Question

Estimate the luminosity and temperature of the star Vega by examining its vertical and horizontal position in the H-R diagram . (Hint: You should make an estimate of these values by interpolating between the values marked on each axis). Using the values you estimated, determine the size of Vega as compared to the Sun using the Stefan-Boltzmann law.

Spectral type 106 Alnilam 、、\Rigel A 、、\ Betelgeuse Adhara Deneb Antares 、 104 Spica A Polaris Spica B 、\-pergian Canopus Arcturus Rigel B ˋ 102 Capella A Mira Capella B. Vega Sirius A Aldebaran A Giants Altair Pollux Procyon A Sun 5 Centauri B CAldebaran B 10-2 40 EridaniB Sirius B 丶丶丶 . . Wolf 1346 丶 10 Barnard's Sta Red dwarfs Ohar Procyon B Van Maanen's Star 10-4 Wolf 486 、 Note: Star sizes are not to scale 30,000 20,000 9,999 5009 000 2000 Temperature (K)

Answer 1

The luminosity is about 10^1.5 and the temperature is about 9500 K. Using these we find that luminosity is: 10^1.5 = L/L L = 10^1.5 * L = 10^1.5 * 3.85 * 10^26 = 1.2175 * 10^25 Watts By using the stefan law we have: R = squareroot L/4 pi sigma T^4 R = squareroot 1.2175 * 10^25/4 * 3.141 * 5.671 * 10^-8 * (9500)^4 R = 4.5803 * 10^7 m Now to convert this to solar radius unit so that we get size in comparison with our sun: R_s = R_m * 1 R /6,96 * 10^8 = 4.5803 * 10^7/6.96 * 10^8 = 0.06581 R

The luminosity is about $10^{1.5}$ and the temperature is about K.

Using these we find that luminosity is :

$10^{1.5} = \frac{L}{L_{\bigodot }}$

$L = 10^{1.5} * L_{\bigodot } = 10^{1.5}*3.85 * 10^{26} = 1.2175*10^{25} Watts$

By using the stefan law we have:

$R = \sqrt{\frac{L}{4\pi \sigma T^4}}$

$R = \sqrt{\frac{1.2175*10^{25} }{4 * 3.141*5.671*10^{-8} * (9500)^4}}$

Now to convert this to solar radius unit so that we get size in comparison with our sun :

$R_s = \frac{R_m * 1 R_{\bigodot }}{6.96*10^8} = \frac{4.5803*10^7}{6.96*10^8} = 0.06581R_{\bigodot }$