Density Profiling

Classes for Density Profiling

The dens_profs_classes module defines the DensProfs and DensProfsGadget classes that provide density profiling capabilities. They inherit from the DensProfsBase class (not relevant for the user).

class dens_profs.dens_profs_classes.DensProfsBase[source]

Bases: CosmicBase

Class for density profile calculations

Its public methods are getR200(), getIdxCat(), getXYZMasses(), getMassesCenters(), _getMassesCenters(), estDensProfs(), fitDensProfs(), estConcentrations(), plotDensProfs(), getObjInfo().

Parameters

  • xyz ((N2,3) floats, N2 >> N1) – positions of all simulation particles in Mpc/h (internal length units)

  • masses ((N2,) floats) – masses of all simulation particles in 10^10 M_sun/h

  • idx_cat ((N3,) integers) – contains indices of particles belonging to an object

  • r200 ((N1,) floats) – R_200 radii of the parent halos in Mpc/h (internal length units)

  • obj_size ((N1,) integers) – indicates how many particles are in each object

  • SNAP (string) – snapshot identifier, e.g. ‘024’

  • L_BOX (float) – simulation box side length in Mpc/h (internal length units)

  • MIN_NUMBER_PTCS (int) – minimum number of particles for object to qualify for morphology calculation

  • CENTER (str) – shape quantities will be calculated with respect to CENTER = ‘mode’ (point of highest density) or ‘com’ (center of mass) of each halo

  • VIZ_DEST (string) – visualization folder

  • CAT_DEST (string) – catalogue destination

  • SUFFIX (string) – either ‘_dm_’ or ‘_gx_’ or ‘_’ (latter for CosmicProfsDirect)

__init__()[source]
Parameters

  • xyz ((N2,3) floats, N2 >> N1) – positions of all simulation particles in Mpc/h (internal length units)

  • masses ((N2,) floats) – masses of all simulation particles in 10^10 M_sun/h

  • idx_cat ((N3,) integers) – contains indices of particles belonging to an object

  • r200 ((N1,) floats) – R_200 radii of the parent halos in Mpc/h (internal length units)

  • obj_size ((N1,) integers) – indicates how many particles are in each object

  • SNAP (string) – snapshot identifier, e.g. ‘024’

  • L_BOX (float) – simulation box side length in Mpc/h (internal length units)

  • MIN_NUMBER_PTCS (int) – minimum number of particles for object to qualify for morphology calculation

  • CENTER (str) – shape quantities will be calculated with respect to CENTER = ‘mode’ (point of highest density) or ‘com’ (center of mass) of each halo

  • VIZ_DEST (string) – visualization folder

  • CAT_DEST (string) – catalogue destination

  • SUFFIX (string) – either ‘_dm_’ or ‘_gx_’ or ‘_’ (latter for CosmicProfsDirect)

estConcentrations()[source]

Get best-fit concentration values of objects from density profile fitting

Parameters

  • dens_profs ((N3, r_res) floats) – density profiles whose concentrations are to be determined, in units of config.OutUnitMass_in_g/config.OutUnitLength_in_cm**3

  • r_over_r200 ((r_res,) floats) – normalized radii at which dens_profs are defined

  • method (dictionary, method[‘profile’] is either einasto, alpha_beta_gamma, hernquist, nfw, minimum requirement) – describes density profile model assumed for fitting, if parameter should be kept fixed during fitting then it needs to be provided, e.g. method[‘alpha’] = 0.18

  • obj_numbers (list of int) – list of object indices of interest

Returns

best-fit concentration for each object

Return type

(N3,) floats

estDensProfs()[source]

Estimate density profiles

Parameters

  • r_over_r200 ((r_res,) floats) – normalized radii at which to-be-estimated density profiles are defined

  • obj_numbers (list of int) – list of object indices of interest

  • direct_binning (boolean) – whether or not direct binning approach or kernel-based approach should be used

  • spherical (boolean) – whether or not spherical shell-based or ellipsoidal shell-based should be used, ignored if direct_binning = False

  • katz_config (dictionary) – dictionary with parameters to the Katz algorithm, with fields ‘ROverR200’, ‘IT_TOL’, ‘IT_WALL’, ‘IT_MIN’, ‘REDUCED’, ‘SHELL_BASED’

Returns

density profiles in units of config.OutUnitMass_in_g/config.OutUnitLength_in_cm**3

Return type

(N2, r_res) floats

fitDensProfs()[source]

Get best-fit results for density profile fitting

Parameters

  • dens_profs ((N3, r_res) floats) – density profiles to be fit, in units of config.OutUnitMass_in_g/config.OutUnitLength_in_cm**3

  • r_over_r200 ((r_res,) floats) – normalized radii at which dens_profs are defined

  • method (dictionary, method[‘profile’] is either einasto, alpha_beta_gamma, hernquist, nfw, minimum requirement) – describes density profile model assumed for fitting, if parameter should be kept fixed during fitting then it needs to be provided, e.g. method[‘alpha’] = 0.18

  • obj_numbers (list of int) – list of object indices of interest

Returns

best-fits for each object

Return type

structured array, containing (N3, n) floats, where n is the number of free parameters in the model method

getIdxCat()[source]

Fetch catalogue

Return idx_cat

contains indices of particles belonging to an object, obj_size: number of particles in each object

Return type

(N3) integers and (N1,) integers

getMassesCenters()[source]

Calculate total mass and centers of objects

Note that the units will be in config.OutUnitLength_in_cm and config.OutUnitMass_in_g.

Parameters

obj_numbers (list of int) – list of object indices of interest

Return centers, m

centers in config.OutUnitLength_in_cm and masses in config.OutUnitMass_in_g

Return type

structured array, containing (N,3) and (N,) floats

getObjInfo()[source]

Print basic info about the objects

getR200()[source]

Get overdensity radii in config.OutUnitLength_in_cm units

getXYZMasses()[source]

Retrieve positions and masses of particles

Return xyz, masses

positions in config.OutUnitLength_in_cm and masses in config.OutUnitMass_in_g

Return type

(N2,3) floats, (N2,) floats

plotDensProfs()[source]

Draws some simplistic density profiles

Parameters

  • dens_profs ((N2, r_res) floats) – estimated density profiles, in units of config.OutUnitMass_in_g/config.OutUnitLength_in_cm**3

  • r_over_r200 ((r_res,) floats) – radii at which dens_profs are defined

  • dens_profs_fit ((N2, r_res2) floats) – density profiles to be fit, in units of config.OutUnitMass_in_g/config.OutUnitLength_in_cm**3

  • r_over_r200_fit ((r_res2,) floats) – radii at which best-fits shall be calculated

  • method (dictionary, method[‘profile’] is either einasto, alpha_beta_gamma, hernquist, nfw, minimum requirement) – describes density profile model assumed for fitting, if parameter should be kept fixed during fitting then it needs to be provided, e.g. method[‘alpha’] = 0.18

  • nb_bins (int) – Number of mass bins to plot density profiles for

  • obj_numbers (list of int) – list of object indices of interest

class dens_profs.dens_profs_classes.DensProfsGadget[source]

Bases: DensProfsBase

Parameters

  • xyz ((N2,3) floats, N2 >> N1) – positions of all simulation particles in Mpc/h (internal length units)

  • masses ((N2,) floats) – masses of all simulation particles in 10^10 M_sun/h

  • idx_cat ((N3,) integers) – contains indices of particles belonging to an object

  • r200 ((N1,) floats) – R_200 radii of the parent halos in Mpc/h (internal length units)

  • obj_size ((N1,) integers) – indicates how many particles are in each object

  • SNAP (string) – snapshot identifier, e.g. ‘024’

  • L_BOX (float) – simulation box side length in Mpc/h (internal length units)

  • MIN_NUMBER_PTCS (int) – minimum number of particles for object to qualify for morphology calculation

  • CENTER (str) – shape quantities will be calculated with respect to CENTER = ‘mode’ (point of highest density) or ‘com’ (center of mass) of each halo

  • VIZ_DEST (string) – visualization folder

  • CAT_DEST (string) – catalogue destination

  • SUFFIX (string) – either ‘_dm_’ or ‘_gx_’ or ‘_’ (latter for CosmicProfsDirect)

Density profile estimation algorithms

The dens_profs_algos module contains the direct-binning and the kernel-based density profile estimation algorithms.

dens_profs.dens_profs_algos.calcDensProfsEllDirectBinning(float[:, :] xyz, float[:] masses, float[:] r200s, float[:] ROverR200, float[:, :] a, float[:, :] b, float[:, :] c, float[:, :, :] major, float[:, :, :] inter, float[:, :, :] minor, int[:] idx_cat, int[:] obj_size, float L_BOX, unicode CENTER)[source]

Calculates ellipsoidal shell-based density profiles for objects defined by indices found in idx_cat

Note: To calculate enclosed mass profiles, envoke CythonHelpers.calcMenclsBruteForceEll() instead of CythonHelpers.calcDensProfBruteForceEll()

Parameters

  • xyz ((N2,3) floats, N2 >> N1) – positions of all simulation particles

  • masses ((N2,) floats) – masses of all simulation particles

  • r200s ((N1,) floats) – R200 values of the objects

  • ROverR200 ((r_res,) float array) – radii at which the density profiles should be calculated, normalized by R200

  • idx_cat ((N3,) integers) – contains indices of particles belonging to an object

  • obj_size ((N1,) integers) – indicates how many particles are in each object

  • L_BOX (float) – box size

  • CENTER (str) – density profiles will be calculated with respect to CENTER = ‘mode’ (point of highest density) or ‘com’ (center of mass) of each halo

  • a ((N1,D_BINS+1,) floats) – major axis eigenvalues

  • b ((N1,D_BINS+1,) floats) – intermediate axis eigenvalues

  • c ((N1,D_BINS+1,) floats) – minor axis eigenvalues

  • major ((N1,D_BINS+1,3) floats) – major axis eigenvectors

  • inter ((N1,D_BINS+1,3) floats) – inter axis eigenvectors

  • minor ((N1,D_BINS+1,3) floats) – minor axis eigenvectors

Returns

density profiles defined at ROverR200

Return type

(N1, r_res) float array

dens_profs.dens_profs_algos.calcDensProfsKernelBased(float[:, :] xyz, float[:] masses, float[:] r200s, float[:] ROverR200, int[:] idx_cat, int[:] obj_size, float L_BOX, unicode CENTER)[source]

Calculates kernel-based density profiles for objects defined by indices found in idx_cat

Note: For background on this kernel-based method consult Reed et al. 2003, https://arxiv.org/abs/astro-ph/0312544.

Parameters

  • xyz ((N2,3) floats, N2 >> N1) – positions of all simulation particles

  • masses ((N2,) floats) – masses of all simulation particles

  • r200s ((N1,) floats) – R200 values of the objects

  • ROverR200 ((r_res,) float array) – radii at which the density profiles should be calculated, normalized by R200

  • idx_cat ((N3,) integers) – contains indices of particles belonging to an object

  • obj_size ((N1,) integers) – indicates how many particles are in each object

  • L_BOX (float) – box size

  • CENTER (str) – density profiles will be calculated with respect to CENTER = ‘mode’ (point of highest density) or ‘com’ (center of mass) of each halo

Returns

density profiles defined at ROverR200

Return type

(N1, r_res) float array

dens_profs.dens_profs_algos.calcDensProfsSphDirectBinning(float[:, :] xyz, float[:] masses, float[:] r200s, float[:] ROverR200, int[:] idx_cat, int[:] obj_size, float L_BOX, unicode CENTER)[source]

Calculates spherical shell-based density profiles for objects defined by indices found in idx_cat

Note: To calculate enclosed mass profiles, envoke CythonHelpers.calcMenclsBruteForce() instead of CythonHelpers.calcDensProfBruteForce()

Parameters

  • xyz ((N2,3) floats, N2 >> N1) – positions of all simulation particles

  • masses ((N2,) floats) – masses of all simulation particles

  • r200s ((N1,) floats) – R200 values of the objects

  • ROverR200 ((r_res,) float array) – radii at which the density profiles should be calculated, normalized by R200

  • idx_cat ((N3,) integers) – contains indices of particles belonging to an object

  • obj_size ((N1,) integers) – indicates how many particles are in each object

  • L_BOX (float) – box size

  • CENTER (str) – density profiles will be calculated with respect to CENTER = ‘mode’ (point of highest density) or ‘com’ (center of mass) of each halo

Returns

density profiles defined at ROverR200

Return type

(N1, r_res) float array

dens_profs.dens_profs_algos.calcMassesCenters(float[:, :] xyz, float[:] masses, int[:] idx_cat, int[:] obj_size, float L_BOX, unicode CENTER)[source]

Calculate total mass and centers of objects

Parameters

  • xyz ((N2,3) floats, N2 >> N1) – positions of all simulation particles

  • masses ((N2,) floats) – masses of all simulation particles

  • idx_cat ((N3,) integers) – contains indices of particles belonging to an object

  • obj_size ((N1,) integers) – indicates how many particles are in each object

  • L_BOX (float) – box size

  • CENTER (str) – density profiles will be calculated with respect to CENTER = ‘mode’ (point of highest density) or ‘com’ (center of mass) of each halo

Return centers, m

centers and masses

Return type

(N,3) and (N,) floats

Density profile fitting and plotting

The dens_profs_tools module provides density profile models such as the NFW profile as well as density profile fitting and plotting tools.

dens_profs.dens_profs_tools.drawDensProfs(VIZ_DEST, SNAP, r200s, dens_profs_fit, ROverR200_fit, dens_profs, ROverR200, obj_masses, obj_centers, method, nb_bins, start_time, MASS_UNIT, suffix='_')[source]

Create a series of plots to analyze object shapes

Plot intertial tensor axis ratios, triaxialities and ellipticity histograms.

Parameters

  • VIZ_DEST (string) – visualisation folder destination

  • SNAP (string) – e.g. ‘024’

  • r200s (N2-long float array) – catalogue of virial radii (of parent halos) in Mpc/h

  • dens_profs_fit ((N, r_res2) floats) – density profiles, defined at ROverR200, in M_sun*h^2/(Mpc)**3

  • ROverR200_fit ((r_res2,) floats) – normalized radii at which the mass-decomposed density profile fits shall be calculated

  • dens_profs ((N, r_res1) floats) – density profiles, defined at ROverR200, in M_sun*h^2/(Mpc)**3

  • ROverR200 ((N, r_res1) floats) – normalized radii at which dens_profs are defined

  • obj_masses ((N,) floats) – masses of objects in 10^10*M_sun/h

  • obj_centers ((N,3) floats) – centers of objects, each coordinate in Mpc/h

  • method (dictionary, method[‘profile’] is either einasto, alpha_beta_gamma, hernquist, nfw, minimum requirement) – describes density profile model assumed for fitting, if parameter should be kept fixed during fitting then it needs to be provided, e.g. method[‘alpha’] = 0.18

  • nb_bins (int) – Number of mass bins to plot density profiles for

  • start_time (float) – time of start of shape analysis

  • MASS_UNIT (float) – conversion factor from previous mass unit to M_sun/h, usually 10^10

  • suffix (string) – either ‘_dm_’ or ‘_gx_’ or ‘_’ (latter for CosmicProfsDirect)

dens_profs.dens_profs_tools.fitDensProf(ROverR200, method, median_r200_obj_nb)[source]

Fit density profile according to model provided

Note that median which is defined at ROverR200 must be in units of M_sun*h^2/(Mpc)**3. r200 must be in units of Mpc/h.

Parameters

  • ROverR200 ((N,) floats) – normalized radii where median is defined and fitting should be carried out

  • method (dictionary, method[‘profile’] is either einasto, alpha_beta_gamma, hernquist, nfw, minimum requirement) – describes density profile model assumed for fitting, if parameter should be kept fixed during fitting then it needs to be provided, e.g. method[‘alpha’] = 0.18

  • median_r200_obj_nb (tuple of (N,) floats, float, int) – density profile (often a median of many profiles combined, in units of M_sun*h^2/(Mpc)**3), virial radius (of parent halo in units of Mpc/h) and object number

Return best_fit, obj_nb

best-fit results, object number

Return type

(n,) floats, int

dens_profs.dens_profs_tools.fitDensProfHelper(dens_profs, ROverR200, r200s, method)[source]

Helper function to carry out density profile fitting

Parameters

  • dens_profs ((N,r_res) floats) – array containing density profiles in units of M_sun*h^2/(Mpc)**3

  • ROverR200 ((r_res,) floats) – normalized radii where density profile is defined and fitting should be carried out

  • r200s ((N,) floats) – R200 values of parent halos in units of Mpc/h

  • method (dictionary, method[‘profile’] is either einasto, alpha_beta_gamma, hernquist, nfw, minimum requirement) – describes density profile model assumed for fitting, if parameter should be kept fixed during fitting then it needs to be provided, e.g. method[‘alpha’] = 0.18

Return best_fits

best-fit results

Return type

(N,n) floats

dens_profs.dens_profs_tools.getAlphaBetaGammaProf(r, model_pars)[source]

Get alpha-beta-gamma density profile at radius r

Parameters

  • r (float) – radius of interest

  • model_pars ((n,) float array) – model parameters

Returns

profile value at r

Return type

float

dens_profs.dens_profs_tools.getEinastoProf(r, model_pars)[source]

Get Einasto density profile at radius r

Parameters

  • r (float) – radius of interest

  • model_pars ((n,) float array) – model parameters

Returns

profile value at r

Return type

float

dens_profs.dens_profs_tools.getHernquistProf(r, model_pars)[source]

Get Hernquist density profile at radius r

Parameters

  • r (float) – radius of interest

  • model_pars ((n,) float array) – model parameters

Returns

profile value at r

Return type

float

dens_profs.dens_profs_tools.getNFWProf(r, model_pars)[source]

Get NFW density profile at radius r

Parameters

  • r (float) – radius of interest

  • model_pars ((n,) float array) – model parameters

Returns

profile value at r

Return type

float