AS1001:Extra-Galactic Astronomy Lecture 8: The Universal Expansion Kenneth Wood 316 firstname.lastname@example.org http://www-star.st-and.ac.uk/~kw25
Hubble’s Discovery • Having proved that M31 was external to our galaxy, Hubble collected images and spectra for many more galaxies • From photographic images he estimated distances using the brightest stars (NB: the fainter galaxies were too distant to find and measure Cepheid stars) • For nearby galaxies he showed that the brightest star methods works as a distance indicator and calibrated it to Andromeda • From spectra he calculated the radial velocities of these galaxies • Plotting distance versus velocity he found:
Hubble’s Law • Most galaxies recede • More distant galaxies recede faster • There is a linear relationship between velocity and distance: • v = velocity (km/s) • d = distance (Mpc) • H0 = The Hubble constant (km/s/Mpc)
Hubble’s Data • For these 5 bright ellipticals in nearby clusters we see that fainter galaxies have their Ca H & K lines • redshifted further • Simply by assuming that the brightest elliptical in a cluster is of comparable absolute magnitude we see Hubble’s law for ourselves
Milky Way Universal Expansion • Hubble’s law appears to violate the Copernican Principle as it seems to place us at a special location: • Everything is moving away from us?
Me You v v 2v 3v v 3v 2v v Universal Expansion • Q) What is so special about our location ? • A) Nothing ! • Consider: • According to Hubble’s Law: • I see: • But if we jump to your location, you see:
The Universal Expansion • A “vector jump” to another galaxy will result in that galaxy seeing all others moving away from it. • Only an expansion or contraction can produce a centre-less but dynamic Universe.
An Expanding Universe • Hubble’s observations resolved Olber’s Paradox and allowed Einstein to remove the fudge from his equations. • It overturned the idea of permanency and replaced it with an approximate age for our Universe. • Why ? V2 V1 For any object we can calculate the time at which it would have been located at our position. From Hubble’s Law this will be the same for all galaxies. d1 d2
The Hubble Constant • The exact value of the Hubble Constant has been the focus of heated debate since its discovery. • Initially Hubble measured it to be 500km/s/Mpc • However he had mistaken RR Lyraes for Cepheids in most of his galaxies. When corrected, the Hubble Constant changed to 100km/s/Mpc • For most of the past few decades measurements have come in in the range 50-100 km/s/Mpc • The Hubble Space Telescope was named after Hubble and its primary aim was to measure H0
The HST Key Program The Hubble Space Telescope enables us to measure Cepeheids in the distant Virgo cluster and thereby obtain our most accurate value for H0
The Age of the Universe • From 1/H0 we can calculate an approximate age for the Universe:
STATIONARY: DOPPLER SHIFT: REDSHIFT: Redshift • An expansion implies a stretching of space-time. • The more space-time there is between you and an object the faster it will appear to be moving away. • It is the expansion which causes a galaxy’s spectrum to be REDSHIFTED: REDSHIFT IS NOT THE SAME AS DOPPLER SHIFT
Redshift • A useful parameter for cosmology is the redshift: • This is analogous to the definition of Doppler shift such that: from which follows: • Although this is the wrong interpretation of redshift it is a good approximation for low-z (z < 0.5)
Calculating distances • Using Hubble’s Law we can easily estimate distances from a galaxy’s measured redshift. • e.g., If H0 = 75 km/s/Mpc and the redshift is measured to be 0.1 what is its distance ? • [This implies that for example its OII line, normally at 3727A, occurred at 4100A]
Peculiar Velocities • If a galaxy has a peculiar velocity then a redshift measured from its spectral lines will be affected. • Such peculiar velocities are caused by gravitational attraction between galaxies and bulk flows can also occur due to clusters and large scale structures. • For example the MW is falling into Virgo which in turn is falling into The Great Attractor. • If we know a galaxy’s peculiar velocity we can correct for this additional velocity component.
What we measure from spectra: VRADIAL or VLINE OF SIGHT Objects velocity wrt surroundings: VPECULIAR or VINFALL Velocity due to expansion: VRECESSION or VEXPANSION VRECESSION VINFALL VIRGO VBULK VBULK Peculiar Velocities THE GREAT ATTRACTOR
EXAMPLE Our infall velocity towards Coma is 1000km/s. Its distance from us as measured from Cepheids is 50 Mpc. If the redshift of the central galaxy is measured to be z = 0.01 from the spectral lines what is H0 ? Note: Be very careful with the sign ofVINFALL & VPECULIAR, it is intuitive ! Typically VINFALL is subtracted but for VPECULIAR it will depend on the direction of the peculiar velocity (towards us= -ve, away= +ve)