Anexo 2
Title:
The RAINY3D code : The treatment of condensations in nova remnant during nebular
phase
Manoel Moraes 1, Marcos Diaz 2
1:
Rua do Matão, 1226, Cidade Universitária, São Paulo, SP – Brasil – 05508090
sala F308 – [email protected]
2:
Rua do Matão, 1226, Cidade Universitária, São Paulo, SP – Brasil – 05508090
sala F303 – [email protected]
Affiliation – 1,2:
IAGUSP : Instituto de Astronomia, Geofísica e Ciências Atmosféricas – Universidade de
São Paulo
Abstract
Classical novae remnants are important scenarios for improving the photoionization modeling.
This work describes the pseudo3D code RAINY3D which drives the photoionization code
CLOUDY as subroutine. Photoionization simulations of old nova remnants are also presents and
discussed. In these simulations we analyse the effect of condensations in the remnant spectra. The
condensed mass fraction affects the Balmer lines by a factor greater than 4 when compared to
homogeneous models and this directly impact the shell mass determination. The He II 4686/H
ratio decrease by a factor of 10 in clumpy shells. These lines are also affected by the clump size and
density distributions. The behavior of the strongest nebular line observed in novae remnants is also
analyzed for heterogeneous shells. The gas diagnostic in novae ejecta are thought to be more
accurate during the nebular phase, but we have obtained that at this phase the matter distribution
can strongly affect the derived shell physical properties and chemical abundances.
1 Introduction
Classical novae remnants are very important scenarios for improving photoionization modeling.
There are still many difficulties to reproduce the observed novae remnant spectra. The emission line
spectrum depends on the ionizing source, the chemical abundances of the shell and strongly on the
mass distribution. There are some spatially resolved novae remnants (e.g. HR Del, Moraes & Diaz,
2009) that are far from having spherical and/or homogeneous mass distribution. Some of these
remnants showed many structures and mass condensations in high resolution images (e.g. Slavin et
al. 1995). The amount of condensed mass, their size and density distribution remain unknown.
Spectral analysis of unresolved novae shells show the presence of emission lines of neutral and high
ionization species simultaneously, during several stages of the shell expansion (e.g. Williams, 1992).
The analysis of [O I] 6300,6364 doublet relative fluxes in several novae showed that the only
process that can drive this line ratio towards unity is the line optical thickness (Williams, 1994). For
typical oxygen novae abundances, such a large optical depth can not be achieved in homogeneous
shells. Williams proposed that the [O I] lines come from high density condensations, where the gas
is neutral. The condensations in the shell could explain the presence of strong lines from elements
which are spread over a wide ionization range, specially in matter bound shells. The globules affect
the transfer of stellar and diffuse continuum radiation in the cloud as well as the ionization structure,
both locally and at large distances from the central source (Diaz, 2001). In fact, this represents a
major discrepancy between current model spectra of nova shells and the observed line fluxes. The
diagnostic lines used to obtain the shell physical and chemical parameters are affected by the mass
distribution. Some emission line ratios observed in nebular phase novae are only possible if the shell
has condensations. The shell physical and chemical diagnostics are thought to be more accurate
during the nebular phase of the spectral evolution, since at the lower densities the spectra would be
less affected by the condensations (Williams et al. 1991). The models often have a spherical or
cylindrical symmetry but the presence of condensations are treated with some extra free parameter
in the density profile (e.g. equivalent radial power laws). Even with homogeneous shells, these 1D
models can not always reproduce the shell geometry such as in the case of bipolar remnants. There
are full 3D photoionization codes, for example those proposed by Gruenwald et al. (1997) and
Ercolano et al. (2003). The last one is based on the Monte Carlo method and can calculate the
diffuse component of the radiation field selfconsistently. However, because of the complexity of 3D
calculations, the statistical treatment is in LTE, which is not correct for novae shells (Hauschildt et
al. 1997). Full 3D codes demand a huge CPU time and enormous space parameters to consider,
specially for highly structured environments. Diaz (2002) and Morisset et al.(2005) proposed
pseudo3D modeling based on several volumeweighted 1D models. These codes have the
advantage of being much faster than full 3D codes and the calculations could be done in NLTE.
This Paper describes the pseudo3D code named RAINY3D which build a 3D shell with
condensations and drives the code CLOUDY (Ferland, 2005) to perform the matterradiation
interaction calculations. The studies of the condensations distribution and how they affect the
emission lines emitted by nova shells are presented.
2 – The RAINY3D code and the condensations treatment.
The problem of calculating 3D models of a nova envelope can be divided into two parts. The first
consists of defining geometry and the mass density distribution in the shell and the second concern
the calculus of photoionization, thermal equilibrium and matterradiation interactions and the
emitted spectrum from the inhomogeneous shell for a given radiation source. The first task was
performed by the code RAINY3D, the second by the code CLOUDY.
The shell is built on the basis of a two component 3D mass distribution. The first is named
background component and consists of a radial power density law r where is the background
power index. The second component is a random distribution of condensations. The shell is
characterized by its condensed mass fraction parameter, fc, which is the mass ratio between the
mass in the clumps and the total mass of the shell. The shell dimensions and mass are also input
parameters of the models. The condensations are defined by its size and density contrast. Each
clump has a Gaussian density profile. In fact, the shell may have many condensations, even for low
fc values. The shell density as function of radius is defined by the expression:
where 0 is the density defined by the power law component and is normalized to 1 at r = rin, k is the
clump contrast density, relative to the local background, defined in the input parameters, ro is the
random position in the shell where the clump is located and c is related to the clump FWHM. The
first term of this expression defines the background component.
The clump size and density distribution are ruled by power laws probability functions: These
probability power law indexes are input parameters for the shell assembling, as the maximum and
minimum value of clump size and density.
Y=[H−L
Hx
LH
]
H Where, L is the lower value, H the higher, x a random variable between 0
and 1 and the power law index. Y is the random value obtained biased by the distribution.
Other shell has input parameters include the expansion velocity and the ejection age. Once they
were configured, the 3D shell could be build. The code adopt a spherical coordinate system and the
shell is divided in angular and radial grid. The shell grid resolution is defined by the dimensions of
the remnant and clumps, a shell with smaller clumps will have a grid with higher angular resolution.
The RAINY3D code put each condensation in a random spherical coordinate position in the
r =0 r−k 0r 0− e
r−r0 2
2c2
background density profile (see figure 1). The globule size and density contrast are defined by the
power law probability. The code iterate until the mass in condensation achieve fc. The angular
element resolution plus the inner and outer radius of the shell define the solid angle element that is
sent to CLOUDY for calculation. Therefore all the 3D shell is divided in solid angle elements and
the RAINY3D code accounts the emission lines contribution of each volume element. The total
emission line flux is obtained by combining individual volumeweighted contributions. The shell
structure is solved locally, using a radial step calculated from the density and pressure gradients.
The physical proprieties of the gas are considered to vary only in the radial direction in each solid
angle element. So far, the transfer of ionizing diffuse field is restricted to the onthespot
approximation or 1D radial transfer. This method allows the treatment of condensation shadows and
partially ionized regions for a matter bounded shell. The NLTE calculation made by Cloudy
(Ferland, 2005) is very important in the nova scenario, because LTE assumption leads to incorrect
synthetic spectra (Hauschildt et al. 1997) and therefore incorrect model parameters.
The RAINY3D code can run in spectral adjustment mode. The emission line data could be used to
constrain the model parameters and the lines fluxes are an additional input parameter. The code read
a input file that contains the line identification code for Cloudy, their flux and the relative error in
the line flux determination. The datamodel comparison is made by a special 2, where the
contribution of each line do not depend of their flux. The expression below are used to obtain the
best model adjustment:
2=
1n ∑i=1
n
[ f oi− f mi∗scf
f oi∗e ]2
where, n is the number of lines, foi and fmi are the line i observed and
model fluxes, scf is a scaling factor (total flux observed/ total flux of model) and e is the observed
line flux error in %.
3 – Results
The study of the effect of the inhomogeneities in novae spectra was made in two steps. The first
analysis concerns the effect of the condensated mass in the line fluxes and line ratios. To perform
this analysis we adopted a central source with luminosity log L = 36 erg.s1 and effective
temperature of 65000K. The ionizing field shape was defined by a high gravity and hot stellar
atmosphere from the Rauch (2003) catalog. The shell abundances were CNO enhanced as observed
in the novae ejecta. In all shell models with constant clump parameters, the increase of the
condensed mass fraction, fc, increase the number of globules. For example, for fc = 0.05 the shell
has typically between 50 and 150 clumps, while for fc = 0.9 there may be more than 10000 clumps.
The increase of fc results in a less dense spherical component. The second analysis made explores
the effect of the clump size and density distribution on the emission line ratios of an unresolved
shell. All other shell and central source parameters were kept constant in the simulations. The only
free parameters are the power law indexes that define the clump size and density probability
distributions.
3.1 The effect of the condensed mass fraction on the emission line ratios
The fc parameter affects the total line luminosity, because the presence globules affect the radiation
– matter interaction and the emission measure. The H luminosity increases with fc as shown in
figure 2 (top). For instance, this line luminosity is more than 2 times larger than expected in
homogeneous shell model. These results show that the shell mass obtained by using the Balmer line
luminosities, could be strongly affected by the condensed mass fraction or the mass distribution of
the ejecta.
The behavior of He II 4686/ H ratio can be seen in figure 2 (bottom). The increase of the
condensed mass fraction yields a decrease in the line ratio. The presence of clumps reduce the He+
ionization zones by shadowing the radiation field. The He II 4686/H ratio value may decrease by a
factor 10 from an homogeneous shell to a shell with 90 % condensed mass. In the same fc range, the
He I 5876/H presents only a 6% variation. Both helium and Balmer lines are used to obtain the
helium abundance and therefore the condensed mass fraction affect this determination. The He/H
abundance obtained by the He II and He I lines in the shell with fc = 0.9 is 45% lower.
The [O III] 5007/H ratio is also affected by condensations. The figure 3 (top) shows the line ratio
behavior with fc. The ratio found in a 90% clumpy shell is ten times larger than the ratio in a shell
with fc = 0.05. The [O III] total luminosity of the shell without condensations is 20 times smaller
than the emission of the shell with 5% condensed mass. The collisionally excited line fluxex will
increase with density. If the clump density increase to close to the critical density of 1D2 level, there
will be a decrease in the [O III] 5007/H ratio. The [O II] 7325 line flux presented a factor 3
variation in the same fc range. However, the [O II]7325/H ratio increases by only 22 % from fc =
0 to fc = 0.9. The increase of mass fraction can rise the neutral oxygen population to a factor of 104
from fc = 0 to fc = 0.9 with a corresponding increase in [O I] 6300 emission.
The nitrogen lines [N II] 6548, 6584 have the same behavior of [O III] 5007. For instance, the
value of [N II] 6584 /H in the shell with fc = 0.9 is 20 times larger when compared to fc = 0.05.
Since the nebular [NII] excited levels have lower critical density than those of [OIII], the density
increase inside clumps may affect the nitrogen line ratios by collisional deexcitation.
At low densities, the [O III] and [N II] auroraltonebular line ratios can be used to obtain the local
electron temperature. The mass fraction ratio affects drastically the temperature of the shell. The
figure 3 (bottom) shows how the fc increase render the shell cooler. Since the globules increase the
emission of cooling lines and the density clump block the radiation field, the mean electron
temperature is lower for clumpy shells.
3.2 The effect of the clump size and density distribution on the emission line ratios
In this analysis, a constant condensed mass fraction of fc = 0.5 was adopted. All models simulate
the nebular phase conditions, with low NH density (102104 cm3) and a hot ionizing source. The
maximum and minimum clump size and density are constant parameters, while the power law
indices are the free parameters in the calculations. The table 1 shows the model parameters used.
There are models with high density clumps, with globule density contrast between 10 and 50 larger
times the background (k1050 models) and models with clumps density between 3 and 10 times the
background (model k310). The effect of the clumps size and density distribution depends on the
average density of the shell and the emission line considered for comparison.
The clump size distribution affects the total H luminosity in a constant shell mass models. Since
this Balmer line is often used to estimate the shell mass, this is an useful simulation. In the lower
density clump models, (hereafter, model k310), the H luminosity vary 30% between models. The
higher line luminosity corresponds to a shell with a larger number of small clumps (and also larger
total number of clumps). For the higher density clumps models (hereafter model k1050), the effect
is even more intense. The shells with a larger number of small clumps have twice the H luminosity
than the shell with a flat size distribution, (see figure 4). Therefore, the clumps size distribution can
affect significantly the shell mass determination in condensed shells. Now, considering only the
density distribution slope (k) in k310 and k1050 models, they have the same H flux variation is
found; about 35% and 2 times the H flux. For both models, the shell with a higher number of
denser clumps have higher H luminosity.
The shell emission line ratios are affected by the power law indices of clump size (fw) and density
(k) distribution. For k310 models, the He II 4686/ H ratio in the shells with smaller clumps is 2.2
times higher than the ratio in a shell with larger clumps. The calculations showed that there is a
plateau, where an increase in the clump size does not affect the line ratio. The clump density
distribution also affect the He II 4686/H ratio, by factor ~2 (see figure 6). The shell with a larger
population of low density clump has a higher line ratio as expected, since the low density clumps
block the ionizing radiation field less effectively and the He++ population rise in number. The
calculations indicate that there is a plateau for k > 2, because the volume shielded from the
ionizing radiation field remains constant. The He I 5876/H ratio have no significant variation with
clumps size and density distribution (only 2%). Both line ratios are used in helium abundance
determination, but in this case the He++ population is more affected by the clumps properties. The
He II 4686 to Hrecombination coefficient ratio vary only 12 % from 5000 to 10000 K, but a factor
2 variation in this line ratio is seen in clumpy shell models, depending on the clump size and density
characteristics. For example, the He abundance determinations using the k310 model indicate that
the measured abundance may be underestimated by 3040%. For the k1050 models the correction
is in the 4050% range.
The calculations showed that for the k310 models, the [O III]5007/H ratio vary by a factor of 3
from models with a less dense clump population to models with a denser clump population, until k
= 2. For k > 2, where vast majority of the clumps are dense, the line ratio is constant. The k1050
models show the same behavior, but the line ratio variation was smaller, (60%) and radiation block
becomes important earlier, at k > 0, where there is a plateau (see figure 5). The clump size
distribution also affects the line ratios derived from shell models. For the k310 models, the line
ratio has a 70% increase from a population of smaller clumps to a population of large clumps. Large
clumps shield the O++ from the UV radiation more effectively in these models. For a denser shell, an
increase of the clump size reduce the O++ population and therefore the [O III] emissivity. This effect
was observed in the k1050 models. In the case of k310 models a 2000 K change was observed in
the mean shell temperature by varying the clump density distribution. The models with a population
of less dense clumps have a higher temperature when compared to the models with a denser clump
population. The size distribution of the clumps produces a 1200 K temperature variation (see figure
6). The hotter shell is the one with the majority of smaller clumps in its globule population. The
colder shell models are those with a majority of large clumps.
The [O II] 7319,7330 emission lines are strong in many old novae remnants and they are
important lines for the oxygen abundance determination. The [O II]7325/H line ratio has a small
variation with clump size and density distribution (around 10%). For k1050 models the line ratio is
somewhat larger, since the shell has a larger density and this increases the O+ population. The
maximum density in all models are lower than the critical density for this line.
On the contrary, the [N II] 5755/H ratio is affected by clump size and density distribution, in a
typical nova shell environment. The k310 models reveal a line ratio increase of 50% for models
with denser clumps. In the k1050 models, the clump density are below the critical density for
collisional deexcitation of the 1S level and the calculations show the same behavior of the k310
models. The [N II] 6548,6584 lines present a larger sensitivity than the 5755 line. For the k310
models the [N II]6584/H ratio has a factor of 5 variation by changing the clump size distribution
and a factor 7 with the clump density distribution. The k1050 models have the same line ratio
behavior, but the variations were smaller, a factor 2 and 3 for size and density distribution
respectively.
3.3 – Robust line ratios
There are some line ratios that do not change significantly with the clump populations
characteristics. The He+ recombination lines show variations smaller than 5% in the models. The
Balmer decrement remains roughly constant in the models. The H/Hratiovaries only 10% for the
whole range of parameters. Therefore the He+ abundance determination is poorly affected and only
the collisional excitation corrections are needed to be done to obtain a fair He+ abundance value. In
the novae scenario, the H line is often blended with [N II] 6548,6584 lines because of the shell
expansion velocity. In reddening corrected spectra, higher H/H values may be due to the [N II]
contribution.
4 – Discussion
The presence of condensations in novae ejecta could be seen in spatial resolved shells, like HR Del,
GK Per, RR Pic and T Pyx. Many nova without resolved shell show some emission lines ratios that
are possible only if the ejecta have heterogeneous mass distribution (Williams 1994). There are
many mechanisms that could form condensations in the nova expanding nebula. The Rayleigh
Taylor instability (RTI), is one possibility. The RTI is excited in the first few seconds of the eruption
and occurs because the ejecta has a velocity distribution and propagate in a stratified media
(Chevalier et al. 1992). The ejecta expansion decreases the mean density and the shell becomes
optically thin to emission lines. The corresponding cooling makes also the shell KelvinHelmholtz
unstable (Chevalier et al 1992). This thermal instability depends on the shell chemical composition,
density and radiation field. The thermal instability was discussed in detail by Pistinner and Shaviv,
1995 who found that it has a much shorter scale (~104 factor) when compared to the shell radius.
The density contrast for this instability is less than 100%. But it could give a rise of a large number
of small clumps. The mass ejection itself is affected by the binary motion and white dwarf rotation.
The orbital motion of the secondary in the “common envelope phase” was studied using 2.5D
hydrodynamical simulations (Livio et al. 1990 and Lloyd et al. 1997). The binary motion
accumulate matter in the polar regions. If the WD is a fast rotator, the effective gravity gradient
from polar to equatorial regions affects the local maximum temperature achieved at the outburst and
therefore the strength of the thermonuclear reactions (Scott, 2000). This makes the ejection velocity
in the polar regions be greater than in the equatorial regions and the ejecta could be prolate or
bipolar, (e.g. RS Oph and HR Del). The Lloyd et al. calculations that include the binary motion and
the WD rotation, found that the density contrast is ~ 16 at a given shell radius and 64 from globules
to the neighborhood diffuse regions. Recent observations of HR Del remnant show that it has a
density contrast of 3 to 16 (Moraes & Diaz, 2009). The RTI are possibly related to the nova speed
class, since the fast nova light curve are associated with higher expansion velocity speeds. Lloyd et
al. 1997 obtained a relation between the nova light curve decay time, t3 , and the maximum length of
the RTI condensations. For very fast novae, or t3 < 12, the maximum size of the condensations is
40% the shell radius (e.g. V1500 Cyg, Slavin et al. 1995). For slower novae, the maximum
condensation length decreases. For very slow novae, the clumps size could be only 104 of the shell
radius. All these effects could give a rise many nova remnant configurations, with a variety of
condensed mass fraction and clump size and density distributions and justify the construction of a
variety of shells models with parametrized clump population distributions.
A full 3D code demands huge CPU time and more parameters number to describe the novae
remnant geometry. The pseudo3D codes, like RAINY3D could treat the condensations by
optimally assembling 1D models and allow to build many different shell geometries with clumps.
The transfer of diffuse radiation is treated in 1D, although no significant differences were observed
by comparing OTS to 1D transfer. The 2.5D simulations make possible to study the effect of the
condensations population characteristics on the emitted spectrum and reveal the ionization structure
both locally and at large scale (shadows). The calculations show that the globules affect the
ionization structure inside and between inhomogeneities. The analysis of the novae spectral
evolution by Williams et al. (1991) showed that any calculation of heavy element abundances with
respect to hydrogen which involves forbidden lines at initial times of the nebular phase must
consider the effect of condensations. The study of the condensations influence on the emitted
spectra of the shell during the nebular phase (optical thin gas) made in this work shows that even
decades after the eruption, the condensations may affect the shell physical and chemicals
diagnostics.
The clumpy models show that the total H luminosity is affected by the condensed mass fraction
and by the globules physical characteristics at the nebular phase. Even at lower density, the Balmer
flux can vary by more than 4 by the presence of condensations in the shell. The presence of clumps
can easily introduce a factor ~5 error in shell mass determinations. At the beginning of nebular
phase the globules effect could be larger. Diaz et al. (accepted) models of recurrent nova U Sco
show that the extreme nebulartoauroral ratios observed require the presence of clumps. The
calculations made in this work show that the He/H abundances determination are underestimated
when the shell is clumpy. Since the He I lines do not show variations, the neutral He population may
increase in the clumps. The He/H determination in different regions of the spatial resolved shell of
HR Del show that in the clumps, the abundance obtained was ~20% lower than other regions
(Moraes & Diaz, 2009). The oxygen abundance determinations also are affected by the
condensations in the shell. The [O III] 5007/H ratio observed in the nova nebular phase is only
obtained by the models when the shell is clumpy. Depending on the ionization structure of the shell,
or O++ ion abundance, this determination could affect the overall oxygen abundance determination.
The nebular phase models calculated in this work show that the main oxygen population is at O+
stage and also that the [O II] 7325 /H ratio has a small variation with the mass in clumps and their
size and density distribution. The nitrogen lines, ([N II] 6548,6584), show the same behavior of
oxygen lines. One important effect of the condensations is to decrease the electronic temperature of
the shell, since some forbidden lines have their emission enhanced and cool the gas. One interesting
result of the calculations is that the lower density contrast clumps models (k310) are much more
affected by the condensations properties. These models show great temperature variations as
function of the clump size and density distribution (see figure 6). If the emission of the line used to
obtain the relative abundance is affected by local temperature, the abundance determination could
be wrong. There are some emission lines that are not strongly affected by presence of the
condensations in the shell. The He I/H and Balmer decrement, show less than 5% variation with
clumps characteristics.
5 Conclusion
The code RAINY3D can built a 3D shell with condensations and combine weighted Cloudy 1D
calculations to obtain a pseudo3D photoionization model of nova remnant. The condensations
formation and survival mechanisms are not known and the RAINY3D simulations provided an
insight on how the condensations parameters could affect the spectra from nova ejecta during the
nebular phase. The condensation amount, defined as fc, and the globules size and density
distribution can affect the emission line ratios and affect the accurate diagnostics of the nebula,
including mass and chemical abundance determinations. Williams (1991) showed that the physical
and chemical diagnostics are thought to be more accurate during the nebular phase, but the
calculations made in this work show that even for low density shells, the condensations could affect
significantly the results of quantitative spectral analysis. The characteristics of the gas
condensations are very important to nebular photoionization models. The clump formation are
related to the ejection mechanisms, binary interaction, white dwarf properties and interactions
between ejected components of the shell. Therefore they could be a constrain for the modeling of
several phenomena related to TNR's and shell expansion. The effort to observe resolved novae
shells with large telescopes and spatially resolved spectroscopy can elucidate the clump size and
density distribution in nova ejecta.
6 References
1992ApJ...392..118C Chevalier, Roger A.; Blondin, John M.; Emmering, Robert T.
2001ASPC..247..227D Diaz, Marcos
2002AIPC..637..538D Diaz, Marcos P.
2003MNRAS.340.1136E Ercolano, B.; Barlow, M. J.; Storey, P. J.; Liu, X.W.
2005AAS...206.3106F Ferland, G. J.
1997ApJ...480..283G Gruenwald, R.; Viegas, S. M.; Broguiere, D.
1997ApJ...490..803H Hauschildt, Peter H.; Shore, Steven N.; Schwarz, Greg J.; Baron, E.;
Starrfield, S.; Allard, France
1990ApJ...356..250L Livio, Mario; Shankar, Anurag; Burkert, Andreas; Truran, James W.
1997MNRAS.284..137L Lloyd, H. M.; O'Brien, T. J.; Bode, M. F.
2009AJ....138.1541M Moraes, Manoel; Diaz, Marcos
2005RMxAC..23..115M Morisset, C.; Stasińska, G.; Peña, M.
1995ApJ...448L..37P Pistinner, Shlomi; Shaviv, Giora
2003A&A...403..709R Rauch, T.
2000MNRAS.313..775S Scott, A. D.
1995MNRAS.276..353S Slavin, A. J.; O'Brien, T. J.; Dunlop, J. S.
1991ApJ...376..721W Williams, R. E.; Hamuy, M.; Phillips, M. M.; Heathcote, S. R.; Wells,
Lisa; Navarrete, M.
1992AJ....104..725W Williams, Robert E.
1994ApJ...426..279W Williams, Robert E.
Tables:
White dwarf temperature (K) 65000
Luminosity (log erg/s) 36
Shell mass (Mʘ) 104
Condensed mass fraction 0,5
Local gravity (log g) 8
Continuum shape Rauch Atmosphere
Abundance He/H (log He/H) 0,85
Abundance C/H (log C/H) 2,5
Abundance N/H (log N/H) 2
Abundance O/H (log O/H) 2,5
Other elements abundance Solar
Shell size (cm) 4x1016
Maximum clump size (log cm) 16
Minimum clump size (log cm) 14
Maximum clump density (bkg) 10
Minimum clump density (bkg) 3
Range fw 2 to 4
Range k 2 to 4Table 1 – Model parameter for clumps size and density distribution analysis.
Figures:
Figure 1 – Radial profile of the background (top) 3D shell component and the globules added to the background (bottom).
Figure 2 – The luminosity of H as function of the condensed mass fraction (top). The increasing of clumps increase the mean density and therefore the recombination rate. The He II 4686/H ratio as function of condensed mass fraction (bottom). The increasing of condensed mass fraction decrease the He++ population.
Figure 3 – The [O III] 5007/ H ratio as function of condensed mass fraction (top). The shell temperature obtained from [O III] line diagnostics. The increasing of the mean density make the cooling of the shell more effective (bottom).
Figure 4 – The H luminosity as function of the density (k) and size (fw) power law indexes. The line luminosity is more affected by the size distribution law of the clumps than the density distribution. A smaller clumps population have a large line luminosity.
Figure 5 – The [O III] 5007 / H ratio as function of the density power law index (k) for models with lower (k310) and higher (k1050) density clumps.
Figure 6 – The He II 4686/ H ratio (top) as function of the density (k) and size (fw) power law index of the clumps population distribution (models k310). The temperature obtained from [O III] diagnostics lines as function of the density and size power law index (bottom). The clumps size and density distribution affect more the lower density globules models (k310).