Transit Method to find extrasolar planets.

[hhhmortal]

Hi, I'm a bit confused on how in theory one could work out the size of a planet knowing the luminosity of the star it is orbiting and also the drop in luminosity as the planet blocks some of the light from the observer. Wouldn't you have to know the surface temperature of the star to work out the radius of it hence the radius of the planet?

 

[mgb_phys]

If you had enough signal (like a planet and the sun) you could get the planet size directly from the time it takes the planet to move across the edge of the star (the slope of the change in the light curve) - I can't see you doing this for an extra solar planet.
The size of the planet would need the size of the star, which you could get from the luminosity and the spectral class.

 

[Ich]

I can't see you doing this for an extra solar planet.

Why not?

 

[hhhmortal]

If you had enough signal (like a planet and the sun) you could get the planet size directly from the time it takes the planet to move across the edge of the star (the slope of the change in the light curve) - I can't see you doing this for an extra solar planet.
The size of the planet would need the size of the star, which you could get from the luminosity and the spectral class.

Ok then. I suppose the spectral class would give you the temperature of the star hence you would simply use equation:

L = 4 pi R^2 (sigma) T_{e}^4

To work out the radius of the star and so the change in luminosity due to the planet transit would give you the change in radius, so the radius of the planet is the difference in radii?

 

[mgb_phys]

Why not?

You would have to be watching the star with high time resolution at the planet started to pass in front of it. High time resolution means short exposures = poor signal-noise and mean you have to be watching lots of starts continously rather than just taking samples.

Then if the planet eclipsed say 1% of the star (eg an extreme case of a Jupiter inside an Earth orbit) to get the radius you would not only have to detect a 1% dip in the star's brightness (possible) but the fractions of 1% as part of the planet moved in front of the star.

 

[hhhmortal]

I was hoping if my question could be answered..thanks


I would get the luminosity without the planet on the way and then the peak in luminosity drop and work it out that way?

 

[Ich]

You would have to be watching the star with high time resolution at the planet started to pass in front of it.

If the planet has usual velocity, say 50 km/s for an orbit < 1 AU, you have at least half an hour until the planet is fully in front of the star. IMHO that should suffice at least to make a good guess at the slope of the lightcurve.

 

[Ich]

I would get the luminosity without the planet on the way and then the peak in luminosity drop and work it out that way?

AFAIK you make a fit to the whole lightcurve during transit, which gives you the relevant parameters.

 

[mgb_phys]

If the planet has usual velocity, say 50 km/s for an orbit < 1 AU, you have at least half an hour until the planet is fully in front of the star. IMHO that should suffice at least to make a good guess at the slope of the lightcurve.

Yes, I don't know what the particular setup for say Kepler is. But if the plan was to take an hour long observations of a star field and then resurvey the same field a month later you wouldn't get a full light curve.

 

[hhhmortal]

AFAIK you make a fit to the whole lightcurve during transit, which gives you the relevant parameters.

Yes. So you can find the dip in absolute magnitude, but how can you derive the size from this? wouldn't you need to know temperature as well as luminosity?

 

[Ich]

But if the plan was to take an hour long observations of a star field and then resurvey the same field a month later you wouldn't get a full light curve.

Agreed, but that would be a bad plan looking for extraterrestrial planets.

So you can find the dip in absolute magnitude, but how can you derive the size from this? wouldn't you need to know temperature as well as luminosity?

You can also find how long it takes until the light curve drops down. This should give you enough information to guess the diameter of the planet.

 

[hhhmortal]

Agreed, but that would be a bad plan looking for extraterrestrial planets.

You can also find how long it takes until the light curve drops down. This should give you enough information to guess the diameter of the planet.

Yes, I know the period of the transit planet (i.e. time it takes for planet to go around the star). I'm doing a research project whereby I need to find the size of the planet but I can't seem to find anything with the information that I have to do so. I've tried endlessly. Any help will be greatly appreciated.

thanks.

 

[buffordboy23]

Yes, I know the period of the transit planet (i.e. time it takes for planet to go around the star). I'm doing a research project whereby I need to find the size of the planet but I can't seem to find anything with the information that I have to do so. I've tried endlessly. Any help will be greatly appreciated.

thanks.

Are you able to determine the velocities from your other known parameters? You already said that you know the radius of the star right. So just use the equation

$$R_{planet} = R_{star} - \frac{v_{star}+v_{planet}}{2}\left(t_{1}-t_{0}\right)$$

and the time difference is just the duration for the drop in the light curve over the transit.

EDIT: I see that you asked about fractional dimming of the star during transit. This could work too. The reduction in light from the star is just the cross-sectional area of the planet multiplied by the star's luminosity. Consider a Jupiter-sized planet orbiting within 1 A.U. of a sun-like star and the dimming is about 1%.