Homing in on Flare Energy

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Nugget
Number:	223
1st Author:	Hugh Hudson
2nd Author:	Ryan Milligan
Published:	April 14, 2014
Next Nugget:	TBD
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Homing in on Flare Energy

Introduction

We often want to represent the distribution of energy in the spectrum of an astronomical object, such as a solar flare. An energy spectrum can have many representations; two common ones are f_λ (in CGS, with wavelength units) ergs/cm² s A, or F_ν (in SI, with frequency units) W/m² s Hz. Needless to say, a profusion of other forms exists, often tailored to a specific kind of observation, and there is much nuisance involved in making comparisons. In flare physics this now has become very interesting, owing to the big breakthrough in Ref. [1], in which the total radiant energy of a solar flare could be determined bolometrically. Now the question is, where within the spectral energy distribution does a flare choose to put this energy? With modern broadband data such as those from [SDO], we are now homing in on the answer to this long-standing question.

This Nugget explains a frequently-used stratagem for a quick visual overview of heterogeneous data. The basic trick is just to note that the energy, in whatever units, is the simple integral of the spectral energy (ie, per unit bandwidth). Thus f_λdλ and F_νd&nu: are both simply energy or power, with suitable adjustments between the cgs and MKS (or other) representations. We realize that everybody understands this, and yet the Nuggeteers here have often confused themselves on this score, hence the Nugget.

Why λf_λ?

Because of Equation (1) here. This shows that if one plots this quantity on a linear-logarithmic basis, equal areas must have equal energies (or power levels, if the quantities are differential in time as well as bandpass). One can mix and match any spectral form here and obtain a correctrepresentation.