White Dwarf Spectra (Fun With Spectra)

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White Dwarf Spectra (Fun With Spectra)

White Dwarf spectra are used to calculate log g and model the physical properties of white dwarfs. Below is an example and a detailed analysis of the affects of convection. Using the theory of blackbody radiation, we model white dwarfs, determine their spectra and hypothesize on further projects.

White dwarf spectra are plots of the dispersed starlight over all the wavelengths for which there are significant radiant flux. The star’s spectrum determine the physical properties of that star. On a spectre graph there are two series of troughs in the curves, which are wavelength versus flux. The first is called the Balmer break and the second is the Paschen. These series correspond to the energy levels in a hydrogen atom.

These particular wavelengths push the electron to the next energy level, so the atom absorbs the electron. The Paschen is smaller because it is started at the third energy level. However the Balmer starts at the second level and jumps up from there. These two energy levels make up blackbody radiation. Usually these are observed on a flattened spectrum, like the one below.

White Dwarf Spectra

Our chosen effective temperature is $9000 K$ and our $\log g$, where $g$ is gravity, is 7. Spectrum are, once found, manipulated in this way to reveal the atomic makeup of the star. Or perhaps they reveal the chemical makeup of nebulous dust that the starlight is shining through. This can cause some difficulties in analyzing the data. Spectra of white dwarfs are valuable to many aspects of research.

Our White Dwarf Spectra Project

The big assumption of our research project is that not all of the stars are the same temperature throughout surface. Usually astronomers assume stars are one temperature and then use the Koester Grid. The Koester grid takes $\log g$ and a single temperature to give a spectre graph for that star. However, stars are not a single temperature all over their surface. This means there must be some error when constructing their spectra with assuming one temperature. The overall goal was to find the difference between the spectra produced from a single temperature reading and our model of convection: Gaussian distribution.

Convection causes shifts in the distribution of hot and cold matter throughout the interior of the star. We are assuming that due to convection, there are patches across the surface of a star that are warmer and cooler by a significant amount of degrees. These different patches are not random, but are in such a way that more of the star are the average temperatures, while less of the star is at either of the extreme temperatures. This assumption is standard throughout white dwarf research.

Our White Dwarf Spectra – What We Did

In order to account for this, we created a weighted average. We do not exactly know how convection will affect the spread of the temperature across the surface of the star. So we assume it creates a Gaussian distribution. This creates the mean temperature as the most common temperature on the surface. The mean and the spread determine the temperature at any point on the surface. The mean temperature is determined by the center of the distribution. The spread of the temperature is the standard deviation of the Gaussian distribution.

Last semester, the researchers working on this project did not use a normal distribution, but used a flat distribution across a range of temperatures. This type of model gives all the temperatures equal weight. This was a good start to the calculations, but essentially not a realistic model. Our first step was to use $T_c$, the center temperature, and $T_{\text{sig}}$, the standard deviation, along with $\log g$, to create a Gaussian distribution, or a normal distribution. Ideally, the number of spectra used would be along a continuous range. However in order to work with the Koester Grid, which is discrete, a discrete number would have to be chosen.

White Dwarf Spectra in the Future

Our next project would create a file to begin creating the spectra that would be comparable to a conventionally created spectra graph. Adhering to tradition in this manner would give our findings more weight, and make them world-renown! Thus, we would be able to see more results. We would assume the center temperature, $T_c$, and vary the standard deviation, $T_{\text{sig}}$, in order to find a multitude of spectra and compare them. On the $y$-axis is $T_{\text{fit}}/T_c$; $T_{\text{fit}}$ would be the temperature as conventionally calculated, and $Tc$ would be the center temperature of the gaussian distribution we assumed. Along the $x$-axis is the $T_{\text{sig}}$, the standard deviation of the temperature.

If there were no error in the conventional methods of selecting temperature, the plot would be a straight horizontal line, as $T_{\text{fit}}/T_c$ would be 1. However, what we see is a decreasing curve, suggesting that there are deviations, and that they increase as $T_{\text{sig}}$ increases. So, as the temperatures get more spread out, our ability to create an accurate spectrum for that white dwarf and so to predict the $\log g$, decreases. This would have been our next step, however, our group did not have enough time to complete this.

Had our project finished completely, we would have used multiple temperatures to find the difference in log g between them. This would eliminate the need for a Gaussian spread of temperatures. However, this model of convection is not necessarily the most realistic model of convection on a white dwarf’s surface. There could be other models that would work even better. For example, the Gaussian distribution was more realistic than a flat average. This new manipulation of spectra is an interesting addition to the recognized way of finding spectrum for white dwarfs.

Works Cited

Koester, D. White dwarf spectra and atmosphere models. Memorie della Societa Astronomica Italiana, v.81, p.921-931 (2010). Web. 3 May 2017.

M., Van Horn H. Unlocking the secrets of white dwarf stars. Cham: Springer, 2015. Print. 3 May 2017.

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About the author Courtney Smith Verified icon 1
I am a fourth year actuarial mathematics major and art history minor at The University of Texas at Austin.

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