Winds

The wind modelling capability in DESPOTIC is located in the despotic.winds module. The unofficial name for this portion of the code is ROCKETSTAR – as named by the primary author’s 5-year old.

The physical model used in the despotic.winds module is described in Krumholz et al. (2017), and users are encouraged to read that paper to understand the physical basis of the calculations. Example scripts using this code can be found in the repository https://bitbucket.org/krumholz/despotic_winds/ associated with this paper.

Compiling

The despotic.winds class relies on a copmlementary C++ library for speed. This must be compiled separately, though the procedure should be automatic for users with standard tools and libraries installed. See Installing the despotic.winds Module for details.

The pwind Class

The front end to the despotic.winds is the pwind class. This class requires that the user specify the generalized Eddington ratio \(\Gamma\) and the Mach number \(\mathcal{M}\) for the wind. By default this will create a spherical, ideal wind, which is fully defined by these two parameters. In addition, the the user can specify a number of other proprties:

  • The rate of cloud expansion, specified by the keyword expansion. Valid values are area, intermediate, and solid angle.
  • The gravitational potential, specified by the keyword potential. Valid values are point and isothermal.
  • The geometry of the wind, specified by the keyword geometry. Valid values are sphere, cone, and cone sheath. For cone the user must also specify the cone tilt (via the keyword phi) and the cone opening angle (via the keyword theta). For cone sheath the user must also specify the inner opening angle (via the keyword theta_in).
  • The driving mechanism, specified by the keyword driver. Valid values are ideal, radiation, and hot. For radiation, the user must specify the optical depth at the mean surface density (via the keyword tau0). For hot, the user must specify the dimensionless hot gas velocity (via the keyword uh).

The are a range of other keywords the affect the behavior of pwind objects. See pwind for a full listing.

An example is:

import numpy as np
from despotic.winds import pwind

Gamma = 0.2
Mach = 50.
tau0 = 100.
phi = np.pi/4.0
theta = np.pi/2.0

pw = pwind(Gamma, Mach, driver='radiation', potential='isothermal',
           expansion='solid angle', geometry='cone',
           tau0=tau0, theta=theta, phi=phi)

This creates a pwind object that represents a radiatively-driven wind in an isothermal potential, with clouds maintaining constant solid angle. The wind is confined to a cone that is tipped by \(45^\circ\) relative to the vertical, with a \(90^\circ\) opening angle. The wind is characterized by a generalized Eddington ratio \(\Gamma = 0.2\) and a Mach number \(\mathcal{M} = 50\), and the optical depth at the mean surface density of the launch region is \(\tau_0 = 100\).

Caculations Using pwind

The pwind class defines a series of methods that can be used to compute the observable properties of the specified wind. There are four basic types of observables that can be computed:

  • pwind.tau: this method computes absorption optical depths. The user must specify the dimensionless velocity or velocities u at which to compute the absorption, as well as the dimensionless transition strength \(t_X/t_w\) for the wind. This can be specified either directly, via the keyword tXtw, or computed from an input oscillator strength Omega, wavelength wl, abundance abd, and wind mass removal timescale tw. The keyword correlated specifies whether the wind should be treated as correlated or uncorrelated. The keyword u_trans specifies that the transition in question is a multiplet, with the individual transitions occurring at dimensionless velocities given by u_trans.
  • pwind.Xi: this method returns the optically thin emission line shape function \(\Xi\), as defined in the Krumholz et al. (2017) paper. The user must specify the dimensionless velocity or velocities u.
  • pwind.temp_LTE: this returns the brightness or antenna temperature for a species in LTE. The user must provide the dimensionless velocity or velocities u and the wind kinetic temperature T. In addition, the user must provide the dimensionless transition strength \(t_X/t_w\) for the wind. This can be specified either directly, via the keyword tXtw, or computed on the fly in one of two ways. First, the user can specify Omega, wl, abd and tw, exactly as for pwind.tau. Second, the user can provide a DESPOTIC emitter object (see emitter) and a wind removal timescale tw. Finally, the keyword correlated specifies whether the wind should be treated as correlated or uncorrelated.
  • pwind.intTA_LTE: this computes the velocity-integrated antenna temperature for an emitting species in LTE. The user must provide the velocity scale v0 for the wind launching region and the wind kinetic temperature T. All other parameters are as for pwind.temp_LTE.

All of these routines accept the keywords varpi and varpi_t which specify the dimensionless axial and transverse position of the line of sight (\(\varpi_a\) and \(\varpi_t\) in the terminology of Krumholz et al. 2017). In addition, all routines except pwind.Xi accept the keywords fj and boltzfac, which specify the fractional level population for the lower level and the Boltzmann factor between the two levels of the transition, respectively.

The are a range of other keywords that affect the behavior of these computation routines. See pwind for a full listing.