Survival analysis of the Swift optical transient data

TL;DR

This paper applies survival analysis to Swift optical transient data, combining upper limits and measured brightness to derive an unbiased brightness distribution and explore its dependence on gamma-ray burst properties.

Contribution

It introduces a survival analysis approach to optical transient data, revealing a linear brightness distribution and its correlation with peak flux.

Findings

The cumulative brightness distribution follows a linear relation with magnitude.

A significant dependence of brightness on peak flux was found.

Upper limits can be effectively incorporated into brightness distribution analysis.

Abstract

In a systematic search of the OTs at GRBs the Swift satellite determined only an upper limit of the apparent brightness in a significant fraction of cases. Combining these upper limits with the really measured OT brightness we obtained a sample well suited to survival analysis. Performing a Kaplan-Meier product limit estimation we obtained an unbiased cumulative distribution of the V visual brightness. The lg(N(V)) logarithmic cumulative distribution can be well fitted with a linear function of V in the form of lg(N(V))= 0.234 V + const. We studied the dependence of V on the gamma ray properties of the bursts. We tested the dependence on the fluence, T90 duration and peak flux. We found a dependence on the peak flux on the 99.7% significance level.