Monte Carlo Radiative Transfer Simulations: Applications to Astrophysical Outflows and Explosions

Abstract

The theory of radiative transfer provides the link between the physical conditions in an astrophysical object and the observable radiation which it emits. Thus accurately modelling radiative transfer is often a necessary part of testing theoretical models by comparison with observations. We describe a new radiative transfer code which employs Monte Carlo methods for the numerical simulation of radiation transport in expanding media. We discuss the application of this code to the calculation of synthetic spectra and light curves for a Type Ia supernova explosion model and describe the sensitivity of the results to certain approximations made in the simulations. Comment: 6 pages, 2 figures. To appear in Proceedings of 4th International Conference on Numerical Modeling of Space Plasma Flows (Chamonix 2009)

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arXiv:0911.1549v1 [astro-ph.SR] 8 Nov 2009
**FULL TITLE**
ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION**
**NAMES OF EDITORS**
Monte Carlo Radiative Transfer Simulations: Applications
to Astrophysical Outflows and Explosions
S. A. Sim1, M. Kromer1, F. K. R¨ opke1, E. I. Sorokina2, S. I.
Blinnikov1,2, D. Kasen3, W. Hillebrandt1
1Max-Planck-Institut f¨ ur Astrophysik, Karl-Schwarzschild-Str. 1, 85741
Garching, Germany
2Institute for Theoretical and Experimental Physics, Bolshaya
Cheremushkinskaya 25, 117218 Moscow, Russia
3University of California Santa Cruz, 1156 High Street, Santa Cruz, CA
95064, USA
Abstract.
physical conditions in an astrophysical object and the observable radiation which
it emits. Thus accurately modelling radiative transfer is often a necessary part of
testing theoretical models by comparison with observations. We describe a new
radiative transfer code which employs Monte Carlo methods for the numerical
simulation of radiation transport in expanding media. We discuss the application
of this code to the calculation of synthetic spectra and light curves for a Type Ia
supernova explosion model and describe the sensitivity of the results to certain
approximations made in the simulations.
The theory of radiative transfer provides the link between the
1. Monte Carlo Radiative Transfer
Since almost all we know about astronomical objects is inferred from the radi-
ation which they emit, the theory of radiation transport often has a key role in
testing our understanding of astrophysics. Although there are a variety of com-
petitive approaches used for radiative transfer simulations, Monte Carlo meth-
ods are particularly well-suited for many modern astrophysical applications. In
the Monte Carlo approach, the radiation field is discretized into quanta which
represent bundles of photons. By propagating these quanta through a model
of an astrophysical object, and simulating their interactions, synthetic spec-
tra and light curves can be obtained. This method has the particular advan-
tage that matter-radiation interactions are always treated locally meaning that
multi-dimensionality, time-dependence and large-scale velocity fields can all be
incorporated readily.
2. The ARTIS code
Here we describe a new radiative transfer code (artis; Kromer & Sim 2009)
which has been developed for application to Type Ia supernova (SN Ia) explosion
models. The code is based on a Monte Carlo indivisible packet scheme described
by Lucy (2002, 2003, 2005) and was developed from the grey radiative transfer
code of Sim (2007).
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Sim et al.
The code is designed to simulate time-dependent, three-dimensional radia-
tion transport in supernova ejecta during the phase of homologous expansion.
The optical display of SNe Ia is powered by the energy released in the radioactive
decay of isotopes synthesized during the explosion, predominantly56Ni and its
daughter nucleus56Co. Therefore, the code starts from an initial distribution of
56Ni in the ejecta and then the subsequent radioactive decays are followed. These
decays initially give rise to gamma-ray photons which, at least for early epochs
when the ejecta are optically thick, are rapidly down-scattered and absorbed
by photoelectric processes. This heats the ejecta. The subsequent re-emission
of ultraviolet, optical and infrared emission by the ejecta is then simulated to
obtain spectra and light curves. The code does not assume local thermodynamic
equilibrium (LTE) but includes an approximate non-LTE (NLTE) treatment of
ionization and a detailed approach to line scattering and fluorescence. For a
complete description of the code see Sim (2007) and Kromer & Sim (2009).
3.Testing ARTIS with a standard explosion model
To test the artis code we have performed a variety of radiative transfer sim-
ulations for the well-known W7 SN Ia explosion model (Nomoto et al. 1984;
Thielemann et al. 1986). Although this one-dimensional model is considerably
simpler than modern three-dimensional explosion models (e.g. R¨ opke & Niemeyer
2007; R¨ opke et al. 2007), it is known to predict spectra and light curves in rea-
sonable agreement with observations (e.g. Jeffery et al. 1992; H¨ oflich 1995;
Nugent et al. 1997; Lentz et al. 2001; Baron et al. 2006; Kasen et al. 2006) and
therefore provides a realistic test model for our radiative transfer simulations.
For our W7 test simulations, the explosion model properties (ejecta density,
composition and initial distribution of radioactive isotopes) were mapped to a
homologously expanding 503Cartesian grid and the expansion followed for 100
logarithmically-spaced time steps spanning the time interval from 2 to 80 days
after explosion. The assumption of homologous expansion in the W7 model
has been tested using the stella code in a manner similar to that described
by Woosley et al. (2007). That test showed that the density structure is af-
fected only slightly during the first weak after explosions and that thereafter
homologous expansion becomes a very good approximation. The propagation of
a total of five million Monte Carlo energy packet quanta were simulated from
their initial release by the radioactive decay of either56Ni or56Co until, af-
ter multiple radiation-matter interactions, they escaped from the computational
domain as bundles of ultraviolet, optical or infrared (UVOIR) photons. The
escaping packets were then binned by time of escape and photon frequency to
construct time-dependent spectra for the model. Since the W7 model is one-
dimensional, it is unnecessary to bin the escaping quanta based on direction of
scape but this can be readily done to obtain viewing-angle dependent spectra
for multi-dimensional models.
3.1. Synthetic spectra from ARTIS
Figure 1 shows a sequence of three optical spectral snapshots obtained with the
artis code for the W7 model. A convenient property of Monte Carlo radiative
transfer simulations is the ease with which the propagation histories of the Monte

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Monte Carlo Radiative Transfer
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Carlo quanta can be used to understand the manner in which the spectra features
are formed. For each escaping quantum, artis records the details of its last
radiation-matter interaction with either a bound-bound, bound-free or free-free
event. This information can then be used to identify the processes responsible
for features in the spectra. In Figure 1, the areas above and below the total
spectrum are shaded to indicate the atomic number of the elements which last
affected the escaping quanta for each wavelength bin. This makes it easy to
understand how the spectral features are formed and one can readily see how
the contributions to the spectra evolve in time. For example, in Figure 1 it
is clear from the shading that the early phase spectra are strongly affected by
intermediate-mass elements such as Si and S while the later time spectra are
dominated by elements of the iron group. This is a well-known consequence of
the layered structure of the W7 model. At early times, the outer layers (which
are rich in the products of partial nuclear burning) are optically thick.
time passes, however, the expansion of the ejecta causes these layers to become
optically thin such that radiation escapes directly from the inner region which
is dominated by iron group material.
For comparison, the observed spectra of a fairly normal SN Ia (SN 1994D,
Patat et al. 1996) are over-plotted for the same epochs. The overall flux distri-
bution and general properties of the observed spectral features (e.g. the charac-
teristic Si ii line at 6355˚ A and the Ca ii infrared triplet at 8549˚ A) are reasonably
well-reproduced by the model, suggesting that the numerical simulations cap-
ture much of the necessary physics required for the interpretation of the obser-
vations. There are, however, some clear discrepancies between the observational
data and the synthetic spectra (e.g. excess emission below ∼4000˚ A in the early-
time model spectra and an extra emission feature around ∼6500˚ A in the later
time spectrum) – but some disagreement is expected since the W7 model has
not been fine-tuned to match observations of any specific SN in detail.
As
3.2. Sensitivity to plasma conditions
Multi-dimensional radiative transfer simulations for SNe Ia require significant
computational resources and approximations must currently be made to make
the simulations feasible. Two particularly important issues are the completeness
of the atomic data set used and the sensitivity of the synthetic observables to the
treatment of the plasma conditions (particularly the excitation/ionization state).
We have therefore used the W7 model as a standard case to investigate some
of these effects with artis; photometric light curves computed from several of
our numerical simulations are shown in Figure 2. We also compared our results
with those of other SN radiative transfer codes to quantify the extent to which
different numerical methods affect the synthetic observables.
Using the sedona code, Kasen (2006) showed that realistic atomic data
sets containing many millions of spectral lines are required to accurately model
radiation transport in SN Ia. This is particularly true at NIR (near-infrared)
wavelengths where the spectrum can be significantly affected by fluorescent emis-
sion in forests of weak lines of iron-group elements. This is confirmed by our
simulations with artis. Figure 2 shows light curves computed with our approx-
imate NLTE treatment of ionization but adopting different atomic data sets
drawn from the line lists computed by Kurucz & Bell (1995) and Kurucz (2006).

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Sim et al.
Figure 1.
and +24 days measured relative to the maximum of the B-band light curve
(which occurs around 19 days after explosion). The emitted model spectra
are shown as the heavy black histogram in each panel. The area under the
curve is shaded to indicate the elements responsible for the last bound-bound
interactions of escaping Monte Carlo quanta in the corresponding frequency
bin. The shaded region at the top of each panel identifies which elements
were last responsible for removing packets from the corresponding frequency
bin (this can be used to identify absorption features in the spectra). The
observed spectra of SN 1994D (Patat et al. 1996) are shown for comparison
(solid blue lines). These have not been corrected for redshift or extinction.
Computed spectra for the W7 model for three epochs: -5, +2
When we use a reasonably large atomic line list (∼ 8×106lines) we obtain NIR
light curves which are significantly brighter around their first maximum than
with an atomic data set restricted to only ∼ 4 × 105lines. The optical light
curves are much less affected although there is a tendency for the U, B and V
bands to be slightly fainter owing to the flux redistributed from these bands to
the NIR. We note that the light curves computed with the larger atomic data
set are also in quantitatively better agreement with observations (see Figure 2).
In Figure 2 we also show light curves computed with a pure LTE treat-
ment of the excitation/ionization state of the ejecta. These light curves were
obtained using the smaller atomic data set (∼ 4 × 105lines) mentioned above.
For early times (up to around 30 days in the optical bands and 20 days in the
NIR bands), these light curves agree well with those obtained with our NLTE
implementation. This is expected since LTE should be a good approximation
when the radiation is strongly trapped. At later times, however, departures from

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Figure 2.
UVOIR bolometric, U, B, V, R, I, J, H and K band light curves obtained from
our time-dependent spectra using the filter functions of Bessell (1990) and
Bessell & Brett (1988). The solid histograms show the light curves obtained
with artis using (i) our approximate NLTE treatment of ionization and an
atomic data set containing ∼ 8×106atomic lines (blue), (ii) NLTE with only
∼ 4×105lines (red) and (iii) an LTE treatment of ionization with ∼ 4×105
lines (green). For comparison we show observations of SN 2001el (Krisciunas
et al. 2003; grey circles) and light curves obtained with the sedona (dotted
lines) and the stella codes (dashed lines; UVOIR, U, B, V, R, and I).
Computed light curves for the W7 model. The panels show the
LTE become strong and our NLTE treatment of ionization predicts significantly
higher ionization states throughout much of the ejecta. This directly affects
the observables causing the U, B and V band to remain significantly brighter
than suggested by LTE. This illustrates the sensitivity of the observations to the
ejecta properties and highlights the need for a realistic treatment of the plasma
conditions if detailed comparisons to observations are to be made.
3.3.Comparison of results from different codes
The agreement between the artis light curves and those obtained by sedona
(Kasen et al. 2006) and stella (Blinnikov & Sorokina 2002; Blinnikov et al.
2006) is encouragingly good (Figure 2). Compared to sedona, the artis light
curves computed with the larger atomic data set agree very well in all bands up
to several weeks after maximum light. The difference which manifest at later
times are most likely attributable to difference in the manner in which the codes
treat the plasma conditions (see Kromer & Sim 2009 for further discussion). The
current version of stella adopts an LTE treatment of the plasma conditions
with photon redistribution modelled using an approximate source function. As
expected, its light curves are similar to those obtained with the LTE implemen-
tation in artis. The stella light curves shown here were computed with an

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extended atomic data set containing 2.6 × 107lines. This atomic data set im-
proves aspects of the comparison with stella relative to that shown in figure 7
of Kromer & Sim (2009; the stella curves there used only 1.6 × 105lines). In
particular, the initial rise of the stella light curves is faster.
4.Future prospects
Our results obtained from the W7 model suggest that our radiative transfer
simulations are able to produce realistic synthetic spectra and light curves as
required for the testing of SNe Ia explosion models. We have already used the
artis code to investigate simple aspherical toy models (Kromer & Sim 2009;
Kromer et al. 2009) and will in the near future use it to compute synthetic
observables for state-of-the-art hydrodynamical explosions models in order that
their predictions can be directly tested against observational data.
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