Mass Determinations of Short Period CV Donors

1
Mass Determinations of Short Period CV Donors

• Authors Christopher D.J. Savoury, S.P
  Littlefair, V.S. Dhillion, T.R. Marsh, B.T.
  Gänsicke,

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 M?, close to
the hydrogen burning limit. For C1300 we find a
donor mass of 0.137 0.002 M?, which is
significantly lower than expected for its orbital
period, suggesting that C1300 may possess an
evolved donor star.
Abstract
Preliminary Analysis
Discussion
Introduction
Recent observations of low mass donors in CVs
suggest that they are up to 20 larger than
expected1. One theory is that this is due to
magnetic activity coupled with the effects of
rapid rotation2. Alternatively it could be
caused by enhanced angular momentum loss3.
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. 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.

Table 1 Orbital Periods
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.
Our first task was to determine the orbital
ephemeris for each system, which was achieved by
least-squares fitting to the mid-eclipse 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.
Figure 2 Light curve for CTCV J2354-4700
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.
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 Levenberg-Marquardt method for
C1300. The system parameters found for both
systems are shown in table 2.
Future Work
Figure 1 Gas stream trajectories
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 donors 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.
It can be shown that the width of the white dwarf
eclipse, ??, depends only upon the inclination i
and the mass ratio q4, 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 before15 and resulted in the
first secure identification of a brown dwarf
donor in an accreting binary6. 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.
Figure 3 Light curve for CTCV J1300-3052
References
Observations

• Littlefair et al, 2008, MNRAS, 388, 1582.
• Chabrier, G., Gallardo, J., Baraffe, I., 2007,
  AA, 472, 17.
• e.g. Willems et al, 2005, ApJ, 635, 1263.
• Bailey, 1979, MNRAS, 187, 645.
• e.g. Littlefair et al, 2007, MNRAS, 381, 827.
• Littlefair et al, 2006, Science, 314, 1578.

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.
Table 2 System parameters for CTCV 2354 and
CTCV 1300
The University of Sheffield, Sheffield, The
University of Warwick, Coventry