SCCC 115
Homework 8 - Due 9 Nov. 2003
Prof. Christina Lacey
R&D: 17-7, 17-8, 17-10, 17-14, 17-16
P: 17-3, 17-4, 17-10

R&D: 17-7
What is the difference between absolute and apparent brightness?

The absolute brightness of a star is an intrinsic property and directly proportional to the luminosity. The absolute magnitude is the brightness of a star at 10 pc. Apparent brightness is the brightness measured by observers at Earth and depends explicitly on the 1/distance$^2$. If the distance is known than the absolute brightness can be calculated from the apparent brightness.

R&D: 17-8
How do astronomers measure stellar temperatures?

The temperature is measured by at least two points, fitted to the black body spectrum. The peak of the spectrum, corresponds to the stellar temperature. Most commonly the points the spectrum are from the B and V (blue and visible (yellow-green) filters. .

R&D: 17-10

Why do some stars have very few hydrogen lines in their spectra?

Either the staqr is too hot or it is too cold. If the star is too hot, then the hydrogen is ionized (the electron is freed from the nucleus), making electronic transitions rare. If the star is too cold, then the photons in the photosphere do not have enough energy to excite the electron in hydrogen, thus creating no lines.

R&D: 17-14

Why does the H-R diagram constructed from the brightest stars differ from the H-R diagram constructed from the nearby stars?

The brightest stars are also intrinsically luminous stars that are very far away. These luminous stars still appear bright due to their greater luminousity. The nearby stars are mostly M type main sequence (red dwarfs) that are very faint. When observing wiht he naked eye, the brightest stars dominate the sky, even though they are very far away.

R&D: 17-16

Which stars are least common in our galaxy?

The massive stars (the O-B blue giants) are the least common; they evolve and die very quickly.

P: 17-3
What is the luminosity of a star having 3 times the radius of the Sun and a temperature of 10,000 K?

If solar units are used:

$$T_{star} = 10,000~K~ \frac{1~ T_\odot}{5800~K}=1.7 T_\odot$$

$$R_{star} = 3R_\odot$$

$$L_{star}~(L_\odot ) = T^4~(T_{\odot})R^2 (R_\odot)= (1.7~ T_{\odot})^4(3R_\odot)^2= 8.35 \times 9~ L_\odot= 75~ L_\odot$$ (1)

P: 17-4

A certain star has a temperate twice that of the Sun and a luminosity 64 times greater than the Sun. What is the radius of the star in solar units?

$$T_{star} = 2~ T_\odot$$

$$L_{star} = 64~ L_\odot$$

$$R = \sqrt{\frac{L}{T^4}}=\frac{\sqrt{L}}{T^2} =\frac{\sqrt{64~L_\odot}}{(2~T_\odot)^2}=\frac {8}{4} ~R_\odot= 2~R_\odot$$ (2)

P: 17-10

A star has apparent magnitude of 10.0 and an absolute magnitude of 2.5. How far away is it?

$$D=10~pc\times 10^{\left (\frac{m-M}{5}\right )}= 10~pc\times 10^{\left(\frac{10.0-(2.5)}{5}\right )}$$ (3)

$$=10~pc\times 10^{\left (\frac{7.5}{5}\right )}=10~pc\times 10^{1.5}$$ (4)

$$=10 \times 31.6~ pc = 316~pc$$ (5)