Mass Determinations of Short Period CV DonorsAuthors: Christopher D.J. Savoury*, S.P Littlefair*, V.S. Dhillion*, T.R. Marsh#, B.T. Gänsicke#,

*The University of Sheffield, Sheffield, #The University of Warwick, Coventry

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 Mּס, close to the hydrogen burning limit. For C1300 we find a donor mass of 0.137 ± 0.002 Mּס, which is significantly lower than expected for its orbital period, suggesting that C1300 may possess an evolved donor star.

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.

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.

ObservationsBoth 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.

Future Work

Preliminary Analysis

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.

Figure 3 – Light curve for CTCV J1300-3052

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.

C2354 94.392350 ± 0.000010 mins

C1300 128.074573 ± 0.000003 mins

Table 1 – Orbital Periods

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.

Figure 2 – Light curve for CTCV J2354-4700

CTCV J2354-4700 CTCV J1300-3052

White Dwarf Mass (Mּס) 0.87 ± 0.02 0.648 ± 0.008

White Dwarf Radius (Rּס) 0.0096 ± 0.0003 0.0123 ± 0.0001

Donor Mass (Mּס) 0.090 ± 0.003 0.137 ± 0.002

Donor Radius (Rּס) 0.141 ± 0.001 0.198 ± 0.001

White Dwarf Temp (K) 11100 ± 600 12000 ± 1000

Discussion

References

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.

Table 2 – System parameters for CTCV 2354 and CTCV 1300

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.

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.

1) Littlefair et al, 2008, MNRAS, 388, 1582.

2) Chabrier, G., Gallardo, J., Baraffe, I., 2007, A&A, 472, 17.

3) e.g. Willems et al, 2005, ApJ, 635, 1263.

4) Bailey, 1979, MNRAS, 187, 645.

5) e.g. Littlefair et al, 2007, MNRAS, 381, 827.

6) Littlefair et al, 2006, Science, 314, 1578.