Star temperature from B-V color

In summary, to calculate the temperature of a star from its B-V color, you can use the equation B-V = -2.5log(F440/F550). From this, you can use the values B-V = -3.684 log(T) + 14.551 (for log(T) < 3.961) or B-V = 0.344 (log(T))^2 -3.402 log(T) +8.037 (for log(T) >3.961) to find the temperature of the star. This equation is based on experimental fits to the HR diagram for a specific cluster and can also be derived from Planck's law and Stefan-Boltzmann's law if the filter bandwidth is known
  • #1
poiuy
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Homework Statement



I need to know how to calculate the temperature of a star from it's B-V color



Homework Equations




B = -2.5log(F440)+C
V = -2.5log(F550)+C
B-V = -2.5log(F440/F550)


The Attempt at a Solution



Really no idea, all my textbooks say that B-V color is used to measure temperature but none of them say how. I also can't find anything linking flux ratios to temperature.

Any help appreciated :)
 
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  • #2
From my list of handy astronomy values
B-V = -3.684 log(T) + 14.551 (for log(T) < 3.961)
B-V = 0.344 (log(T))^2 -3.402 log(T) +8.037 (for log(T) >3.961)

Note that B-V is also called the color-index of a star.

These are experimental fits to the HR diagram for some cluster - you can probably derive it from Planck's law + stefan-boltzmann if you know the filter bandwidth.
 
Last edited:
  • #3


I can provide some information on how to calculate the temperature of a star from its B-V color. B-V color is a measure of the difference in brightness between a star's blue (B) and visible (V) light. This difference in brightness is due to the temperature of the star's surface, as hotter stars emit more blue light and cooler stars emit more red light.

To calculate the temperature of a star from its B-V color, we can use the following equation:

T = 10^(3.979-0.234(B-V))

Where T is the temperature in Kelvin, and (B-V) is the B-V color index.

This equation is derived from the Wien's displacement law, which states that the peak wavelength of a blackbody spectrum is inversely proportional to its temperature. In simpler terms, a hotter star will emit more blue light, which has a shorter wavelength, while a cooler star will emit more red light, which has a longer wavelength.

Therefore, by measuring the B-V color index of a star and using the equation above, we can estimate its temperature. Keep in mind that this is only an estimate and other factors such as the star's composition and age can also affect its B-V color.

I hope this helps with your homework. If you have any further questions, please don't hesitate to ask.
 

FAQ: Star temperature from B-V color

1. What is the significance of using B-V color to determine star temperature?

The B-V color index is a measure of the difference in brightness between a star's blue and visual (yellow-green) light. This index is directly related to the temperature of the star, with hotter stars having lower B-V values and cooler stars having higher B-V values. Therefore, by measuring a star's B-V color, we can estimate its temperature.

2. How accurate is the B-V color method for determining star temperature?

The B-V color method is a reliable and accurate way to estimate the temperature of a star. However, it is important to note that other factors such as distance, composition, and luminosity can also affect a star's color and therefore, its temperature estimation. Therefore, while the B-V color method is a useful tool, it should be used in conjunction with other methods for a more accurate temperature determination.

3. Can the B-V color method be used for all types of stars?

Yes, the B-V color method can be used for all types of stars, including main sequence, giant, and dwarf stars. However, it may not be as accurate for stars with unusual compositions or those that are very far away.

4. How is the B-V color index calculated?

The B-V color index is calculated by measuring the brightness of a star in two different wavelengths of light - blue and visual. The difference between these two measurements is then divided by the visual brightness to determine the B-V color index.

5. Is there a specific formula for converting B-V color to star temperature?

Yes, the Ballesteros formula is commonly used to convert B-V color to star temperature. This formula takes into account the luminosity class of the star and uses a logarithmic scale to determine temperature. However, there are other formulas and methods that can also be used for this conversion.

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