Working Out Star Radius from Bolometric Flux, Wavelength & Parallax

[Brewer]

How do I go about working out the radius of a star when I have the bolometric flux, the wavelength of the peak flux of its spectrum, and its parallax?

I've also calculated the temperature of its photosphere (Wein's law right?).

Or is it more to do with the parallax?

 

[SpaceTiger]

I've also calculated the temperature of its photosphere (Wein's law right?).

How does a blackbody's temperature relate to its area and luminosity?

Or is it more to do with the parallax?

What quantity does a parallax give you? How might you use this to derive a luminosity from a flux?

 

[Brewer]

I haven't touched on luminosity for this question, as it asks for that in the next part (and I know how to get that).

As I understand it, radius of the star is d*tanP where d is the distance to the star, and P is the parallax. Is $$10^11$$ the correct order of magnitude for a star do you think? Its bigger than the sun, but its not overly huge for a star is it?

 

[lightgrav]

you have its parallax? so it must be fairly close ... right?
that means it should appear fairly bright ... right?
Temperature determines how much light is emitted by each sq. meter of surface - not how much light comes off the entire surface.

Do you know how these are related?

 

[SpaceTiger]

Please don't double-post, it's very annoying to those trying to help you.

I haven't touched on luminosity for this question, as it asks for that in the next part (and I know how to get that).

You'll need it for this part.

As I understand it, radius of the star is d*tanP where d is the distance to the star, and P is the parallax. Is $$10^11$$ the correct order of magnitude for a star do you think? Its bigger than the sun, but its not overly huge for a star is it?

10¹¹ what? Meters?

 

[Brewer]

Please don't double-post, it's very annoying to those trying to help you.



You'll need it for this part.




10¹¹ what? Meters?

Yes $$10^1^1m$$. Sorry about the double post

 

[SpaceTiger]

Yes $$10^1^1m$$.

That's about the distance from the Earth to the sun, so it's a bit too close for a star. I just noticed that you were associating the parallax with the radius -- actually, it gives you a distance. The distance, in parsecs, is given by:

$$d=\frac{1}{\theta}$$

where $\theta$ is the parallax angle in arcseconds.

 

[Brewer]

Is it in metres if you use radians and parsecs if you use it in degress, arcmin and arcsec then?

I've just realized how its done though - distance can be used with the bolometric flux to find the bolometric luminosity. This is turn can be used with $$P = \sigma AeT^4$$ to find the raduis of the star right?

I'm a little confused how the question was intended to be worked out though - 2 marks for this, and a further two in the next part for writing down something you've already calculated in order to do this question (luminosity).

 

[SpaceTiger]

Is it in metres if you use radians and parsecs if you use it in degress, arcmin and arcsec then?

More generally, the expression is:

$$d=\frac{d_{earth}}{\theta}$$

where $d_{earth}$ is the distance from Earth to sun. The expression I gave you is only valid in units in which the angle is in arcseconds and the distance is in parsecs. Use the above expression for meters and radians.

I've just realized how its done though - distance can be used with the bolometric flux to find the bolometric luminosity. This is turn can be used with $$P = \sigma AeT^4$$ to find the raduis of the star right?

Yep.