A&A 382, 124-129 (2002)
DOI: 10.1051/0004-6361:20011627
M. R. Schreiber ^{1,2} - B. T. Gänsicke ^{1}
1 - Universitäts-Sternwarte, Geismarlandstr. 11, 37083 Göttingen,
Germany
2 - Department of Astronomy, University of Cape Town, Private Bag,
Rondebosch 7700, Cape Town, South Africa
Received 2 November 2001 / Accepted 6 November 2001
Abstract
We analyse the consequences of the recently measured
parallax of SSCygni (Harrison et al. 1999) on the accretion disc
limit cycle model. Using the observed long term light curve of
SSCyg and
,
we obtain for the mean mass
transfer rate
.
In addition, we calculate the vertical structure of the accretion disc
taking into account heating of the outer disc by the stream impact.
Comparing the mean accretion rate derived from the observations with
the calculated critical mass transfer rate, we
find that the disc instability model disagrees with the observed long
term light curve of SSCyg as
is greater or similar to the critical mass
transfer rate.
The failure of the model indicated by this result can be confirmed by
considering that the accretion rate at the onset of the decline should
be exactly equal to the value critical for stability. In contrast to
this prediction of the model, we find that the accretion rate required
to explain the observed visual magnitude at the onset of the decline must be significantly higher than the critical mass transfer rate.
Our results strongly suggest that either the usually assumed temperature
dependence of the viscosity parameter
is not a realistic description
of the disc viscosity,
that the mass transfer rate in SSCyg noticeably
increases during the outbursts or, finally, that the HST distance of
pc, is too high.
Key words: accretion, accretion discs - binaries: close - stars: individual: SSCygni - novae, cataclysmic variables
The dwarf nova SSCyg is among the visually brightest CVs and has a detailed long term light curve covering more than a century. SSCyg has, therefore, become the reference object for accretion disc instability analyses, and its observed light curve has been used to calibrate the viscosity parameter . Cannizzo & Mattei (1992) examined the long term light curve of SSCyg (Fig. 1) in detail in order to test the limit cycle model (Cannizzo 1993a) and found a mean outburst duration of d and a mean quiescence time of d (corresponding to a mean cycle duration of d). In a later paper, Cannizzo & Mattei (1998) again examined the light curve of SSCyg, deriving the rise and decay times. Only the mean values are important in the context of our analysis: d, d. These values are obtained using a conservatively low estimate of the outburst magnitude of m_{v}=8.5.
Figure 1: The visual long term light curve of SSCyg compiled from observations made by members of the Association Francaise des Observateurs d'Étoiles Variables. | |
Open with DEXTER |
However, even though the brightness variation of SSCyg has been monitored to a high level of precision, its distance has been highly uncertain. As a consequence, the absolute magnitude and the accretion rate, have also been ill-defined. Recently, a high-quality parallax of SSCyg was obtained using the Hubble Space Telescope (HST) Fine Guidance Sensor (FGS), which moves the system to a distance 1.5-2 times larger than previously thought (Harrison et al. 1999). The HST/FGS distance of pc is confirmed by Beuermann (2000), who showed that the accretion disc in SSCyg contributes significantly to the observed K band flux. As a consequence of the now firmly established (larger) distance, the absolute magnitude of SSCyg in outburst increased, too. Figure 2 shows the absolute visual magnitudes of dwarf novae at outburst maximum as a function of their orbital period, adapted from Warner (1987). The arrow displays the impact of the HST/FGS parallax on SSCyg: the system is now the absolute brightest dwarf nova in outburst and its maximum absolute magnitude is brighter than one would expect from its orbital period (Cannizzo 1998).
The mean accretion rate in SSCyg inferred from its long term
light curve depends, in addition to the absolute magnitude, on the
inclination i of the accretion disc. This system parameter is
somewhat uncertain, most studies of SSCyg suggest
(Ritter & Kolb 1998). A significantly
higher value of
was derived by
Voloshina & Khruzina (1997), but, throughout this paper we assume
the lower value. To account for the influence of the inclination on
the absolute magnitude we follow
Paczynski & Schwarzenberg-Czerny (1980):
(1) |
Throughout this paper we use the system parameters of SSCyg given in the literature, i.e. the primary mass (Ritter & Kolb 1998; van Teeseling 1997), secondary mass , and orbital period in hours (Ritter & Kolb 1998).
The goal of this section is to check if the "standard'' disc instability model can reproduce the absolute magnitude of the outbursts of SSCyg, taking into account the larger HST/FGS distance, the inclination, and the mean outburst time scales derived from the long term light curve.
Figure 2: The absolute magnitudes of dwarf novae adapted from Warner (1987) corrected to a mean inclination of and with m_{v}=8.5 for the maximum magnitude of SSCyg. Due to the increased distance, SSCyg has become the absolute brightest dwarf nova. | |
Open with DEXTER |
Figure 3 shows a light curve computed with the FE/FD DIM code used for the first time in Schreiber & Hessman (1998) and described in detail in Schreiber et al. (2000b). We adapted the parameters suggested by Ludwig et al. (1994) and two different values for the mass transfer rate.
Figure 3: Simulated light curves using the orbital parameters of SSCyg, , , (upper panel) and . | |
Open with DEXTER |
During an outburst cycle the disc subsequently goes through a
phase of quiescence, rise, adjustment, quasi-stationary outburst
state, and decay. After the heating front has brought the entire disc
into the hot state (rise), the disc redistributes its mass
(adjustment) until it accretes without radial variations of the
accretion rate (quasi-stationary state). Almost all the mass accreted
during an outburst cycle is transferred onto the white dwarf during
this quasi-stationary outburst state (Fig. 3). Thus, to derive a
lower limit for the mass accreted during a mean outburst cycle, one
simply has to multiply the accretion rate of a stationary standard
disc which reaches
with the mean
quasi-steady state duration,
d^{}. Throughout this paper we assume a very
large disc for SSCyg during outburst, i.e. % of the
primary's Roche radius
.
(Ritter 1980; Harrop-Allin & Warner 1996)
(
cm for the binary parameter of
SSCyg). Following Buat-Ménard et al. (2001),
we describe the
additional heating of the outer disc due to the stream disc impact
with
(2) |
The accretion rate necessary to reproduce the observed visual
flux during the outburst can be described with a power-law:
= | |||
(3) |
(4) |
(5) |
In the absence of stream impact heating the critical accretion rate is given
by the accretion rate at the upper turning point of the
S-curve
and
can be approximated by a power-law, i.e.
(6) |
Taking into account heating of the outer edge of the disc by the
impact of the stream, the critical mass transfer rate is given by an
implicit equation as the turning point of the modified S-curve
depends on the mass transfer rate
itself;
.
The critical mass transfer rate is then given by a solution of
(7) |
(8) |
= | |
(9) |
(10) |
+ | |||
(11) |
Figure 4: S-curves for outer radii [in units of 10^{10}cm, (dotted), (solid), (short dashed line)] using gs^{-1}(solid horizontal line, see Eq. (5)). At the outer edge of the disc (dotted line) the instability is completely suppressed by the additional heating due to the stream ( ). Moving inward, the additional heating decreases (see Eq.(2)) but the mean mass transfer rate (solid horizontal line) is still clearly above the value critical for stability. The critical accretion rate (see Eq.(10)) is represented by the dashed horizontal line. Notice, the S-curves are calculated with . | |
Open with DEXTER |
For the mean mass transfer rate we obtain (Fig. 4), which would lead to steady disc accretion. Considering the uncertainties of the involved parameters, we find .
The critical and the mean mass transfer rate derived in the previous section are sensitive to the uncertainties in the binary parameters and the assumed efficiency of stream impact heating as the additional heating can significantly reduce the critical mass transfer rate. Thus, while our results presented in Sect.3 suggest that the DIM fails in describing the observations of SSCyg, they do not allow to categorically exclude the validity of the DIM.
However, in this section we show in an independent way that the observed light
curve of SSCyg provides additional evidence for the failure of the DIM,
independent from the details of stream impact heating or the uncertainties
in the system parameters.
For the mass accretion rate at the onset of the decline
the DIM
predicts
an essentially lower value than required by the
observations as, (a) the DIM predicts that the start of the cooling
front at the outer edge
of the disc defines the onset of the decline in the outburst light curve.
The cooling front starts when the
accretion rate of the quasi stationary disc is exactly equal to the
critical rate, thus,
(12) |
(13) |
It is worth noting that even if we completely neglect stream impact heating
the DIM cannot explain the observations. Then, the critical mass transfer rate
can be approximated by
Eq.(6) and the accretion rate necessary to reach the visual flux
during outburst somewhat increases:
(14) |
(15) |
(16) |
Considering the "larger'' distance of SSCyg and the observed long term light curve, we calculated the mean mass transfer rate . Taking into account stream impact heating of the outer disc we find (Fig. 4) which contrasts with the predictions of the DIM: with such a high mean mass transfer rate, SSCyg should not be a dwarf nova at all, but a novalike variable with a stationary hot accretion disc. This result is, however, sensitive to the assumed efficiencies of stream heating and disk irradiation and the uncertainties of the binary parameters, the inclination, and the distance. While this result on its own is not sufficient to proclaim a general failure of the DIM, an independent suggestion for a major problem with the DIM comes from comparing the accretion rate predicted by the DIM at the onset of the decline with the accretion rate required by the observed visual magnitude at this point (see Sect.4). Hence, the conclusion from both these results must be: the current DIM cannot explain the observations of SSCyg for a distance of pc.
There are three possibilities that may resolve this problem: (a) the temperature dependence of , the key ingredient in the accretion disc limit cycle model, has to be modified, (b) increased mass transfer during the outburst plays an important rôle, or finally (c) the HST/FGS distance of 166pc and/or the assumed inclination are wrong.
Considering (a), it seems that we do not yet have an adequate understanding of the viscosity in accretion discs. The instability necessary to obtain the limit cycle behaviour appears mainly due to an artificial change of , given by Eq.(11), at the point where the small "natural'', i.e. without a change of , ionisation instability has been found in the S-curves. There is no physical reason for this assumption and it might be the case that starts to change at higher temperatures than previously assumed. This would lead to a higher value of the critical mass transfer rate. As such a modification would affect the dividing line between dwarf novae and nova likes, one should carefully consider the consequences for other dwarf nova before changing Eq.(11).
With respect to (b), we point out that another possibility to solve
the problem obtained in Sects. 2-4 is to assume that the mass transfer
increases during the outbursts, e.g. due to irradiation of the
secondary star. Assuming a mean mass transfer rate of
gs^{-1}during quiescence, rise, and decay, the mean mass transfer rate during
the outburst state should be
= | (17) |
Finally, considering (c), we can only note that at least one of the additional CV parallaxes measured with HST, namely UGem, agrees very well with previous distance estimates (Harrison et al. 1999). UGem has a noticeably lower accretion rate than SSCyg, therefore the distance estimated based on K band magnitude and/or spectroscopy of the secondary star is much less affected by emission from the disc than in SSCyg. Thus, at least for UGem an error in the HST/FGS parallax appears extremely unlikely. However, assuming and demanding gs^{-1} for SSCyg leads to gs^{-1}and requires pc for agreement with the DIM.
Acknowledgements
This research has made use of the AFOEV database, operated at CDS, France. Special thanks are extended to Jean-Marie Hameury, Hans Ritter and Rick Hessman for interesting discussions at the CV-Conference in Göttingen (2001). We also wish to thank an anonymous referee for helpful comments. MRS thanks the Astronomy Department of the UCT for the warm hospitality during a nice and productive stay in March-May 2001 and the DAAD (PKZ:D/01/05718) for financial support. BTG thanks for support from the DLR under grant 50OR99036.