The 5 million data for pulse width do not fit the given distributions.

[KingwithQueen]

Hi Kaitlyn Shin, I recently read your article, part of which deals with the Initial model and the 5 million data sets generated by that model. I searched for the model parameters in your code.

I plotted the probability density distribution given by the model using the scale and shape of DM, pulse width and scattering time given in the code. However, while the 5 million data sets for DM and scattering time match the Initial model very well, the pulse widths are way off!

As shown in the three pairs of plots. When plotting the plots, I manually adjusted the normalisation factors as the histograms were normalised in a slightly different way to the model. This doesn't change the shape of the model though, it just makes the plots look a little better.

Is this because I'm mistaken? Are the parameters given in the code the ones in the corresponding distribution model for the previously mentioned dataset?

PS: I am not sure the unite of scattering time in 5 million data sets is second.

[KingwithQueen]

In the code, the scale of the pulse width takes the value of 0.0010586528808992726 * conv_factor, I'm not sure why need to multiply conv_factor, but when I remove the conv_factor, i.e., take the scale of the pulse width takes the value of 0.0010586528808992726, the result matches the data. So should the true scale of the pulse width be 0.0010586528808992726 and why is the conv_factor multiplied additionally in the code and is the result of multiplying the conv_factor also used when calculating the weights?

[kaitshin]

Ah this is a subtlety: the synthetic pulses are injected with a width defined at the FWHM, while the catalog 1 data have widths defined in 1 sigma. The conversion factor is to go from FWHM->1 sigma so I can more accurately compare the synthetic bursts to the observed bursts. If you're comparing the distribution to itself, then you don't need conv_factor.

[KingwithQueen]

Ah this is a subtlety: the synthetic pulses are injected with a width defined at the FWHM, while the catalog 1 data have widths defined in 1 sigma.

Thank you for your answer. Am I to understand that the data generated by the model is half-height width, but CHIME will consider the value as 1 sigma width? Or is it that the model produces data that is half-height wide and needs to be converted to 1 sigma width before injecting it, and then the converted value is injected into the system?

For example, if I use Equation 12 in ApJ 2023,944:105 to calculate the weights, what width should I use for calculation? FWHM or 1 sigma?

[kaitshin]

CHIME observationally defines its burst widths at 1 sigma; the injections were (mistakenly) defined at FWHM, so we corrected for that afterwards (the conv_factor) in order to be working consistently with the 1 sigma width definition in our analysis. So the 1 sigma widths were used for the weights calculation.