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Numerical simulations of solar flares are often used to produce synthetic GOES light curves that can be compared against data (e.g., Warren 2006; Reep & Toriumi 2017; Zhu et al. 2018). There are a few different methods that have been used in the past to synthesize these light curves, but the literature does not generally discuss advantages and disadvantages of each method. In this note, we briefly discuss three different methods that can be used.
First, one can use a temperature and emission measure (EM) averaged across the coronal section of a loop. The SolarSoft IDL routine "goes_fluxes" then can be used to calculate the emission in both channels for any GOES satellite given the temperature and EM (SunPy has similar routines). In 0D models like EBTEL (Klimchuk et al. 2008) and ebtel++ (Barnes et al. 2016), this method is the only option because the model only solves for the average values. In higher dimensional models, the temperature and EM can be averaged directly before synthesizing the light curves. While this method is quick and relatively easy to implement, it is often inaccurate.
Second, one can sum the emission across many grid cells, as if each had its own light curve. For example, in a 1D model, the EM can be calculated as n2AΔs where Δs is the width of a grid cell, A the cross-section, and n the number density. The routine "goes_fluxes" can then be run on each individual grid cell before summing into a composite light curve. There are caveats with this method: a full spectrum is not calculated, rather the emission is based on look-up tables of GOES channel ratio versus temperature; the routine is only valid at temperatures >1 MK, so emission from low temperature-high EM must be ignored; and, at the time of writing, the routine does not use the most up-to-date version of CHIANTI for the atomic physics. This method requires more computation than the previous one, but produces more accurate results.
Third, one can sum the emission across all grid cells and this time use a full spectrum calculation. For example, the CHIANTI software (Del Zanna et al. 2015) has a routine "isothermal" which can calculate the (optically thin) spectrum at X-ray wavelengths given a temperature and EM for an isothermal plasma (for speed, we recommend that look-up tables be created rather than calling "isothermal" on each grid cell). Within a numerical grid cell, the plasma should be close to isothermal so this method is valid. There are therefore four steps: calculate the EM for each grid cell, calculate the X-ray spectrum for each grid cell, sum the emission across all grid cells, and finally convolve the emission with the detector response for the appropriate GOES satellite (note: "goes_fluxes" automatically convolves the detector response). This method requires significantly more computation, but should be the most accurate.
To demonstrate how the methods compare, we show an example of the light curves synthesized with the three different methods (making the bad assumption that a flare has only one loop since we are not worried about the physics at the moment). We use one of the simulations from Reep & Toriumi (2017), performed with the HYDRAD code (Bradshaw & Cargill 2013), with a total loop length of 50 Mm, heated by a strong electron beam to flare-like temperatures and densities. We assume a cross-section of 1017 cm2, uniform across the loop. We use photospheric abundances. In the coronal-averaged case, we average over 90% of the loop (omitting the first and last 2.5 Mm of the loop).
Figure 1 shows the light curves calculated with each method (method 1 solid line, method 2 dotted, method 3 dashed). From the figure, it is clear that all the methods are of comparable magnitude, though the first method misses some features such as the initial rise in temperature. The timing of the peak emission is different, as well. Methods 2 and 3 produce similar curves with all the same features, and agree almost perfectly in the impulsive phase.
Figure 1. The GOES light curves synthesized with the three methods from the same numerical simulation. Method 1 is shown with a solid line, method 2 dotted, method 3 dashed. All three methods are comparable, though the first misses some features in the impulsive phase.
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In summary, there are a few viable methods to synthesize GOES emission from numerical simulations. Given the option, summing over grid cells should be preferred to using a coronal average. There is a trade-off of accuracy versus computation speed, but all three methods produce sensible results.