SpiralDensityWave

class dysmalpy.models.SpiralDensityWave(Vrot=None, rho0=None, f=None, k=None, dVrot_dR=None, **kwargs)

Bases: HigherOrderKinematicsPerturbation, _DysmalFittable3DModel

Model for a spiral density wave, assumed in the galaxy midplane.

Parameters:

• m (int) – Number of photometric/density spiral arms.

• cs (float) – Sound speed of medium, in km/s.

• epsilon (float) – Density contrast of perturbation (unitless).

• Om_p (float) – Angular speed of the driving force, \(\Omega_p\).

• phi0 (float, optional) – Angle offset of the arm winding, in degreed. Default: 0.

Notes

This model is implemented following the derivation given in the Appendix of Davies et al. 2009, ApJ, 702, 114 [1].

Functions for the following must also be passed when setting up the model, which take the midplane galaxy radius R as an input:

• Vrot(R) [Unperturbed rotation velocity of the galaxy]

• dVrot_dR(R) [Derivative of Vrot(R) – ideally evaluated analytically, otherwise very slow]

• rho0(R) [Unperturbed midplane density profile of the galaxy]

• f(R, m, cs, Om_p, Vrot) [Function describing the spiral shape, \(m\phi = f(R)\), with \(k \equiv df/dR\)]

• k(R, m, cs, Om_p, Vrot) [Function for the radial wavenumber]

References

[1]

https://ui.adsabs.harvard.edu/abs/2009ApJ…702..114D/abstract

Attributes Summary

Om_p
cs
epsilon
m
outputs
param_names	Names of the parameters that describe models of this type.
phi0

Methods Summary

ep_freq_sq(R)	Return kappa^2, square of the epicyclic frequency
evaluate(x, y, z, m, phi, cs, epsilon, Om_p, ...)	Evaluate the spiral density wave at x,y,z
f(R)	Shape of spiral arms, with f=m*phi = Int_0^R(k dR)
k(R)	Calculate wavenumber
light_profile(x, y, z)
rho_perturb(x, y, z)	Return the density perturbation -- consider only the midplane Given by Eq.
vLOS_perturb(x, y, z)	Return the projected LOS velocity combining both radial and phi components.
vel_direction_emitframe(x, y, z[, _save_memory])	Method to return the velocity matrix in the output Cartesian frame.
velocity(x, y, z, *args)	Evaluate the spiral density velocity amplitude as a function of position x, y, z, for the different radial and phi components.
vphi_perturb(x, y, z)	Return the phi-direction velocity perturbation Given by Eq.
vr_perturb(x, y, z)	Return the radial velocity perturbation Given by Eq.

Attributes Documentation

Om_p = DysmalParameter('Om_p', value=0.0, prior=<dysmalpy.parameters.UniformPrior object>)

cs = DysmalParameter('cs', value=50.0, bounds=(0, None), prior=<dysmalpy.parameters.UniformPrior object>)

epsilon = DysmalParameter('epsilon', value=0.1, bounds=(0, None), prior=<dysmalpy.parameters.UniformPrior object>)

m = DysmalParameter('m', value=2.0, fixed=True, bounds=(0, None), prior=<dysmalpy.parameters.UniformPrior object>)

outputs = ('vr', 'vphi', 'vz')

param_names = ('m', 'phi0', 'cs', 'epsilon', 'Om_p')

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

phi0 = DysmalParameter('phi0', value=0.0, bounds=(0, 360), prior=<dysmalpy.parameters.UniformPrior object>)

Methods Documentation

ep_freq_sq(R)

Return kappa^2, square of the epicyclic frequency

evaluate(x, y, z, m, phi, cs, epsilon, Om_p, Vrot, rho0)

Evaluate the spiral density wave at x,y,z

f(R)

Shape of spiral arms, with f=m*phi = Int_0^R(k dR)

k(R)

Calculate wavenumber

light_profile(x, y, z)

rho_perturb(x, y, z)

Return the density perturbation – consider only the midplane Given by Eq. A9, Davies et al. 2009, ApJ, 702, 114

vLOS_perturb(x, y, z)

Return the projected LOS velocity combining both radial and phi components. For use in visualizing. Handled via matrix multiplication & projection for model_set.simulate_cube()

Uses NEGATIVE for inflow, POSITIVE for outflow

vel_direction_emitframe(x, y, z, _save_memory=False)

Method to return the velocity matrix in the output Cartesian frame.

As the native geometry is cylindrical (ignoring z dir), and the velocity is multicoordinate, we need a more complex output than a single vector for a dotproduct.

vel = (R, phi, z). Need matmul(vel_dir_matrix, vel) = vel in (x,y,z). So:

vel_dir_matrix = [[Rtox, phitox, ztox],
                [Rtoy, phitoy, ztoy],
                [Rtoz, phitoz, ztoz]]

Parameters:

• x (float or array) – xyz position in the output reference frame.

• y (float or array) – xyz position in the output reference frame.

• z (float or array) – xyz position in the output reference frame.

• _save_memory (bool, optional) – Option to save memory by only calculating the relevant matrices (eg during fitting). Default: False

Returns:

vel_dir_matrix – Transform of the velocity from the native coordinates to the output cartesian frame.

Return type:

3x3-element matrix

velocity(x, y, z, *args)

Evaluate the spiral density velocity amplitude as a function of position x, y, z, for the different radial and phi components. Return a tuple of (vr, vphi, vz).

vphi_perturb(x, y, z)

Return the phi-direction velocity perturbation Given by Eq. A11, Davies et al. 2009, ApJ, 702, 114

vr_perturb(x, y, z)

Return the radial velocity perturbation Given by Eq. A10, Davies et al. 2009, ApJ, 702, 114

Here inflow is NEGATIVE, outflow is POSITIVE.