1. Detailed Plasma and Fluorescence Diagnostics of a Stellar X-Ray Flare Paola Testa (1) Fabio Reale (2), Jeremy Drake (3), Barbara Ercolano (3), David Huenemoerder (1), David Garcia-Alvarez (3,4) 1 MIT, 2 Universita’ di Palermo (Italy), 3 SAO, 4 Imperial College July 11 2007 - CXC X-ray spectroscopy workshop

2. Rationale X-ray activity in evolved intermediate mass stars Coronal structuring Physics of stellar flares Plasma diagnostics, and geometry diagnostics: –hydrodynamic loop modeling (Testa et al. 2007, ApJ, 663) –fluorescence emission July 11 2007 - CXC X-ray spectroscopy workshop HETGS observation of the G1 III giant HR 9024 Hertzsprung gap giant, 3M , 13R , peak Lx~10 32 ergs/s Diagnostic Tools: Comparison of results from the two independent analyses Motivations: (see also Ayres et al 2007, Nordon & Behar 2006)

3. HETGS Spectrum July 11 2007 - CXC X-ray spectroscopy workshop HR 9024 : Hertzsprung gap giant, 3M , 13R , peak Lx~10 32 ergs/s

4. Light curve and hardness ratio July 11 2007 - CXC X-ray spectroscopy workshop HR 9024 : Hertzsprung gap giant, 3M , 13R , peak Lx~10 32 ergs/s

5. X-ray activity of intermediate-mass giants HR 9024 : Hertzsprung gap giant, 3M , 13R , Lx ~ 10 32 ergs/s Evolved intermediate mass star: what are the characteristics of the X-ray production mechanisms? How is the corona structured (typical size, filling factors, …)? (e.g., Ayres et al. 1998, Ayres et al. 2007) These giants are thought to develop a dynamo when they enter the convective region of the H-R diagram, also given their typical fast rotation in MS (when they are non-coronal late-B/early-A dwarfs) Variability: flares are very unusual in these massive evolved giants July 11 2007 - CXC X-ray spectroscopy workshop

6. Hydrodynamic Modeling For the hydrodynamic modeling we use information mainly from the continuum that is strong, and it probes the hot flaring plasma: we derive T and EM by fitting the continuum in line-free regions (according to both APED and CHIANTI ) Loop Model: 1.start with an educated guess for the parameters 2.synthesize the HETG spectrum of the solution 3.repeat the analysis carried out on the observed spectrum and compare the same quantities 4.refine the model if needed July 11 2007 - CXC X-ray spectroscopy workshop

7. MEG cts/s T EM T vs. n Hydrodynamic Modeling (Testa et al. 2007, ApJ, 663, 1232)

8. Model parameters: loop semi-length L = 5 · 10 11 cm ~ R  /2, as in normal coronae cross-section radius r ~ 4.5 · 10 10 cm, i.e. aspect ratio r/L~0.1 as in typical solar loops impulsive heating ( 15 ks ; starting 8 ks before the beginning of the observation) at the footpoints; volumetric heating ~ 4 erg/cm 3 /s, heating rate ~ 10 33 erg/s Hydrodynamic Modeling July 11 2007 - CXC X-ray spectroscopy workshop

9. Cross-check of results: light curves in strong spectral features: Fe XXV, Si XIV, Mg XII Hydrodynamic Modeling July 11 2007 - CXC X-ray spectroscopy workshop (Testa et al. 2007, ApJ)

10. Cross-check of results: EM(T) (flare) Hydrodynamic Modeling July 11 2007 - CXC X-ray spectroscopy workshop (Testa et al. 2007, ApJ)

11. Cross-check of results: cross-section radius - we derive estimates from the normalization of different light curves: (a) integrated MEG counts (r ~ 4.9· 10 10 cm), (b) EM from continuum (r ~ 4.3 · 10 10 cm), (c) single spectral features (r ~ 4.8 · 10 10 cm); they all agree with each other within a 15% Hydrodynamic Modeling July 11 2007 - CXC X-ray spectroscopy workshop

12. Geometry Diagnostics from Fluorescence July 11 2007 - CXC X-ray spectroscopy workshop HEG In the HEG spectrum there is evidence of Fe K  fluorescence (1.94Å, 6.4keV) that provides an independent diagnostic for the coronal geometry

13. Geometry Diagnostics from Fluorescence July 11 2007 - CXC X-ray spectroscopy workshop the solid angle subtended by the cold material as seen by the X-ray source h the inclination angle at which the reflecting surface is viewed by the observer  the Fe abundance of the cold material the fluorescence efficiency depends on (e.g., Bai 1979):

14. Geometry Diagnostics from Fluorescence July 11 2007 - CXC X-ray spectroscopy workshop Measured value (  1  ) Prediction from hd model

15. the X-ray characteristics of HR9024 are typical of normal coronae but scaled up to the larger stellar radius HETGS allows for the first time to test HD models predictions for single spectral features: we find very good agreement at least for the hottest feature of Fe XXV the HEG spectrum shows evidence of Fe K  fluorescence emission, and its analysis provides an independent check of the results of the hydrodynamic modeling: the fluorescence efficiency predicted from the HD model is in agreement with the observed one within the uncertainties Results July 11 2007 - CXC X-ray spectroscopy workshop

16. Thank you! July 11 2007 - CXC X-ray spectroscopy workshop

17. Hydrodynamic Modeling Cross-check of results: light curves in strong spectral features: Fe XXV, Si XIV, Mg XII

18. t =0-10ks t =10-15ks t =15-30ks t =30-45ks Hydrodynamic Modeling Comparison of MEG observed spectrum with predictions of loop model

19. Hydrodynamic Modeling Comparison of MEG observed spectrum with predictions of loop model t=0-10ks t=10-15ks t=15-30ks t=30-45ks

20. Hydrodynamic Modeling Apex T Apex n e Apex p max v

21. Hydrodynamic Modeling