# Sparse Bayesian Inference and the Temperature Structure of the Solar Corona

## Abstract

Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are “inverted” to determine the distribution of plasma temperatures along the line of sight. This inversion is ill posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of the solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions.

- Authors:

- Space Science Division, Naval Research Laboratory, Washington, DC 20375 (United States)
- Materials Science and Technology Division, Naval Research Laboratory, Washington, DC 20375 (United States)
- Naval Center for Space Technology, Naval Research Laboratory, Washington, DC 20375 (United States)

- Publication Date:

- OSTI Identifier:
- 22663762

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 836; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DISTRIBUTION; ELECTRON TEMPERATURE; EMISSION; ION TEMPERATURE; PLASMA; SOLAR CORONA; SUN; TEMPERATURE DISTRIBUTION

### Citation Formats

```
Warren, Harry P., Byers, Jeff M., and Crump, Nicholas A..
```*Sparse Bayesian Inference and the Temperature Structure of the Solar Corona*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA5C34.

```
Warren, Harry P., Byers, Jeff M., & Crump, Nicholas A..
```*Sparse Bayesian Inference and the Temperature Structure of the Solar Corona*. United States. doi:10.3847/1538-4357/AA5C34.

```
Warren, Harry P., Byers, Jeff M., and Crump, Nicholas A.. Mon .
"Sparse Bayesian Inference and the Temperature Structure of the Solar Corona". United States.
doi:10.3847/1538-4357/AA5C34.
```

```
@article{osti_22663762,
```

title = {Sparse Bayesian Inference and the Temperature Structure of the Solar Corona},

author = {Warren, Harry P. and Byers, Jeff M. and Crump, Nicholas A.},

abstractNote = {Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are “inverted” to determine the distribution of plasma temperatures along the line of sight. This inversion is ill posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of the solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions.},

doi = {10.3847/1538-4357/AA5C34},

journal = {Astrophysical Journal},

number = 2,

volume = 836,

place = {United States},

year = {Mon Feb 20 00:00:00 EST 2017},

month = {Mon Feb 20 00:00:00 EST 2017}

}