Populations of Supersoft X-ray Sources: Novae, tidal disruption, Type Ia supernovae, accretion-induced collapse, ionization, and intermediate-mass black holes?
Rosanne Di Stefano, Francis A. Primini, Jifeng Liu, Albert Kong, Brandon Patel
aa r X i v : . [ a s t r o - ph . C O ] S e p Astron. Nachr. / AN , No. , 1 – (2009) /
DOI
Populations of Supersoft X-ray Sources:Novae, tidal disruption, Type Ia supernovae, accretion-induced collapse,ionization, and intermediate-mass black holes?
Rosanne Di Stefano ,⋆ , Francis A. Primini , Jifeng Liu , Albert Kong , and Brandon Patel , Harvard-Smithsonian Center for Astrophysics National Tsing Hua University Rutgers UniversityReceived 30 July 2009
Key words
X-rays: binaries – white dwarfs – nova, cataclysmic variables – stars: neutron – black hole physics – X-rays:ISM – galaxies: general – supernovae: generalObservations of hundreds of supersoft x-ray sources (SSSs) in external galaxies have shed light on the diversity of theclass and on the natures of the sources. SSSs are linked to the physics of Type Ia supernovae and accretion-inducedcollapse, ultraluminous x-ray sources and black holes, the ionization of the interstellar medium, and tidal disruption bysupermassive black holes. The class of SSSs has an extension to higher luminosities: ultraluminous SSSs have luminositiesabove erg s − . There is also an extension to higher energies: quasisoft x-ray sources (QSSs) emit photons withenergies above keV, but few or none with energies above keV. Finally, a significant fraction of the SSSs found inexternal galaxies switch states between observations, becoming either quasisoft or hard. For many systems “supersoft”refers to a temporary state; SSSs are sources, possibly including a variety of fundamentally different system types, thatpass through such a state. We review those results derived from extragalactic data and related theoretical work that aremost surprising and that suggest directions for future research. c (cid:13) Supersoft x-ray sources (SSSs) are unusual among x-raysources because they emit few photons with energies above keV. They are unusual in another way: the definition of theclass is very general and can in principle encompass manydifferent types of physical systems.SSSs were established as a class by ROSAT in the early1990s. The original definition of SSSs is often expressed asfollows: luminosities in the range of approximately − erg s − and effective temperatures with k T in therange of tens of eV. This phenomenological definition isbased on the detection of a small number of sources. By1996, seven SSSs had been discovered in the Galaxy, andeleven in the Magellanic Clouds (Greiner 1996).The empirical definition of SSSs suggests effective radiicomparable to the radii of white dwarfs. Indeed, some SSSsare associated with hot white dwarfs in recent novae or sym-biotic binaries, or with the central stars of planetary nebulae.Not all SSSs are associated with systems known to con-tain white dwarfs. Roughly half of those with optical IDsare binaries with orbital periods ranging from hours to a fewdays. These close-binary supersoft sources (CBSSs) may be ⋆ Corresponding author: e-mail: [email protected] white dwarfs accreting at high enough rates to allow incom-ing matter to undergo quasisteady nuclear burning. van denHeuvel et al. (1992) developed a model in which a Roche-lobe filling donor which is more massive than the whitedwarf and/or slightly evolved can provide mass at the req-uisite high rates ( ∼ − M ⊙ yr − ).The CBSS model was important not only as a possibleexplanation of SSSs, but also because it provided a chan-nel through which white dwarfs could retain accreted mat-ter, thereby avoiding nova explosions that would deplete thewhite dwarf. Genuine mass retention by a white dwarf isexciting because it provides a way for some white dwarfs toachieve the Chandrasekhar mass and to undergo accretion-induced collapse (AIC; van den Heuvel et al. 1992) or Type Iasupernova explosions (Rappaport, Di Stefano & Smith 1994).Although the white dwarf models seemed ideally suitedto the first group of SSSs that had been discovered, otherexplanations were naturally explored as well. Kylafis andXilouris (1993) considered a neutron star model in whichthe photospheric radius is comparable to the radius of awhite dwarf.Stellar-mass black holes sometimes exhibit states referredto as “high soft” or “thermal dominant” states (Remillard& McClintock 2006). In these cases, however, the effec-tive values of k T are around keV, making the sourcesmuch harder than SSSs. Nevertheless, CAL 87, a Magel-lanic Cloud source often referred to as one of the “classical c (cid:13) Di Stefano et al.: Populations of Supersoft X-ray Sources
SSSs”, has been considered as a black hole candidate (Cow-ley et al. 1990).During the past years, more information has beengathered about the SSSs in the Galaxy and in the Magel-lanic Clouds. Much of the new data is consistent with whitedwarf models. Yet, definite identification of the nature of theaccretors has proved difficult. The small population of 16 SSSs found by
ROSAT in M31represents a total population that could be as large as ∼ (Di Stefano & Rappaport 1994). The advent of Chan-dra and
XMM-Newton provided the opportunity to discovermore of the M31 SSSs and to identify SSSs in a variety ofother external galaxies. Discovering more SSSs allows us toestablish the full range of source properties and the distribu-tions of temperatures and luminosities. Clues to the naturesof the sources can be gathered by studying their locationwithin galaxies. For example, are SSSs associated primarilywith old or young stellar populations?Are the numbers ofSSSs in typical galaxies large enough to support the hypoth-esis that they are the dominant class of Type Ia progenitors?After a decade of extragalactic x-ray surveys, we canbegin to answer some of these questions. Beyond this, wehave made discoveries along new lines that reveal SSSs tobe an even more interesting class of sources than many ofus anticipated. In this short paper we summarize the resultsthat are most surprising and that suggest new lines of inves-tigation.
Only two external galaxies in the Local Group, M31 andM32, are known to have supermassive black holes. Becauseof the relative proximity of these galaxies,
Chandra is ableto resolve x-ray sources with L x greater than approximately erg s − within a few arcseconds of the nucleus. InM32, Ho et al. (2003) find three sources within ′′ of thegalactic center. One of these is the nucleus itself, a . ± . × M ⊙ black hole. The source closest to the nucleuslies . ′′ away, roughly pc, in projection. It is an SSSwhich can be fit by a eV thermal model or by a power-lawmodel with Γ = 9 . +1 . − . and L X = 2 . × erg s − . Be-cause SSSs constitute a relatively small fraction of all x-raysources, it seems remarkable that the closest x-ray sourceto the supermassive black hole happens to be an SSS. In-terestingly enough, however, the situation in M31 is similar.Within a few arcseconds of the black hole is a soft source,marginally hotter than the “classical” SSSs known in theMagellanic Clouds (Di Stefano rt al. 2004). It is unlikely tobe coincidental that very soft sources lie so close to the cen-tral black hole in the only two galaxies within which such aphenomenon can be detected. There may be several possibleexplanations. One possibility is that the soft sources are the cores ofgiant stars that have been tidally disrupted by the super-massive black hole (Di Stefano et al. 2001). Tidal disrup-tion is a well-studied phenomenon from the theoretical per-spective (Rees 1988; Loeb & Ulmer 1997; Ulmer 1999).The flare which follows such a disruption can be bright( > erg s − ), and can last for days to months. In recentyears, flare events that may be associated with tidal disrup-tions in distant galaxies have been detected (see, e.g., Esquejet al. 2008). When the disrupted star is a giant , the remnantis a long-lasting ( > year) hot core that could be detectedas an SSS. The computed rate of disruptions (Magorrian &Tremaine 1999) is high enough that large galaxies may eachhouse several stripped cores.Whatever the natures of the soft sources in the nuclei ofM31 and M32, the tidal stripping of cores is a definite pre-diction, and must produce an excess of soft x-ray sources inthe central regions of some galaxies. The sources may be onorbits that bring them far from the nucleus, even while stillhot enough to be detected at x-ray wavelengths This meansthat tidal disruption can have long-lasting consequences thatare detectable in nearby galaxies, even though flares arerare and are therefore preferentially observed in very dis-tant galaxies.This example shows that some SSSs in galaxy centersmay have evolutionary paths different from those computedfor supersoft sources descended from primordial binaries. In the CBSS model derived by van den Heuvel et al. (1992),the requisite high rate of accretion is produced by the ther-mal time scale adjustment of the donor star to a shrinkingRobe lobe. Dynamical stability dictates that the initial donormass be less than roughly . M ⊙ (see, e.g., Langer et al.2000). In a second class of CBSS models, the white dwarf isfueled by irradiation-driven winds from a donor that is evenless massive (van Teeseling & King 1998). Given this massrange, most CBSSs should begin their period of high masstransfer and possible SSS-like activity more than yearsafter the binary is formed. The primary must first have achance to evolve to become a white dwarf. Once it does,there is generally a wait time before the donor can begin tocontribute mass. The orbit must shrink (most likely to oc-cur through magnetic braking) and/or the donor must beginto evolve. In either case, the binary has time to move awayfrom the place where it formed. We would therefore not ex-pect SSSs to be primarily associated with regions containingyoung stars.It was therefore surprising to find, even in the first Chan-dra observations of the disk of M31 (Di Stefano et al. 2004),that SSSs in the disk are clustered near star-forming regions,possibly indicating that they are young. This result was con-firmed and strengthened by observations of other galaxies Only giants can be disrupted by black holes with mass larger thanabout M ⊙ , because main sequence stars cross the event horizon beforebeing disrupted. c (cid:13) stron. Nachr. / AN (2009) 3 Fig. 1
SSSs in the spiral galaxy M101. SSSs are found inthe bulge, but most cluster in or near the spiral arms. What-ever their nature(s), SSSs can ionize the ISM (Rappaportet al. 1994; Chiang & Rappaport 1996). So far, searchesfor nebulae associated with SSSs have had limited success(Pakull & Motch 1989; Remillard et al. 1995)
Fig. 2
All x-ray sources in M101. The position of eachdetected source is marked with a blue cross. As above, redsquares mark the positions of SSSs. Red stars correspondto x-ray sources with L X > erg s − . Red diamondsare for quasisoft sources ( § Note thatthe distribution of x-ray sources is far more extendedthan the distribution of SSSs. Furthermore, many x-raysources (and few SSSs) occupy the area between spiralarms. (Di Stefano & Kong 2004). Liu (2008) has identified SSSsin 383 galaxies. The location of SSSs in M101 relative toother sources and to the optical features of the galaxy isshown in Figures 1 and 2.The connection with star-forming regions confirms thatmany sources are young. The donors are likely to be sig-nificantly more massive than white dwarfs. They thereforecannot stably transfer mass to a white dwarf through theL1 point. Instead, they are likely to be contributing massthrough a wind. Many SSSs near star-forming regions maybe high-mass x-ray binaries (HMXBs) or symbiotic bina-ries.
One of the surprises of population studies is that the class ofSSSs has extensions to both higher luminosities ( > erg s − )and higher energies ( k T in the range of a − eV). Sources with x-ray luminosities above erg s − are re-ferred to as ultraluminous x-ray sources (ULXs). Becausetheir luminosities are larger than the Eddington luminosityfor a ten-solar-mass object, it has been suggested that somemay be intermediate-mass black holes (IMBHs). Some SSSsare ultraluminous; such sources are sometimes referred toas ULSs. Several of these sources are well studied. (See,e.g., Fabbiano et al. 2003; Soria & Ghosh 2009; Mukai etal. 2005; Kong et al. 2004; Kong & Di Stefano 2005). Ithas been suggested that some are white dwarfs in super-Eddington outbursts and/or white dwarfs with beamed emis-sion. Stellar-mass and intermediate-mass black holes havealso been considered. When we started to look for SSSs in external galaxies, weexpected that there would be a gap between their spectraand the spectra of the canonical hard sources normally as-sociated with neutron star and black hole accretors. Instead,we found a continuum of soft source energies.In fact, many sources provide some photons above keV,while exhibiting no emission above keV. Sources with k T near eV can have such spectral properties, partic-ularly if they are highly absorbed. Such sources are impor-tant, even if one is interested only in white dwarfs, becausethey could be accreting white dwarfs with mass close to theChandrasekhar mass.It could therefore have been the case that the harder softsources were merely highly absorbed hot white dwarfs. Totest this hypothesis, we identified all of the sources in sev-eral external galaxies, with the goal of finding a significantnumber of soft sources bright enough for reliable spectralfits. This process identified both absorbed sources with k T in the supersoft range and sources that are intrinsically hot-ter. (Di Stefano et al. 2006) Indeed, some sources have fits c (cid:13) Di Stefano et al.: Populations of Supersoft X-ray Sources
Fig. 3
QSSs in the spiral galaxy M101. Note that QSSsalso appear to be concentrated near the spiral arms, althoughthey are somewhat more spread out than SSSs.with k T ∼ − eV. These sources are not natu-ral candidates for nuclear-burning white dwarfs (NBWDs).Sources with luminosities above erg s − which pro-duce few or no photons with energies above keV are calledquasisoft x-ray sources (QSSs). QSSs represent a high-energyextension of the class of SSSs. Like SSSs, QSSs have beendiscovered in every galactic environment. (See Figure 3 andTable 1.) The eighteen SSSs comprising the first-discovered set havebeen observed at occasional intervals over a period of ∼ years. Although changes in flux are common, none of the“classical” SSSs have been reported maintain a high lumi-nosity while switching to a harder spectal state. Among themuch larger number of sources observed in external galax-ies, however, several state changers have been well-documented.One of these is M101-ULS-1. As Figure 4 shows, this sourcehas been detected in supersoft, quasisoft, and hard states.It is very likely a black hole, either of stellar or interme-diate mass (Mukai et al. 2005; Kong et al. 2004; Kong& Di Stefano 2005). Two state-changers have been discov-ered in M31 (Pietsch et al. 2005; Orio 2006; Patel et al.2009). These are different from M101-ULS-1 in that theyare sources of much lower luminosity. They are not likelyto be black holes. The light curve of one of the M31 sourcesis shown in Figure 5. SSSs and QSSs have now been discovered in every galac-tic environment: early type galaxies, in both the bulges and
Fig. 4
Energy distribution of photons received fromM101-ULS-1. Note that during some observations all of thephotons have energies below ∼ keV; the source is su-persoft. In others, there is emission above keV, but noneabove keV; the sources is quasisoft. The source also passesthrough hard states with lower luminosity than during thesoft states. M101-ULS-1 is a considered to be a black holecandidate. Stellar-mass and intermediate-mass models havebeen considered. Table 1
Soft Sources in External Galaxies
Galaxy SSSs QSSs Other SourcesM101 42 21 24M83 28 26 74M51 15 21 56M104 5 17 100NGC4472 5 22 184NGC4697 4 15 72 spiral arms of late-type galaxies, and in globular clusters.Table 1 shows the results for a set of six galaxies that haveeach been carefully analyzed. M101, M83, and M51 are spi-ral galaxies. M104 is a bulge-dominated spiral, while bothNGC4472 and NGC4697 are elliptical galaxies. Very softsources (either SSS or QSS) constitute a larger fraction ofall x-ray sources in late-type galaxies. For SSSs there is adramatic decline in their numbers for early-type galaxiesrelative to late-type galaxies.An automated source selection and identification pro-cess was employed by Liu (2008) to study x-ray sources infields containing 383 nearby galaxies. SSSs and QSSs wereidentified using the same algorithm used for the galaxies inTable 1. Liu found that . of all sources bright enoughfor spectral classification are SSS. For every SSS there arefour QSSs. The combination of SSSs and QSSs constituteabout of all x-ray sources. The high ratio of QSSs toSSSs likely reflects the prevalence of older stellar popula- c (cid:13) stron. Nachr. / AN (2009) 5 Obsdate (MJD)-0.00500.0050.010.0150.02 SCR MCR HCR
Fig. 5
The light curve of r1-25, an x-ray source in M31.
Black: count rate in the soft band (0.1-1.1 keV);
Green: count rate in the medium band (1.1-2 keV);
Red: count ratein the hard band (2-7 keV). Note that the soft band dom-inates during the first set of observations, with few or nocounts in the medium and hard bands. The source is SSS.In later observations, the count rate is higher in the mediumband; during some observations there are significant detec-tions in the hard band. This source passes through SSS,QSS, and hard states. The estimated luminosity in all casesis less than erg s − .tions among the galaxies in Liu’s survey. In addition, Liuestimates that ∼ of the SSSs are state-changers.Among the SSSs alone, Liu identifies sources with L X > × erg s − , and sources with L X > × erg s − . In estimating the luminosities, Liu has used apower-law model, which may underestimate the luminosityof the SSSs. In order for an accreting white dwarf to achieve the Chan-drasekhar mass and explode as a Type Ia supernova, it mustgenerally gain at least . M ⊙ . Retention of matter by WDsappears to require nuclear-burning. The burning of matterreleases a great deal of energy, > erg s − for whitedwarf masses near M C . In the simplest model, these sourcesshould radiate as SSSs, with k T > eV.The progenitors of Type Ia supernovae should be thehottest and brightest SSSs. Di Stefano & Rappaport (1994)showed that those SSSs which are Type Ia progenitors couldbe detected in nearby galaxies with high efficiency. Becauseit takes time ( > × yr) to accrete > . M ⊙ at rates of ∼ − M ⊙ yr − , the numbers of actively accreting, hot, bright progenitors in galaxies such as our own and M31must be large. N = 750 (cid:16) ∆ M . M ⊙ (cid:17)(cid:16) × − M ⊙ yr β ˙ M in (cid:17)(cid:16) L B L ⊙ (cid:17) . (1)For most spiral galaxies (and even for ellipticals, with alower rate of SNe Ia), N cannot be much smaller than sev-eral hundred, and is likely to be larger.Comparing the number of hot, bright NBWDs neededto account for the expected Type Ia supernovae to the num-bers of SSSs and QSSs actually detected in each galaxy, wefind a discrepancy larger than a factor of ten. In fact, the truediscrepancy is almost certainly larger. This is because not allSSSs, and possibly only a small fraction of QSSs, are NB-WDs. Furthermore, of those soft sources that are NBWDs,many are too dim and cool for the white dwarf to have amass near M C . Thus, x-ray observations of external galaxies falsify thehypothesis that the majority of Type Ia supernovae are gen-erated by NBWDs that are detectable as SSSs during theepoch in which the white dwarf’s mass is increasing. Thereare two possibilities: either the majority of Type Ia progeni-tors are not NBWDs approaching the Chanadrasekhar limit,or they are, but we cannot detect them as SSSs.In fact, it may be the case that those accreting whitedwarfs on the way to becoming Type Ia supernovae tendto eject more winds, which can then block the soft radia-tion and obscure the source. In addition, a low duty cycle ofactivity, expected for recurrent novae, could also make thesources less likely to be detected in a supersoft phase.
The most serious bottleneck found in binary evolution cal-culations of accreting white dwarfs that might be Type Iaprogenitors is the difficulty in channeling enough mass tothe accretor to allow it to achieve the Chandrasekhar mass.This problem is less severe for those white dwarfs that startwith masses within a few tenths of M C . These tend to beO-Ne white dwarfs which experience AIC when reachingthe Chandrasekhar mass, instead of Type Ia explosions.Because the white-dwarf progenitors of AIC must bemassive, the binaries in which they form must be wide. Fur-thermore, the companion which donates mass to the whitedwarf is likely to be massive. AICs are therefore likely totake place near star-forming regions. Before the collapse,the white dwarf is likely to be accreting winds ejected by thedonor star, with matter infalling at rates of roughly − M ⊙ yr − .The white dwarf should appear as an SSS, at least episodi-cally. After the collapse, the winds will continue. The new-born accreting neutron star will be highly luminous and mayappear as a ULX. This model (Di Stefano, Pfahl, & Harris2009) links the SSSs found near star forming regions witha subset of ULXs. ULXs are also preferentially found nearstar-forming regions. c (cid:13)(cid:13)
The most serious bottleneck found in binary evolution cal-culations of accreting white dwarfs that might be Type Iaprogenitors is the difficulty in channeling enough mass tothe accretor to allow it to achieve the Chandrasekhar mass.This problem is less severe for those white dwarfs that startwith masses within a few tenths of M C . These tend to beO-Ne white dwarfs which experience AIC when reachingthe Chandrasekhar mass, instead of Type Ia explosions.Because the white-dwarf progenitors of AIC must bemassive, the binaries in which they form must be wide. Fur-thermore, the companion which donates mass to the whitedwarf is likely to be massive. AICs are therefore likely totake place near star-forming regions. Before the collapse,the white dwarf is likely to be accreting winds ejected by thedonor star, with matter infalling at rates of roughly − M ⊙ yr − .The white dwarf should appear as an SSS, at least episodi-cally. After the collapse, the winds will continue. The new-born accreting neutron star will be highly luminous and mayappear as a ULX. This model (Di Stefano, Pfahl, & Harris2009) links the SSSs found near star forming regions witha subset of ULXs. ULXs are also preferentially found nearstar-forming regions. c (cid:13)(cid:13) Di Stefano et al.: Populations of Supersoft X-ray Sources
At the time SSSs were discovered, NBWDs provided themost natural explanation for their observed ranges of lumi-nosities and temperatures. Indeed, the significant associa-tion between novae and SSSs verifies that many transientSSSs are indeed hot white dwarfs (Pietsch et al. 2005),while observations of nearby CBSSs provide evidence thatNBWD models are likely to apply.In the time since the early 1990s, however, two develop-ments argue for extensions of the physical models. The firstdevelopment is the extension of the ranges of source tem-peratures and luminosities described in § M ⊙ and M ⊙ (Orosz et al. 2007; Prestwich et al. 2007)have been discovered. Second, IMBH models have been de-veloped as explanations of ULXs. For black hole accretorswith masses larger than a few solar masses, an opticallythick inner disk can emit as a QSS or SSS. (See Figure 6.) Ifthe system is in a thermal dominant state, the state in whichit is possible determine the black hole mass, it may appearas a QSS or, for more massive black holes, as an SSS. (SeeDi Stefano et al. 2003a, 2003b, 2004a, 2004b; Di Stefano &Kong 2003a, 2003b, 2004a, 2004b)While back hole models are natural for some QSSs andSSSs, neutron star models should also be reconsidered. Dur-ing the early 1990s, when the only known neutron star ac-cretors were hard x-ray sources, it seemed to require finetuning to achieve a white-dwarf-like photospheric radius.The discovery of QSSs allows a wider range of photosphericradii, perhaps removing the need for fine tuning. In addition,white dwarf models in which a cooling white dwarf pro-duces soft radiation, but harder emission is produced throughaccretion, can also be used to model state-changing softsources (Patel et al. 2009). Conclusions:
SSSs are found in all galactic environments.Many are young stellar systems. Several evolutionary pathscan produce soft sources, while not all NBWDs, even thoseof high mass, are detectable as SSSs. The sum of these dis-coveries suggest that soft x-ray sources provide a rich areafor research on many astrophysical topics of great interest.
Acknowledgments:
This work was supported in part byNASA through AR-10948.01-A-R and GO8-9092X.
References
Chiang, E., & Rappaport, S. 1996, ApJ , 469, 255Cowley, A. P., Schmidtke, P. C., Crampton, D., & Hutchings, J. B.1990, ApJ , 350, 288Di Stefano, R., Friedman, R., Kundu, A., & Kong, A. K. H. 2003a,arXiv:astro-ph/0312391Di Stefano, R., Greiner, J., Murray, S., & Garcia, M. 2001, ApJ ,551, L37Di Stefano, R., & Kong, A. K. H. 2004a, ApJ , 609, 710
38 40 420200400600 LOG[L]38 40 420200400600 LOG[L]
Fig. 6 k T versus
Log [ L ] for the inner portion of the ac-cretion disk around black holes. Each pair of two curvesof a single color corresponds to a fixed black hole masswhich labels the regions between the curves. The uppercurve of each color corresponds to a disk with inner radius M BH G/c , while the lower curve corresponds to an innerdisk with times the radius. The point at the bottom (top) ofeach curve corresponds to the luminosity of the inner diskbeing L Eddington ( L Eddington ). Di Stefano, R., & Kong, A. K. H. 2003a, arXiv:astro-ph/0311374Di Stefano, R., & Kong, A. K. H. 2003b, ApJ , 592, 884Di Stefano, R., et al. 2004b, ApJ , 610, 247Di Stefano, R. et al. 2003b, ApJ , 599, 1067Di Stefano, R., Primini, F. A., Kong, A. K. H., & Russo, T. 2004a,arXiv:astro-ph/0405238Di Stefano, R. 2008, AAS/HEAD, 10, c (cid:13) stron. Nachr. / AN (2009) 7Rees, M. J. 1988, Nature, 333, 523Remillard, R. A., & McClintock, J. E. 2006, ARA&A , 44, 49Remillard, R. A., Rappaport, S., & Macri, L. M. 1995, ApJ , 439,646Soria, R., & Ghosh, K. K. 2009, ApJ , 696, 287Ulmer, A. 1999, ApJ , 514, 180van den Heuvel, E. P. J., Bhattacharya, D., Nomoto, K., & Rappa-port, S. A. 1992, A& A, 262, 97van Teeseling, A., & King, A. R. 1998, A& A, 338, 957 c (cid:13)(cid:13)