1. March 4, 2003Lynn Cominsky - Cosmology A3501 Professor Lynn Cominsky Department of Physics and Astronomy Offices: Darwin 329A and NASA EPO (707) 664-2655 Best way to reach me: lynnc@charmian.sonoma.edu Astronomy 350 Cosmology

2. March 4, 2003Lynn Cominsky - Cosmology A3502 Is the Universe really expanding?  Take a look at the handout  How do you interpret the 3 graphs?  Try to draw graphs of a Universe that has Static galaxies (not moving) Turbulent galaxies (random motion) Rotating galaxies (like the planets around the Sun) Uniformly contracting galaxies

3. March 4, 2003Lynn Cominsky - Cosmology A3503 Cepheid variables and Nebulae  In 1923, Hubble used new Mt. Wilson 100 inch telescope to observe Cepheid variables in the nearby “nebula” Andromeda. He recognized that the fuzzy patches called nebulae were actually distant galaxies, outside of our own Milky Way L =K P 1.3 This relation was calibrated by Hertzsprung and Shapley

4. March 4, 2003Lynn Cominsky - Cosmology A3504 Hubble Law The Hubble constant H o = 558 km s -1 Mpc -1 is the slope of these graphs Compared to modern measurements, Hubble’s results were off by a factor of ten!

5. March 4, 2003Lynn Cominsky - Cosmology A3505 Redshift and Doppler Shift  Redshift z is a non-relativistic approximation that relates the Doppler shift to the velocity of the object  Redshift is determined by comparing laboratory wavelength  to observed wavelength   =    v c = z =

6. March 4, 2003Lynn Cominsky - Cosmology A3506 Hubble Law  v = H o d = cz where v = velocity from spectral line measurements d = distance to object H o = Hubble constant in km s -1 Mpc -1 z is the redshift Space between the galaxies expands while galaxies stay the same size

7. March 4, 2003Lynn Cominsky - Cosmology A3507 Measuring Distance and Time If the Universe expands at a constant rate v = H o d and d= vt Solving for t, we find the age of the Universe: t = 1/H o = 9.78 x 10 9 y h -1 where h = H o /(100 km s -1 Mpc -1 ) Current value for H o is 68 km s -1 Mpc -1 So the age of the Universe is ~14 x 10 9 y

8. March 4, 2003Lynn Cominsky - Cosmology A3508 Expanding Universe  Expanding Universe of Students The farther things are, the faster they are moving away  Expanding Universe of Dots Why it looks as though you are at the center of the expanding universe

9. March 4, 2003Lynn Cominsky - Cosmology A3509 Doppler shifting spectral lines  When a star or galaxy is moving, its spectral lines are Doppler shifted by  = obs – lab  The redshift Z =  / lab  The velocity of the star or galaxy is found from the redshift using v = Z AVG c H and K lines

10. March 4, 2003Lynn Cominsky - Cosmology A35010 Hubble constant  You will plot the velocities (km/sec) vs. the distances (Mpc) that you obtain from a sample of galaxies  The slope of this line is known as the Hubble constant – it is given in km/sec/Mpc H = v/D

11. March 4, 2003Lynn Cominsky - Cosmology A35011 The age of the Universe  The age of the Universe is the inverse of the Hubble constant  Age = 1/H = D/v  But H must be in the correct units!  D must be in km  V must be in km/sec  This will give you the age of the Universe in seconds  To convert to years, divide by 3.15 x 10 7

12. March 4, 2003Lynn Cominsky - Cosmology A35012 Web Resources  CLEA Astronomy Laboratories http://www.gettysburg.edu/academics/physics/clea /CLEAsoft.overview.html http://www.gettysburg.edu/academics/physics/clea /CLEAsoft.overview.html  Hubble diagram http://physics.ucsd.edu/students/courses/fall2001/ physics5/notes/ch17/sld005.htm  Thanks also to Dr. Gordon Spear for providing his Hubble Law Lab spreadsheet!

13. March 4, 2003Lynn Cominsky - Cosmology A35013 Web Resources  Astronomy picture of the Day http://antwrp.gsfc.nasa.gov/apod/astropix.html  Imagine the Universe http://imagine.gsfc.nasa.gov http://imagine.gsfc.nasa.gov  Ned Wright’s ABCs of Distance http://www.astro.ucla.edu/~wright/distance.htm http://www.astro.ucla.edu/~wright/distance.htm  Prof. Pogge’s class notes at OSU http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit4/nebulae.html