Chapter 7
Results and Discussion

Each of the isophotal maps displayed in appendix II were produced with the following standard parameters:

Each of the isophotal maps used within this report is plotted on a log-log scale, and therefore each one is labelled by the name "log X",” (log 1, log2 etc.). This is necessary to increase the dynamic range of colours that represent the different brightness’ of the discs. The central star is so bright that without the log-log plots it dominates most of the colour range allowing little or no disc detail to be seen. Each "atlas" is produced from a single set of fixed variables, only the observing angle is changed. In this way the entire star is viewed, the angles to which the observer is rotated are & radians. Atlas 1, log plots 1 through 5, are to be the standard to which all others are compared. Each atlas has only one of the variable parameters, which are deemed important, changed from the reference atlas. This enables conclusions on how each parameter changes the plot, to be drawn. The nodules that can be observed on the outer edges of some discs are due to statistical noise and are feature of the Monte Carlo technique used to model the discs.

The atlases can be viewed in appendix II. Each plot has its simulation data in table, which is adjacent to the map. The parameter, which has been varied, is highlighted in yellow.

7.1 Atlas 1: The Reference maps

The results of the reference model give an indication that the model works correctly. From an angle of 0 radians, a circular disc can be seen. However, towards the outer edges of the plot statistical noise causes nodules on the disc. The disc is much brighter at its centre with the brightness dropping of steadily towards its external edge. Rotating to 0.4 radians, we note that the statistical noise has all but disappeared. The circular symmetry of the plot has been retained but has been shifted about the brightest central image. No disc structure is observable from this shallow viewing angle. The brightness has increased by an order of magnitude implying either that there is an obscuring medium directly above the pole of the star or that more light is scattered at angles less than . Rotating to 0.8 radians, only the brightest regions of the plot have retained their circular symmetry, most regions are now elliptical, as would be expected when viewing a circle form an angle. The brightness for all regions has remained constant. The beginnings of a disc structure is now evident, two small indentations have appeared at the outer edges of the disc. This is the area where photons find it hard to enter due to the high dust density and thus the brightness here is less than the surrounding area. Log 4 shows us the system from 1.2 radians. Brightness has increased marginally and the disc structure is now much more prominent. The plot is now larger than the area allowed it and some of the external imagery is lost. Viewing the system from the equatorial plane, 1.57 radians, the brightness, as expected due to the lack of light escaping directly through the disc, falls off. The disc structure is now very prominent and is at the equator of the star, as is normally observed in such systems. The plot is symmetrical about the disc, whilst a slight dimming of the brighter areas is observed in the southern hemi-sphere.

7.2 Atlases 2 & 3: The varying of the radial power law

The radial power law index is varied.

Theoretically the larger alpha, the more centrally condensed the dust will be, or similarly the faster the dust distribution will fall off with radius. This is most readily observed in the isophotal maps of atlas 3 where it can be easily seen that the dust distribution is much more condensed. The effect is less observable in atlas 2, which has a smaller value than that of atlas 1, but can be seen. The brightness levels are unchanged; this is expected, as all scattering variables have remained constant.

7.3 Atlas 4: The Varying of the Optical Depth

The equatorial depth is varied

Lowering should give a brighter isophotal map when viewed at radians, the equator of the star. This is because there are less scattering events which can take place in any one optical depth, the density of dust within an optical depth has not been changed, and therefore there is less extinction for any particular photon. This effect can be seen in log 20 of atlas 4. Also observed, is what appears to be a quicker radial drop off, similar to the effect of lowering . It is believed this should happen, there is more chance of a photon scattering out of the final optical depth (OPD) it must travel, whilst still in the beginning stages of this OPD as the dust distribution is more rarefied. Originally, it was planned to simulate stars with an increased as well as stars with a decreased , with reference to atlas 1, however increasing to 10 doubled the run-time. Therefore, these runs were regrettably, abandoned.

7.4 Atlas 5: The varying of g

g The parameter controlling the directional scattering properties of the grains’ is varied.

With g set to zero the photons should scatter symmetrically, but not necessarily isotropically. This can be observed in atlas 5, viewing log 35 it can be seen that the disc structure, which runs off the edge of the plot, has taken on a bright configuration. While g=0 it was hard for the photons to propagate through the disc and it was viewed as a darkened structure on the plots. However, now that the grains will scatter equally in all directions photons are more readily scattered all the way through giving it, its brightened appearance.

7.5 Atlas 6 & 7: The varying of the dust above the disc surface

The parameter controlling the amount of dust above the disc surface is varied

Lowering should decrease the thickness of the disc. This is evident from FIGURE 10, the schematic of the distribution that the dust has. At first look, the flaring of the disc appears to have changed. However, on consideration the change of the apex angle of the “notches” at the sides of plots, log 45 & log 50, demonstrate an increase/decrease in the thickness of the disc. The flaring of the disc cannot have changed, as the parameter that controls it has remained constant. The thinner disc, log 45, has an equal brightness to that of the reference plot, however log 50, the thicker disc, has an increased brightness level. The authors conjecture on this is that a thicker disc, an area where photons find in hard to enter, will encourage a denser distribution of photons above the disc; The denser photon count giving a more radiant brightness.

7.6 Atlas 8 & 9: the varying of Z₀

The parameter controlling the collimation of the bipolar outflows is varied.

By varying , the height of the top surface of the disc, above the mid-plane of the star, should also vary. This is observed in atlas 9, the thicker disc can be observed earlier in the rotational sequence and is most notable in log 60. Both equatorial plots (log 55 & log60) are notably brighter than their reference plot.

7.7 Atlas 10: virgin Radiation

The virgin radiation, photons that escape directly from the star without scattering, is removed in these plots. It is expected that the plots will be identical to those of atlas 1, except that the level of brightness will be lower. This is observed in virgin 1 → virgin 4 but not in virgin 5, the plot in the equatorial plane is brighter than its reference plot.

7.8 Atlas 11: HST Simulation

The observational image captured by the HST can be seen it atlas 11. The image shows the circumstellar disc as a dark-band across the equatorial plane of the star. A notable difference from the simulations achieved is the band reaches across the entire width of the star. In trying to simulate this dark-band the programs parameters were varied to values consist with the observational data. An image with a dark band through its equator could not be simulated. Atlas 11 was the closest match that could be achieved. The disc is more noticeable than in other runs and the map is symmetric about this disc. The brightness of the map is equal to that of its reference plot. The jets visible in the HST data are not observed in the simulation, this leads to the conjecture that; bipolar out-flows are not created by the relatively simple process of scattering.

7.8 Conclusion

Many groups have simulated circumstellar discs using Monte Carlo techniques. Most notably the results of B. Lazareff, R.E. Pudritz J.L. Monin, 1990, Infrared Images of Protostellar Discs: Theoretical Models, match those obtained. The problem encountered in simulating jets was also incurred by B. Lazareff et. al.

B.A. Whitney, L. Hartmann, 1992, Model Scattering Envelopes of Young Stellar Objects. I. Method and Application to Circumstellar Discs, used a multiple scattering model, which is a conjecture often over looked. Whitney et. al. concluded that un-extincted light, light that is received directly from the star without dust interaction, swamps the simulation results and makes it hard for detail to be distinguished, a result which is borne out in this report.

Good results have been obtained using a simple scattering and absorption model, and it is concluded that the method of Monte Carlo simulation to generate circumstellar discs is a valid one; the process of scattering is random. The albedo of the dust grains around HH30 is marginally above 0.5, with best fits to observations being achieved at 0.64. Virgin radiation swamps results obtained from this type of simulation. Even when the virgin radiation has been removed, a log-log plot is required to increase detail to a level sufficient to allow analysis. Disc flaring is a relatively simple process to achieve in simulation, but the reason for flaring cannot be concluded from this work. The generation of bipolar outflows is not achieved from a the scattering process.