We are calculating models of atmospheres and according spectra of supernovae. Atmospheres of supernovae were among the first atmospheres that were modelled with PHOENIX.

Types of supernovae

A supernova is the most luminous event known. Its luminosity matches those of whole galaxies. The name derives from the works of Walter Baade and Fritz Zwicky who studied supernovae intensively in the early 1930s and used the term supernova therein.
Nowadays supernova is a collective term for different classes of objects, that exhibit a sudden rise in luminosity that drops again on a timescale of weeks.
Those objects are subdivided into two classes, supernovae of type I or II (SNe I and SNe II). The distinguishing feature is the absence or the presence of spectral lines of hydrogen. SNe I show no such lines as SNe II do. The class of SNe I is further subdivided in the classes a, b and c. This time the distinguishing feature are spectral features of helium and silicon. SN Ia show silicon features, SN Ib show helium but no silicon features and SN Ic show both no silicon and no helium spectral features.
The class of SN II is further subdivided in two classes. Those are distinguished by the decline of the lightcurve. Those SN II that show a linear decline are named SN II-L and those that pass through a plateau-phase are referred to as SN II-P.

supernovascheme
There seem to exist quite a few examples of supernova that don't fit perfectly into this scheme. For those cases there exist other classes e.g. SN IIn and SN IIpec, but those are not in common use.

Mechanisms of supernovae

Supernova of type Ia are believed to be white dwarfs that accrete matter from a companion star and exceed the Chandrasekhar-mass in this process. The resulting collaps kindels thermonuclear fusion processes and the star deflagrates. The resulting hot gas expands rapidly and forms thereby the supernova.
Supernova of type II, Ib and Ic are believed to be the fate of massive stars (With a mass greater than 8 times that of the sun). Such a star passes through numerous phases of core-contractions that ingnite new thermo-nuclear fusion processes. As soon as iron is synthesized such a process is impossible. An iron nucleus has the lowest binding energy and therefore no selfsustained fusion process of iron is possible. Hence iron starts to pile up in the center of the star. More and more iron rains down on this core as the ashes of silicon burning is iron.
At some point this iron core exceeds the Chandrasekhar-mass and the core collapses. Hence this kind of supernova is also called core-collaps supernova. During the collaps the iron nuclei are transformed to neutrons. Most of the gravitational energy (about 99%) is transferred to neutrinos that leave the core.
The density in the inner part of the core (dark grey in fig. 2) is high enough that the local speed of sound is greater than the infall velocity. This part collapses self similar. The speed of sound in the outer part of the core (light grey in fig. 2) is too small and therefore this part falls shocked towards the center.
The degenerate neutrons (fermions) stop the infall at some point. Hence a huge pressure builds up that propagates outwards. The inner core is still dense enough so that the speed of sound is not exceeded. When the pressure wave reaches the outer part of the core the wave becomes a shock. This shock propagates outward. In the shockfront the gas is extremely heated and many kinds of nuclear processes occur. The propagation of the shock drains a lot of energy from the shock but the densities in the shockfront are that high that the neutrinos interact with the shockfront and transfer energy and momentum. Hence the shock is revived and can reach the surface of the star.
The hot gas rapidly expands and the shell around an inner core is ejected and leaves the gravitational potential well. In the early stages of development this gas is optically thick and forms the visible supernova atmosphere. The core that is situated in the center is composed of the dense matter that the pressure wave could transverse unshocked and the matter that was not ejected and accreted in another shock back on the core. This core consists of degenerate neutrons and is appropriatly called a neutron star. If too much matter is accreted on the neutron star the Chandrasekhar-mass is exeede again and the everlasting journey to a black hole begins.
The energy that is set free during the collaps is incredibly large. But just about a 1/1000th part of the energy is transmuted into light. 99% of the energy are deposited in neutrinos and about 1% in the kinetic energy of the atmophere. So a supernova is the most luminous single object we know with just using the 1/1000th part of the available energy.
In figure 2 the production of the shock is displayed.
shock

Modelling of supernova atmospheres

All kinds of supernovae have a rapidly expanding atmosphere in common. The expansion velocity can reach a few percent of the speed of light. Therefore the radiative transport not only has to be calculated in moving media but even so relativistically.
Furthermore scattering is important in the atmosphere. Hence the description of radiative transport demands to fully include the effects of NLTE (non-local thermodynamical equilibrium).


The structure of the supernova is assumed to be spherically symmetric. This may not be a very good assumption, but it has to be made as long as the radiative transfer is treated onedimensionally.
The expansion of the atmosphere is not modelled with a hydrodynamical code. At the point when the supernova is detectable the atmosphere is already in uniform motion and hydrodynamical effects exert no force on the atmosphere. Hence hydrodynamical effects are negligible at the time when the spectrum of the supernova is calculated. For the expansion of a shocked gas in spherical symmetry there exists an analytical solution from Sedov. This states that the velocity is linearly dependent on the radius. Hence a linear velocity law is used in the modelling.

v(r) = v(R0)*(r/R0)

The density profile of the atmosphere is desribed by a power law:

ρ(r) = ρ(R0)*(r/R0)^(-n)

The atmosphere of a supernova evolves with time. But we can only model snapshots of this development. This means that all derivatives with respect to time in the formulae of radiative transfer vanish. This holds if the timescales on which the radiation field evolves are much shorter than the hydrodynamical ones.

There are a number of key-parameters that strongly influence the outcome of the modelling:
  • the effective temperature
  • the characteristic velocity in the atmosphere: v(R0)
  • the exponent in the density-power-law: n
  • the age of the supernova
  • which species are treated in complete NLTE

What has been done with PHOENIX on Supernovae

PHOENIX was sucessfully used in supernova related research. There are quite a few publications out there:
  • Analysis of the Flux and Polarization Spectra of the Type Ia Supernova SN 2001el: Exploring the Geometry of the High-Velocity Ejecta
    Kasen, Daniel; Nugent, Peter; Wang, Lifan; Howell, D. A.; Wheeler, J. Craig; Höflich, Peter; Baade, Dietrich; Baron, E.; Hauschildt, P. H.
    ApJ 593, 788 (2003)
  • Detectability of Mixed Unburnt C+O in Type Ia Supernova Spectra
    Baron, E.; Lentz, Eric J.; Hauschildt, Peter H.
    ApJ 588, L29 (2003)
  • Determination of Primordial Metallicity and Mixing in the Type II-P Supernova 1993W
    Baron, E.; Nugent, Peter E.; Branch, David; Hauschildt, Peter H.; Turatto, M.; Cappellaro, E.
    ApJ 586, 1199 (2003)
  • Detectability of Hydrogen Mixing in Type Ia Supernova Premaximum Spectra
    Lentz, Eric J.; Baron, E.; Hauschildt, Peter H.; Branch, David
    ApJ 580, 374 (2002)
  • Detailed Spectroscopic Analysis of SN 1987A: The Distance to the Large Magellanic Cloud Using the Spectral-fitting Expanding Atmosphere Method
    Mitchell, Robert C.; Baron, E.; Branch, David; Hauschildt, Peter H.; Nugent, Peter E.; Lundqvist, Peter; Blinnikov, Sergei; Pun, Chun S. J.
    ApJ 574, 293 (2002)
  • Non-LTE Synthetic Spectral Fits to the Type Ia Supernova 1994D in NGC 4526
    Lentz, Eric J.; Baron, E.; Branch, David; Hauschildt, Peter H.
    ApJ 557, 266 (2001)
  • 56Ni Mixing in the Outer Layers of SN 1987A
    Mitchell, Robert C.; Baron, E.; Branch, David; Lundqvist, Peter; Blinnikov, Sergei; Hauschildt, Peter H.; Pun, Chun S. J.
    ApJ 556, 979 (2001)
  • Analysis of Type IIn SN 1998S: Effects of Circumstellar Interaction on Observed Spectra
    Lentz, Eric J.; Baron, E.; Lundqvist, Peter; Branch, David; Hauschildt, Peter H.; Fransson, Claes; Garnavich, Peter; Bastian, Nate; Filippenko, Alexei V.; Kirshner, R. P.; Challis, P. M.; Jha, S.; Leibundgut, Bruno; McCray, R.; Michael, E.; Panagia, Nino; Phillips, M. M.; Pun, C. S. J.; Schmidt, Brian; Sonneborn, George; Suntzeff, N. B.; Wang, L.; Wheeler, J. C.
    ApJ 547, 406 (2001)
  • SN 1984A and Delayed-Detonation Models of Type IA Supernovae
    Lentz, Eric J.; Baron, E.; Branch, David; Hauschildt, Peter H.
    ApJ 547, 402 (2001)
  • Preliminary Spectral Analysis of the Type II Supernova 1999EM
    Baron, E.; Branch, David; Hauschildt, Peter H.; Filippenko, Alexei V.; Kirshner, R. P.; Challis, P. M.; Jha, S.; Chevalier, R.; Fransson, Claes; Lundqvist, Peter; Garnavich, Peter; Leibundgut, Bruno; McCray, R.; Michael, E.; Panagia, Nino; Phillips, M. M.; Pun, C. S. J.; Schmidt, Brian; Sonneborn, George; Suntzeff, N. B.; Wang, L.; Wheeler, J. C.
    ApJ 545, 444 (2000)
  • Metallicity Effects in Non-LTE Model Atmospheres of Type IA Supernovae
    Lentz, Eric J.; Baron, E.; Branch, David; Hauschildt, Peter H.; Nugent, Peter E.
    ApJ 530, 966 (2000)
  • Spectral Models of the Type IC Supernova SN 1994I in M51
    Baron, E.; Branch, David; Hauschildt, Peter H.; Filippenko, Alexei V.; Kirshner, R. P.
    ApJ 527, 739 (1999)
  • Synthetic Spectra of Hydrodynamic Models of Type IA Supernovae
    Nugent, Peter; Baron, E.; Branch, David; Fisher, Adam; Hauschildt, Peter H.
    ApJ 485, 812 (1997)
  • The Hubble constant, supernova light curves and spectra, and radiation transport
    Branch, David; Baron, E.; Nugent, Peter; Hauschildt, Peter H.
    PhPl 4, 2016 (1997)
  • Non-local thermodynamic equilibrium effects in modelling of supernovae near maximum light
    Baron, E.; Hauschildt, P. H.; Nugent, P.; Branch, D.
    MNRAS 283, 297 (1996)
  • Evidence for a Spectroscopic Sequence among Type 1a Supernovae
    Nugent, Peter; Phillips, Mark; Baron, E.; Branch, David; Hauschildt, Peter
    ApJ 455, L147 (1995)
  • Non-LTE spectral analysis and model constraints on SN 1993J
    Baron, E.; Hauschildt, P. H.; Branch, D.; Austin, S.; Garnavich, P.; Ann, Hong Bae; Wagner, R. M.; Filippenko, A. V.; Matheson, T.; Liebert, James
    ApJ 441, 170 (1995)
  • Spectrum synthesis of the Type IA supernovae SN 1992A and SN 1981B
    Nugent, Peter; Baron, E.; Hauschildt, Peter H.; Branch, David
    ApJ 441, L33 (1995)
  • Supernova 1993J: one year later
    Baron, E.; Hauschildt, P. H.; Young, T. R.
    PhR 256, 23 (1995)
  • Low Hubble Constant from the Physics of Type Ia Supernovae
    Nugent, Peter; Branch, David; Baron, E.; Fisher, Adam; Vaughan, Thomas; Hauschildt, Peter H.
    PhRvL 75, 394 (1995)
  • Analysis of the early spectra and light curve of SN 1987A
    Hauschildt, Peter H.; Ensman, Lisa M.
    ApJ 424, 905 (1994)
  • Interpretation of the Early Spectra of SN 1993J in M81
    Baron, E.; Hauschildt, P. H.; Branch, D.; Wagner, R. M.; Austin, S. J.; Filippenko, A. V.; Matheson, T.
    ApJ 416, L21 (1993)
  • Relativistic effects in supernova photospheres
    Hauschildt, P. H.; Best, M.; Wehrse, R.
    A&A 247, L21 (1991)
  • Theoretical models for the continuum and colors of SN 1979 C and SN 1980 K
    Hauschildt, P. H.; Wehrse, R.; Shaviv, G.
    A&A 210, 262 (1989)
  • An atlas of calculated continuum energy distributions for supernovae of type II
    Hauschildt, P. H.; Wehrse, R.; Shaviv, G.
    A&AS 77, 115 (1989)