DISCOVERY AND CHARACTERIZATION OF AN EXTREMELY DEEP-ECLIPSING CATACLYSMIC VARIABLE: LSQ172554.8–643839

To compare all our observations, which were recorded over a time span of ∼1 month, we corrected all exposure times to the reference frame of the solar system's barycenter. An initial determination of P was then determined from the LSQ data alone. A much more accurate measurement was then obtained by searching for the period value near this initial determination that best predicts the central times of the deep eclipses we observed in all the light curves over the one-month span of our observations (18 separate epochs). The resulting ephemeris for the barycentric Julian Date, T_o, at central eclipse versus cycle count, E, is

$$\begin{equation} T_{\rm o} = {\rm BJD }\,2455312.5995 \pm 0.0003 + {\it PE}, \end{equation} \tag{ 1 }$$

where P = 0.065734 ± 0.000001 days (94.657 minutes).

Figure 2 shows the Q_st-band light curve, Q*_st versus θ, where Q*_st is the magnitude of the target relative to a nearby field star and θ is the orbital phase. The zero point for the magnitude scale has been adjusted to match the peak Q*_st value to the peak V value observed later with the SMARTS 1.3 m. More than four periods have been folded to yield the result. To display a full cycle clearly, we overplot the same data shifted to the right one whole phase. Figure 3 shows an expanded plot of the values near θ = 1. Note that all the Q*_st values in the middle of the deep eclipse, from θ = 0.98 to 1.03, are 1σ upper limits to Q*_st. The signal from the target at these phases is not significantly different from the sky background.

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The resulting light curve consists of three contiguous regions with distinctly different behavior:

Region 1: a deep and narrow eclipse (width Δθ ∼ 0.05 centered at θ = 0), with duration ∼4.7 minutes, where there is no detectable signal from the source (see Section 4.2 for a detailed discussion of the uncertainty for Δθ).

Region 2: a wide and relatively shallow eclipse (θ = 0.03–0.45), with duration ∼39.8 minutes, and where the magnitude brightens linearly with time by 0.5 mag, starting at a value of 2 mag fainter than peak.

Region 3: the un-eclipsed part of the light curve (θ = 0.45–0.98), with duration ∼50.2 minutes, where the signal reaches peak brightness, and varies roughly as a sinusoid with peak-to-peak amplitude ∼1.0 mag and frequency nearly double that of the whole light curve.

To determine a lower limit to the depth of the Q_st-band eclipse, ΔQ_st, we averaged the 10 LSQ images with phases closest to middle of the deep eclipse (after subtracting the sky background) to produce a deep image, I_deep. With no source visible above background in I_deep, we measured the rms signal, σ, of the background and calculated the limiting flux, F_lim = 3σπ^1/2, that we would expect for a target with brightness 1σ above background inside an aperture of 3 pixel radius. Using the same radius aperture, we also measured the flux, F_o, of the target in an image, I_o, recorded at θ = −0.05. We also measure the flux for a nearby field star in both I_deep and I_o. Normalizing F_lim and F_o to the field star flux, we find the 1σ limiting flux in I_deep to be 195 times fainter than target flux at θ = −0.05. Hence, we obtain ΔQ_st = 5.7 mag.

Figure 4 shows the phased light curves we obtained from our SMARTS 1.3 m and 1.0 m observations in different wavelength bands. Here we have assigned arbitrary magnitude zero points to those light curves that we did not calibrate to standards (the y-axis label appears with an asterisk in these cases). For the other cases, the magnitude zero points are calibrated to standards as described above. All light curves are repeated with a horizontal shift of one whole period. The vertical scale is identical for each band. In all bands except J, a deep eclipse was detected where the source became undetectable. The eclipse appears as a gap in the light curves at phase θ = 1. To guide the eye, we draw a line connecting the points for each light curve, but only for the phases from θ = 0 to 1. We leave out the connecting line from θ = 1 to 2.

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Inspection of Figure 4 shows that the light-curve shape is generally repeated in each of the visible bands (U to z), with regions 1, 2, and 3, evident as defined above. The most significant change is an increase in the slope of region 2 as the band wavelength changes from U to z. There is also a slight change in the shape of region 3 from sinusoidal to saw tooth. In the J band there is a dramatic change. The deep eclipse is completely absent and there is no clear distinction in the light-curve shape in the phase ranges corresponding to regions 2 and 3. Interestingly, there is a sudden drop in brightness by ∼1 mag at θ = 0.9. This precedes the onset of the deep eclipse that is apparent in the optical bands by ∼5 minutes. During the phase range covering the deep eclipse, the J-band brightness is increasing.

The night-to-night variations in the shape of the light curve are apparent in the scatter of the V-band observations, which span seven nights. The scatter ranges from ±0.1 mag for region 2 to ±0.5 mag at the peak of the light curve where region 3 begins. There do not appear to be any long-term changes. The Q_st-band light curve recorded on April 29 is nearly identical to the B- and V-band light curves observed on May 10–18. Hence, there is no evidence of any outbursts or significant change in activity level over a three-week interval.

Figure 5 shows the band ratios (in magnitudes) with respect to V as a function of orbital phase. We obtain these by subtracting each measured magnitude by the V-band magnitude at the nearest orbital phase. For reference, the top panel shows the phased V-band light curve from Figure 4. Note that the zero point of the magnitude scale for U*−V, V−I*, and V−z* is arbitrary since we do not have absolute photometry for the U, I, and z bands. In each panel, we omit magnitude ratios measured within and near the deep eclipse because the optical flux is too faint to measure accurately, or not detectable.

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Inspection of Figure 5 shows that the B−V and V−R are relatively constant with orbital phase. Although there is significant variation, it is generally less than 1 mag peak to peak. In Table 3, we show the phase-averaged values for B−V and V−R for regions 2 and 3 of the light curve. The source is slightly redder in region 3 than in region 2 (the mean B−V increases by 0.23 mag) but V−R only increases by 0.09 mag. Table 3 also lists a lower limit, V−J > 7.1, that we estimate for region 1. This is the V-band lower bound (V_lim = 24.1) we estimate at the center of the deep eclipse minus the phase-averaged J-band magnitude (J = 17.1 mag) we measure from θ = −0.02 to 0.03. We derive V_lim from the magnitude, V = 18.4, just before the onset of the eclipse (at θ = −0.05) plus ΔQ_st derived above. The Q_st- and V-band light curves are likely to have the same eclipse depths because they are centered on the same wavelength (5500 Å).

Figure 6 shows the six different spectra we recorded for the binary, with the first three spectra (starting at the bottom) corresponding to phase region 3, and the next three spectra corresponding to phase region 2. Each panel is labeled with orbital phase, θ_mid, corresponding to the mid-time of the exposure (see also Table 2), and determined using Equation (1).

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It is immediately apparent that Balmer-series emission lines are present at all observed phases, with H_α (6563 Å), H_β (4861 Å), H_γ (4341 Å), H_δ (4102 Å), and H_ε (3970 Å) clearly resolved in phase region 2 (θ = 1.08, 1.19, and 1.30). In this region, the spectra also clearly resolve He i (5876 Å). It is also apparent that the continuum varies significantly with orbital phase, with a significant wavelength-independent brightening in region 3 (θ = 0.72, 0.78, and 0.84) relative to region 2. This is consistent with the phases of maximum intensity in the optical light curves. The continuum is noticeably flat at all wavelengths in region 3, but slopes toward blue wavelengths in region 2.

Figure 7 shows the same spectra as Figure 6, expanded around the H_α line. It is clear that the shape, width, and center of the lines are changing with orbital phase owing to phase-dependent variation in the source region's radial velocity. Similar variations also appear for the H_β and H_γ lines. Using fitting routines in IRAF ("splot" with Voigt fit), we have measured the line centers (shown by the vertical dashed lines in Figure 7) and widths versus phase for all three emission lines at each light-curve phase. For each emission line, Figure 8 shows the resulting radial-velocity values as a function of θ. Assuming a source in synchronous rotation, we fit a best-fit cosine function for each line of the form

$$\begin{equation} v_r {\rm } = {\rm }\gamma {\rm } + {\rm }K^*\cos (2\pi [\theta - \theta _0 ]), \end{equation} \tag{ 2 }$$

where γ is the mean radial velocity, K is the amplitude of variation, and θ₀ is the phase at which v_r reaches a maximum (largest redshift). Table 4 lists the parameters of resulting fits, which yields rms residuals of 16, 26, and 36 km s⁻¹ for H_α, H_β, and H_γ, respectively (about ¼ pixel resolution). For each emission line, the errors on the fitted parameters are calculated assuming an observational uncertainty in v_r equal to the rms with respect to the best fit, and taking the ±1σ error for each parameter to be the range that keeps χ² less than the minimal χ² + 1. Table 4 also shows the mean width (FWHM) measured for each line for the Lorentzian component of the Voigt fit, which dominates in nearly all cases.

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We begin with the hypothesis that the source is an eclipsing polar, like J015543.40+002807.2. Our observations of a very short-period light curve and two eclipses—one very narrow and deep, the other relatively shallow and persisting for one half rotation—match the phenomena we would expect for such a system. In our case, there is at least one bright spot on the surface of the WD in synchronous rotation with the orbit. The spot rotates behind the WD each half period, producing the wide, shallow eclipse (region 2). Just after it rotates from view, there is a brief eclipse by a cool companion star, invisible at optical wavelengths. This produces the short, deep eclipse. The average color ratios we measure for region 2 (B−V = −0.02 and V−R = 0.20), when the hot spot is presumably occluded but the WD is visible, are consistent with a typical WD (Schwartz 1972). Also, the spectral shape and Balmer emission lines we observe at phases covering region 2 (θ = 1.08, 1.19, and 1.30) are similar to spectral features observed by Schmidt et al. (2005) for polar J015543.40+002807.2.

There are some features that we expect for a polar, but do not see. Cyclotron emission should produce broad humps in the red part of the optical spectrum. These may be present at a low level in our data, or they may not be present at the orbital phases we observed. Schmidt et al. (2008) find the intensity of cyclotron emission varies with time and orbital phase for polar SDSS J0921+2038. Polars are also known to produce strong He ii emission at 4686 Å. While this line appears in our spectra at θ = 1.08, 1.19, and 1.30, it is much weaker than typically observed. However, the spectrum of SDSS J0921+2038 also shows He ii at a weak level, comparable to the level we see in our candidate polar. For polar UW Pic, Romero-Colmenero et al. (2003) observer the He ii line to vary from weak to strong on yearly timescales. Hence, the absence of cyclotron emission and of strong He ii lines in our limited spectral series does not rule out a polar.

A second possibility is that we are observing a system with an accretion disk and a hot spot where the stream from the secondary impacts the disk edge. The increase in source intensity just prior to the deep eclipse (θ = 0.6–0.95) might then be explained as an orbital hump, as in Z Cha (W95) or IY UMa (Patterson et al. 2000). However, this would not explain the extremely sharp rise in optical intensity we observe at θ = 0.45, where region 2 ends. From orbital phase 0.452–0.464 the source brightens by 0.9 mag. This is much faster than the typical brightness change expected for the egress of hot spot from behind a disk. For example, the orbital hump in Z Cha requires 20% of an orbital period to reappear. In IY UMa, the hump rises in 30% of a period. On the other hand, Schwope & Mengel (1997) observed the eclipsing polar EP Dra to brighten in the V band by ∼50% over very narrow range of orbital phase, outside of the eclipse (0.72–0.75).

The rapid intensity rise we see at the end of region 2 is peculiar and may be consistent with neither scenario discussed above. There are other unexplained features in our light curve: the drop in optical brightness from θ = 0.6 to 0.8, just after the steep increase at the end of region 2; also the sharp drop in the J-band brightness at θ = 0.95, just before the onset of the deep optical eclipse. Perhaps a complete model could explain these features, taking into account the intensity versus emission angle for the hot spot, the inclusion of an accretion disk in the system, and eclipses of the WD by the accretion column. However, such detailed modeling is beyond the scope of this paper and should wait for more extensive follow-up observations.

To estimate the binary parameters—mass and radius of the secondary (R_sec and M_sec), the binary separation, a, and the inclination, i—we assume the secondary has relaxed to a circular orbit and fills its Roche lobe. The strong hydrogen emission lines we see in the spectrum are evidence that there is infalling gas, and hence a Roche-lobe filling secondary. Following Patterson et al. (2005) and Knigge (2006, hereafter K06), we also assume a WD mass, M_WD = 0.75 (here and in the following discussion, we use the solar values for radius and mass units). This value for M_WD matches the values determined for other eclipsing CVs to within 20%. We also assume a WD radius, R_WD = 0.013, which matches the radii measured for WDs with masses 0.50–0.90 to within ±0.002 (Parsons et al. 2010).

With these assumptions, we can now use the empirical mass/radius relation for CV secondaries determined by K06, based on an analysis of super-humping in eclipsing systems:

$$\begin{equation} R_{\sec } = A(M_{\sec } /M_{\rm o})^\alpha, \end{equation} \tag{ 3 }$$

where A = 0.110 ± 0.005, M_o = 0.063 ± 0.009, α = 0.21(+0.05, −0.10) for M_sec < 0.063 and A = 0.230 ± 0.008, M_o = 0.20 ± 0.02, α = 0.64 ± 0.02 for 0.063 < M_sec < 0.20 and P < 2.15 hr. Here the change in the constants at mass 0.063 relates to the evolutionary status of the secondary. Owing to the competing effects of mass transfer and to the loss of angular momentum by magnetic breaking and gravitational radiation, CVs are expected to evolve from longer to shorter periods with the secondary continuously losing mass. Eventually the secondary becomes too light for hydrogen burning and becomes supported by electron degeneracy pressure. Thereafter, with further mass loss, the secondary grows in size and P also increases. Hence, for M_sec < 0.06, Equation (3) describes secondaries that have evolved through a period minimum (post-bounce systems). For 0.063 < M_sec < 0.20, the equation describes pre-bounce systems. For M_sec > 0.20, K06 provides a third set of values for the constants in Equation (3), corresponding to CVs that have not yet evolved below the period gap (P > 3.18 hr). K06 also warns that the post-bounce mass/radius relation is very uncertain, as it is derived from observations of only a few CVs.

We can also use the density/period relation from W95, valid for Roche-filling secondaries, which K06 restates as

$$\begin{equation} R_{\sec } = 0.2361\big[M_{\sec } ^{1/3} P^{2/3} \big], \end{equation} \tag{ 4 }$$

where P is in hours. Combining Equations (3) and (4), we thereby determine R_sec and M_sec from P. We also use Kepler's law to determine a from P, M_sec, and M_WD.

The final binary parameter, i, is fixed by the eclipse viewing geometry and Δθ:

$$\begin{equation} \sin (i) = [1 - (R_{\sec } /a)]^{1/2} /\cos (\pi \Delta \theta), \end{equation} \tag{ 5 }$$

where Δθ = θ_e − θ_i, where θ_i and θ_e are the respective orbital phases of mid-ingress and mid-egress. Because our light curves do not have the time resolution to reveal these contact points, we estimate lower and upper bounds as follows (indicated by the dashed lines in Figure 3). The eclipse ends no later than θ = 1.037, where we make our first post-eclipse detections. We thus have θ_e < 1.036 − R_WD/2πa, where R_WD/2πa is half the egress phase duration. Egress also begins no earlier than θ = 1.022, where we have our last null detection and the source intensity is within a few percent of minimum. Hence, θ_e > 1.022 + R_WD/2πa. By similar reasoning, given our last pre-eclipse detection at θ = 0.970 and our first null detection at θ = 0.982, we have θ_i > 0.968 + R_WD/2πa and θ_i < 0.982 − R_WD/2πa. With these extremes for θ_e and θ_i, we thus have Δθ > 0.040 + R_WD/πa and Δθ < 0.067 − R_WD/πa.

Solving the above equations for R_sec, M_sec, a, and i, we have separate solutions for the pre- and post-bounce cases. The resulting values and their uncertainties are listed in Table 5. The table also lists two values for Δθ, corresponding to the two solutions for a. We derive the results by running iterative solutions, assigning Gaussian-distributed random values to A, M_o, α, Δθ, M_WD, and R_WD within their respective uncertainty ranges on each trial. This provides a distribution of solutions for each parameter for which the mean and standard deviation are the value and uncertainty respectively listed in Table 5. Note that Equation (5) restricts the range of values the parameters can take because the deep eclipse cannot occur if R_sec/a > sin(πΔθ).

Comparing the two solutions, it is apparent that the post-bounce solution yields a secondary that is much less massive (M_sec = 0.034 ± 0.012) and smaller (R_sec = 0.102 ± 0.011) than the pre-bounce case (M_sec = 0.104 ± 0.025, R_sec = 0.150 ± 0.012). The values for a differ by only a few percent, since the WD mass dominates the system in both cases. Both the pre- and post-bounce solutions require a highly inclined orbit, with i > 80°. While the pre-bounce mass is typical of known short-period CVs, the post-bounce mass would be extremely unusual. In the Ritter & Kolb catalog, only 2 of the 128 CVs with measured secondary masses have a lower value. However, post-bounce systems are predicted to dominate the CV population because they are a long-lived end state (Kolb 1993). Recently, faint CVs detected in spectroscopic surveys by the Sloan Digital Sky Survey (SDSS) reveal a substantial fraction of post-bounce systems, supporting the existence of the large population (Littlefair et al. 2008; Gänsicke et al. 2009). Given that our source is faint, comparable in magnitude to the CVs detected by SDSS, the likelihood that it could be a post-bounce system is enhanced. In the following section, we consider the possibility we are seeing such a low-mass companion based on photometric constraints.

From our photometry during the deep eclipse, we see that the secondary is a very red object with V−J > 7.1. According to the table of grizJK colors for low-mass stars compiled by Dupuy & Liu (2009), and using the conversion from g−r to g−V from Fukugita et al. (1996), this color corresponds to a spectral-type M8 or later. This is extremely rare among the known WD binaries. Only 2 of 153 WD binaries in the Two Micron All Sky Survey (2MASS) by Hoard et al. (2007) and only one of the 91 CV secondaries tabulated by K06 have such a late spectral type. Mass estimates for M8 stars range from 0.02 to 0.08 (Riddick et al. 2007). This overlaps our post-bounce value for M_sec but is only marginally consistent with the pre-bounce value. Hence, if the very red color we measure is a valid indication of the spectral class of the secondary, it supports the possibility that we are observing a very unusual, low-mass companion in a post-bounce system.

We must also consider the possibility that our spectral classification is in error, owing perhaps to a J-band emission from an extended source adding to the emission from the secondary at deep eclipse. However, if the pre-bounce solution for the binary mass were correct, we would expect a much bluer color for the secondary. The fits to spectral type and color versus period provided by K06 yield spectral-type M6.3 and V−J = 5.5 at the period we observe for our source. Hence, a pre-bounce solution implies that IR emission contaminates our J-band measurement at mid-eclipse by 1.6 mag, or a factor of four relative to the secondary. The source would have to be located far from the WD primary and its hot spot, and it would have to be much fainter than these sources at optical wavelength. Otherwise the J-band light curve would mirror the optical light curve. A weakly emitting accretion disk or accretion column might meet these criteria.

Assuming our spectral classification is correct and that the secondary's magnitude–color relation is the same as for isolated low-mass stars, then we can determine the minimum absolute J magnitude, M_J, and minimum distance, D, to the binary. From Hawley et al. (2002), who fit M_J versus spectral class, we have

$$\begin{equation*} M_J = 8.83 + 0.29 \times {\rm spectral}\;{\rm type}, \end{equation*}$$

where spectral type = 0–10 for M0–M9, and 11–20 for L0–L9. For spectral-type M8.0 or later, this yields M_J > 11.2. Then with J = 17.1 at the deep eclipse midpoint, we obtain distance D = 150 pc.

The fits we derive to the radial-velocity curves for H_α, H_β, and H_γ yield consistent values for the amplitude, K, and phase, θ_o, of the radial-velocity oscillation. Averaging the results, we obtain K = 500 ± 22 km s⁻¹ and θ_o = −0.01 ± 0.01. Assuming the Doppler shift is caused by the Keplerian motion of the source region on a circular orbit (such as the hot spot on the edge of an accretion disk), then a maximum redshift at θ_o = −0.01 places the source region at a phase 90° ahead of the secondary, which is not consistent with a typical accretion-disk morphology. Furthermore, the source orbit would have radius, r_H, given by

$$\begin{equation*} r_H = KP/2\pi \sin (i) \end{equation*}$$

or a limiting lower value r_H > 0.65 for i = 90°. However, the maximum radius we can expect for the accretion disk, rd*, is much smaller. W95 provides the following expression (Equation (2.61)):

$$\begin{equation*} r_d^{*} = 0.6a/(1 + M_{\sec } /M_{{\rm WD}}). \end{equation*}$$

This yields r*_d < 0.369 ±.030 (post-bounce) and r*_d <0.315 ± 0.029 (pre-bounce). Thus, it is clear that emission line properties we observe are inconsistent with a hot spot on the edge of an accretion disk.

On the other hand, the large amplitude of the radial-velocity oscillations, the near zero phase at which they reach maximum redshift, and the extreme Doppler broadening we observe for the emission lines (600–1300 km s⁻¹) are consistent with the radiation emitted from the accretion column in a typical polar (W95). In this case, the Doppler shift derives from the infall velocity of the gas pulled from the secondary and falling onto to the WD. Near θ = 0°, the view is directly along the accelerated gas flow, and the redshift is maximal. Furthermore, the light-curve variations we observe in region 2, where the hot spot is visible, would then be related to the changing orientation of the accretion column with respect to the line of sight, as for V834 Centauri (W95).