THREE NEW ECLIPSING WHITE-DWARF–M-DWARF BINARIES DISCOVERED IN A SEARCH FOR TRANSITING PLANETS AROUND M-DWARFS

Reduction of the PTF/M-dwarfs data is performed in two steps: the standard PTF real-time data reduction software first calibrates the images, and then a custom pipeline performs source extraction, association, and precision photometry.

Immediately after observations, PTF data are transferred to Lawrence Berkeley National Laboratory where cross-talk corrections are applied to each chip, standard bias/overscan subtraction is performed, and a superflat based on recently acquired data is applied.

After the calibrated data are transferred to the Dunlap Institute for Astronomy and Astrophysics at University of Toronto, the PTF/M-dwarfs pipeline extracts sources from the calibrated images, produces an optimal photometric solution, associates sources in images taken at different times, and applies a range of eclipse-detection algorithms to the resulting light curves. We summarize the system here; the pipeline is described in more detail in Law et al. (2011).

Initial source extraction is performed on individual CCD chip images by SExtractor (Bertin & Arnouts 1996) using radius-optimized aperture photometry with a locally optimized background. The extracted sources are filtered to remove those close to bad pixels, diffraction spikes from bright stars, and those that may be affected by nearby sources. Heliocentric Julian dates (HJD) are used for time measurements throughout the pipeline.

The photometric zero points for each epoch are initially estimated based on either SDSS or USNO-B1 photometry for bright stars in the field. The pipeline then optimizes the zero point of each epoch to minimize the median photometric variability of all the remaining sources. This first optimization typically improves the long-term photometric stability to below the percent level. The pipeline then filters the generated light curves, searching for epochs that produce anomalous photometry for a large fraction of the sources; those epochs are usually those affected by clouds, moonlight, or some other effect that varies across the images. Typically 0%–2% of epochs are flagged by this process and are removed from further consideration. A second iteration of variable-source removal and zero-point optimization is then performed. The final zero points are applied to each light curve, along with flags for poor conditions, nearby sources that could cause confusion, bad pixels, and other problems that could affect the photometry. Running on a 2.5 GHz quad-core desktop computer the pipeline processes a 300 epoch set of 11 chips (54 GB of image data) in less than 24 hr.

The pipeline typically achieves a photometric stability of 3–5 mmag over periods of months (Figure 2). The photometric precision is photon limited for all sources fainter than m_R ≈ 16, except in regions of crowding or nebulosity. The pipeline has been used for several PTF programs such as the open cluster rotation project (Agüeros et al. 2011).

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The pipeline produces light curves for 25,000–100,000 stars per field. The large number of light curves makes the processing time involved in searching for eclipses an important consideration. An initial cut is made on the basis of the estimated spectral type of the source, based on photometry from the USNO-B1, Two Micron All Sky Survey (2MASS), and (where available) SDSS data (Monet et al. 2003; Skrutskie et al. 2006; York et al. 2000). The photometric data are fit to updated versions of the spectral energy distributions (SEDs) given in Kraus & Hillenbrand (2007), yielding an accuracy of approximately 1 subclass. Sources with late-K, M, or L estimated spectral types are passed to our eclipse-search algorithms.

2.2.1. High-variability Source Searches

2.2.2. A Parallel Eclipse Search Using Graphics Processing Units

After the systems were detected in PTF data as planet candidates we followed the standard PTF/M-dwarfs follow-up strategy: high-cadence multi-color photometry with the Palomar 60 inch, BOS, and FTN, along with RV observations with the HIRES spectrograph on Keck I. The multi-color photometry (Section 3.1.1) rapidly revealed that these objects had a strongly varying eclipse depth with color (Figures 5 and 6), suggesting we were seeing eclipses between two self-luminous objects with different temperatures. Low-resolution spectra (Section 3.1.4) were sufficient to immediately confirm a white-dwarf component in one system (PTFEB11.441), but required detailed modeling to recover the white-dwarf components in the other two systems (Section 4.1). RV observations were scheduled to allow determinations of the white-dwarf mass.

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3.1.1. High-cadence, Multi-color Photometry with BOS

3.1.2. Faulkes-North Photometry

3.1.3. Dunlap Institute Arctic Telescope Photometry

3.1.4. Low-resolution Spectra

3.1.5. Keck/HIRES Radial-velocity Observations

3.1.6. Robo-AO Laser Guide Star Adaptive Optics Observations

Robo-AO is a visible and near-infrared laser guide star adaptive optics system specifically engineered for 1–3 m class telescopes (Baranec et al. 2011). The Robo-AO system comprises an ultraviolet Rayleigh laser guide star, an integrated adaptive optics and science camera system, and a robotic control system. The system currently incorporates both an electron-multiplying CCD and an InGaAs infrared array camera for imaging.

Robo-AO obtained images of PTFEB11.441 and PTFEB28.235 during a commissioning run at the Palomar 60 inch telescope on the night of 2011 November 18 UT. Robo-AO was operated without tip-tilt correction, instead relying on post-facto shift-and-add processing of the individual frames. We used a long-pass filter with a 600 nm cut-on to obtain increased signal compared to a bandpass filter, along with relatively long 1 s exposure times to compensate for the faintness of the targets (m_R > 16.8). We used the Lucky Imaging plus adaptive optics pipeline described by Law et al. (2009b) to perform the image alignment, along with frame selection at the 10% level to boost the imaging resolution. After processing, images with approximately 02 FWHM point-spread functions were obtained on these targets during ∼1'' seeing conditions. These observations were limited by residual tip-tilt errors during the 1 s exposures; similar bright targets observed the same night with 33 ms exposures had a diffraction-limited angular resolution of ≈0.13 arcsec FWHM (Figure 7).

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The Robo-AO imaging reveals a bright companion to PTFEB11.441, located at 0.43 ± 0.06 arcsec and at a position angle of 211° ± 3° east of north.

Multi-color through-eclipse photometry of the three detected systems showed that the eclipse depths were much larger in blue bands than in red bands. The sharp ingress and egress of the eclipses suggest a small body, while the flat-bottomed shape argues against that body occulting the M-dwarf, as limb darkening would then be apparent. RV observations showed a very large amplitude of more than 100 km s⁻¹. These observations suggest the presence of a small, hot, massive object undergoing total eclipses in these systems. The white-dwarf/M-dwarf binary scenario is consistent with all these observations.

The properties of the systems are summarized in Table 3. We detail each system below.

3.2.1. PTFEB11.441

3.2.2. PTFEB28.235

3.2.3. PTFEB28.852

We model the low-resolution spectra of our targets as a combination of a M-dwarf and a white-dwarf spectrum. Template M-dwarf spectra are taken from the HILIB stellar flux library (Pickles 1998) and have steps of a single spectral subclass. The white-dwarf models¹⁶ were kindly provided by Detlev Koester and are on a grid with 250 K steps between 6000 K and 10,000 K (and larger steps up to 20,000 K), and 0.25 dex steps between log g = 6.0 and log g = 9.5, where the units of g are cm s⁻².

We simultaneously fit the white-dwarf and M-dwarf spectra using a downhill simplex algorithm and a bootstrap (e.g., Press et al. 1992) method to find the uncertainties in the fit. Figure 8 shows the fitted models and each component of the binaries with the model for the other component subtracted. In each case subtraction of the template M-dwarf spectrum revealed a (noisy) DA white-dwarf spectrum with clear Balmer lines.

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PTFEB11.441 is well fit by a simple combined white-dwarf and M-dwarf spectrum, suggesting that the third component in the system is also an M-dwarf, and that the two M-dwarfs have similar spectral types. In the following sections, we use the measured spectral type for the M-dwarfs in PTFEB11.441, assuming that it is the spectral type of the M-dwarf closest to the white dwarf.

The M-dwarf spectral types measured from the two-component fit to the system spectra closely agree with those estimated from infrared photometry of the systems (Table 3). This suggests that reddening is not a significant problem for the M-dwarf spectral types and thus for the mass and radius estimates as well.

However, we note that reddening will affect the estimated white-dwarf temperature more severely as its flux is mostly in the blue end of the spectrum. The estimated galactic extinction along the line of sight to PTFEB11.441 is E(B − V) = 0.02 (Schlegel et al. 1998) and will be lower for the target itself which is located at a distance of ≈400 pc. The other two targets are located in regions of higher line-of-sight extinction, at E(B − V) = 1.5 and 1.1 mag for PTFEB28.235 and PTFEB28.852, respectively. The actual extinction for the two targets is, however, likely to be much lower as they are located at distances of only ≈200 pc. This is supported by several different arguments: the very good match of the M-dwarf model spectrum to the observed spectrum; the match between the infrared-color-estimated spectral types and the spectrally measured spectral types; and the GALEX detections of both objects, which require a small NUV and FUV extinction.

We fit the M-dwarf masses, radii, and distances in the following manner. We first fit survey photometry of the system with the stellar SEDs listed in Kraus & Hillenbrand (2007), yielding a photometric spectral type and distance. Despite the availability of other photometric data such as USNO-B1, we restrict our fits to 2MASS J, H, and K colors that are unlikely to be affected by the light from the white dwarf. We assume a 25% distance uncertainty (Kraus & Hillenbrand 2007; Law et al. 2010a), and ±1–2 spectral subclass uncertainty (Kraus & Hillenbrand 2007); the SED estimates for the spectral types are consistent with those derived from the two-component fits to our low-resolution spectroscopy. We also attempted to determine the M-dwarf spectral type from the TiO5 narrowband spectroscopic index (Gizis 1997), but found implausibly high values of the index, suggesting possible contamination by white-dwarf emission. In the following sections, we adopt the spectral types estimated from the two-component fits to the low-resolution spectra, as that method yields the uncertainty in the spectral type.

We estimate the M-dwarf masses from the spectral type vs. mass calibrations detailed by Delfosse et al. (2000), assuming they are on the main sequence and have solar metallicity and age. All three of our targets have a measured spectral type of M3, giving an estimated mass of 0.35 ± 0.05 M_☉. We note that a small fraction of the systems measured by Delfosse et al. (2000) have much lower masses at the M3 spectral type, for reasons that are still unclear. To derive the masses in an alternative manner, we estimated the M-dwarf effective temperatures by the relation described in Luhman (1999). We then combined those estimates with the 5 Gyr isochrones of solar-metallicity stars in Baraffe et al. (1998) to estimate the stellar masses. These relations also predict a much lower mass for our M-dwarf targets, of 0.23^+0.06_0.04 M_☉. In the following sections, we adopt the higher masses measured by Delfosse et al. (2000). We, however, note that two-component RV measurements for our systems giving masses for each component would help understand the mass vs. spectral type relation in this mass range.

We estimate the M-dwarfs' radii from a fit to the eclipsing-binary-derived mass/radius relation. We note that M-dwarfs in close binaries appear to be biased toward larger radii compared to systems with wider orbital radii (Kraus et al. 2011). We adopt a mass/radius relation for close (<1 day period) binaries based on the measurements summarized by Kraus et al. (2011):

$$\begin{equation} R = 1.096 M - 0.052 \quad {\rm for}\quad 0.1\, M_{\odot } < M < 0.7\, M_{\odot }, \end{equation} \tag{ 1 }$$

where M is the mass in solar masses and R is the radius in solar radii. The radii in this relation are approximately 5%–10% larger than both those measured for larger orbital radius systems and theoretical expectations (e.g., Baraffe et al. 1998; Kraus et al. 2011). The results are summarized in Table 3.

We determine the white-dwarf masses from the measured RV curves, assuming the M-dwarf masses derived above. We fit a simple model to the velocity curves (Figure 9 and Table 4), assuming zero eccentricity because of the short circularization timescales for these compact systems (for example, see Devor et al. 2008). PTFEB28.235 and PTFEB28.852 have sufficient numbers of RV points to allow an eccentric orbit fit, but the fitted eccentricities are consistent with being zero. The white-dwarf masses (M_WD) are related to the fit mass function (F), the M-dwarf masses (M_MD), and the inclination (i) by

$$\begin{equation} {F} = \frac{M_{\rm WD}^3 \sin ^3{i}}{(M_{\rm MD} + M_{\rm WD})^2} \end{equation} \tag{ 2 }$$

which can be solved as a cubic equation. The results are summarized in Table 5. The inclination has only a weak effect on the derived white-dwarf masses; we marginalize it across all ranges allowed by the eclipse geometry.

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We estimate the white-dwarf radii in two ways: first, models of the white-dwarf effective temperature, mass, and surface gravity cooling curves, and second a direct fit to the white dwarf's eclipse light curve.

Our model radius estimates are based on the Bergeron cooling curves for DA white dwarfs (Holberg & Bergeron 2006; Kowalski & Saumon 2006; Tremblay et al. 2011; Bergeron et al. 2011), for which we derive the allowed surface gravity range from the white-dwarf mass range measured above. The effective temperature has only a small effect on the surface gravity estimates and so we fix it at the best-fit value from the low-resolution spectra.

We obtain a direct upper limit for the white-dwarf radius in the PTFEB11.441 system from high-cadence eclipse data acquired with the BOS telescope (Figure 10). Using a clear filter to boost the signal levels, we were able to obtain 10 s cadence data with ≈5% photometric stability, sufficient time resolution to give stringent constraints on the ingress and egress timing of the system.

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We fit the light curves with a simple two-spherical-body model. The flat-bottomed light curves show that the white dwarf is completely eclipsed, allowing a simple model based on the Mandel & Agol (2002) transiting-planet model to be used. We modified the model to allow both stars to be moving relative to a common center of mass, to allow both bodies to be self-luminous, and to include a linear limb-darkening term for the white dwarf.

Inspection of the light curves shows that the white-dwarf ingress and egress is at best marginally resolved, and so we only attempt to estimate an upper limit for the white-dwarf radius. We obtain a maximal estimate of the white-dwarf radius when the inclination is assumed to be 90°, and so we fix the inclination to that value in our modeling. For the white dwarf, we conservatively use a linear limb-darkening coefficient of 0.5; we tested a range of coefficients and found that the limb darkening has no significant effect on the radius estimates, because the eclipse ingress and egress are barely resolved. We fix the M-dwarf radius and the stellar mass ratio q during the fits, although we marginalize over the estimated 1σ ranges of both parameters.

We vary the semimajor axis of the system, the white-dwarf radius, and the flux from both components (and hence the contribution from the system's unresolved wide companion). When the inclination is fixed at 90°, the best-fit semimajor axis value is within the error bars of our measurements based on the eclipse timing and the estimated M-dwarf radius, although those estimates suggest that a somewhat lower inclination may be preferable (which would lead to a smaller white-dwarf radius). We estimate the range of fitted parameters and a 95% upper limit on the white-dwarf radius using the Bootstrap algorithm.

This procedure puts the upper-limit white-dwarf radius in the PTFEB11.441 system as <0.025 R_☉ at 95% confidence, a value consistent with the radii estimated from cooling models and log g fits to the white-dwarf's Balmer lines. The fitted semimajor axes are around 10% larger than those expected from the period of the system and the estimated masses of the components, suggesting we have slightly overestimated the mass of at least one component, most likely the M-dwarf in the system.

All three systems show evidence of active M-dwarfs, including strong Hα emission and variability on a variety of timescales. None are detected in the ROSAT All-Sky Faint Source Catalog (Voges et al. 2000), although the M-dwarfs would have to be exceptionally active to be detected at these distances (e.g., Law et al. 2008).

The positioning of PTFEB11.441 near M31 allows more archival data to be found. The system is co-incident with the Chandra X-ray source¹⁷ CXO J004545.8+415029 (2.8 × 10⁻¹³ erg s⁻¹ cm⁻²) located within 1σ of the PTF position for the system. Using the 2MASS K-band photometry of the system (which is dominated by the M-dwarf luminosity) and the empirical relations in Leggett (1992) and Tinney et al. (1993) to estimate the bolometric luminosity of the system, we calculate log (L_x/L_bol) = −1.5. Although the flare event described below suggests that the M-dwarf in the system is indeed active, this is an extremely high activity compared to typical field M-dwarfs (e.g., Delfosse et al. 1998; Law et al. 2008). This suggests that the X-ray detection is a spurious association with the system, the X-ray observation was taken in a time of extreme activity, or that the bulk of the X-ray emission does not originate in the M-dwarf chromosphere.

We also identified a flare event during one high-cadence observation of PTFEB11.441 (Figure 11). The observation was taken without a filter to boost our S/N, limiting the detailed interpretation of the event. The shape of the event is as expected for an M-dwarf flare, with a rapid rise followed by an approximately exponential decay.

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The light curves show out-of-eclipse sinusoidal variability correlated with the orbit. The overall shape is consistent with irradiation of the side of the M-dwarf facing the white dwarf, where the flux maximum is expected half an orbital phase from the occultation. Other mechanisms that may affect the out-of-eclipse light curves of such compact systems are tidal ellipsoidal distortion and the beaming effect (e.g., Zucker et al. 2007; Shporer et al. 2010a), but simple estimates show that both effects are expected to be at the 1% level or below for the binaries presented here and so cannot be identified in the available data.

PTFEB11.441 shows much lower levels of out-of-eclipse variations than the other two systems. This is most likely due to light from its possible companion diluting the variations (and eclipse depths) in unresolved photometry of the system.