PowerLawCutoffPotential

class gala.potential.potential.PowerLawCutoffPotential(m, alpha, r_c, units=None, origin=None, R=None)

Bases: gala.potential.potential.CPotentialBase

A spherical power-law density profile with an exponential cutoff.

The power law index must be 0 <= alpha < 3.

Note

This potential requires GSL to be installed, and Gala must have been built and installed with GSL support enaled (the default behavior). See http://gala.adrian.pw/en/latest/install.html for more information.

Parameters:

m : Quantity, numeric [mass]

Total mass.

alpha : numeric

Power law index. Must satisfy: alpha < 3

r_c : Quantity, numeric [length]

Cutoff radius.

units : UnitSystem (optional)

Set of non-reducable units that specify (at minimum) the length, mass, time, and angle units.

origin : Quantity (optional)

The origin of the potential, the default being 0.

R : Rotation, array_like (optional)

A Scipy Rotation object or an array representing a rotation matrix that specifies a rotation of the potential. This is applied after the origin shift. Default is the identity matrix.

Attributes Summary

mass_enclosed(q, t)	Estimate the mass enclosed within the given position by assuming the potential is spherical.
to_latex

Methods Summary

__call__(q)	Call self as a function.
acceleration(q[, t])	Compute the acceleration due to the potential at the given position(s).
circular_velocity(q[, t])	Estimate the circular velocity at the given position assuming the potential is spherical.
density(q[, t])	Compute the density value at the given position(s).
energy(q[, t])	Compute the potential energy at the given position(s).
gradient(q[, t])	Compute the gradient of the potential at the given position(s).
hessian(q[, t])	Compute the Hessian of the potential at the given position(s).
integrate_orbit(*args, **kwargs)	Warning This is now deprecated. Convenient orbit integration should
plot_contours(grid[, filled, ax, labels, …])	Plot equipotentials contours.
plot_density_contours(grid[, filled, ax, …])	Plot density contours.
save(f)	Save the potential to a text file.
total_energy(x, v)	Compute the total energy (per unit mass) of a point in phase-space in this potential.
value(*args, **kwargs)

Attributes Documentation

mass_enclosed(q, t)

Estimate the mass enclosed within the given position by assuming the potential is spherical. This is not so good!

Parameters:

q : array_like, numeric

Position to compute the mass enclosed.

to_latex

Methods Documentation

__call__(q)

Call self as a function.

acceleration(q, t=0.0)

Compute the acceleration due to the potential at the given position(s).

Parameters:

q : PhaseSpacePosition, Quantity, array_like

Position to compute the acceleration at.

Returns:

acc : Quantity

The acceleration. Will have the same shape as the input position array, q.

circular_velocity(q, t=0.0)

Estimate the circular velocity at the given position assuming the potential is spherical.

Parameters:

q : array_like, numeric

Position(s) to estimate the circular velocity.

Returns:

vcirc : Quantity

Circular velocity at the given position(s). If the input position has shape q.shape, the output energy will have shape q.shape[1:].

density(q, t=0.0)

Compute the density value at the given position(s).

Parameters:

q : PhaseSpacePosition, Quantity, array_like

The position to compute the value of the potential. If the input position object has no units (i.e. is an ndarray), it is assumed to be in the same unit system as the potential.

Returns:

dens : Quantity

The potential energy or value of the potential. If the input position has shape q.shape, the output energy will have shape q.shape[1:].

energy(q, t=0.0)

Compute the potential energy at the given position(s).

Parameters:

q : PhaseSpacePosition, Quantity, array_like

The position to compute the value of the potential. If the input position object has no units (i.e. is an ndarray), it is assumed to be in the same unit system as the potential.

Returns:

E : Quantity

The potential energy per unit mass or value of the potential.

gradient(q, t=0.0)

Compute the gradient of the potential at the given position(s).

Parameters:

q : PhaseSpacePosition, Quantity, array_like

The position to compute the value of the potential. If the input position object has no units (i.e. is an ndarray), it is assumed to be in the same unit system as the potential.

Returns:

grad : Quantity

The gradient of the potential. Will have the same shape as the input position.

hessian(q, t=0.0)

Compute the Hessian of the potential at the given position(s).

Parameters:

q : PhaseSpacePosition, Quantity, array_like

The position to compute the value of the potential. If the input position object has no units (i.e. is an ndarray), it is assumed to be in the same unit system as the potential.

Returns:

hess : Quantity

The Hessian matrix of second derivatives of the potential. If the input position has shape q.shape, the output energy will have shape (q.shape[0],q.shape[0]) + q.shape[1:]. That is, an n_dim by n_dim array (matrix) for each position.

integrate_orbit(*args, **kwargs)

Warning

This is now deprecated. Convenient orbit integration should happen using the gala.potential.Hamiltonian class. With a static reference frame, you just need to pass your potential in to the Hamiltonian constructor.

Integrate an orbit in the current potential using the integrator class provided. Uses same time specification as Integrator.run() – see the documentation for gala.integrate for more information.

Parameters:

w0 : PhaseSpacePosition, array_like

Initial conditions.

Integrator : Integrator (optional)

Integrator class to use.

Integrator_kwargs : dict (optional)

Any extra keyword argumets to pass to the integrator class when initializing. Only works in non-Cython mode.

cython_if_possible : bool (optional)

If there is a Cython version of the integrator implemented, and the potential object has a C instance, using Cython will be much faster.

**time_spec

Specification of how long to integrate. See documentation for parse_time_specification.

Returns:

orbit : Orbit

plot_contours(grid, filled=True, ax=None, labels=None, subplots_kw={}, **kwargs)

Plot equipotentials contours. Computes the potential energy on a grid (specified by the array grid).

Warning

Right now the grid input must be arrays and must already be in the unit system of the potential. Quantity support is coming…

Parameters:

grid : tuple

Coordinate grids or slice value for each dimension. Should be a tuple of 1D arrays or numbers.

filled : bool (optional)

Use contourf() instead of contour(). Default is True.

ax : matplotlib.Axes (optional)

labels : iterable (optional)

List of axis labels.

subplots_kw : dict

kwargs passed to matplotlib’s subplots() function if an axes object is not specified.

kwargs : dict

kwargs passed to either contourf() or plot().

Returns:

fig : Figure

plot_density_contours(grid, filled=True, ax=None, labels=None, subplots_kw={}, **kwargs)

Plot density contours. Computes the density on a grid (specified by the array grid).

Warning

Right now the grid input must be arrays and must already be in the unit system of the potential. Quantity support is coming…

Parameters:

grid : tuple

Coordinate grids or slice value for each dimension. Should be a tuple of 1D arrays or numbers.

filled : bool (optional)

Use contourf() instead of contour(). Default is True.

ax : matplotlib.Axes (optional)

labels : iterable (optional)

List of axis labels.

subplots_kw : dict

kwargs passed to matplotlib’s subplots() function if an axes object is not specified.

kwargs : dict

kwargs passed to either contourf() or plot().

Returns:

fig : Figure

save(f)

Save the potential to a text file. See save() for more information.

Parameters:

f : str, file_like

A filename or file-like object to write the input potential object to.

total_energy(x, v)

Compute the total energy (per unit mass) of a point in phase-space in this potential. Assumes the last axis of the input position / velocity is the dimension axis, e.g., for 100 points in 3-space, the arrays should have shape (100,3).

Parameters:

x : array_like, numeric

Position.

v : array_like, numeric

Velocity.

value(*args, **kwargs)