X-RAY ECLIPSE DIAGNOSIS OF THE EVOLVING MASS LOSS IN THE RECURRENT NOVA U SCORPII 2010

The X-ray eclipse provides a means for constraining the geometry of the emitting region. Assuming a spherically symmetric source with no limb-darkening and the system parameters of Hachisu et al. (2000a), the 27% ± 5% dimming on day 15 implies that the X-ray source had roughly four times the area and twice the radius of the companion star, corresponding to a source radius of 5.1 ± 0.6 R_☉. This is consistent with a fit to the light curve using a quadratic function and analytic transit model (Mandel & Agol 2002) assuming the same geometry, for which we obtained a radius 4.5 ± 0.2 R_☉ and center epoch 14.988 ± 0.007 days post-outburst; see Figure 2(a). By adopting the slightly more compact system parameters of Thoroughgood et al. (2001), radius estimates are smaller by a factor of ∼0.8. This emitting region within the residual outflow is large in comparison to the underlying white dwarf and was referred to as a "corona" by Ness et al. (2012).

The development of the source region can be studied by comparing the above radii with the XMM-Newton results taken at two different epochs (Ness et al. 2012). The X-ray light curve on day 23 exhibited a dimming of up to ∼50% with ∼20% oscillations during an eclipse. The latter could be caused by absorption in a reforming accretion disk (Ness et al. 2012), or by the geometrical eclipse of a photometrically varying photon escape region caused by inhomogeneities and/or density instabilities in the radiatively driven flow (e.g., Shaviv & Dotan 2010; Shaviv 2005; Owocki et al. 1988). In contrast, the X-ray light curve on day 35 showed a clear eclipse with a ∼40% dimming, corresponding to a source radius of ∼4.2 R_☉, indicating that the X-ray source shrunk by about 10%–20% between 15 and 35 days after the outburst. This is the first quantitative X-ray measurement of the shrinking of the source radius of an emerging SSS in a nova outburst.

The standard nova paradigm posits that the SSS emission emerges as ejecta expand and decline in the radiatively driven flow allows photon escape at successively smaller radial distance from a white dwarf surface until supersoft X-ray temperatures are reached. Once this begins and the outer ejecta are thin, the source radius is of the order of a few solar radii or smaller and the atmosphere is possibly puffed-up and porous (e.g., Shaviv & Dotan 2010). This allows it to be much larger than the Eddington luminosity and X-ray temperature would otherwise suggest (e.g., Shaviv 2005). A few thousand km s⁻¹ outflow traverses the source in only ∼100 s; at this point, any further change in radius probes the instantaneous mass-loss rate in the outflow. We investigate this below, first assuming the simplest ejecta model, and then examining the implications of an energy-dependent opacity by comparing source radii in optical and X-rays on day 15.

Assuming a spherically symmetric flow from the white dwarf surface, the X-ray photon escape radius R_x is related to the optical depth by

$$\begin{equation} \tau {} = \int _{R_{x}}^{R_{{\rm out}}}\kappa {}\rho {}dr, \end{equation} \tag{ 1 }$$

where R_out is the outermost radius of the ejecta, κ is the ejecta opacity, and ρ is the density as a function of radial distance r. We define the X-ray photon escape layer as a point at which τ is approximately unity. Assuming that the ejected gases are accelerated within a small radial distance and that the terminal velocity v_∞ has not changed appreciably since the eruption (i.e., the timescale of the terminal velocity decline is much larger than the time for the ejecta to reach R_out), R_out ≈ v_∞t. We adopt v_∞ = 3000 km s⁻¹ from the estimate of Yamanaka et al. (2010) based on Hα line profiles, and κ = 0.4 cm² g⁻¹ as the Thomson scattering opacity in a fully ionized hydrogen-dominated gas. The radial density profile is given by

$$\begin{equation} \rho {} = \frac{1}{4\pi {}r^{2}}\frac{\dot{M}}{v_{\infty {}}}, \end{equation} \tag{ 2 }$$

where $\dot{M}$ is the mass-loss rate. We next assume a time-dependent mass-loss rate from the white dwarf given by (e.g., Bode & Evans 2008)

$$\begin{equation} \dot{M} = \dot{M}_{0}(t_{0}/t)^{p}, \end{equation} \tag{ 3 }$$

where $\dot{M}_{0}$ is an initial value normalized at time t = t₀ = 1 s and p is a measure of the speed of its decline. Using these relations, we fitted the observed radii of the X-ray source regions at 3 epochs (days 15 (Suzaku), 23 and 35 (XMM-Newton)) with 2 free parameters $\dot{M}_{0}$ and p. We used the Gaussian estimate with the Hachisu et al. (2000a) parameters on day 15 in order to compare directly the eclipse depths with the other epochs. We further adopted 10% uncertainties on the source radii derived by XMM-Newton based on the light curves in Ness et al. (2012). The source radius on day 23 depends on the interpretation of the light-curve oscillations, thus both cases of 30% and 50% eclipse dimming (cases 1 and 2, respectively) were treated separately. The best-fit results and 1σ confidence regions are shown in Figure 3, where $\dot{M}_{0}= 1\times 10^{-3}$ (6 × 10⁻⁵–3 × 10⁻²) M_☉ yr⁻¹ and p = 0.23 ± 0.22 in case 1; $\dot{M}_{0}$ = 5 × 10⁻³ (3 × 10⁻⁴–2 × 10⁻¹) M_☉ yr⁻¹ and p = 0.33 ± 0.25 in case 2.

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Integration over the time-dependent mass-loss rate yields a rough estimate of the total ejecta mass M_ej as a function of elapsed time and is shown in Figure 3. Assuming that the SSS faded and the mass outflow was terminated on day 40 (Figure 1(b)), the total ejecta mass is about 5–8 × 10⁻⁶ M_☉ for the simple model. This is consistent with the changing orbital period from long-term optical monitoring (4.3 ± 6.7 × 10⁻⁶ M_☉; Schaefer 2011), but slightly higher than theoretical estimates for U Scorpii (e.g., 4 × 10⁻⁷ M_☉: Starrfield et al. 1988; 2 × 10⁻⁶ M_☉: Hachisu et al. 2000b). We here note that mass-related values also become smaller by a factor of ∼0.8 by adopting Thoroughgood et al. (2001) parameters.

Schaefer et al. (2011) found that the eclipse shapes in optical were consistent with a spherical source with a radius of 4.1 R_☉ on days 15–26. Since we have assumed spherically symmetric source regions whereas the optical eclipses (Schaefer et al. 2011) and the day 23 XMM-Newton eclipses (Ness et al. 2012) were accompanied by more complicated structure, we cannot conclude with certainty that there is a significant difference between the sizes of the optical and X-ray photon escape regions, though at face value the different inferred radii suggest this on day 15 with the system parameters of Hachisu et al. (2000a).

A remaining puzzle is the origin of the optical plateau started from ∼10 to 15 days post-outburst. This optical flux clearly exceeds the extrapolated X-ray blackbody with the Eddington luminosity of a Chandrasekhar white dwarf, though a blackbody is grossly inadequate to describe the true spectrum and the magnitude of any optical excess remains uncertain. Hachisu et al. (2000a) argued that the optical flux included reprocessing photospheric emission on the surface of the reappearing accretion disk. Currently, no clear evidence is found for this because it is unknown how early the accretion process resumes after the explosion, though recent studies imply that the non-accretion case is more likely, at least on day 15. Simulations of Drake & Orlando (2010) found that the accretion disk was completely destroyed by the blast. Mason et al. (2012) and Worters et al. (2010) suggest resumption of accretion based on spectroscopy and optical flickering, respectively, around day 8, though the short-term variability disappeared on day 15 (Munari et al. 2010). Schaefer et al. (2011) found the optical source spherical until day 26 based on eclipse mapping. Ness et al. (2012) further discussed reforming accretion still on day 23. Alternatively, the reprocessing might occur in surrounding ejecta with a substantial optical depth in supersoft X-rays, though it has to be noted that any scenario at this time remains largely speculative.

If we assume that the optical flux on day 15 originated mostly from the surrounding ejecta, the possible difference between the radii of optical (R_o ∼ 4 R_☉) and X-ray (R_x ∼ 5 R_☉) sources can arise from the energy dependence of the photon escape radii that would result from different optical and X-ray opacities (κ_o and κ_x, respectively). For a plasma at temperatures of 10–100 eV, the opacity in the supersoft X-ray range can be significantly larger than the Thomson cross-section owing to abundant elements (primarily C, N, O, and Ne) not being fully ionized. For a low-density plasma, the optical opacity will instead be close to the Thomson value. Using the PINTofALE⁷ routine IONABS (Kashyap & Drake 2000), we computed the cross-section assuming collisional equilibrium at the temperature of 50 eV and found κ_x ∼ 50 cm² g⁻¹ in the 0.2–1.0 keV range, or ∼100 times the Thomson value. The plasma in the ejecta is in fact likely to be photoionized rather than in collisional equilibrium. For a constant wind velocity, Equations (1) and (2) imply for optical depth unity κρr ∼ 1, or ρ ∼ 5 × 10¹² H atoms cm⁻³ at 4 R_☉. The ionization parameter, ξ = L/n_er² (e.g., Tarter et al. 1969), is then of the order of 10² for the Eddington luminosity and indicates the outflow is photon-dominated. Nevertheless, our cross-section estimate suggests that the true supersoft X-ray opacity could be an order of magnitude or more larger than that in the optical.

The density profile, and consequently the mass-loss rate and total mass loss, derived from the X-ray eclipses scales inversely with the gas opacity, so that the total mass-loss rate would be 5–8 × 10⁻⁶ (κ_o/κ_x) M_☉. We have argued that the X-ray opacity at the photosphere is higher than the Thomson value that characterizes the optical range, and that this would give rise to the observed difference in optical and X-ray source radii. Theoretical mass-loss estimates are in the range 4 × 10⁻⁷–2 × 10⁻⁶ M_☉ (Starrfield et al. 1988; Hachisu et al. 2000b), indicating the true X-ray opacity might be higher than the optical one by a factor of about 2–20. Drake & Orlando (2010) found the initial explosion threw off probably no more than 10⁻⁷ M_☉ using non-spherical hydrodynamic models and early X-ray luminosity constraints. Estimates of the subsequent mass loss then imply that most of the mass was lost during later evolution, confirming theoretical expectations (e.g., Gallagher & Starrfield 1978).