# Cephid Variables: Finding Distance from Parallax & Magnitude

• Unto
In summary, the two cepheid variables have different distances and periods, but this tells us nothing about their luminosity or brightness.
Unto
This one has me stumped:

A galactic Cephid variable has a parralax of 0.002 arcseconds. What is it's distance in parsecs? A second cephid variable with the same period is 20 magnitudes fainter. What is the distance to this second star?

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Now I worked out that the distance to the former is 500pc.

Then using a flux equation I learned in lectures, I gathered that since the difference in the maginuteds is 20, one of the the stars must be 1E8 times brighter. So if we denote the second star as flux 1, the first star has flux 1E8.

But how then would I work out the distance to the second star of flux 1?

If a star is twice as bright it must be 4x nearer (since light spreads out in an inverse square)

The link between apparent magnitudes and distance is called the "distance modulus"

Thank you for your informative reply, but I don't want to jump into this just yet.

I have values (which are know exact but are representative) in fluxes. I understand that distances are usually correlated with luminosities and apparent magnitudes. Do I just jump the gun and say 'since this star is 1E8 times dimmer, it must be so-so further away?

And the question states that the two stars also have the same period, what does this tell me?

Is there anyway where I can get the magnitudes of the stars? I would be gratified for some more help as I really like astrophysics.

Unto said:
I have values (which are know exact but are representative) in fluxes. I understand that distances are usually correlated with luminosities and apparent magnitudes. Do I just jump the gun and say 'since this star is 1E8 times dimmer, it must be so-so further away?
Pretty much
You don't need to convert the magnitude to fluxes since the 'log' in the distance formula effectively does that. Since one star is 10^8 times fainter than it must be 10,000 times further away (assuming they are the same brightness)

And the question states that the two stars also have the same period, what does this tell me?
The period of a of a cepheid depends on it's absolute magnitude - so the same period means the same power.

Is there anyway where I can get the magnitudes of the stars?
If you have the period - yes there is a formula

Alas I was not given the period.

## 1. What are Cepheid variables and how do they help in finding distance from parallax and magnitude?

Cepheid variables are a type of pulsating stars that have a predictable period of brightness changes. By measuring the period of these changes, scientists can calculate the intrinsic brightness of the star. This, combined with the star's observed magnitude, can be used to determine its distance through the inverse square law.

## 2. How are Cepheid variables different from other types of variable stars?

Cepheid variables have a specific relationship between their period of brightness changes and their intrinsic brightness, known as the period-luminosity relation. This makes them more reliable for distance measurements than other types of variable stars.

## 3. How is parallax used in conjunction with Cepheid variables to determine distance?

Parallax is a technique used to measure the distance to nearby stars by observing their apparent shift in position as the Earth orbits the Sun. By combining parallax measurements with the intrinsic brightness of Cepheid variables, scientists can determine the distance to these stars with greater accuracy.

## 4. What are the units used for measuring Cepheid variable periods?

The period of Cepheid variables is typically measured in days or hours, as these stars have relatively short periods of brightness changes compared to other types of variable stars which may have periods of years or even decades.

## 5. Can Cepheid variables be used to measure distances beyond our own galaxy?

Yes, the period-luminosity relation of Cepheid variables has been calibrated to measure distances up to tens of millions of light years away. This has allowed scientists to accurately measure the distance to other galaxies in our local group and beyond.

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