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University of Waterloo
SCI 238
Mike Fich

L18 galaxy masses:  rotation curve o works well for nearby, edge-on spiral galaxies o best measured from gas (HI or HII), needs orderly, systematic orbits o not applicable to faint or elliptical galaxies  velocity dispersion o measure the spread in velocities from the width of the spectral lines o velocity spread depends on mass
  motions of galaxies in orbit around each other or in a cluster  from measurements of the Doppler Shift we can measure the rate at which galaxies rotate... but the rotation rate is determined by the mass of the galaxy.  Milky way rotational speed around 200-250 km/s Flat rotation curve => mass with distance ...v2/r = acceleration in circular motion mass of luminous matter (mainly stars) is not enough to match rotation curve spectral line width of a galaxy -> rotation rate -> mass Mass to-Light Ratio...  the mass of a galaxy divided by its luminosity. o we measure both mass [M ] ansunuminosity [L ] in Ssunr units  Within the orbit of the Sun, M/L = 6 M /sun sunfor the Milky Way o this is typical for the inner regions of most spiral galaxies o for inner regions of elliptical galaxies, M/L = 10 MsunL sun  not surprising since ellipticals contain dimmer stars  However, when we include the outer regions of galaxies... o M/L increases dramatically
 o for entire spirals, M/L can be as high as 50 M sun sun o dwarf galaxies can have even higher M/L  Thus we conclude that most matter in galaxies is not stars. o the amount of M/L over 6 M#/ L# is the amount of dark matter       Physical Properties of Galaxies Spirals; Ellipticals Irregulars Barred Spirals Mass (MSun) 109 1012 105 1013 108 3!1010 Luminosity(LSun) 108 4!1010 103 1011 107 3!109 M/L 225 100 1 Diameter (kpc) 550 1200 110 Measuring the mass of galaxies from their motions around each other: Pairs of galaxies in orbit around each other – same situation as binary stars, BUT no transverse motion seen – only radial velocity clusters of galaxies – a statistical study that gives the total mass in the cluster Measuring the Mass of a Cluster  There are three independent ways to measure galaxy cluster mass: 1. measure the speeds and positions of the galaxies within the cluster 2. measure the temperature and distribution of the hot gas between the galaxies 3. observe how clusters bend light as gravitational lenses Measuring the Mass of a Cluster: 1. Galaxy Orbits  Orbiting Galaxies:
 o assume the galaxies orbit about the cluster center o measure the orbital velocities of the galaxies o measure each galaxys distance from the center o apply Keplers Law to calculate mass of cluster o in pioneering studies, Fritz Zwicky found huge M/L ratios for clusters. o his proposals of dark matter were met with skepticism in the 1930s Measuring the Mass of a Cluster 2: Hot gas between galaxies – intracluster medium . Hot (107-108 K) gas between galaxies emits X-rays . from the X-ray spectrum, we can calculate the temperature . temperature tells us the average speed of the gas particles again, we can estimate mass -> the mass required to retain the hot gas . Coma cluster of galaxies (optical) (X-ray) hot gas in galaxies and galaxy clusters also => dark matter predominance Measuring the Mass of a Cluster 3: lensing  the angle at which the light is bent depends on the mass of the cluster. 
 o by analyzing lensed images, we can calculate cluster mass  all previous methods for finding mass depended on Newtons Law of Gravity. 
 o this method uses a different description/model of gravity Gravitational Lensing a galaxy in the foreground can act as a lens for galaxies in the background. Measuring the Mass of a Cluster 3: lensing this galaxy cluster is a gravitational lens. . Einsteins Theory of Relativity states that massive objects distort spacetime. . a massive cluster will bend the path of light which approaches it (like a lens) . blue arcs are the lensed images of a galaxy which is behind the cluster . . Einstein Cross: background quasar (point source) lensed by a foreground galaxy . The amount of lensing depends on the mass of the objects acting as a lens another way to measure the mass . Strong lensing: makes large distorted images. But needs good alignment . Weak lensing: a more subtle effect, look for statistical effects – much more common, but harder to measure. . A2667: another example of lensing . this method has rich potential for understanding the distribution of mass . Galaxy and Cluster Masses: dark matter . The cluster masses which are measured by all three of these independent methods agree: o M/L for most galaxy clusters is greater than 100 M sun sun o galaxy clusters contain far more mass in dark matter than in stars... o this is even greater than the factor of 10 found for individual galaxies . There are only two possible explanations for this: o we do not understand gravity on galaxy and cluster o the observed velocities are caused by the gravitational attraction of unseen matter: dark matter What is Dark Matter Made Of? o dark matter could be made out of protons, neutrons, & electrons – i.e. baryonic matter o so-called ordinarybaryonic matter, the same matter we are made up of o if so, then the only thing unusual about dark matter is that it is dim . some or all of dark matter could be made of particles which we have yet to discover. 
 o this would be extraordinary – i.e nonbaryonic matter . dark matter is found in the halo and far beyond the luminous regions of galaxies An Extraordinary Matter Candidate neutrinos
 o low masses and high speeds => will escape a galaxy o cannot account for the dark matter observed what if there existed massive weakly interacting particles?(WIMPS) o these weakly interacting massive particles are the nature of dark matter is a theoretical; they have not yet been discovered o would be massive enough to exert gravitational influence o would emit no electromagnetic radiation (light) or be bound to any charged matter which could emit light "!since they are weakly interacting particles, they would not collapse with a galaxy’s disk
 o yet they would remain gravitationally bound in the galaxy’s halo Hubble Relation, the Expanding Universe: galaxy radial velocity correlates with distance=> v=H0d o Hubble observed that virtually all galaxies are moving away from our own Milky Way galaxy o the distances between gal
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