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Using DEM models to test for 2 thermal components in 23-Jul-2002 flare

Using DEM models to test for 2 thermal components in 23-Jul-2002 flare. J. McTiernan 26-Aug-2009. A.Caspi: Fit spectra for July 23 flare, using detector 4, with improved cal. results, which he can explain in a future meeting. Fits include lines, nonthermal component, 2 thermal components.

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Using DEM models to test for 2 thermal components in 23-Jul-2002 flare

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  1. Using DEM models to test for 2 thermal components in 23-Jul-2002 flare J. McTiernan 26-Aug-2009

  2. A.Caspi: Fit spectra for July 23 flare, using detector 4, with improved cal. results, which he can explain in a future meeting. Fits include lines, nonthermal component, 2 thermal components. Spectra for thermal continuum consistently fit well to two components, and those components are well-behaved in time. Low T component from 14 to 24 MK, high T component from 22 to 40 MK. The question is, can a DEM calculation resolve two components? We can test this. Motivation:

  3. Calculations all use a temperature response matrix obtained by integrating fluxes from CHIANTI_KEV over DRM’s from ospex object. Given EM(T), model counts in channel i: mi =Ri(T)#[EM(T)*dT] Gain offset, and pulse-pileup are accounted for by fixing the model count rate before comparison with obs. data. Uses Amoeba function for minimization of χ2. Fit is to expected continuum thermal component – Observed counts spectrum minus the expected counts spectra for nonthermal and lines. DEM calculation: Note that these curves are for Att_state=0, and are shown for example purposes only, and were not used for the fits.

  4. Methods for DEM calculation: 1 • NTEEMFIT: The DEM is a series of N delta-functions in T. This is similar to the single temperature or two-temperature fit from SPEX, but calculated differently, and has the option of more than two components. • First try 1 component, obtain reduced χ2, defined as: • Next try 2 components, compare new value to old one, if it’s smaller, keep it. • Keep adding components until you get a minimum value. • For this case we hope that we get two components with T and EM close to the SPEX values. (It turns out to work well.) This provides a sanity check for the T response curves.

  5. Methods for DEM calculation: 2 • NBINFIT: The DEM is a histogram with the EM defined in N temperature bins. Here’s a sample plot. • First try a small number of bins, obtain reduced χ2, defined as: • Next add a bin, compare new value to old one, if it’s smaller, keep it. • Keep adding bins until you get a minimum value. • For this case we hope that we get two bins with width of a few MK, separated by 20 MK or so with T and EM close to the SPEX values.

  6. Methods for DEM calculation: 3 • NPLFIT: The DEM is an N-component power law in T. • First try a small number of PL components (usually 1, 2 or 3), obtain reduced χ2, defined as: • Next add a PL, compare new value to old one, if it’s smaller, keep it. • Keep adding PL’s until you get a minimum value. • For this case we also hope that we get two peaks separated by 20 MK or so with T and EM close to the SPEX values. From tests for 2008 AGU poster, we expect that this should work.

  7. Nbin fit for Interval 17: Nteem fit: Black +’s from SPEX, red +’s from Nteem fit. Good agreement, ~1 MK for low T, < 1MK for high T. Also 2 T’s fit better than 1 T or 3T’s. • Nbin fit not bad, this sort of resolves into two T components. But … • Χ2 for this DEM is about twice the value for the Nteem model. • Also (next slide) final results seem to be dependent on initial model input. • This suggests that there are some systematic errors, and that the fit is finding local minimum.

  8. Another Nbin fit for Interval 17: • This also sort of resolves into two T components. But … • Here the initial condition was the Nteem fit (Actually 2 1MK bins with the EM calculated from that fit.) It *should* have stayed there.

  9. Npl fit for interval 17: • Again a hint of two components. (Error bars aren’t shown here, but tend to get very large for T<10 MK.) • Again a (smaller) dependence on the initial model. • Again a higher χ2 than the Nteem fit. • Systematically lower high T peak.

  10. Residuals: (Full Spectrum)

  11. Conclusions: • The Nteem fit procedure recovers the two T components from the SPEX fits pretty well, giving confidence in T response calculations. (Note that this is true for all time intervals) • The Nbin fit performs less well – there seem to be some systematic effects that need to be dealt with, and it looks as if fit procedure is stuck near a local minimum. • The Npl fit does show a small second component at high T, but this also looks as if there are some systematic effects. • Future work, use Monte Carlo fitting procedure (very slow in IDL).

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