Mem. S.A.It. Vol. 83, 779 c SAIt 2012 Memorie della Theoretical understanding of nova light curves Physics and application Mariko Kato Dept. of Astronomy, Keio University, 4-1-1 Hiyoshi, Kouhoku-ku, Yokoyama, 223-8521, Japan e-mail: [email protected] Abstract. I review current theoretical understanding of light curves of novae. Optical and infrared emissions are basically reproduced by free-free emission decaying as t−1:75, inde- pendent of the white dwarf (WD) mass or chemical composition of the envelope. This prop- erty, we call it the universal decline law, is explained using the optically thick wind theory of nova outbursts. Using the universal decline law, we derive a theoretical relation between the maximum-magnitude and the rate of decline (MMRD). Theoretical light curves well reproduce observed data from low mass to very massive WDs close to the Chandrasekhar mass. Multiwavelength observation is required to determine the WD mass accurately be- cause UV or soft X-ray light curves evolve with different parameter dependence. I also address some important issues related to light curve analysis, i.e., super-Eddington lumi- nosity, no optically-thick wind evolution of PU Vul, transition from static to wind evolution in some slow novae, and helium nova. Key words. binaries:close – binaries: symbiotic – novae, cataclysmic variables, Stars: mass loss – white dwarfs – X-rays:stars 1. Introduction tospheric temperature rises with time, the main emitting wavelength of photon shifts from op- Novae are thermonuclear runaway events on a tical to UV and then to supersoft X-rays. The mass-accreting white dwarf (WD) in a close bi- optically thick winds continue until the photo- nary system. After the thermonuclear runaway spheric temperature reaches log T (K) > 5:2. sets in, the photosphere of the WD expands The WD photosphere emits supersoft X-rays greatly up to ∼ 100 R or more, and the com- until hydrogen nuclear burning stops. Then panion star is engulfed deep inside the pho- the nova enters a cooling phase and finally tosphere. After the maximum expansion, the the WD becomes dark. These timescales de- photospheric radius shrinks with time and free- pends mainly on the WD mass and secondary free emission of expanding ejecta outside the on the chemical composition of the envelope. photosphere dominates the optical and infrared Therefore, multiwavelength observation is im- emission. Due to strong wind mass-loss a large portant to determine nova parameters. part of the envelope matter is blown in the wind and the photosphere moves inside. As the pho- The optically thick winds is accelerated due to a prominent peak of OPAL opacity Send offprint requests to: M. Kato at log T (K)=5.2, that locates deep inside the 780 Kato: Nova theory photosphere. Thus, the wind is a so called continuum-radiation-driven wind. The mass- loss rate is much larger than that of optically thin winds, namely, line-driven wind, which is accelerated outside the photosphere. 2. Nova light curve 2.1. A universal decline law The decay phases of novae can be followed by a sequence of steady-state solutions. We solve the equations of motion, mass continuity, ra- diative diffusion, and conservation of energy, Fig. 1. Our model free-free light curves for various from the bottom of the hydrogen-rich enve- white dwarf masses, from 0.55 to 1:2 M for opti- lope through the photosphere assuming steady- cal and infrared band. The decay timescale depends mainly on the white dwarf mass. Observational y state. Evolutions of nova outbursts can be fol- magnitudes of V1668 Cyg (1978) (open squares: lowed by a sequence of such steady-state solu- Gallagher et al. 1980) are well fitted to 0:9 M WD tions (Kato & Hachisu 1994). model (taken from Hachisu & Kato 2010). Optical and infrared light curves are calcu- lated assuming free-free emission which origi- nates from the optically thin ejecta outside the photosphere. The free-free emission of opti- cally thin ejecta is estimated by Z Z 1 M˙ 2 M˙ 2 F / N N dV / wind r2dr / wind ; (1) λ e i 2 4 2 Rph vwindr vphRph during the optically thick wind phase, where Fλ is the flux at the wavelength λ, Ne and Ni are the number densities of electrons and ions, respectively, Rph is the photospheric radius, M˙ wind is the wind mass-loss rate, vph is the photospheric velocity, and Ne / ρwind and Ni / ρwind. These M˙ wind, Rph, and vph are calculated from our optically thick wind solu- tions. As the wind mass-loss rate quickly decreases with time the flux at a given wavelength also de- Fig. 2. Schematic nova light curve for free-free creases with time. Note that the shape of the light emission model. Nova light curve decays as t−1:75. curve is independent of the wavelength, whereas the When the nova enters the nebular phase and strong absolute magnitude, i.e., proportionality constant of emission lines dominate, the light curve is lift up Equation (1) depends on it. This wavelength-free (thin solid line) from the template nova light curve light curve is one of the characteristic properties of (thick solid line). free-free emission (see Hachisu & Kato 2006). Figure 1 shows calculated light curves for var- ious WD masses. The light curve decays quickly some factor, i.e., shift in the horizontal direction in more massive WDs, mainly because of smaller in logarithmic timescale, all the light curves essen- envelope masses. Observational y magnitudes of tially converge into a single curve (for the factor see V1668 Cyg follows very well our 0:9 M WD Tables 2 and 3 in Hachisu & Kato 2010). This tem- model. plate light curve is plotted in Figure 2. After the peak If we plot these light curves in a logarithmic magnitude, the main body of a optical/infrared light time since the outburst, the light curve decays as curve decays as t−1:75 (thick line) until the nova en- t−1:75 independently of the WD mass except the early ters the nebular phase. When strong emission lines, phase near the peak and a later phase where emis- such as [O III], begin to contribute to the optical sion lines dominate. If we further multiply by a flux, the light curve is gradually lift up from the Kato: Nova theory 781 Fig. 4. Light curve fitting of V2491 Cyg. Fig. 3. Light curve fitting of V1974 Cyg. Theoretical free-free and supersoft X-ray light Calculated optical, UV and X-ray fluxes from the curves are dipcted by the solid lines: from left to WD photosphere are plotted against time for WD right, 1:32 M (green line), 1:3 M (thick blue line), and 1:27 M (thin black line). The best-fit model, masses of 1.0 (right), 1.05 and 1.1 M (left). The large open circles at the right end of optical light- that reproduce the optical and X-ray light curves curve denote the epoch when the optically thick simultaneously, is 1.3 M WD with the envelope wind stops. Dots and open circles represent visual chemical composition of X = 0:20, Y = 0:48, and V magnitude, respectively. There is a system- XCNO = 0:20, XNe = 0:10, and Z = 0:02. Large open triangles: observational X-ray (0.2–0.6 keV) count atic discrepancy in V-magnitudes among different −3 V systems due to contamination of emission lines at rates obtained with Swift. The Fλ / t law (ma- the shorter edge of the V-bandpass. The difference genta) is added for the nebular phase (taken from becomes more prominent in the later nebular phase. Hachisu & Kato 2009) Large circles represent IUE data, and squres supre- soft X-ray data (taken from Hachisu & Kato 2006) lation which is very consistent with observatinaly derived empirical relations. It is well known that template nova light curve and decays as the thin MMRD relation stands for only an average and is line. When the optically-thick winds stops, the mag- not so accurate for individual nova. This properties nitude decays as t−3. We recommend observations is naturally explained as an intrinsic deviation due with narrower band filters such as Stromgren¨ y-band to a diffrent ignition mass associated with a differ- to accurately follow continuum flux even in the neb- ent mass-accretion rate. (see Fig. 15 and Section 5 ular phase (taken from Hachisu & Kato 2006). in Hachisu & Kato (2010) for more detail.) 2.2. MMRD relation 2.3. Light curve fitting for V1974 Cyg and V2491 Cyg There is a well known empirical relation between the maximum absolute magnitude and the rate of Figure 3 shows light curve fitting of V1974 Cyg. decline (MMRD) of nova light curves (e.g. Schmidt The optical light curve decays as t−1:75 from the op- 1957). A brighter nova decays more rapidly. Using tical peak at t = 2:67 days until the strong emis- the universal decline law, we can derive a theoreti- sion lines begin to contribute in the nebular phase. cal MMRD relation. If we take a typical maximum This figure also shows UV 1455 Å narrow band magnitude for a WD, we get a decline rate from light curve. This bands is selected to avoid promi- the template light curve (Figure 2). This template nent emission or absorption lines in UV spectra and curve is common for all the WD mass with some to represent continuum emission (Cassatella et al. squeeze/expand factor of the timescale and the mag- 2002). Changing the WD mass for a given chemical nitude.