DASCH DISCOVERY OF A POSSIBLE NOVA-LIKE OUTBURST IN A PECULIAR SYMBIOTIC BINARY

J0757 was measured on 694 plates near the M44 field noted by its peculiar long-term variability. These plates cover 5°–25°on a side with typical limiting magnitudes B  ∼  14–15 mag, and most of them are blue sensitive emulsions. We used the GSC 2.3.2 catalog (Lasker et al. 1990) for photometric calibration, and our typical uncertainty is ∼0.1–0.15 mag (Laycock et al. 2010; S. Tang et al., in preparation). There are ∼1.2 × 10⁵ objects with more than 100 mag measurements distributed over ∼100 years from these plates covering the M44 field. J0757, which is N2211021132 in the GSC catalog, is the only one found with >1 mag outburst on a ∼10 year timescale above a well-defined quiescence level.

The DASCH light curve of J0757 is shown in Figure 1. We supplement the figure with V-band data from ASAS starting in the year 2000 (J0757 has the designation ASAS J075731+2017.6; Pojmanski 2002). J0757 is classified by ASAS as a semi-detached/contact binary with best-fit period of 119.2 days with 0.16 mag variations in the V band. Since ASAS data are in the V band, while DASCH magnitudes are in B, we added 1.5 mag to the ASAS V mag in the plot, which is about the sum of the maximum galactic extinction (E(B − V) = 0.06; Schlegel et al. 1998) and the typical B − V value for an M0III star (1.43; Pickles 1998). We will discuss the spectral classification in Section 2.2.

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As shown in Figure 1, J0757 was in quiescence until about 1942 March. J0757 then brightened over the rest of the year of 1942, and slowly decayed until about 1950. The peak magnitude was reached around 1943 January. There is a seasonal gap between 1942 April and October when the star was low or not visible in the night sky, and thus we do not know when exactly the outburst started. If we naively assume that its magnitude increased linearly, then the outburst rise time is ∼88.5 days (see the lower right panel in Figure 1).

Before and after the outburst when data are available (i.e., 1890–1942 and 1962–1990), the magnitudes of J0757 were reasonably stable (note that the relatively constant B  ∼  11.9 from ∼1950–1954 was not yet the quiescent value). The median DASCH magnitude before the outburst (e.g., before 1942 June) is 12.24 and the median magnitude after the outburst (after 1960) is 12.26. The median magnitude of the entire DASCH light curve excluding the period between 1942 June and the start of 1960 is 12.25, with rms scatter = 0.14 mag for the 607 data points outside the outburst. The median ASAS V magnitude is 10.75 mag, which corresponds to B = 12.24, assuming the typical colors of an M0III star with galactic extinction.

Both the DASCH and ASAS light curves show ellipsoidal variations. The ellipsoidal variation amplitude is ∼0.11 mag in the DASCH data (B band, 1890–1942 and 1962–1990), and ∼0.16 mag in the ASAS data (V band, 2003–2009).

We folded the light curves of J0757 to search for its photometric period. We divided DASCH light curve into two phases, i.e., before the outburst and after the outburst, as described in Section 2.1. We then got four sets of light curve data: ASAS light curve, DASCH light curve excluding the outburst (before or after the outburst), DASCH light curve before the outburst, and DASCH light curve after the outburst.

We first folded the ASAS light curve with a given period, and fit it with a three harmonics Fourier model (an example is shown as the blue line in the upper panel of Figure 2). We fixed the model line in shape, but allow two free parameters, i.e., median magnitude and amplitude, for adjustments. Next, we fit the four sets of light curve data to the three harmonics Fourier model, and derived the reduced χ² as a function of different trial periods, as shown in the lower panels in Figure 2. DASCH data were binned by phase at the given period in the fitting. Our best-fit period is 119.18  ±  0.07 days. The fact that the binary period is unchanged (within the errors) sets limits on the change of the orbit (due to mass transfer or onset of common envelope evolution). The resulting value for $\dot{a}/a$ is (0  ±  4)  ×  10⁻⁶ yr⁻¹.

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Spectra were obtained with the FAST spectrograph (Fabricant et al. 1998) on the 1.5 m Tillinghast reflector telescope at the F. L. Whipple Observatory (FLWO) for spectral classification. The spectra were reduced and wavelength calibrated with standard packages (Tokarz & Roll 1997). Figure 3 shows the FAST 300 grating spectrum, which has a resolution of about 7 Å. The upper panel shows the whole spectrum, which suggests that its spectral type is M0. The lower panels show two luminosity indicators, which suggest that DASCH J0757 belongs to luminosity class III. The lower-left panel shows Ca i at 4226 Å, which disappears with increasing luminosity, indicating that DASCH J0757 is not a luminosity class I star. The lower-right panel shows the CaH B band at 6385 Å, and the blend near 6362 Å consisting of Ti, Fe, and Cr. The weakness of CaH B band suggests that DASCH J0757 is not a main-sequence (MS) star. We therefore adopt a spectral type of ∼M0III for DASCH J0757, with uncertainties of ∼  ± 1 in both spectral type and luminosity class.

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We also obtained spectra using the MIKE echelle spectrograph (Bernstein et al. 2003) on the 6.5 m Magallen/Clay telescope with a 07 × 5'' slit on 2011 January 17. The spectral resolution is R ∼ 30, 000. The spectra were extracted using an IDL pipeline developed by S. Burles, R. Bernstein, and J. S. Prochaska.³ The reduced spectra have signal-to-noise ratio (S/N) ∼ 50–100 in 4300–9000 Å and S/N ≳ 10 in 3700–4300 Å. We computed a grid of spectrum templates for a range of abundances, effective temperatures, and gravities using Kurucz's programs ATLAS12 and SYNTHE (Kurucz 2005). We derived the projected rotation velocity of 10 ± 1 km s⁻¹. In M giants the continuum opacity is mainly H- which varies with metal abundance. The ratio of line to continuum does not change strongly with abundance. The TiO background is strong at any abundance because both Ti and O are alpha enhanced at low abundances. We estimated an effective temperature of T_eff = 3850 ± 50 K; a surface gravity of log  g = 1.0 ± 0.5 cgs; and a metallicity of [Fe/H] = −0.6 ± 0.1, assuming J0757 is a population II star with alpha enhancements. The spectra can also be fit with Population I solar abundance templates. There is no sign of emission lines or wind in its spectra.

To measure the radial-velocity curve of J0757, we obtained spectra on 15 different nights from 2010 October through 2011 April with the Tillinghast Reflector Echelle Spectrograph (TRES; Szentgyorgyi & Furész 2007) on FLWO 1.5 m. These spectra were reduced and wavelength calibrated with standard packages (Mink 2011). The spectral resolution is R ∼ 44, 000. The reduced spectra have typical S/N ∼10–30 in 4500–9000 Å, and S/N ∼5–10 in 4000–4500 Å.

Radial velocities of DASCH J0757 were derived from the TRES spectra and were fitted to a model velocity curve using the derived photometric period (see Figure 4). The derived orbital parameters are listed in Table 1. The resulting mass function is

$$\begin{equation} f_1(M_2)=(3.31\pm 0.02)\times 10^{-2}\ M_\odot , \end{equation} \tag{ 1 }$$

and

$$\begin{equation} M_2 \sin i = (0.3211 \pm 0.0006) (M_1+M_2)^{2/3}\ M_\odot , \end{equation} \tag{ 2 }$$

where subscript 1 denotes the red giant and 2 denotes its companion.

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Table 1. Astrophysical Parameters for DASCH J0757

Parameter	Value
Observational parameters with highest confidence
Spectral type	M0III
T0 (HJD)	2455597.980 ± 0.054
Period (days)	119.18 ± 0.07
γ (km s−1)	−33.57 ± 0.04
K1 (km s−1)	13.906 ± 0.025
Eccentricity	0.025 ± 0.01
ω (deg)	70.49 ± 0.09
Vrotsin i (km s−1)	10 ± 1
Parameters derived from atmosphere fitting
Teff (K)	3850 ± 50
log g (cgs)	1.0 ± 0.5
[Fe/H]	−0.6 ± 0.1
Estimates based on models
i (deg)	60 ± 15
M1 (M☉)	1.1 ± 0.3
M2 (M☉)	0.6 ± 0.2
Orbital separation (R☉)	120 ± 11
R1 (R☉)	35 ± 9
L1 (L☉)	250 ± 130
Distance (kpc)	1.0 ± 0.3
hz (pc)	400 ± 110
MB in quiescence	2.2 ± 0.6
MB outburst	0.7 ± 0.6
$L_{\tt{outburst\; peak}}$ (L☉)	102–104 (if no constraint on Thot)
	100 (if Thot ∼ 8100 K)
	2.5 × 104 (if Thot ∼ 90, 000 K)
Lhot in quiescence (L☉)	∼2–8
$\dot{M}$ in quiescence (M☉ yr−1)	∼(1–4) × 10−9

Note. Details are discussed in Sections 2 and 3.

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For comparison, we have also fit a model velocity curve without using the photometric period of P = 119.18 ± 0.07 days, and got similar results: T₀ = 2455597.969 ± 0.06, P = 118.89 ± 0.080 days, γ = −33.57 ± 0.04 km s⁻¹, K = 13.885 ± 0.023 km s⁻¹, e = 0.024 ± 0.015, and ω = 7038 ± 009. In the following discussion throughout the paper, we adopt the parameters obtained using the photometric period of P = 119.18 ± 0.07 days, as listed in Table 1.

Using archival data from WISE, IRAS, AKARI/IRAC, 2MASS, FON, SDSS, GALEX, and ROSAT, we plotted the spectral energy distribution (SED) of J0757, as shown in Figure 5. The phase of the GALEX observation is 0.603 ± 0.01, and the phase of ROSAT observation is 0.426 ± 0.02. Here phase 0.5 is defined as inferior conjunction of the red giant. The SED is well matched by a synthetic spectrum of a T_eff = 3750 K, and log g = 1.5 giant (Lejeune et al. 1997), from IR to optical, as shown in the black line in Figure 6. However, there is an excess in the GALEX NUV (∼1900–2700 Å), which suggests a hot component in addition to the giant.

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We derive system parameters from the light and velocity curves. For this purpose we used the ELC code of Orosz & Hauschildt (2000) to model the ASAS V-band light curve and the TRES radial-velocity curve. The ELC model is based on standard Roche geometry and uses specific intensities from model atmospheres, in particular the NextGen models of Hauschildt et al. (1999). ELC's use of the model atmosphere specific intensities eliminates the need for a parameterized limb darkening law, which is important in cases with red giants where the limb darkening near the stellar limb is very nonlinear (Orosz & Hauschildt 2000). We do not have model atmosphere specific intensities appropriate for WDs. However, since the red giant dominates the V-band flux, this is not a serious limitation.

In our initial runs, we had eight free parameters: the orbital period P, the time of periastron passage T₀, the inclination i, the Roche lobe filling factor f₁, the eccentricity e, the argument of periastron ω, the K velocity of the red giant K, and the mass of the red giant M₁. We assumed synchronous rotation. The models are somewhat insensitive to the temperature of the red giant, and that parameter was held fixed at T₁ = 3720 K. In addition to the light and velocity curve, we used the projected rotational velocity of the red giant as an extra constraint.

The model fits were optimized using ELC's genetic code and its Monte Carlo Markov Chain code. After inspection of the post-fit residuals, additional free parameters were considered. We allowed the red giant's rotation to be asynchronous with the orbit, where Ω is the ratio of the spin frequency to the orbital frequency. We also accounted for heating by the WD. In this case, we fixed the luminosity of the irradiating source to log L_i = 36.6 (cgs units) and allowed the albedo A₁ to be a free parameter (the choice of A₁ is somewhat arbitrary since different combinations of L_i and A₁ can give identical light curves). Finally, we included an accretion disk that is parameterized by the outer radius in terms of the Roche radius r_out, the temperature at the inner rim T_d, and the exponent of the disk temperature distribution ξ, where T(r) = T_d(r/r_i)^ξ.

Some typical results are shown in Figure 6. The binned ASAS light curve has maxima with different heights, which could be indicative of an eccentric orbit. However, the simultaneous fit to the radial velocities indicates a small eccentricity (0.012). Also, the minimum near phase 0.5, corresponding to the inferior conjunction of the red giant, is deeper than the minimum at phase 0.0. For a pure ellipsoidal light curve, the minimum at phase 0.0 would be the deeper one. Heating by the irradiating source "fills in" the minimum near phase 0. However, in all of the models considered, we never had a case where the model curve had a deeper minimum near phase 0.5, so simple heating cannot explain the difference in the observed minima.

An accretion disk could potentially eclipse the red giant near phase 0, thereby making the minimum there deeper. This is opposite of what we want. Normally, the accretion disk does not give phase modulated light in the ELC model (if it is not eclipsed by the star). However, a "hot spot" on the disk rim can be used to mimic the place where the matter transfer stream impacts the disk. As the binary turns in space, different areas of this spot are visible, giving rise to extra light at certain phases. An example model is shown in Figure 6. The hot spot has an angular width of 18°, an azimuth (measured from the line of centers in the direction or the orbital motion) of 66°, and has a temperature of 3800 K, which is 4.3 times hotter than the rest of the disk rim. The maximum near phase 0.75 is fit, but the minimum near phase 0.5 is still not well fit.

We did two runs of fitting with a Monte Carlo Markov Chain, one with an external constraint on the rotational velocity and one without the constraint. Results from both runs are similar. The best-fit ellipsoidal models have inclination of 60°  ±  5°, WD mass of 0.5 ± 0.1 M_☉, red giant mass of 1 ± 0.3 M_☉, and red giant radius of 43 ± 4 R_☉.

We note that in order to match the observed rotational velocity of V_rotsin i = 10 ± 1 km s⁻¹ derived from the MIKE spectra, the red giant must be rotating 0.7 times slower than its synchronous velocity. Given the typical tidal synchronization timescale of ∼10⁵ yr (Zahn 1989) adopting the parameters listed in Table 1, the red giant is expected to be corotating with the binary. Consequently, the size of the giant should be R₁ = PV_rot/2π = 23.5/sin i R_☉, which is 27 R_☉ if i = 60°, which are smaller than the radius derived from ellipsoidal fitting. Such a discrepancy has been seen in many symbiotic binaries and is an unresolved "embarrassing problem" (Mikołajewska 2007). It probably comes from the extended atmosphere, and that limb darkening near the limb is very nonlinear. The light curve models with near-linear limb darkening produce ellipsoidal light curves with amplitudes that are too small. Also, the rotational broadening kernel can be a lot different than the usual analytic kernel, which in turn leads to strange biases in the V_rotsin i value (Orosz & Hauschildt 2000).

Here we estimate the astrophysical parameters of DASCH J0757 based on the results in Sections 2 and 3.1. Since the galactic extinction is small (E(B − V) = 0.06; Schlegel et al. 1998), we do not take it into account for simplicity. The following estimated parameters are summarized in Table 1.

The inclination from the ellipsoidal fitting is i ∼ 55°–65°, and we adopt a more tolerant value of i = 45°–75° in the following estimates. The radius of the red giant ranges from ∼25–33 R_☉ (from V_rot assuming synchronized rotation) to ∼43 R_☉ (from ellipsoidal fitting), as discussed in Section 3.1. Therefore, we adopt a radius and error bar that encompasses both methods as R₁ = 35 ± 9 R_☉. At T_eff = 3850 ± 50 K, the bolometric luminosity of the red giant is L = 250 ± 130 L_☉, and its distance is 1.0 ± 0.3 kpc. The absolute magnitude of the system in quiescence is then M_B = 2.2 ± 0.6.

Combining the radius, effective temperature, log  g = 1.0 ± 0.5 cgs, and [Fe/H] = −0.6 ± 0.1, the red giant mass inferred from stellar evolutionary models (Bertelli et al. 2008) is M₁ ∼ 0.9 ± 0.4 M_☉. This mass estimate for the giant is determined solely from the equations of stellar structure and is therefore independent of its prior evolution. The mass of the giant may have been greater in the past. However, considering the giant is only partially filling its Roche lobe as inferred from the ellipsoidal fitting, and given the M0III wind loss rate of ∼10⁻⁹–10⁻⁸ M_☉ yr⁻¹ (Cox 2000), we do not expect it has lost a significant fraction of its current mass over the ∼10⁷ yr lifetime of the giant in its current phase of evolution. Requiring 0.8 M_☉ to turnoff from MS within a Hubble time, we then have M₁ ∼ 1.1 ± 0.3 M_☉. From Equation (2) and our adopted i = 45°–75°, this implies the secondary mass is M₂  ∼  0.6  ±  0.2 M_☉, and the orbital separation a ∼ 120 ± 11 R_☉. Therefore, the Roche lobe radii of the two stars are R_{RL, 1} ∼ 53 ± 4 R_☉ and R_{RL, 2} ∼ 38 ± 6 R_☉ for the M giant and the secondary, respectively (Eggleton 1983). The Roche lobe filling factor of the M giant is then f_RL = R₁/R_{RL, 1} = 0.66 ± 0.17.

If the deviation of the ASAS folded light curve and the ellipsoidal model with a giant alone is caused by a hot component due to a WD companion, its accretion disk and/or a tidal stream, then it is about 3% the luminosity of the giant in the V band. The luminosity of the hot component is then 2–8 L_☉, for an effective temperature in the range of 3800–10, 000 K. For an M₂ ∼ 0.6 M_☉ WD with R₂ ∼ 0.01 R_☉, assuming all the gravitational potential energy is converted to thermal radiation, the corresponding accretion rate is (1–4) × 10⁻⁹ M_☉ yr⁻¹.

During the 1942–1950s outburst, the B magnitude of J0757 increased by ∼1.5 mag at the peak. At a distance of D ∼ 1 kpc, the absolute B magnitude of the outburst is M_{B, outburst peak} ∼ 0.7 mag. The peak bolometric luminosity of the outburst L_{outburst peak} depends on its SED. If the outburst has similar SED as an M0III star, then L_{outburst peak} ∼ 750 L_☉. The minimum required bolometric luminosity would be when the radiation is peaked in the B band, i.e., L_{outburst peak} ∼ 100 L_☉ at T ∼ 8100 K. Such a temperature is consistent with the observed hot component temperature of CH Cyg during its 1992 outburst powered by accretion (Skopal et al. 1996). If the outburst is powered by hydrogen shell burning, the temperature during the outburst would be much hotter, i.e., T_outburst ∼ 10⁵ K as observed in some symbiotic stars (Mürset et al. 1991). For example, Z And is found to have a temperature of ∼9 × 10⁴ K during its 2000–2002 outburst (Sokoloski et al. 2006). If the outburst in J0757 has a temperature of 9 × 10⁴ K, most of the radiation is in the UV, and the corresponding bolometric luminosity of ΔB = 1.5 mag increase is L_{outburst peak} ∼ 2.5 × 10⁴ L_☉ assuming black body radiation.