Emission Measure Distributions: A Tutorial

Nancy S. Brickhouse

Harvard-Smithsonian Center for Astrophysics

• From Spectral Lines to Emission Measures

• Emission Measure Distributions of Different Stars

• Hot Research Questions

Coronal Structure

Coronal Abundances

Coronal heating: flares and nanoflares

New England Space ScienceCambridge, MA March 1, 2006

We use UV, EUV, and X-ray Lines from log T = 4.0 to 8.0

Chandra

From Spectral Lines to Emission Measure

Line Flux = ∑ ε (T) EM(T) / (4 π R2), where

R is the distance,

EM (T) = ∫ Ne NH dV is the emission measure, and

ε (T) depends on a lot of atomic physics, e.g.

ionization and recombination rates collisional excitation rates radiative decay rates

AND we make a number of assumptions, such as negligible optical depth collisional ionization equilibrium

Emission Measure Distributions for Different Stars

I .Understanding Coronal StructureRotation and ActivityEvolution

Sun (G2 V)Yohkoh Image

Capella (G8 III + G1 III);Expanding Loops?

Hot Research Questions

Chandra Gratings

Capella

Electron Density Determination

•Compelling evidence for high density, small emitting region(s)

•Multiple pressures in the system

Lower Pressure; L=.02 R*

High Pressure; L=.003 R*

II. Abundances: Continuum and Line Modeling

HR 1099High Neon AbundanceAn Inverse FIP Effect?

Hot Research Questions

Hot Research QuestionsIII. Coronal heating: flares

> 1 day flare with exponential decay

Eclipse gives the extent of the flare loop

Algol

Hot Research Topics

III. Coronal heating: nanoflares

Discrepancies are not explained by: atomic rate uncertainties calibration uncertainties absorption time variability

IEUV ΩEUV [Te]

—— = ———— exp (-ΔE/kTe)

IX-ray ΩX-ray[Te]

6 MK EMD peak

Breaking the Assumptions of Emission Measure Distribution Analysis

We consider episodic heating (nanoflares) with:

- heat input to the chromosphere

- adiabatic expansion with rapid cooling.

We calculate the time-dependent ionization state

and obtain the resulting line emission.

Chromosphere

B

Te(0) = 12 MKNe(0) = 4 x 1012 cm-3

~cs

Loop Footpoint

Energetic Beam Te(t) = 5 MK

Ne(t) = 1012 cm-3

Δt~ 1 sec

Chromosphere