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Statistical determination of chromospheric density structure

using RHESSI flares

Pascal Saint-HilaireSpace Sciences Lab, UC Berkeley

RHESSI WorkshopGenova, 2009/09/02

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Sato, 2005: (similar to Matsushita et al., 1992)

(L:14–23,M1:23–33, M2:33–53, H:53–93 keV)

L-M1: 460 ± 40 kmL–M2: 880 ± 90 kmL-H: 930 ± 150 km

Aschwanden, 2002:

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DATA:

• Visibilities from 830 RHESSI flares (took all flares “imageable above 25 keV”, as per Jim McTiernan’s “official RHESSI flare list”)

• SC 3-9, energy bins from 4-100 keV• Found position at different energies by forward

fitting the visibilities: his_vis_fwdfit.pro• No big difference if taking only events >50 keV

or other SC combinations. Better with longer accumulations (1-3 mins)

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Average height differences:

Average altitude of emission at energy hν, compared to altitude of 35 keV emission.

METHOD:• Assume footpoints emission at different energies extend radially• Choose two energies• Plot altitude differences r vs. altitude r for all flares (projected)• Obtain slope s, h = s RS

• Repeat for any position-energy pairs of data

r

r [RS] Thermal contamination

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dz

d

Kdz

dNzn

)(

For injected power-law of electrons in steeply increasing density gradients: Most of the emission at energy is emitted where the electrons have traveled a column density N≈ 2/2K (Brown, 1972; Brown et al., 2002; Xu et al., 2008)”. There is a dependence on .

90 keV

40 keV

10 keV

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CICM (H)VAL-C

Aschwanden et al (2002)

Href (35 keV)≈ 1.8 Mm

above photosphere

Comparisons with a few models:

•Arbitrary shift in the X-direction. •Last points to the right : ~15-20 keV: contamination by thermal plasma•Points on the left: energies > 80 keV: fewer statistics•Assumed uniform target ionization! High-energy emissions should actually yield ~2.8 times higher densities…It’s a fitting game…

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Forward-fitting attempts:

1. Double exponentials (0% ionized at low altitude, 100% ionized at higher altitude)

2. Assuming CICM (Caltech Irreference Chromospheric Model, Ewel et al., 1993) is “the truth” (!), trying to determine at which height the ionization level (suddenly) changes…

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Fitting double exponentials:

CICM (H)VAL-C (H)

Fit

Gabriel Corona, models A & D

HIGHLOW HhHIGH

HhLOW enen

hn //

8.2)(

hREF = 0.69 +/- 0.43 @ 35 keVhacc = 8.6 +/- 4.3; nacc = (1.3 +/- 2.2) x1010 cm-3 (!!)

Scale heights: HHIGH= 1.5 +/- 1.8 Mm; HLOW= 0.11 +/- 0.06 Mm

Additional pt

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Fitting step ionization:

Fit

VAL-C (H)

CICM (H)

h* = 1.38 +/- 0.09 Mm (at E*≈45 keV) (height of ionization change)

hacc = 27.3 +/- 61.3 Mm (acceleration height)

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Conclusions:

• Used 800+ RHESSI flares to statistically study chromospheric densities

• Double-exponential chromospheric fittings:– h35 keV = 0.7 +/- 0.4 Mm; hacc= 8.6 +/- 4.3 Mm– HLOW= 0.11 +/- 0.06 Mm, HHIGH ≈ 1 Mm

• Step ionization fitting: – h*=1.38 +/- 0.09 Mm

• Difficult to trust results from models with more than a few parameters: error bars still rather large

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Type III radio burst density (with the Nancay Radioheliograph, 1998):

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Density structure using dm radio bursts (preliminary):

•Same method•12’000 radio bursts over 10 years•164-432 MHz•νp ≈ 9000 ne

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Forward-fitting an exponential atmosphere: Scale height H = 95.3 +/- 1.2 Mm

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Statistical approach: data from 830 flares…(inspired from Matsushita et al., 1992)

cossin)( 11 rhX

cossin12 hXXX

cossin)( 22 rhX

SR

h

r

h

X

X

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•(X1,Y1) position of source at hν1 (e.g. arcsecs from sun center)•(X2,Y2) position of source at hν2

•Assume both sources are radially distributed above solar photosphere

Slope yields height difference.Tilt of magnetic field (and other) effects should average out!!

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1. Step ionization height(assuming CICM nH model)

“Ionization changes from 100% to 0% at an altitude of ~1.34 Mm”

CICM nH

CICM ne

FAL-P

Gabriel

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1. Step ionization height(100 MC runs)

h* = 1.38 +/- 0.09 Mm (height of step ionization change, E*≈45 keV)hacc = 27.3 +/- 61.3 Mm, i.e. is unreliable (height of acceleration region)

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2. Double exponential atmosphere(low: neutral; high: 100% ionized)

hREF = 0.8 @ 35 keVhacc = 6.2 Mm ; nacc = 2.9 x 1010 cm-3

Scale heights: HHIGH= 1.0 Mm; HLOW=126 km (Kontar et al., 2008: 140 +/- 30)

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2. Double exponential atmosphere(low: neutral; high: 100% ionized)

hREF = 0.69 +/- 0.43 @ 35 keVhacc = 8.6 +/- 4.3; nacc = (1.3 +/- 2.2) x1010 cm-3 (!!)

Scale heights: HHIGH= 1.5 +/- 1.8 Mm; HLOW= 0.11 +/- 0.06 Mm…not really enough reliable low-E points to determine well high altitude exp characteristics

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Adding low-energy points leads to problems… (as expected).

(nice fit, though…)

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“For a steep (power-law) accelerated electron spectrum propagating through an increasingly denser plasma, there is a peak in emission at energy hν= located at column density N ≈ 2/K. N is the column density required to stop electrons of initial energy .”(K actually varies with ionization level and with : see e.g. Kontar et al., 2002, Xu et al., 2008)

*1 keV

3 keV

10 keV

20 keV

50 keV

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Aschwanden et al., 2002:

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Average altitude of emission at energy hν, compared to altitude emission at 35 keV.

Contamination from thermal emission in loops.(probably up to 30 keV…)

dz

d

Kdz

dNzn

)(

“Direct derivation or inversion”(assumes uniform ionization, here)

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Direct derivation (100% ionization):

FAL model P

CICM radio mm limb

Gabriel corona, models A & D

My new measurements!

•Arbitrary shift in the X-direction. •Last points to the right : ~15-20 keV: contamination by thermal plasma•Points on the left: energies > 100 keV: fewer statistics•Assumed uniform target ionization! High-energy emissions should actually yield ~2.8 times higher densities…It’s a fitting game…