Exploring Apogee's abundances space with chemical evolution models

Starting point

Jan Rybizki arrived Feb 1, 2016 and brought with him his one-zone chemical evolution model. The overall plan is to explore what we can learn about a) the Milky Way (its chemical evolution and the yields of the stars), b) the Apogee abundances, and c) Jan's one-zone model and its limitations.
.. and then learn it. Here's a set of HWR notes after talking with Jan.

Jan overplayed his (fiducial) model predictions to the Apogee abundances as-is. It looks like in the plots below, basically a mismatch... which is an OK starting point.

Towards understanding the data-model (mis-)match

The reasons why data and model may disagree are manyfold ...disagreement is good, it teaches us something new. 

Model parameters

The most immediate advantage of Jan's models is that it can 'fit data' via MCMC,

which makes the variation of many, even all model parameters feasible. The model parameters fall into two categories:

Galaxy History: This entails the SFR, the inflow and outflow terms form the box, and the IMF; this is a 'handful of parameters'

Stellar physics: this entails essentially the yields; these are in some sense parameters, but presumably the space of all possible yields is not spanned by a set of continuous parameters. Hence, see below.

Data Calibration

It is well known that the Apogee ASCAP pipeline, at least for some elements has systematic offsets that are far in excess of the typical error bars. One simple way to explore the role of possible offsets is to make a basic abundance offset [X/Fe]_0 a fitting parameter, presumably with some prior on it (to avoid complete 'runaway').

Yields

It would be good to think about how one can turn the options on yields into something that is parameterizable, and therefore fit-able.

Applicability of a 1-zone Model

The model as is, makes a 'unique prediction' for [X/H] or [X/Fe] = f(age). Clearly, the data show a 'spread' in their abundance patterns, well beyond their errors. In a galaxy where radial migration must be prevalent, a 1-zone model cannot be correct.

In the longer run, we should explore in which regime it is a useful approximation: this could be done by restricting the observations to a limited range in [Fe/H], if [Fe/H] has been a good birth-radius predictor (for stars younger than 8Gyrs). Or we could fit a superposition of 1-zone models.

Next Steps

What portion of [X/H]-age space can be reached by varying the parameters of a one-zone model of a given yield-table?

How to go about it? Perhaps by simply defining the fill range of plausible model parameters, (galaxy evolution and IMF, not yields)  and then sampling model predictions uniformly.

It would be good to have an approach, to figure out how degenerate (or not), variations in the IMF and of the SFH are (if one has Apogee-type data).

What is the best one-zone fit to the Apogee data under the (untenable) assumption that all yields are right, and the data have no systematic offsets?

Apparently for historical reasons it is still not 'easy' in Jan's model to hold an arbitrary number of parameters (including none) fixed, fitting the rest via emcee. That piece of infrastructure should probably be put in place as one of the first steps.

What is the best one-zone fit to the Apogee data under the (untenable) assumption that all yields are right, and the data may have systematic offsets?

Apparently for historical reasons it is still not 'easy' in Jan's model to hold an arbitrary number of parameters (including none) fixed, fitting the rest via emcee. That piece of infrastructure should probably be put in place as one of the first steps.

Can we learn about the yields?

Conceptually the next step would be to have a few yield-knobs to tune, and let them loose in the data fitting.

Sample selection:

We need to decide what good sample cuts are, to make the one-zone model a sensible framework. Options are:

-- spatial cut (solar radius)

-- abundance cut (FeH==birth radius) at solar FeH +- 0.x dex

-- no cuts