Analysis Module

windsoln.py:

Contains the class for handling the wind solution file generated by Wind-AE. Generates windsoln object which contains the solution data (including postfacto calculations) and methods for analysis.

Perform postfacto calculations

Any values that can be computed from velocity, temperature, density, and ionization structure are (and can be, upon requested) included in add_user_vars() and are accessible via the dataframe sim.windsoln.soln[]

• sim.windsoln.soln[] values are all as a function of radius (normalized values available via sim.windsoln.soln[]):

  • Radius - ‘r’ (cm), ‘z’ (\(r = R_min + q*z\)),

  • Mass density - ‘rho’ (g/cm^3)

  • Velocity -‘v’ (cm/s)

  • Temperature - ‘T’,

  • Per-element “Neutral” fraction - ‘Ys_HI’, etc. (“neutral” refers to the the lowest ionization state in the simulation as Wind-AE can currently only model one ionization state per metal)

  • Per-element Column density -‘Ncol_HI’, etc.

  • Number densities (1/cm^3) -

    • Total electron - ‘n_e’

    • Element - Total: ‘n_H’, neutral: ‘n_HI’, ionized: ‘n_HII’. Such that ‘n_H’ = ‘n_HI’ + ‘n_HII’

    • Total of all species: ‘n_tot’

  • Mean molecular/atomic weight - ‘mu’ (dimensionless)

  • Pressure - ‘P’ (dyne/cm^2 = barye = microbar = \(10^{-6}\) bar)

  • Ram pressure - ‘ram’ (barye)

  • Sound speed - ‘cs’ (cm/s)

  • Mach number - ‘Mach’ (dimensionless)

  • Density scale height - ‘Hsc’ (cm)

  • Multispecies Ionization Balance:

    • Ionization rate (per unit volume)- ‘ion_rate_HI’, etc. (\(s^{-1} cm^{-3}\))

    • Recombination rate (per unit volume) - ‘recomb_HI’, etc. (\(s^{-1} cm^{-3}\))

    • Advection rate (per unit volume) - ‘advec_HI’, etc. (\(s^{-1} cm^{-3}\))

  • Heating and Cooling Rates (per unit volume):

    • Currently Included in Wind-AE:

      • Photoionization rate - ‘heat_ion’ (ergs \(s^{-1} cm^{-3}\))

      • Recombination cooling - ‘cool_rec’ (ergs \(s^{-1} cm^{-3}\))

      • Advective Heating/Cooling - ‘heat_advect’ (ergs \(s^{-1} cm^{-3}\))

      • Bolometric Heating/Cooling - ‘boloheat’, ‘bolocool’ (ergs \(s^{-1} cm^{-3}\))

      • Line cooling:

        • Lyman-alpha cooling - ‘cool_lyman’ (ergs \(s^{-1} cm^{-3}\))

        • Carbon line cooling - “cool_CII_1570000A” (15700000 \(\AA\) line), “cool_CII_2326A”,”cool_CII_1334A”, “cool_CIII_1910A”, “cool_CIII_977A”

        • Oxygen line cooling - “cool_OII_834A” (834 \(\AA\) line), “cool_OII_2741A”, “cool_OII_3727A”, “cool_OII_7320A”, “cool_OIII_520000A”, “cool_OIII_5000A”, “cool_OIII_166A”, “cool_OIII_84A”

      • PdV cooling (work done by expanding gas) - ‘cool_PdV’ (ergs \(s^{-1} cm^{-3}\))

    • Not included in Wind-AE:

      • Conductive cooling - ‘cool_cond’ (ergs \(s^{-1} cm^{-3}\)) [PLANNED]

      • Gravitational heating/cooling - ‘cool_grav’ (ergs \(s^{-1} cm^{-3}\))

    • Cumulative differential heating - ‘cum_heat’ (ergs \(s^{-1} cm^{-3}\))

  • Bernoulli Constants - ‘bern’,

  • Hydrogen Knudsen number - ‘Kn_hb_HI’ (hardbody), ‘Kn_Co_HI’ (Coloumb), ‘Kn_mx_HI’ (mix of hardbody and Coloumb) [multispecies PLANNED]

• A selection of helpful sim.windsoln variables:

  • soln - DataFrame containing all solution variables that vary as a function of radius.

  • soln_norm - DataFrame containing all solution variables normalized by their scales (then sim.windsoln.soln['rho'] = sim.windsoln.soln_norm['rho'] * sim.windsoln.scales_dict['rho'])

  • scales_dict - Dictionary containing the scale factors for temperature, density, radius, etc.

  • Planet parameters: Mp (g), Rp (cm), semimajor (cm), Mstar (g), bolometric luminosity Lstar (ergs/s), flux at semimajor axis Ftot (ergs \(s^{-1} cm^{-2}\))

  • Physics parameters: nspecies (number of unique elements), HX (mass fraction array of elements), species_list, atomic_masses (g), molec_adjust (\(m_H\), average mean molecular weight of region of the atmosphere below the wind)

  • Spectrum parameters:

    • npts - number of wavelength points in smoothed spectrum

    • E_wl - energy per wavelength bin (ergs)

    • wPhi_wl - photon density normalized by total flux (\(=\phi e^{-\tau} / F_{tot}\)) ()

    • F_wl - flux per wavelength bin (ergs \(cm^{-2} s^{-1}\)) (sum(F_wl) = Ftot)

    • Generating spectrum: spec_src_file, spec_kind, spec_window (nm), etc.

  • Boundary Condition parameters:

    • Lower: Rmin (Rp), rho_rmin (RHO0 = sim.windsoln.scales_dict[‘rho’]), T_rmin (T0), per-element neutral fraction Ys_rmin_HI, etc.

    • Upper: Rmax (Rp), per-element Ncol_sp_HI, etc. (g/cm^2)

  • Flags:

    • lyacool - Line cooling on/off.

    • tidalforce - Tidal force from star on/off.

    • bolo_heat_cool - Complementary error function that governs the transition from layer below wind where molecules may be present and bolometric heating / cooling dominate the energy budget on/off.

    • integrate_outward - Integrate outward from the lower boundary to the Coriolis radius (Rmax = R_cori) on/off.

  • Useful Radii:

    • Sonic point radius - R_sp (Rp)

    • XUV radius / wind launch radius / photoionization front - R_XUV (Rp), lowest radial extent of substantial photoionization energy deposition (i.e., where wind “launches”)

    • Coriolis radius - R_cori (Rp)

    • Hill sphere - R_hill (Rp)

    • Exosphere - R_exo (Rp)

  • Optical depth - taus (dimensionless) 2D array of size [len(radii),len(spectrum bins)] (Not to be confused with the function tau_array)

Assorted Useful Functions

wind_solution.calc_mu()

Calculates dimensionless mean molecular weight (mu).

wind_solution.calc_massloss()

Calculates mass loss in g/s. NOTE: Multiplied by a factor of 0.33 which encodes adjustments for spherical geometry (to account for Wind-AE taking the substellar point in the planet’s atmosphere) and horizontal heat redistribution (Murray-Clay et al. 2009).

wind_solution.tau_array(photon, units='eV')

Returns an array with the optical depth for the provided photon energy (or wavelength) for each radius in the windsoln.

Parameters:

• photon (float) – energy or wavelength of photon of units units

• units (str) – cm, nm, or eV

Returns:

optical depth array of size len(r)

Return type:

tau (array)

wind_solution.calc_tau1_radius(photon, units='eV')

Returns radius in Rp and index where tau=1 surface is for the photon of the provided energy (or wavelength).

Parameters:

• photon (float) – energy or wavelength of photon of units units

• units (str) – cm, nm, or eV

Returns:

(r, idx) where r is the radius in Rp and idx is the index where tau=1 surface is located.

Return type:

tuple

Rarely useful and somewhat deprecated

wind_solution.calc_R_exo(Kn='Kn_mx_HI')

Calculating exosphere radius in Rp and index. DEPRECATED, requires updated Knudsen number calculations for all species.

Parameters:

Kn (str) – Knudsen collision number for a given species. Default: “Kn_mx_HI”, which is a weighted mix of hardbody and Coulomb Kn for HI. Where a Kn > 1 indicates that the flow is collisionless for that species and a fluid solution is no longer valid.

Returns:

R_exo: exosphere radius in Rp.

If Kn always < 1, then R_exo = NaN (R_exo is outside of the range of the simulation). If R_exo > R_sp, then R_exo = Rmax

int: exo_index: index of exosphere radius in soln

Return type:

float

wind_solution.calc_Jeans()

DEPRECATED. Calculates Jeans length and mass loss rate via Jeans escape. If R_exo is outside of the bounds of the simulation, R_exo is NaN, so result will be NaN. Currently uses R_exo computed only from HI collisionality.

wind_solution.calc_Coriolis()

Calculates the Coriolis turning radius as the radius where the outflow velocity, integrated starting at the sonic point and ignoring pressure acceleration, is deflected by one radian due to the Coriolis force. Computes self.cori_pos, the x and y coordinates of the streamline.

wind_solution.calc_ballistic(n_ball=31)

wind_solution.regrid(q_arr=None, simple=True)

Regrid the solution onto a new set of q values, where q is a radius-like parameter that ranges from 0 to 1 (Murray-Clay et al. 2009). Where radius, r = R_min + q*z and z is a dependent variable because R_sp is not know apriori (z := R_sp - R_min)

Basically never necessary.