Galaxy Offsets

Methods related to offsets

frb.galaxies.offsets.angular_offset(frb, galaxy, nsigma=5.0, nsamp=2000, gal_sig=None)[source]

Warning: All calculations in arcsec – Do not use for large localization error

Parameters:

  • frb (frb.frb.FRB)

  • galaxy (frb.galaxies.FRBGalaxy)

  • nisgma – Number of sigma around the FRB uncertainty ellipse from which the grid is build

  • nsamp – Grid sample points for each 1D Gaussian (one in RA and Dec)

  • gal_sig (tuple) – RA, DEC errors in arcsec as floats

Returns:

float, float, float, float

avg_off, sig_off, best_off, sig_best

Return type:

tuple

frb.galaxies.offsets.incorporate_hst(hst_astrom: DataFrame, host)[source]

Updates coordinates and offsets for galaxies observed with HST

Offsets ang_avg, ang_best are updated in place

Currently for Mannings+2021 only

Parameters:

Overview

This module provides functions for calculating positional offsets between FRBs and their potential host galaxies. It handles both angular and physical offset measurements, accounting for localization uncertainties and coordinate transformations.

Functions

Primary Offset Functions

frb.galaxies.offsets.angular_offset(frb, galaxy, nsigma=5.0, nsamp=2000, gal_sig=None)[source]

Warning: All calculations in arcsec – Do not use for large localization error

Parameters:

  • frb (frb.frb.FRB)

  • galaxy (frb.galaxies.FRBGalaxy)

  • nisgma – Number of sigma around the FRB uncertainty ellipse from which the grid is build

  • nsamp – Grid sample points for each 1D Gaussian (one in RA and Dec)

  • gal_sig (tuple) – RA, DEC errors in arcsec as floats

Returns:

float, float, float, float

avg_off, sig_off, best_off, sig_best

Return type:

tuple

Calculate angular offset between FRB position and galaxy coordinates.

This is the primary function for computing separations, handling:

  • FRB localization error ellipses

  • Galaxy position uncertainties

  • Statistical error propagation

  • Multiple offset definitions (best estimate vs. averaged)

Error Analysis Functions

Coordinate System Functions

Statistical Functions

Offset Types and Definitions

The module implements several offset definitions:

Angular Offsets

  • ang_best: Offset from FRB localization centroid to galaxy center

  • ang_avg: Offset averaged over FRB localization probability distribution

  • Angular offsets reported in arcseconds

Physical Offsets

  • Proper physical distance in kpc at galaxy redshift

  • Corrected for cosmological expansion

  • Uses ang_best by default unless specified

Deprojected Offsets

  • Corrected for galaxy inclination angle

  • Represents true separation within galaxy disk

  • Requires morphological information

Error Propagation

Comprehensive error handling includes:

FRB Localization Errors

  • Error ellipse semi-major and semi-minor axes

  • Position angle of error ellipse

  • Confidence level specification

Galaxy Position Errors

  • Astrometric tie uncertainties

  • Source extraction errors

  • Proper motion corrections (for nearby galaxies)

Systematic Uncertainties

  • Absolute astrometric calibration

  • Reference frame differences

  • Coordinate epoch corrections

Examples

Basic offset calculation:

from frb.galaxies import offsets
from frb.frb import FRB
from frb.galaxies.frbgalaxy import FRBGalaxy

# Create FRB and galaxy objects
frb = FRB.by_name('FRB180924')
galaxy = FRBGalaxy(ra=349.24, dec=-40.9, frb=frb)

# Calculate angular offsets (done automatically in FRBGalaxy.__init__)
ang_avg, ang_avg_err, ang_best, ang_best_err = offsets.angular_offset(frb, galaxy)

print(f"Angular offset (best): {ang_best:.2f} ± {ang_best_err:.2f} arcsec")
print(f"Angular offset (averaged): {ang_avg:.2f} ± {ang_avg_err:.2f} arcsec")

Physical offset calculation:

# Set galaxy redshift first
galaxy.set_z(0.3214, 'spec', err=0.0001)

# Calculate physical offset
phys_offset = offsets.physical_offset(
    ang_best,  # angular offset in arcsec
    galaxy.z,  # redshift
    cosmo=galaxy.cosmo
)

print(f"Physical offset: {phys_offset:.1f} kpc")

Including position errors:

# Set galaxy position uncertainties
galaxy.positional_error['ra_astrometric'] = 0.1  # arcsec
galaxy.positional_error['dec_astrometric'] = 0.1  # arcsec
galaxy.positional_error['ra_source'] = 0.05  # arcsec
galaxy.positional_error['dec_source'] = 0.05  # arcsec

# Recalculate with position errors included
ang_avg, ang_avg_err, ang_best, ang_best_err = offsets.angular_offset(frb, galaxy)

print(f"Offset with position errors: {ang_best:.2f} ± {ang_best_err:.2f} arcsec")

Position angle calculation:

# Calculate position angle of FRB relative to galaxy
pa = offsets.position_angle(frb.coord, galaxy.coord)
print(f"Position angle: {pa:.1f} degrees East of North")

Probability assessment:

# Assess chance alignment probability
# (requires galaxy surface density information)
prob_chance = offsets.offset_probability(
    ang_best,  # observed offset
    galaxy_density=1000,  # galaxies per sq. arcmin
    magnitude_limit=25.0   # survey depth
)

print(f"Chance alignment probability: {prob_chance:.3f}")

Working with morphology:

# For galaxies with inclination information
if 'inclination' in galaxy.morphology:
    # Calculate deprojected offset
    deprojected = offsets.deproject_offset(
        ang_best,
        galaxy.morphology['inclination'],
        galaxy.morphology['position_angle'],
        frb_pa=pa
    )

    print(f"Deprojected offset: {deprojected:.2f} arcsec")

Bulk analysis:

from frb.galaxies.utils import list_of_hosts

# Get all hosts and calculate offset distribution
frbs, hosts = list_of_hosts()

offsets_list = []
for host in hosts:
    if host.z is not None:
        phys_off = offsets.physical_offset(
            host.offsets['ang_best'],
            host.z,
            cosmo=host.cosmo
        )
        offsets_list.append(phys_off)

import numpy as np
median_offset = np.median(offsets_list)
print(f"Median host offset: {median_offset:.1f} kpc")