This repository contains the code used to perform the analysis described in the paper "A stacked search for spatial coincidences between IceCube neutrinos and radio pulsars" (https://arxiv.org/abs/2306.03427). The code is written in Python 3.10 and uses the following packages: numpy, scipy, matplotlib, pandas, numba, multiprocessing. The code is provided as is, without any warranty. If you use this code, please cite the paper.
The repository is organized as follows:
- core
- data
- outputs
The core/ directory contains the following files:
- download_ATNF.py : downloads the ATNF pulsar catalogue and saves it in data/ATNF.txt
- download_IC.py : downloads the IceCube neutrino data package and saves it in data/icecube_10year_ps
- stacking_analysis.py : defines the functions used to calculate the Test statistic, and the signal flux model and other miscellaneous functions used in the analysis indicated in the paper https://arxiv.org/abs/2306.03427
- req_arrays.py : Stores the required data in the form of numpy arrays for faster and easier computation
- readfiles.py : Reads and refines the data from the files and stores them in the form of panda.Dataframes
- signal_bag.py : (depercated) defines the functions used to compute the Signal and Background PDF in the analysis indicated in the paper https://arxiv.org/abs/2306.03427
- weights.py : (depercated) defines the functions used to compute the weights of pulsars for the analysis indicated in the paper https://arxiv.org/abs/2306.03427
The data/ directory contains the data used in the analysis. The data are taken from the following sources:
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The IceCube neutrino data are taken from the public HESE and EHE data releases (http://icecube.wisc.edu/data-releases/20210126_PS-IC40-IC86_VII.zip). The data are stored in the data/icecube_10year_ps/ directory. The IceCube contains observations spanning over 10 years and is separated into 10 files, each corresponding to 1 year/1 IceCube season.
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The radio pulsar data are taken from the ATNF pulsar catalogue (https://www.atnf.csiro.au/research/pulsar/psrcat/).
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The CHIME/FRB data are taken from the CHIME/FRB collaboration (https://www.chime-frb.ca/).
The outputs/ directory contains the results of the analysis in the form of images.
The signal PDF requires heavy computation which consists:
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Angles between 2374 pulsars * 1134450 neutrinos = 269,500,850 values.
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$\omega_{acc}$ for 2374 pulsars. Each pulsar is attributed a weight$\omega_{acc}$ which is proportional to the declination and detector effective area. It is given by:$\omega_{acc,j} = T \times \int A_{eff}(E_{\nu}, \delta_j)E_{\nu}^{\Gamma} dE_{\nu}$ where
$T$ is the livetime of the detector,$A_{eff}$ is the effective area of the detector,$\Gamma$ is the spectral index of the neutrino flux, and$\delta_j$ is the declination of the$j^{th}$ pulsar. The effective area of the detector is a function of the neutrino energy and the declination of the source. The effective area is calculated for 1134450 neutrinos and 2374 pulsars. -
The above integral is calculated using np.trapz for 1e7 energies for each of the 10 seasons of the IceCube and for 3 different spectral indices for 2374 pulsars.
- The no.of signal events for each pulsar indexed by
$j$ is given by:
$\hat{n}{s_j} = T \times \intop A{eff}(E_{\nu}, \delta_j)\dfrac{dF}{dE_{\nu}}dE_{\nu}$
$T$, $A_{eff}$, and $\delta_j$ are the same as above. $\dfrac{dF}{dE_{\nu}}$ is the expected neutrino spectrum from the source and can be modelled using a power-law as follows:
$\dfrac{dF}{dE_{\nu}} = \phi_0 \left( \dfrac{E_{\nu}}{100 \text{ TeV}}\right)^{\Gamma}$
where $\phi_0$ is the flux normalization and $\Gamma$ is the spectral index. Each $\hat{n}_s$ is calculated for 1e7 energies for each of the 10 seasons of the IceCube and for 3 different spectral indices for 2374 pulsars.
<!-- This requires computing 2374 * 1e7 * 30 = 7.122e11 values. -->
- The above two integrals are calculated using np.trapz for 1e7 energies for each of the 10 seasons of the IceCube and for 3 different spectral indices for 2374 pulsars. This requires computing 2374 * 1e7 * 30 = 7.122e11 values.
Then the stacked Signal PDF for each neutrino
The Likelihood of
where
The background PDF is the no.of neutrinos within 5$^\circ$ declination band of the
The Likelihood is calculated for 3 different spectral indices.
We then easily calculate upper limits by using scipy.interp1d as the no.of values required are less
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This is a very large number of values to compute. To overcome this challenge, we use the following techniques:
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Use the numba.njit package to speed up the computation. The numba package is used to compile the python code into machine code.
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The integrals are evaluated using functions accelerated by numba.vectorize package and np.trapz, which is faster than scipy.quad or scipy.dblquad.
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Used numba.vectorize package to replace a for loop calling functions like
ns_sing_season,psr_wt_acc. This reduce the computation time by a factor of 10. -
Used multiprocessing to parallelize the computation. The multiprocessing package is used to run the code in parallel on multiple cores of the CPU.
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Running the code normally requires ~ 2e12 calculations which take > 2 days of continuous computation.
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Using the above techniques, the computation time is reduced to ~ 2 hours.