Units and Conventions

Nyx supports both CGS and Cosmological units. In the equation of state calls, conversions must be made between CGS units and code units. Table [table:units] shows some of the common symbols / names used throughout the code documentation and papers.

[table:units] Common quantities and units.
name units description
\(t\) s time
\(\rho\) \(\gcc\) mass density
\(\ub\) \(\cms\) velocity vector
\(p\) \(\presunit\) pressure
\(\gb\) \(\accelunit\) gravitational acceleration
\(\Sb\) varies source term
\(S_{\Lambda}\) varies source term
\(E\) \(\ergg\) specific total energy
\(e\) \(\ergg\) specific internal energy
\(T\) \(K\) temperature

words

We support two different systems of units in : CGS and Cosmological. All inputs and problem initialization should be specified consistently with one of these sets of units. No internal conversions of units occur within the code, so the output must be interpreted appropriately. The default is cosmological units. If you want to use CGS units instead, then set USE_CGS = TRUE in your GNUmakefile. This will select the file constants_cgs.f90 instead of constants_cosmo.f90 from the Nyx/constants directory.

[table:inputs] Units expected for inputs and outputs.
         
Location Variable CGS Cosmologica l Conversion Data
         
         
inputs file geometry. prob_lo cm Mpc 1Mpc = 3.08568025e 24 cm
  geometry. prob_hi cm Mpc 1Mpc = 3.08568025e 24 cm
         
         
Hydro Initializat ion density g / cm:math:` ^3` M\(_ \odot\) / Mpc:math: ^3 1 (M:math:_odot / Mpc:math: ^3) = .06769624e- 39 (g/cm:math: ^3)
         
         
Hydro Initializat ion velocities cm/s km/s 1km = 1.e5 cm
         
         
Hydro Initializat ion momenta (g/cm:math: ^3) (cm/s) (M:math:_odot/Mpc:m ath:^3) (km/s) 1km = 1.e5 cm
        1 (M:math:_odot / Mpc:math: ^3) = .06769624e- 39 g/cm:math :^3
         
         
Hydro Initializat ion temperature K K 1
         
         
Hydro Initializat ion specific energy (\(e\) or \(E\)) erg/g= (cm/s):math :^2 (km/s):math :^2 1 (km/s):math :^2 = 1.e10 (cm/s):math :^2
         
         
Hydro Initializat ion

energy (\(\rh o e\) or :math:`rho

E`)
 erg / cm:math:` ^3 =` (M:math:_odot/Mpc:m ath:^3) (km/s):math :^2 1 (km/s):math :^2 = 1.e10 (cm/s):math :^2
    (g/cm:math: ^3) (cm/s):math :^2   1 (M:math:_odot / Mpc:math: ^3) = .06769624e- 39 g/cm:math :^3
         
         
Particle Initializat ion particle mass g M\(_ \odot\) 1 M\(_ \odot\) = 1.98892e33 g
         
         
Particle Initializat ion particle locations cm Mpc 1 Mpc = 3.08568025e 24 cm
         
         
Particle Initializat ion particle velocities cm/s km/s 1 km = 1e5 cm
         
         
Output Pressure g (cm/s):math :^2 / cm:math:` ^3` M\(_ \odot\) (km/s):math :^2 / Mpc:math: ^3 1 M\(_ \odot\) (km/s):math :^2 / Mpc:math: ^3 =
        .06769624e- 29 g (cm/s):math :^2 / cm:math:` ^3`
         
         
Output Gravity (cm/s) / s (km/s):math :^2 / Mpc 1 M\(_ \odot\) (km/s):math :^2 / Mpc:math: ^3 =
         
         
Output Time s (Mpc/km) s 1 Mpc = 3.08568025e 19 km
         

[Table:Inputs]

The only other place that dimensional numbers are used in the code is in the tracing and Riemann solve. We set three small numbers which need to be consistent with the data specified. Each of these can be specified in the inputs file.

  • small_dens – small value for density
  • small_p – small value for pressure
  • small_T – small value for temperature

These are the places that each is used in the code:

  • small_dens

    • subroutine enforce_minimum_density (called after subroutine consup) – there are two choices for this. In the flooring routine,
      subroutine enforce_minimum_density_floor – density is set to small_dens, (rho e) and (rho E) are computed from small_temp,
      and momenta are set to zero. In the conservative routine, subroutine enforce_minimum_density_cons, an iterative procedure
      is used to create diffusive fluxes that adjusts all the variables conservatively until density is greater than small_dens.
    • subroutine tracexy / tracez / tracexy_ppm / tracez_ppm:
      qxp = max(qxp,small_dens)
      qxm = max(qxm,small_dens)
      and analogously for qyp/qym and qzp/qzm. This only modifies density inside the tracing, not the other variables

    • subroutine riemannus – we set

      wsmall = small_dens * csmall

      and then

      wl = max(wsmall, sqrt(gaml * pl * rl))
      wr = max(wsmall, sqrt(gamr * pr * rr))

      Also, we set

      ro = max(small_dens,ro)

      where ro = 0.5 * (rl + rr) – this state is only chosen when ustar = 0, and

      rstar = max(small_dens,rstar)

      where rstar = ro + (pstar-po)/co:math:^2

    • subroutine react_state – only compute reaction if \(\rho >\) small_dens

  • small_temp:

    • subroutine ctoprim: if \(\rho e < 0\), then
      call subroutine nyx_eos_given_RTX (e,…,small_temp,…) in order to compute a new energy, \(e\).
      This energy is then used to
      call subroutine nyx_eos_given_ReX in order to compute the sound speed, \(c.\)
      Coming out of this the temperature is equal to small_temp and the energy \(e\) has been reset.
    • subroutine react_state: if \(\rho e < 0\), then
      call subroutine nyx_eos_given_RTX (e,…,small_temp,…) in order to compute a new energy, \(e\).
      This energy is then used to proceed with the burner routine.
    • subroutine reset_internal_energy: if \(e < 0\) and \(E - ke < 0\) then
      call subroutine nyx_eos_given_RTX (e,…,small_temp,…) in order to compute a new energy, \(e\). This energy is also used to
      define a new \(E = e + ke\)

  • small_pres:

    • subroutine riemannus – we set

      pstar = max(small_pres,pstar)
      pgdnv = max(small_pres,pgdnv). Note that pgdnv is the pressure explicitly used in the fluxes.

    • subroutine uflaten – small_pres is used to keep the denominator away from zero

    • Everywhere we define values of pressure on a face, we set that value to be at least small_pres.