The Age, Size, and Expansion Ohio University - Lancaster Campus slide 1 of 17 Spring 2009 PSC 100 Hubble’s Law: The Age, Size, and Expansion of Our Universe

In the early 20th century, Vesto Slipher and Ohio University - Lancaster Campus slide 2 of 17 Spring 2009 PSC 100 In the early 20th century, Vesto Slipher and Edwin Hubble discovered that all galaxies outside of our Local Group are moving away from us. http://www.thunderbolts.info/tpod/2004/images/041109hubble-redshift.jpg Lunarmark.blogspot.com

The motion of every galaxy has 2 components: proper motion (perpendicular to our line of sight) and radial motion (along our line of sight.) The radial motion component of nearly every galaxy we can see is away from us. How can we tell this? actual motion proper motion radial motion Earth

The Doppler Effect If the source of light is moving away from an Ohio University - Lancaster Campus slide 4 of 17 Spring 2009 PSC 100 The Doppler Effect If the source of light is moving away from an observer, the wavelength of the light is stretched. This is a redshift. Image Credit: Wikipedia (Redshift)

Hubble determined the distances to many of Ohio University - Lancaster Campus slide 5 of 17 Spring 2009 PSC 100 Hubble determined the distances to many of these galaxies using cepheid variable stars as ‘standard candles.’ What he discovered was astounding: The radial velocity of a galaxy is directly proportional to its distance. A galaxy 100 MLY away from us is receding away from us twice as fast as a galaxy 50 MLY away.

This relationship, which has come to be known Ohio University - Lancaster Campus slide 6 of 17 Spring 2009 PSC 100 This relationship, which has come to be known as Hubble’s Law, can be used to establish both the size and the age of the universe. Credit: imagine.gsfc.nasa.gov

Doppler Shift Equation: change in wavelength = speed of recession Ohio University - Lancaster Campus slide 7 of 17 Spring 2009 PSC 100 Doppler Shift Equation: change in wavelength = speed of recession unshifted wavelength speed of light Δλ = vr λ0 c

Example: The normal wavelength of H-α light is Ohio University - Lancaster Campus slide 8 of 17 Spring 2009 PSC 100 Example: The normal wavelength of H-α light is 656.3 nm. This light is observed to be shifted to 670 nm when coming from a galaxy. What is the recessional velocity of the galaxy? (670 nm – 656.3 nm) = vr 656.3 nm 3.00 x 105 km/s 13.7 nm x 3.00 x 105 km/s = 6300 km/s 656.3 nm

Velocity = H0 · distance Hubble determined the distance to many such Ohio University - Lancaster Campus slide 9 of 17 Spring 2009 PSC 100 Hubble determined the distance to many such galaxies, finding that their velocities and distances were directly proportional. Today, Hubble’s Law is written: Velocity = H0 · distance velocity is in km/sec distance is in MLY or MPc H0 is the Hubble Constant. H0 has units of 1/time.

Different experiments have attempted to define H0 accurately: Ohio University - Lancaster Campus slide 10 of 17 Spring 2009 PSC 100 Different experiments have attempted to define H0 accurately: 70.1 ± 1.3 km/sec/MPc (WMAP) 72 ± 8 km/sec/MPc (HST) 70.8 ± 4 km/sec/MPc (NASA average) What is NASA’s average value for H0 in units of km/sec/MLY?

Velocity ÷ H0 = distance How does this determine the age and size of Ohio University - Lancaster Campus slide 11 of 17 Spring 2009 PSC 100 How does this determine the age and size of the visible universe? Re-arrange the equation: Velocity ÷ H0 = distance Since light moves at a finite speed (3 x 105 km/s) it takes time to cover distance.

This value includes a number of assumptions, which Ohio University - Lancaster Campus slide 12 of 17 Spring 2009 PSC 100 3.00 x 105 km/s ÷ 21.7 km/s/MLY = 13,825 MLY Our universe has been expanding for 13.8 billion years, and our “horizon” i.e. the edge of our visible universe is 13.8 billion light years away. This value includes a number of assumptions, which we’ll look at when we study cosmology.

Ohio University - Lancaster Campus slide 13 of 17 Spring 2009 PSC 100 Credit: www.astroex.org - ESA/ESO’s Astronomy Exercise Series

How fast should a galaxy be receding from us, Ohio University - Lancaster Campus slide 14 of 17 Spring 2009 PSC 100 Some Examples: How fast should a galaxy be receding from us, if the galaxy is 200 MLY away? H0 · distance = velocity 21.7 km/s/MLY · 200 MLY = 4340 km/sec

How far away is a galaxy that has a Ohio University - Lancaster Campus slide 15 of 17 Spring 2009 PSC 100 How far away is a galaxy that has a recessional speed of 35,000 km/sec? Give your answer in both MLY & MPc. velocity ÷ H0 = distance 35,000 km/sec ÷ 21.7 km/s/MLY = 1613 MLY or 1.61 billion LY or 495 MPc

Ohio University - Lancaster Campus slide 17 of 17 Spring 2009 PSC 100 What happens when you do too much math! Credit: snoedel.punt.nl