AS1001:Extra-Galactic Astronomy
Lecture 8: The Universal Expansion
Simon Driver Theatre B [email protected] http://www-star.st-and.ac.uk/~spd3 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) Universal Expansion Hubble’s law appears to violate the Copernican Principle as it seems to place us at a special location:
Milky Way
Everything is moving away from us? Universal Expansion Q) What is so special about our location ? A) Nothing ! Me You Consider:
According to Hubble’s Law: v I see: v 2v 3v But if we jump to your location, you see:
3v 2v v v 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 ? V1 V2 For any object we can calculate the time at d1 which it would have been located at our d2 position. From Hubble’s Law this will be the same for all galaxies. 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: 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: STATIONARY: DOPPLER SHIFT:
REDSHIFT:
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 • Gravitational attraction between galaxies, and between galaxies and larger objects • Velocity not just expansion of the universe
• 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. Peculiar Velocities • What we measure from spectra: VRECESSION
VRADIAL or VLINE OF SIGHT VINFALL VIRGO
• Objects velocity wrt surroundings:
VPECULIAR or VINFALL VBULK VBULK • Velocity due to expansion:
VRECESSION or VEXPANSION THE GREAT ATTRACTOR Example
• For MW-Coma Vpec is 1000km/s. • Distance is 50 Mpc (from Cepheids)
• If the redshift, z = 0.01, what is H0 ?
Note: Be very careful with the sign of VINFALL & 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)
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 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. EXAMPLE
MW-Coma Vpec 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 of VINFALL & 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)