1. Emission measure distribution in loops impulsively heated at the footpoints Paola Testa, Giovanni Peres, Fabio Reale Universita’ di Palermo Solar Coronal Loop Workshop — Palermo 9/3/2004

2. Rationale Solar Coronal Loop Workshop — Palermo 9/3/2004  GENERAL PROBLEMS  OBSERVATIONAL EVIDENCE  CORONAL LOOPS MODELS :  standard hydrostatic models vs. observations need for improved models need for improved models  hydrodynamic model with footpoint heating

3. GENERAL PROBLEMS: spatial and thermal structuring, heating, dynamic properties of solar and stellar coronae DIAGNOSTIC TOOLS: Solar Coronal Loop Workshop — Palermo 9/3/2004  SOLAR CORONA : high spatial and temporal resolution, spectral information  STELLAR CORONAE : X-ray spectral coverage with high spectral resolution

4. Coronal Loops Loops are basic components of the solar corona Coronal Loops Loops are basic components of the solar corona Solar Coronal Loop Workshop — Palermo 9/3/2004 development of loop models: development of loop models: e.g. Rosner et al. 1978, Vesecky et al. 1979, Serio et al. 1981 TRACE 171Å Yohkoh/SXT

5. Coronal Loops Loops are basic components of the solar corona Coronal Loops Loops are basic components of the solar corona Solar Coronal Loop Workshop — Palermo 9/3/2004 apparent disagreement mostly with EUV observations (TRACE, SoHO) : apparent disagreement mostly with EUV observations (TRACE, SoHO) : e.g. Aschwanden et al. 2000,2001, Winebarger et al. 2002, Warren et al. 2003 location of heating? : location of heating? : e.g. Priest et al. 2000, Aschwanden 2001, Reale 2002

6. Coronal Loops Loops are basic components of the solar corona Coronal Loops Loops are basic components of the solar corona Solar Coronal Loop Workshop — Palermo 9/3/2004 how are active stars structured? how are active stars structured? can simple loop modelsexplain the emission from active stars? can simple loop models explain the emission from active stars? solar analogy for interpreting stellar coronae ?

7. Coronal Loops in Stellar Coronae? Coronal Loops in Stellar Coronae? Solar Coronal Loop Workshop — Palermo 9/3/2004 Lack of spatial resolution we must resort to indirect means for comparing properties of stellar coronal structures with solar loops spectral observations : high resolution EUV (EUVE) and X-ray spectra (Chandra, XMM-Newton) Emission Measure Distribution EM(T) =   T n e 2 (T) dV

8. Coronal Loops in Stellar Coronae? Coronal Loops in Stellar Coronae? Solar Coronal Loop Workshop — Palermo 9/3/2004 EM(T) expected for hydrostatic loop models  T 3/2 however EM(T) derived from observations are steeper and with bumps, i.e. large amounts of almost isothermal plasma Scelsi et al. (2004) 31 Com e.g.EM(T) of 31Com from XMM spectra

9. New Loop Models? New Loop Models? Solar Coronal Loop Workshop — Palermo 9/3/2004 can footpoint heating yield loops with characteristics compatible with observations? Problem: INSTABILITY ( e.g. Serio et al.1981 ) dynamic loops since static solutions do not exist for heating concentrated at the footpoints how do EM(T) change with characteristics of heating? how do EM(T) change with characteristics of heating?

10. Loop Model Solar Coronal Loop Workshop — Palermo 9/3/2004 1-D hydrodynamic loop model symmetric equations solved for half loop uniform cross-section footpoint heated by periodic heat pulses Palermo-Harvard code (Peres et al.,1982; Betta et al.,1997) consistently solves the time-dependent density, momentum and energy equations for the plasma confined by the magnetic field

11. Loop Model Solar Coronal Loop Workshop — Palermo 9/3/2004 INITIAL CONDITIONS: solutions of hydrostatic loop model (Serio et al. 1981) HEATING FUNCTION: satisfy the scaling laws p 0 ~ (T max /1.4·10 3 ) 3 ·1/L E 0 ~ 10 5 p 0 7/6 ·L -5/6 E H (s,t) = E H (s)·E H (t) E H (s) = H 0 ·e -(s-s 0 ) 2 /2  2  spatial distribution :  temporal distribution : periodic pulses with duty cycle 10%  intensity of heating scaled from the static model  = L/3, L/5, L/10

12. Set of simulations [MK] [dyn/cm 2 ] [erg cm -3 s -1 ] [s] T max p 0 E 0  cool Initial Conditions 0.4513 ~ 2200 303610 ~ 1200 Solar Coronal Loop Workshop — Palermo 9/3/2004

13. Set of simulations Solar Coronal Loop Workshop — Palermo 9/3/2004 Heat Pulses  cool /4,  cool /2 E 0,4 E 0 L/3,L/5,L/1010000 5000  H  t run [s]  cool /4,  cool /2 E 0,4 E 0 L/3,L/5,L/10

14. Evolution of footpoint heated loops Constant heating Solar Coronal Loop Workshop — Palermo 9/3/2004

15. Evolution of footpoint heated loops Impulsive heating Solar Coronal Loop Workshop — Palermo 9/3/2004

16. Evolution of footpoint heated loops Temperature and Density at loop apex Solar Coronal Loop Workshop — Palermo 9/3/2004

17. Emission measure distribution Solar Coronal Loop Workshop — Palermo 9/3/2004

18. Emission measure distribution: models vs. observations Solar Coronal Loop Workshop — Palermo 9/3/2004

19. Conclusions Conclusions Solar Coronal Loop Workshop — Palermo 9/3/2004

20. Loop Model Solar Coronal Loop Workshop — Palermo 9/3/2004 adaptive grid initial model atmosphere uses Vernazza, Avrett and Loeser (1980) to extend the S81 static model to chromospheric temperatures  effective plasma viscosity  fractional ionization n e /n H  hydrogen ionization potential