XMM-Newton Science Analysis System


ekstest (ekstest-2.8.1) [xmmsas_20230412_1735-21.0.0]

Comments

The fractional variability amplitude (F$_{var}$) test (Edelson et. al., 2002, ApJ, 568, 610 and Vaughan et. al., 2003, MNRAS, 345, 1271) is now implemented as of 3rd April 2012.

$$F_{var} = \sqrt{\frac{S^2 - \langle \sigma^{\scriptscriptstyle 2}_{\scriptscriptstyle err} \rangle)}{ \langle x \rangle^2}}$$

where,

$$S^2 = \frac{1}{N-1} \sum_{i=1}^N (x_i - \langle x \rangle)^2$$

and $N$ is the number of bins, $x_i$ the net rate for the $i$th data point and $\langle x \rangle$ is the mean of the net rate (= $\frac{1}{N} \sum_{i=1}^N (x_i)$) and

$$\langle \sigma^{\scriptscriptstyle 2}_{\scriptscriptstyle err} \rangle = \frac{1}{N} \sum_{i=1}^N (NetRateErr_i)^2$$

The error on F$_{var}$ is then given by :

$$err(F_{var}) = \frac{1}{2 F_{var}}\sqrt{\left ( \sqrt{\frac{2}{N}... ...iptscriptstyle err} \rangle}{N}}\frac{2 F_{var}}{\langle x \rangle} \right )^2}$$