dukes 1.0.3

Diffuse boosted dark matter from supernova neutrinos in early Universe

Diffuse boosted dark matter yielded from supernova neutrinos in the early Universe

dukes is a package for evaluating the signature of DiffUse boosted darK mattEr yielded by Supernova neutrinos in the early Universe based on arXiv:24xx.xxxx.

Installation

To install, excute the following command on the prompt

$ pip install dukes

and everything should be processed on-the-fly.

Dependency

dukes requires these external packages

• numpy >= 1.20.0
• scipy >= 1.10.0
• vegas >= 6.0.1

where vegas is a the backend engine for evaluating multidimensional integrals based on adaptive Monte Carlo vegas algorithm, see its homepage: https://pypi.org/project/vegas/.

Other packages, e.g. gvar, maybe required by these dependencies during the installation. The versions of these dependencies are not strict, but are recommended to update to the latest ones to avoid incompatibility.

Usage

We briefly summarize the usage in this section and a comprehensive tutorial can be found in the jupyter notebook stored in tutorial/tutorial.ipynb.

To import, do

>>> import dukes

in python terminal and is similar in the jupyter notebook. All module functions named funcname can be called by typing dukes.funcname.

Examples

Boosted dark matter velocity

A boosted dark matter (BDM) with mass $m_\chi$ and kinetic energy $T_\chi$ has the velocity $v_\chi$,

$$ \frac{v_\chi}{c} = \frac{\sqrt{T_\chi(2m_\chi+T_\chi)}}{m_\chi+T_\chi}. $$

Let $T_\chi=$ Tx and $=m_\chi=$ mx, the corresponding function that evaluates $v_\chi/c$ is

>>> Tx,mx = 5,1  # MeV
>>> dukes.vBDM(Tx,mx)
0.9860132971832694

The diffuse BDM flux

The averaged diffuse BDM (DBDM) flux on the Earth is given by

$$ \frac{d\Phi_\chi}{dT_\chi} = \frac{v_\chi}{H_0} \int_0^{z_{\rm max}} \frac{dz}{\varepsilon(z)} \int dM_G \frac{d\Gamma_{{\rm SN}}(z)}{dM_G}\frac{d\bar N_\chi(M_G)}{dT_\chi^\prime}. $$

Same as the above example,

>>> dukes.flux(Tx,mx,usefit=True,nitn=10,neval=50000)
4.422705310516041e-08

as in MeV⁻¹ cm⁻² s⁻¹.

Throughout the entire package, we have implemented the differential DM-neutrino scattering cross section in CM frame is isotropic and energy-independent

$$ \frac{d\sigma_{\chi \nu}}{d\Omega_{\rm CM}}=\frac{\sigma_0}{4\pi} $$

where $\sigma_0=10^{-35}$ cm².

The argument usefit is to turn on/off the fitting function used in obtaining the average supernova position on the galactic plane for galaxy with baryonic mass $M_G$. If usefit=False, the function will call galacticDensityProfile to evaluate the area density for galaxy with arbitrary $M_G$. It requires quadrature integration quad from scipy and the computation time surges accordingly, but the accuracy is improved insignificantly.

The arguments nitn and neval are passed to vegas and determine how many chains of iteration and how many numbers to be evaluated in each chain. Increasing them will improve the accuracy of the results but also cost longer computation time. We relegate the detail to vegas documentation.

Physical constants

We have a class named constant that contains multiple physical constants and conversion factors frequently used in this package. For instance, electron mass

>>> dukes.constant.me
0.511

as in MeV and the speed of light

>>> dukes.constant.c
29980000000.0

as in cm s⁻¹. Conversion factors such as converting kiloparsec to centimeters

>>> dukes.constant.kpc2cm
3.085e21

and year to seconds

>>> dukes.constant.year2Seconds
31560000.0

Scripting

In python script (see subsidiary tests/duke_example.py), one can write

# dukes_example.py

import sys
import dukes

if __name__ == '__main__':

    Tx = float(sys.argv[1])  # DM kinetic energy, MeV
    mx = float(sys.argv[2])  # DM mass, MeV
    vx = dukes.vBDM(Tx,mx)    # BDM velocity
    
    print(vx)                # Print the BDM velocity

and excute this on the prompt

$ python dukes_example.py 5 1
0.9860132971832694

or whatever style you like!

Misc

Bug report and troubleshooting please contact the author Yen-Hsun Lin via [e-mail].