Hubble Law, Distances & Structure in the Universe Today’s Lecture: Hubble Law, Distances & Structure in the Universe Hubble Law Cosmic Distances Galaxy Clusters/Mass of Clusters Large Scale Structure of Universe Homework 8 due: Tuesday, April 15 Reading for today: Chapter 18 Reading for next lecture: Chapter 19 Final Exam: Friday, May 2, 1:30 pm, Hasb. 138 Help Session: Thursday, May 1, 1:30 pm, LGRT 1033

Motion of Galaxies In the early part of the 20 th century astronomers were photographing the optical spectra of galaxies inabling them to measure the “Doppler shift” and thus the radial velocity. In 1912 Vesto Slipher obtained the first galaxy radial velocity measurement. Found that Andromeda galaxy was moving toward us at a velocity of 300 km s -1 (~1 million km/hr). He expanded his measurements and was surprised to find that 21 of the next 25 galaxies were redshifted – moving away from us. In fact almost all galaxies are redshifted !!!

Hubble Law Edwin Hubble obtained distances to the galaxies with radial velocities measured by Slipher and Humanson using Cepheids. In 1929 reported a remarkable discovery, there was a relation between recessional velocity and distance !! Below is the original figure from Hubble's paper. Hubble found that the further away a galaxy was, the larger its recessional velocity or redshift.

The spectrum (below) is of a spiral galaxy and shows an expanded view of the absorption lines of calcium (the H and K lines). The rest wavelengths are marked and shows that this galaxy is redshifted. Above the H and K lines of calcium in galaxies of varying distance. See that the most distant galaxies have larger and larger redshifts.

The relation between distance and velocity is known as the Hubble Law and is expressed as: V = H  D, where V is velocity, D is distance and H the Hubble constant. A Hubble diagram using Cepheid distances (HST) to local galaxies: If V is in km/sec and D in Mpc (megaparsecs – 10 6 parsecs), we find that the Hubble constant is around 75 km s -1 Mpc -1. The extent of Hubble's original data.

What does the Hubble law imply about our Universe ? It has a more profound meaning - we are living in an expanding universe. As the “fabric” of space/time expands, it carries with it the galaxies. The same Hubble Law is seen by any observer in the Universe !!! To measure the pure expansion motion, must look on large scales, so the expansion dominates galaxies individual random motions. We are not in a preferred location in the universe where all galaxies are moving away.

The redshift is NOT a Doppler shift, not due to the motion of galaxies through space, but instead it is due to expansion of space. The wavelength of light is stretched as the Universe expands. For this reason we often refer to the shift of spectral lines to longer wavelengths as a cosmological redshift, where a galaxy's redshift (z) is expressed: Redshift = z = ( obs  o )  o =  / o

The scatter in the Hubble Law shown below is that not only do galaxies have a cosmological redshift (due to the expansion of the Universe), but they also have motions through space (Doppler shift). To measure the expansion of the Universe, need to look are even larger scales.

Cosmic Distance Ladder Fundamental Distance Determinations: Radar: For distances within the solar system, radar reflection can be used to measure distances very accurately. Can be used to distances out to ~20 AU ( parsecs). Stellar Parallax: The stellar parallax can be measured for nearby stars. Hipparcos satellite measured the parallax of 120,000 stars and Gaia will soon measure 200 million stars to distances as large as 8 Kpc with a 10% accuracy.

Stellar parallax permits calibration of the luminosity (absolute magnitude) of stars on the main sequence. Spectroscopic Parallax: Measure apparent magnitude and spectral type, deduce absolute magnitude, and estimate distance. Good for star clusters within Milky Way. Standard Candles: At greater distances, need objects of known luminosity (or absolute magnitude). By measuring the objects apparent magnitude, can derive the distance: m – M = 5 log (d/10pc), of course may need dust correction.

Cepheid Variable Stars: Pulsating stars that vary in light output. The period-luminosity relations makes Cepheid variable stars a very good standard candle. Thus, the period of pulsation provides a measure of the luminosity. Combining the apparent brightness and luminosity results in the distance. Cepheid stars can seen to great distances, as large as Mpc.

Cepheid Variable Stars: A key project for HST was to determine accurate distances to nearby galaxies using Cepheids. This permits the calibration of additional (secondary) distance indicators – most importantly Type Ia supernovae.

Type-Ia supernova result from the detonation of white dwarf stars when their mass (slightly) exceeds 1.4 M sun. The brightness of the explosion should be roughly the same for every Type-1a supernova. Calibrate by measuring the host galaxies distances with Cepheids – Hubble Key Project. Type-I Supernovae are standard candles. Knowing their luminosity (absolute magnitude), and comparing to their measured flux density (apparent magnitude), yields distance. Useful for determining distances out to billions of pc. Type 1a SN

Type Ia Supernova: Can be seen to distances of billions of parsecs. Useful as cosmological probes. Used to calibrate the Hubble constant.

From the Type Ia supernovae, we determine that H = 71 ± 2 km s -1 Mpc -1. Remember the Hubble Law: V = H  D, so if we measure the redshift and use the above to estimate the distance to very distant galaxies (D = V/H). D = V/H = 14,200 km/sec/71 km s -1 Mpc -1 = 200 Mpc. Assume H = 71 km s -1 Mpc -1, if we measure the recession velocity (or redshift) of a galaxy to be 14,200 km s -1, what it its distance ?

Summary of the distance “ladder”, it is a ladder because the distances build on each other. Hubble Law Type Ia SN Tully-Fischer (not discussed) Cepheid Variables Spectroscopic Parallex Parallax Radar

How are these Galaxies Arranged ? The Hubble Ultra Deep Field obtained with 400 orbits of Hubble. Over 10,000 galaxies detected, but area covered only 1 part in 13 million of the entire sky !!!!

Galaxy Clusters Galaxies are not uniformly distributed in space. Significant clustering (see right the distribution of 1.5 million nearby galaxies from 2MASS). Poor Clusters: Few cluster members, irregularly shaped, dominated by spiral and dwarf irregular & elliptical galaxies. Rich Clusters: Contain hundreds to thousands of galaxies, spherical distribution, dominated by elliptical and S0 galaxies. Often a giant elliptical galaxy at center.

The remaining ~40 galaxies in the Local Group are all dwarf elliptical and irregular galaxies. Size of Local Group about 1 Mpc. The Local Group The Local Group is a poor cluster containing our Milky Way galaxy and two other large spiral galaxies.

Poor galaxy clusters or small galaxy groups are very common.

The closest rich galaxy cluster is the Virgo Cluster (distance 16.5 Mpc) with about 1500 galaxies within a radius of 2 Mpc (inner region shown below). Dominated by 3 giant elliptical galaxies. Elliptical galaxies are very common in rich clusters.

Abel 1689 is another rich cluster at a distance of 754 Mpc. One of the more massive galaxy clusters known. Again see domination by giant elliptical galaxies. Although impressive, only about 5% of galaxies reside in rich galaxy clusters.

Rich clusters of galaxies have hot (10 million degrees K) gas (intercluster gas) seen in x-rays. Optical X-rays The mass of hot gas greatly exceeds the sum of the mass in stars and cold gas in all the galaxies in the cluster.

Mass of Galaxy Clusters The galaxies in clusters are in orbit about the center of mass of the cluster. Again by measuring the velocities of individual galaxies relative to the mean velocity of the cluster (velocity dispersion), we can estimate the total mass of the galaxy cluster. Coma Cluster – distance 100 Mpc

Mass of Galaxy Clusters From measurements of the radial velocity of each galaxy in a cluster, we can determine the velocity dispersion. In elliptical galaxies we applied the virial theorem to the measured line of sight velocity dispersion for the stars to estimate the mass. Likewise, we can use the galaxy velocity dispersion to deduce the mass: The mass is given by: M = 5/3 v 2 R/G Again we assume the galaxy motions are isotropic, so 〈 v 2 〉 = 3 σ 2, where the line-of-sight dispersion of the galaxies velocities is σ. Find that the visible matter (stars and gas) in galaxies typically represents only a few % of the total mass of the galaxy clusters.

The temperature of the hot gas gives us the velocity of the gas atoms. As before, we can determine the total mass needed to bind the gas to the galaxy cluster. Composite image of Abel 1689 showing x-ray emission in purple. Although the mass of hot gas exceeds the mass of stars and cold gas in galaxies, much more dark matter is needed to explain the confinement of the gas and the motion of the galaxies in the cluster.

Gravitational Lensing General relativity allows light to be bent by gravity (remember that mass distorts space-time, and distorted space-time impacts the motion of both particles and light). A concentration of mass (such as a galaxy cluster) can act like a lens and image background galaxies. This can distort and produce multiple images of a background galaxy.

Hubble image of a galaxy cluster Abel 2218 showing the effect of the gravitational lens on background objects. By modeling the lensing effects, astronomers can determine the total mass of the galaxy cluster.

Two more examples of the lensing effect of a galaxy clusters. Abell 370 to the left. The image to the right show the multiple images of a single blue galaxy that lies behind the cluster ( ).

The mass of galaxy clusters is not dominated by the visible stars. If fact, in rich galaxy clusters there can be as much as 10 times more mass in the hot gas than there is in stars. However, all of the methods for measuring the mass of the galaxy clusters demonstrate that most of the mass must be in dark matter. Rich Galaxy Clusters are composed of: 1-2 % stars and “cold” gas % hot gas 85 % dark matter

Galaxy Superclusters Galaxy clusters are grouped into larger structures called superclusters (clusters of clusters of galaxies). Superclusters contain many galaxy clusters and can be hundred million parsecs across. The Local group is part of a large supercluster called the Local Supercluster (also called the Virgo supercluster). Contains about a dozen galaxy clusters and is about 30 Mpc across.

Local Superclusters

Large-Scale Structure Redshift surveys provide a “slice” of the universe. Measure the redshifts for a large number of galaxies in a slice on sky. Third dimension is redshift or distance.

Example: Two-Degree Field Galaxy Redshift Survey (2dFGRS) with redshifts for 220,000 galaxies. On large scales Universe is structured with galaxy clusters, superclusters and large voids.

The Sloan Digital Sky Survey (SDSS) performed the largest redshift survey of galaxies. See the very non-uniform distribution of galaxies and galaxy clusters – the cosmic web. Probe structure out to about 1 billion parsecs.