Photometric detection of non-transiting short-period low-mass companions through the beaming, ellipsoidal and reflection effects in Kepler and CoRoT light curves

Abstract

We present a simple algorithm, BEER, to search for a combination of the BEaming, Ellipsoidal and the Reflection/heating periodic modulations, induced by short‐period non‐transiting low‐mass companions. The beaming effect is due to the increase (decrease) in the brightness of any light source approaching (receding from) the observer. To first order, the beaming and the reflection/heating effects modulate the stellar brightness at the orbital period, with phases separated by a quarter of a period, whereas the ellipsoidal effect is modulated with the orbital first harmonic. The phase and harmonic differences between the three modulations allow the algorithm to search for a combination of the three effects and identify stellar candidates for low‐mass companions. The paper presents the algorithm, including an assignment of a likelihood factor to any possible detection, based on the expected ratio of the beaming and ellipsoidal effects, given an order‐of‐magnitude estimate of the three effects. As predicted by Loeb & Gaudi and by Zucker, Mazeh & Alexander, the Kepler and the CoRoT light curves are precise enough to allow detection of massive planets and brown‐dwarf/low‐mass‐stellar companions with orbital period up to 10–30 days. To demonstrate the feasibility of the algorithm, we present two examples of candidates found in the first 33 days of the Q1 Kepler light curves. Although we used a relatively short time‐span, the light curves were precise enough to enable the detection of periodic effects with amplitudes as small as one part in 104 of the stellar flux.

The Nature of V1464 Aql: A New Ellipsoidal Variable with a δ Scuti Component

“…Some of them are eclipsing binaries with a pulsating component, and some semi-regular variables with unknown short-term variations or some pulsating ellipsoidal variables (Derekas et al 2006;Nie, Zhang, & Jiang 2010;Faigler & Mazeh 2011;Faigler et al 2012). In several studies, V1464 Aql was classified as a spectroscopic binary system, RR Lyr (RRc), an eclipsing binary, possibly contact (EC) or semi-detached system (ESD) (Duerbeck 1997;Pourbaix et al 2004;Pribulla & Rucinski 2006; PASA, 30, e016 (2013) doi:10.1017/pasa.2012.016 Aerts et al (2002).…”

“…However, if the most dominant one were the cos (θ ) term, we would consider the other effects such as magnetic activity occurring on the surface of cool stars. There are many systems that are similar to V1464 Aql, such as 75 Pegasi and 42 Persei (Martin, Hube, & Lyder 1990;Martin, Hube, & Brown 1991), including several others (Faigler & Mazeh 2011;Faigler et al 2012). …”

“…According to Morris (1985), Beech (1985), and Morris & Naftilan (1993), if the main variation occurs due to the ellipsoidal effect, the light curves of the ellipsoidal variables can be modelled by the Fourier analysis given by Equation (2), and one will also expect that the cos (2θ ) term must be dominant among all other terms in the results of the Fourier analysis. This is the base of the modern methods used in recent studies, such as Mazeh (2011) andFaigler et al (2012):…”

BEER analysis ofKeplerand CoRoT light curves

“…To confirm BEER detections, one needs to perform RV follow-up observations (Faigler & Mazeh 2011). The first RV confirmation of non-eclipsing beaming binaries was reported by Faigler et al (2012).…”

“…To find non-eclipsing short-period beaming binaries, Faigler & Mazeh (2011) introduced the BEER algorithm, which searches light curves for a combination of the three photometric effects caused by a short-period companion -the BEaming, Ellipsoidal, and Reflection periodic modulations. BEER approximates each of the three effects by a sine/cosine function relative to phase zero taken at the time of conjunction -when the lighter component is in front of the heavier one.…”