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The green dot—dashed line is atomic hydrogen obtained without PDR calculations i. All these correspond to the torus-3dpdr code.
Photoionization and photodissociation dynamics of H2 after (3+1) REMPI via the B state
The green and blue dashed lines correspond to 3d-pdr runs using equation 1 to account for the attenuation of the radiation field. In this section we present the capabilities of the code in simulating three-dimensional density structures interacting with one or two sources, either by invoking the on-the-spot approximation or including the diffusive component of the ionizing radiation, thus exploring the importance of these components in regulating the chemistry of PDRs.
To do this we consider an oblate spheroidal cloud with a uniform density distribution.
The choice of such an object was based on the assumption it is not spherically symmetric hence not reproducible by an equivalent one-dimensional approach, while at the same time it offers simplified results. The centre of the spheroid defines the centre of a Cartesian coordinate system. In all simulations we use the MC photoionization routine described in Section 3.
Set-up of the three-dimensional oblate spheroidal cloud case discussed in Section 6. The x - and y -axis dimensions are in pc. The centre of the cloud defines the centre of a Cartesian coordinate system.
The middle black point corresponds to the position of the ionizing source for the simulations, S1 Section 6. The grey points, S3 1 and S3 2 , correspond to the two positions of the stars in the S3 simulation Section 6. All stars are placed at a distance D from the centre of the oblate spheroidal cloud.
We perform three simulations.
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In the second simulation S2 , we use the same set-up but we switch on the contribution of the diffuse component of the radiation field. Thus by comparing simulations S1 and S2 we examine the effect of the diffuse radiation field on the abundance distribution. In the third simulation S3 we replace the single exciting source with two sources emitting half the number of photons per second, compared to the S1 and S2 cases.
Therefore, in the S3 simulation we test the capabilities of the code in treating PDRs interacting with multiple sources and we examine the consequent effects introduced in the abundances distribution as well as on the distribution of the local emissivities of the most important cooling lines. The stellar spectra in the models presented here are blackbodies, which are probabilistically randomly sampled by the MC photon packets.
There are therefore occasionally high-frequency ionizing photon packets that can propagate far into the neutral gas since the photoionization cross-section is proportional to the inverse cube of the photon frequency, i. These high-frequency packets are responsible for regions of localized heating exterior to the main ionization front. This is why the temperature distribution within the ellipse and particularly in the ionization front is subject to spurious heating which has a significant but very local effect in determining the abundances distribution.
This can be alleviated by using more photon packets so the energy per packet is reduced , however, at the cost of computational expense. We will thus exclude this effect from all discussion below.
Journal of the Optical Society of America
We also note that in the particular case of simulation S3 and because the ionizing photons have lower frequency than in the S1 and S2 cases, this effect is not present. As a first test we explore the effect of using different levels of healpix refinement corresponding to different angular resolutions per direction in each cell of the computational domain. Overall we find excellent agreement in the gas temperature distribution and minor changes in the H 2 abundance distribution, showing that even at low angular resolution i.
We note that in more complicated simulations with non-uniform density distribution, a higher level of angular resolution must be used. Cross-section plots of the S1 simulation using different levels of healpix refinement. Top row is gas temperature and bottom row is the abundance distribution of H 2. It can be seen that there are no significant differences for the tests presented here when moving to high angular resolution.
The grey colour in the background of the bottom row indicates a zero value. The dense oblate spheroidal cloud on the other hand shields the propagation of the UV photons behind it. Note that the gas temperature and ionization fraction transition from the ionized medium to the PDR is very abrupt. Cross-section plots for the S1 simulation.
The axes are in pc. Panel A shows the gas temperature distribution. The abundances of these species are with respect to the total hydrogen nucleus abundance. In panels B — F the grey background indicates a zero value. The shielding of the UV radiation allows the formation of atoms and molecules in the interior of the cloud.
This creates a layer rich in atomic hydrogen as shown in Fig. Here, the north surface shows an increase in the abundance of atomic hydrogen. Immediately behind the ionization front i. This line is predominantly emitted from a thin region located at low optical depths, i. In the work presented here, none of the three-dimensional simulations uses high spatial resolution in order to study this transition in detail. However, by using the AMR techniques as described in Appendix A , torus-3dpdr is able to perform such detailed studies at the cost of computational expense.
Cross-section plots showing the relative change between S1 and S2 simulations left-hand column and S2 and S3 simulations right-hand column. Thus the left-hand column corresponds to the effects observed when including the diffuse component of the radiation field while the right-hand column corresponds to when a multiple source treatment is taken into consideration. From top to bottom, we plot the relative change of the gas temperature, atomic hydrogen abundance, and atomic carbon abundance. The x - and y -axes are in pc. The relative change in the gas temperature is shown in Fig.
As a consequence, the abundance of atomic hydrogen is higher in the S2 simulation reducing at the same time the abundance of H 2.
However, in the innermost region, both S1 and S2 simulations are in excellent agreement. Hence inclusion of the diffuse component of the radiation field primarily affects the abundance distribution at low optical depths, while it is able to heat up the gas at intermediate optical depths. This shows that high-J CO lines may be used as gas temperature diagnostics in regions of intermediate optical depths where the diffuse radiation can penetrate the cloud deeper. The first column corresponds to the S1 simulation, the second column corresponds to the S2 simulation, and the third one to the S3.
The diffuse component of the radiation field heats up the inner part of the cloud by a few K which result in changing the emissivity of the different J transition lines with the high ones to be more affected, as we observe by comparing the S1 and S2 simulations. However, a multiple source treatment simulation S3 results in an emissivity map not significantly different from that of the S2 simulation, although it affects the emission at low optical depths i.
The effect of multiple sources interacting with PDRs is particularly interesting and very poorly studied due to the lack of numerical codes that are able to treat such systems.
Both sources in this simulation have the same distance D from the centre of the oblate spheroidal cloud as in the S1 and S2 simulations. The diffuse component of the radiation field is taken into consideration, hence this set-up ensures that any changes observed between S2 and S3 will be a result of the structure of the radiation field emitted by two sources instead of a single source.
The right-hand panel of Fig. The spatial distribution of the UV field has an impact in the abundances distribution between S2 and S3 particularly at low optical depths. Similarly to what has been discussed in Section 6. The middle and right-hand columns of Fig.
We argue that in more complicated structures involving multiple sources the effects introduced by the realistic UV treatment can be of significant importance. Furthermore, we plot in Fig.
These point to the conclusion that emission lines do become dependent on the spatial structure of the radiation field even when the total intensity received is the same as the intensity emitted by a single source at the same distance. Thus three-dimensional codes such as torus-3dpdr are often needed in order to compare as closely as possible numerical simulations with observations. Cross-section plots showing the relative change of the local emissivities for various cooling lines for the S2 and S3 simulations and where in both cases diffuse radiation has been taken into consideration.
Both axes are in pc. From these plots we see that overall multiple sources have an impact on the emissivities of the cloud, although in both S2 and S3 simulations the total intensity of UV radiation used was the same.
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