Answer Key Testname: MT S

Transcription

1 Answer Key Testname: MT S 1) B 2) A 3) E 4) C 5) C 6) C 7) C 8) A 9) E 10) C 11) A 12) C 13) C 14) C 15) C 16) D 17) A 18) D 19) A 20) C 21) B 22) A 23) A 24) C 25) B 26) C 27) A star with apparent magnitude 2 is 100 times brighter than a star with apparent magnitude 7. (Five magnitudes indicates a factor-of-100 difference; larger apparent magnitude stars are always fainter.) 28) vesc = 600 km/s * sqrt[m/r], where M and R are mass and radius in solar units. a. vesc = 600 sqrt(2/(1/2)] = 600 sqrt[4] = 1200 km/s b. vesc = 600 sqrt[(1/2)/2]= 600*sqrt[1/4] = 600/sqrt[4] = 300 km/s 29) L ~ T 4 A ; A ~ R 2 a. L /Lsun = (T/Tsun) 4 (R/Rsun) 2 = 2 4 (1/2) 2 = 4 => L = 4 Lsun b. L /Lsun = = = 10 6 => L = 10 6 Lsun 30) 31) a. d=1/0.2 = 5 pc b. s(au) = d(pc)*a(arcsec) = 5*1 => s=5 AU 32) P^2 = a^3/m = 27/3 = 9 => P = 3 years. 33) a. d=1/0.2 = 5 pc b. s(au) = d(pc)*a(arcsec) = 5*1 => s=5 AU 34) 35) a. d=1/0.2 = 5 pc b. s(au) = d(pc)*a(arcsec) = 5*1 => s=5 AU 36) 1. D -- The upper main sequence of hot, luminous short-lived star is all present. 2. C -- Lowest turnoff point from main sequence, implying that even long-lived, low-luminosity stars are running out H-fuel. 3. B -- Turnoff point is at the solar luminosity and sun has an expected main sequence life of ca. 10 billion years. 12

2 38) Which of the following terms is given to a pair of stars that we can determine are orbiting each other only by measuring their periodic Doppler shifts? A) eclipsing binary B) spectroscopic binary C) visual binary D) double star E) none of the above 38) PROBLEMS: Answer the question(s), showing the work of any calculations needed. For mulitple part problems, if you can't answer an inital part, just define a symbol for it to use as needed in any subsequent part. 39) (3 points) Which is brighter in our sky, a star with apparent magnitude +1 or a star with apparent magnitude +6? By how much is that star brighter? 40) (3 points) The escape speed from the surface of the sun is about 600 km/s. What is the escape speed from the surface of a star with Mass = 4 M sun and Radius = 16 R sun? 41) (3 points) A star has an effective surface temperature that is twice that of the sun, but a diameter of only half the solar diameter. In terms of the solar luminosity L sun, what is the star's total luminosity L? 7

3 42) (4 points) a. An electron in a neutral hydrogen atom jumps from the first excited level (n=2) to the ground state (n=1). What is the energy (in ev) and wavelength (in nm) of the emitted photon? b. Given that the numbers of quantum states in the excited and ground states are respectively g 2 =6 and g 1 =2, at what temperature would there be an equal number (n 1 = n 2 ) of atoms in these two states? 43) (8 points) A glowing sphere of a given physical diameter is moved to five times greater distance. a. By what factor does the angular diameter change? b. By what factor does its solid angle change? c. By what factor does the apparent brightness (observed flux from the sphere) change? d. By what factor does its surface brightness change? 8

4 44) (3 points) A planet orbits a star with mass of 2 times the solar mass at a distance of 2 AU. In earth years, about how often do beings on this planet celebrate birthdays? 45) (6 points) A star with a parallax of 0.05 arcsec is observed to have a companion star at an angular separation of 2 arcsec. a. What is the distance in parsec (pc) from the earth to the star system? b. What is the physical separation distance in AU from the star to its companion? c. If the stars take 40 years to orbit each other at this fixed disttance, what is the sum of their masses, in M sun.? 9

5 46) (4 points) The sun has a surface temperature of about 6000 K and a peak intensity at a wavelength of around 500 nm. a. What is the peak wavelength (in nm) of a star with a surface temperature of 30,000 K? b. About what is the energy E (in ev) of a photon with this wavelength? 47) (4 points) A main sequence star has a mass that is 20 times the mass of the sun. a. About what is the star's luminosity, in units of the sun's luminosity L sun? b. About how long will this star live on the main sequence? 10

6 The following question refers to the representations below of H-R diagrams for different clusters of stars. Figure ) (6 points) Giving a brief reasoning for each of your answers, identify which cluster is a. oldest. b. youngest. c. About 10 billion years old. 11

7 49) (4 points) A flashlight shines through an absorbing medium of opacity κ = 0.1 cm 2 /g and density ρ = 0.5 g/cm 3. a. What is the mean free path of light in this medium? b. If the flashlight's emitted intensity (not flux) is observed to be reduced by a factor 1/e, how far away is the flashlight from the observer? 50) (6 points) Two main sequence stars with the same spectral type have apparent magnitudes m1 and m2. a. If m 1 -m 2 = +5, what is the ratio of their distances D 1 /D 2, assuming no interstellar absorption for either star? b. If the stars indeed have the distance ratio in part a, but now star 1 is now behind a cloud with total absorption optical depth τ 1 =5 (while τ 2 is still zero), what now is m 1 -m 2? c. If one didn't know about this absorption, what would be the inferred distance ratio? How does this compare to the actual distance ratio from part a? 12

8 51) (8 points) In observations of a spectroscopic binary system, a spectral line that normally has a wavelength of 500 nm splits into two lines, taking 1 month to go from a single line to two lines with maximum separation at wavelengths nm and nm. a. What is the period of the binary orbit, in months and fraction of a year? b. Assuming our line of sight is perpendicular to the orbital axis, what are the orbital speeds of the two stars, in km/s? c. About what is the separation between the two stars, in AU? (Recall the earth's orbital speed around the sun is 30 km/s.) d. What are the masses of each star, in Msun? 13