The splashback analysis computes the splashback radius and mass of a halo over time based on the Splashback results of individual particles.

Algorithm

The splashback analysis is run at the end of a halo’s life, when all splashback events have been collected. First, we exclude particles that belonged to subhalos greater than some maximum sub-to-host mass ratio (the anl_rsp_max_smr parameter) because they are, on average, influenced by the dynamical friction that large subhalos experience. We use the particles’ Infall results to determine whether they were part of a large subhalo.

After removing such particles, the radial distribution of splashback events tends to be well fit by a Gaussian profile with a tail toward high radii. We smooth the contribution from each splashback event in time using a Gaussian with a width of anl_rsp_sigma_tdyn dynamical times. We now have, for each snapshot, a set of weighted particle splashback events. We calculate splashback properties for this time if the accumlated weight is at least anl_rsp_min_weight. Possible definitions include the mean of the distribution or precentiles. We note that, especially for higher percentiles, the statistical uncertainty due to the limited number of particle splashback events can become significant. To estimate such errors, we run a few hundred bootstrap samples (if requested by the user).

Finally, we need to correct for two biases that occur at the end of the simulation (typically at z = 0). First, the number of splashback events in the final time bin (between the second-to-last and last snapshots) is drastically lower than in the previous time bins. Thus, we ignore any splashback events that have occurred after the time of the second-to-last snapshot as they are likely biased in some nontrivial way. Second, the distribution of splashback events considered in the final snapshots becomes asymmetric due to the smoothing discussed above: the Gaussian filter is sensitive to events at earlier times, but there are no events at later times. This asymmetry can lead to a significant and systematic bias because the splashback radius is, in most cases, increasing with time. We correct for this asymmetry by linearly extrapolating the past evolution of the splashback radius into the future.

We find the splashback mass by considering the distribution of enclosed masses of the particle splashback events. The algorithm is described in detail in Diemer 2017.

Splashback definitions

The splashback analysis can compute a number of different definitions of the splashback radius and mass. These can be set using the anl_rsp_defs parameter. Of course, only definitions that can actually be computed by the Rsp analysis can be chosen. Those include:

• Rsp-apr-mn: mean of the apocenter distribution

• Rsp-apr-p50: median of the apocenter distribution

• Rsp-apr-p<n>: any percentile of the apocenter distribution

• Msp-***: the corresponding masses

• ***_err: the one-sigma uncertainty on any of the above quantities. For percentiles, this leads to bootstrapping and thus a significant performance penalty.

For details on the string format and possible definitions, see Halo radius and mass definitions.

Compile-time parameters

Parameter

Explanation

OUTPUT_ANALYSIS_RSP

Write Rsp analyses to output file

ANALYSIS_RSP_MAX_SNAPS

The max. num. of snapshots for which analysis can be saved; must be at least num. of requested redshifts

ANALYSIS_RSP_MAX_DEFINITIONS

The maximum number of splashback definitions (radii, masses etc) that can be requested by the user

If memory is an issue, the ANALYSIS_RSP_MAX_SNAPS and ANALYSIS_RSP_MAX_DEFINITIONS parameters should be adjusted close to the values they must have to accommodate a given simulation and user preferences.

Run-time parameters

Parameter

Type

Default

Explanation

anl_rsp_redshifts

list

-1

A list of redshifts where splashback properties should be computed, or -1 (all)

anl_rsp_defs

list

None

A list of splashback definitions to be computed (see above)

anl_rsp_min_rrm

float

0.0

Minimum r / R200m of splashback events to use in Rsp analysis

anl_rsp_max_rrm

float

1.0

Maximum r / R200m of splashback events to use in Rsp analysis

anl_rsp_min_smr

float

-2.0

Minimum sub-to-host ratio to use in Rsp analysis (for subhalo particles)

anl_rsp_max_smr

float

0.01

Maximum sub-to-host ratio to use in Rsp analysis (for subhalo particles)

anl_rsp_demand_infall_rs

bool

FALSE

Only use splashback results if they have a corresponding infall result

anl_rsp_sigma_tdyn

float

0.2

The width in time over which events are smoothed, in units of the dynamical time

anl_rsp_min_weight

float

10.0

The minimum total weight in a bin for Rsp to be estimated

anl_rsp_n_bootstrap

int

200

The number of bootstrap samples used to estimate the statistical uncertainty

anl_rsp_do_correction

bool

TRUE

Correct the final snapshots for the asymmetry in events (recommended)

Note that choosing redshifts using the anl_rsp_redshifts parameter saves memory and disk space, but can lead to issues when creating halo catalogs with MORIA. If in doubt, it is probably best to output the analysis for all snapshots.

Output fields

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_rsp

Always

The (original, first-snapshot) halo ID to which this analysis refers.

status

int8

n_al_rsp * n_snaps

Always

A status field that indicates whether the Rsp analysis was successful (see below)

<halo definition>

float

n_al_rsp * n_snaps

Always

One field for each halo definition (see above)

Here, n_snaps is, of course, the number of redshifts chosen by the user of the number of snapshots in the simulation if anl_rsp_redshifts is -1. The status field can take on the following values:

Value

Parameter

Explanation

0

ANL_RSP_STATUS_UNDEFINED

Placeholder, should never occur in output file

1

ANL_RSP_STATUS_SUCCESS

The analysis succeeded, all output values can be used

2

ANL_RSP_STATUS_HALO_NOT_VALID

Halo could not be analyzed at this snapshot, e.g. because too young

3

ANL_RSP_STATUS_HALO_NOT_SAVED

Halo was not saved to the SPARTA output file at all (used in MORIA)

4

ANL_RSP_STATUS_NOT_FOUND

5

ANL_RSP_STATUS_INSUFFICIENT_EVENTS

There were not enough particle splashback events

6

ANL_RSP_STATUS_INSUFFICIENT_WEIGHT

There were enough particle splashback events, but their weight was too low

Analyses

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