3. Is the companion a neutron star or a white dwarf ?
3.1. The ROSAT observation
In November 1992 the companion of HD 49798, listed in the WGA Catalogue as J0648.0-4418 (White et al. 1994), has been observed with the ROSAT PSPC (0.1-2.4 keV). Israel et al. (1995) found the signal to be modulated with a period of 13.18 s and an energy independent pulsed fraction of about 60 %.
In order to obtain information on the possible spectral parameters, we analyzed the PSPC data, extracted from the ROSAT archive. The total net exposure time is 5453 seconds. In the extraction of the source photons, care was taken to exclude possible contamination from a nearby () unrelated weak source. The background was estimated from a source-free nearby region. The source spectrum is soft, but a weak hard component, which cannot be attributed to contamination from the weaker source, is clearly visible. We fitted the spectrum to a combination of a blackbody (for the soft component) and thermal Bremsstrahlung (for the hard component). Given the weakness and limited spectral coverage of the hard component, we fixed the temperature of the Bremsstrahlung component to 10 keV, which is an average temperature, and used in similar cases (Haberl & Motch 1995). From the fact that the two components dominate in different regions of the spectrum, it is certain that the results on the blackbody component are not heavily affected by the specific choice of the model for the hard component.
As is always the case with soft PSPC spectra with unknown column absorption, the two spectral parameters blackbody temperature and absorption column density are not well determined, since they are strongly correlated with each other. In Fig. 3 the 90% contour level for and is shown. The accepted region is open on the low-temperature side, so the only firm contraint on the basis of the goodness of fit comes from the high-temperature side. From this constraint ( eV, cm-2) we derive erg/s and a blackbody radius km. On the low-temperature side the luminosity can only be constrained by the value of the Eddington limit of erg/s, above which accretion is not possible. To obtain such a high luminosity at low temperature, the emitting area must be large : km. Also plotted are the luminosity levels (dotted lines) and the different radii for the blackbody emission (assuming a distance of 0.65 kpc). The luminosity of the hard component, under the assumption of a Bremsstrahlung temperature of 10 keV is in the range erg/s.
The observation of pulsations in this X-ray source puts limits on the size of the emitting area, as it must be self-occulted by the compact object. If the soft component in the spectrum is well represented by a blackbody, we can constrain the luminosity at high values. For a neutron star it turns out that it would be located at the right end of Fig. 1, with erg/s and eV, implying an extremely low accretion rate (see Chapt 3.3).
In case of a white dwarf the radius would be km and thus the luminosity should be below erg/s, corresponding to a blackbody temperature above eV. A white-dwarf spectrum however, might not be represented satisfactorily by a blackbody, as Heise et al. (1994) showed in their calculations of spectra from model atmospheres. They found about one order of magnitude lower X-ray luminosity at the same temperature. As we shall see later this result is very important if the compact object is a white dwarf. Then such a model atmosphere would fit well with an "accretion spot" at the magnetic pole of the white dwarf.
3.2. Soft intermediate polars
The fast pulse period, reflecting the spin period of the compact object, suggests that it is a neutron star, but if we compare the X-ray spectrum with that of other X-ray pulsars, we note that not one neutron star is known with such a huge soft component and weak hard spectral tail.
The X-ray spectrum is, however, remarkably similar to the spectra of soft intermediate polars (Haberl & Motch 1995). They show a soft component with eV and a weak hard tail (which they fix at keV). The distances and thereby the luminosities of the sources reported by Haberl & Motch are not well known. The general idea about intermediate polars is that they are magnetized white dwarfs which have their magnetic axes misaligned with their rotational axes. The accreted matter will be funnelled onto the polar caps by the magnetic field, thus giving rise to a rotating "hot spot" which may be occulted by the white dwarf itself. They have luminosities in the range erg/s.
In a subgroup of the intermediate polars, the DQ Herculis systems, one finds very rapidly spinning white dwarfs. It appears that the shortest period systems tend to have the softest X-ray spectra (Patterson 1994). Their magnetic fields are, in general, not very strong, Gauss, as the radius of the magnetopause should be smaller than about the radius of a Keplerian orbit with . The shortest spin period so far found in these systems is that of AE Aquarii, which has s (Patterson 1979). The observed ROSAT spectrum of this source, consisting of a large soft component and a weak hard tail (Clayton & Osborne 1996), is similar to that of HD 49798 / WGA J0648.0-4418. The timing analysis of the latter is presently being done by Israel et al. (in prep) and might reveal more similarities. It thus appears that the X-ray spectrum and luminosity of this source are fully consistent with that of a rapidly rotating weakly magnetized white dwarf. This would make this the fastest spinning white dwarf observed so far.
3.3. Accretion from wind of the subdwarf
If the upper limit of the distance to HD 49798 is correct, the radius of the subdwarf is less than (KS78) and hence smaller than the smallest possible Roche lobe for its mass range. As in this case the X-ray luminosity cannot be caused by accretion due to Roche-lobe overflow, we will consider accretion from a stellar wind.
Modelling of the wind parameters of this subdwarf presents a number of problems. The velocity of the wind has been estimated by Hamann et al. (1981) and Bruhweiler et al. (1981). Hamann et al. found from the P-Cygni profile of N V a value of 1350 km/s, although they had to locate this maximum velocity, which is normally reached at infinity, at a distance of from the star. This could mean that the ionisation fraction of N V drops to zero at that distance, with the wind still being accelerated further out. Bruhweiler et al. found, apart from the wind indicated by the N V profile (they report 1500 km/s), a low velocity wind, km/s, from the N IV profile as well.
Springmann & Pauldrach (1992) show from calculations that in hot thin winds radiative decoupling of H and He from the heavier elements is likely to occur. They suggest that this effect is important for this subdwarf as well, like in Sco for which they calculate a reduction of 40 % in H- and He-wind velocity. This would mean that the velocity of the bulk of the wind matter may be as low as 800 km/s.
The amount of mass lost in wind has also been estimated by Hamann et al. (1981). Their lower limit of /yr is estimated with the aid of a wind model, but since wind theory has changed substantially since 1981, the limit might change if newer models were used. Their upper limit of /yr is based on the assumption that the stellar atmosphere is approximately in hydrostatic equilibrium. This last estimate only indicates an order of magnitude for the mass-loss rate and does not exclude an upper limit which is three times as high (W.R. Hamann 1996, private communication).
On the other hand, from the evolutionary calculations by IT93 we see that a shell-burning star, in the allowed mass range, must lose matter at a rate /yr to stay within its Roche lobe (see Table 2). As HD 49798 is definitely inside its Roche lobe we conclude that the mass-loss rate must be about /yr for the low mass models and up to /yr for the most massive ones. We will adopt a rate /yr, which is consistent both with the spectroscopic analysis and the evolutionary models.
We can make an estimate of the amount of mass captured from the wind by the gravitational field of the compact star, and of the luminosity , due to the release of potential energy in the process of accretion, by using the Bondi-Hoyle formalism as described by Davidson & Ostriker (1973):
Here G is the constant of gravitation, and the mass and radius of the compact object, a the orbital separation, the mass lost in the wind of the subdwarf and the relative velocity of the compact star and the wind.
The accretion rate , and therefore also the luminosity, strongly depends on the relative wind velocity (). A reduction of 40 %, from 1350 km/s to 810 km/s, as mentioned in Springmann & Pauldrach (1992) for a similar stellar wind, would already increase the luminosity with more than a factor 7. The relation between between and is shown in Fig. 4, for both a neutron star and a white dwarf companion.
We can see from Fig. 4 that, with /yr and km/s, a neutron star is expected to produce an accretion luminosity of erg/s, corresponding to an accretion rate /yr. In order to be consistent with the low luminosity of erg/s at the small blackbody radii inferred from Fig. 3, there should be a much higher wind velocity or much lower mass-loss rate to reduce the accretion rate by more than a factor 100. Then also the low-velocity wind component must be absent, which is exactly the opposite to what Springmann & Pauldrach (1992) suggest for the subdwarf's wind.
From the curve indicating the white dwarf, we see that with /yr, a wind velocity between 1350 and 800 km/s will result in an accretion luminosity between erg/s. So, even when the low-velocity wind component is absent or when the wind mass-loss rate is lower, the accretion luminosity is still consistent with the observed X-ray luminosity.
We thus conclude that, taking the constraints set by , , , soft X-ray luminosity and radius of the emitting region into account, a white dwarf model with accretion onto a limited "spot" near the magnetic pole(s) can consistently explain all the observations, whereas a neutron star cannot. What the latter cannot explain is in particular the extreme softness of the spectrum in combination with a low X-ray luminosity.
3.4. The birthrate problem implied by a neutron-star companion
If the pulsating X-ray source in the system were a neutron star, the final evolutionary state of this system would be: a binary radio pulsar with a circular orbit, consisting of a massive white dwarf and a recycled pulsar, as argued by Van den Heuvel (1994). The latter type of pulsars tend to have much weaker magnetic fields and faster spin than ordinary non-recycled pulsars (see, for example, the reviews by Bhattacharya and van den Heuvel 1991, and Bhattacharya 1995). At present four such binary pulsars consisting of a massive white dwarf and a recycled pulsar in a circular orbit (hereafter intermediate-mass binary pulsars or IMBPs) are known: PSR 0655+64, PSR J2145-0750, PSR J1022+1001 and PSR J0621+1002 (Bailes et al. 1994, Camilo et al. 1996). In all these systems the spin-down age of the pulsar is extremely long, yrs, implying an extremely old age and long lifetime of these systems.
By contrast, the duration of the present evolutionary state of HD 49798, until the subdwarf has transferred its hydrogen and helium envelopes, is only of order years or less (IT93). As the system is quite close to us (0.65 kpc), systems of this type should be quite common in the Galaxy. If HD 49798 contains a neutron star and is the progenitor of an IMBP, the birthrate of systems like HD 49798 should be equal to (or less than) that of IMBPs. Because of the very different lifetimes, this implies that in a steady state the total Galactic number of IMBPs should be at least 4000 times larger than that of HD 49798-like systems. The four known IMBPs are all within 2 kpc distance, and comprise about 20 % of the presently known population of low-mass binary pulsars (LMBPs) within that distance. Lorimer (1995) estimates that the local Galactic surface density of LMBPs is 20 kpc-2, but that the true number could be up to an order of magnitude larger due to an unseen low-luminosity population and beaming effects. We therefore estimate that the local surface density of IMBPs is kpc-2, which implies a local density of HD 49798-like systems of 0.01 kpc-2 if the birthrates are equal. Assuming that we have no preferential position within the space distribution of either IMBPs or HD 49798-like systems in the Galaxy, the probability to find (at least) one HD 49798 within 0.65 kpc is less than 1.3 %. We therefore conclude that, on the basis of the relative closeness of HD 49798 and the implied birthrate of such systems if the companion were a neutron star, a neutron-star companion can be excluded at the 98.7 % confidence level.
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998