[mesa-users] beta decays and electron captures

[Josiah Schwab]

Hi Kelly,

Here's a whirlwind tour of the weak reactions stuff that is in MESA.
(When I cite line #s, they correspond to MESA r7624.)

The rates module provides MESA's weak reaction rates.  When atoms are
fully ionized [fn:1] these rates are based (in order of precedence) on
the tabulations of Langanke & Martı́nez-Pinedo (2000), Oda et al.
(1994), and Fuller et al. (1985).  These are the "weaklib" rates.

These tables cover 1 ≤ log(ρYe) ≤ 11 and 7 ≤ log(T) < 10.5, but are
relatively coarse, with 11 points in the ρYe dimension (∆ log ρYe = 1)
and 12 points in the T dimension (∆ log T ≈ 0.25). [fn:2]

You can find this input data at

  data/rates_data/weakreactions.tables

For each isotope pair, the tables have

  + positron emission rate
  + electron capture rate
  + total neutrino energy loss rate
 
  + electron emission rate
  + positron capture rate
  + total anti-neutrino energy loss rate

Given this data, the routine where this is all evaluated is the aptly
named "do_eval_weaklib_reaction_info", which lives in

  rates/private/eval_weak.f90

beginning on L133.  Given that you're interested in the gory details,
you should probably grab a coffee and give this routine a read.

The part where it will get more interesting for you is around L294.

MESA has already gotten the rate (lambda) and the log of the energy loss
rate (lneutrino) from the tables.  It also has the chemical potential
from the eos (mue).

In pseudo-code, then what happens is 

  Qx = mass_excess(lhs) - mass_excess(rhs)
      	   
  if (electron capture)
    Q = Qx + mue 
  else ! (electron emission)
    Q = Qx - mue 
  end if

  Qneu = exp10(lneutrino) / lambda


To recap things in the context of your questions:

> I’m working on a project that’s attempting to calculate neutrino
> spectra from various processes in the late stages of a large star’s
> evolution.  Right now, I’m trying to work out some of the finer points
> of beta decay/electron capture.  This brings me to my questions.
>
> I know MESA calculates the energy output from these nuclear reactions,
> and I’m wondering how and where the Q-values for the beta decay and
> electron capture reactions are defined in MESA.  Are all possible
> initial and final states accounted for separately, or is there some
> kind of effective Q value (eg. Langanke and Martinez-Pinedo
> arXiv:nucl-th/0101039v1 defines an effective Q value as one that
> accurately reproduces the average neutrino energy)?

All initial and final states were (presumably) accounted for separately
in the generation of the tables.  But the tables themselves have only
the total rate and the total neutrino loss rate.  From those quantities, 
MESA constructs Qneu which is (by definition) the average neutrino energy.

> I’ve read a few papers that disregard beta decays altogether and only
> worry about the electron/positron captures (that same Langanke and
> Martinez-Pinedo paper). Does MESA calculate both decay and capture?

Yes, MESA calculates both.

Hope that helps.  It will at least leave you with more questions :)

Best,
Josiah

Footnotes:

[fn:1] This is implemented as a cut in T; see for example
http://mesa.sourceforge.net/star_job_defaults.html#T9_weaklib_full_off
http://mesa.sourceforge.net/star_job_defaults.html#T9_weaklib_full_off_hi_Z

[fn:2] There is also the option to bypass the weaklib tables completely
and calculate the rates from a set of input transitions; see Section 8
of MESA Instrument Paper III and Schwab et al. (2015).  This capability
is designed for situations where only a few transitions dominate the
rate (and you a priori know what they are).  It also was designed with
lower temperatures in mind (T < 1e9 K).  If you think something like
that is useful for the calculations you want to do, we should talk about
how you might adapt it to your needs.