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
|
# -*- coding: utf-8 -*-
# vispy: testskip
# -----------------------------------------------------------------------------
# A Galaxy Simulator based on the density wave theory
# (c) 2012 Ingo Berg
#
# Simulating a Galaxy with the density wave theory
# http://beltoforion.de/galaxy/galaxy_en.html
#
# Python version(c) 2014 Nicolas P.Rougier
# -----------------------------------------------------------------------------
import math
import numpy as np
class Galaxy(object):
""" Galaxy simulation using the density wave theory """
def __init__(self, n=20000):
""" Initialize galaxy """
# Eccentricity of the innermost ellipse
self._inner_eccentricity = 0.8
# Eccentricity of the outermost ellipse
self._outer_eccentricity = 1.0
# Velocity at the innermost core in km/s
self._center_velocity = 30
# Velocity at the core edge in km/s
self._inner_velocity = 200
# Velocity at the edge of the disk in km/s
self._outer_velocity = 300
# Angular offset per parsec
self._angular_offset = 0.019
# Inner core radius
self._core_radius = 6000
# Galaxy radius
self._galaxy_radius = 15000
# The radius after which all density waves must have circular shape
self._distant_radius = 0
# Distribution of stars
self._star_distribution = 0.45
# Angular velocity of the density waves
self._angular_velocity = 0.000001
# Number of stars
self._stars_count = n
# Number of dust particles
self._dust_count = int(self._stars_count * 0.75)
# Number of H-II regions
self._h2_count = 200
# Particles
dtype = [('theta', np.float32),
('velocity', np.float32),
('angle', np.float32),
('m_a', np.float32),
('m_b', np.float32),
('size', np.float32),
('type', np.float32),
('temperature', np.float32),
('brightness', np.float32),
('position', np.float32, 2)]
n = self._stars_count + self._dust_count + 2*self._h2_count
self._particles = np.zeros(n, dtype=dtype)
i0 = 0
i1 = i0 + self._stars_count
self._stars = self._particles[i0:i1]
self._stars['size'] = 3.
self._stars['type'] = 0
i0 = i1
i1 = i0 + self._dust_count
self._dust = self._particles[i0:i1]
self._dust['size'] = 64
self._dust['type'] = 1
i0 = i1
i1 = i0 + self._h2_count
self._h2a = self._particles[i0:i1]
self._h2a['size'] = 0
self._h2a['type'] = 2
i0 = i1
i1 = i0 + self._h2_count
self._h2b = self._particles[i0:i1]
self._h2b['size'] = 0
self._h2b['type'] = 3
def __len__(self):
""" Number of particles """
if self._particles is not None:
return len(self._particles)
return 0
def __getitem__(self, key):
""" x.__getitem__(y) <==> x[y] """
if self._particles is not None:
return self._particles[key]
return None
def reset(self, rad, radCore, deltaAng,
ex1, ex2, sigma, velInner, velOuter):
# Initialize parameters
# ---------------------
self._inner_eccentricity = ex1
self._outer_eccentricity = ex2
self._inner_velocity = velInner
self._outer_velocity = velOuter
self._angular_offset = deltaAng
self._core_radius = radCore
self._galaxy_radius = rad
self._distant_radius = self._galaxy_radius * 2
self.m_sigma = sigma
# Initialize stars
# ----------------
stars = self._stars
R = np.random.normal(0, sigma, len(stars)) * self._galaxy_radius
stars['m_a'] = R
stars['angle'] = 90 - R * self._angular_offset
stars['theta'] = np.random.uniform(0, 360, len(stars))
stars['temperature'] = np.random.uniform(3000, 9000, len(stars))
stars['brightness'] = np.random.uniform(0.05, 0.25, len(stars))
stars['velocity'] = 0.000005
for i in range(len(stars)):
stars['m_b'][i] = R[i] * self.eccentricity(R[i])
# Initialize dust
# ---------------
dust = self._dust
X = np.random.uniform(0, 2*self._galaxy_radius, len(dust))
Y = np.random.uniform(-self._galaxy_radius, self._galaxy_radius,
len(dust))
R = np.sqrt(X*X+Y*Y)
dust['m_a'] = R
dust['angle'] = R * self._angular_offset
dust['theta'] = np.random.uniform(0, 360, len(dust))
dust['velocity'] = 0.000005
dust['temperature'] = 6000 + R/4
dust['brightness'] = np.random.uniform(0.01, 0.02)
for i in range(len(dust)):
dust['m_b'][i] = R[i] * self.eccentricity(R[i])
# Initialise H-II
# ---------------
h2a, h2b = self._h2a, self._h2b
X = np.random.uniform(-self._galaxy_radius, self._galaxy_radius,
len(h2a))
Y = np.random.uniform(-self._galaxy_radius, self._galaxy_radius,
len(h2a))
R = np.sqrt(X*X+Y*Y)
h2a['m_a'] = R
h2b['m_a'] = R + 1000
h2a['angle'] = R * self._angular_offset
h2b['angle'] = h2a['angle']
h2a['theta'] = np.random.uniform(0, 360, len(h2a))
h2b['theta'] = h2a['theta']
h2a['velocity'] = 0.000005
h2b['velocity'] = 0.000005
h2a['temperature'] = np.random.uniform(3000, 9000, len(h2a))
h2b['temperature'] = h2a['temperature']
h2a['brightness'] = np.random.uniform(0.005, 0.010, len(h2a))
h2b['brightness'] = h2a['brightness']
for i in range(len(h2a)):
h2a['m_b'][i] = R[i] * self.eccentricity(R[i])
h2b['m_b'] = h2a['m_b']
def update(self, timestep=100000):
""" Update simulation """
self._particles['theta'] += self._particles['velocity'] * timestep
P = self._particles
a, b = P['m_a'], P['m_b']
theta, beta = P['theta'], -P['angle']
alpha = theta * math.pi / 180.0
cos_alpha = np.cos(alpha)
sin_alpha = np.sin(alpha)
cos_beta = np.cos(beta)
sin_beta = np.sin(beta)
P['position'][:, 0] = a*cos_alpha*cos_beta - b*sin_alpha*sin_beta
P['position'][:, 1] = a*cos_alpha*sin_beta + b*sin_alpha*cos_beta
D = np.sqrt(((self._h2a['position'] -
self._h2b['position'])**2).sum(axis=1))
S = np.maximum(1, ((1000-D)/10) - 50)
self._h2a['size'] = 2.0*S
self._h2b['size'] = S/6.0
def eccentricity(self, r):
# Core region of the galaxy. Innermost part is round
# eccentricity increasing linear to the border of the core.
if r < self._core_radius:
return 1 + (r / self._core_radius) * (self._inner_eccentricity-1)
elif r > self._core_radius and r <= self._galaxy_radius:
a = self._galaxy_radius - self._core_radius
b = self._outer_eccentricity - self._inner_eccentricity
return self._inner_eccentricity + (r - self._core_radius) / a * b
# Eccentricity is slowly reduced to 1.
elif r > self._galaxy_radius and r < self._distant_radius:
a = self._distant_radius - self._galaxy_radius
b = 1 - self._outer_eccentricity
return self._outer_eccentricity + (r - self._galaxy_radius) / a * b
else:
return 1
|
