by Eq. (9) are described below. From general considerations, it is clear that this profile peaks at the periastron and that the sharpness of the peak depends on the quantity . Since , and typical values of for the current problem are in the range 10^{2}10^{3} (BB), we see that the profile is expected to be sharply peaked at the periastron even for realtively low values of eccentricity, such as .
4 Viscous flow in accretion disks
Matter transferred through L_{1} into the Roche lobe of the neutron
star first forms a ring around the neutron star, the radius
of this ring being related to the specific angular momentum
of the transferred matter as (Pringle 1981):
Through effective viscous stresses, this ring spreads into an accretion disk, wherein matter slowly spirals inward towards the neutron star as the viscous stresses remove angular momentum from it. The accretion disk extends from its outermost radius inward upto the magnetospheric boundary , where the propeller torques expel the matter by depositing energy and angular momentum in it, as explained above.
The rate at which the matter drifting radially inward through the accretion disk arrives at depends, therefore, both on the profile of mass supply at L_{1}, as described above, and on the rate of viscous radial drift through the accretion disk, which occurs on a timescale .
In a quasisteady state, the relation between the two profiles
and
is of the form
The convolution integral in Eq. (15) describes the viscous drift with the timescale of the mass supplied to the disk at earlier times t_{0} at the rate , as indicated above. In principle, the integral extends over all previous times, but in practice it is sufficient to keep track of only about N orbital periods in the past (as the lower limit of integration indicates). This is so because of the rapid fall of of the viscousevolution profile of the accretion disk at large values of (see below).
Viscousevolution profiles have been calculated analytically and
numerically at various levels of approximation by several authors
(LyndenBell & Pringle 1974; Lightman 1974). For our purposes here, we have
adopted an analytic approximation of the generic form
introduced and utilized by Pravdo & Ghosh (2001, hereafter PG). This reference has discussions of earlier analytical and numerical investigations. The generic PG profile in Eq. (16) reaches its maximum at , and decays subsequently as . Clearly, therefore, most of the contribution to the above convolution integral comes from those orbital cycles which are closest to the earlier time , and N is determined by the sharpness of the fall of the profile, i.e., n. In our computations, we estimated the optimal values of N by running test cases with increasing values of N until the desired accuracy was obtained. For example, in the bestfit case reported below, we found that N=9 gave an accuracy of 10%, while N=15 gave an accuracy of 1%. Given the error bars on the data points in the observed light curve, further accuracy was unnecessary.
Figure 1: Xray light curve of 1E. Shown is the observed light curve from dL06, superposed on the (common) bestfit model light curve for IStype and RUKLtype propellers. Left panel: model curve for (nonrotating companion). Right panel: same for (synchronously rotating companion). 

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The following generic feature of viscous evolution of accretion disks is a key aspect of the phenomenon we are exploring here. Whereas the orbital modulation of the masssupply rate to the disk at its outer radius is expected to sharply peaked at periastron for typical values of the scale height in the companion's atmosphere, as above, the viscous drift of matter through the accretion disk would decrease the sharpness of this modulation, since variations on timescales much shorter than tend to be ``washed out'' by viscous diffusion. This is what makes the orbital modulation of the massarrival rate at the disk's inner radius gentler, and therefore also the modulation of the propeller luminosity L(t), leading naturally to light curves of the form observed in 1E. Quantitative details follow.
5 Model light curves
We constructed model light curves for 1E by combining the model of mass transfer described in Sect. 3 with that of viscous flow through the accretion disk described in Sect. 4. We then fitted these models to the observed light curve of 1E in 2005 (dL06). The fitting parameters were (, e), which come from the above BB masstransfer model in elliptic orbit, and also ( , n), which come from the above PG parametrized description of viscous evolution of accretion disks. In this introductory work, we kept constant at a canonical value of (BB), and varied the parameters e, , and n to obtain acceptable fits. For the viscous timescale, we found it more convenient to work in terms of the ratio of this timescale to the known period hr of the system, which we of course identify with the orbital period in this model. The ratio is of immediate physical significance, since it measures the relative importance of viscous diffusion to orbital modulation in the system. For , viscous diffusion would be so rapid as to enable the disk flow to adjust to the orbital modulation of masssupply rate, and flowrate would essentially follow the supply rate. For , on the other hand, the viscous diffusion would be so slow as to wash out any rapid variations in the masssupply rate, and the modulation would be essentially determined by the disk viscosity. As we see below, values of a few seem to describe the 1E system, indicating comparable importance of the two effects in this system.
Table 1: Best fit model parameters: IStype torque.
Table 2: Best fit model parameters: RUKLtype torque.
We fitted model light curves corresponding to both IStype and RUKLtype torques to the data on 1E, the bestfit values of the parameters being given in Tables 1 and 2. In each case, we have considered both a nonrotating secondary () and a synchronouslyrotating secondary (), as indicated. Note that the bestfit values for the two types of torques are very close to each other, as may have been expected. This is so because the closeness of the scaling of L with between the two types, as discussed in Sect. 2, since only this aspect of the torque is relevant for fitting the profile of the light curve. Other aspects, e.g., the fact that the RUKLtype propeller luminosity is about three orders magnitude below the IStype propeller lumnosity for identical vaues of , and , have important consequences elsewhere, as detailed in Sect. 6.3, but not in this matter. Further, the absolute values of the observed luminosities in the light curves are easily accounted for, e.g., by having the stellar spin rate higher for RUKLtype torques by about a factor of 10 than that for IStype torques, and , identical for the two types, as the scalings in Eqs. (8) and (3) show. This implies neutronstar spin periods in the range s, i.e., the canonical range for propellers, for both type of torques, as explained in Sect. 1.
This closeness of bestfit parameters is reflected in the bestfit light curves, which are visually essentially identical for the two types of torques. In Fig. 1, we display this common bestfit light curve, superposed on the data on 1E.
Our inferred bestfit value of in the above tables indicates that the dominant contribution to the convolution integral described in the last section comes from the second and third orbits preceding the time of observation. The corresponding viscous timescale h is consistent with a rather thick disk with and a canonical value 0.11 for the disk viscosity parameter (Shakura & Sunyaev 1973). This seems consistent with the results of the RUKL numerical simulations. Note also that the bestfit value of the viscousprofile index nis consistent with the range of values generally expected for neutronstar systems, as per the discussion given in PG. Indeed, we found that values of n in the above range generally worked for the 1E system. Regarding the orbital eccentricity e, the bestfit values are as given in the tables, and we found that values of the eccentricity e in the range 0.350.45 genearlly worked for the 1E system: we discuss this in the next section. It is clear, therefore, that the model explored in this paper can account quantitatively for the observed 1E light curve in 2005, for both IStype and RUKLtype torques. We discuss in Sect. 7.2 possible reasons for the apparently different, ``jagged'' light curve hinted at by the 2001 observations of this system (dL06).
6 Formation and evolution of prototype systems
As indicated in Sect. 1, we are exploring in this work a model for systems like 1E wherein the binary system of a Hestar and a lowmass star (left after completion of the CE evolution phase in which the extensive envelope of the evolved primary has been expelled and its Hecore left behind) produces the preLMXB when the Hestar explodes in a supernova (SN), leading to a newborn neutron star with a lowmass companion. Essential features of the formation and subsequent evolution of such systems are, therefore, essential components of this model. We now discuss these features in brief, considering in this section first the immediate postSN status of the system, and then the evolution of this system with the lowmass companion in an eccentric orbit at or near the point of Rochelobe contact at periastron, producing a system like 1E where orbitallymodulated mass transfer proceeds through the inner Lagrangian point, and the newborn, fastspinning neutron star is operating in the propeller regime, expelling this matter instead of accreting. Subsequently, we summarize further evolution of such systems.
6.1 Immediate postSN systems
A major question that concerns us here is the expected eccentricity of systems formed by the SN in the above scenario, since this eccentricity is crucial for the proposed mechanism. Qualitatively, it is obvious that the immediate postSN system is almost guaranteed to be highly eccentric, as the mass loss from a typical preSN system of, say, a Hestar and a lowmass companion (see below) in forming the postSN system of neutron star with its lowmass companion is , which is close enough to maximum allowed value of mass loss (=half of the initial total mass of for zero kick velocity) to ensure that the postSN orbit would be very eccentric. We shall use these values for the stellar masses throughout the rest of this paper.
To see this quantitatively, we can adapt the extensive calculations of
Kalogera, who computed the probability of the formation of Xray
binaries as a funtion of orbital parameters (Kalogera 1996). In the
following, we shall use the same masses for the pre and postSN
system as given above for illustrative purposes. The probability
density from Kalogera's work is:
Here,
and is the modified Bessel function of zeroth order. Further, is the ratio of semimajor axes of the pre and postSN orbits, is the ratio of the total mass of the postSN binary to that of the preSN one, and , being the velocity dispersion in the SN kickvelocity, and the orbital velocity of the exploding star relative to its lowmass companion just before the SN (Kalogera 1996).
Figure 2: Formation probabilitydensity of immediate postSN binaries as a function of eccentricity efor various values of the dispersion in the SN kick velocity (see text). Curves labeled by the value of in units of 100 km s^{1}. Each curve so normalized that . 

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In the problem we are studying here, the semimajor axis of the postSN binary is determined by Kepler's third law from our assumed stellar masses above, and the known orbital period of 1E. However, when there is a kick associated with the SN, the inferred semimajor axis of the preSN binary is not determined uniquely by the semimajor axis and the eccentricity of the postSN binary: rather, there is a range of values corresponding to the range of the kickvelocity. Thus, there is a range in the values of : it is wellknown that the allowed range for is limited from 1/(1+e) to 1/(1e), these limits being first identified by Flannery and van den Heuvel (1975). Thus, for our purposes, it is aprropriate to integrate over the above allowed range of , and display the resultant probability density as a function of the eccentricity e. We show this in Fig. 2 for various typical values of as indicated. In this figure, we have used the symbol vk_{5} there to denote in units of 10^{5} m s ^{1} = 100 km s^{1}, the typical scale for the SN kick dispersion, and we have normalized the probability density so that in each case. As explained above, the closeness of the value of in this typical case to its lower limit for no binary destruction in the SN (this limit is 0.5 for zero kick velocity) ensures that the probability peaks at a high value of e, as Fig. 2 shows. It is clear, therefore, that such a preLMXB would generically have a considerable eccentricity at the time of its formation in the SN.
6.2 Tidalevolution phase of preLMXBs
The above newlyformed preLMXB undergoes tidal evolution, wherein three simultaneous processes occur, namely, (1) tidal circularization, i.e., decrease in the orbital eccentricity e; (2) tidal orbitshrinkage or hardening, i.e., decrease in the orbital semimajor axis a; and (3) tidal synchronization, whereby the rotation frequency of the lowmass companion approaches the orbital angular frequency . These processes happen through tidal torques, and their quantitative descriptions pioneered by Zahn (1978,1977) are widely used for calculations: we use them here, as have P08. Complete equations are given in Zahn (1977), and an Erratum was published by Zahn (1978). We have found a further algebraic or transcription error in the original paper, which we describe below, and which seems to have gone unnoticed so far.
Complete formulations for the rates of change of e, a, and
are given in Zahn (1977), but for our work here we shall
utilize a widelyused simplification which comes naturally out of
these formulations, namely, that the timescale for tidal synchronization
comes out to be much shorter than that for tidal circularization and
tidal hardening (see, e.g., Meibom & Mathieu 2005; P08). This is appropriate,
since we shall be interested in this work only in phenomena which
occur on the timescales of tidal circularizatuion or longer. Under
such circumstances, we can look upon the system as being roughly
synchronous at all times, and describe tidal circularization and
tidal hardening respectively by Zahn's (1977) Eq. (4.7) and the
appropriately simplified (i.e., synchronized) version of Zahn's
Eq. (4.3), thereby obtaining:
and
In Eqs. (18) and (19), in terms of the mass ratio defined above in Sect. 3, k_{2} is the apsidal motion constant for the lowmass companion, and is the ``friction time'' of Zahn (1977), which, for stars with convective envelopes (as in the present case) is given by Zahn's (1977) pioneering prescription of the turbulent eddyviscosity timescale :
Equations (18) and (19) describe simultaneous tidal circularization and hardening of close binaries, but before presenting our results, we need to correct two errors related to them. First, if we define a circularization timescale in the usual way, we get from Eq. (18) the result:
which would be identical to Zahn's (1977) Eq. (4.13), except that the factor of 4 on the righthand side is missing in Zahn (1977). Unfortunately, this error has propagated over the years into numerous papers, e.g., in P08, in their Eq. (2)^{} We have corrected this now. Secondly, in an erratum published in 1978, Zahn corrected a few other (generally smaller) numerical errors, of which the one relevant to our work is that the numerical coefficient on the righthand side of our Eq. (18) should be 21 instead of 63/4. In all calculations reported here, we have made these corrections.
We have integrated Eqs. (18) and (19)
numerically for close binary systems like 1E, with values of
initial postSN semimajor axes and eccentricities, a_{i} and e_{i},
chosen over a range of plausible values for such systems. We find
that, in all cases, the systems circularize and harden in a way
that, in the (e vs. a) plane, the circularization point is
approached in a ``cut off'' like manner. This is shown in
Fig. 3 for a possible prototype 1Elike system, so
chosen that the parameters of it evolve to those roughly
corresponding to 1E in 2000 years. This cutoff approach
is similar to what Meibom & Mathieu (2005) found. Of course,
our detailed shape is slightly different from that of these authors,
since they fitted their results to an assumed parameterized
distribution shape applicable to observations on a collection of
``normal'' binaries.
These details will be given in a separate publication. For our
purposes here, we note that the total time
taken to
reach this circularization point (Meibom & Mathieu 2005) can be expressed
roughly as:
where a_{i} and e_{i} are the initial semimajor axis and eccentricity of the immediate postSN orbit, and the scale parameter is given by:
Equation (22) is a rough analytic fit to the mumerical results, adequate for our purposes. Note that the scale parameter depends on the companion mass , its value being yr for the inferred companion mass of 1E.
Figure 3: Tidal evolution of a prototype 1Elike system in the e vs. a plane. Semimajor axis a in units of solar radius. Note the ``cut off'' like approach to the circularization point (see text). 

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It is clear from Eq. (22) that circularization is faster for orbits which are born more compact and more eccentric. The scaling with a is straightforward from the above equations of tidal evolution; the scaling with e is more complicated (although inspection of the same equations gives some clue), involving details of the numerical solution.
The lifetime of the eccentric phase of the preLMXB is obviously also the lifetime of its orbitalmodulation phase which we are investigating in this work. The sensitive dependence of this lifetime on the initial postSN orbital parameters and the companion mass (through the scale parameter and due to the massdependence of in Eq. (22)) makes for a wide range of possible values of this lifetime, 10^{3}10^{8} years.
A crucial point is, of course, that if the companion is at or close to filling its Roche lobe at periastron in the postSN orbit, it must remain so throughout most of this eccentric phase in order for the scenario to be selfconsistent. The size of the Roche lobe at periastron is simply p=a(1e) multiplied by a wellknown function of the mass ratio q. Since the latter does not change significantly during this phase, we need only study the evolution of the former. Our integration of the tidalevolution equations show that, while a and e both decrease during this phase, p=a(1e) decreases slowly through most of this phase, reaching a minimum and increasing thereafter at late stages. This is shown in Fig. 4 for the prototype 1Elike system displayed in Fig. 3 (see above). Thus, if the companion is initially at or close to filling its Roche lobe at periastron, it will remain so over most of this phase, and if it is inside its Roche lobe initially, it is likely to fill its Roche lobe later during this phase. It is also seen that Rochelobe contact ends at the last parts of this phase (when the orbit is nearly circular), since p increases and becomes roughly constant there.
Figure 4: Evolution of periastron distance p=a(1e) during tidal evolution of a prototype 1Elike system (see text). Shown is p in units of the solar radius vs. time in years. 

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Thus, this tidalevolution phase is a rough measure of the lifetime of Rochelobe contact and orbital modulation of the propeller output. After this, the preLMXB becomes detached, and remains so until angularmomentum loss through gravitational radiation and/or magnetic braking brings it back to Rochelobe contact on a long timescale of 10^{8}10^{9} yrs. We discuss this phase below in Sect. 6.4.
6.3 Duration of propeller phase
When the above tidalevolution phase ends, is the neutron star
still operating in the propeller phase? To answer this question,
we consider the spindown of the neutron star from an initial
spin period
to a final, longer spin period
under the action of the propeller torque given by
either the IStype torque (Eq. (1)) or the
RUKLtype torque (Eq. (7)). In each case,
this spindown is decsribed by
where I is the moment of inertia of the neutron star and is the propeller spindown timescale.
First consider IStype torques, for which
is
given by
where I_{45} is I in units of 10^{45} gm cm^{2}, and other units are as before. Equation (24) can be integrated readily in this case, the total spindown time from to being:
As discussed earlier, the ratio is believed to be in the range 10100 (Ghosh 1995, and references therein), and its exact value does not matter because of the logarithmic dependence. On taking m_{X}=1.4 and the corresponding moment of inertia for a standard modern EOS, we arrive at
for canonical values of , and I.
Now consider RUKLtype torques, for which
is given by
Equation (24) can be integrated readily in this case also, the total spindown time from to being:
the second equality in the above equation coming from the fact that the ratio is believed to be in the range 10100, as indicated above. The numerical value of in this case is thus
which implies that, for canonical range s, as indicated in Sect. 2, we arrive at
for canonical values of the variables , and I.
In comparing the total spindown times given by the two types of torques, we notice that the time taken by the RUKLtype torque is 23 orders of magnitude longer than that taken by the IStype torque for identical values of , and I. This reflects the relative weakness of the RUKLtype torque discussed in Sect. 2. Next, comparing the values of given by the above two types of propeller torques with the lifetime of the eccentric phase given in the previous section, we reach the following conclusions. For the IStype torque, we find that, over most of the parameter space, the neutron star would still be in the propeller phase at the end of the above tidalevolution phase of the binary. For the RUKLtype torque, we find that this conclusion is valid over the entire parameter space. Thus, the RUKLtype torque makes the conclusion stronger.
As shown above, the companion has moved out of Rochelobe contact by the time that the tidalevolution phase of the binary reaches conclusion, so that mass transfer stops, and so does the propeller action and its consequent soft Xray production. Accordingly, throughout this first Rochelobe contact phase, we expect the system to be in the propeller phase.
6.4 Recontact with Roche lobe and LMXB phase
After orbit circularization and the loss of its first Rochelobe contact, as described above, the preLMXB thus ceases to be an Xray source. But its orbit shrinks (i.e., the binary hardens) on a long timescale ( 10^{8}10^{9} yr) due to two mechanisms of angular momentum loss from the system, viz., graviational radiation and magnetic braking (Ghosh 2007, and references therein). These are the standard mechanisms through which shortperiod preLMXBs are believed to harden, until Rochelobe contact is regained and mass transfer restarts. But the transferred mass is now accreted by the neutron star, because its spin has been slowed down sufficiently over this long time that it acts as an accretor and not a propeller at the (large) masstransfer rates that occur at this second Rochelobe contact in the circularized binary. The system thus turns on as a canonical LMXB now, emitting strongly ( erg s^{1}) in the canonical Xray band characteristic of emission from the neutronstar surface, rather than the soft Xray band characteristic of propeller emission from the vicinity of the magnetospheric boundary.
The timescale
of orbit shrinkage due to gravitational
radiation is given by (see, e.g., Faulkner 1971; Banerjee & Ghosh
2006):
where , and all masses are in solar units. In this equation, we have scaled to the value for 1E, and substitution of the masses we have used above for this system gives yr. Generally, 1Elike systems with shorter periods and/or somewhat different companion masses will have yr. Magnetic braking is believed to be comparable or weaker in strength to shrinkage by gravitational radiation at these orbital periods, so that the above estimate is a reasonable one for the 1Etype systems we have in mind here.
Thus, the system becomes a canonical, bright LMXB with a circular orbit and in the range of, say, 210 h. It is wellknown that systems with exceeding about 12 h cannot come into Roche lobe contact by the above orbitshrinkage mechanisms, since the time required would exceed the Hubble time, as Eq. (32) readily shows. However, these longperiod systems also come into Rochelobe contact eventually, as the lowmass companion completes its mainsequence evolution and expands. These systems thus also become canonical longperiod LMXBs with circular orbits. The lifetime of this standard, bright LMXB phase is yr.
7 Discussion
In this work, we have explored a preLMXB model of 1E, wherein the eccentric orbit of the very young preLMXB causes an orbital modulation in the masstransfer rate, and the newborn, fastrotating neutron star operates in the propeller regime, the propeller emission in soft Xrays following the above modulation after viscous smoothening in the accretion disk. In this section, we first discuss first some essential spectral and luminositydependent features of 1E, and their connections with corresponding features in old, lowmass, soft Xray transients (SXRTs) in their low/quiescent states, the prime example of this class being Aquila X1 (Campana et al. 1998). Note that the wellknown transient accretionpowered millisecond pulsar SAX J1808.43658 also shows a similar behavior (Stella et al. 2000). In these classes of lowmass Xray binaries with old neutron stars, the neutron star is thought to operate in the propeller regime when the sources are in their low/quiescent states during decays of their outbursts. We then compare our model with the magnetar model which has been proposed recently for 1E (P08), and discuss how distinction between the two kinds of models might be attempted in future. Finally, we summarize our conclusions.
7.1 Xray spectra
The XMMNewton/EPIC (0.58 keV) Xray spectra of 1E have been described by dL06. The timeaveraged spectra from the 2005 lowstate observations, when the source luminosity was erg s^{1}, can be fitted by a twocomponent model consisting of a blackbody (BB) of temperature keV and an equivalent blackbody radius km, plus a powerlaw (PL) of index , with 70% of the total flux coming from the blackbody component. Alternatively, the second component can also be a blackbody with a higher temperature. A reanalysis of the earlier 2001 XMMNewton data, when 1E had a higher luminosity (by a factor 6), yielded a similar twocomponent (BB+PL) model with essentially the same blackbody temperature and powerlaw index , but a larger equivalent blackbody radius km, and a higher contribution from the PL component (the blackbody contribution was 50% of the total flux as opposed to the above 70%), which made the overall spectrum harder (dL06).
We stress the remarkable similarity of the above observations with those of the spectra of SXRTs in their low/quiescent states (when the neutron stars in them are believed to be functioning in the propeller regime), taking the wellknown source Aquila X1 as the example. A detailed analysis of the BeppoSAX observations of Aquila X1 in 1997 (Campana et al. 1998) has yielded the following results. At the lowest state, with source luminosity erg s^{1}, the (BB+PL) fit had a BB of temperature keV and an equivalent blackbody radius km, plus a powerlaw (PL) of index , with 60% of the total flux coming from the blackbody component. As the luminosity increased by a factor 150 to erg s^{1}, the (BB+PL) fit yielded a BB of temperature keV and an equivalent blackbody radius km, plus a powerlaw (PL) of index , with 20% of the total flux coming from the blackbody component. Remembering that the total range of luminosities in these Aquila X1 lowstate observations during outburst decay is roughly 10^{33}10^{35} erg s^{1} (Campana et al. 1998), essentially identical to that of the 1E observations reported by dL06, the correspondence is very suggestive.
SXRTs are believed to be old systems with a neutron star and a lowmass companion in a close circular orbit, undergoing outbursts due to instabilties either in the accretion disk or in the mass supply from the lowmass companion. In their low/quiescent states during decays of outbursts, the fastspining neutron star (spun up by accretion as per standard LMXB scenario) is believed to operate in the propeller regime. What we suggest in this work is that 1Elike systems are very young systems in the same regime: the young systems can show orbital modulation because of the orbital eccentricity, while the old systems are in circular orbit and cannot show such orbital modulation. However, the spectral signatures are very similar at similar luminosities, which supports our basic suggestion. We note that the timescales associated with 1E outburst appear to be 23 years while those associated with Aquila X1 outbursts appear to be 3070 days. It is possible that the basic phenomenon is rather similar in the two cases, and that the difference in detail is caused by the fact that accretion onto the neutronstar surface (with attendant high luminosities and hard Xray spectra) does occur at the high states during the outbursts for old systems like Aquila X1, but not for young systems like 1E.
A comprehensive theory of the emission spectra of propeller sources appears to be lacking, though Illarionov and coauthors have studied some effects of Comptonization in propellers in windaccreting massive Xray binaries (Illarionov et al. 1993; Illarionov & Kompaneets 1990). Attempts at constructing such a theory for propellers in preLMXBs and in old LMXBs in low/quiescent states is clearly beyond the scope of this paper, and we shall confine ourselves here to the comment that the importance of Compton heating, considered in the above works on propellers in massive binaries, is also likely to be crucial for the systems we are focusing on in this work, as the observed powerlaw tails in the spectra at low luminosities suggest. These tails are particularly prominent in the lowstate spectra of Aquila X1 (Campana et al. 1998).
7.2 Luminosity dependence of light curve
dL06 have compared the 1E light curve in the 2005 lowstate observations with that during the 2001 observations when the source luminosity was a factor 6 higher. While the former light curve is relatively smooth with some cycletocycle variations, the latter one shows more complex, somewhat ``jagged'' structure, with an occasional dip. Further, the pulsed fraction decreses from 43% to 12% as the luminosity increases. We discuss qualitatively how such features may arise. First, a propeller system is inherently more fluctuating than an accreting system, because of a variety of fluctuations possible at the site of shockheating and outflow. As masssupply rate through the accretion disk increases, these fluctuations may increase, causing more complex profiles. Secondly, accretion disks in lowmass systems like LMXBs and CVs are thought to develop structures at their outer edges, which obscure emission from the compact object, and lead to dips. If these obscuring structures increase in size as masssupply rate through the accretion disk increases, this would provide a natural explanation for the above appearance of the dips. Thirdly, as the massarrival rate at increases, decreases (see Sect. 2), matter at the magnetospheric boundary becomes hotter, and the propeller becomes less supersonic, ultimately becoming subsonic. Now, it is wellknown that the subsonic propeller torque is independent of (see Ghosh 1995, and references therein), and so will not follow the modulations of . Hence, as and L increase, the following phenomenon is likely to happen. As the upper limit of the excursions in goes beyond the critical crossover point from supersonic to subsonic propeller regime, the pulsed fraction will decrease because that part of which is above this critical point will not contribute to the pulsed flux, and this decrease will increase with increasing . This may be a natural explanation for the above observation of reduced pulsed fraction at higher luminosity. More quantitative considerations will be given elsewhere.
7.3 Comparison with magnetar model
In a recent paper, P08 have described a model in which 1E is a magnetar, i.e., a neutron star with a superstrong magnetic field 10^{15} G with a lowmass companion. The 6.7 h period is interpreted in this model as the spin period of the neutron star, the idea being that a neutron star with such strong magnetic field as above can be spun down to such long spin period, or such low spin frequency, in 2000 yrs. Magnetars are a fascinating possibility, and their relevance to soft gamma repeaters (SGRs) and possibly to anomalous Xray pulsars (AXPs) has been the subject of much recent study. P08 have invoked an analogy with polars or AM Hertype cataclysmic variables containing white dwarfs with unusually strong magnetic fields, wherein torques acting on the magnetar spin it down in a short time to spin periods in close synchronism with the binary orbital period. In this analogy, they have been inspired by the similarity of the shape the 1E light curve to those of AM Her systems.
We have desribed in this work a model which does not require a neutron star with a superstrong magnetic field, but rather interprets the 6.7 h period as the orbital period of the binary system consisting of a neutron star with a canonical magnetic field of 10^{12} G with a lowmass companion, the newborn, fastrotating neutron star being in the propeller phase, and the propeller emission being modulated in the eccentric orbit of a young postSN binary. We find that the observed 1E light curve can be quantitatively accounted for by our model. Our analogy is with propeller regimes of SXRTs like Aquila X1 in their low/quiescent states, which we consider to be old, circularized analogues of 1E which are no longer orbitally modulated, but which have remarkably similar spectral properties. In this analogy, we have been inspired by the similarity between 1E and the SXRTs in both the spectral characteristics and their changes with source luminosity, as well as the shapes of the outbursts and the way in which propellerlike properties emerge at low luminosities during outburst decays.
An interesting question is that of possible discriminators between the above two models. It appears to us that if all observed properties of 1E and similar systems can be accounted for by known characteristics of early stages of preLMXBs born according to the standard CE evolution and Hestar supernova scenario, such as we have described in this paper (or by other possible models involving standard evolutionary scenarios), there would not be any compelling need for invoking exotic objects like magnetars for this class of objects. On the other hand, if one finds unique observed features in this class of objects that cannot be explained at all within the framework of standard evolutionary scenarios, presence of magnetars in such objects may well be hinted at. However, answering this question is beyond the scope of this paper: we are pursuing the matter, and the results will be reported elsewhere.
7.4 Conclusions
The work reported here suggests that 1Etype systems are early stages of preLMXBs born in the SN of Hestars in binaries of (Hestar + lowmass star) produced by commonenvelope (CE) evolution. As long as the postSN binary is eccentric, and the neutron star is in the propeller regime, soft Xray emission modulated at the orbital period may be expected to occur. As the orbit circularizes, modulation would stop, and as the lowmass companion moves out of Rochelobe contact, the source would not be observed in Xrays. The companion would come into Rochelobe contact again on a long timescale due to orbit shrinkage by emission of gravitational radiation and magnetic braking, and/or by the evolutionary expansion of the companion. This would lead to a standard LMXB: an old neutron star in circular orbit with a lowmass companion. Thus, steadystate arguments, with lifetimes of 1Etype systems estimated at 10^{6}10^{7} yrs and those of LMXBs estimated at 10^{8}10^{9} yrs, would lead us to expect 1 1Etype systems per 100 LMXBs, which is consistent with current observations. However, we must be careful here, as these are overall arguments for the whole population. If one specifically investigates young supernova remnants (SNRs), the chances of finding such systems may be considerably higher, since eccentric binary systems are to be found preferentially in such SNRs. More detailed considerations will be given elsewhere.
The lifetime of the eccentricbinary phase may be increased by an effect we have not included in this introductory work. The effect is that of an enhancement of eccentricity when mass and angular momentum are lost from a binary system which is already eccentric. This dynamical effect is wellknown in the literature (see, e.g., Huang 1963) and its applications to compact Xray binaries have been made earlier (Ghosh et al. 1981). For an eccentric compact binary with the neutron star in the propeller regime leading to the loss of both mass and angular momentum from the system, such considerations are applicable. However, it is possible that, at the rates of mass transfer and loss inferred for 1Etype systems, this effect is a minor one.
Several lines of further investigation are naturally suggested by the considerations we have given in this paper. Foremost among them is a theory of the spectral characteristics of propeller emission in diskfed propeller systems. This would help clarify the remarkable spectral similarity (including changes in spectral parameters with luminosity) between 1E and SXRTs like Aquila X1 in their low/quiescent state, as described in Sect. 7.1. A search for point soft Xray sources in other young SNRs would clarify the observational situation greatly. We note that these sources may or may not be periodically modulated, as we have argued in Sect. 7.2 that such modulations may decrease and disappear in certain luminosity states. However, the spectral characteristics would still be a most valuable diagnostic. These and other investigations are under way, and results will be reported elsewhere.
AcknowledgementsIt is a pleasure to thank A. de Luca for sending data on the light curves, to thank E. P. J. van den Heuvel and L. Stella for stimulating discussions, and to thank the referee for comments which improved the paper considerably.
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Footnotes
 ... Eq. (2)^{}
 Because of this, the parameters adopted for 1E by P08 and by ourselves in this work actually give yr. In our work, we have used the values of the apsidalmotion constant k_{2} given by Landin et al. (2009).
All Tables
Table 1: Best fit model parameters: IStype torque.
Table 2: Best fit model parameters: RUKLtype torque.
All Figures
Figure 1: Xray light curve of 1E. Shown is the observed light curve from dL06, superposed on the (common) bestfit model light curve for IStype and RUKLtype propellers. Left panel: model curve for (nonrotating companion). Right panel: same for (synchronously rotating companion). 

Open with DEXTER  
In the text 
Figure 2: Formation probabilitydensity of immediate postSN binaries as a function of eccentricity efor various values of the dispersion in the SN kick velocity (see text). Curves labeled by the value of in units of 100 km s^{1}. Each curve so normalized that . 

Open with DEXTER  
In the text 
Figure 3: Tidal evolution of a prototype 1Elike system in the e vs. a plane. Semimajor axis a in units of solar radius. Note the ``cut off'' like approach to the circularization point (see text). 

Open with DEXTER  
In the text 
Figure 4: Evolution of periastron distance p=a(1e) during tidal evolution of a prototype 1Elike system (see text). Shown is p in units of the solar radius vs. time in years. 

Open with DEXTER  
In the text 
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