INFRARED PHOTOMETRY AND SPECTROSCOPY OF VY Aqr AND EI Psc: TWO SHORT-PERIOD CATACLYSMIC VARIABLES WITH CURIOUS SECONDARY STARS*

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Published 2009 March 10 © 2009. The American Astronomical Society. All rights reserved.
, , Citation Thomas E. Harrison et al 2009 AJ 137 4061 DOI 10.1088/0004-6256/137/4/4061

1538-3881/137/4/4061

ABSTRACT

We present new K-band spectra of VY Aqr and EI Psc obtained with NIRSPEC on the Keck II telescope. We find a best-fitting spectral type of K4 for EI Psc, in agreement with the previous classification. The Keck spectrum of VY Aqr suggests an M0 spectral type, much hotter than previously derived. We re-reduce the original data for VY Aqr that were obtained using ISAAC on the Very Large Telescope (VLT) and find a best-fitting spectral type of M6 for VY Aqr. We are unable to reconcile the two data sets. We analyze new phase-resolved optical spectroscopy of VY Aqr, obtained using UVES on the VLT, to derive the mass ratio, and show that the mass of its secondary star is very likely below the stellar/substellar boundary. We also present and model phase-resolved JHK infrared light curves for both objects, and g- and I-band light curves for EI Psc. While the light curve models for EI Psc are consistent with its spectral type, we are unable to model the light curves of VY Aqr without assuming binary star parameters outside the published range for this object.

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1. INTRODUCTION

Cataclysmic variables (CVs) are short-period binaries where a white dwarf primary is accreting material from a cool, low-mass secondary star that fills its Roche lobe. The standard evolutionary paradigm (see Howell et al. 2001) expects that long-period CVs should slowly evolve into short-period systems. In the process, the secondary stars in CVs continually lose mass, and over time evolve toward the stellar/substellar mass boundary. Population synthesis models by Howell et al. find that the majority of CVs of very short orbital period (Porb ⩽ 2 hr) should contain degenerate, brown dwarf-like donors. While there is some evidence for CV secondary stars at, or slightly below, the mass limit for main sequence stars (EF Eri: Howell et al. 2006, WZ Sge: Steeghs et al. 2007), only in the polar J1212+0136 (Farihi et al. 2008) is there evidence for the direct detection of flux from a brown dwarf-like (L8) object.

As shown by Harrison et al. (2005a), the secondary stars in polars appear to be relatively normal late-type main sequence stars, in contrast to nonmagnetic systems that have secondary stars with abnormally weak CO features (Harrison et al. 2004, 2005b). But the K-band spectroscopic survey of polars concentrated on short-period systems (Porb ⩽ 3 hr), while the nonmagnetic systems all had periods longer than this. What do the secondary stars of short-period, nonmagnetic CVs look like? Are they relatively normal like those found in polars, or do they show peculiar abundance patterns?

VY Aqr is a dwarf nova of the SU UMa subclass with infrequent outbursts (Howell et al. 1995). It has an orbital period of 1.51 hr. Littlefair et al. (2000) obtained a J-band spectrum of VY Aqr where they believed they might have detected the water vapor band at the red edge of the bandpass. They warn, however, that the other atomic and molecular features expected from a star of late enough type to have a water vapor feature were not present. The continuum was flat, or rising slightly to the red. Mennickent & Diaz (2002) present low-resolution JHK spectra of VY Aqr which reveal a relatively blue spectrum. They did, however, see absorption features in the J-band which they associate with K i and Na i. They assigned a spectral type of M9V to the secondary star.

EI Psc is a peculiar CV in that it has a period of 1.07 hr, below the theoretical minimum period for contact binaries having secondary stars of normal composition. Unexpectedly, Thorstensen et al. (2002) found that the secondary star in EI Psc has an apparent spectral type of K4 ±2, and it exhibits ellipsoidal variations in visible light. They suggest that the secondary star in this system is enriched in helium, and that such an object is in agreement with models for CVs where the secondary evolved off of the main sequence prior to contact. Such systems should be extremely rare (Howell et al. 2001).

We present new K-band spectra and phase-resolved infrared photometry for both VY Aqr and EI Psc, and new optical spectroscopy of VY Aqr. Both objects are nonmagnetic CVs below the period gap. We find that the secondary star in EI Psc truly appears to be a K4, much hotter than expected for such a short orbital period. For VY Aqr, however, the exact spectral type of its secondary star is difficult to ascertain. Both objects appear to have very weak/nonexistent CO features, suggesting large deficits of carbon.

2. OBSERVATIONS

2.1. Photometry

Infrared photometry for both VY Aqr and EI Psc was obtained using the Simultaneous Quad Infrared Imaging Device7 (SQIID) on the KPNO 4 m. The SQIID obtains JHK images simultaneously. EI Psc was observed on 2004 July 31 from 7:39 to 8:46 UT. VY Aqr was observed on 2004 August 1, with the first exposure occurring at 6:03 UT and running to 7:35 UT. Thorstensen & Taylor (1997) have published an ephemeris for VY Aqr, and we have phased our data to that ephemeris. We found that we had to offset the observed light curve by −0.055 in phase to match the model ellipsoidal light curves discussed below. This small offset is within the error bars of the Thorstensen & Taylor ephemeris given the eight years between the two data sets. Thorstensen et al. (2002) have published an ephemeris for EI Psc. We found that we had to add 0.04 to the phase predicted by the ephemeris for EI Psc to insure the observed minima matched the model minima. This difference is also well within the errors of the ephemeris.

Optical photometry of EI Psc was obtained on 2006 December 15 (g-band) and 16 (I-band) using the widefield MOSAIC CCD imager on the KPNO 0.9 m telescope. Individual exposure times were 180 s for the g-band and 240 s for the I-band. The data were reduced in the normal way, and differential photometry with respect to a nearby field star was performed. The g-band light curve spanned 2.6 hr, covering nearly 2.5 orbital periods of EI Psc. The I-band light curve was obtained over 3.7 hr, and covered 3.5 full orbits.

2.2. Spectroscopy

New infrared spectra for VY Aqr and EI Psc were obtained using NIRSPEC on Keck II on the night of 2007 August 27. NIRSPEC was used in low-resolution mode with a 0farcs432 slit, providing a dispersion of ∼4 Å pixel−1. Four exposures with durations of 240 s were obtained in an ABBA pattern for both objects. The total sequence spanned about 13 minutes, corresponding to 0.16 in phase for VY Aqr, and 0.20 in phase for EI Psc. Thus, there is a small amount of orbital smearing that cannot be avoided for such faint, very short-period objects. These data were reduced in the normal fashion and tellurically corrected using nearby A0V stars. A0V stars are nearly featureless in the K-band, except for a prominent H i absorption feature (Br γ) at 2.16 μm. After division by the spectrum of the A star, the spectra were multiplied by a calibrated spectrum of Vega to attempt to recover the continuum shape, its flux, as well as the intrinsic H i emission feature of the two CVs. Note that the spectrum of Vega may have an H i absorption feature that differs from that of the A0V stars used for telluric correction, so the profiles of the H i emission lines in VY Aqr and EI Psc can be compromised by this process.

Mennickent & Diaz (2002) used ISAAC8 on the Very Large Telescope (VLT) to obtain JHK spectra of VY Aqr. It is clear from their Figure 1, however, that the telluric correction of their object spectra was not optimal. This was partially due to the fact that they only had a single telluric star observation with which to reduce their data, but also due to the fact that their telluric correction star (HD216009) was observed using a different slit width (1'') than their program objects (0farcs6). As we describe below, the apparent spectral type of the secondary star visible in our Keck data for VY Aqr is dramatically different from that derived by Mennickent & Diaz. Thus, we downloaded the ISAAC data set for VY Aqr from the European Southern Observatory Archive9 to re-reduce it to allow for direct comparison with our Keck spectrum. In addition, we also downloaded all ISAAC observations of the telluric star (HD216009) in the ESO archive. Fortunately, there have been several more recent observations of HD216009 that used the 0farcs6 slit in the H- and K-bands with identical grating settings. Unfortunately, we could not find any narrow slit observations of HD216009 in the J-band covering the same bandpass. The ISAAC data were reduced in the same fashion as our NIRSPEC data. Because the three observations of HD216009 required to reduce the individual JHK spectra all occurred on different dates, we used the ephemeris of Thorstensen & Taylor (1997) to determine the orbital phases of each of the VY Aqr spectra, and then flux calibrated the ISAAC spectra using the observed magnitudes from our JHK light curves. Note that the time of the first ISAAC J-band spectrum of VY Aqr differs from the last K-band spectrum by 37 minutes, or 0.45 in orbital phase. Using the Thorstensen & Taylor ephemeris, the orbital phases at the midpoints of the VLT observations in J, H, and K were 0.85, 0.95, and 0.14, respectively. Mennickent & Diaz extract synthetic magnitudes for VY Aqr which are about 0.1 mag brighter than the mean values from our JHK light curves.

Figure 1.

Figure 1. K-band spectra of VY Aqr and EI Psc compared to the spectra of several late-type dwarfs. To provide a slightly more realistic match to the program object spectra, the data for the K5V, M0V, M5V, and M8V have been rotationally broadened to 300 km s-1 (note that both VY Aqr and EI Psc suffer from orbital smearing due to their very short orbital periods, and that the line widths are broadened by this affect). We have rebinned the spectra of VY Aqr and EI Psc by three pixels. The strongest atomic and molecular absorption features have been identified.

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Optical spectroscopic observations of VY Aqr were obtained on 2002 August 8 with UVES10 on the VLT using the "Blue CCD" in a nonstandard setup. The selected central wavelength was λc = 4360 Å allowing the spectral coverage 4020–5245 Å at a dispersion of ∼0.030 Å pixel−1. The slit width was set to 0farcs9 providing a resolving power of R⩾ 30,000. Exposures were 300 s in length, and a total of 15 exposures were recorded between UT 00:01 and UT 01:44. Having selected a nonstandard setup, no spectrophotometric standard was observed as part of the queue scheduled observations; hence, these spectra have not been flux calibrated. They have been otherwise calibrated in the usual manner with bias frames, flat fields and arcs which were taken during the day following the observing night. These data were reduced according to the standard procedures using a revised version of the UVES (MIDAS based) pipeline.

3. INFRARED SPECTROSCOPY

3.1. VY Aqr—NIRSPEC

Due to its short orbital period, the standard paradigm would predict that the secondary star in VY Aqr should have a spectral type near mid-M. We present the Keck K-band spectrum of VY Aqr in Figure 1, where it is compared to the spectra of K5, M0, M5, and M8 dwarfs. The spectrum of VY Aqr has a very strong Na i doublet suggesting a late spectral type, but it lacks the strong CO (λ ⩾ 2.29 μm), or water vapor absorption one would expect for such a cool star. The Na i feature is most similar to that of an early/mid M dwarf, but is observed to be slightly stronger than that of any of our templates. In contrast, other atomic absorption features, such as the Ca i triplet, the Al i and Mg i lines, and the slope of the continuum indicate a hotter secondary star, closer to that of the K5V and M0V templates. In a K-band spectroscopic survey of the secondaries of nonmagnetic CVs, Harrison et al. (2004, 2005b) found that CO features were abnormally weak in nearly all of the systems. So the lack of strong CO absorption in the spectrum of VY Aqr is not too surprising. However, in our spectroscopic surveys, the water vapor absorption features were not abnormal in any of the CVs with secondaries cool enough to show them. The lack of significant water vapor features in VY Aqr suggests a hotter secondary star.

It is interesting to investigate the sensitivity of the absorption features of Na i, Ca i, and CO to both temperature and gravity. As shown in Harrison et al. (2005b), for late-type dwarfs, the Na i doublet and the strength of the CO absorption features increase in strength with decreasing temperatures, while the Ca i triplet gets weaker with decreasing temperatures. For late-type giants, the same behavior is seen for both Na i and CO (Kleinmann & Hall 1986). However, the same is not true for Ca i. In giant stars, Kleinmann & Hall (1986) found that the Ca i triplet increases in strength from F8III (EQW = 1.5 Å) to M7III (EQW = 5.9 Å). Gorlova et al. (2003) have investigated the behavior of the Na i doublet, the Ca i triplet, and the strength of the CO features as a function of gravity. They find that for both Na i and Ca i, at any one spectral type, the equivalent width of these features increase with increasing gravity. The reverse is true for CO: it is stronger at lower gravities.

If we believe that these trends are true for the secondaries of CVs, then the strong Na i and Ca i lines, combined with the weak CO features suggest that the secondary star of VY Aqr could be a late K/early M-type star with a slightly larger gravity than a main sequence dwarf (perhaps due to a degenerate core). It is difficult to test this conclusion since there are no model atmospheres at these temperatures with gravities higher than those found in main sequence dwarfs, but lower than those found in white dwarfs. Of course, we could simply be dealing with highly peculiar atmospheric abundance patterns. For example, if the secondary star in VY Aqr has a normal gravity and the temperature of a M0 star, then it has to have a modest enhancement of Na, keeping the abundances of Ca, Mg, and Al near their normal values, while having a significant deficit of carbon (or oxygen). If we assume a mid/late M-type secondary star, then we need strong deficits of carbon and oxygen, enhanced levels of Mg, Al, and Ca, and a significant contamination from a source that can produce the observed continuum. It is important to note that the analysis of Hubble Space Telescope Space Telescope Imaging Spectrograph (HST STIS) data by Sion et al. (2003) found a subsolar abundance for carbon in VY Aqr, suggesting the transfer of carbon-poor material from the secondary star.

Given that there is bound to be some contamination from the accretion disk in VY Aqr, as evidenced by the emission lines in the optical spectra discussed below, using the slope of the continuum to gain insight into the nature of the secondary might be somewhat dangerous. As discussed above, however, the slope of the continuum best matches that of the K5V or M0V shown in the figure. Using the calibrated spectrum, we can make an estimate for the K-band magnitude of VY Aqr, and we derive K ∼ 14, consistent with both previously published infrared photometry (Sproats et al. 1996), and that presented below. Thus, VY Aqr does not appear to have been in an unusual state when we observed it. It would appear that of the alternatives for the nature of the secondary star in VY Aqr, the one that assumes an M0 spectral type is the more palatable.

3.2. VY Aqr—ISAAC

Mennickent & Diaz (2002) believed that the secondary star in VY Aqr has a spectral type near M9V, much different to the results just derived. Thus, we decided to re-reduce their data, especially given the evidence for the rather poor telluric correction visible in their published data. Shown in Figure 2 are the infrared spectra for VY Aqr reduced using the same telluric standard used by Mennickent & Diaz, but for which the observations of HD216009 in the H and K bands were obtained using the same slit width (0farcs6) as the VY Aqr observations. In this figure, we compare the VLT observations of VY Aqr to three M dwarfs using data from the IRTF Spectral Library11 (see Cushing et al. 2005). We have also plotted (in red) the K-band spectrum of VY Aqr as observed at Keck. It is clear that in the VLT K-band spectrum, there appear to be water vapor features at the blue and red ends of the K band. In contrast to the Keck data set, we cannot confidently identify any other absorption features in the VLT K-band spectrum. While there is some choppiness in the continuum at the red end of this spectrum that might be associated with CO absorption, the spectrum has insufficient signal-to-noise ratio (S/N) in this region for useful analysis (note that in this region of the Keck spectrum of VY Aqr, the Na i doublet at 2.34 μm is visible).

Figure 2.

Figure 2. VLT spectra of VY Aqr (black) compared to M0V, M6V, and M9V templates from the IRTF Spectral Library (green). As in Figure 1, these data have been rebinned by three pixels. The M6V and M9V template spectra have been normalized to VY Aqr in the K-band, while the M0V spectrum has been normalized in the H band. The K-band spectrum obtained with NIRSPEC is plotted in red, and has been normalized to the M0V spectrum. Prominent emission lines have been identified.

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As can be seen from the comparison, spectral types between M6V and M9V provide a fair match to the overall continuum slope in the K band. But if the spectral type was this late, and there was a normal amount of CO absorption, than these features would almost certainly have been detected. It is also interesting that the H i Brackett-γ emission line is much weaker in the Keck spectrum than in the VLT spectrum. This would suggest that the accretion disk component was weaker at the time of the Keck observations, implying less contamination, and a clearer view of the secondary star. This appears to be borne out by the fact that we easily detect the atomic absorption features expected to be present for an M dwarf secondary star in that spectrum.

Due to their much shorter total exposure times, the J- and H-band data sets are substantially noisier. The H band is dominated by emission lines from the H i Brackett series that effectively hide any stellar absorption features. The continuum does show a small hump that suggests the presence of an M-type star, but any spectral type between M0 and M6 can effectively reproduce this hump. The M6V spectral type is more realistic in the H-band as it allows for some Brackett continuum emission to be present, though small changes in normalization could allow earlier spectral types.

Much of the reasoning for Mennickent and Diaz's (2002) classification of the secondary star as an M9 comes from their analysis of the J-band spectrum of VY Aqr. To better show this region, we present just the J-band spectra in Figure 3. There are five prominent absorption features in the J-band spectra of M dwarfs that are useful for classification: two sets of K i doublets near 1.173 μm and 1.249 μm, the Na i doublet at 1.141 μm, the broad FeH feature at 1.24 μm, and the strong water vapor feature that begins near 1.33 μm. Of these five features, however, only the Na i and K i doublets are clearly present in the VLT spectrum of VY Aqr. There does appear to be a turnover that one could associate with the onset of the water vapor feature, but we are not very confident in the quality of the spectrum here. This region is especially sensitive to the telluric correction which is not very good in this J-band spectrum—note that there is a dip in the spectrum immediately preceding the onset of the water vapor feature that is as large as the dip which one might associate with the water vapor feature. Poor telluric correction is also responsible for the noisiness between the Na i doublet and the H i Paschen γ emission line (at 1.094 μm). The region near 1.13 μm contains strong telluric features that can be difficult to correct even with high S/N data. The Na i doublet, and the two K i doublets are best matched by the M6V template, though the bluer K i doublet is clearly compromised by the low S/N of the data. The FeH feature is not seen, but there are a number of telluric features at the position of the FeH absorption that could cause the discontinuity seen at this wavelength.

Figure 3.

Figure 3. VLT J-band spectrum of VY Aqr compared with the M0V, M6V, and M9V templates. The most prominent absorption features have been identified.

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Using the J-band spectrum, we would classify the secondary star as M6. This, of course, assumes that there is very little contamination present in this bandpass, or in the H and K bands. A spectral type of M9V could also explain the J-band spectrum, especially given the fact that there would be significant levels of contamination if this were the actual spectral type. In Figure 2, we normalized the M9 continuum to that of VY Aqr in the K band. The result is that there is no contamination from the accretion disk allowed with this normalization. The preferred fit that Mennickent & Diaz (2002) found for these data suggested a 44% accretion disk contamination in the K band. With this normalization, the secondary star would only supply ∼25% of the J-band flux. We re-address contamination issues in our light curve modeling for VY Aqr.

One detail that we are unable to explain is why the J-band spectrum we derive from the VLT observations differs from that presented by Mennickent & Diaz (2002). Our extraction of these data results in a peak count level of 275 which results in S/N ≈ 24 (there were two J-band spectra). After division by HD216009, the best parts of the continuum have S/N ≈ 20. Most of the rest of the spectrum, however has S/N ⩽ 15. We were forced to use observations of HD216009 with the same mismatched slit width as that used by Mennickent & Diaz. This should result in superficially similar spectra. But the region around the Na i doublet, and blueward, differ dramatically between the two data sets. The data reduction technique used by Mennickent & Diaz was unlike that used here, and there are insufficient details presented in their paper to allow us to reconstruct their process. It is clear, however, that our reduction technique for the H- and K-band data produced spectra with a much better telluric correction than those presented by Mennickent & Diaz. We are unable to produce a higher quality J-band spectrum than that presented here using those same techniques.

3.3. EI Psc

The K-band spectrum of EI Psc is also shown in Figure 1 and closely resembles that of VY Aqr. The main differences being a slightly weaker Na i doublet, a weaker Ca i triplet, no evidence for CO features, and stronger Mg i and Al i lines. Thorstensen et al. (2002) derived a spectral type of K4 ±2 for this object, and that agrees with what we see here. The redder Na i doublet at 2.34 μm appears to be excessively strong, but this is simply due to the lack of CO absorption at these wavelengths. A similar affect is seen in the spectrum of U Gem (see Figure 10 of Harrison et al. 2005b). This redder Na i doublet has an almost identical strength to the one at 2.20 μm, but the CO features in late type stars remove much of the continuum flux, making this feature appear to be less prominent. Without the CO features, this doublet reveals its true strength. Except for the absence of the CO features, the spectrum of EI Psc does not show strong evidence for other abundance anomalies.

Figure 4.

Figure 4. Average UVES spectrum of VY Aqr. Note the strong H i Balmer emission and the broad absorption dips from the underlying white dwarf, especially for Hγ and Hδ. Emission from He i (4471 Å) and Fe ii are also present.

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4. OPTICAL SPECTROSCOPY OF VY AQR

We present the average UVES spectrum of VY Aqr in Figure 4 and show the details of the Hβ line profile as a function of phase in Figure 5. The spectrum is dominated by strong emission lines of Hβ, Hγ, and Hδ, as well as He i 4471 Å, and Fe ii emission (at 4923 Å, 5018 Å, and 5169 Å), the bluest two lines of which are blended with He i (4922 Å and 5016 Å). Fe ii (multiplet 38) emission may be weakly present just redward of He i 4471 Å, with other lines likely present at 4508, 4523, 4549 and 4584 Å. The Balmer emission lines have FWHM values of ∼1800 km s-1 and FWZI values of ∼3200 km s-1, while He i 4471 Å shows slightly smaller values of 1543 and 2680 km s-1, respectively. These velocities are average values with phase-dependent deviations of 100–200 km s-1, most likely due to absorption from the underlying white dwarf. The Balmer line widths we measure are commensurate with those derived by Thorstensen & Taylor (1997).

Figure 5.

Figure 5. Hβ line profile as a function of phase for VY Aqr. The double-peaked nature of the line is always present, but details of the line profile changes throughout the orbit. The y-scale in each plot remains constant to illustrate the changing line shape and flux. The phase of each spectrum is labeled.

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We measured line velocities by fitting a single Gaussian profile to the Balmer emission lines, He i (4471 Å), and the three Fe ii emission lines. While these lines are clearly multicomponent, a single Gaussian provided a "barycenter" measurement for each line, and is a common technique used for complex emission lines. However, it is apparent that at some phases (see Figure 5), a single Gaussian did not provide a consistent line center measurement. The Hγ and Hδ lines are highly contaminated by the underlying, moving white dwarf absorption features (as shown in Mennickent & Tappert 2006). The two bluest Fe ii lines are blended with He i, and thus show a messy velocity curve, while the reddest Fe ii line was too close to the detector edge for reliable line fitting. He i velocities were phased on the orbital period but were offset from the Balmer lines by +0.3 in phase, presumably a hot spot bias effect. Hδ and Hγ line measurements suffered from local continuum changes due to the broad white dwarf absorption, although they agree in phase and amplitude with our Hβ measurements. Hβ suffers a bit from the underlying absorption as well, but provided our most reliable velocity solution. Hα, as used by Thorstensen & Taylor (1997), is likely to be the best Balmer line to use as it will be the least affected by the broad white dwarf absorption lines.

We phased our velocities using the period and ephemeris provided in Thorstensen & Taylor (1997) based on their fitting of the Hα emission line. Sine curve fits to the velocity curve for the Hβ emission line yielded K1 = 44 ± 8 km s-1. With only 14 points covering the orbit, the variable absorption from the white dwarf, and the strong hot spot velocity deviations near phases 0.25 and 0.75, the fit was not optimally constrained and is inferior to the Hα fit (K1 = 49 ± 4 km s-1) in Thorstensen & Taylor. However, the location of phase zero and the K1 amplitude are consistent with their analysis.

Measuring Vd sini (defined as the half width at zero intensity) for the emission lines we get a mean value of 940 ± 20 km s-1, a value in agreement with the UV spectral analysis presented in Sion et al. (2003). Using the technique first put forward by Warner (1973; but see Shafter 1983) we can estimate q with

Equation (1)

where

Equation (2)

is from Silber (1992), valid over the range 0.04 ⩽ q ⩽ 1. Using K1 = 49 ± 4 km s-1 and Vd sini = 940 ± 20 km s-1, we find 0.048 ⩽ q ⩽ 0.058. This is lower than the value preferred by Augusteijn (1994) where an inclination of 30° ⩽ i ⩽ 40° was estimated. If the limits on the inclination inferred by Thorstensen (2003) are used (63 ± 13), the values for q found by Augusteijn drop to the range 0.054 ⩽ q ⩽ 0.078. Taking the white dwarf mass to be 0.55 ± 0.2 M (Urban & Sion 2006) with our derived limits on q, leads to a secondary star mass in the range 0.017 ⩽ M2 ⩽ 0.044 M, below the stellar/substellar boundary if the donor is of normal composition. Using the most extreme value for q from Augusteijn, and MWD = 0.75 M, puts the secondary star mass right at the stellar/substellar boundary. Even given the uncertainties inherent in this analysis, the secondary star in VY Aqr clearly appears to be of very low mass.

5. LIGHT CURVE MODELING: VY AQR

The phase-resolved infrared light curves of VY Aqr are presented in Figure 6, along with the (JK) color evolution over an orbit. The light curves appear to be dominated by ellipsoidal variations, except for a small flux enhancement in the J band between 0.25 ⩽ ϕ ⩽ 0.5. There is no evidence for strong irradiation of the secondary, which would be expected to be greatest (bluest) near phase 0.5. With 〈(JK)〉 = 0.9, the color of VY Aqr is consistent with an M4V, but only 0.06 mag redder than an M0V. An M9V is significantly redder with (JK) = 1.18.

Figure 6.

Figure 6. Phase resolved JHK light curves for VY Aqr, and the change in the (JK) color over the orbit (solid circles, the data have been repeated in all of the light curve plots for clarity). In the top three panels, the green curve is the light curve model assuming an M6 secondary star with an inclination angle of 35°, while the blue curve is a model with i = 52°, but with a contaminating source that provides 30% of the total flux in the K band, 15% in the H band, and no contamination in the J band. In the bottom panel, the blue dashed line represents the color of an M0V, and the red line an M6V.

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Clearly, the secondary star is an important source of flux at near-infrared wavelengths. The question is, how much contamination from the accretion disk is present to dilute these ellipsoidal variations? As noted earlier, the K-band spectrum obtained with NIRSPEC is most consistent with an M0 spectral type, while the VLT data suggest a much later spectral type. As we have shown, spectral types of M6 or earlier are consistent with very little accretion disk contamination. But given that there are strong emission lines from both He i and H i in the spectra of VY Aqr, and the optical spectrum is dominated by disk emission, there must be some disk contamination.

Thorstensen (2003) gives a distance for VY Aqr of 97+15-12 pc, and using the mean value from our K-band light curve, implies an absolute magnitude of MK = 9.4 ± 0.3. An M6V star at that distance would have an apparent magnitude of mK = 14.2 in good agreement with what is observed. A main sequence M9V at the distance of VY Aqr would have mK = 15.2. Obviously, a normal M0 dwarf would be much too luminous to explain the observations, so such an object cannot be on, or near the main sequence. We use these values, and those gleaned above, as limits on the nature of the secondary for modeling the light curves of VY Aqr.

In the following we use Phoebe,12 a graphically driven and enhanced implementation of the Wilson–Divinney light curve modeling code to model the JHK light curves of VY Aqr. Thorstensen (2003) notes that the double peaked emission lines and lack of eclipses indicate an orbital inclination between 50° ⩽ i ⩽ 75°. For the initial set-up, we included a white dwarf primary with Teff = 13,500 K (Urban & Sion 2006). As noted above, those authors also estimate a mass for the white dwarf of 0.55 ± 0.2 M from the IUE observations, substantially lower than the 0.8 M found in the Sion et al. (2003) determination which was obtained without the constraint imposed by the parallax. We set the gravity of the primary to be logg = 8.0 for all models. We use the mean value of the mass ratio (〈q〉 = 0.053) derived above, and assume a contact binary, where the secondary fills its Roche lobe. We also input the square root limb darkening coefficients as tabulated by Claret (1998). Other modeling parameters, such as albedos, and the gravity darkening (and white dwarf limb darkening) coefficients assumed a radiative primary star, and a convective secondary star (see Lucy 1967; Van Hamme 1993; and Claret 2000). Since there is uncertainty in the true nature of the secondary star and the level of disk contamination, we explore ellipsoidal models for M0, M6, and M9 secondary stars.

5.1. Light Curve Models with M6 and M9 Secondary Stars

As noted above, a normal M6 dwarf at the distance of VY Aqr supplies ∼100% of the observed flux. Using the appropriate parameters for an M6V without any additional sources of contamination, we find that there is only one solution, shown in Figure 6 (plotted in green), that fits the data: an orbital inclination angle of 35°. The minima at phase 0.5 in the light curves for this model are slightly too shallow due to reflection (see below). The total absolute K magnitude predicted by Phoebe (after applying bolometric corrections) is MK = 9.7, slightly fainter than the observed value. As noted above, it is believed that the orbital inclination is in excess of 50°, thus this model is ruled out. Larger inclination angles result in larger amplitude variations than are observed, requiring a source of dilution. If we include a "third light" component (i.e., the nonstellar contribution to the system luminosity), we can fit the data with an orbital inclination of 65° if the contaminating source is 15% of the flux in J, 40% in H, and 65% in K. With this level of contamination, Phoebe predicts a total absolute magnitude of MK = 9.1, slightly more luminous than observed (but allowed by the error on the parallax). The best fitting model (blue curves in Figure 6) that exactly reproduces the observed luminosity has i = 52.0°, and has a contamination in the K band of 30%. Note that even though this model fits the data quite well, the radius of the secondary star is 0.1 R, and it has a mass of 0.03 M. This is not a normal M6 dwarf.

There are two issues with using an M9 secondary star. The main difficulty is that with a 13,500 K white dwarf, the reflection is so strong that the minima at phase 0.5 are extremely shallow (see Figure 7) in all configurations. In close binaries such an effect is due to the combination of irradiation and reflection. Barman et al. (2004) show that significant irradiation in these type systems only occurs for TWD ⩾ 20,000 K. The affect here is due to reflected light. Because of its low luminosity, the flux intercepted by the secondary star is a considerable fraction of the locally emitted flux. There are two ways to reduce the reflected flux, lowering the secondary star's albedo, or having a lower luminosity (lower temperature) white dwarf resulting in a smaller incident flux. One could also postulate that the secondary star is shielded from the white dwarf's illumination by the accretion disk, and thus does not see the full intensity of the white dwarf. This would require an optically thick disk in quiescence, something that is not expected. We find that we can get equal depth minima with an extremely low albedo: ⩽ 5% (lower than that of the Earth's moon!). Alternatively, we can achieve equal depth minima at phases 0 and 0.5 if the white dwarf has a temperature of 7500 K, or lower. Neither of these solutions is appealing.

Figure 7.

Figure 7. Light curve models for VY Aqr, assuming an M9 secondary star. This model has i = 75°, a 30% contamination in the K band, 15% in the H band, and no contamination in the J band. The minimum at superior conjunction (phase 0.5) is very shallow due to the reflection of flux from the primary star by the secondary star.

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The second issue is the total luminosity of the system: with an M9V secondary, a very large third light component (130%) is required to match the observations. Even with an inclination angle of 75°, this level of contamination dilutes the ellipsoidal variations too much, and we are unable to match the observations. To achieve a reasonable fit to both the light curves and the absolute K magnitude requires us to relax one or more of our input parameters. For example, if we increase the mass ratio to q = 0.3 (to get a physically larger secondary star), set i = 30°, and no contamination, we achieve a model that has the correct peak-to-peak amplitude and the observed luminosity. There is a range of models near this solution where q, i and the contamination levels can be played off of each other that will produce equally good models. But such values for q and i are well outside of the bounds derived for this object and none of them reproduce the observed minima at phase 0.5. The best fitting model, with our standard input parameters is shown in Figure 7, and has i = 75° while requiring a 30% contamination in K, 15% in H, and no contamination in J. This model produces a system that is nearly a magnitude too faint with MK = 10.2.

5.2. Light Curve Models with an Undersized M0 Secondary Star

A main sequence M0V star has a mass of ∼0.5 M and a radius of ∼0.60 R. Such an object is physically too large by a factor of ∼4 to fit within the orbit required at Porb = 1.51 hr (assuming M1 = 0.55 M). For our models, we fixed the temperatures of the primary and secondaries to 13,500 and 4,000 K, respectively, and attempted to find a best-fit model. Like the results for the M6V model, there is one solution with no contamination that explains the light curves and it has i = 35°. This model results in a system with MK = 9.2, similar to what is observed. Unlike the cooler secondary star models, however, both minima in this model have the proper depths. To get a model with i ⩾ 50° requires contamination, and thus the total system luminosity will be much too high using our fixed input parameters. For such a model to work requires a more compact binary, and therefore a smaller white dwarf mass (while maintaining logg = 8.0). Our final model, shown in Figure 8, has i = 50°, MWD = 0.32 M, M2 = 0.017, and has equal levels of contamination (50%) in the J, H, and K bands.

Figure 8.

Figure 8. Light curve models for VY Aqr, assuming a secondary star with a temperature of 4000 K (M0). This model has i = 50°, and 50% contaminations in the J, H, and K bands.

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While this is an extremely odd binary, it results in a better fit to the minima in the observed light curves than secondaries of later spectral type, while explaining the Keck K-band spectrum. It contains significant levels of contamination, consistent with the evidence for the disk emission noted above. The model contaminating source has a flat spectrum, as one might expect from optically thin free–free emission. Note that this is the only model for which we found identical levels of contamination in the JHK bands, and thus there is little alteration in the underlying infrared colors of the secondary star.

6. LIGHT CURVE MODELING: EI Psc

There is less uncertainty about the apparent spectral type of the secondary in EI Psc–it is clearly a mid-K star. The detection of this object in an optical spectrum, and the presence of classic ellipsoidal variations in unfiltered visual photometry, both suggest a very low contamination level. Thorstensen et al. (2002) estimate a mass ratio of q = 0.185 from the superhump period excess, and with M1 = 0.7 M, this implies M2 = 0.13 M. They also estimate that the orbital inclination is 47°, and that the radius of the secondary is R2 = 0.124(M1/0.7 M). Thorstensen et al. infer that the absolute magnitude for the secondary is MV = 10.4 ± 0.7, and use this to estimate a distance of 210 (+110/− 70) pc. We use these values and the albedoes, limb and gravity darkening for a main sequence K5V star as starting points for our light curve models.

If we assume that MV = 10.4, then MBol ≈ 9.9. As noted above, Phoebe calculates MBol for both stellar components. If we assume no contamination in the K band, the light curve model with the input parameters listed above requires i = 55°. But the light curve amplitudes for this model in g, I, and J are a little too large, requiring a contamination of 40% in each bandpass (no contamination in H or K). In addition, the reflection effect at phase 0.5 is too strong in the g and I bands, causing the models to have minima that are too shallow at superior conjunction. We had to reduce the secondary star albedo by 40% to get the light curve models in g and I to match the data. We have no explanation for this result, but given the peculiar nature of this secondary star, it is probably invalid to expect it to have the same albedoes and limb darkening coefficients as a main sequence star. Alternatively, the accretion disk could be slightly more efficient in shielding the secondary star from the flux of the primary in the g and I bands. The final model, shown in Figure 9, has M2 = 0.13 M, R2 = 0.12 R, and MBol = 10.4. The secondary is slightly less luminous than the counterpart proposed by Thorstensen et al. and therefore closer, d = 150 pc, but this remains within the error bars on their distance estimate.

Figure 9.

Figure 9. Light curve models (green lines) for EI Psc, assuming a secondary star with a temperature of a K4 star. These models have i = 55°, and 40% contamination in the g, I and J bands (no contamination in H and K bands). The top panel shows the g-band (blue) and I-band (red) data. The green line in this panel is the g-band model, while the black dashed line is the I-band model. The bottom panel shows how the (JK) color changes over an orbit. The dashed line below the data represents the (JK) color of a K0V star, while the upper dashed line is the color of a K5V.

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7. DISCUSSION

We have confirmed the surprising K4 ± 2 spectral type found by Thorstensen et al. (2002) for EI Psc. Not only does the spectrum resemble a K-type dwarf, but the infrared light curves appear to be consistent with those expected for ellipsoidal variations from such an object. To have a hot secondary star in such a short-period system is remarkable. Thorstensen et al. note that such an object can be explained using the models of Baraffe & Kolb (2000) in which the secondary star has evolved well off of the zero-age main sequence before becoming a contact binary. Such objects end up with a depletion of hydrogen in their cores and are able to evolve to very short period, while maintaining high effective temperatures. As noted by Thorstensen et al., these secondary stars should show extreme deficits of C, normal levels of O, and enrichments of N due to the CNO process. The apparent absence of CO features in our K-band spectrum is consistent with this scenario. This is basically the same conclusion reached by Harrison et al. (2004, 2005b) to explain the lack of 12CO absorption, and the presence of enhanced 13CO absorption, for nonmagnetic CVs above the period gap.

Our results for VY Aqr are confusing. The expectation was that its secondary star should have a spectral type near mid-M, and this is consistent with the spectral type we feel best matches the VLT data set. But the object visible in the Keck spectrum of VY Aqr is much hotter. It is impossible to conclusively determine the spectral type of the secondary star in VY Aqr using the current data set without relaxation of certain assumptions about the binary system. The light curve modeling and the VLT data set would be consistent with a relatively normal M6 dwarf if we could ignore the orbital inclination constraint and assume that there is no significant contribution from the accretion disk. The current orbital inclination limits rest on the observation of double-peaked emission line profiles. It is hard to envision how one could distribute material around the primary in such a fashion to mimic a disk-like line profile, and not be a disk. Even if we overlook this discrepancy, we must still confront the presence of a much hotter companion star in our Keck data. It might be tempting to suggest that irradiation heats one face of the secondary to produce the M0 spectral type, and at other orbital phases it looks like an M6 star. But such a large change due to irradiation seems implausible, and there is no evidence for this type of variability in the infrared colors.

The second interesting issue is the obvious difference in the H i Brackett γ emission features between the two spectra, and what this may imply about the accretion disk contamination. When observed at Keck, the H i emission line is weaker than that in the VLT spectrum, suggesting less accretion disk activity. This is supported by the clear detection of atomic absorption features throughout the K band in those data. Meanwhile the VLT spectrum has no detectable absorption features besides that tentatively associated with water vapor. While the S/N of the Keck data is superior, the strong Na i doublet at 2.2 μm should probably have been visible in the VLT spectrum. Even more surprising, however, is the complete lack of evidence in the VLT spectrum for the strong Ca i absorption features found just blueward of 2.0 μm. In Harrison et al. (2005b) we presented spectra of a number of longer period CVs where these were the only clearly detected secondary star absorption lines. It seems peculiar to us that the rather shallow water vapor features are easily seen in the VLT spectrum, but that none of the strong, narrower atomic features are evident. This implies significant contamination from the accretion component, in agreement with that demanded by light curve models with i⩾ 50°. But such models produce a system that is much too luminous without making the secondary star much smaller than a normal main sequence M6 dwarf.

The alternative to this is to assume that the secondary star in VY Aqr does have a spectral type near M0, and is of very low mass. Such an object best explains the observed light curves and the Keck spectrum, and has the required flat contaminating source. Such an object is also not grossly inconsistent with either the J- or H-band spectra. But it cannot explain the VLT K-band spectrum without adding another component, such as a cool blackbody-like source. Such a source is necessary to produce both the continuum shape and the infrared "excess" (see Figure 2). This blackbody would also supply sufficient diluting flux to explain the absence of atomic absorption features in this spectrum. But for this to be viable requires a transient source that was only present during the VLT observations, a rather contrived scenario.

Even with the spectral type confusion, there is one conclusion that is clear: the CO features in VY Aqr are much weaker than expected if the secondary star was truly an M dwarf. There is no hint of the CO features in the Keck data, even though the redder Na i doublet is detected. EI Psc and VY Aqr join GK Per and AE Aqr (see Harrison et al. 2005a) as the only CVs we have observed where these features should have been detected, but were not. One could postulate that these CO absorption features are filled-in by CO emission, as CO emission has been detected in the short-period system WZ Sge (see Howell et al. 2004). But if this CO emission resides in the disk, as appears to be the case in WZ Sge, then its profile will be much broader than the underlying stellar absorption features. If they are to be of similar strength, as required under this conjecture, than the emission features would have absorption cores. Since we have never seen any evidence for CO emission in a CV other than WZ Sge (and its secondary star eludes detection), we cannot demonstrate the exact line profiles one would observe, but we can present an analog: narrow H i absorption lines on top of H i emission lines. In Figure 10, we present high resolution spectra of GK Per and SS Cyg centered on the Br γ region along with those for three late-type templates. As we have shown elsewhere (Harrison et al. 2005a, 2005b), the K-type secondary stars in GK Per and SS Cyg dominate their K-band spectra. The three absorption features redward of Br γ in the template star spectra are due to Si i (2.1785 and 2.1825 μm) and Ti i (2.1789). As is clear from the location of the Si i and Ti i lines, the central dips in the H i emission line profiles for GK Per and SS Cyg are due to the underlying secondary star. This difference in line width will always be true for an emission line that originates in the disk of a CV, as it suffers a much greater velocity broadening than the underlying absorption features from the more slowly moving secondary star.

Figure 10.

Figure 10. High-resolution infrared spectra, centered near H i Brackett γ, of the long period cataclysmic variables GK Per and SS Cyg compared with the spectra of three late-type stars. The locations of the absorption lines noted in the text have been aligned to show that the origin of the dip in the H i emission line profiles are due to the underlying secondary star. These data were obtained using NIRSPEC in high-resolution mode (R≈ 25,000; T. E. Harrison et al. 2009, in preparation).

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8. CONCLUSIONS

We have obtained new K-band spectra of VY Aqr and EI Psc along with phase resolved infrared light curves. The spectrum of EI Psc is clearly much hotter than would be expected for a CV with a period this short. The nature of the secondary star in VY Aqr, however, is less clear. If we ignore the inclination constraint, then a relatively normal M6 dwarf can simultaneously explain the light curves and the VLT spectra. It cannot, however, explain our higher S/N Keck observations. For an M6 to be consistent with that spectrum requires an enhanced calcium abundance, and a level of disk contamination at the time of those observations that would both hide the water vapor absorption, and generate an M0 continuum. Clearly, VY Aqr would benefit from higher S/N infrared spectroscopic observations around a full orbit to ascertain if spectral type changes do occur. Such observations would also allow a more in-depth abundance analysis, and the possibility of obtaining a radial velocity curve that could help constrain its mass. It is rare for the secondary stars of short-period CVs to be so easily detected, and both of these binaries are well within the reach of existing instrumentation.

Some of the data presented herein were obtained at the W.M. Keck Observatory (proposal no. U010NS), which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

Footnotes

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10.1088/0004-6256/137/4/4061