deletions | additions       diff --git a/subsubsection_Excess_Variance_The_usefulness__.tex b/subsubsection_Excess_Variance_The_usefulness__.tex  index 31bdbfe..986ce81 100644  --- a/subsubsection_Excess_Variance_The_usefulness__.tex  +++ b/subsubsection_Excess_Variance_The_usefulness__.tex 
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\end{equation}  $S^2$ is the standard sample variance of the light curve, $\overline{\sigma^2_{\rm err}}$ is the average error in the count rate, and $\mu$ is the mean count rate. $\sigma^2_{\rm XS}$ is also the integral of the PSD over the sampled timescales of the light curve and can be used for lower flux and variable sources since it works in the time rather than frequency domain.  \cite{Soldi_2014} \citet{Soldi_2014}  used a maximum likelihood estimate of $\sigma^2_{\rm XS}$ \cite{Almaini_2000} \citep{Almaini_2000}  to study the variablilty properties of a much larger sample of the BAT AGN than ours in \cite{Shimizu_2013}. \citet{Shimizu_2013}.  However, just as in our PSD analysis, the lack of short timescales able to be probed (\cite{Soldi_2014} (\citet{Soldi_2014}  had to use time bins of 1 month) limited their results to only weak or nonexistent relationships between the variability and intrinsic properties of the AGN. With \nustar\ lightcurves, we will be much closer and much more affected by the changes of the break frequency as shown in Figure~\ref{fig:sims}. If the ultra-hard X-ray break frequency is changing as function of $M_{\rm BH}$ and/or $L_{\rm Bol}$ we should detect it not only through our PSD analysis, but also in an analysis of $\sigma^2_{\rm XS}$ over a large sample of AGN. The \nustar\ archive provides just such a large sample. A search of the archive returns 114 BAT AGN with at least one observation with $>10$ ks on-source exposure with most having $\sim20$ ks on-source exposure as part of one of \nustar's legacy surveys. These archival observations will allow us to significantly study the general variability properties of AGN at high energies and determine if and how they are related to the AGN physical properties such as $M_{\rm BH}$, $L_{\rm Bol}$, $N_{\rm H}$, $\Gamma$ (power law spectral index), etc.  \subsubsection{Energy Dependence}  A further advantage of the archival \nustar\ observations is the broadband energy range from 3--79 keV. We can then generate light curves in specific energy ranges and characterize the variability as function of energy for both our PSD and excess variance analysis.   A test of the energy dependence would give insight into the physical processes that are controlling the emission in each energy range. At low energies, emission is thought to be dominated by a power-law continuum and is also affected by absorption. At higher energies, absorption is negligible, but reflection becomes important which is considered to be fairly constant. At the highest energies, changes in the cutoff energy will greatly affect the variability.  Both \citet{Shimizu_2013} and \citet{Soldi_2014} found that the variability strength over the broad 2--10 keV and 14--150 keV energy ranges are consistent with being equal with even a hint it is stronger at higher energies. This would argue against a constant reflection dominated spectrum in the 14--150 keV range. However these comparisons were based on extrapolating the 2--10 keV PSD to the low frequencies covered by \bat\ which could introduce large uncertainties. Further, the comparisons are over different epochs. With \nustar, we can construct PSDs as well as calculate $\sigma^2_{\rm XS}$ over the same timescales for different energy ranges that cover the same points in time.