Mass Determinations of Short Period CV Donors
Authors: Christopher D.J. Savoury*, S.P Littlefair*, V.S. Dhillion*, T.R. Marsh#, B.T. Gänsicke#,
Abstract:
We present high-speed, three colour photometry of two short period cataclysmic variables: CTCV J2354-4700 and CTCV J1300-3052. By fitting a physical model of the
binary, we are able to determine component masses with few assumptions. In the case of C2354, we find the mass of the secondary star M2 = 0.090 ± 0.003 M‫סּ‬, close to
the hydrogen burning limit. For C1300 we find a donor mass of 0.137 ± 0.002 M‫סּ‬, which is significantly lower than expected for its orbital period, suggesting that C1300
may possess an evolved donor star.
Preliminary Analysis
Introduction
Recent observations of low mass donors in CVs suggest that they are up to 20%
larger than expected[1]. One theory is that this is due to magnetic activity coupled
with the effects of rapid rotation[2]. Alternatively it could be caused by enhanced
angular momentum loss[3]. There is currently insufficient observational evidence
to choose between these alternatives. Binary population models suggest that as
much as 70% of the current CV population should possess a brown dwarf donor,
of which statistically a large proportion should be eclipsing. Such low mass
donors are ideal for investigating the discrepancies between observed radii and
theoretical predictions.
C2354
C1300
Discussion
94.392350 ± 0.000010 mins
128.074573 ± 0.000003 mins
Table 1 – Orbital Periods
Our first task was to determine the orbital
ephemeris for each system, which was
achieved by least-squares fitting to the mideclipse times. We found the mid-eclipse times
by averaging the times of white dwarf ingress
and egress, which are determined by the
minimum and maximum of the light curve
derivative respectively. The orbital periods
found can be seen in table 1.
The light curve of an eclipsing system can be used to determine the masses and
radii of each component by making three assumptions: 1) the bright spot lies on a
ballistic trajectory from the donor (see fig 1) 2) the donor fills its Roche lobe 3) the
white dwarf follows a theoretical mass-radius relationship.
Figure 2 – Light curve for CTCV J2354-4700
Figure 2 shows 7 eclipses for C2354 phase
folded in the g’ band. The white dwarf eclipse is
clearly visible, but the bright spot egress is not
clear, and affected by flickering. The mass ratio
for C2354 must thus be treated with caution.
C1300 shows clear white dwarf and bright spot
eclipses (figure 3). To determine the system
parameters we used a physical model of the
binary system to calculate eclipse light curves
for each component (shown in figure 2 - green
= disc, dark blue = wd, light blue = bright spot,
purple = donor). The best fit (shown in red),
and errors were found using an MCMC
analysis for C2354 and the LevenbergMarquardt method for C1300. The system
parameters found for both systems are shown
in table 2.
Figure 1 – Gas stream trajectories
It can be shown that the width of the white dwarf eclipse, ΔФ, depends only upon
the inclination i and the mass ratio q[4], and the path of the gas stream depends
solely on q (see fig 1). Thus the contact phases of the bright spot eclipse depend
upon q and i. If we can determine the duration of the white dwarf ingress and
egress, the width of the white dwarf eclipse, and the contact phases of the bright
spot, we can infer the radius of the white dwarf and mass ratio q. Assuming the
white dwarf follows a theoretical mass-radius relationship, we can thus deduce
the properties of each component to a reasonably high degree of precision.
This technique has been applied several times before[1][5] and resulted in the
first secure identification of a brown dwarf donor in an accreting binary[6]. Here,
we apply the same technique to CTCV J2354-4700 and CTCV J1300-3052
(C2354 and C1300 thereafter) in an effort to determine why donor stars in CVs
are larger than expected.
Observations
Both systems were observed between 08/06/07 and 21/06/07 using ULTRACAM
on the 8.2-m Very Large Telescope in Chile. Typical seeing was 1 arcsec. We
used a nearby comparison star to correct for transparency variations and a
standard star to correct the magnitudes to the SDSS system. We observed 9
eclipses for C2354 and 3 eclipses for C1300 in the u’ g’ and r’ bands, of which 7
and 2 respectively were of high enough quality for fitting.
Figure 4 – Evolutionary
models of Baraffe & Kolb
(1999) calculated with
different
mass-transfer
rates and evolutionary
states for the donor. Mass
determinations for donors
using ULTRACAM data
are also shown.
Figure 3 – Light curve for CTCV J1300-3052
For C2354, figure 4 shows that the donor mass is similar to systems with comparable
periods. This supports the picture of oversized donors in CVs. For its orbital period the
donor mass of C1300 is significantly lower than expected. Figure 4 shows that whilst
changing the angular momentum loss rate has little effect at these periods, tracks with an
evolved donor can potentially explain the mass of C1300. Clearly the question of whether
C1300 contains an evolved donor needs to be settled before it is used to constrain CV
models. With so few mass determinations at periods around 130 minutes it is not clear
whether C1300 is an exception or represents a typical CV at this period.
Future Work
Over the coming months we aim to determine the masses for several more short period
systems which we hope will enable us to further constrain the donor’s mass-radius
relationship. These systems include SDSS J1555-0010, for which we have obtained and
reduced data and determined the orbital period to be 113.5 minutes, placing it below the
period gap. The period of J1555 is ideal as there are few mass determinations of CV donors
between 100 and 130 minutes. We have also applied for time to make spectroscopic
observations of C1300. These observations should allow us to determine the spectral type
and temperature of the star which in turn will allow us to establish the nuclear evolutionary
state of the donor. In addition, the spectroscopic observations will also enable us to find the
radial velocity of the donor, and thus provide an independent test of our mass determination.
CTCV J2354-4700
CTCV J1300-3052
White Dwarf Mass (M‫)סּ‬
0.87 ± 0.02
0.648 ± 0.008
White Dwarf Radius (R‫)סּ‬
0.0096 ± 0.0003
0.0123 ± 0.0001
Donor Mass (M‫)סּ‬
0.090 ± 0.003
0.137 ± 0.002
1) Littlefair et al, 2008, MNRAS, 388, 1582.
0.198 ± 0.001
2) Chabrier, G., Gallardo, J., Baraffe, I., 2007, A&A, 472, 17.
0.141 ± 0.001
Donor Radius (R‫)סּ‬
References
3) e.g. Willems et al, 2005, ApJ, 635, 1263.
White Dwarf Temp (K)
11100 ± 600
Table 2 – System parameters for CTCV 2354 and CTCV 1300
12000 ± 1000
4) Bailey, 1979, MNRAS, 187, 645.
5) e.g. Littlefair et al, 2007, MNRAS, 381, 827.
6) Littlefair et al, 2006, Science, 314, 1578.
*The University of Sheffield, Sheffield, #The University of Warwick, Coventry