Pulsar Nulling

A mixture model for analyzing nulling in pulsars, improved on Kaplan+2018. In addition to the standard Gaussian mixture implemented by Kaplan+2018, this extends the analysis to the cases where the distribution is more accurately described by an exponentially modified Gaussian. This also allows to study the correlations in nulling, particularly looking for periodicities in the nulling patterns. Can also be used to study basic drifitng phenonmenon.

It can be installed via pip:

git clone [email protected]:AkashA98/pulsar_nulling.git
cd pulsar_nulling/
pip install .

Or in the standard way as

python ./setup.py install

Example of the code usage:

If the user has the ON and OFF window intensities as arrays

from nulling.get_nf import nulls
nf = nulls(on, off, ncomp=2, model='exp_tail', nwalkers=32, burnin=200, nsteps=5000)
nf.run_mcmc(corr=True)

If the user wants to take into account the finite correlation length of the chain in order to get independent samples, then they can set the corr flag to True. All the results are available as class attributes. For example, the best fit values can be obtained by nf.fit_val and the errors can be obtained by nf.fit_err. The ordering or parameters will always be

[means, standard deviations, tau(optional), weights]

For example, in the case of a 2 component Gaussian model, they will be [mu1, mu2, std1, std2, nf] (Remember all the weights are not independent) and in the case of a 2 component exponentially modified gaussian, they will be [mu1, mu2, std1, std2, tau, nf]

The posteriors for the model parameters and the fit for the histograms can be plotted using

nf.plot_fit()

Comaprison of different models can be done using the Akaike information criterion AIC and Bayesian information criterion BIC and can be obained by calling

nf.AIC()
nf.BIC()

and accessed as nf.aic_val and nf.bic_val.

Once the nulling results are available, one can look for correlations in nulling. This depends on the null probabilities, the probability that a single pulse is null.

from nulling.correlations import *
NP = get_nf_prob(on, model="exp_tail", ndim=2, fit_val=nf.fit_val)
freq, power, lim, fwhm = get_nfprob_fft(NP)

where freq is the fourier frequencies, power is the stacked power from stacks of 256 single pulses (to mitigate ISM effects) and the lim is the analytical limit assuming FAR=0.001 under the null hypothesis of pure noise.

One can also look at the null and emission length histograms

null_len_dist, em_len_dist, null_len_tau, em_len_tau = get_null_em_dist(NP)

which gives the null and emission length distributions and the decay constant assuming an exponential fit.

Finally, one can look for drifitng patterns using the 2D pulse stack. If sps is the 2D array of the single pulses

freq, 2d_power = get_sps_fft(sps, plot=True)