PTF1 J071912.13+485834.0: AN OUTBURSTING AM CVn SYSTEM DISCOVERED BY A SYNOPTIC SURVEY

Palomar 60 inch data were de-biased and flat-fielded using the P60 pipeline (Cenko et al. 2006). The FTN data were processed using the LCOGT pipeline. The BOS data were de-biased and flat-fielded using IRAF tasks, astrometrically calibrated using Astrometry.net (Lang et al. 2010), and cosmic rays were removed using the L.A. Cosmic algorithm (van Dokkum 2001). The Sextractor package (Bertin & Arnouts 1996) was used to identify sources in each exposure and their instrumental magnitudes were obtained using optimal point-spread function photometry (Naylor 1998) as implemented by the Starlink¹⁴ package autophotom.

Light curves were calculated using a matrix-based, least-squares minimization, relative photometry algorithm. The primary goal of any such algorithm is to minimize noise, typically by assuming certain stars in the field are non-variable and identifying an optimal zero point for each exposure. We expanded on this to simultaneously solve for both the zero point and additional de-trending terms that corrected for airmass and instrument changes. The algorithm is similar to that developed in Honeycutt (1992) and is described in the Appendix of Ofek et al. (2011).

To accomplish the de-trending, we modeled each observation as

$$m_{i,j}=\overline{M}_{j}+Z_{i}+\alpha c_{j}A_{i}+\sum _{k=1}^{n_k}\beta _{k}c_{j},$$

where the data needed are as follows.

• 1.  
  m_{i, j}: the magnitude of source j on exposure i.
• 2.  
  c_j: a color for each source. The color is required to compensate for the stronger effects of airmass on blue stars, as well as the differences in CCD efficiency over a range of wavelengths. For our light curves, we used c_j = g'_j − r'_j, where g'_j and r'_j refer to the magnitudes of the jth source in the respective SDSS filters.
• 3.  
  A_i: the airmass of each exposure.

The terms to be fitted are as follows.

• 1.  
  Z_i: the optimal zero-point term of each exposure.
• 2.  
  $\overline{M}_{j}$: the mean magnitude term of the source.
• 3.  
  α: the airmass calibration coefficient for all exposures and sources.
• 4.  
  β_k: the kth telescope/instrument calibration coefficient, for k = 1, 2, ..., n_k where n_k is the number of telescopes. This term is introduced to take into account the different responses of each telescope/instrument. For light curves with data from only one instrument, these terms were not used.

It is important to ensure that all stars used for the solution (calibration stars) are themselves not variable. We restricted the stars used to those found in 80%–100% of exposures, depending on the light curve, and iteratively removed any sources with high residuals. Since the solution is not unique unless reference magnitudes are provided, we used blue magnitudes from USNO-B 1.0.

This algorithm provided very good results—even light curves taken over months with different telescopes and conditions obtained a magnitude scatter (rms) of ∼0.035 mag for g' ≈ 16 and ∼0.055 mag for g' ≈ 19.4, the quiescent magnitude of PTF1J0719+4858. The rms errors provided with the figures in this paper are based on the median scatter of other stars with similar magnitude present in at least 50% of observations. Additionally, individual errors—the combination of the Poisson error and the fit errors—are provided for some of the light curves. These are typically very close to the magnitude scatter, except for those exposures obtained during bad weather.

For high-cadence light curves, period analysis was performed with SigSpec (Reegen 2007). All default options were used, except as noted for individual cases, and weights for measurements were always provided. SigSpec produces a list of significant periods and corresponding "sig" values. A "sig" value of c means that the period has a chance of 1 in 10^c of being noise.

The long-term light curve of PTF1J0719+4858 from FTN and P60 is presented in Figure 2. We note the pattern of "high" states and "quiescent" states. Additionally, we note the presence of "normal" outbursts (as opposed to the "super-outbursts" more commonly associated with AM CVn systems).

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We observed the 2011 January super-outburst in its entirety and find a rise time from the last measurement in quiescence to the peak magnitude of 3.2 days with Δmag = 3.6. Immediately following this rise, we see a drop to a plateau that may be the cycling state seen in other AM CVn systems (e.g., Patterson et al. 2000). Finally, 22 days after the beginning of the super-outburst, PTF1J0719+4858 returned to quiescence.

The recurrence time was significantly different between the two super-cycles we observed. We approximate (assuming the behavior of the super-outburst itself is the same) that the recurrence time from the first super-outburst to the second was 65 days. However, the recurrence time from the second super-outburst to the third is greater than 78 days (this uncertainty is due to weather impacting our observations).

Between super-outbursts, we observed normal outbursts in PTF1J0719+4858, which have also been identified in CR Boo (Kato et al. 2000). After initially observing single data points indicating a sudden jump in luminosity, we successfully predicted the 2011 January 29 outburst and obtained a total of 41 exposures, of which 12 are from BOS and are not included in the long-term light curve. The light curve of this outburst is presented in Figure 3. During this normal outburst, PTF1J0719+4858 experienced a luminosity increase of 2.5 mag over 7 hr from the last observation at g' > 19.4 to the brightest point measured. If we consider only the increase from g' > 19 we find an increase of 2.1 mag over only 4 hr.

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The recurrence time of the normal outbursts was stable throughout the first super-cycle. We observed three normal outbursts with a recurrence time of ∼10.5 days. This most likely represents all the normal outbursts in this super-cycle, due to our almost daily coverage. The delay between the end of the second super-cycle and the first normal outburst was the same as that in the first super-cycle. However, it appears that the normal outburst recurrence time was significantly different in the second super-cycle, likely associated with the longer recurrence time of the super-outburst. Given our poor coverage (as a result of weather), we cannot make any statements about these differences.

Short-term photometric variability was detected in several high-cadence observations of PTF1J0719+4858 (see Table 1 and labels in Figure 2).

During the first super-outburst (labeled HC1), we detected photometric variability of Δmag ≈ 0.1 (see Figure 4) with a shape consistent with that of superhumps in other AM CVn systems (e.g., Patterson et al. 1997; Wood et al. 2002). Analysis of the period using a Lomb–Scargle periodogram suggests it is ∼27 minutes, while a SigSpec analysis found a period of ∼26 minutes. Given that we observed only two cycles, we cannot state a more accurate superhump period.

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A second set of high-cadence observations (labeled HC2) was obtained almost immediately after PTF1J0719+4858 returned to quiescence following the first observed super-outburst. Here, we see photometric variability of Δmag ≈ 0.2. We performed a SigSpec analysis of the light curve for these two nights with the AntiAIC anti-aliasing feature enabled and found a period of 1606.3 ± 2.5 s with a "sig" of 13.7. Since we observed many periods of this variability, we present a phase-binned light curve in Figure 5. Additional observations that allow a more precise determination of the superhump period could be used along with the quiescent photometric period to determine a mass ratio (Patterson et al. 2005).

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We also obtained a set of high-cadence observations (labeled HC3) coincident with our phase-resolved spectroscopy at Keck-I (see Section 4.2). These observations also showed photometric variability, with Δmag ≈ 0.06. PTF1J0719+4858 was in quiescence at the time of the observations. A SigSpec analysis identified a period of 1550 s with a sig of 3.1. Given the short observation time and the low significance, we folded the light curve at both this period and the spectroscopic period obtained in Section 4.2. These produced similar results and, thus, we believe that the true period is that obtained via phase-resolved spectroscopy. We discuss the simultaneous photometry and spectroscopy in Section 5.2.

The identification spectra were reduced as part of the PTF spectroscopic program using standard IRAF tasks. We present a typical outburst spectrum—taken with WHT/ACAM (Benn et al. 2008) on 2010 November 6 and labeled as OS in Figure 2—in Figure 6 with the prominent lines identified. The outburst spectra varied slightly, with absorption lines being more prominent on some than on others. However, He i λ4471 was always visible. The best spectrum in quiescence is the co-added spectrum of the phase-resolved observations, shown in Figure 7, again with lines identified.

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The quiescence spectrum features very broad, double-peaked emission lines, some with a possible central spike. Shortward of 4000 Å, the spectrum shows an interplay of lines that is consistent with Ca ii H and K emission interwoven with He i λ3888 (see Roelofs et al. 2006a), but the low resolution of the current observation and the broadness of the lines make their presence difficult to establish. We can establish the presence of Fe ii, Si, and N i emission lines in the rest of the spectrum. It is also possible that He ii λ4200 is seen in the spectrum, albeit very weak. He ii λ4200 has not been previously seen in an AM CVn system. In the outburst spectrum, we see weak absorption lines of He i and He ii, as well as Fe ii. Si is not seen, but we note the presence of N i λ8223, which has not been seen this strong in other high-state AM CVn systems.

Table 2 lists the equivalent widths of the most prominent emission lines. Based on the presence of the noted elements, we find that the spectra of PTF1J0719+4858 are most similar to those of 2003aw (Roelofs et al. 2006a) and SDSSJ0804+1616 (Roelofs et al. 2009). Future work in identifying abundances may shed light on the chemical composition and evolutionary history of such systems (Nelemans et al. 2010).

Here, we discuss the phase-resolved spectroscopy undertaken at the Keck Observatory (see Table 3). The spectra were reduced using optimal extraction (Horne 1986) as implemented in the Pamela code (Marsh 1989) as well as the Starlink packages kappa, figaro, and convert. For these exposures, wavelength calibration exposures were taken at the beginning, middle, and end of each set of observations using the Hg, Cd, and Zn lamps for the blue CCD and the Ne and Ar lamps for the red CCD. Wavelength calibration for individual spectra was interpolated between these calibration spectra. We present a co-added spectrum in Figure 7.

We use a technique similar to previous analyses of AM CVn system phase-resolved spectra, first developed by Nather et al. (1981), to establish the orbital period. Each spectrum was re-binned to the same wavelengths and the locations of individual emission lines were identified. Because of the large number of cosmic rays on the red side despite processing with L.A. Cosmic (van Dokkum 2001), we concentrated on the blue side and used the helium lines at 4026 Å, 4387 Å, 4471 Å, 4686 Å, 4921 Å, and 5015 Å. The lines from each exposure were re-binned and co-added to produce a summed He emission line. We then subtracted the red 40% of the line from the blue 40% of the line, and divided by the continuum. This produced a time series of flux ratios, which we analyzed using SigSpec. We identified a period of 1606.2 ± 0.9 s with a "sig" of 3.1. The statistical significance spectrum is in Figure 8.

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While not a very high confidence level, we believe the above period is, in fact, the orbital period, for two reasons. First, the period found is within the error bars of the previously discussed quiescent photometric period (see Section 3.3). Second, the movement of the disk's hot spot can be identified by creating a phase-binned, trailed spectrum of the He emission line. The rotation of the disk produces an "S-wave" that has been observed previously in known systems (e.g., Roelofs et al. 2005; Rau et al. 2010). In the case of PTF1J0719+4858, this S-wave is very weak, but still discernible. We present the trailed spectrum in Figure 9. This is not the first system where the S-wave was difficult to detect. As reported in Roelofs et al. (2009), an S-wave in SDSSJ0804+1616 was not found in one of two sets of spectra. Further observations are required to establish whether PTF1J0719+4858 has similar variability in the strength of the S-wave or if it is simply a weak feature.

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We broadly group the known outbursting AM CVn systems into two categories: those having super-outbursts that occur at least every three months and those with less frequent super-outbursts. The latter group has either poorly determined or undetermined recurrence times. We summarize their properties in Table 4.

It appears that these sources can be cleanly divided by orbital period, with the break between 1606 s and 1699 s. For the first group, the recurrence times are fairly well determined and appear to correlate with the orbital period. The second group is more difficult to understand, primarily due to a lack of known recurrence times. The one published recurrence time, for SDSSJ0926, is very poorly determined (Copperwheat et al. 2011). However, there does appear to be a clear gap between the determined recurrence times of PTF1J0719+4858 and the much more poorly determined recurrence time of SDSSJ0926+3624, and we question whether this difference in recurrence time is purely a result of the increased orbital period (and thus decreased mass-transfer rates) or if different parameters also place a role (such as the mass of the primary and/or the entropy of the secondary).

We can draw parallels to the much more common CVs. The class of CVs most like outbursting AM CVn systems are the SU UMa-type CVs, which also exhibit both normal outbursts and super-outbursts with superhumps (Warner 1995). SU UMa-type systems typically have super-outburst recurrence times of several hundred days and orbital periods between 90 and 120 minutes (Osaki 1996), but have been found to have two extreme cases. The ER UMa-type systems have recurrence times between 19 and 45 days (Buat-Ménard & Hameury 2002), while WZ Sge-type systems have recurrence times of decades and lower orbital periods of 80–90 minutes. The long recurrence times of WZ Sge-type systems are explained by the lower mass-transfer rates of WZ Sge-type systems, as a result of their more evolved state (CVs are believed to have negative $\dot{P}$, as opposed to AM CVn systems; Osaki 1996).

In Kato et al. (2000), CR Boo was proposed to be the helium equivalent of an ER UMa-type CV. However, given that all four of the frequently outbursting systems appear to have fairly similar behavior, we believe that this is typical behavior for AM CVn systems with these orbital periods, as opposed to an extreme case. On the other hand, the recurrence times of the longer period outbursting AM CVn systems indicate that these systems are more akin to the WZ Sge-type CVs. This is consistent with the assumption that AM CVn systems have positive $\dot{P}$ and thus have lower mass transfer with greater orbital periods. Additional discoveries of AM CVn systems, as well as better, more systematic observations of known systems, are necessary to understand the reality of the difference in recurrence times.

The high-cadence photometric observations discussed in Section 3.3 and labeled as HC3 were coincident with the phase-resolved spectroscopy discussed in Section 4.2, providing us with an opportunity to determine the source of the observed photometric variability. We present a binned, phase-folded photometric light curve in Figure 10, together with the radial velocity of the hot spot. The binning provides an increase in the signal-to-noise and gives a roughly 5σ detection. We remind the reader that HC3 was observed in quiescence, during which time superhumps are not believed to occur in either AM CVn systems or CVs.

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The increase in brightness immediately follows the blueshifted portion of the radial velocity curve and is coincident with a lack of radial velocity. This indicates that the photometric variability in PTF1J0719+4858 is caused by the hot spot and the associated heated edge of the disk being closest to the observer (see drawings in Figure 10). We assume here that the S-wave is, in fact, caused by the hot spot.

AM CVn system variability in quiescence has been observed for other non-eclipsing systems such as CR Boo (Provencal et al. 1997) and KL Dra (Wood et al. 2002), but no study has been done of the origin. However, such studies for CVs have linked the hot spot to the observed photometric variability (e.g., Schoembs & Hartmann 1983).

The concern with this explanation is the lack of precision in the photometric data and the lack of time resolution as a result of the binning. This also makes it difficult to compare Figure 10 to observations of other AM CVn systems or CVs. However, we believe that there is sufficient data to link the quiescent variability to the location of the hot spot relative to the observer.

How many additional AM CVn systems might be discovered by PTF? First, we estimate the fraction of all AM CVn systems that are outbursting. Consider a simple model of a single system's evolution by assuming that gravitational wave radiation and angular momentum loss from mass transfer are solely responsible for the evolution of the orbital period (Paczyński 1967; Nelemans et al. 2001). Then, using typical mass values for an AM CVn system at its minimum period (0.6 M_☉ and 0.25M_☉, although similar values do not significantly affect the results) we find that an AM CVn system spends ∼0.5% of its life between orbital periods of 20 and 27 minutes (the frequent outbursters) and ∼3.3% of its life between orbital periods of 27 and 40 minutes (the less frequent outbursters). We use these numbers as a simple estimate of the percentage of AM CVn systems that are outbursting.

We now estimate the number of systems PTF could discover. Given that AM CVn systems have outbursts with Δmag ≳ 3, we conservatively assume that any outbursting system with a quiescent magnitude of ≲ 23 can be detected in outburst by PTF. We assume a scale height of 300 pc (Roelofs et al. 2007b) and a scale length of 2.5 kpc (Sackett 1997) in the Galaxy and an AM CVn system space density of ρ_o = 3.1 × 10⁻⁶ pc⁻³ (the observed space density based on pessimistic population models from Roelofs et al. 2007b). Given that the systems are in quiescence, we further assume that the accretor provides all of the system's luminosity, and use Equation (5) from Roelofs et al. (2007b), which is a parameterization of Figure 2 in Bildsten et al. (2006), to calculate the absolute magnitudes of the AM CVn systems. This likely means that our estimate is conservative since the disk is known to provide part of the luminosity (∼30% for SDSSJ0926+3624; see Marsh et al. 2007) in quiescence. We find that there are approximately $\frac{1.3\;{\rm systems}}{100\,\deg ^{2}}$ with orbital periods between 20 and 40 minutes and at 20° < |b| < 60° (the galactic latitudes for most of PTF's observations). Given PTF's footprint of 10,000$\,\deg ^{2}$, we estimate that PTF might detect up to 136 such systems. However, the uncertainty in the AM CVn system population density estimates likely means that this number is only accurate to within a factor of 10.

However, the apparent long outburst recurrence times of longer period systems will make these much more difficult to detect. If we consider only those systems with frequent outbursts and thus orbital periods between 20 and 27 minutes, we find that there are up to 18 such systems. Given the recurrence times of 45–80 days, the presence of normal outbursts in at least two systems, and the super-outburst duty cycle of 30%–50%, it is very likely that all 18 systems can be detected as part of the PTF transient search.

We note that searches in lower galactic latitudes make detection much more likely. The population distribution of outbursting AM CVn systems almost doubles between 20° < |b| < 25° and 15° < |b| < 20°. Although the analysis of lower-latitude data is more difficult due to the larger number of sources overall, it still presents the best opportunity to discover a large number of AM CVn systems.

Despite the exciting possibilities of using synoptic surveys to search for outbursting systems with quiescent magnitudes up to R ∼ 23–25 (and even deeper for future surveys), we caution that confirmation of these systems will be difficult. The established method for finding orbital periods is via phase-resolved spectroscopy, requiring large telescopes and short exposure times for even fairly bright objects. Even objects with a quiescent magnitude of R ∼ 23 cannot be observed in such a fashion with today's telescopes. Instead, such systems can be observed in outburst. The hot spot has been observed in high-state AM CVn systems (Roelofs et al. 2006b) and it is likely that it can be seen in the high state of outbursting systems as well. Additionally, as demonstrated with PTF1J0719+4858 and other AM CVn systems, photometric periods can be obtained from both superhumps and (potentially) in quiescence, providing a good estimate of the orbital period.