Astronomy 104: Homework Set 6 Due: Wednesday, April 1, 2015 1. The table below lists information for seven Cepheid variables where ‘Period’ is the pulsation period of the star, and 𝐿/𝐿⊙ is the luminosity in solar units. Period (days) L/L⨀ 3.0 4.8 10.0 19.5 34.4 55.2 115.0 835 1418 3761 8176 16623 28220 75140 a) Plot the PL relation for these stars using the logarithms of the values in the table (that is, 𝑙𝑜𝑔(𝑃) vs 𝑙𝑜𝑔(𝐿/𝐿⊙ )) and extract the slope and y-intercept of the relation the data define. DO NOT ASSUME THIS IS THE SAME PL RELATION AS IN THE TEXT. b) Let’s say that from Earth we observe that a Cepheid in the LMC has a period of 100 days and a Cepheid in M 31 has a period of 5.2 days. Use the PL relation you discovered in part (a) of this problem to estimate the luminosities of these stars. c) The Cepheid in the LMC is 10000 times brighter than the one in M31 as seen from Earth. Use the relation between brightness (flux), luminosity and distance (see Destination 7) to determine the ratio of the distance to M 31 and the distance of the LMC? If the LMC is 50 kpc distant, how far is M 31 from Earth? Is your result with 10% of the value for the distance of M31 given in Destination 14? 2. Find basic information about a Cepheid variable other than 𝛿 𝐶𝑒𝑝ℎ𝑒𝑖. List its name or designation, its location in the sky (constellation is sufficient), its pulsation period, its luminosity and at least one other interesting factoid. Using the period you found for the star, calculate its luminosity using the PL relation in the text in Destination 14 (not the one from problem 1!). Compare your result to the luminosity of the star given in your source. 3. The dwarf spheroidal galaxies of our Galaxy are among the least luminous elliptical galaxies known. Centaurus A (often abbreviated to ‘Cen A’ and pronounced with a soft ‘c’) is one of the most luminous normal elliptical galaxies. a) If Cen A is 50 times further away than one of these dwarf spheroidal galaxies but Cen A appears 10 times brighter as seen from Earth, how much more luminous is Cen A? Use the same relation between distance, brightness and luminosity we originally defined for stars (Destination 7). b) Assume the mass ratio of the two galaxies is the same as the luminosity ratio you just calculated. Report an example among fish, mammals, birds, or reptiles (extinct ones are ok) of a pair of species that have a similar ratio of weights among adults of the respective species. 4. Use the Hubble Law for the expansion of the Universe (Destination 16) to answer the following questions. a) What is the distance to a galaxy with a recession velocity of 10,000 km/s for an assumed Hubble constant of 90 km/s/Mpc? b) You measure the distance to a galaxy to be 120 Mpc and its recession velocity is 6,600 km/s. What Hubble constant would you derive from this galaxy? c) What is the distance to a galaxy for which you measure the Hydrogen-beta line to be at 505 nm? The normal wavelength of this line is 486 nm and you can assume a Hubble constant of 70 km/s/Mpc. Use the Doppler Equation: Δ𝜆/𝜆 = 𝑉/𝑐, where Δ𝜆 is the difference between the observed and true wavelength of the emission line. 5. Look up a galaxy cluster other than Virgo or Fornax that is located within a distance of about 100 Mpc from the Sun. Report on the basic properties of the cluster (distance, velocity dispersion, content, mass, size, etc.) and report on one or two of its unique or particularly noteworthy features.
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