1. Emission measure distribution from plasma modeling
Fabio Reale
Dipartimento di Scienze Fisiche & Astronomiche
Università di Palermo, Italy

2. Summary Introduction: The concept of loop modeling
EM from modeling nanoflare-heated loops
EM from modeling confined vs non-confined flaring plasma
EM from modeling stellar flares: a flare on Prox Cen

3. The Coronal Loops
Loops are the building blocks of the solar emitting corona
Loops are independent miniatmospheres
Plasma magnetically confined in loops
Plasma moves and transports energy along B
Plasma described as a compressible fluid
1-D description

4. Loop modeling: static loops
Hydrostatic loops:
Uniform heating: scaling laws (Rosner et al. 1978)
Non-uniform heating + pressure scale height (Serio et al. 1981)

5. DEM from static model loops
Hydrostatic loops (Serio et al. 1981):
Uniform heating
Symmetric w/ resp/ apex
Half-length: 2 x 109 cm
Increasing heating rate
DEM
Monotonic
Slope: ~1.5

6. Loop modeling: Transient loops
Time-dependent hydrodynamics 1-D including:
Gravity component along the loop
Optically thin radiative losses
Plasma thermal conduction
Heating function H(s,t)
Thermal viscosity (important in flares, Peres & Reale 1993)
Numerical solution: loop codes (e.g., the Palermo-Harvard code, Peres et al. 1982, Betta et al. 1997).
Input:
Initial atmosphere
Heating function and parameters
Output:
Time-sampled distributions of n,T,p,v along the loop
Extensively used since ’80s for modeling:
solar and stellar flares (e.g. Peres et al. 1987, Reale et al. 1988, and many others) and
loop evolution (e.g., nanoflaring, Peres et al. 1993, loop ignition Reale et al. 2000)

7. EM from flaring loop model
20 MK flare
Heating:
Duration: 180 s
Location: TOP
Palermo-Harvard code
DEM evolution:
High T soon
DEM increases
Self-similar (see hydrostatic loops)

8. Modeling nanoflaring loops (Testa, Peres & Reale, ApJ, 2005)
Starting points:
Loops continuously heated at the footpoints known to be unstable (e.g. Serio et al. 1981)
DEM of active stars shows multiple peaks and the slope is >1.5
Nanoflares candidates as major coronal heating mechanism (e.g., Parker 1988, Cargill 1994)
Question:
Can pulsed heating deposited at the footpoint:
make a loop stable?
Yield a steeper DEM closer to that observed on active stars?
Approach:
Time-dependent loop modeling with heat pulses periodically deposited at the footpoints

9. Modeling nanoflaring loops (Testa, Peres & Reale, ApJ, 2005)
DEM and connection to stellar coronae:
Loop models with nanoflares at the footpoints
Stabilized if heating extended more than 1/5 loop
DEM with a peak, steep on the cool side
Similar to DEM of active stars

10. Loop evolution
DEM and connection to stellar coronae (Testa, Peres, Reale 2005):
Loop models with nanoflares at the footpoints
Stabilized if heating extended more than 1/5 loop
DEM with a peak, steep on the cool side
Similar to DEM of active stars

11. Loop evolution
Temperature and density at the top of the loop: stability vs instability

12. DEM Corona covered by nanoflaring loops Corona covered by static loops
DEM and connection to stellar coronae:
DEM with a peak, steep on the cool side
Similar to DEM of active stars
Corona covered by nanoflaring loops
Corona covered by static loops

13. Modeling non-confined flaring plasma (Reale, Bocchino, Peres 2002, A&A, 383, 952)
Rationale:
Stellar flares typically long (hours to days) and intense
Large loop structures and/or long heating involved
Question:
Can big flares be explained by disruption of “magnetic cage” and evolution in open atmosphere?
Approach:
Modeling a flare event in a non-confined atmosphere

14. Modeling non-confined flaring plasma (Reale, Bocchino, Peres 2002, A&A, 383, 952)
Concept:
Simulating a flare triggered by a heating pulse in a stratified corona
Model:
Time-dependent 2-D hydrodynamics including isotropic thermal conduction
Code:
Improved FCT-2D (Reale et al. 1990),
time-splitted thermal conduction (ADI, Reale 1995),
made parallel with HPF

15. Modeling flares in non-confined coronae
Heating rate: 10 erg/cm³/s
Heating width: km
Duration: 100 s
Tmax~12 MK
Density and Temperature modelled evolution
Density
Temperature
Heating position
Simulation time lapse: 200 s

16. Quantitative evolution

17. Light curves Parameter space explored: Heating intensity
Heating location
Heating width
BKG coronal pressure
Results:
Evaporation in a non-confined corona implies low densities and expanding fronts
Cooling by conduction and decay of expanding fronts is very fast
The expected light curves decay invariably in few minutes
Conclusion: Confinement seems to be required even by intense long-lasting flares
ASCA/SIS light curves
from hydro models
Higher BKG pressure
More intense heating
Longer
heating

18. Non-confined vs confined flares: Line profile

19. Emission measure no horizontal branch Slope ~1
Density-temperature diagram:
no horizontal branch
Slope ~1
DEM: decreasing trend (as the open atmosphere)

20. Loop modeling of a stellar flare (Prox Cen) (Reale, Güdel, Peres, Audard, A&A, 2004)
Rationale:
Solar and stellar flares have similar light curves: flaring loops?
Loop modeling of stellar flares explains many features
Experience in modeling stellar flares with detailed simulations (e.g. Reale et al. 1988)
New generation stellar missions (e.g. XMM-Newton, Chandra) obtain data of higher quality
XMM-Newton observed a flare on Prox Cen very well: more constraints for modeling?
Detailed loop modeling required!

21. The XMM/Newton flare (Reale, Güdel, Peres, Audard, A&A, 2004)
The data (XMM/EPIC):
Very detailed light curve: multiple peaks and decays
Time-resolved spectroscopy
More constraints: one flaring loop is no longer enough!
2 peaks
Multiple decays

22. Light curve segmentation

23. The data: the high resolution spectra
O VII
Ne IX

24. The data: the low resolution spectra

25. Modeling the flare L Loop length Heating function/parameters:
Set-up initial and heating conditions:
Loop length
Heating function/parameters:
Pulse or pulse + exponential decay
Footpoints or corona
Results: time sequence of loop distributions of
Temperature
Density
Velocity L

26. Modeling the flare L Folded spectra Light curve
Synthesize emission in the EPIC band:
Folded spectra
Light curve
Data-like spectral fitting: T, EM L

27. Best model: loop + arcade
First peak and initial decay:
Single flare loop (L= 1010 cm)
Heating:
Pulse at the footpoints
Gradual decay in the corona
Second peak:
Same loop reheated? NO: T should increase again
A second loop is needed:
Length: same
same time and space dependence
delay of 2600s
Arcade

28. Best model: loop + arcade
Results - Animation:
Light curve
1-T fitting: EM, T
Resolved loop emission (XMM/EPIC)

29. Why an arcade? The Bastille Day flare (14 July 2000)
Yokohk/SXT
(Aschwanden & Alexander 2001)
Aschwanden & Alexander 2001
Time (s)
EPIC-PN light curve

30. The Bastille Day flare: TRACE observation

31. The scenario

32. The best-fit model: details
Spectra: data vs model

33. The Emission measure distributions
From the data (Guedel et al. 2004)
From modeling
(time averages,
2 loops)
Polynomial reconstruction
(order 6)
Integral inversion w/
regularization

34. THE (OLD) END

35. Analysis of a brightening coronal loop observed with TRACE (Reale et al. 2000, ApJ, 535, 412 , Reale et al. 2000, ApJ, 535, 423)
The observation (26 June 1998):
171 A filter band
Start time: 13:01 UT
End time: 15:25 UT
213 full frames
Cadence: 30 s (Exposure 23 s)
Six gaps (140 – 568 s)
Region: AR 8253

36. Data analysis: the loop geometry
Total length of the main loop (L4): 2L 1010 cm
Inclination: 60°

37. Data analysis: the loop evolution
Loop initially invisible: empty (e.g. T=50,000 K)
Loop brightening between t=1875 s and t=4044 s (t  2200 s)

38. Questions Location? Spatial distribution? Time evolution?
Can we reproduce this loop brightening with time-dependent single-loop modeling?
Can we constrain the heating function:
Location?
Spatial distribution?
Time evolution?
Can we fit the observation in detail?
Can we obtain further diagnostics?

39. Guideline Loop length and inclination Initial conditions (empty loop)
Data analysis (e.g. loop geometry, emission profiles, light curves)
Constraints on model set up:
Loop length and inclination
Initial conditions (empty loop)
Heating intensity (to reach 1 MK)
Numerical simulations w/ different (guided) assumptions on the heating function location, distribution and evolution
Synthesis of loop emission (folded w/ TRACE 171 A filter response) from density and temperature evolution along the loop
Detailed comparison w/ observations (e.g. emission profiles along the loop)
Constraints on the heating function

40. The specific model

41. Loop modeling
Heating at left (northern) footpoint

42. Loop modeling
Uniform heating: symmetric evolution

43. Loop modeling Constant heating High and then exp. decaying
Heating in the coronal part of the loop (asymmetric):
Constant heating
High and then exp. decaying

44. The result of the modeling
Heating in corona
Heating at the footpoint
Data (loop model format)

45. Implications
This work shows that:
Loop modeling is useful for detailed comparison with observational data
Loop modeling can provide qualitative and quantitative constraints to heating mechanisms

46. THE (REAL) END

47. The concept of forward modeling
Observation:
data analysis
estimate phys. param.
Physical model
Time dependent hydrodynamic 1-D (loop) code L
Model set up:
Initial condition
Heating
Other parameters
Numerical simulations
Plasma emission model
Instrument energy response
Emission synthesis
Comparison w/ observation
Model diagnostics