Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <cmath>
7 :
8 : #include "Utilities/ConstantExpressions.hpp"
9 :
10 : namespace hydro {
11 : /*!
12 : * \brief Functions, constants, and classes for converting between different
13 : * units.
14 : *
15 : * In SpECTRE we prefer to use geometric units where \f$G=c=M_{\odot}=1\f$, as
16 : * is standard in numerical relativity. However, in order to interface with
17 : * other codes, we need to sometimes convert units. This namespace is designed
18 : * to hold the various conversion factors and functions. A unit library/system
19 : * would be nice, but is a non-trivial amount of work.
20 : */
21 1 : namespace units {
22 : /*!
23 : * \brief Entities for converting between geometric units where
24 : * \f$G=c=M_{\odot}=1\f$ and CGS units.
25 : *
26 : */
27 1 : namespace cgs {
28 :
29 : /// The speed of light in cm/s (This is exact)
30 1 : constexpr double speed_of_light = 29979245800.0;
31 : /// Newton's gravitational constant as given by
32 : /// https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93.025010.
33 : /// G is likely to vary between sources, even beyond the reported uncertainty
34 1 : constexpr double G_Newton = 6.67430e-8;
35 : /// Note G*M_Sun = 1.32712440042x10^26 +/- 1e16 [1/cm]
36 : /// G*M_Sun factor from https://doi.org/10.1063/1.4921980
37 1 : static constexpr double G_Newton_times_m_sun = 1.32712440042e26;
38 : /// k_B factor in erg/K from
39 : /// https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.93.025010.
40 : /// (This is exact)
41 1 : static constexpr double k_Boltzmann = 1.380649e-16;
42 :
43 : /// `mass_cgs = mass_geometric * mass_unit`
44 : /// Heuristically the mass of the sun in grams
45 1 : constexpr double mass_unit = G_Newton_times_m_sun / G_Newton;
46 : /// `length_cgs = length_geometric * length_unit`
47 : /// Heuristically, half the schwarzschild radius of the sun
48 : /// in cm
49 1 : constexpr double length_unit = G_Newton_times_m_sun / square(speed_of_light);
50 : /// `time_cgs = time_geometric * time_unit`
51 : /// Heuristically, half the light crossing time of a
52 : /// solar schwarzschild radius in seconds
53 1 : constexpr double time_unit = length_unit / speed_of_light;
54 : /// `rho_cgs = rho_geometric * rho_unit`
55 : /// Heuristically, the density in g/cm^3 of matter ~2200 times the density of
56 : /// atomic nuclei. Note this is much larger than any density realized in the
57 : /// universe.
58 1 : constexpr double rest_mass_density_unit =
59 : mass_unit / (length_unit * length_unit * length_unit);
60 : /// `pressure_cgs = pressure_geometric * pressure_unit`
61 : /// Heuristically, the quantity above but times the speed of light squared in
62 : /// cgs
63 1 : constexpr double pressure_unit =
64 : mass_unit / (length_unit * time_unit * time_unit);
65 :
66 : // Extra constants, which are known to greatest precision in SI / (equvialently
67 : // CGS)
68 : /// The accepted value for the atomic mass unit in g, uncertainty +-30e-10
69 1 : constexpr double atomic_mass_unit = 1.66053906660e-24;
70 : /// The neutron mass, given in grams, uncertainty at 5.7 x 10^-10 level
71 1 : constexpr double neutron_mass = 1.67492749804e-24;
72 : /// The proton mass, given in grams. Uncertainty at 2e-8 level
73 1 : constexpr double proton_mass = 1.672621898e-24;
74 : /// The electron-volt (eV) given in ergs, which is known exactly in SI/cgs
75 1 : constexpr double electron_volt = 1.602176634e-12;
76 :
77 : /*!
78 : * \brief CGS unit of Gauss.
79 : *
80 : * Equals `mass_unit^(1/2) * length_unit^(-1/2) * time_unit^(-1)`.
81 : *
82 : * Conversion rule for electromagnetic fields is
83 : * ```
84 : * magnetic_field_cgs = magnetic_field_geometric * gauss_unit
85 : * ```
86 : * or
87 : * ```
88 : * electric_field_cgs = electric_field_geometric * gauss_unit
89 : * ```
90 : *
91 : * \warning Before changing units using this value, make sure the unit systems
92 : * you are converting values between are using the same unit convention for
93 : * electromagnetic variables as well. Gaussian and Heaviside-Lorentz unit
94 : * convention (in electromagnetism) have a factor of \f$\sqrt{4\pi}\f$
95 : * difference in variables. See
96 : * <a href="https://en.wikipedia.org/wiki/Heaviside%E2%80%93Lorentz_units">this
97 : * Wikipedia page</a> for how to convert between different unit systems in
98 : * electromagnetism.
99 : *
100 : * Note that ForceFree and grmhd::ValenciaDivClean evolution systems are
101 : * adopting the geometrized Heaviside-Lorentz unit for magnetic fields.
102 : *
103 : * e.g. Suppose magnetic field has value \f$10^{-5}\f$ with the code unit in the
104 : * ValenciaDivClean evolution system. This corresponds to
105 : * ```
106 : * 10^(-5) * gauss_unit = 2.3558985e+14 Gauss
107 : * ```
108 : * in the CGS Heaviside-Lorentz unit.
109 : *
110 : * If one wants to convert it to the usual CGS Gaussian unit, extra factor of
111 : * \f$\sqrt{4\pi}\f$ needs to be multiplied:
112 : * ```
113 : * 10^(-5) * gauss_unit * sqrt(4pi) = 8.35144274e+14 Gauss
114 : * ```
115 : */
116 1 : constexpr double gauss_unit = 2.3558985e+19;
117 : } // namespace cgs
118 :
119 : /*!
120 : * \brief The defining quantities of the nuclear fm-MeV/c^2-fm/c unit system
121 : *
122 : * Constants are defined in terms of cgs units where possible, which are, in
123 : * many cases known exactly due to their relation to SI.
124 : */
125 1 : namespace nuclear {
126 : /// `mass_nuclear = mass_unit * mass_geometric`
127 : /// Heuristically a solar mass in MeV/c^2
128 1 : constexpr double mass_unit =
129 : cgs::mass_unit /
130 : (1.0e6 * cgs::electron_volt / square(cgs::speed_of_light));
131 : /// `length_nuclear = length_unit * length_geometric`
132 : /// Heuristically GM_sun/c^2 in fm
133 1 : constexpr double length_unit = cgs::length_unit / (1.0e-13);
134 : /// `time_nuclear = time_unit * time_geometric`
135 : /// Heuristically GM_sun/c^3 in fm/c
136 1 : constexpr double time_unit =
137 : cgs::time_unit / (1.0e-13 / cgs::speed_of_light);
138 : /// `pressure_nuclear = pressure_geometric * pressure_geometric`
139 : /// Heuristically the rest-mass energy density of
140 : /// ~2200 the density of atomic nucli expressed in MeV/fm^3
141 1 : constexpr double pressure_unit = mass_unit / (length_unit * square(time_unit));
142 : /// `rest_mass_density_nuclear = rest_mass_density_geometric *
143 : /// rest_mass_density_geometric` Heuristically ~2200 the density of atomic nucli
144 : /// expressed in MeV/c^2/fm^3
145 1 : constexpr double rest_mass_density_unit = mass_unit / cube(length_unit);
146 0 : constexpr double neutron_mass =
147 : cgs::neutron_mass /
148 : (1.0e6 * cgs::electron_volt / square(cgs::speed_of_light));
149 0 : constexpr double atomic_mass_unit =
150 : cgs::atomic_mass_unit /
151 : (1.0e6 * cgs::electron_volt / square(cgs::speed_of_light));
152 : /// The proton mass in MeV, uncertainty at 5.8eV.
153 1 : constexpr double proton_mass =
154 : cgs::proton_mass /
155 : (1.0e6 * cgs::electron_volt / square(cgs::speed_of_light));
156 :
157 : /// The saturation number density of baryons in nuclear matter, in
158 : /// units of 1/fm^3. This is a standard value, consistent with e.g.
159 : /// https://journals.aps.org/prc/abstract/10.1103/PhysRevC.102.044321
160 1 : constexpr double saturation_number_density = 0.16;
161 :
162 : } // namespace nuclear
163 : /*!
164 : * \brief Quantities given in terms of geometric units G = c = M_odot =
165 : * 1
166 : *
167 : * All quantities are given in terms of unit systems which are related exactly
168 : * to SI units. The limiting factor in conversions is the poorly known value
169 : * of G; which leads to large uncertainties in the relative value of SI-derived
170 : * masses to the solar mass. For this reason, it is best to avoid using
171 : * geometric units in calculations except where conversion is explicitly needed.
172 : */
173 1 : namespace geometric {
174 : /// Neutron mass in G = c = M_sun = 1.0 units
175 1 : constexpr double neutron_mass = cgs::neutron_mass / cgs::mass_unit;
176 : /// The rest mass density of matter at the saturation point
177 1 : constexpr double default_saturation_rest_mass_density =
178 : 1 / nuclear::rest_mass_density_unit *
179 : (nuclear::saturation_number_density * nuclear::atomic_mass_unit);
180 : /// The default baryon mass in geometric units.
181 : /// Accepted value of atomic mass unit as expressed in
182 : /// solar masses
183 : /// Limited by precision of knowledge of solar mass.
184 1 : constexpr double default_baryon_mass = cgs::atomic_mass_unit / cgs::mass_unit;
185 : } // namespace geometric
186 :
187 : } // namespace units
188 : } // namespace hydro
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