1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
|
# 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_fast(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
|
