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Spectrum Analysis

By coordinating multiple frequency observation, we may dervive the spectrum of the emission. The obtained variable is $\alpha$ whose definition is

\begin{displaymath}
F_{\nu} \propto {\nu}^{\alpha}.
\end{displaymath}

In real, $\alpha$ is not uniform over the frequencies. But the spectrum in microwave range is approximately fitted by the fucntion in the form :
\begin{displaymath}
F_{\nu} = \widehat{F_{\nu}}
\left(\frac{\nu}{\widehat{\nu}}\...
... tn}}
& \mbox{for $\nu \gg \widehat{\nu}$}
\end{array}\right.
\end{displaymath} (1)

Here are 4 fitting parameters: $\widehat{\nu}$ is turn-over frequency, $\widehat{F_{\nu}}$ is turn-over flux density, $\alpha_{\rm tk}$ is power index of low frequency side (optically thick side) and $\alpha_{\rm tn}$ is power index of high frequency side (optically thin side), respectively. The procedures are as follows: IDL> day='2000-4-8'
IDL> norp_rd_dat,day,mvd,tim,fi,fv,freq $<$CR$>$
IDL> norp_rd_avg,day,timavg,fiavg,fvavg $<$CR$>$
IDL> for m=0,6 do fi(m,*)=fi(m,*)-fiavg(m) $<$CR$>$
IDL> norp_alpha,freq,fi,mvd,mvdfit,alpha_tk,alpha_tn,freqpk,fluxpk $<$CR$>$
After subtracting the pre-flare flux levels (here daily averages are used), the flare fluxes are given to the IDL procedure norp_alpha. mvdfit is an array including the values of unity (1) for valid data or zero (0) for non-valid data.


Note: The fitting will usually fail in the simple manner shown here. We need (1) to take longer intergation time for getting better S/N ratio and (2) to remove the inadequate data for fitting (because, say, the emission in that frequency is not due to gyrosynchrotron). See 3.8.3 for better procedures.



Subsections
next up previous contents
Next: Optically-Thin Non-Thermal Gyrosynchrotron Emission Up: Analysis Previous: Plot   Contents
NRO Operator
2000-12-21