Non-LTE luminosity and abundance diagnostics of classical novae in X-rays

The complete version of my dissertation is available at ProQuest and arXiv.org. In the following I give a brief summary what inspired me to start working on this topic, how far I got and what needs to be considered in the future to get a better understanding. The scopes of my work were: to understand modeling stellar atmospheres with TLUSTY/SYNSPEC; to search for, organize and incorporate new atomic data in the calculations and finally to apply all these for supersoft sources.

Introduction

Classical novae (CNe) are cataclismic variable stars (CV) that are close binaries with a white dwarf (WD) primary and a main sequence (MS) companion star filling its Roche-lobe. In the gravitational potential of the WD the accreted material transfers to the surface of the WD through an accretion-disk. Typical mass trasfer rates are between 10-8–10-11 M☉/year and magnetic fields are negligible. As this hydrogen rich material builds up in the surface layer of the WD, its density and temperature increase until it reaches degeneracy. In this state of the material the pressure is almost independent of the gas temperature. The gas can heat up until nuclear fusion starts. Because this positive feedback adds more energy to the layer a chain-reaction starts and tremendous energy release occurs. Degeneracy depends on temperature and density, the higher the density and lower the temperature the more degenerate the matter is. In the core of WDs the temperature is low compared the high density and the matter is safely degenerate. This holds for the critical surface layer as well. When fusion stars, however, the temperature increase is so high that degeneracy lifts which in turn decreases the density. As a result, the material acts like normal gas agian and explodes off from the WD. During the outburst the atmosphere expands and cools adiabatically. The nova reaches its optical maximum at this phase. The WD gains a red-giant-like atmosphere reaching out nearly 100 R☉ and forms a common envelope around the binary. Due to the strong radiation and dynamical friction with the secondary the atmosphere loses mass and the photosphere recedes. As we can see deeper and deeper in the atmosphere where temperature is higher, the peak of the energy distribution gradually shifts towards shorter wavelengths. Meanwhile a stable hydrogen fusion (hence a constant bolometric luminosity of the nova) is assumed on the surface of the WD.

Figure 1.1 summarizes the response of WDs for accretion as function of WD mass and accretion rate (Kato, 2010). The abscissa is the WD mass in solar masses and the ordinate is the accretion rate (Ṁ) in M☉/year. If the accretion rate is low, on the order of 10-8–10-11 M☉/year, the burning is episodic. In this case the, a hydrogen-rich envelope builds up on the surface of the WD and it becomes a classical nova system. The supersoft stage starts with a nova event and its duration depends on the WD mass and the chemical composition of the accreted material. Next to the curves are the envelope masses necessary for a nova outburst. It can be seen that more massive WDs require less material for an outburst. This also implies that massive WDs produce more frequent outbursts (recurrent novae). Just below the critical accretion rate (Ṁcr ≈ 10-7 M☉/year) the ongoing burning is continuousliy supported by fresh material. Ṁcr slightly increases with WD mass. Over about 4·10-7 M☉/year the released gravitational potential energy can stop further accretion, regulating the mass transfer and the luminosity. For even higher accretion rates optically thick winds, and finally, a common envelope forms.

During nova cycles WDs are believed to gain mass hence the fate of these objects is also interesting. If ONeMg WDs gain enough mass they can collapse to neutron stars. When a more common CO WD reaches the Chandrasekhar limit the star explodes in Type Ia supernova (SN-Ia). Hence, supersoft sources are believed possible SN-Ia progenitors. The lack of hydrogen in SN-Ia spectra can be explained by such nova cycles.

Figure 1.1: Response of WDs for mass accretion in the WD mass and mass-accretion rate plane by Kato (2010).

Modeling hot atmospheres

The calculation of model atmospheres involves the solution of equations governing the stellar structure and the flow of radiation. One must make some simplifying assumptions to pursue self-consistent solutions. We assume that the stellar photosphere is thin compared to the radius (plane-parallel atmospheres) of the WD. If the plane-parallel approximation is valid the surface gravity can be considered constant. This is a good starting point for supersoft sources, but a more elaborated model must involve spherical geometry. We assume a steady-state atmosphere, neglecting the effects of pulsation, shocks, stellar winds, magnetic and tidal heating. The atmosphere is in radiative equilibrium, energy transportation by convection, conduction or other means are neglected.

Computatinally the problem is addressed in two basic iterative steps as shown in Figure 2.1: First, one finds the radiation field, determining the flow of radiation from the interior. Second, keeping energy conserved, one determines the structure and finds the corrections to the radiation field. Repeating these steps iteratively until self-consistency is achieved gives a solution. The model atmosphere is given by the effective temperature (Teff), surface gravity (log g) and the chemical composition of the star (εi). Here &epsiloni refers to abundances as well as atomic data (level energies, oscillator strengths, cross-sections, etc.) for each element in the model. Turbulent and microturbulent velocities are denoted by ξturb in the Figure.

Figure 2.1: The main steps of a model atmosphere calculation.

Model atoms

I will write this later ...

Figure 3.1: Grotrian diagram for N VII. Black lines show NIST levels and transitions, blue ones are from TOPbase. The red horizontal bar is the ionization limit. For transitions, line widths are proportional to oscillator strengths. The 1s level is not on the linear scale for better clarity of the graph. The 70 Å bar represents the long wavelength limit for practical purposes. Levels that are farther apart (Lyman-series) than this limit have transitions in the supersoft range. (higher resolution version)

Figure 3.2: Grotrian diagram for Al X. Unlike simple hydrogenic atoms, multi electron systems have more levels and transitions. The levels over the ionization limit are autoionizing levels.

X-ray modeling of classical novae

Figure 4.1: The grid of calculated models. The shaded region is the super-Eddington regime, not available for TLUSTY. Different sequences were calculated to model the spectral variations at certain temperatures, gravities, temperature-gravity ratio and along the Eddington limit. A bunch of models were calculated around 600 000 K and log g = 8, these fitted the V4743 Sgr data the best.

Figure 4.2: Corrections for interstellar absorption. Galactic abundances were taken from Morrison and McCammon (1983) and a hydrogen column density NH = 4·1020 cm-2 was used.

Observations of classical novae

Figure 1.: Spectral fits for the four Chandra observations. The black lines are the NLTE synthetic spectra (labelled with temperature and log g), observed data are shaded and continuum models are shown with dashed lines.

Figure 1.: Evolution of V4743 Sgr in the temperature-gravity diagram. The WD was very cloes to the Eddington limit in 2003.

Conclusions

Starting out from simple continuum models of light metals including only their ground states (black line in Figure 6.1) I built multi-level model atoms from NIST/ASD and TOPbase atomic data. I collected atomic data on radiative transition strengths and natural broadening for about 70,000 spectral lines in the supersoft range from low ionization degrees of C, N, O, Ne, Mg, Al, Si, S, Ar, Ca and Fe, up to hydrogenic ions. Altogether 21,148 energy levels and 542,914 transitions were included. On boundfree cross sections, data were extracted from TOPbase for all multiplets. With these opacity sources it is now possible to calculate full non-LTE line blanketed spectra in the supersoft range (the grey line shows in Figure 6.1) with TLUSTY and SYNSPEC. SYNSPEC also required slight modifications to increase the highest ionization degrees to match the new input files. With an extensive grid I showed the effects of surface temperature, gravity, abundance and the influence of model atoms on the final spectrum. These relationships suggest that static plane-parallel models over-estimate the effective temperature and surface gravity for classical novae.

Figure 6.1: Emergent flux from a continuum (black line) and a full NLTE (grey line) model. The numerous spectral lines redistribute flux to higher energies. The spurious emission features need further attention, they might be numerical artifacts (laser lines). Hydrogen and ions of He, C, N, O, Ne, Mg, Al and Si were included with detailed model atoms. Energy levels of S, Ar and Ca were averaged into 9–10 superlevels, Fe was included only with its ground states.

My work also required numerous little programs to effectively manipulate TLUSTY and SYNSPEC input and output files for spectral modeling. For example, model atoms have complex structures and any change in the level structure must be propagated through the entire model atom. By deleting one level, all higher level indices will change. Bound-free transition of the given level must be removed and all transitions originating from or ending on the given level must be removed. Such tasks can be done easily by hand for a few levels, but certainly not for hundreds of levels. Level averaging requires similar automated methods as well. TLUSTY stores the atmospheric structure and level populations in its own format. These data blocks must be processed for graphing or to calculate ionization balance and conditions in the atmosphere. Short Python scripts create Grotrian diagrams from model atoms, convergence logs during model calculation, carrying out Gaussian convolution of the spectra or calculating interstellar absorption.

With TOPAtom one can build arbitrarily complex model atoms directly from the original TOPbase or NIST data files. Any other atomic data sets can be easily incorporated by reformatting them to the original format of one of these primary atomic data tables. Model atoms with superlevels and superlines (OS mode) are also available.

As part of this work a task-oriented pipeline (TGRID) was developed. TGRID can do spectral analysis from grid calculations up to abundance analysis. However, inaccuracies in the input atomic data, coupled with strong blanketing and the enormous interstellar reddening, made quantitative fits impossible. Steps of the spectral analysis are in modular format, which makes them scriptable and they can also be used independently in other applications.

Application of these techniques to some classical novae have shown the validity of the model atoms. I showed in the example of V4743 Sgr and V2491 Cyg how the new model atoms fit observed data of Chandra and XMM-Newton satellites. V4743 Sgr was very close to the Eddington limit in March – September 2003. The blue-shifted nitrogen and oxygen spectral lines confirm this. By February 2004 the luminosity decreased significantly and spectral lines appeared at their laboratory wavelengths, which suggests that hydrogen burning was turned off, the stellar wind stopped and the WD returned to a static state. Abundance analysis showed enhancement of helium, nitrogen and oxygen compared to solar values. The abundance of nitrogen is about 10–20 times greater than was found by Petz et al. (2005). Oxygen is over-abundant by a factor of a few, while carbon is around solar values. Enhancement of neon, magnesium and aluminum of about 50 times the solar values were found. A slight over-abundance of silicon and sulfur is possible (up to twice the solar value). Argon and calcium are depleted compared to solar abundance. However, the abundance analysis still suffers from large uncertainties and these figures should be considered only to approximations. These tests also showed the need for a comprehensive upgrade of TLUSTY/SYNSPEC to model CNe. The case of V2491 Cyg was a good example showing the limitation of static, plane-parallel modeling of luminous supersoft sources. The blue-shifted lines and the extended blue continuum indicate a strong wind. The simultaneous strong lines of NVI and NVII suggest an extended line-forming region and these features together cannot be modeled by static atmospheres. These objects need hydrodynamic calculations in spherical geometry, treating both the extended line formation region and stellar wind explicitly. This was beyond the scope of the current project. However, the technique used here work well for supersoft sources below the Eddington limit. Finally, for quantitative analyses on the abundance and luminosity evolution of classical novae, many more spectroscopic observations are required.

References

    Wikipedia