DQ Herculis in Profile: Whole Earth Telescope Observations and Smoothed Particle Hydrodynamics Simulations of an Edge‐on Cataclysmic Variable System

Abstract

The old nova DQ Herculis was the Whole Earth Telescope Northern Hemisphere target for the 1997 July campaign and was observed on four nights with the SARA 0.9 m telescope during 2003 June. We present updated ephemerides for the eclipse and 71 s timings. The Fourier transform displays power at the presumed white dwarf spin period of 71.0655 s, but no significant power at either 142 or 35.5 s. The mean pulsed light curve is obtained by folding on the orbital period modulus the mean ephemeris of the 71 s period, and from this we calculate an O À C phase diagram and amplitude versus orbital phase diagrams. In addition to the phase variations during eclipse ingress and egress, the WET data reveal significant phase variations outside of eclipse. These must result from the self-eclipse of a nonaxisymmetric disk. We simulated the disk in DQ Her using smoothed particle hydrodynamics. We improve our effective spatial signal-to-noise ratio by combining 250 snapshots of the N ¼ 20;000 phase space solution over time to obtain a 5 million particle ensemble disk. From the surface shape of the ensemble disk, the radius and vertical height above the midplane of the rim of the reprocessing region can be derived as a function of azimuthal angle. From this profile we can calculate the O À C phase and amplitude diagrams as a function of inclination angle. The calculated O À C diagrams are a remarkably good match to the observed phase and amplitude variations of the 71 s signal. The best match is for inclination angle 89N7.

Plausible explanations for the variations of orbital period in the old nova DQ Herculis

“…3 which suggests a trend of cyclic variation. Although Wood et al (2005) pointed out that a sinusoidal fit is formally significant but not compelling, the two new eclipsing times we obtained could alter this conclusion because the O-C values since 1985 cannot be fitted by a straight line. Moreover, we suggested that the most important cause of the non-compelling sine fit is the neglect of a quadric term in the O-C analysis.…”

“…4. Although Pringle (1975), and Wood et al (2005) suggested that the orbital period of DQ Herculis is constant, the residuals of this quadratic-plussinusoidal fit shown in the bottom panel of Fig. 5 never show a detectable variation, which implies the existence of quadratic variation in O-C diagram.…”

“…Thus, a calculation gives F(4, 220) = 26.0, which indicates that it is significant well above the 99.99% level. Therefore, both separate and simultaneous fits suggest that the best-fit of the O-C diagram for DQ Herculis should be the ∼17.7(±0.3) yr quasi-periodic modulation shown in the top and middle panels of Wood et al (2005). Although this poor fit is caused mainly by the visual data, two photoelectric observations at cycles 60 281 and 60 286, also present a large departure from the fit, as the visual data do.…”

“…In this case, the average value should be reliable and may be applied. In addition, Zhang et al (1995) and Wood et al (2005) reported their 44 eclipse times in Heliocentric Julian Ephemeris Dates (HJED), which correspond to ephemeris time (ET). Thus, we converted them to Heliocentric Julian Dates (HJD), which correspond to coordinated Universal time (UTC).…”

“…Mumford (1969) and Nather & Warner (1969) suggested that the orbital period is increasing, and later works (Patterson et al 1978;Zhang et al 1995;Wood et al 2005) indicated that a sinusoidal modulation with a period of ∼14 yr is likely. However, an updated O-C analysis concluded that there is not strong evidence for a secular orbital period increase.…”