A NEW MERGING DOUBLE DEGENERATE BINARY IN THE SOLAR NEIGHBORHOOD^*

We observed WD 1242–105 with the blue and red chips of the MIKE spectrograph (Bernstein et al. 2003) installed at the 6.5 m Magellan Clay Telescope at Las Campanas Observatory (LCO; Chile) as part of a survey of nearby WDs for the presence of photospheric metal lines. All runs used a 07 × 50 slit, yielding an average spectral resolution of R ∼ 35,000 at 3933 Å. The spectra cover wavelengths between 3335 and 9500 Å. Each exposure was taken with a 600 s integration time to ensure sufficient signal-to-noise ratio. Table 1 lists the 27 observations of the WD, which were taken over multiple epochs starting in 2008 March with the first discovery spectra, and intensive follow-up in 2009 April and May. A nearly full period of the orbit was obtained in 2009 May, allowing us to place precise constraints on the orbital period.

The data were extracted and flatfielded using the MIKE reduction pipeline written by D. Kelson, with methodology described in Kelson et al. (2000) and Kelson (2003). Each spectrum was corrected for heliocentric motion and each epoch was converted to heliocentric Julian date. The continuum around the Hα line was fit with a polynomial and the narrow Hα core was used to measure radial velocities for both components of the binary system via the simultaneous fitting of two Gaussian curves. In general, this was sufficient to determine the radial velocity of the two components at a precision of ∼3–5 km s⁻¹. When the two components of the binary were close to conjunction, the corresponding uncertainty in the line centers increased. In those cases uncertainties in fitting each velocity were closer to ∼20 km s⁻¹.

The spectrum was also inspected for any evidence of Ca or Mg absorption, indicative of accretion due to dust or some external source of metal-rich material. We saw no evidence of this in the raw epoch-to-epoch spectra, but a more detailed analysis is beyond the scope of this paper. More stringent upper limits for each component of the binary will be presented in a future paper (Z. R. Todd et al. 2015, in preparation).

When the first spectra of WD 1242–105 showed evidence for the presence of a companion with a very small orbital separation, we conducted a search for eclipses or any sign of photometric variability. This included observations taken on 2009 May 4 using the MagIC-E2V instrument on the Baade Telescope (Osip et al. 2004), a fast readout instrument designed for high cadence photometry. In total we took roughly five hours of data, covering nearly 1.75 orbital periods and using the V filter with exposure times of 60 s. The MagIC instrument had a field of view of 40'' × 40'' which was large enough to fit both the target and a fainter comparison star. A photometric aperture of 25 pixels was used for both WD 1242–105 and the comparison.

We measured the trigonometric parallax using CAPScam (Boss et al. 2009) with the DuPont 2.5 m telescope, also at LCO. With a field of view of 66, the star and a sufficient number of references were observed simultaneously in the standard imaging mode (2048 × 2048 pixels, with a pixel scale of 0194). Each observing run consisted of taking 15–20 exposures of 30–45 s depending on the seeing. Five epochs were obtained between 2009 June and 2010 July (June 8th, January 27th, April 10th, June 22nd, and July 31st). The source extraction, source cross matching, geometric calibration, and astrometric solution have been obtained using the ATPa software (Boss et al. 2009; Anglada-Escudé et al. 2012). The overall precision for the target star and the reference frame stars is 1 mas/epoch. The reference stars are selected by the software iteratively based on their epoch to epoch rms. A robust reference frame of 33 stars is used. Parallax and proper motion of the reference stars are also obtained as a by-product. Several reference stars have unambiguous USNO B1 and 2MASS counterparts and the B-K color with the 2MASS magnitudes are used to estimate the photometric distance to them. Reference stars with parallaxes $\lt 5$ mas were used, taken either from direct measurements or from photometric estimates. At the end the correction from relative to absolute parallax/proper motion is obtained based on 13 reference stars. The final parallax and corresponding distance estimation are 25.5 ± 0.9 mas and $39.2_{1.3}^{+1.4}$ pc. The statistical uncertainty in the parallax is obtained from a Monte Carlo resampling of the astrometry at the same observation dates which properly takes into account all significant parameter correlations. The original estimated spectroscopic distance to WD 1242–105 was 25 pc when it was believed to be a single WD—extrapolating the spectroscopic distance for two WDs results in a distance of 35 pc, consistent with our parallax measurement.

Table 1 lists the measured velocities for all epochs of the WD 1242–105 system. The velocities were fit with the nonlinear least squares fitting routine curvefit.pro in the Interactive Data Language, using sinusoidal curves of the form $K{\rm cos} (p{\rm HJD}-{\rm HJ}{{{\rm D}}_{{\rm o}}})+\gamma$, with p equal to the period, γ equal to the velocity offset of each component, ${\rm HJ}{{{\rm D}}_{{\rm o}}}$ equal to the reference epoch, and K equal to the velocity semi-amplitude. The long baseline of observations as well as the dense sampling of the orbit in 2009 May allowed the fitting routines to converge on a precise period for the components. These fits give the final ephemeris of the system:

$$\begin{eqnarray}&&\phi =({\rm HJD}-{\rm HJ}{{{\rm D}}_{{\rm o}}})p\end{eqnarray} \tag{ 1 }$$

where ${\rm HJ}{{{\rm D}}_{{\rm o}}}$ = 2454970.5901 ± 0.0001, and p = 0.118765 ± 0.000002.

Figure 1 shows the final phased radial velocities for both components, while Table 2 details the velocity semi-amplitudes and γ for each component of the system as well as the inferred mass functions for each component. Because of the two components' differing masses, their velocity offsets represent a combination of the binary's systemic velocity and the gravitational redshift of each component. This can be used in combination with the traditional mass–radius relations to solve uniquely for the masses of the two systems, which we investigate in Section 4.

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Table 2.  The WD 1242–105 Binary

Parameter	Primary	Uncertainty	Secondary	Uncertainty
K (km s−1)	124	1.2	178	1.4
γ (km s−1)	41.9	0.8	30.3	1.0
M (${{M}_{\odot }}$)	0.56	0.03	0.39	0.02
${{T}_{{\rm eff}}}$ (K)	7935	92	8434	36
log g	7.94	0.05	7.54	0.05
T$_{{\rm cool}}$ (Gyr)	1	⋯	0.6	⋯

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Figure 2 shows both the phase folded light curve of the V band photometry of WD 1242–105, with a measured rms of 3 mmag and 60 s sampling, along with a Fourier transform (FT) of the photometry. No obvious periodicity is seen in the data to a 4σ level of 1.1 mmag, and the overall standard deviation of the photometry matches the estimates of the photometric uncertainty. A peak in the FT at 4.28 hr is seen, but since this is not coincident with the orbit of the system we attribute this to slowly varying atmospheric extinction. The comparison star most likely had a different spectral energy distribution (SED) than WD 1242–105, and would suffer from differential atmospheric extinction which could explain the small variation. Rebinning the data along the phase of the orbit does not show any obvious additional structure, implying that the two components are well detached, non-eclipsing, and not suffering from any tidal distortion.

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We can calculate the mass ratio of the two components $q=0.70\pm 0.01$ from the ratio of the radial velocity semi-amplitudes. The difference in systemic velocity, or γ, provides a constraint on the difference of the two objects' gravitational redshifts:

$$\begin{eqnarray}&&{\Delta }\gamma =\frac{G}{c}\left( \frac{{{M}_{1}}}{{{R}_{1}}}-\frac{{{M}_{1}}}{q{{R}_{2}}} \right)\end{eqnarray} \tag{ 2 }$$

where M₁ and R₁ denote the mass and radius of the more massive companion, respectively, and R₂ denotes the radius of the less massive companion. We measure a velocity offset difference of 11.6 ± 1.3 km s⁻¹. Under the assumption of theoretical mass–radius relations for WDs (which does require an estimate of T$_{{\rm eff}}$), one can uniquely fit the mass ratio and gravitational redshift to give masses of the two components (Napiwotzki et al. 2002). In a recent study by Holberg et al. (2012), most field DAs showed good agreement with theoretical mass–radii relations. Similarly, careful observations of DDs show that low mass WDs that have experienced post-common envelope evolution also generally behave consistently with expected model mass–radius relations (Bours et al. 2014). To obtain the mass estimates, we minimized a ${{\chi }^{2}}$ metric for the expected ${\Delta }\gamma$ for a given primary mass and mass ratio, and using the derived T$_{{\rm eff}}$ from Section 4.2. Using this approach, we find masses of $0.56_{-0.07}^{+0.05}$ and $0.39_{-0.05}^{+0.04}$ M$_{\odot }$. We compare this determination of the masses with those determined in the next section.

Barring a measurement of the inclination of the binary orbit, the unknown masses and radii of the binary components need to be disentangled with additional information that can be derived from modeling the two components' optical spectra and their photometric SED. This modeling, in concert with the constraints derived from the mass ratio and the parallax, allows determination of the WD fundamental parameters complementary to Section 4.1.

In an era of all-sky surveys in the UV through mid-IR, high quality SEDs are now routine. In particular, WD 1242–105 is within the sky coverage of GALEX GR7 (Martin et al. 2005), SDSS DR9 (Ahn et al. 2012), 2MASS (Skrutskie et al. 2006), and ALLWISE (Wright et al. 2010), resulting in 14 photometric measures of the system's SED. With an accurate measure of the system's parallax, we determine both ${{T}_{{\rm eff}}}$ and ${\rm log} \;g$ by fitting synthetic spectra to the observed photometry and spectroscopy under the constraints of the observed mass ratio. Fitting the spectroscopic and photometric measurements alone introduces degeneracies where multiple similar temperatures and gravities are possible.

The procedure to fit the spectrum is the same as that used for single WDs where the profiles of the hydrogen Balmer lines are compared to detailed model atmospheres (Bergeron et al. 1992; Liebert et al. 2005). We rely on a combination of spectra taken when the components were well separated in velocity space, namely the spectra obtained on HJD 2454548 (See Table 1). Each individual (blended) line was normalized to a continuum set to unity at a fixed distance from the line center, for both observed and model spectra. The atmospheric parameters are then found using the nonlinear least-square method of Levenberg–Marquardt (Press et al. 1986). The uncertainties on fitted values were derived from a combination of the covariance matrix of the spectroscopic fitting algorithm, which mostly impacts ${{T}_{{\rm eff}}}$, and error propagation of the trigonometric parallax and mass ratio uncertainties, which mostly influence ${\rm log} \;g$ values. We determine ${{T}_{{\rm eff}}}$ for both components from the spectroscopic fit but the ${\rm log} \;g$ values are fixed from the result of the photometric fit.

For our procedure of fitting the photometry, we included the Sloan ugriz photometry and converted these measurements into flux densities using the appropriate filters, which are then compared with the predictions from model atmosphere calculations (Bergeron et al. 1997; Holberg & Bergeron 2006). We apply a correction to the u, i, and z bands of −0.040, +0.015, and +0.030, respectively, to account for the offsets between the SDSS filter zero points and the AB magnitude system (Eisenstein et al. 2006). From the photometry we only fit the solid angle with the constraint from the trigonometric parallax. From the observed mass ratio and spectroscopic ${{T}_{{\rm eff}}}$ values, we can then determine both gravities assuming a mass–radius relation. We iterate on the spectrosopic and photometric fits until we converge to a solution on the atmospheric parameters.

To fit the observations, we rely directly on a grid of mean 3D spectra from pure-hydrogen atmosphere 3D simulations (Tremblay et al. 2013). In this range of ${{T}_{{\rm eff}}}$, 3D effects on the gravities can be quite dramatic. The gravities were converted to masses and radii using evolution sequences with thick hydrogen layers from Fontaine et al. (2001) for the C/O core component and Althaus et al. (2001) for the lower mass He core component. The choice of composition for the core comes from the implied masses determined in Section 4.1; He-core WDs generally experienced extreme mass loss during the red giant branch, leaving a core less than 0.5 ${{M}_{\odot }}$.

Figure 3 shows the resulting model fits to both the optical spectroscopy and the SED of the two components under the assumption of the parallax and mass ratio for the system. In addition to a good fit to the Sloan photometry, the predicted photometry for GALEX, 2MASS, and ALLWISE photometry is consistent within the uncertainties. Table 2 lists the final ${{T}_{{\rm eff}}}$, ${\rm log} \;g$, and masses as derived from our fitting procedure. From this procedure we obtain exact agreement in the masses of the two components with that determined in Section 4.1. This is not completely surprising as the two measurements are linked via the inferred mass ratio of the binary system as well as the same theoretical WD mass–radius relationships, but does provide confidence in the resulting answer. For our further discussions, we adopt the masses and uncertainties derived from the spectroscopic and photometric fitting.

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In summary, the WD 1242–105 DD binary is composed of a C/O core WD with a mass of 0.56 ${{M}_{\odot }}$ and a less massive 0.39 ${{M}_{\odot }}$ helium core WD. They orbit each other in a period of less than 2.85 hr, with an inclination to the line of sight of 451. The semimajor axis of their orbit is 1 ${{R}_{\odot }}$, which at a distance of 39.2 pc corresponds to a maximum angular separation of 120 μas.