# How Does the Balmer Break Influence Star Opacity Measurements?

• desperate_student
In summary, to demonstrate the Balmer Break, you will need to obtain a spectrum of the star and use the Boltzmann and Saha Equations to calculate the number of hydrogen atoms at different energy levels. This will allow you to plot a graph of opacity vs wavelength and observe the Balmer Break.
desperate_student
Homework Statement
Write an expression for κ(3647+)/κ(3647−), the ratio of the opacities just above and below the Balmer break for (i) low-temperature atmospheres where the opacity above the Balmer break is due to the H− ion, and (ii) high-temperature atmospheres where the opacity above the Balmer break is due to the n = 3 level of neutral hydrogen. Your results should show that at low temperatures, the Balmer discontinuity depends on both temperature and electron pressure, while at high temperature, it depends only on temperature.
Relevant Equations
Saha Equation, Boltzmann Equation, Kramers Opacity for free-free and free-bound and any other relevant equations.
I am not sure where to start for this. Considering it needs to be demonstrate Balmer Break, I am assuming it needs to be wavelength based. As a result I am assuming I cannot use mean (Kramers) Opacity but rather express in terms of Opacity k= n*sigma/rho.
My thoughts are to use Boltzmann Equation to obtain n_h,n=2,3 and Saha Equation to find n_h- and sub into n*sigma/rho and find k ratio based on that

and then plot a graph of k vs wavelength.

Hello there,

Thank you for sharing your thoughts on how to approach this task. I would like to offer some additional suggestions that may help you in your research.

Firstly, you are correct in assuming that the Balmer Break is a wavelength-based phenomenon. The Balmer Break refers to the discontinuity in the spectrum of a star caused by the absorption of hydrogen atoms in the star's atmosphere. This absorption occurs at specific wavelengths, known as Balmer lines, which are determined by the energy levels of the hydrogen atoms.

In order to demonstrate the Balmer Break, you will need to obtain a spectrum of the star in question. This can be done using a spectrometer, which measures the intensity of light at different wavelengths. You can then use this spectrum to identify the Balmer lines and their corresponding wavelengths.

Next, as you mentioned, you can use the Boltzmann Equation to calculate the number of hydrogen atoms in the star's atmosphere at energy levels n=2 and n=3. This will give you the population of hydrogen atoms at these energy levels.

To further understand the Balmer Break, you can also use the Saha Equation to determine the ratio of the number of hydrogen atoms at energy level n=2 to the number of hydrogen atoms at energy level n=3. This will give you an idea of the relative population of these two energy levels.

Finally, you can plot a graph of the opacity (k) vs wavelength using the values obtained from the Boltzmann and Saha Equations. This will allow you to see how the opacity changes at the Balmer lines, demonstrating the Balmer Break.

I hope this helps in your research. Good luck!

## 1. What is "star opacity" and why is it important?

Star opacity refers to the measure of how much light is absorbed by a star's atmosphere. It is important because it affects the overall brightness and color of the star, which can provide information about its temperature, composition, and evolutionary stage.

## 2. What is the "Balmer Break" and how is it related to star opacity?

The Balmer Break is a sharp decrease in the intensity of a star's spectrum at a specific wavelength range. It is caused by the absorption of light by hydrogen atoms in the star's atmosphere. This break is related to star opacity because it can be used to measure the amount of hydrogen present in the star's atmosphere, which is a key factor in determining its opacity.

## 3. How do astronomers use the Balmer Break to study stars?

Astronomers use the Balmer Break as a tool to study the properties of stars. By measuring the intensity of light at different wavelengths, they can determine the amount of hydrogen in a star's atmosphere and use this information to infer its temperature, composition, and evolutionary stage.

## 4. Can the Balmer Break be used to study all types of stars?

Yes, the Balmer Break can be used to study all types of stars, from main sequence stars to white dwarfs. However, it is most commonly used for studying hot, massive stars due to their strong hydrogen absorption lines.

## 5. How does the Balmer Break change over the lifetime of a star?

The Balmer Break can change over the lifetime of a star as its temperature, composition, and evolutionary stage change. For example, as a star evolves and its outer layers become cooler and less dense, the Balmer Break may become less pronounced. This change can provide valuable insights into a star's evolution.

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