Spectroscopic Study of Heating Distributions and Mechanisms Using Hinode/EIS

Abstract Heating distributions along coronal loops are obtained from spectroscopic data with the Hinode/EUV Imaging Spectrometer. The loop half-lengths L half are in the range of 24–107 Mm for our analysis of 18 loops. By using the analytical approximations to 1D hydrostatic numerical calculations of electron temperature T e ( s ) and density distributions n e ( s ) along a loop, the heating distribution that decreases with a heating scale height s H toward the loop top with a heating rate E 0 at the height of the transition region is estimated by applying a Bayesian analysis to the observed T e ( s ) and n e ( s ) derived by emission line ratios. We obtain s H = 10 ± 4 Mm increasing with L half , E 0 = 10 −2.0±0.5 erg cm −3 s −1 decreasing with L half , and the heating flux F H = 10 7.0±0.4 erg cm −2 s −1 . These loops show s H / L half = 0.21 ± 0.07, suggesting the concentration of the heating near the lower part. Compared to the previous study using imaging data, s H is comparable, while E 0 and F H are about an order of magnitude larger. We find that using the imaging data leads to the underestimation of the electron density and consequently the underestimation of E 0 and F H . We examine heating mechanisms using the power-law relation for F H , the field strength B base and L half : <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>base</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:msubsup> <mml:msubsup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>half</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> . We find <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>β</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>1.04</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.36</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.18</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.99</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.05</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.04</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , which show that the reconnection heating model is the most plausible.