High School Why Do We Use Different Pairs of Filters to Determine the Temperature of Stars?

[heavystray]

Hi, in determining the temperature of stars using colour index (U-B,B-V,V-R, etc), why do we need to use the appropriate pairs of filters based on their range of temperature? (this is what i read from wiki)

For cool stars, we use R-I, and for hotter stars, we use B-V. I don't understand how using different pairs of filters make a difference because isn't radiation curve of blackbodies with different temperature have different shape and thus, the values of (B-V, U-B, V-R) will also be different? (I hope you understand what I'm trying too say)

My idea is this has to do with the star's peak wavelength...but i still don't see the justification to that...
your help would be greatly appreciated

 

[Drakkith]

For cool stars, we use R-I, and for hotter stars, we use B-V. I don't understand how using different pairs of filters make a difference because isn't radiation curve of blackbodies with different temperature have different shape and thus, the values of (B-V, U-B, V-R) will also be different? (I hope you understand what I'm trying too say)

I'm betting that astronomers use the R-I filters instead of the B-V filters for cooler stars so that you don't block out most of the light. Cool stars don't put out much visible light in the higher frequencies, so using a bandpass in the red-infrared range makes them easier to see and measure.

 

[phyzguy]

I'm betting that astronomers use the R-I filters instead of the B-V filters for cooler stars so that you don't block out most of the light. Cool stars don't put out much visible light in the higher frequencies, so using a bandpass in the red-infrared range makes them easier to see and measure.

Right. Look at this plot showing the filter bandpasses with a 3000 K (red) blackbody and a 10,000K (blue) blackbody. You can see that the hot blue star doesn't have much light in the I band, and the cool red star doesn't have much in the B band.

 

[heavystray]

Right. Look at this plot showing the filter bandpasses with a 3000 K (red) blackbody and a 10,000K (blue) blackbody. You can see that the hot blue star doesn't have much light in the I band, and the cool red star doesn't have much in the B band.
View attachment 219165

but the question is, why does it affect the accuracy of temperature calculated based on the star's U-/B/B-V/V-R?? because we're just going to get either lower or higher values of B-V, V-R, R-I which correspond to temperatures. I mean for cooler stars, we already expected their U-B will be low. so, it shouldn't be a problem to determine their temperature based on the U-B value. Isn't the accuracy going to be just the same if we determine the temperature using R-I filters? (i hope you understand my question)

thanks for your answer

 

[heavystray]

I'm betting that astronomers use the R-I filters instead of the B-V filters for cooler stars so that you don't block out most of the light. Cool stars don't put out much visible light in the higher frequencies, so using a bandpass in the red-infrared range makes them easier to see and measure.

yes it's easier to measure, but the question is, why does it affect the accuracy of temperature calculated based on the star's U-/B/B-V/V-R?? because we're just going to get either lower or higher values of B-V, V-R, R-I which correspond to temperatures. I mean for cooler stars, we already expected their U-B will be low. so, it shouldn't be a problem to determine their temperature based on the U-B value. Isn't the accuracy going to be just the same if we determine the temperature using R-I filters? (i hope you understand my question)

thanks for your answer

 

[phyzguy]

yes it's easier to measure, but the question is, why does it affect the accuracy of temperature calculated based on the star's U-/B/B-V/V-R?? because we're just going to get either lower or higher values of B-V, V-R, R-I which correspond to temperatures. I mean for cooler stars, we already expected their U-B will be low. so, it shouldn't be a problem to determine their temperature based on the U-B value. Isn't the accuracy going to be just the same if we determine the temperature using R-I filters? (i hope you understand my question)

The lower the light intensity, the fewer photons there are to measure and the lower the accuracy. If you take a star, which is dim to begin with, then add a filter that removes most of the photons, you can end up with a surprisingly small number of photons. Since the photons are distributed according to a Poisson distribution, the error goes down as 1/(sqrt(N). So the more photons you have, the smaller the error.