utilities module

A collection of useful functions that don’t fit into any of the other classes.

galaxy.utilities.wolf_mass(sigma, Re)

Wolf mass estimator from Wolf+ 2010

Args:

sigma :

1D line of sight velocity dispersion in km/s

Re :

2D radius enclosing half the stellar mass in pc

Returns: estimate of the dynamical mass within the half light radius in Msun

galaxy.utilities.sersic(R, Re, n, Mtot)

Function that returns Sersic Profile for an Elliptical System (See in-class lab 6)

Input

R:

radius (kpc)

Re:

half mass radius (kpc)

n:

sersic index

Mtot:

total stellar mass

Returns

Surface Brightness profile in Lsun/kpc^2

galaxy.utilities.HernquistM(r, a=<Quantity 60. kpc>, M_halo=<Quantity 1.97e+12 solMass>)

Args:

r (Quantity, units of kpc): distance from center a (Quantity, units of kpc): scale radius M_halo (Quantity, units of M_sun): total DM mass

Returns:

Total DM mass enclosed within r (M_sun)

galaxy.utilities.jacobi_radius(r, M_host, M_sat)

The Jacobi Radius for a satellite on a circular orbit about an extended host, where the host is assumed to be well modeled as an isothermal sphere halo:

R_j = r * (M_sat / 2 M_host(<r))}^(1/3)

For MW/LMC, the Isothermal Sphere approximation is not a bad one within 50 kpc.

In other contexts, can be called the Roche radius, Roche limit or Hill radius.

Args:

r:

distance between stellite and host (kpc)

M_host:

host mass enclosed within r (M_sun)

M_sat:

satellite mass (M_sun)

returns:

Jacobi radius (kpc)

galaxy.utilities.jacobi_mass(Rj, r, Mhost)

Function that returns min mass of a satellite given its observed size + distance from a massive host: Msat = (Rj/r)**3 * 2 * Mhost

Args:

Rj:

Jacobi radius (approx as observed size) (kpc)

r:

distance between stellite and host (kpc)

Mhost:

mass enclosed within r (M_sun)

returns:

Minimum mass Msat of a satellite given its current size (M_sun)

galaxy.utilities.rotation_matrix_to_vector(old_axis, to_axis=None)

Args:

old_axis (3-vector)

Vector to be brought into alignment with to_axis by rotation about the origin

to_axis (3-vector)

Angular momentum vector will be aligned to this (default z_hat)

Returns:

3x3 rotation matrix

Based on Rodrigues’ rotation formula Ref: https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

Note that orientation in the plane perpendicular to ‘to_axis’ is arbitrary

galaxy.utilities.z_rotation_matrix(pt1, pt2)

Rotates about z-axis to line up two given points along the x-axis

Args:

pt1, pt2 (2-component iterables)

define points to be placed on the x-axis

Returns:

3x3 rotation matrix

galaxy.utilities.find_nearest(array, value)

Find the entry in array which is closest to value Modified from https://stackoverflow.com/questions/2566412/find-nearest-value-in-numpy-array

Returns: index and corresponding value