# The Milky Way, Hubble Law, the expansion of the Universe and Dark Matter Chapter 14 and 15 The Milky Way Galaxy and the two Magellanic Clouds.

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1 The Milky Way, Hubble Law, the expansion of the Universe and Dark Matter Chapter 14 and 15 The Milky Way Galaxy and the two Magellanic Clouds. Image taken from the European Southern Observatory in Chile

2 The Structure of our Galaxy Disk is about 300pc thick at the Sun Globular clusters reside in a nearly spherical halo. 1 parsec = 3.3 light-years

3 Almost every object that our eyes see in the sky is part of the Milky Way galaxy, the Galaxy. Only three objects outside the Milky Way, the romeda Galaxy and the two Magellanic Clouds are visible to the naked eye The band of diffuse light that stretches across the sky is what we see when looking along the plane of the Galaxy. The dark regions are regions of higher concentration of dust. We cannot see the stars behind the dust

4 How do we measure the mass of the Milky way Galaxy? From Kepler s 3 rd Law (as modified by Newton), applied to the orbit of the Sun: P 2 (in Earth years) = a 3 (in AU) / M total (in M sun ) M total is the mass of the Sun + mass of the Galaxy interior to the Sun s orbit The mass of the Sun can be neglected compared to the mass of the Galaxy Parameters of the Sun s orbit around the Galactic Center: Radius (= a) = 8 kpc = 1.65 x 10 9 AU Period (=P) = 225 million years M total = 9 x M sun 100 billion Suns! This is the mass located inside the orbit of the Sun. It is not the total mass of the Galaxy; There is more mass outside the orbit of the Sun

5 . There is a relation between the mass of the galaxy and the orbital speed v of objects in orbit around the galaxy The orbital speed is: v = (G M interior / radius) G is a constant The radius is the orbital radius of the object. The distance from the object to the center of the galaxy The mass of the galaxy inside the orbit of the objects is M interior This relationship is also valid for the orbital velocities and distance of the planets from the Sun

6 The orbital speeds of the planets follow a similar equation: v = sqrt(g M Sun / radius) Solar system Milky way Outside the Galaxy, as in the Solar System, M interior = M total and again v = (G M interior / radius) In the inner part of the Galaxy (in the bulge), M interior increases with radius, so v may stay constant or even increase with radius.

7 Edge of visible Galaxy at 15 kpc - rotation speed yields 2 x M sun At 40 Kpc, rotation speed yields 6 x M sun Dark Matter Problem Within Galactic bulge - spherical distribution, v r If the mass ended at 15 kpc, we should find v = sqrt(1/radius). Important conclusion: The rotational curve reveals the presence of invisible matter. That unseen matter is only detected by its gravitational effect on stars or object inside the orbit of those objects. This matter is called Dark Matter

8 Dark Matter Problem 2/3 of the Galaxy s mass is invisible!?! mostly beyond the visible light radius! There is lots of stuff out here

9 Dark matter does not emit light, its presence is only detected by its gravitational attraction, but there is a lot of dark mass in the outer part of the Galaxy (About 2/3) Dark Matter candidates:? White Dwarf Stars? Very Low Mass Stars Red Dwarfs? (0.2 M sun ) Brown Dwarfs (<0.08 M sun ) Neutron Stars Black Holes Should be far too few. Massive star are a few percentage of total number of stars? Massive Compact Halo Objects MACHOs? Exotic sub-atomic particles Weakly Interacting Massive Particles WIMPs

10 The Search for Stellar Dark Matter (brown dwarfs or white dwarfs): MACHOs Search using Gravitational Lensing The faint foreground object (brown or white dwarf) bends the light of the background star because of its gravitational field (gravitational lensing) The light from the background star is focused or lensed by this effect and the star appears brighter. A few thousand of these events have been observed, suggesting at least in part that some of the dark matter can be accounted by white dwarfs but not for all the dark matter inferred from the dynamical studies

11 An example of gravitational lensing caused by the mass in a group of galaxies: The Cheshire Cat Dark matter is present in clusters of galaxies Gravitational lensing is caused by the distortion of space due to the presence of mass. Light propagate in a curved path. This is predicted by Einstein relativity theory Light from distant galaxies is distorted by the mass and dark mass of a closer cluster of galaxies The combination of the visible matter and the dark matter produce a curvature of the space around the group of galaxies in the cluster

12 Variable Stars -Stars whose luminosity change with time -The star is physically pulsating - A few of these stars pulsate periodically Let s take a look to two important types of these variable stars: RR Lyrae (Lyra constellation) Cepheid (Cepheus constellation) All pulsate in the same way Periods 0.5 to 1 day Each pulsates somewhat differently Periods range from 1 to 100 days

13 How can we use these variable stars? There is a relationship between the pulsation period of these variable and its luminosity. What does this mean and how we can use it? We can observe nearby variables and determine their distances using trigonometric or spectroscopic parallax. Once we know the distances. We can determine the luminosity. We plot the period and luminosity to find the relationship For more distant variables, we can measure the pulsation period and determine their luminosity and then the distance They can be used Luminosity to determine distances!! Flux distance 2 Cepheids are very bright We can see Cepheids in nearby galaxies!

14 Edwin Hubble Discovered Cepheids in the what was known as a spiral nebula (Now we know is actually a galaxy) in the romeda galaxy in the 1920s His notes about a variable star Hubble then derived the distance to romeda, and showed that it was external to our Galaxy (~2.5 million light years away) another galaxy in its own right! (Remember that the diameter of our galaxy is about 100,000 ly) This had a profound impact on our understanding of our place in the universe, similar to the Copernican revolution. Note the date: 6 Oct 1923

15 The Hubble Law and the expansion of the Universe Hubble began measuring distances to other galaxies, outside the Local Group (The local group galaxies are gravitationally bound, some are moving away, some are moving toward the Milky Way) He and others measured the distance and the speed of recession of many distant galaxies He found that galaxies outside the Local Group are all moving away from us He found a linear relationship between speed of recession and distance The farther the galaxies are, the faster they are receding from us The universe is expanding! Hubble Law Recessional Velocity (in km/sec) = H o distance (in Mpc) V = H o D where H o is Hubble s constant (~70 km/sec per Mpc)

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