snorer is a package for evaluating time-of-flight signatures of supernova-neutrino-boosted dark matter (SNν BDM) from our Milky Way (MW), SN1987a in Large Magellanic Cloud (LMC) and SN in arbitrary distant galaxy based on Phys. Rev. Lett. 130, 111002 (2023) [arXiv:2206.06864] and Phys. Rev. D 108, 083013 (2023) [arXiv:2307.03522].

If you use this package or part of the code in your research, please cite the followings:

1. Y.-H. Lin et al., Phys. Rev. Lett. 130, 111002 (2023), arXiv:2206.06864
2. Y.-H. Lin et al., Phys. Rev. D 108, 083013 (2023), arXiv:2307.03522
3. snorer: https://github.com/yenhsunlin/snorer

To install, excute the following command on the prompt

$ pip install snorer

and everything should be processed on-the-fly.

snorer requires python >= 3.8 and the following external packages

• numpy >= 1.20.0
• scipy >= 1.10.0
• vegas >= 6.0.1
• astropy >= 6.0.0

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 maybe required by these dependencies during the installation, see requirements.txt for details. The versions of these dependencies are not strict, but are recommended to update to the latest ones to avoid incompatibility.

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

To import, do

>>> import snorer

in python terminal and is similar in the jupyter notebook. All functions and classes can be accessed by typing snorer.foo() where foo is the function/class/module name.

We document various useful physical constants and conversion factors...etc as the attributes of the instance snorer.constant. For example, we can retrieve

>>> snorer.constant.me      # electron mas, MeV
0.511
>>> snorer.constant.kpc2cm  # kpc to cm
3.085e+21

We did this instead of naming them as constant variables in some module to prevent them from being edited.

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 $(T_\chi,m_\chi)=(15,0.075)$ MeV, we can use snorer.get_vx() to evaluate

>>> Tx,mx = 15,0.075
>>> snorer.get_vx(Tx,mx)
0.9999876239921284

The BDM flux, or afterglow to the ${\rm SN}\nu$, due to SN exploded at $R_\star$ distant away from us can be evaluated by

$$ \frac{d\Phi_{\chi}(T_\chi, t^\prime)}{dT_{\chi}dt} = \tau\int_0^{2\pi} d\phi\int_{0}^{\pi/2}\sin\theta d\theta~ \mathcal{J} j_{\chi}(r(\phi),D,T_{\chi},\psi) $$

where $t$ is the BDM ToF with time-zero at the discovery of SNν on Earth and $t^\prime$ is the total time. We focus on $t$ instead of $t^\prime$. Zenith angle $\theta$ and azimuthal angle $\phi$ are relative to the SN-Earth line-of-sight. The default DM-ν cross section is $\sigma_{\chi\nu}=10^{-45}$ cm².

The function to evaluate this is snorer.flux() with $(t,T_\chi,m_\chi,R_\star,\beta)$ are the necessary inputs. Suppose SN's location is at GC, we have $R_\star=8.5$ kpc and $\beta=0$, with default GC-Earth distance $R_e=8.5$ kpc, too. With DM spike included, the BDM flux can be calcualted

>>> t,Tx,mx,Rstar,beta = 100,15,1e-2,8.5,0
>>> snorer.flux(t,Tx,mx,Rstar,beta,is_spike=True,neval=15000)
4.572295175982701e-16

Users can of course turn off the spike feature by setting is_spike=False and will find both numerical results are similar. It implies the contribution to the BDM flux comes from the place outside the spike's influence.

The BDM event number in a detector after exposing to the flux for a period of time, $(t_{\rm min},t_{\rm max})$, can be evaluated by

$$ N_{\rm BDM} = \int_{t_{\rm min}}^{\rm t_{\rm max}} dt \int_{T_{\chi,{\rm min}}}^{T_{\chi,{\rm max}}} \frac{d\Phi_{\chi}(T_\chi, t^\prime)}{dT_{\chi}dt} \times N_e \sigma_{\chi e} $$

where $N_e$ is the total electron number in the detector and $\sigma_{\chi e}$ the DM-e cross section. This task can be accomplished by snorer.event() with $(m_\chi,R_\star,\beta)$ the necessary inputs. The default $(t_{\rm min},t_{\rm max})=(10~{\rm s},35~{\rm yrs})$ and $(T_{\chi,{\rm min}},T_{\chi,{\rm max}})=(5,30)$ MeV.

Note that this function is normalized to $N_e=1$ and $\sigma_{\chi e}=1$ cm². To have the correct $N_{\rm BDM}$ in a specific detector, users have to mutiply the corresponding $N_e$ and $\sigma_{\chi e}$.

Now let $m_\chi=0.015$ MeV,

>>> mx,Rstar,beta = 0.015,8,0
>>> N_BDM = snorer.event(mx,Rstar,beta,is_spike=False,neval=50000)
>>> N_BDM
1.662174035857532e-06

For Super-Kamiokande, it has $N_e\approx 7\times 10^{33}$ and assume $\sigma_{\chi e}=10^{-35}$ cm². The associated $N_{\rm BDM}$ is

>>> Ne,sigma_xe = 7e33,1e-35
>>> N_BDM*Ne*sigma_xe
1.1635218251002724e-07

The aforementioned functions for evaluating BDM signatures are based on model-agnostic picture. It means the cross sections between dark and visble sectors are generally independent of physical quantities, eg. energy, mass and coupling constants.

The most important feature snorer carries is that it offers a general interface for users to implement their favorite particle models. Furthermore, SN is not necessary exploding in our MW or LMC. As long as users can provide these celetial objects' coordinates and expressed them in ICRS J2000.0 metrics, snorer can do the calculation. snorer also allows users to customize the halo shape, by manipulating $\rho_s$, $r_s$ and $n$...etc, and including or excluding spike feature, of such distant galaxy.

This will be done by the class snorer.GeneralInterface. All these user-specified features will be composed into an instance of snorer.GeneralInterface. The BDM signatures can be evaluated by calling the associated methods within it. We have an example in examples/tutorial.ipynb, also see the in-class docstring for more information.

We also provide many useful functions and classes at users' disposal. See examples/tutorial.ipynb for details.

To evaluate BDM event, snorer uses vegas to handle the multidimensional integration. The sampling method of vegas cannot manipulate event calculation, e.g. snorer.event() and the method in the instance of snorer.GeneralInterface, properly, when SN is exactly at GC with spike and no DM self-annihilation.

Since the spike is a highly singular behavior, the sampling method may miss the substantial DM contribution from the inner galactic region and causes underestimate of $N_{\rm BDM}$ plus unstable results. To avoid this, users may try to displace the SN from GC a little bit when evaluating $N_{\rm BDM}$ with DM sipke and no DM annihilation. For BDM flux evaluation, there is no such issue.

To be fair, the probability of a very cuspy DM spike surving the gravitational disturbance without annihilating away and SN happening exactly at the GC might be very rare.

This issue is scheduled to fix in the next major update of snorer.

Please report to the author, Yen-Hsun Lin, via yenhsun@phys.ncku.edu.tw.