Implemented Models

Medium

HomoEarth

template<typename Vector3 = Vector3d<double>, typename Value = double>
class HomoEarth : public darkprop::Earth<Vector3d<double>, double>

A homogeneous Earth model composed of 8 components.

Public Functions

virtual Value propagate(Particle<Vector3, Value> &particle, RandomNumber<Value> &rn) override

Propagate a particle.

Sample a free path and propagate the particle and determine whether the particle is in the Medium or not. Set Particle::in_medium to false if the simulation should stop.

virtual Target sampleTarget(const Particle<Vector3, Value> &particle, RandomNumber<Value> &rn) const override

Sample a target before scattering.

PREMEarth

template<typename Vector3 = Vector3d<double>, typename Value = double>
class PREMEarth : public darkprop::Earth<Vector3d<double>, double>

Preliminary reference Earth model (PREM).

Public Functions

virtual Value propagate(Particle<Vector3, Value> &particle, RandomNumber<Value> &rn) override

Propagate a particle.

Sample a free path and propagate the particle and determine whether the particle is in the Medium or not. Set Particle::in_medium to false if the simulation should stop.

virtual Target sampleTarget(const Particle<Vector3, Value> &particle, RandomNumber<Value> &rn) const override

Sample a target before scattering.

Value densityIntegral(Value r0, Value cosa, Value L, std::size_t layer)

Analytic integration of the density.

HomoElectronEarth

template<typename Vector3 = Vector3d<double>, typename Value = double>
class HomoElectronEarth : public darkprop::Earth<Vector3d<double>, double>

Public Functions

inline virtual Value propagate(Particle<Vector3, Value> &p, RandomNumber<Value> &rn) override

Propagate a particle.

Sample a free path and propagate the particle and determine whether the particle is in the Medium or not. Set Particle::in_medium to false if the simulation should stop.

inline virtual Target sampleTarget(const Particle<Vector3, Value> &particle, RandomNumber<Value> &rn) const override

Sample a target before scattering.

Sun

template<typename Vector3 = Vector3d<double>, typename Value = double>
class Sun : public darkprop::MediumBall<Vector3d<double>, double>

A Sun model.

Currently, the Sun only works with SolarDM which has constant cross section.

Public Functions

void init(const std::string &filename)

Load the tabular normalized number density integral function.

Value densityIntegral(Value y)

For certain y, the maximal value of the integrated number density, i.e.

the value of integrated number density at $x=\sqrt{1-y^2}$. unit: cm^-3. Same as number density. y ranges in [0,1].

inline Value densityIntegralNormalized(Value y, Value x)

The normalized density integral.

inline Value densityIntegralInverseNormalized(Value y, Value z)

The inverse of the normalized density integral.

virtual Value propagate(Particle<Vector3, Value> &particle, RandomNumber<Value> &rn) override

Propagate a particle.

Sample a free path and propagate the particle and determine whether the particle is in the Medium or not. Set Particle::in_medium to false if the simulation should stop.

virtual Target sampleTarget(const Particle<Vector3, Value> &particle, RandomNumber<Value> &rn) const override

Sample a target before scattering.

This Sun model is implemented only working with the SolarDM model which assumes constant cross section and only couples to proton, and includes only proton and ${}^4\mathrm{H}\mathrm{e}$. So the free path equation (Eq. (8)) can be written as

(13)$${\sigma }_{\chi p}{\int }_0^L(n_p+4n_{\mathrm{H}\mathrm{e}})\mathrm{d}l=-\ln \xi ,$$

where ${\sigma }_{\chi p}$ is DM-proton scattering cross section, $n_p$ ($n_{\mathrm{H}\mathrm{e}}$) is the number density of proton (${}^4\mathrm{H}\mathrm{e}$), and $1-\xi$ is replaced with $\xi$ since they have the same distribution. Note that the factor of 4 comes from coherent scattering. Using the reasonable approximation that the density of the Sun is isotropic, we use the coordinates $(x,y)$ as shown in Fig. 2.

Fig. 2 The coordinates $(x,y)$ for the isotropic Sun.

The direction of $x$ aligns with the velocity of the particle. The radius has been normalized to 1. So $y$ ranges in $(0,1)$ and $x$ ranges in $(-\sqrt{1-y^2},\sqrt{1-y^2})$. We further define the normalized density integral

(14)$$z(y,x)\equiv \frac{{\int }_{-\sqrt{1-y^2}}^x(n_p+4n_{\mathrm{H}\mathrm{e}})\mathrm{d}{x}^{\prime }}{{\int }_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}}(n_p+4n_{\mathrm{H}\mathrm{e}})\mathrm{d}{x}^{\prime }}.$$

Thus $0\le z\le 1$. Now suppose the particle starts at $x_0$, Eq. (13) can be solved as follows

(15)$$z(y,x)=z(y,x_0)+\frac{\ln \xi }{{\sigma }_{\chi p}{R}_{\odot }z(\sqrt{1+y^2},y)},$$

where $R_{\odot }$ is the radius of the Sun. Then $x$ is solved with the inverse of $z$, $x=x(y,z)$, and the free path is $L=(x-x_0)R_{\odot }$.

Particle

SIDM

template<typename Vector3 = Vector3d<double>, typename Value = double>
class SIDM : public darkprop::ParticleElastic<Vector3d<double>, double>

Spin independent elastic scattering DM model with constant cross section.

Subclassed by darkprop::SIFFCutDM< Vector3, Value >, darkprop::SIFFExpDM< Vector3, Value >, darkprop::SIHelmDM< Vector3, Value >, darkprop::SIHelmDiscreteDM< Vector3, Value >

Public Functions

inline virtual Value totalCrossSection(const Target &t) const override

Total cross section scattering with Target t.

Use current this->T as initial kinetic energy. Return the statistical weight.

inline virtual Value scatteringSampleTr(const Target &t, RandomNumber<Value> &rn) override

Sample recoil kinetic energy of the target particle in laboratory frame.

SIHelmDM

template<typename Vector3 = Vector3d<double>, typename Value = double>
class SIHelmDM : public darkprop::SIDM<Vector3d<double>, double>

Spin independent elastic scattering DM model with Helm form factor.

Public Functions

inline virtual Value scatteringSampleTr(const Target &t, RandomNumber<Value> &rn) override

Sample recoil kinetic energy of the target particle in laboratory frame.

inline virtual Value totalCrossSection(const Target &t) const override

Total cross section scattering with Target t.

Use current this->T as initial kinetic energy. Return the statistical weight.

DMElectron

template<typename Vector3 = Vector3d<double>, typename Value = double>
class DMElectron : public darkprop::ParticleElastic<Vector3d<double>, double>

A DM-electron vector coupling model.

Used to cross check for arXiv:2403.08361.

Public Functions

inline virtual Value totalCrossSection(const Target &t) const override

Total cross section scattering with Target t.

Use current this->T as initial kinetic energy. Return the statistical weight.

inline virtual Value scatteringSampleTr(const Target &t, RandomNumber<Value> &rn) override

Sample recoil kinetic energy of the target particle in laboratory frame.

SolarDM

template<typename Vector3 = Vector3d<double>, typename Value = double>
class SolarDM : public darkprop::Particle<Vector3d<double>, double>

The Solar DM model.

Public Functions

inline void setTempScale(Value t_temp_scale)

Set the temperature scaling factor multiplied to the real temperature.

This is used to adjust the temperature of the Sun.

inline virtual Value totalCrossSection(const Target &t) const override

Total cross section scattering with Target t.

Use current this->T as initial kinetic energy. Return the statistical weight.

virtual Value scatter(const Target &t, RandomNumber<Value> &rn) override

Sample final state DM particle.

The changes are made directly. Return the statistical weight.