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Astron. Astrophys. 348, 364-370 (1999)

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4. The observed linewidth/K vs mass ratio relation in dwarf novae

In this section we investigate the validity of the linewidth/K vs mass ratio relationship among SU UMa stars using new spectroscopic data and predictions of the tidal resonance model. For comparison, we also include published data of dwarf novae above the period gap.

As a working hypothesis we will assume that the mass ratio of SU UMa stars is actually given by the "superhump" mass ratio [FORMULA] derived from Eq. 7, an assumption that seems well founded as previously discussed.

In order to calibrate Eq. 4 we selected 17 SU UMa stars with orbital and superhump period known and published FWHM and K values. We also included EG Cnc measuring their linewidth from published spectra. For WZ Sge, 6 very discrepant FWHM values spanning a time interval of four decades were included. Two of these measures were made by the author on two H[FORMULA] spectra obtained at the 2.5 m telescope of Las Campanas Observatory in August 5, 1991 (Fig. 1). Multiple FWHM records were just found for WZ Sge, due to the far more abundant literature existing for this star. The data are shown in Table 2.

[FIGURE] Fig. 1. H[FORMULA] profiles of WZ Sge taken with 15-minute integration time and 3 Å spectral resolution. The spectra are labeled with the heliocentric julian day. The upper spectrum has been displaced by 2 continuum units for clarity.


Table 2. Orbital and superhump periods (in days), and spectroscopic parameters FWHM and K and their errors (in km s-1) for a sample of SU UMa stars. The recurrence time ([FORMULA] in days, sometimes corresponding to the mean value) is from Nogami et al. (1997) and references therein, except for BR Lup (Mennickent & Sterken 1998). These recurrence times are for normal outbursts except for WX Cet, EG Cnc and WZ Sge where are for superoutbursts. N/A means not available.
FWHM are for H[FORMULA], [FORMULA] and [FORMULA] from Patterson (1998) and references therein, except when indicated. FHWM and K are from (1) Mennickent 1995a (2) O'Donoghue & Soltynski 1992, FWHM from Mennickent 1995b (3) Mennickent & Sterken 1998, also [FORMULA] and [FORMULA], FWHM measured from Munari & Zwitter 1998 (4) Mennickent & Diaz 1996, also [FORMULA], [FORMULA] is from Vogt (1981) (5) Mennickent et al. 1999, also [FORMULA], [FORMULA] is from Kato et al. 1998. (6) Thorstensen et al. 1986 (7) Rayne & Whelan 1981, H[FORMULA] values (8) Horne et al. 1991, [FORMULA] values (9) Martin-Paris & Casares 1995 (10) Warner et al. 1998 (11) Arenas & Mennickent 1998, also [FORMULA], [FORMULA] is from Kato (1994) (12) Thorstensen & Taylor 1997 (13) Mennickent & Arenas 1998, also [FORMULA], [FORMULA] is from Vogt & Semeniuk (1980) (14) Mennickent 1995b (15) Patterson et al. 1998 (16) Mennickent 1994 (17) FWHM from Honeycutt et al. 1987, as given by J94, H[FORMULA] values (18) FWHM measured from Greenstein 1957, H[FORMULA] values (19) This paper (20) FWHM measured from Neuostroev 1998 (21) FWHM measured from Gilliland et al. 1986.

In the following analysis we also include the 10 above-the-gap dwarf novae used by J94 along with CZ Ori 1

From Fig. 2 it is evident that the linear relation found by J94 (the dashed line) is not valid for SU UMa stars. The relation fits well data for dwarf novae above the period gap but clearly deviates for SU UMa stars. The larger deviations are observed in the the post-period-minimum candidates EG Cnc and WZ Sge. In addition, it is remarkable the large dispersion observed in the R values of WZ Sge. The supercycle phase was assigned to each observation of this star (T = 32.5 yr, e.g. Patterson et al. 1981). The path followed by R seems to be phase-dependent, with a minimum at phase 0.3 and a maximum at phase 0.5 (Fig. 2). However, the supercycle is not completely resolved in our limited dataset, so is not clear if the variation is smooth or random through the whole cycle. However, the observed behaviour contrasts with the monotonic increase of the peak separation during the supercycle (Neuostroev 1998). In addition, the FWHM variability (up to 60% of the mean value) is larger than the variability shown by the peak separation (less than 15% of the mean value, Neuostroev 1998). This probably indicates important changes in the disk structure during the superoutburst cycle. A long-term monitoring of this star - likely obtaining just a few snapshot spectra through quiescence - is needed to fully clarify any dependence of the line parameters on the supercycle phase.

[FIGURE] Fig. 2. The dashed line represents the Jurcevic et al. (1994) calibration of Eq. 4. Data for dwarf novae above the period gap (filled boxes, mostly from J94, see text) and SU UMa stars ([FORMULA], from Table 2) are also shown."Period bouncer" candidates are labeled. WZ Sge data is enclosed inside the solid line rectangle. These points are slightly displaced in the horizontal axis for clarity. They are labeled accordingly to their supercycle phases (T = 32.5 years). The J94 relations fails in the domain of SU UMa stars.

The fact that the post-period-minimum candidates show the larger residuals of Eq. 4, suggests the possibility of a dependence of the residuals on the mass accretion rate. To check that possibility, we choose the minimum time between outbursts as a comparison parameter. Current outburst models indicate that this parameter is inversely related to [FORMULA] (e.g. Osaki 1996). As a result, Fig. 3 suggests that the larger deviations are found in the disks with the highest and lowest accretion rates. This impression remains valid inclusive after removing the objects showing only superoutbursts (WX Cet, EG Cnc and WZ Sge). More studies of extreme SU UMa stars are needed to confirm this point.

[FIGURE] Fig. 3. The relative residuals of Eq. 4 for [FORMULA] = 2.0 (Jurcevic et al. 1994 's calibration) versus the recurrence time. Symbols are as in Fig. 2. The mean value of [FORMULA] was used for dwarf novae above the period gap (Ritter & Kolb 1998). The mean R value of WZ Sge is plotted. Some stars with the larger residuals are labeled; in general they correspond to SU UMa stars with the longest and shortest recurrence times.

In Fig. 4 we compare q and R showing the best (non-linear Levenberg-Marquardt) fitting function


This equation basically reproduces the J94 relation above the period gap but improves the fit for most SU UMa stars. As shown in Fig. 4, the mean relative dispersion is 22% for all dwarf novae, above and below the period gap, except for the "period-bouncers" EG Cnc and WZ Sge. These stars do not fit the general tendency shown by other dwarf novae. Accordingly, we regard Eq. (8) as a new mass estimator for dwarf novae with the exception of post-period minimum systems.

[FIGURE] Fig. 4. The mass ratio versus the [FORMULA] ratio. The best fit, given by Eq. 8 (solid line) is also shown. Symbols are as in Fig. 2. Relative residuals are plotted in the enclosed graph. The dotted lines enclose the region with relative errors less than 50%. The mean relative dispersion is 16% above the period gap and 26% for SU UMa stars, excluding the post-period minimum candidates EG Cnc and WZ Sge which deviate from the general tendency. The mean R value of WZ Sge has been considered.

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Online publication: July 26, 1999