Estimate proplyd inclination from the theta' value where shell brightness drops off

[will-henney]

The proplyd arcs all stop well before \theta' = 90. In the \xi = 0.8 model, the proplyd wind drops off to zero between about \theta = 70 – 90, so typical value of about 80 deg. That should correspond to where the brightness falls off (obviously this ignores the flow from the tail, but that should be much weaker).

As inclination increases, \theta = 80 will correspond to smaller values of \theta'. We should calculate this so we can use it to estimate the inclination.

Observed values of theta' for LV arcs:

• LV5 : 30 deg
• LV4 : 60 deg
• LV2 : 30 deg (but asymmetric)
• LV3 : 40 deg (but this is continuum, not HA, so may be different)
• 166-316 : 60 deg
• 177-341 : 40 deg

Farther out arcs that have an inner shell that looks like it might come from a proplyd

• 4578-251 : 50 deg
• 072-134 : 30 deg
• 101-233 : 45 deg
• 124-131 : 30 deg
• 005-514: 30 deg
• LL3 : 60 deg
• LL2 ? : 20 deg
• 116-3101 : 40 deg
• 266-558 : 30 deg
• LL5 : 30 deg
• 308-3036 : 45 deg

[will-henney]

Better observational methodology

Plot the contour where shell minus background brightness has fallen to half the peak value, and use that to estimate the theta' values.

[will-henney]

Theoretical calculation

In principle, the brightness will be proportional to $\sigma^2 / h$, plus a contribution from the shock itself that is probably small. And see #35 for calculation of the projection effect.

We should be able to calculate sigma(theta) from the CRW model, but this requires resolving issue #36. We already did a lot of work on h(theta) but I'm not sure if it came to anything.

[will-henney]

Simple empirical comparison with another estimate of inclination

This wouldn't require any theory. We could use, for instance, the length-to-width ratio of the tail. All other things being equal, this will be smaller for higher inclinations.

Unfortunately, there are only about 4 or 5 of the outer proplyds where we can clearly see the end of the tail