Classical Novae as Super-Eddington Objects

Several of the inconsistencies plaguing the field of novae are resolved once we consider novae to be steady state super-Eddington objects. In particular, we show that the super-Eddington shell burning state is a natural consequence of the equations of stellar structure, and that the predicted mass loss in the super-Eddington state agrees with nova observations. We also find that the transition phase of novae can be naturally explained as “stagnating" winds. Introduction: Classical novae exhibit long duration super-Eddington luminosities while in their eruptive state. At least, this is the conclusion that should be reached when combining that the peak luminosity of novae (with MWD ∼0.5M⊙, Livio 1992) is always super-Eddington and that in all cases where the bolometric evolution was recovered (using UV observations), it was shown to decay slowly (e.g., Friedjung 1987, Schwarz et al. 2001, Shaviv 2001b). Thus, if classical novae are super-Eddington for durations much longer than any relevant dynamical time scale, two basic questions arise: • How can super-Eddington objects exist for durations much longer than their dynamical time scale? • Even if such super-Eddington states exist, why do novae choose this state instead of following the known core-mass luminosity relation (CMLR)? A seemingly unrelated question, which we try to address as well, is • Why do the theoretical simulations consistently under predict the amount of ejected mass, as compared with actual observational determinations of ejecta mass? The notion that novae are super-Eddington contradicts the common wisdom usually invoked in which objects cannot shine beyond their classical Eddington limit, LEdd , since no hydrostatic solution exists. In other words, if objects do pass LEdd , they are highly dynamic. They have no steady state, and a huge mass loss should occur since their atmospheres are then gravitationally unbound and should therefore be expelled. Thus, classical novae according to this picture, can pass LEdd but only for a short duration corresponding to the time it takes them to dynamically stabilize after the onset of the thermonuclear runaway (TNR). This is indeed seen in detailed 1D numerical simulations of nova TNRs, where novae can be super-Eddington but only for several thousand seconds (e.g., Starrfield, 1989). However, once they do stabilize, they are expected and indeed do reach in the simulations a state given by the CMLR which describes the Hydrogen shell burning state. Namely, we naively expect to find no steady state super-Eddington atmospheres. This, however, is not the case in nature. The Super-Eddington State: To existence of a super-Eddington state becomes natural, once we consider that: 1. Atmospheres become unstable as they approach the Eddington limit. In addition to instabilities that operate under various special conditions (e.g., Photon bubbles in strong magnetic fields or the s-mode instability under special opacity laws), two instabilities were found to operate in Thomson scattering atmospheres (Shaviv 2001a). Moreover, one of these instabilities does not depend on the boundary conditions and is therefore extremely general. It implies that all atmospheres will become unstable already before reaching the Eddington limit. 2. The effective opacity relevant for the calculation of the radiative force on an inhomogeneous atmosphere is not necessarily the microscopic opacity (Shaviv 1998). Instead, it is given by κ f f V ≡ 〈FκV 〉V /〈F〉V . The situation is very similar to the Rosseland vs. Force opacity means used in non-gray atmospheres, where the inhomogeneities are in frequency space as opposed to real space. For the special case of Thomson scattering, the effective opacity is always reduced. To summarize, we find that as atmospheres approach their classical Eddington limit, they will necessarily become inhomogeneous. These inhomogeneities will necessarily reduce their effective opacity such that the effective Eddington limit will not be surpassed even though the luminosity can be super-classical-Eddington. This takes place in the external part of luminous objects, where the radiation diffusion time scale is shorter than the dynamical time scale of the atmosphere. Further inside the object, convection is necessarily excited such that the total energy flux may be super-Eddington, with the radiative part of it necessarily being sub-Eddington and with the convective flux carrying the difference. Nevertheless, one of the key features of super-Eddington atmospheres is that a wind will necessarily be accelerated. It is not the catastrophic wind naively expected from super-Eddington conditions, however, it is going to be significant. Super-Eddington Winds: The atmosphere can remain effectively sub-Eddington while being classically super-Eddington, only as long as the inhomogeneities comprising the atmosphere are optically thick. Clearly however, this assumption should break at some point where the density is low enough. From that radius upwards, the radiative force overcomes the gravitational pull and a wind is generated. The mass loss rate can then be obtained by identifying the sonic point of a steady state wind with the critical point, which is the radius where the radiative and gravitational forces balance each other. We then have Ṁ = 4πRρcriticalvsonic. Furthermore, this can generally be reduced to the form of Ṁ = W (Γ)(L−LEdd) cvs , (1) where W is a dimensionless wind “function”. In principle, W can be calculated from first principles only after the nonlinear state of the inhomogeneities is fully understood. This however is still lacking as it requires elaborate 3D numerical simulations of the nonlinear steady state. Nevertheless, it can be done in several phenomenological models which only depend on geometrical parameters such as the average size of the inhomogeneities in units of the scale height (β ≡ d/lp), the average ratio between the surface area and volume of the blobs in units of the blob size (Ξ), and the volume filling factor α of the dense blobs. For example, in the limit where the blobs are optically thick, one obtains that W = 3Ξ/32 √ ναβ(1−α)2 (Shaviv 2001b). Here ν is the ratio between the effective and adiabatic speeds of sound. Thus, W depends only on geometrical factors. It does not depend explicitly on the Eddington parameter Γ. Moreover, typical values of W ∼ 1-10 are obtained. The mass loss predicted by the super-Eddington theory (eq. 1) was compared with observations of super-Eddington objects which have good observational data. These were two novae which are not very fast and which have the best determined absolute bolometric evolution: FH-Ser and LMC 1988 #1. The theory was also applied to the Luminous Blue Variable star η-Car. For the two novae, we find that the predicted mass loss rates agree with their observations if W ≈ 10±5, which is clearly consistent with the theoretical estimate for W . The agreement is also with the temporal evolution of the velocities, if those are taken to be the primary absorption line component. Using W ≈ 10±5, the mass loss equation can also be applied to η-Car, which is an entirely different object from novae (in mass, mass loss rate and duration, photospheric size etc), yet, the predicted integrated mass loss is in total agreement with the observed 1-2M⊙ of ejecta, while the terminal velocity is consistently predicted as well. For more information on the models, see Shaviv (2001b) Steady State Shell Burning: The next step is to show why novae become superEddington to begin with. In particular, the nova shell burnings steady state should be given by the CMLR (Paczynski 1970), counter to observations. Given the contradiction, we look for new solutions to the stellar structure equations for systems with shell burning. This should describe the steady state of novae after they undergo a TNR. Unlike the standard derivation of the CMLR, we allow the atmospheres to be inhomogeneous. Namely, if the Eddington parameter is larger than a threshold (taken to be 0.85) the effective opacity is reduced. We still do not know the exact behavior of κe f f as a function of Γ. This could later be obtained by comparing the steady state obtained to the actual observations of novae, or through detailed 3D radiative hydro simulations. At this point however, we want to show that using a reasonable behavior of κe f f (Γ), a super-Eddington steady state does exist. We take κe f f (Γ > Γcrit = 0.85) = κ0Γcrit/Γ andW = 10 (somewhat different choices do not change the conclusions). We find that the CMLR obtains a super-Eddington branch. The main differences between the structure in this branch and the structure in the sub-Eddington branch are the following: (1) The super-Eddington branch has a SEW at the top of it, with the photosphere located in the wind. The sub-Eddington branch has no wind (though it could have one if a non-Thomson opacity is considered). Since the wind is “heavy” the actual luminosity at the photosphere could be sub-Eddington. (2) The super-Eddington branch has a convective layer that penetrates into the burning shell (most of the energy is actually released in the convection zone). In the sub-Eddington branch, the burning shell is all radiative. (3) The luminosity in the sub-Eddington branch is not a function of the core mass. It is a function of the core mass in the super-Eddington branch. Except for the very fast novae, the shell burning evolution can then be described as a steady state which slowly evolves due to mass loss (e.g., as is done by Kato & Hachisu 1994, for sub-Eddington evolution and opacity driven winds). The preliminary results show that predictions for L(t), T (t), v∞ and Me jecta agree with observations.