Emission measure distribution from plasma modeling Fabio Reale Dipartimento di Scienze Fisiche & Astronomiche Università di Palermo, Italy E-mail: reale@astropa.unipa.it

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

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

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

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

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)

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)

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

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

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

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

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

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

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

Modeling flares in non-confined coronae Heating rate: 10 erg/cm³/s Heating width: 10000 km Duration: 100 s Tmax~12 MK Density and Temperature modelled evolution Density Temperature Heating position Simulation time lapse: 200 s

Quantitative evolution

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

Non-confined vs confined flares: Line profile

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

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!

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

Light curve segmentation

The data: the high resolution spectra O VII Ne IX

The data: the low resolution spectra

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

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

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

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

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

The Bastille Day flare: TRACE observation

The scenario

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

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

THE (OLD) END

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

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

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)

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?

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

The specific model

Loop modeling Heating at left (northern) footpoint

Loop modeling Uniform heating: symmetric evolution

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

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

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

THE (REAL) END

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