Include Shklovskii effect in the timing model

[abhisrkckl]

Perhaps not as a fittable parameter, but it will be useful to take that information into account in the timing model if its magnitude is known.

[dlakaplan]

There is derived_quantities.shklovskii_factor. And there is also utils.pmtot. I'm not sure that having this in the timing model is needed since it is completely degenerate with other terms, and the precision on the distance is usually the limiting factor. How did you see this working?

[scottransom]

I was wondering the same things that @dlakaplan has asked.

[abhisrkckl]

In the tempo2 paper (Hobbs et al), there is a section on the Schklovskii effect (section 3.6) where they state that the Schklovskii effect can be specified in the timing model (i.e., the par file). However, they don't give any equation there.

Digging into the code, I found that there is a parameter DSHK which is related to the Schklovskii effect, and I understand from context that this is some kind of distance with units of kpc.

In secularMotion.C, there is an equation which amounts to
bbat = bat - shklovskii
where
shklovskii = some_const * (t - PEPOCH)**2 * DSHK * (PMRA**2 + PMDEC**2)

I found a similar-looking equation in Willem van Straten's PhD thesis (eq 3.17), although I haven't checked how it's derived.

Here, bat is the barycentered TOA. bbat rather than bat is used to compute things like binary delays. So I presume the Shklovskii effect gets applied to binary delays as well.

[abhisrkckl]

OK... DSHK is supposed to be the pulsar distance, which is basically some_const / PX. So I don't think it makes sense to have DSHK as a separate parameter. However, we can still have a boolean parameter (SHKLOVSKII or something) which tells the Astrometry class to include/exclude the Shklovskii term. We already have all the info to do this in the Astrometry class itself, namely PX and proper motion parameters.

[dlakaplan]

I'm still not sure about this. Is it needed for some specific compatibility? I guess what it's doing is applying the Shklovskii PDOT to all of the TOAs, such that no further corrections are needed (to spin, orbit, etc). Which makes some sense, although it also hides some things.

But the choice of distance can be an issue. Rarely is the distance known with enough precision that it wouldn't significantly contribute to the TOA uncertainty after this correction, but that is not tracked. There is also no way to consider a separate timing vs astrometric parallax (which don't always agree) and the 1/PX -> distance conversion can have issues/uncertainties too.