Monte Carlo Radiative Transfer:
Application to the Minkowski’s Footprint envelope
Gilles Niccolini
Javier Alcolea
Valentin Bujarrabal
g.niccolini@oan.es
Observatorio Astronómico Nacional
Granada - 14/09/2004 (Prosper/LATEX) – p.1
Summary
• Introduction
• Monte Carlo Radiative Transfer
• The particular case of M1-92: a dust envelope model
WARNING: work in progress
• Conlusion & Perspectives
Granada - 14/09/2004 (Prosper/LATEX) – p.2
Hertzprung-Russel diagram
log (L?)
Stars with 1 M M
8 M
95 % of the stars follow this evolutionary track
(e.g. Lattanzio et al., 1997)
frag replacements
log (Teff )
Granada - 14/09/2004 (Prosper/LATEX) – p.3
Hertzprung-Russel diagram
log (L?)
post-AGB
BD
we start from something rather spherical . . .
AGB
HB
frag replacements
de Laverny, P., Mauron, N., Lopez, B.
RGB
MS
WD
log (Teff )
Granada - 14/09/2004 (Prosper/LATEX) – p.3
Hertzprung-Russel diagram
log (L?)
post-AGB
BD
and we end up with . . .
AGB
HB
frag replacements
RGB
MS
Sahai et al. ApJ, 1998
WD
log (Teff )
Granada - 14/09/2004 (Prosper/LATEX) – p.3
Hertzprung-Russel diagram
frag replacements
log (L?)
post-AGB
BD
•
The reasons of this change are
still undetermined.
•
We need to determine the structure of the nebula to constrain
the models (interaction between 2
winds, magnetic field, binary star
. . . ?).
AGB
HB
RGB
MS
WD
log (Teff )
Granada - 14/09/2004 (Prosper/LATEX) – p.3
Integral form of the RT equation
ˆ
Iλ (~r, n
b) = Iλ (~r0 , n
b) e−τλ (~r0 ,~n,s) +
Zs
0
ˆ
ˆ
ηλ (~r0 +s0 n
b, n
b) e− τλ (~r0 ,~n,s)−τλ (~r0 ,~n,s ) ds0
+
0
τλ (~r0 , n
b, s) =
ηλ (~r, n
b) =
Zs
0
0
0
κext
(~
r
+
s
n
b
)
ds
.
0
λ
κabs
r ) Bλ
λ (~
T (~r) +
ZZ
1
sca
gλ (~r, n
b0 , n
b) Iλ (~r, n
b 0 ) d2 n
b0 .
+ κλ (~r)
4π
Granada - 14/09/2004 (Prosper/LATEX) – p.4
Integral form of the RT equation
ˆ
Iλ (~r, n
b) = Iλ (~r0 , n
b) e−τλ (~r0 ,~n,s) +
Zs
0
ˆ
ˆ
ηλ (~r0 +s0 n
b, n
b) e− τλ (~r0 ,~n,s)−τλ (~r0 ,~n,s ) ds0
+
NO !
0
τλ (~r0 , n
b, s) =
ηλ (~r, n
b) =
Zs
0
0
0
κext
(~
r
+
s
n
b
)
ds
.
0
λ
κabs
r ) Bλ
λ (~
T (~r) +
ZZ
1
sca
gλ (~r, n
b0 , n
b) Iλ (~r, n
b 0 ) d2 n
b0 .
+ κλ (~r)
4π
Granada - 14/09/2004 (Prosper/LATEX) – p.4
Radiative transfer
b) [W m−2 µm−1 str−1] ?
Iλ(~r, n
n
b
b) = source
Iλ(~r0, n
~r
O
PSfrag replacements
~r0
considered volume
sca [cm−1]
κabs
,
κ
λ
λ
Granada - 14/09/2004 (Prosper/LATEX) – p.5
Radiative transfer code
Description
• Based on the work of Lopez, B., Mékarnia, D., Lefèvre, J.,
296, 752, A&A(1995)
• Geometry (2D) (axi-symmetry)
• Temperature independent opacities (κabs , κsca )
λ
λ
• Coupling with dust formation (Berlin: P. Woitke)
• Parallel version (OpenMP)
• . . . see Niccolini, G., Woitke, P., Lopez, B., A&A, 703, 716, 2003
Granada - 14/09/2004 (Prosper/LATEX) – p.6
Monte Carlo radiative transfer
τλ
• We only consider the
most probable
trajectories.
• The probability for a
photon to cross an
optical depth τλ is
proportional to e−τλ .
• The probability to be
scattered in a particular
direction n
b is
proportional to
gλ (~r, n
b0 , n
b),
• etc. . . .
PSfrag replacements
star
envelope
Granada - 14/09/2004 (Prosper/LATEX) – p.7
M1-92: ID
Quantities
Units
Values
Teff
L∗
d
R?
α∗
Mdisc
Mshell
K
L
kpc
m
rad
M
M
2 × 104
104
2.5
5.8 × 109
7.5 × 10−11
0.2
0.7
structure of the nebulae determined from
CO spectral data. (Bujarrabal & Alcolea,
ApJ, 1998), IRAM Plateau de Bure
Granada - 14/09/2004 (Prosper/LATEX) – p.8
M1-92: the model
• our goal: to determine the structure of the nebular
environment.
• our tool: the Monte Carlo Radiative transfer code
• our constraints: HST image (0.55 µm) and photometry.
• dust grain opacities: Mie Theory.
• optical properties of silicate from Suh,
K.-W., MNRAS, 304, 389, 1999.
• size distribution function ∝ aβ .
• this distribution does not depend on
location (though it is possible).
• The mass is given by the CO data.
• We “played” around to finally end up with
the density law on the left . . .
density law (best model to date)
Granada - 14/09/2004 (Prosper/LATEX) – p.9
M1-92: The fits
HST image
Model
Bujarrabal et al., A&A, 331, 361, 1998
Granada - 14/09/2004 (Prosper/LATEX) – p.10
M1-92: The fits
scattering
dark lane
PSfrag replacements
Granada - 14/09/2004 (Prosper/LATEX) – p.10
M1-92: The (preliminary) results
• The mass determined by the CO data is compatible with the
dust model (gas to dust ratio of 100).
• The disc is flared, which could not be told by the CO
observations (disc not resolved). This could be tested with
the MIDI VLTI instrument or ALMA.
• A single size for dust grains cannot reproduced the
observations.
◦ on one hand we need small grains to get “isotropic
scattering”.
◦ on another hand the 20 µm emission implies large grains
• the best model size distribution ranges from 0.01 µm up to
3 µm with f (a) ∝ a−4 .
Granada - 14/09/2004 (Prosper/LATEX) – p.11
Conclusion & Perspectives
Conclusions
• We tested the validity of the density structure determine
from CO data.
• We determined a possible geometry for the disc.
• We determined dust grain parameters.
Perspectives
• Looking at other wavelengths (2.2 µm, 800 µm, mm . . . )
• unfortunately, the best model for the SED and the image do
not coincide !
• Radiative Transfer: we are developping a 3D code which is
being tested (1D benchmarks from Ivezic et al., MNRAS,
291, 121, 1997), based on the Monte Carlo method and
using an adaptative grid.
Granada - 14/09/2004 (Prosper/LATEX) – p.12
Conclusion & Perspectives
3 stars and a few photons . . .
Granada - 14/09/2004 (Prosper/LATEX) – p.12