Splashback results

The splashback result routines measure the time and location of a tracer’s first apocenter after infall into a halo. The main point of the splashback results is that they can be used in the Splashback radius analysis to determine a halo’s slashback radius and mass.

Algorithm

The splashback measurement can be somewhat tricky because we can only keep a small fraction of a trajectory in memory, and because the trajectories may be noisy. For simplicity, we ignore all angular information and consider only the tracer’s radius and radial velocity. We consider the four last snapshots in time.

Before we can look for apocenter, we need to establish pericenter, i.e., the first passage of the tracer through the host halo. This event is much clearer in the radial velocity than in radius, as the radial velocity must switch from negative to positive. We look for this upwards crossing of zero velocity and require that it is robust in the sense that the first two time bins have negative velocity and the second two positive velocity. If the trajectory is ambiguous, for example if v becomes positive for only one snapshot, we record the number of such invalid switches. If the number exceeds one, we abort the trajectory as it is likely under-sampled in time (that is, the orbital time is shorter than the snapshot spacing). When we find a pericener, we interpolate the radial trajectory in time to find the radius of closest approach.

Once we have found a pericenter, we begin looking for an apocenter. Again, we search for a zero- crossing in the radial velocity, but this time from positive to negative. We again require the first two bins to have positive v and the second two negative, otherwise we abort. We then linearly interpolate the trajectory to find the time and radius of the apocenter.

Finally, we compute the mass enclosed within the splashback event by interpolating the halo’s mass profile in time and radius. This algorithm identifies a splashback event for about 90% of the particle trajectories, about 85% of subhalo trajectories (see Diemer 2017 for details).

Compile-time parameters

Parameter	Explanation
OUTPUT_RESULT_SPLASHBACK	Write splashback results to output file
OUTPUT_RESULT_SPLASHBACK_MSP	Save the splashback mass as well as the radius in output file
OUTPUT_RESULT_SPLASHBACK_RRM	Save the pericenter radius (closest approach to halo center in units of R200m) of the tracer
OUTPUT_RESULT_SPLASHBACK_TMIN	Save the pericenter time (closest approach to halo center)
OUTPUT_RESULT_SPLASHBACK_POS	Save the 3-dimensional coordinates (rather than just radius) of the splashback event in output file

Run-time parameters

This result does not add any config parameters.

Output fields

Field	Type	Dimensions	Exists if	Explanation
halo_first	int64	n_halos	Always	The index of the first result for each halo (or -1 if none exists for a halo).
halo_n	int32	n_halos	Always	The number of results of this type for each halo (can be 0).
tracer_id	int64	n_rs_splashback	Always	The ID of the tracer to which this result refers.
tsp	float	n_rs_splashback	Always	The time of splashback in Gyr since the Big Bang
rsp	float	n_rs_splashback	Always	The apocenter (splashback) radius of the tracer in physical kpc/h
msp	float	n_rs_splashback	OUTPUT_RESULT_SPLASHBACK_MSP	The mass enclosed within the apocenter radius in Msun/h
rrm	float	n_rs_splashback	OUTPUT_RESULT_SPLASHBACK_RRM	rmin/R200(tmin), the radius at pericenter in units of R200m
tmin	float	n_rs_splashback	OUTPUT_RESULT_SPLASHBACK_TMIN	tmin, the time at pericenter
theta	float	n_rs_splashback	OUTPUT_RESULT_SPLASHBACK_POS	First angular coordinate of splashback event (see below)
phi	float	n_rs_splashback	OUTPUT_RESULT_SPLASHBACK_POS	Second angular coordinate of splashback event (see below)

The polar coordinates theta and phi are given in the convention where

\[\begin{split}x = r \times sin(\theta) cos(\phi) \\ y = r \times sin(\theta) sin(\phi) \\ z = r \times cos(\theta)\end{split}\]