Generate point source maps with pixell and convert to HEALPix

Testing the pixell sim_objects functionality to create maps of point sources pre-smoothed with a gaussian beam. The purpose is to include this functionality in PySM to be able to generate on the fly maps of source starting from a catalog.

Compared to the previous notebook, here I also use reproject to convert the map to HEALPix, plot the result and check the flux in HEALPix also agrees with the input.

Setup

from pixell import enmap, utils, resample, curvedsky as cs, reproject, pointsrcs
import numpy as np
import healpy as hp

fwhm = 5 * utils.degree

shape, wcs = enmap.fullsky_geometry(res=fwhm / 3, proj="car")

shape

(109, 216)

Convert flux to amplitude

def fwhm2sigma(fwhm):
    return fwhm / (2.0 * np.sqrt(2.0 * np.log(2.0)))

def flux2amp(flux, fwhm):
    sigma = fwhm2sigma(fwhm)
    return flux / (2 * np.pi * sigma**2)

assert flux2amp((2 * np.pi * fwhm2sigma(5) ** 2), 5) == 1

Simulate a single point source

n_sources = 1
flux_sources = np.arange(n_sources) + 10

amplitude_sources = flux2amp(flux_sources, fwhm)

source_pos = np.array([[np.pi/4], [np.pi/3]])

r, p = pointsrcs.expand_beam(fwhm2sigma(fwhm))

source_map = pointsrcs.sim_objects(shape, wcs, source_pos, amplitude_sources, ((r, p)))

import matplotlib.pyplot as plt

source_pos

array([[0.78539816],
       [1.04719755]])

plt.imshow(source_map)

<matplotlib.image.AxesImage at 0x7f81203692d0>

Aperture photometry

def aperture_photometry(
    thumbs, aperture_radius, annulus_width=None, modrmap=None, pixsizemap=None
):
    """
    Flux from aperture photometry.

    from https://github.com/msyriac/orphics/blob/master/orphics/maps.py

    Parameters
    ----------
    thumb : ndmap
        An (...,Ny,Nx) ndmap (i.e. a pixell enmap) containing the thumbnails.
    aperture_radius : float
        Aperture inner radius in radians
    annulus_width : float
        Annulus width for mean subtraction in radians.
        Defaults to sqrt(2)-1 times the aperture inner radius.
    modrmap : ndmap, optional
        An (Ny,Nx) ndmap containing distances of each pixel from the center in radians.
    modrmap : ndmap, optional
        An (Ny,Nx) ndmap containing pixel areas in steradians.

    Returns
    -------
    flux : ndarray
        (...,) array of aperture photometry fluxes.

    """
    if modrmap is None:
        modrmap = thumbs.modrmap()
    if annulus_width is None:
        annulus_width = (np.sqrt(2.0) - 1.0) * aperture_radius
    # Get the mean background level from the annulus
    mean = thumbs[
        ...,
        np.logical_and(
            modrmap > aperture_radius, modrmap < (aperture_radius + annulus_width)
        ),
    ].mean()
    if pixsizemap is None:
        pixsizemap = thumbs.pixsizemap()
    # Subtract the mean, multiply by pixel areas and sum
    return (((thumbs - mean) * pixsizemap)[..., modrmap <= aperture_radius]).sum(
        axis=-1
    )

from astropy import units as u

box_half_size_rad = 2 * fwhm
box_center = [source_pos[0, -1], source_pos[1, -1]]
box = np.array(
    [
        [box_center[0] - box_half_size_rad, box_center[1] - box_half_size_rad],
        [box_center[0] + box_half_size_rad, box_center[1] + box_half_size_rad],
    ]
)  # in radians

box_center

[0.7853981633974483, 1.0471975511965976]

cutout = source_map.submap(box)

plt.imshow(cutout)

<matplotlib.image.AxesImage at 0x7f810b46c210>

aperture_photometry(cutout, 2 * fwhm)

9.982631206252375

fwhm/3

0.02908882086657216

Convert to HEALPix

from pixell import reproject

source_map_healpix = reproject.map2healpix(source_map)

hp.npix2nside(source_map_healpix.size)

64

hp.nside2resol(_)

0.015989479811663883

hp.mollview(source_map_healpix)

hp.gnomview(source_map_healpix, rot=hp.vec2ang(hp.ang2vec(source_pos[0], source_pos[1]), lonlat=True), xsize=1900, reso=.5)

Aperture photometry in HEALPix

from pysm3.utils import healpix_aperture_photometry

healpix_aperture_photometry(source_map_healpix, source_pos[0,0], source_pos[1,0], 2 * fwhm)

9.995092243734167