darkmatter 0.0.1

Dark matter simulation engine — gravitational fields, particle dynamics, halo stability, and cosmological constants
Documentation 
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

use crate::constants::physical::G;
use std::f64::consts::PI;

pub fn chandrasekhar_friction_acceleration(
    m_satellite: f64,
    rho_background: f64,
    v_sat_km_s: f64,
    sigma_v_km_s: f64,
    coulomb_log: f64,
) -> f64 {
    let v = v_sat_km_s * 1e3;
    let sigma = sigma_v_km_s * 1e3;
    let x = v / (sigma * 2.0_f64.sqrt());
    let erf_x = crate::utils::math::erf_approx(x);
    let derf = 2.0 * x / PI.sqrt() * (-x * x).exp();
    let factor = erf_x - derf;
    -4.0 * PI * G * G * m_satellite * rho_background * coulomb_log * factor / (v * v * v)
}

pub fn coulomb_logarithm(m_host: f64, m_sat: f64, r: f64, v: f64) -> f64 {
    let b_max = r * m_host / (m_host + m_sat);
    let b_min = G * m_sat / (v * v);
    if b_min >= b_max || b_min <= 0.0 {
        return 1.0;
    }
    (b_max / b_min).ln()
}

pub fn dynamical_friction_timescale_gyr(
    m_satellite_solar: f64,
    m_host_solar: f64,
    r_orbit_kpc: f64,
    v_circ_km_s: f64,
    coulomb_log: f64,
) -> f64 {
    let m_sat = m_satellite_solar * 1.989e30;
    let m_host = m_host_solar * 1.989e30;
    let r = r_orbit_kpc * 3.0857e19;
    let v = v_circ_km_s * 1e3;
    let tau = 1.17 * r * r * v / (G * m_sat * coulomb_log) * (m_host / m_sat);
    tau / 3.156e16
}

pub fn orbital_decay_radius(
    r_initial_kpc: f64,
    t_gyr: f64,
    m_satellite_solar: f64,
    m_host_solar: f64,
    v_circ_km_s: f64,
    coulomb_log: f64,
) -> f64 {
    let tau = dynamical_friction_timescale_gyr(
        m_satellite_solar,
        m_host_solar,
        r_initial_kpc,
        v_circ_km_s,
        coulomb_log,
    );
    if tau < 1e-20 {
        return 0.0;
    }
    r_initial_kpc * (1.0 - t_gyr / tau).max(0.0).powf(0.5)
}

pub fn velocity_dependent_friction(
    m_satellite: f64,
    rho_background: f64,
    v_sat_km_s: f64,
    sigma_v_km_s: f64,
    coulomb_log: f64,
    power_index: f64,
) -> f64 {
    let base = chandrasekhar_friction_acceleration(
        m_satellite,
        rho_background,
        v_sat_km_s,
        sigma_v_km_s,
        coulomb_log,
    );
    let v_ratio = v_sat_km_s / sigma_v_km_s;
    base * v_ratio.powf(power_index)
}

pub fn friction_energy_loss_per_orbit(
    m_satellite_solar: f64,
    rho_avg_kg_m3: f64,
    v_orbit_km_s: f64,
    sigma_v_km_s: f64,
    r_orbit_kpc: f64,
    coulomb_log: f64,
) -> f64 {
    let m_sat = m_satellite_solar * 1.989e30;
    let v = v_orbit_km_s * 1e3;
    let r = r_orbit_kpc * 3.0857e19;
    let a_fric = chandrasekhar_friction_acceleration(
        m_sat,
        rho_avg_kg_m3,
        v_orbit_km_s,
        sigma_v_km_s,
        coulomb_log,
    );
    let orbit_period_s = 2.0 * PI * r / v;
    a_fric.abs() * m_sat * v * orbit_period_s
}

pub fn sinking_timescale_isothermal_gyr(
    r_kpc: f64,
    v_circ_km_s: f64,
    m_sat_solar: f64,
    coulomb_log: f64,
) -> f64 {
    let r = r_kpc * 3.0857e19;
    let v = v_circ_km_s * 1e3;
    let m_sat = m_sat_solar * 1.989e30;
    let sigma = v / 2.0_f64.sqrt();
    let rho = sigma * sigma / (2.0 * PI * G * r * r);
    let a = chandrasekhar_friction_acceleration(
        m_sat,
        rho,
        v_circ_km_s,
        v_circ_km_s / 2.0_f64.sqrt(),
        coulomb_log,
    );
    if a.abs() < 1e-100 {
        return f64::INFINITY;
    }
    (v / a.abs()) / 3.156e16
}

pub fn friction_in_cored_halo(
    m_satellite: f64,
    rho_core: f64,
    r_core_kpc: f64,
    v_sat_km_s: f64,
    r_sat_kpc: f64,
) -> f64 {
    let r_c = r_core_kpc * 3.0857e19;
    let r = r_sat_kpc * 3.0857e19;
    let v = v_sat_km_s * 1e3;
    if r < r_c {
        let enclosed_mass = 4.0 / 3.0 * PI * rho_core * r.powi(3);
        let coulomb_log = (r_c / (G * m_satellite / (v * v))).ln().max(1.0);
        -4.0 * PI * G * G * m_satellite * rho_core * coulomb_log / (v * v) * enclosed_mass
            / (enclosed_mass + m_satellite)
    } else {
        let coulomb_log = (r / (G * m_satellite / (v * v))).ln().max(1.0);
        chandrasekhar_friction_acceleration(
            m_satellite,
            rho_core,
            v_sat_km_s,
            v_sat_km_s / 2.0_f64.sqrt(),
            coulomb_log,
        )
    }
}

pub fn core_stalling_radius_kpc(
    m_satellite_solar: f64,
    rho_core_kg_m3: f64,
    r_core_kpc: f64,
) -> f64 {
    let m_sat = m_satellite_solar * 1.989e30;
    let r_core = r_core_kpc * 3.0857e19;
    let m_enclosed_core = 4.0 / 3.0 * PI * rho_core_kg_m3 * r_core.powi(3);
    let r_stall = r_core * (m_sat / m_enclosed_core).powf(1.0 / 3.0);
    r_stall / 3.0857e19
}