# Hear pulsars

Pulsars have characteristic integrated pulse profile which you’d get after folding many pulses.

I got inspired by this tweet and thought “hey, can we hear integrated pulse profiles?”

# Hear them there

### J1713+0747

This is like shot noise. J1713+0747 pulse profile is like that of a delta function. So, shot noise makes sense. J1713+0747 pulsar profile

### J2145-0750

It sounds like a two stroke engine. There are auto rickshaws in India (that’s where I am from) and this sound resembles that. Well, in all fairness, J2145-0750 has two peaks, so I am not suprised that it sounds like 2T engine. J2145-0750 pulsar profile

### J1939+2134

This legit sounds like my trimmer. I am not kidding. J1939+2134 pulsar profile

## How did I do that?

I took data from the CSIRO Data portal which hosts millions of Pulsar observations. I took Frequency, Time crunched profiles of three pulsars:

• J1713+0747
• J2145-0750
• J1939+2134

An integrated pulse profile which is usually shown on a $$[0,2\pi]$$ axis and which can be linearly mapped to $$[0, P]$$ where $$P$$ is period of the pulsar.

Human ear can hear sounds with frequencies ranging from 20 Hz to 20,000 Hz. So, I map $$[0,Nbin]$$ to $$[20, 20000]$$ linearly.

In other words, I map ever every bin to a frequency and use the intensity value at that frequency as weight.

Mathematically,

$p(t) = \sum_{i=0}^{N_{bin} P[i] * cos(2\pi t freq[i])$

### caveats

• I use cosine which makes this kind of like Discrete Cosine Transform. My reasoning is that since integrated pulse profile is purely real. Sine terms don’t come in.

• I initially thought of using Fourier Transform and the property of Inverse Fourier Transform of real signal (in frequency domain) is real and even. But, then I would have to take care of the appropriate frequency scaling and do many many manipulations since integrated profile isn’t actually frequency domain stuff anyway. So, I did something which is called _Extended Fourier Transform__ and manually did the transform.

• To define a fudicial point in the integrated pulse profile, and to make the result same across all the pulsars. I rotate the profile so that maximum intensity exactly lies in the middle of the pulsar.

• To also standardize, I hardcoded the length of the sound from pulsar to be 2 seconds. I couldn’t think of any other method to make the length sensible and charactistic to each pulsar.