*
Cococubed.com


Electron and Positron Chemical Potentials

Home

Astronomy research
Software instruments
   Stellar equation of states
   EOS with ionization
   EOS for supernovae
   Chemical potentials
   Stellar atmospheres

   Voigt Function
   Jeans escape
   Polytropic stars
   Cold white dwarfs
   Adiabatic white dwarfs

   Cold neutron stars
   Stellar opacities
   Neutrino energy loss rates
   Ephemeris routines
   Fermi-Dirac functions

   Polyhedra volume
   Plane - cube intersection
   Coating an ellipsoid

   Nuclear reaction networks
   Nuclear statistical equilibrium
   Laminar deflagrations
   CJ detonations
   ZND detonations

   Fitting to conic sections
   Unusual linear algebra
   Derivatives on uneven grids
   Pentadiagonal solver
   Quadratics, Cubics, Quartics

   Supernova light curves
   Exact Riemann solutions
   1D PPM hydrodynamics
   Hydrodynamic test cases
   Galactic chemical evolution

   Universal two-body problem
   Circular and elliptical 3 body
   The pendulum
   Phyllotaxis

   MESA
   MESA-Web
   FLASH

   Zingale's software
   Brown's dStar
   GR1D code
   Iliadis' STARLIB database
   Herwig's NuGRID
   Meyer's NetNuc
Presentations
Illustrations
cococubed YouTube
Bicycle adventures
Public Outreach
Education materials

AAS Journals
AAS Youtube
2020 Celebration of Margaret Burbidge
2020 Digital Infrastructure
2021 MESA Marketplace
2021 MESA Summer School
2021 ASU Solar Systems
2021 ASU Energy in Everyday Life


Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

* The tool in chem_poten.tbz returns the electron and positron chemical potentials as a function of temperature, density and Ye for a fully ionized stellar plasma.

The electron chemical potentials returned do not include the electron rest mass, so the value returned is the "kinetic chemical potential". This means that the positron chemical potential must have the rest-mass terms appear explicitly, ηpos = -ηele - 2mec2. One can see this being applied at the end of the relevant routine.

This tool is derived from the Helmholtz equation of state. A stand-alone electron/positron chemical potential solver may be useful for Compton opacities (e.g., Poutanen 2017) weak reaction rates, reaction rate screening factors, and others where invoking the full machinery of an equation of state may not be as desirable.


Ten tips about the chemical potential (from Peter Saeta)
  1. It expresses how eager a system is for particles.
  2. In equilibrium it is equal in two systems placed in diffusive contact.
  3. Particles move from a region of high chemical potential to a region of low chemical potential.
  4. It can be found by differentiating thermodynamic potentials with respect to N.
  5. It has an internal part and an external part; the external part is just a normal per-particle potential energy, such as mgh.
  6. It is the Gibbs free energy per particle, G/N.
  7. It is used to describe chemical equilibria.
  8. For a monatomic ideal gas, it is kT ln (νQ/ν).
  9. It is enormously useful in describing equations of state.
  10. It is the factor you use to get the particle number right!

Number 10 is probably the most pragmatic. In the tool chem_poten.tbz, one balances the number density of electrons from fully ionized material with the net number density of electrons and positrons coming from the relevant Fermi-Dirac statistics.
 



Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.