Source Variability

Mean Count Rate

The mean count rate (var_mean) is the time-averaged source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.

Count Rate Standard Deviation

The count rate standard deviation (var_sigma) is the time-averaged 1σ statistical variability of the source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.

Minimum Count Rate

The minimum count rate (var_min) is the minimum value of the source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.

Maximum Count Rate

The maximum count rate (var_max) is the maximum value of the source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.

Intra-Observation Gregory-Loredo, Kolmogorov-Smirnov, and Kuiper's Variability Probability

The Gregory-Loredo, Kolmogorov-Smirnov (K-S) test, and Kuiper's test intra-observation variability probabilities represent the highest values of the variability probabilities (var_prob, ks_prob, kp_prob) calculated for each of the contributing observations (i.e., the highest level of variability among the observations contributing to the master source entry).

Intra-Observation Variability Index

The intra-observation variability index (var_intra_index) represents the highest value of the variability indices (var_index) calculated for each of the contributing observations.

Inter-Observation Variability Probability

The inter-observation variability probability (var_inter_prob) is a value that records the probability that the source region photon flux varied between the contributing observations, based on the hypothesis rejection test described in the hardness ratios and variability memo. Given the $N$ individual Bayesian probability distribution of the aperture fluxes for the same source in $N$ different observations (their means and standard deviations), we estimate for each band the maximum likelihood ${\mathcal{L}}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and the corresponding maximizing arguments $F_{⟨band⟩}^{i,\mathrm{m}\mathrm{a}\mathrm{x}}$, of the observed fluxes assuming a different flux for each observation, as well as the maximum likelihood ${\mathcal{L}}_2^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and the corresponding maximizing argument $F_{⟨band⟩}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ of the observed fluxes assuming a single flux (the latter is the null hypothesis of no variability). As per Wilks' theorem, the quantity:

follows ${\chi }^2$ distribution with $N-1$ degrees of freedom, under the null hypothesis. Therefore, the null hypothesis (non-variability) is rejected with a probability proportional to the cumulative distribution of the ${\chi }^2$ statistic for values smaller than the estimated $D$. The quantity var_inter_prob represents this cumulative probability, and therefore gives the probability that the source is variable.

The reason for this careful definition is that the probabilities for intra-observation and inter-observation variability are, by necessity, of a different nature. Whereas one can say with reasonable certainty whether a source was variable during an observation covering a contiguous time interval, when comparing measured fluxes from different observations one knows nothing about the source's behavior during the intervening interval(s). Consequently, when the inter-observation variability probability is high (e.g., var_inter_prob > 0.7), one can confidently state that the source is variable on longer time scales, but when the probability is low, all one can say is that the observations are consistent with a constant flux.

Inter-Observation Variability Index

The inter-observation variability index (var_inter_index) is an integer value in the range $[0,8]$ that is derived according to the estimated value of the quantity $D/(N-1)$ defined above. It is used to evaluate whether the source region photon flux is constant between the observations. The degree of confidence in variability expressed by this index is similar to that of the intra-observation variability index. Below we tabulate the association between the value of $D/(N-1)$ and inter-observation variability index.

Inter-Observation Count Rate Variability

The inter-observation flux variability (var_inter_sigma) is the absolute value of the difference between the error weighted mean of the source region photon flux density PDF when a single flux is assumed $\left(F_{⟨band⟩}^{\mathrm{m}\mathrm{a}\mathrm{x}}\right)$, and the mean of the source region photon flux density PDF for the individual observation that maximizes the absolute value of the difference $\left(F_{⟨band⟩}^{i,\mathrm{m}\mathrm{a}\mathrm{x}}\right)$:

Of all the contributing observations, the observation that yields the highest value for this equation, is used in computing this value, which is recorded in var_inter_sigma. Intuitively, this quantity can be interpreted as the variance of the individual observation fluxes.

Inter-Observation Spectral Variability Probability