The Masses and Evolutionary State of the Stars in the Dwarf Nova SS Cygni Edward L. Robinson

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The Masses and Evolutionary State of the Stars
in the Dwarf Nova SS CygniEdward L. Robinson
Martin A. Bitner Department of Astronomy,
University of Texas at Austin, Austin, TX 78712,
USA(appeared 2007, ApJ, 662, 564)
1. INTRODUCTION As the brightest dwarf nova and
one of the brightest cataclysmic variables of any
kind, SS Cygni has been extensively observed.
Its outbursts, for example, have been
continuously monitored since 1896 and their
properties are the gold standard against which
accretion disk instability models for dwarf nova
outbursts must be compared (Cannizzo Mattei
1992 Lasota 2001). The basic properties of SS
Cyg are thought to be well established. The
primary star is a white dwarf, the secondary is a
K4-5 V star, and the orbital period is P
0.27624 d. According to the Ritter and Kolb
(1998) catalog, the masses of its two component
stars MK 0.704 M? and MWD 1.19 M?. However,
standard techniques for measuring the masses of
binary stars do not work for SS Cyg because the
radial velocity curve of the white dwarf is not
measured and the orbital light curve does not
show eclipses. Previous measurements of the
masses of its stars have, therefore, been forced
to rely on dubious assumptions about the
properties of the accretion disk or about the
interior structure of the K star. We report here
a measurement of the masses using a method that
was first developed for black hole X-ray binaries
and does not require these assumptions. The
technique has three steps (see, eg, Casares 2005)
1) The amplitude of the secondary's radial
velocity curve, KK, and the orbital period give
the mass function 2) The rotational period of
the secondary star is tidally locked to the
orbital period. Since the secondary fills its
Roche lobe (demonstrated by the mass transfer),
the ratio of its rotational velocity, Vrot sin i,
to KK yields the mass ratio (Figure 1 shows how
this works) 3)
The distorted secondary star shows ellipsoidal
variations. In principle the ellipsoidal
variations give a relation between the mass ratio
and the orbital inclination, although in practice
systematic errors must be carefully considered
because of contamination by light from the
accretion disk. 2. OBSERVATIONS We obtained
23 spectrograms of SS Cyg with the High
Resolution Spectrograph (HRS) on the Hobby-Eberly
Telescope between JD 2452084 and JD 2452114 (June
and July 2001). SS Cyg was in quiescence at the
time (see Figure 2). The spectrograms covered
5300 Å to 7000 Å at a resolution R 30,000. The
exposure times were all 600 seconds, long enough
to achieve the necessary signal-to-noise ratio
without excessive spectral smearing from the
changing radial velocity of the secondary star as
it progressed around its orbit. A portion of the
mean spectrum is shown in Figure 3.
ABSTRACT We have obtained new spectroscopic
observations of SS Cyg. Fits of synthetic
spectra for Roche-lobe-filling stars to the
absorption-line spectrum of the K star yield the
amplitude of the K star's radial velocity curve
and the mass ratio KK 162.5
1.0 km s-1 and q MK/MWD 0.685 0.015. The
fits also show that the accretion disk and white
dwarf contribute a fraction f 0.535 0.075 of
the total flux at 5500 Å. Taking the weighted
average of our results with previously published
results obtained using similar techniques, we
find ?KK? 163.7 0.7 km s-1 and ?q? 0.683
0.012. The orbital light curve of SS Cyg shows an
ellipsoidal variation diluted by light from the
disk and white dwarf. From an analysis of the
ellipsoidal variations we limit the orbital
inclination to the range 45 lt i lt 56. The
derived masses of the K star and white dwarf are
MK 0.55 0.13 M? and MWD 0.81 0.19 M?,
where the uncertainties are dominated by
systematic errors in the orbital inclination.
The K star in SS Cyg is 10 to 50 larger than
an unevolved star with the same mass and thus
does not follow the mass-radius relation for
Zero-Age Main-Sequence stars. Its mass and
spectral type are, however, consistent with
models in which the core hydrogen has been
significantly depleted.
Figure 4 The dots are the mean V-band orbital
light curve of SS Cyg from Voloshina Khruzina
(2000). The basic double-humped variation is
produced by ellipsoidal variations of the K star.
The extra amplitude and asymmetry of the hump at
phase 0.75 is produced by a bright spot on the
outer edge of the disk. The solid line is a
synthetic light curve fitted to the data.
3. ANALYSIS OF THE
SPECTRUM We used our LinBrod program to
analyze the spectrum of SS Cyg (Bitner Robinson
2006). This program calculates the spectrum of a
star that fills its Roche lobe in a close binary
star by summing wavelength-dependent specific
intensities over the visible surface of the star.
The surface of the star is approximated by many
(10,000 50,000) flat tiles. Specific
intensities as a function of wavelength are
calculated for each tile using ATLAS9 and a
modified version of the spectrum synthesis
program MOOG 2002 (Sneden 2002). Then for each
orbital phase, LinBrod calculates the emergent
intensities, shifts the intensities to the radial
velocity of the tile, and adds Doppler-shifted
intensities for all the visible tiles together to
give the synthetic spectrum. The spectrum is
smeared to account for orbital motion and
instrumental resolution. We fit the synthetic
spectra to all the individual spectrograms of SS
Cyg simultaneously (not to the mean spectrum) by
?2 minimization. The fits yield KK, q, and the
fraction of the flux f coming from the accretion
disk and white dwarf. The results are shown in
the following table. Martinez-Pais et
al. (1994) and North et al. (2002) used
techniques similar to ours to measure KK and q,
and their results are also shown in the table.
As we see no reason to prefer one result over
another, we have calculated the weighted means of
the three measurements and recommend them as the
best estimates of these parameters for SS Cyg.
Figure 3 - Top Portion of the average spectrum
of SS Cyg in the rest frame of the K star.
Bottom Synthetic spectrum for a single,
non-rotating star with the same spectral type.
The width of the absorption lines in the spectrum
of SS Cyg is caused by a combination of rotation,
orbital motion, and instrumental resolution.
Figure 5 The orbital inclination as a function
of V-band flux contributed by the disk. The
solid line from lower left to upper right is
measured from the amplitude of the ellipsoidal
variations the parallel dashed lines are the 1-s
confidence limits. The vertical lines are
measured from the dilution of the absorption
lines in the spectrum. The region enclosed by
the dashed lines gives the allowed range of
inclinations.
K (km/s) q f _at_ wavelength
Our Results 162.5 1.0 0.685 0.015 0.54 0.08 _at_ 5500 Å
Martinez-Pais et al. (1994) 162.5 3 0.45 _at_ 6550 Å
North et al. (2002) 165 1 0.68 0.02 0.315 0.004 _at_ 6400 Å
Weighted Mean 163.7 0.7 0.683 0.012
Figure 2 - The eruption light curve of SS Cyg in
1981 and 2001. The horizontal bars mark the
dates when Hessman et al. (1984) measured the
radial velocity curve of SS Cyg in 1981 and when
we obtained our data in 2001. Both sets of data
were obtained during quiescence but SS Cyg was
0.6 magnitudes fainter when we obtained our data.
REFERENCES
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