Type Ia Supernova Observations. Supernova Results:The Context. Supernova Results. Physics 121 December 4, fainter. brighter

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1 Physics 11 December 4, 009 Today Supernovae revisited Galaxy Rotation Curves Dark Matter & Dark Energy Scaling Factor a(t) Course Evaluations Type Ia Supernova Observations Distant supernovae are than nearby, and their light curves (observed at Earth) evolve more slowly, due to time dilation and other relativistic effects. Supernova Results Supernova Results:The Context The results of the supernova brightness measurements surprised everyone. They show that supernova in high redshift galaxies are than expected. Crudely speaking, this means that they are more distant than predicted by the Hubble law. This implies that the expansion of the universe is accelerating. The expansion causes the supernova light to be spread more thinly over space, so that less of it is captured by the telescope. Hubble s observations found that Galaxies at small redshifts (Z~0.003) are streaming away from us, with velocities proportional to distances. The universe is expanding. Observations of supernovae in more distant galaxies (Z~1.00) found that they are than expected. The expansion of the universe is accelerating, that is, the speeds with which galaxies are moving away from one another are increasing. This was a surprise, because gravitational forces between the galaxies should cause them to decelerate. We conclude that there must be some sort of anti-gravity force, which we call dark energy or cosmological constant. What is this dark energy? Let s put that question aside for the moment and look at yet another kind of mysterious stuff. 1

2 Galaxy Rotation Curves Galaxy Rotation Curves, continued Stars in spiral galaxies such as our own Milky Way follow nearly circular orbits around the centers of the galaxies. Consider a star at distance R from the center of the galaxy, moving at speed v. We expect v to be large for small R and small for large R. This is easy to prove if the force on each star is dominated by gravity from a single massive lump in the center of the galaxy. R v In reality, the net force on a star results from gravitational interactions with all the other stars in the galaxy, so it is a complicated thing to calculate. Nevertheless, because most of the stars are relatively close to the center, if motion of stars is due only to gravity from other stars, then we expect velocity, v, to be smaller for stars at larger distance, R. Milky Way rotation curve: Sofue et al 1999, Astrophysical Journal 53: 136 r v measured expected Measurement of Doppler shifts of stars in our Galaxy (and therefore their speeds) give a surprising result: speeds do not get smaller as distance from the center gets larger. Stars in the outer reaches of our Galaxy are moving faster around their orbits than expected. Something must be wrong with our model of the galaxy: the net force on a given star is larger than that expected from the gravitational attraction of other stars in the Galaxy. Conclusion: there must be additional matter in our galaxy, pulling on stars and causing them to move more quickly in their orbits. We call this stuff dark matter: dark: we can t see it matter: it interacts via the gravitational force, just like normal matter. Galaxy Rotation Curves, continued Measurements in other galaxies give similar results: velocities are more-orless constant as distance from the center of the galaxy is increased. Left: Right: Expected drop-off of speed with distance from center of galaxy Constant speed at all distances from center of galaxy In a typical spiral galaxy, stars can be found as far as kiloparsecs from the center. Beyond that, there are no stars, but there are clouds of gas which allow us to measure rotation curves to larger distances. The rotation curves remain flat to remarkably large distances (The animation might work better in a browser than in PowerPoint.) Animation from: Rotation curves: Bosma 1978 PhD Thesis via Faber & Gallagher 1979 Annual Review of Astronomy and Astrophysics

3 MACHOS: MAssive Compact Halo Objects? Machos is basically a fancy name for dead stars, which you can t see any more: Massive because they are heavy, compact because dead stars are very dense, Halo because they would form a halo around the galaxy. There are, in fact, dead stars in the galaxy, but are there enough to make up the dark matter? The answer turns out to be no. Dead stars will occasionally come close to the line-of-sight between us and ordinary stars. Their gravity of these dead stars will distort the space through which light travels from the ordinary star to us. This is called a microlensing event. Such events have been seen, but not enough to account for the dark matter. WIMPS: Weakly Interacting Massive Particles? These would be tiny particles (tiny in the sense that protons and electrons are tiny). They could not interact through the electromagnetic force; otherwise we would see them. Hence they must interact through the weak force (and gravity). Physicists are actively searching for WIMPs, but none have been found. Something else entirely? What is Dark Matter? Perhaps the most exciting possibility is that neither of these is right, and that there are as-yet-discovered physical processes, different from Newton/Einstein gravity, contributing to motions around galaxies. The story so far Too much gravity on small scales (<~0.1 Megaparsec) In and around galaxies, things are moving too fast. The attractive forces between masses are larger than we expect. We infer that there must be dark matter: massive, gravitationally interacting stuff which we cannot otherwise see. Anti-gravity on large scales (~1000 Megaparsec) Galaxies are rushing away from each other, and this process is accelerating. Our usual explanation is that there must be a force or phenomenon (such as Einstein s cosmological constant) which is not part of our standard physical laws. This is sometimes called dark energy. We can think of dark energy as a peculiar sort of stuff which has mass (so it does gravitationally interact) but which also interacts through a new, not-yet-understood, repulsive (anti-gravity) force. So What s the Universe Made of Today? So What s the Universe Made of Today? Dark Energy 7% Only 5% of the content of the universe (measured by energy content) is normal matter, stuff we can see. The other 95% is dark energy and dark matter. Radiation (Light) <0.01% Normal Matter 4.5% In this jar, 95% of the jellybeans are black. Imagine how different this would look if we could only see the colored jellybeans. Dark Matter 3% Image Credit: Fermilab. To see this jar constructed, search on jelly bean universe on YouTube. 3

4 So What s the Universe Made of Today? The table shows the energy content of the universe, tabulated using all available evidence. Refence: M. Fukugita and P. J. E. Peebles, 004, The Cosmic Energy Inventory, Astrophysical Journal, 616: 643. For a copy of the full paper, do a web search on astro-ph/ The Metric for an Evolving Universe We can describe the expansion of the universe by defining a scale function, a(t). By definition, a=1 right now. At earlier times t, when the universe was smaller, a(t) was smaller. As the universe expands, a(t) is getting larger. We can take the flat-space metric, Δs = Δt (Δx + Δy + Δz ) And modify it to allow for an expanding (or contracting) universe: Δs = Δt a (t)(δx + Δy + Δz ) We model the universe as homogenous, so a(t) is the same everywhere. The universe is not in steady state, so a(t) changes with time. [Note: in an earlier handout, I called the scale factor R(t). Starting today, I am changing notation and calling it a(t) instead.] The scale factor a(t) changes over time. Write its first and time derivatives as: a = da dt a = d a dt a light w = 1/3 cosmological constant (dark energy) w = 1 General relativity gives a formula for the acceleration of the scale factor. It depends on two characteristics of the stuff which causes the acceleration, which we label ε and w: a Here G is Newton s gravitation constant, G= m 3 /kg s. Typically in physics we write ρ (greek letter rho) to denote density, that is, mass divided by volume. However, when we talk about stuff that doesn t have mass in the usual sense (dark energy) we need to do something different. So we use ε to represent energy density. Thus ε is the amount of energy in a given volume of space. For normal matter at rest, E=mc, so ε = energy/volume=mc /V. The variable w is the equation of state parameter. It is related to how the pressure of something changes with density. Here are the rules: light (photons) w = 1/3 dark energy w = 1 4

5 a light w = 1/3 cosmological constant (dark energy) w = 1 How does this fit our picture of the evolution of the Universe? In the early Universe (but after inflation...more about that later), the Universe was dense, and was dominated by normal matter. Plugging w=0 into the above equation, we see that ä is negative, so the scale factor, a(t), decelerates over time. The Universe was rapidly expanding, but the expansion was slowing over time. Later on, as the Universe expanded, the density of ordinary matter got smaller. However, the density of dark energy did not. (If Einstein s cosmological constant is the correct model, the density of dark energy never changes.) If most of the energy is in dark energy, with w= 1 in the above equation, then ä becomes positive and the scale factor a(t) accelerates. This is the present picture: The Universe has been expanding since the big bang. Early on, its expansion slowed down over time. (It continued to expand, but more and more slowly). Later, as dark energy came to dominate the Universe, the expansion started speeding up. 5