EVIDENCE FOR THE WHITE DWARF NATURE OF MIRA B

Variations in the strength of emission from the accretion region around a compact object can reveal fundamental properties of the compact object and its accretion structure. For example, the frequencies associated with features in the power density spectra (PDS) of these brightness variations are linked to physical timescales at different locations in the accretion disk (e.g., Mauche 2002; Warner 2004; Done et al. 2007). Such PDS features include quasi-periodic oscillations, "breaks" where the slope of the PDS changes, and broadband components that can be fitted with Lorentzian functions (Psaltis et al. 1999). Empirically, the locations of these features depend on the type of object; in X-ray binaries, the highest frequency at which significant variability exists is greater for neutron star than black hole accretors (Sunyaev & Revnivtsev 2000), consistent with the higher Keplerian frequency at the inner edge of the accretion disk around a neutron star. Even an apparently featureless PDS may hold the imprint of the underlying accreting object, as is evidenced by the correlation between the normalization of the PDS at a particular frequency and the mass of the black hole in active galaxies compared to X-ray binaries (Nikołajuk et al. 2004; Gierliński et al. 2008).

An important case where accretion-related variations can reveal the nature of an accreting object is the wide, interacting binary-star system Mira AB (o Ceti). Mira AB is a "symbiotic-like" or "weakly symbiotic" system at a distance of 107 pc (Knapp et al. 2003). According to the preliminary orbit of Prieur et al. (2002), the orbital period is 497.9 years and the inclination is 1120 (i.e., we see the binary nearly edge-on). The donor star is the prototype of the Mira-type class of pulsating AGB stars, with a pulsation period of 332 days (Hoffleit 1997). A more compact companion, whose nature has been controversial, accretes from the wind of the AGB star. Although most indicators suggest that the accretor is a white dwarf (WD; e.g., Warner 1972; Reimers & Cassatella 1985), several authors have argued that the low X-ray luminosity implies it is a main-sequence (MS) star (Jura & Helfand 1984; Kastner & Soker 2004). Determining whether Mira B is a WD or an MS star is imperative because its nature and evolutionary status impact our understanding of (1) the efficiency of wind-fed accretion, (2) mass transfer through disks with sizes of ∼10¹³ cm, (3) X-ray emission from symbiotic stars, and (4) the generation of the bipolar structure in planetary nebulae (PNe).

Because Mira AB is spatially resolved in the optical, X-ray, and radio (Karovska et al. 1997, 2005; Matthews & Karovska 2006), it is an excellent place to investigate the accretion of a stellar wind from a detached companion. Roche lobe overflow is thermally unstable when the donor star in a binary is an evolved giant with a mass in excess of 5M/6 (where M is the mass of the accretor; Webbink et al. 1983). Hence, symbiotic binaries, which typically have low-mass accretors (Mikołajewska 2003), tend to transfer material via gravitational capture of the red giant wind. In Mira AB, X-ray observations revealed a bridge of material between the two stars (Karovska et al. 2005) that likely arises from gravitational effects, as the wind speed (6 km s⁻¹; Knapp & Morris 1985) is of the same order as the stellar velocities. Mira may thus be the first clear example of a new mode of mass transfer—dubbed "wind Roche lobe overflow" (Mohamed & Podsiadlowski 2007) or "gravitational focusing" (de Val-Borro et al. 2009)—that lies somewhere between standard Roche lobe overflow and Bondi–Hoyle accretion. This type of mass transfer may occur in those wide binaries that ultimately explode as type Ia supernovae (SNIa; e.g., Patat et al. 2007; Simon et al. 2009; Blondin et al. 2009), with the yield from this channel of SNIa production depending on the efficiency of the mass transfer from the red giant (RG) to the WD. Since the inferred accretion rate onto Mira B ($\dot{M}= L R/G M$, where L is the luminosity due to accretion, R is the radius of the accretor, and G is the gravitational constant) differs by almost 2 orders of magnitude depending upon whether Mira B is a WD or an MS star, determining the nature of Mira B is critical for estimating $\dot{M}$ and the ability of this channel to produce an SNIa.

Mira AB will also test the hypothesis that the shapes of PNe are the result of interactions between a star in its final stages of evolution and a binary companion (De Marco 2009). Observations indicate that pre-PNe commonly have bipolar morphologies and jets (e.g., Bujarrabal et al. 2001; Sahai et al. 2007), and most models for producing these structures require a binary companion (e.g., De Marco 2009; Huggins et al. 2009, and references therein). Miszalski et al. (2009), however, estimated that only 10%–20% of PNe contain binary central stars with separations small enough for the binary to have experienced a phase of common-envelope evolution, and Huggins et al. (2009) argued that the roundness of the majority of the halos of pre-PNe indicates that any binary companions in these systems must either be quite distant (as in Mira) or have very low masses. Mira A is near its evolutionary end state, it has a distant binary companion, and recent ultraviolet (UV) images from the Galaxy Evolution Explorer (GALEX) satellite revealed bipolar "streams" of knots to the north and south (Martin et al. 2007). Therefore, resolution of the issue of the nature of the companion would clear the path for models of Mira AB to confront questions such as how wide binaries generate bipolar structure in PNe, which stellar component launches the bipolar outflows, and when asymmetry first appears.

In this paper, we use fast B-band photometry to show that Mira B is a WD. We describe our rapid photometric observations in Section 2, and the resulting light curves and PDS in Section 3. In Section 4, we explain how the amplitude of the optical variations on timescales of minutes reveals Mira B to be a WD. We also estimate a characteristic accretion rate onto Mira B and reinterpret the X-ray emission. We summarize our conclusions and explore several implications in Section 5.

As part of a photometric survey of 35 symbiotic stars (see Sokoloski et al. 2001, hereafter SBH), we observed Mira AB with the 1 m Nickel Telescope at UCO/Lick Observatory on Mt. Hamilton, near San Jose, California, on five nights between 1997 September and 1998 September. Table 1 contains a log of the observations, each of which consisted of a series of exposures with an unthinned, 2048 × 2048 Loral CCD (referred to at Lick Observatory as "CCD 2") that had 15 μm pixels and a 63 × 63 field of view. We chose exposure times, t_e, of 18–50 s to maximize the signal-to-noise ratio (S/N) while avoiding saturation of the program star or the one bright comparison star in the field of view (HD 14411). Keeping the exposure times at or above 18 s also kept the observing efficiency (t_e/Δt, where Δt is the time between observation starts) from dropping much below ∼50% and minimized scintillation noise, which can dominate the error at very short exposure times (SBH). Including chip pre-processing and readout times of between 20 and 22 s, Δt ranged from 39 to 70 s. To obtain evenly spaced data points within a given observation, and thereby produce data that were compatible with standard fast Fourier transform (FFT) routines, we employed a timing system developed especially for this project by W. Deitch (UCO/Lick). The resulting light curves spanned from 1.1 to 4.6 hr. To minimize the contribution of the red giant while still obtaining adequate flux from the bluer hot component to generate a high S/N on timescales of minutes, we used a Johnson B filter and observed only near the minima of the 332 day Mira pulse period, as displayed in Figure 1.

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For each observation, we reduced the CCD images using standard techniques and performed aperture photometry, as described in SBH. For each image, our reduction included subtracting the electronics zero point and bias pattern and dividing by an average of multiple images of the sky, using IDL software based upon IRAF routines (see Gilliland 1992; Massey 1997). We produced differential light curves with respect to either the one bright comparison star in the field or a weighted, ensemble average of 2–4 comparison stars (depending upon whether the additional comparison stars improved the S/N enough to warrant the additional lost points due to cosmic rays). We estimated the background for each star from an annulus around that star. We omitted data points contaminated by radiation events ("cosmic rays"), points with extremely high background, and data taken during exceptionally poor weather conditions. None of the comparison stars showed any evidence for intra-night variability.

Rapid aperiodic variability, like the variability from cataclysmic variables that is often termed "flickering" (CVs; e.g., Warner 1995; Bruch 2000), is evident on all five nights. Figure 2 shows the differential light curves from the five observations. On each night, the measured root-mean-square (rms) variation, s, exceeded the rms variation expected from the known errors, s_exp, by more than an order of magnitude. Table 2 lists s and s_exp (the estimation of which is discussed in detail in SBH) for each observation. Figure 2 demonstrates that the B-band flux can change by more than 5% (≈50 mmag) in less than 5 minutes and more than 25% (≈0.25 mag) in less than 2 hr. Taking into account the non-variable light from the red giant, which contributes ≈50% of the flux at B band (since Mira A and B had similar brightness in the Hubble Space Telescope (HST) F501N filter when Mira A was near pulse minimum in 1995; Karovska et al. 1997), these rapid fluctuations correspond to variations of approximately 10%–50% in the B-band light from Mira B. In summary, correcting for the contribution from the red giant, the B-band flux from Mira B varied as fast as a few per cent (or tens of mmag) per minute, and by order unity in tens of minutes, as exhibited in the light curve from 1998 August 20 (Figure 3).

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The PDS of all five light curves reveal broadband power with a power-law shape—P_ν ∝ ν^α (where P_ν is the power density and ν is the frequency)—between approximately 0.1 and 10 mHz (see Table 2). Since our data points were evenly spaced, we used the IDL routine fft to compute the PDS. We normalized the PDS to the variance of the light curves using the Miyamoto normalization (Miyamoto et al. 1991), in which the square root of the integrated power between two frequencies is equal to the fractional rms variation between those two frequencies. For PDS with a power-law index α = −2, the square root of the power at a given frequency equals the fractional rms variation summed over all frequencies above that frequency. Figure 4 shows the PDS corresponding to the light curves in Figure 2. Table 2 lists the power-law indices for each observation; they ranged from −1.8 to −2.4. The weighted average of the five power-law indices is α = −1.969 ± 0.004. Since this value is very close to α = −2, we refer to the stochastic variations from Mira as red noise.

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Extrapolating the PDS where necessary using a power-law index of α = −2, and taking into account the constant light from the red giant, we find that the average rms variation from Mira B between 0.1 and 10 mHz is approximately 9%. We derived this value from a measured rms variation for the total B-band light in this same frequency range of 4.5%, since emission from the red giant, which does not vary at these frequencies, constitutes approximately half of the B-band flux. Thus, the B-band rms variation from Mira B is at least twice the rms variation of the total B-band light. In the restricted frequency range of 1–10 mHz, which is useful for comparison with published rms variations in this frequency range for CVs, the average rms variation from Mira B is 3% (correcting a measured rms variation of 1.5% in this frequency range for the contribution from the red giant).

We did not find any evidence for coherent, periodic variations on timescales of minutes to hours in the optical brightness of Mira B. Taking the broadband power into account (as discussed in the Appendix of Sokoloski & Kenyon 2003), no peaks in the PDS rose significantly above the level of the red noise.

The nature of the accreting companion to Mira A may hold the key to improved understanding of mass transfer via a wind, as well as the way in which binaries generate asymmetrical structure in PNe. Whereas early observations of rapid CV-like optical variability by Walker (1957) and Warner (1972) originally led most authors to assume that Mira B was a WD, later revelations that the X-ray luminosity was lower than expected motivated Jura & Helfand (1984) and then Kastner & Soker (2004) to propose that Mira B was instead an accreting MS star. Though Ireland et al. (2007) reported some marginally significant (4σ) features in the optical spectrum that appeared to suggest an MS companion, the UV spectrum is much more indicative of a WD (Reimers & Cassatella 1985). Below, we use a quantitative examination of the amplitude of the optical variability on timescales of minutes, along with an estimate of the expected optical depth of the accretion-disk boundary layer (BL), to show that the optical to X-ray observations are more consistent with a WD accretor.

4.1. Rapid Optical Variations and the Nature of Mira B

4.2. Reinterpretation of the X-ray Emission

Our main conclusion is that the rapid optical variability from Mira AB reveals Mira B to be a WD. The amplitude of the optical brightness fluctuations from Mira B on timescales of minutes is the same as those from accreting WDs in CVs, and significantly larger than one would expect from an accreting MS star. The UV spectra—especially the ionization states and widths of the lines—are consistent with the conclusion that Mira B is a WD. The X-ray luminosity and spectrum are also consistent with this conclusion if the accretion-disk BL is optically thick, as one would reasonably expect for our estimated accretion rate of ∼10⁻¹⁰ M_☉ yr^-1 (e.g., see Wheatley et al. 2003).

This accretion rate, which we infer from the optical and UV luminosities of Mira B, is consistent with constraints on the effective temperature of the WD from UV spectra. Sion (1999) noted that prolonged accretion will re-heat an otherwise cooling WD, making it potentially visible in the UV or optical continuum. Such rejuvenated WDs are seen in dwarf novae systems during quiescence, revealing effective temperatures of T_eff= 10,000–20,000 K (Townsley & Gänsicke 2009). This WD re-heating (Townsley & Bildsten 2003; Townsley & Gänsicke 2009) and the resulting T_eff depend on both M and the time-averaged accretion rate, $\langle \dot{M}\rangle$, thereby providing another constraint for our analysis of Mira B. From the UV continuum flux upper limit F_λ(1250 Å) < 10⁻¹⁴ erg cm^-2 s⁻¹, Reimers & Cassatella (1985) found T_eff < 14,000 K for R = 0.012 R_☉ (for a WD with M = 0.6 M_☉ and a distance of 77 pc; a slightly higher T_eff is allowed at our adopted distance of 107 pc). A direct application of Townsley & Bildsten (2003, see their Figure 1) converts this upper limit on T_eff into the long-term accretion rate constraint $\langle \dot{M}\rangle < 2 \times 10^{-10}\;M_\odot \;{\rm yr^{-1}}$, in agreement with our earlier estimate.

At this accretion rate ($\dot{M}\approx 10^{-10}\;M_\odot \;{\rm yr^{-1}}$), the accumulated matter on the WD will burn unstably and cause a classical novae, leading to the violent ejection of ∼10⁻⁴ M_☉ of material at >1000 km s^-1. This ejected mass is larger than the total mass of the wind between the WD and the red giant, leading to little deceleration of the shock as it plows through the wind in the few months following the eruption. A nova eruption from Mira would thus perhaps look more like those of the symbiotic slow novae than, say, an X-ray bright eruption of the symbiotic recurrent nova RS Ophiuchi (Sokoloski et al. 2006) or the γ-ray producing explosion of the symbiotic V407 Cygni (Abdo et al. 2010). From the work of Townsley & Bildsten (2004), we would expect a nova recurrence time of ≈10(2) × 10⁵ yr for M = 0.6(1.2) M_☉ and $\langle \dot{M} \rangle =2\times 10^{-10}\;M_\odot \;{\rm yr^{-1}}$.

Our conclusion that Mira B is a WD accreting at $\dot{M} \sim 10^{-10}\;M_\odot \;{\rm yr^{-1}}$ has implications for the mode and efficiency of mass transfer in wide binaries. Although Mohamed & Podsiadlowski (2007) and de Val-Borro et al. (2009) have suggested that a focused wind could enable up to tens of percent of the donor wind to be captured, the accretion rate needed to produce Mira B's luminosity and effective temperature is just 0.1% of the RG wind mass-loss rate (Ryde et al. 2000). It is also below the Bondi–Hoyle accretion rate of $\dot{M}_{{\rm BH}} \approx 10^{-8}\;{M}_{\odot }\;{\rm yr^{-1}}(M/0.6\;{M}_{\odot })^2(7\;{\rm km\; s}^{-1}/v_\infty)^3,$ where v_∞ is the relative velocity of the wind at Mira B. Thus, we find no evidence that either gravitational focusing or wind Roche lobe overflow is enhancing the accretion efficiency onto the WD in this binary, despite the image showing a bridge of X-ray emitting material between the two stars (Karovska et al. 2005).

Identifying Mira B as a WD also has ramifications for the launch site of the bipolar "streams" that have been imaged in the near- and far-UV with GALEX (Martin et al. 2007) and in the optical from the ground (Meaburn et al. 2009). Based on the behavior of other WDs that accrete from wind-fed disks in symbiotic binaries, we speculate that the bipolar streams emanate from the accreting WD rather than, or in addition to, the pulsating AGB star. Mikołajewska (2003) has suggested that symbiotic stars in which the wind of the red giant is focused toward orbital plane—as has been seen to be the case for Mira (Karovska et al. 2005)—preferentially contain large, unstable accretion disks, which tend to produce sporadic bipolar outflows (Sokoloski 2003). GALEX observations indicate that the streams from Mira contain about 10⁻⁷ M_☉ of material (D. Neill 2009, private communication), and Meaburn et al. (2009) estimated that the streams were ejected over the course of the past ∼1000 yr. The average rate of flow into the streams was thus roughly $\langle \dot{M}_{\rm streams}\rangle \sim 10^{-10}\;{M}_{\odot }\;{\rm yr^{-1}}$. Given our estimate of the accretion rate, Mira B could fairly easily pump ∼10⁻¹¹ M_☉ yr^-1 into the streams, which is roughly consistent with the observational estimate of the mass loss from the WD by Wood et al. (2002) during the IUE era. Given the large uncertainties on both the rate of accretion onto Mira B, the average rate of mass loss from Mira B, and the rate of flow in the bipolar streams, we conclude that the WD remains a viable launch site, and that the streams do not necessarily originate from the RG. Mira AB therefore does not necessarily require a mechanism for generating fast, bipolar outflows from the AGB star itself, and it does not provide evidence that such mechanisms are needed to generate bipolar symmetry in PNe.

J.L.S. is grateful to many colleagues for useful discussions, including J. Patterson, M. Karovska, J. Applegate, G. Luna, G. Hussain, S. Kenyon, K. Mukai, and E. Sion. Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award SAO G09-0027X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060, and by the National Science Foundation under grants PHY 05-51164 and AST 07-07633. We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research.

Facilities: Nickel - Lick Observatory's 1m Nickel Telescope, AAVSO - American Association of Variable Star Observers International Database