Spectral gradient of the thermal millimetre continuum as a diagnostic for optical thickness in the solar atmosphere

Rodger, A.S. and Labrosse, N. (2018) Spectral gradient of the thermal millimetre continuum as a diagnostic for optical thickness in the solar atmosphere. Astronomy and Astrophysics, 617, L6. (doi:10.1051/0004-6361/201833848)

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Abstract

Aims. In this Letter we aim to show how the gradient of the thermal millimetre continuum spectrum, as emitted from the quiet solar atmosphere, may be used as a diagnostic for the optical thickness regime at the centre of the observing frequency band. Methods. We show the theoretical derivation of the gradient of the millimetre continuum for both logarithmic- and linear-scale spectra. We compare this expression with the empirical relationship between the slope of the millimetre continuum spectrum and the plasma optical thickness computed from both isothermal and multi-thermal two-dimensional cylindrical radiative transfer models. Results. It is found that the logarithmic-scale spectral gradient provides a clear diagnostic for the optical thickness regime for both isothermal and multi-thermal plasmas, provided that a suitable correction is made for a non-constant gaunt factor over the frequency band. For the use of observers we present values for this correction at all ALMA bands and at a wide range of electron temperatures. Conclusions. We find that the spectral gradient can be used to find (a) whether the source is fully optically thin, (b) the optical thickness of the source if it lies within the transitional regime between optically thin and thick plasma (τ ≈ 10−1−101), or (c) whether the source is fully optically thick for an isothermal plasma. A multi-thermal plasma will act the same as an isothermal plasma for case (a), however, the transitional regime will only extend from τ ≈ 10−1 to τ ≈ 100. Above τ = 1 the slope of the continuum will depend increasingly on the temperature gradient, as well as the optical thickness, reducing the reliability of the diagnostic.

Item Type:Articles (Letter)
Additional Information:AR acknowledges support from a STFC studentship ST/N504075/1. NL acknowledges support from STFC grant ST/P000533/1. The authors would like to acknowledge the members of ISSI team number 374 “Solving the Prominence Paradox” led by NL for helpful discussion around the results and applications presented in this study.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Labrosse, Dr Nicolas and RODGER, ANDREW
Authors: Rodger, A.S., and Labrosse, N.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Astronomy and Astrophysics
Publisher:EDP Sciences
ISSN:0004-6361
ISSN (Online):1432-0746
Published Online:05 September 2018
Copyright Holders:Copyright © 2018 ESO
First Published:First published in Astronomy and Astrophysics 617:L6
Publisher Policy:Reproduced under a Creative Commons License
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
714155STFC DTPMartin HendryScience & Technology Facilities Council (STFC)ST/N504075/1S&E P&A - PHYSICS & ASTRONOMY
728901Consolidated Grant in Solar PhysicsLyndsay FletcherScience & Technology Facilities Council (STFC)ST/P000533/1S&E P&A - PHYSICS & ASTRONOMY