Density profile analysis

The density profile analysis outputs the mass enclosed within a set of radial bins at a user-defined number of redshifts. One special feature of SPARTA’s profile analysis is that it uses Orbit count results to separate the profiles of particles on a first infall trajectory and those that are orbiting in the halo (the so-called 1-halo term).

Algorithm

The basic algorithm is simple: we create a set of logarithmically spaced radial bins between the limits chosen by the user and compute the mass profile in these bins. However, things get more complicated when we split the particle population by their dynamics. Here, we search for Orbit count results which should exist for all particle tracers. If the pericenter count is at least one, the particle is part of the 1-halo term, the material orbiting inside the halo. In some cases, the orbit count is a lower limit because the particle was already in the halo when the halo was first detected by the halo finder. We include such particles in the 1-halo term, as they are extremely likely to have already had at least one pericenter.

Density profiles are computed in the same way for subhalos and even ghosts. Here, R200m is typically smaller than the all-particle R200m because it is measured from subhalo tracers only. Thus, the profile may not actually reach a density of 200m anywhere. The orbit counter keeps running for subhalo tracers, meaning that the 1-halo term has the same meaning in principle. However, in subhalos (and especially in ghosts) we expect the tracer trajectories to be messy and the orbit counting to be unreliable.

In ghost halos, the 1-halo term of the ghost is also computed from the particles’ orbit counts, but as the tracers have typically orbited at least once, this 1-halo term is almost identical to a profile of the ghost tracers. Since the orbit counter is not increased any more in ghosts, this profile should be interpreted with care.

Compile-time parameters

Parameter	Explanation
OUTPUT_ANALYSIS_PROFILES	Write profile analyses to output file
OUTPUT_ANALYSIS_PROFILES_ALL	Write the density profiles including all particles around a halo
OUTPUT_ANALYSIS_PROFILES_1HALO	Write the density profiles of the 1-halo term, that is, only including particles that have orbited
OUTPUT_ANALYSIS_PROFILES_VR	Write the average radial velocity profiles
OUTPUT_ANALYSIS_PROFILES_SIGMAVR	Write the radial velocity dispersion profiles
ANALYSIS_PROFILES_MAX_SNAPS	The maximum number of snapshots that can be requested by the user
ANALYSIS_PROFILES_N_BINS	The number of radial bins in the profiles

Run-time parameters

Parameter	Type	Default	Explanation
anl_prf_redshifts	[float]	-1	Redshifts where profiles are output; list of floats, or -1 for all
anl_prf_rmin	float	0.01	Minimum radius of bins in units of R200m
anl_prf_rmax	float	3.0	Maximum radius of bins in units of R200m
anl_prf_do_subs	bool	TRUE	Output profiles for subhalos (they will be influenced by the host)
anl_prf_do_ghosts	bool	TRUE	Output profiles for ghost halos (they will be influenced by the host)

Note that the number of profile redshifts must be smaller or equal than the ANALYSIS_PROFILES_MAX_SNAPS define. It is recommended to give a list of redshifts rather than outputting profiles at all snapshots because the latter can lead to large output and memory consumption.

Note

Profiles of the 1-halo term at the final snapshot of a simulation are slightly biased low because pericenter events are recorded one snapshot after they occur. SPARTA then corrects profiles at the previous snapshot with those events, but that is not possible if the profile is output at the final snapshot. Thus, it is recommended to output profiles at the second-to-last snapshot instead.

Output fields

Here, n_prf_snp is the number of snapshots at which profiles are output, determined by the anl_prf_redshifts parameter listed above. n_bins is the number of radial bins which is given by the ANALYSIS_PROFILES_N_BINS define.

Field	Type	Dimensions		Exists if	Explanation
halo_first	int64	n_halos		Always	The index of the first analysis for each halo (or -1 if none exists for a halo).
halo_n	int32	n_halos		Always	The number of analyses of this type for each halo (can be 0).
halo_id	int64	n_al_profiles		Always	The (original, first-snapshot) halo ID to which this analysis refers.
status	int8	n_al_profiles * n_prf_snp | Always			A status field that indicates if the profile analysis was successful (see below)
M_all	float	n_al_profiles * n_prf_snp * n_bins | OUTPUT_ANALYSIS_PROFILES_ALL			The total density profile (including all particles, mass enclosed within r bins).
M_1halo	float	n_al_profiles * n_prf_snp * n_bins		OUTPUT_ANALYSIS_PROFILES_1HALO	The mass of the 1-halo term (ptls. that have undergone at least one pericenter)
vr	float	n_al_profiles * n_prf_snp * n_bins		OUTPUT_ANALYSIS_PROFILES_VR	The average radial velocity profile
sigma_vr	float	n_al_profiles * n_prf_snp * n_bins		OUTPUT_ANALYSIS_PROFILES_SIGMAVR	The radial velocity dispersion profile

The status field can take on the following values:

Value	Parameter	Explanation
0	ANL_PRF_STATUS_UNDEFINED	Placeholder, should never occur in output file
1	ANL_PRF_STATUS_SUCCESS	The analysis succeeded, all output values can be used
2	ANL_PRF_STATUS_HALO_NOT_VALID	Halo could not be analyzed at this snapshot, e.g. because too young
5	ANL_PRF_STATUS_SEARCH_RADIUS	The search radius had to be reduced, the profile was not computed
6	ANL_PRF_STATUS_CATALOG_RADIUS	R200m_all could not be computed, the radius was taken from catalog; the profile was not computed

The ANL_PRF_STATUS_SEARCH_RADIUS error reflects the rare case where SPARTA underestimates a halo radius, leading to too small a particle box. The particles can then not be loaded after the fact as that would mean re-doing a large fraction of SPARTA’s work on the snapshot. As particles were almost certainly missed, we do not compute a profile in this case.

The ANL_PRF_STATUS_CATALOG_RADIUS error means that R200_all was not computed. This is a rare case where the halo is next to a (typically much larger) halo that dominates its density field. While the bound-only mass from the catalog may be small, R200m_all would include the entirety of the larger halo. In this case, SPARTA may fall back to the catalog radius (see the halo_max_radius_ratio_cat configuration parameter).