Stellar physics (number crunching)

In summary, the conversation discusses an extra credit assignment involving data for ~9000 stars and various calculations such as creating an HR diagram, approximating the luminosity function to Gaussian distributions, constructing frequency histograms for stellar luminosity, calculating spatial density of stars in the Sun's neighborhood, and testing error propagation and distribution. The conversation also mentions seeking guidance from the professor for certain aspects of the assignment.
  • #1
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Decided to have a go at an extra credit assignment:

Homework Statement


I am given some data for ~9000 stars of 21 known spectral types along with their:
  • measured parallax & uncertainty
  • proper movements in right ascension & declination per year
  • (B-V) color & relative mag (V).
I am asked to compute the following:

a) HR diagram
b) Show that the luminosity function can be approximated to Gaussian distributions of a given form.

^^Working on these, good so far.

c) Construct the frequency histograms with respect to the absolute magnitude, grouped into different intervals of Mv. These will provide the stellar luminosity function for a given spectral type.
d) Calculate the spatial density of stars in the Sun's neighborhood and show that its density it is approximately constant (function of radial position from the Sun)
e) Show how the measurement errors([itex]\Delta m_v \approx 0.2 [/itex]) affect the calculated absolute magnitude. If the parallax measurements follow a Gaussian distribution, will Mv's error also follow a Gaussian curve?


The Attempt at a Solution



On (c), I'm not exactly sure what is meant by frequency histogram, nor how large of an interval should I pick for Mv? I think I better ask my prof for this one.

(d) How would I go about doing this? I've got enough to find the distance in parsec for all the stars, but what kind of function should I try to fit them to? 3rd degree polynomial?
I could plot density = 3*(N stars)/4*pi*r^3, which I expect will taper off to a flat slope if the density really is constant, but how far should I consider the "Solar neighborhood" to be (in parsec)?
Or is my approach totally wrong?

(e) My expression for error propagation looks like this (see attachment), I pray that I have not offended the Calculus gods. Is it correct? Not sure how to respond to the other part of the question, what specifically should I plot to test this?

Many thanks in advance.
 

Attachments

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  • #2


First of all, great job on your progress so far! It's always exciting to take on extra credit assignments and challenge yourself in your studies.

For (c), a frequency histogram is a visual representation of how often a certain value occurs in a given dataset. In this case, you can create a histogram with the absolute magnitude (Mv) on the x-axis and the number of stars in each interval on the y-axis. The intervals for Mv can be chosen based on the range of values in your dataset and what makes the most sense for your analysis. It may be helpful to consult with your professor for guidance on this.

Regarding (d), you can use your data to plot the spatial density of stars as a function of radial position from the Sun. This can be done by plotting the distance of each star from the Sun (in parsecs) on the x-axis and the density (calculated using the formula you mentioned) on the y-axis. The "Sun's neighborhood" can be defined as a certain range of distances from the Sun, and again, the specific range may depend on your dataset and the goals of your analysis.

For (e), your expression for error propagation looks correct. To test if the error in Mv also follows a Gaussian curve, you can plot the distribution of the errors and see if it resembles a bell-shaped curve. This can be done by creating a histogram with the errors (calculated using your expression) on the x-axis and the number of stars in each interval on the y-axis. If the distribution looks similar to a Gaussian curve, then you can conclude that the error in Mv follows a Gaussian distribution.

I hope this helps guide you in your analysis. Keep up the good work and don't hesitate to reach out to your professor for further clarification or guidance. Good luck!
 

1. What is stellar physics?

Stellar physics is a branch of astronomy that studies the physical properties and processes of stars, such as their formation, evolution, and death. It uses mathematical models and simulations to understand the behavior and characteristics of stars.

2. What is the importance of studying stellar physics?

Studying stellar physics helps us understand the fundamental processes that govern the behavior of stars, which are essential for understanding the universe. It also has practical applications, such as developing technologies for space exploration and energy production.

3. What is number crunching in stellar physics?

Number crunching in stellar physics refers to the use of complex mathematical calculations and data analysis techniques to understand and predict the behavior of stars. This involves processing large amounts of data and using advanced algorithms to make sense of the data.

4. What are some common tools used for number crunching in stellar physics?

Some common tools used for number crunching in stellar physics include computer simulations, mathematical models, statistical analysis, and data visualization techniques. These tools help researchers analyze and interpret large amounts of data to gain insights into the behavior of stars.

5. How does stellar physics contribute to our understanding of the universe?

Stellar physics helps us understand the processes that govern the formation and evolution of stars, which are the building blocks of the universe. By studying stars, we can gain insights into the origins of the universe, the distribution of matter and energy, and the potential for life in other parts of the universe.

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