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# Copyright (c) 2016 Zhixian MA <zxma_sjtu@qq.com>
# MIT license
import numpy as np
import healpy as hp
# from .psparams import PixelParams
from .base import BasePointSource
from ...utils import grid
from ...utils import convert
from .psparams import PixelParams
class StarForming(BasePointSource):
"""
Generate star forming point sources, inheritate from PointSource class.
Reference
---------
[1] Fast cirles drawing
https://github.com/liweitianux/fg21sim/fg21sim/utils/draw.py
https://github.com/liweitianux/fg21sim/fg21sim/utils/grid.py
"""
def __init__(self, configs):
super().__init__(configs)
self.columns.append('radius (rad)')
self.nCols = len(self.columns)
self._set_configs()
# Number density matrix
self.rho_mat = self.calc_number_density()
# Cumulative distribution of z and lumo
self.cdf_z, self.cdf_lumo = self.calc_cdf()
def _set_configs(self):
""" Load the configs and set the corresponding class attributes"""
super()._set_configs()
pscomp = "extragalactic/pointsources/starforming/"
# point sources amount
self.num_ps = self.configs.getn(pscomp+"numps")
# prefix
self.prefix = self.configs.getn(pscomp+"prefix")
# redshift bin
z_type = self.configs.getn(pscomp+"z_type")
if z_type == 'custom':
start = self.configs.getn(pscomp+"z_start")
stop = self.configs.getn(pscomp+"z_stop")
step = self.configs.getn(pscomp+"z_step")
self.zbin = np.arange(start, stop + step, step)
else:
self.zbin = np.arange(0.1, 10, 0.05)
# luminosity bin
lumo_type = self.configs.getn(pscomp+"lumo_type")
if lumo_type == 'custom':
start = self.configs.getn(pscomp+"lumo_start")
stop = self.configs.getn(pscomp+"lumo_stop")
step = self.configs.getn(pscomp+"lumo_step")
self.lumobin = np.arange(start, stop + step, step)
else:
self.lumobin = np.arange(17, 25.5, 0.1) # [W/Hz/sr]
def calc_number_density(self):
"""
Calculate number density rho(lumo,z) of FRI
References
----------
[1] Wilman et al.,
"A semi-empirical simulation of the extragalactic radio continuum
sky for next generation radio telescopes",
2008, MNRAS, 388, 1335-1348.
http://adsabs.harvard.edu/abs/2008MNRAS.388.1335W
Returns
-------
rho_mat: np.ndarray
Number density matris (joint-distribution of luminosity and
reshift).
"""
# Init
rho_mat = np.zeros((len(self.lumobin), len(self.zbin)))
# Parameters
# Refer to Willman's section 2.4
alpha = 0.7 # spectral index
lumo_star = 10.0**22 # critical luminosity at 1400MHz
rho_l0 = 10.0**(-7) # normalization constant
z1 = 1.5 # cut-off redshift
k1 = 3.1 # index of space density revolution
# Calculation
for i, z in enumerate(self.zbin):
if z <= z1:
rho_mat[:, i] = (rho_l0 * (10**self.lumobin / lumo_star) **
(-alpha) * np.exp(-10**self.lumobin /
lumo_star) * (1 + z)**k1)
else:
rho_mat[:, i] = (rho_l0 * (10**self.lumobin / lumo_star) **
(-alpha) * np.exp(-10**self.lumobin /
lumo_star) * (1 + z1)**k1)
return rho_mat
def get_radius(self):
"""
Generate the disc diameter of normal starforming galaxies.
Reference
---------
[1] Wilman et al., Eq(7-9),
"A semi-empirical simulation of the extragalactic radio continuum
sky for next generation radio telescopes",
2008, MNRAS, 388, 1335-1348.
http://adsabs.harvard.edu/abs/2008MNRAS.388.1335W
"""
# Willman Eq. (8)
delta = np.random.normal(0, 0.3)
log_M_HI = 0.44 * np.log10(self.lumo) + 0.48 + delta
# Willman Eq. (7)
log_D_HI = ((log_M_HI - (6.52 + np.random.uniform(-0.06, 0.06))) /
1.96 + np.random.uniform(-0.04, 0.04))
# Willman Eq. (9)
log_D = log_D_HI - 0.23 - np.log10(1 + self.z)
self.radius = 10**log_D / 2 * 1e-3 # [Mpc]
return self.radius
def gen_single_ps(self):
"""
Generate single point source, and return its data as a list.
"""
# Redshift and luminosity
self.z, self.lumo = self.get_lumo_redshift()
# angular diameter distance
self.param = PixelParams(self.z)
self.dA = self.param.dA
# Radius
self.radius = self.param.get_angle(self.get_radius()) # [rad]
# W/Hz/Sr to Jy
dA = self.dA * 3.0856775814671917E+22 # Mpc to meter
self.lumo = self.lumo / dA**2 / (10.0**-24) # [Jy]
# Position
x = np.random.uniform(0, 1)
self.lat = (np.arccos(2 * x - 1) / np.pi * 180 - 90) # [deg]
self.lon = np.random.uniform(0, np.pi * 2) / np.pi * 180 # [deg]
# Area
self.area = np.pi * self.radius**2 # [sr] ?
ps_list = [self.z, self.dA, self.lumo, self.lat, self.lon,
self.area, self.radius]
return ps_list
def draw_single_ps(self, freq):
"""
Designed to draw the circular star forming and star bursting ps.
Prameters
---------
nside: int and dyadic
number of sub pixel in a cell of the healpix structure
self.ps_catalog: pandas.core.frame.DataFrame
Data of the point sources
freq: float
frequency
"""
# Init
npix = hp.nside2npix(self.nside)
hpmap = np.zeros((npix,))
# Gen Tb list
Tb_list = self.calc_Tb(freq)
# Iteratively draw the ps
num_ps = self.ps_catalog.shape[0]
resolution = self.resolution / 60 # [degree]
for i in range(num_ps):
# grid
ps_radius = self.ps_catalog['radius (rad)'][i] # [rad]
ps_radius = ps_radius * 180 / np.pi # radius [deg]
c_lat = self.ps_catalog['Lat (deg)'][i] # core_lat [deg]
c_lon = self.ps_catalog['Lon (deg)'][i] # core_lon [deg]
# Fill with circle
lon, lat, gridmap = grid.make_grid_ellipse(
(c_lon, c_lat), (2 * ps_radius, 2 * ps_radius), resolution)
indices, values = grid.map_grid_to_healpix(
(lon, lat, gridmap), self.nside)
hpmap[indices] += Tb_list[i]
return hpmap
def draw_ps(self, freq):
"""
Read csv ps list file, and generate the healpix structure vector
with the respect frequency.
"""
# Init
num_freq = len(freq)
npix = hp.nside2npix(self.nside)
hpmaps = np.zeros((npix, num_freq))
# Gen ps_catalog
self.gen_catalog()
# get hpmaps
for i in range(num_freq):
hpmaps[:, i] = self.draw_single_ps(freq[i])
return hpmaps
def calc_single_Tb(self, area, freq):
"""
Calculate brightness temperatur of a single ps
Parameters
------------
area: float
Area of the PS
Unit: [arcsec^2]
freq: `~astropy.units.Quantity`
Frequency, e.g., `1.0*au.MHz`
Return
------
Tb:`~astropy.units.Quantity`
Average brightness temperature, e.g., `1.0*au.K`
"""
# Init
freq_ref = 1400 # [MHz]
freq = freq # [MHz]
# Luminosity at 1400MHz
lumo_1400 = self.lumo # [Jy]
# Calc flux
flux = (freq / freq_ref)**(-0.7) * lumo_1400
# Calc brightness temperature
Tb = convert.Fnu_to_Tb(flux, area, freq)
return Tb
def calc_Tb(self, freq):
"""
Calculate the surface brightness temperature of the point sources.
Parameters
------------
freq: `~astropy.units.Quantity`
Frequency, e.g., `1.0*au.MHz`
Return
------
Tb_list: list
Point sources brightness temperature
"""
# Tb_list
num_ps = self.ps_catalog.shape[0]
Tb_list = np.zeros((num_ps,))
sr_to_arcsec2 = (np.rad2deg(1) * 3600) ** 2 # [sr] -> [arcsec^2]
# Iteratively calculate Tb
for i in range(num_ps):
ps_area = self.ps_catalog['Area (sr)'][i] # [sr]
area = ps_area * sr_to_arcsec2
Tb_list[i] = self.calc_single_Tb(area, freq)
return Tb_list
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