Astronomy: Find Star Rotation Period with Given Data

[AllHailBritania]

Homework Statement

Find period of the star's rotation assuming that the axis of rotation is perpendicular to the direction of view.
Given data:
- distance d = 25 pc
- bolometric luminosity observed m = 8^m
- effective temperature T = 4000 K
- bolometric absolute brightness of the Sun M_m = 4,75^m
- luminosity of the Sun J_s = 4 * 10²⁵ W

I also know that the star's spectrum line corresponding to the wavelength exhibits extreme variation of +/- Δλ (symmetrical widening of the line), and the |Δλ| / λ= 10^-4.

I would be greatful for your help.

 

[Matterwave]

Have you tried to start this problem? What do you think the first step might be to solving this problem? What do we need to know about the star in order to deduce its rotation?

 

[AllHailBritania]

I know that as a result of the rotation one half of the disc Star is coming at us, and the other is moving away, resulting in a Doppler upcoming star of the disc causes shift towards blue line on the receding part - the red. And i supose that we can designate speed form this. But I don't know how, or even if this is a good path to follow.

 

[Matterwave]

Ok, so the speed of the edges of the star dictate how much blue/red shift there is right? So the spread in the frequencies we see determines the speed of the outer-most edges of the star. What is the (non-relativistic) formula for blue/red shift in terms of this speed? That will allow me to find this speed right, since the blue/red shifts are given.

But speed is not the only thing we need. We want to know the period of rotations of the star. Imagine a ball rotating. If I know the speed of its outer most edge, what other things do I need to know in order to find the period of rotation?

 

[AllHailBritania]

Ok i found it. Δλ = λ*ν*sini/c, and if the axis of rotation is perpendicular to the direction of view sini = 1 so v = Δλ*c/λ. To know the period of the star's rotation we use the formula T=2πR/v. L = 4πR²σT⁴ from this formula I want to designate R. So I need to find L. Can i designte L from the formula m_star = m_sun - 2,5log₁₀ (L/L_sun*(d_sun/d)²) ?

 

[Matterwave]

Yes, looks like you got it. Just carry through your calculation. :)

 

[AllHailBritania]

Ok I get it know :D. I'm really greatful for your help, and I'm delighted that such a tutors exist. I was never good at astronomy. Again thank you very much for your time.