Color Indices and Absolute and Apparent Bolometric Magnitude

In summary, the student attempted to find the absolute and apparent bolometric magnitudes for a star using luminosity, distance modulus, radiant flux, and peak wavelength information. However, he ran into problems with equations that required more variables than he was able to provide. He plans to post his work and problems with each equation in order to help others who may be struggling with the same problem.
  • #1
HeLiXe
440
1

Homework Statement


Given: Spherical blackbody with
surface temperature of 30000K
radius of 6.0 x 10^9 m
located 123pc from earth

Homework Equations



Find the absolute and apparent bolometric magnitudes

The Attempt at a Solution



My camera needs batteries so I cannot post my work, but I will explain what my reasoning and attempts. Please bear in mind this is my first astrophysics class and this is all new to me e.g. I am totally clueless!

From the given data I have found the luminosity, distance modulus, radiant flux at the star's surface and the Earth's surface and the peak wavelength. I know what a bolometric magnitude is by definition, but every equation I have seems to need more variables and cannot be solved by a system of equations. I think my key problem is I do not know how to find the star's absolute color magnitudes. My textbook indicates that the star's absolute color magnitudes can be found once the distance from Earth is known, but there is no equation given for this. Information that I have been given in the textbook is the UBV filters centered and the effective bandwith.


I will screenprint the equations I have used and post them along with the problems I encounter for each one.
 
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  • #2
You need to show your work/calculations. Also, so far all your problem statement says is that you need to find the absolute and apparent bolometric magnitudes. If you know the luminosity of the star, then you can calculate the first one easily just from the definition of bolometric magnitude.
 
  • #3
Thanks cepheid. I just cannot see where it is so easy. I will type out my work and post it.
 
  • #4
Hey HeLiXe! :smile:

What's a bolometric magnitude?
 
  • #5
ILS! <3

The bolometric magnitude is the magnitude for all wavelengths emitted by a given star. I figured out how to do this...the task of retyping all of my work in latex seemed daunting to me so I asked my professor for guidance. I totally overlooked the most essential equation with the comparison of luminosity and I totally saw how easy it was as cepheid indicated :D
 

1. What is a color index in astronomy?

A color index in astronomy is a numerical value that represents the difference in brightness between two objects or regions of the sky at different wavelengths. It is typically calculated by taking the difference between the magnitudes of an object or region in two different filters or wavelengths.

2. How is color index used to determine the temperature of stars?

Color index is used in combination with the absolute and apparent bolometric magnitudes of stars to determine their temperature. By comparing the color index of a star to a standard set of values, scientists can estimate the star's temperature based on its spectral energy distribution.

3. What is the difference between absolute and apparent bolometric magnitude?

Absolute bolometric magnitude is the intrinsic brightness of a celestial object, taking into account all wavelengths of light. Apparent bolometric magnitude, on the other hand, is the perceived brightness of an object as seen from Earth, and can be affected by factors such as distance and interstellar dust.

4. How is color index related to the composition of stars?

The color index of a star can provide information about its composition, as different elements emit light at different wavelengths. For example, a star with a high color index in the infrared region may indicate the presence of dust or molecular gas in its atmosphere, while a low color index in the ultraviolet region may suggest a hot, young star with a high metal content.

5. Can color index be used to study the evolution of stars?

Yes, color index is an important tool in studying the evolution of stars. By tracking changes in a star's color index over time, scientists can determine its age and track its progression through different stages of its life. Color index can also provide insight into the physical processes and changes happening within a star as it evolves.

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