Take log derivative of fit or data and come up with ways to identify shock

[chihway]

either finite difference or SG?

[bhuvjain]

Finite difference seems better since at the shock the derivative goes to infinity, so SG may get confused? Or maybe both will...the alternative is what Qsh does: allow for the amplitude to jump.

[tdacunha]

[chihway]

Here's an attempt to come up with some definition of a detected shock:

1. when doing the measurements, take the median instead of the mean in the annuli (this may or may not matter), use scaled R/R500 as x-axis
2. bootstrap errors as before, log R bins
3. estimate background as before
4. SG smooth the measurements as well as the bootstrap samples, find the R where SG and background intersects, call this R_cross
5. log-derivative the SG as well as the bootstrap SG, use the bootstrap SG to get error bars on the log derivative
6. in the log-derivative plot, remove all scales above R_cross, look for slopes steeper than -3 (taking into account error bars), call that a shock

This is of course kinda sketchy, but something to start with!

[chihway]

Here are some plots following the above steps

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5