Velocity moments

Pairwise velocity moments are computed by measure_velocity_moments, which delegates to the pairvel Python wrapper around PairVel.jl. For every auto and cross mass-bin pair (same convention as xi_hh) the function returns the mean radial pairwise velocity plus a small set of central moments, all binned in separation r.

Output

Each velocity_moments.hdf5 file contains one HDF5 group per pair M{i}_M{j} (i <= j) with the following datasets:

Key	Description
npairs	pair count per r bin
m10	mean radial pairwise velocity ⟨v_r⟩ (km/s)
c20	second central moment of v_r
c02	second central moment of v_t (transverse)
c12	mixed third moment
c30	third central moment of v_r
c40, c04, c22	fourth-order central moments

Each group additionally carries r (centres), the log10M1 / log10M2 bin edges as HDF5 attributes, and the halo counts n1 / n2.

Loading from HDF5

There is no dedicated Loader class — read it directly with h5py:

import h5py
from halocat import config as C

vel_path = f"{C.get_output_dir('LCDM', 0.25, 1, 1)}/velocity_moments.hdf5"

with h5py.File(vel_path, "r") as f:
    r_edges    = f["r_edges"][...]
    mass_bins  = f["mass_bins"][...]                  # (P, 2)
    moment_keys = [s.decode() if isinstance(s, bytes) else s
                   for s in f.attrs["moment_keys"]]
    groups = sorted(k for k in f.keys()
                    if k.startswith("M") and "_M" in k)
    autos = [g for g in groups
             if g.split("_")[0] == g.split("_")[1]]

    # Pull one auto for inspection
    g = f[autos[0]]
    r       = g["r"][...]
    m10     = g["m10"][...]
    log10M  = g.attrs["log10M1"]
    n_halo  = int(g.attrs["n1"])

Default binning

The defaults live in halocat.config:

• VEL_R_EDGES — linear r edges in Mpc/h
• VEL_MASS_BINS — same as MASS_BINS by default

Measuring directly

measure_velocity_moments takes a halo dict, the box size, mass bins, and r_edges, and returns the same dict-of-groups structure that write_velocity_moments serialises:

from halocat.io import read_halo_hdf5
from halocat.velocity import measure_velocity_moments
from halocat import config as C

data = read_halo_hdf5(f"{C.get_output_dir('LCDM', 0.25, 1, 1)}/halo.hdf5")
vel  = measure_velocity_moments(
    data, C.BOX_SIZE, C.VEL_MASS_BINS, C.VEL_R_EDGES,
)
# vel['M0_M0']['m10']  -> (K,) ndarray

Driver

The pipeline produces velocity_moments.hdf5 automatically when you run halocat/run_single/run_all. There is no standalone script for just velocity moments — the measurement is always part of the bundled pipeline.