Calculating Flux, Blackbody Surface Fluxes, and Radii of Sirius A & B

[sukisa]

Homework Statement

The central wavelength and the flux calibration are given in Table 2 (f5500= Cv * 10^-0.4V)
Calculate the flux measured at Earth f5500, the blackbody surface fluxes B5500, and the radius (in m and solar radii)

For Sirus A and B

Table 1:
brightness Sirius A: Va= -1.46
brightness Sirius B: Vb= 8.44
TeffA= 9900K
TeffB=25,200K

Table 2: Data for the Johnson V filter
central wavelength lambda=5500 Angstrom
filter Constant Cv= 3.58*10^-2 W m^-2 m^-1

The Attempt at a Solution

I noted when attempting the problem that the apparent magnitude is the same as Va and Vb respectively.

I used the equation in the question to figure out the flux f5500 = (3.58*10^-2)(10^-0.4*-1.46)

I get an answer of 0.137 Wm^-2 for the flux.

I can tell this is wrong because I then need to find the radius and hence luminosity and I get figures several orders of magnitudes off from the actual values.

Do I need the surface flux B5500 to figure out the radius also? And is the surface flux B5500 the blackbody plank function?

If I get the flux I should be able to determine the luminosity (and thus radius) using L=4piR^2F then using L=4piR^2(boltsman)Teff^4 for the radius of sirius.

I know the distance to sirius as I figured out from a previous problem. My answer is 2.639pc which is constant with the measured values. Any help would be greatly appreciated.

 

[mark726]

Thank you for posting your question. It seems like you are on the right track in your attempt to solve this problem. To answer your questions, yes, you do need the surface flux B5500 to determine the radius. The surface flux B5500 is indeed the blackbody Planck function, which can be calculated using the Stefan-Boltzmann law: B5500 = σTeff^4, where σ is the Stefan-Boltzmann constant and Teff is the effective temperature.

To determine the radius, you can use the equation you mentioned: L = 4πR^2B5500, where L is the luminosity and R is the radius. You can then use the luminosity and the distance to Sirius A and B to calculate the radius in both meters and solar radii.

Hope this helps. Good luck with your calculations!