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iancze / million-points-of-light

A few orders of magnitude more than a thousand. About how many pixel intensities we need to calculate to fit spectral line datasets from ALMA.
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Line profile #3

Open iancze opened 6 years ago

iancze commented 6 years ago

I had a bit of confusion today about what sets the "line profile" in the velocity direction, for a fixed image position. E.g., why does this line profile (Teague 18) look Gaussian?

teague

Because, it shouldn't, necessarily. It's not actually a tracer of the disk turbulence, but actually a function of how the emission becomes optically thin / the temperature profile changes. Put differently, if we had zero line width and constant temperature everywhere, and high density everywhere, then this function would start to look like a top-hat. Teague does have some examples in his notebooks which look like they start to illustrate this.

In the "Using eddy" notebook: spectra, theta, velax = gaussian_ensemble(vrot=1500., tau=5.0)

image

iancze commented 6 years ago

Another way to think of this might be via a "transfer function" a la Wilkins. Basically, there is some cone with some intensity profile, and some projected velocity. The transfer function maps the emission where the ray intersects the cone to the frequency. We could follow something like Teague, where he says the transfer function is the same at all radii in the disk. However, we may want to look into what Wilkins does again.