Dark Matter, Dark Energy, and the Fate of the Universe

Review: What is Hubble’s law? Hubble’s law tells us that more distant galaxies are moving away faster. It allows us to determine a galaxy’s distance from the speed at which it is moving away from us, which we can measure from the Doppler redshift in its spectrum. Hubble’s Law: velocity = H 0 x distance y =mx is the equation of a straight line with slope m = Rise/Run.

REVIEW: Supermassive Black Holes Orbital speed and distance of gas orbiting center of M87 indicate a black hole with mass of 3 billion M Sun NOTE: For a 1 Msun black hole the Event Horizon is 3 km and so for M87 it must be 9 billion km. But 20 AU = 3 billion km. So this event horizon is 60 AU in radius which is larger than most of the solar system (40AU radius). This is a monster of a black hole!

QUASARS are very distant (hence very young) and extremely luminous. They are the core of galaxies with very active nuclei. We know that they are compact because they vary rapidly in brightness over hours, which is the light travel time across something about the size of the Solar System. Each quasar is a ~BILLION solar mass Black Hole; the luminosity comes from the exceedingly hot accretion disk. Many nearby galaxies have supermassive black holes at their centers. Many seem to be dormant; our galaxy (Milky Way) has a modest (quiet) black hole of 4 million solar masses! Most galaxies may have passed through a quasar-like stage There are no “nearby” quasars; most occurred when the universe was about 1/3 its present size, i.e. they are at a “redshift” of z = 2. Review: Quasars

Expansion stretches photon wavelengths causing a cosmological redshift directly related to lookback time Redshift Redshift = change in wavelength divided by original wavelength; Symbol = z The “size” of the universe at a given time is proportional to 1/(1 + z) At z = 1, universe = ½ current size

What is the universe made of? W have left two crucial questions unanswered! –1. What is the source of the gravity that causes galaxies to form and holds them together against the expansion? –2. What will happen to the expansion of the universe in the future? In the last two decades we have come to realize that the dominant source of gravity in the universe is a dark form of matter that differs fundamentally from the atoms that make people, stars and galaxies In addition, there appears to be a dark form of energy throughout the universe that counteracts gravity and is driving the expansion

Unseen Influences in the Cosmos Our goals for learning: What do we mean by dark matter and dark energy?

Dark Matter: An undetected form of mass that emits little or no light but whose existence we infer from its gravitational influence Dark Energy: An unknown form of energy that seems to be the source of a repulsive force causing the expansion of the universe to accelerate Unseen Influences

Remember, because of E = mc 2 we need to account for both matter and energy “Normal” Matter: ~ 4.4% –Normal Matter inside stars:~ 0.6% –Normal Matter outside stars:~ 3.8% Dark Matter: ~ 23% Dark Energy~ 73% Contents of Universe

What have we learned? What do we mean by dark matter and dark energy? –“Dark matter” is the name given to the unseen mass whose gravity governs the observed motions of stars and gas clouds –“Dark energy” is the name given to whatever might be causing the expansion of the universe to accelerate

Evidence for Dark Matter Our goals for learning: What is the evidence for dark matter in galaxies? What is the evidence for dark matter in clusters of galaxies? Does dark matter really exist? What might dark matter be made of?

We measure the mass of the solar system using the orbits of planets Orbital Period Average Distance Or for circles: Orbital Velocity Orbital Radius Mass Enclosed: M = r v 2 /G

Rotation Curve A plot of orbital velocity versus orbital radius Solar system’s rotation curve declines because Sun has almost all the mass: r v 2 = MG = constant

A Merry-go- Round (or any solid-body disk) has a different Rotation Curve. Who has the largest orbital velocity? A, B, or C?

Who has the largest orbital velocity? A, B, or C? Answer: C In this case the object with the largest radius has greatest velocity, because the angular speed (ω = 2π/period) is fixed: v = ωr

Rotation curve of merry-go- round rises with radius For stars in orbit about the central mass of the Galaxy we expect the rotation curve to decline, but …

Rotation curve of Milky Way stays flat with distance!? Mass must be more spread out than in solar system. Although it looks as if there is more mass in the center, the observations suggest that this is not true.

Mass in the Milky Way is spread out over a larger region than the stars, and it does not glow like stars or nebulae. Most of the Milky Way’s mass seems to be dark matter!

Mass within Sun’s orbit: 1.0 x M Sun But, The total mass: ~10 12 M Sun There is 10x as much matter in the Milky Way as we can “see” in stars!

The visible portion of a galaxy lies deep in the heart of a large sphere of DARK MATTER Is it just the Milky Way?

No! We can measure rotation curves of other spiral galaxies using the Doppler shift of the 21- cm line of atomic H. Here we do not rely on stars but use the abundant interstellar hydrogen gas itself.

Spiral galaxies all tend to have flat rotation curves, indicating large amounts of dark matter in all of them

It is not just spiral galaxies! Broadening of spectral lines in elliptical galaxies tells us how fast the stars are orbiting. These galaxies also have dark matter; about 10x the amount in stars.

We can also measure the velocities of galaxies in a cluster from their Doppler shifts. The mass we find from galaxy motions in a cluster is about 50 times larger than the mass in stars within the galaxies!

We now know that Galaxy Clusters contain large amounts of X-ray emitting hot gas. The temperature of the hot gas (particle speeds) tells us cluster mass: 85% dark matter 13% hot gas 2% stars

Gravitational lensing, the bending of light rays by gravity, can also tell us a cluster’s mass

All three methods of measuring cluster mass indicate similar amounts of dark matter Gravitational lensing reveals much more mass than we can “see” in starlight from these galaxies. More evidence for truly dark matter.

Does Dark Matter Really Exist? Our Options 1.Dark matter really exists, and we are observing the effects of its gravitational attraction 2.Something is wrong with our understanding of gravity, causing us to mistakenly infer the existence of dark matter

Our Options 1.Dark matter really exists, and we are observing the effects of its gravitational attraction 2.Something is wrong with our understanding of gravity, causing us to mistakenly infer the existence of dark matter Because gravity is so well tested, most astronomers prefer option #1 Alternative theories of gravity have been investigated but don’t seem to make sense

Some observations of the universe are very difficult to explain without dark matter

Ordinary Dark Matter (MACHOS) –Protons, neutrons etc, as usual, but in very dim objects –Massive Compact Halo Objects: dead or failed stars in halos of galaxies Extraordinary Dark Matter (WIMPS) –Not protons, neutrons or any form of normal matter –Weakly Interacting Massive Particles: mysterious neutrino-like particles (but not neutrinos because they are too fast - relativistic) Two Basic Options

MACHOs occasionally make other stars appear brighter through lensing, which has been observed … but not enough lensing events to explain all the dark matter.

There’s simply not enough ordinary matter! WIMPs could be left over from the Big Bang –There are plausible models of such weakly interacting particles generated under the Big Bang conditions Models involving WIMPs explain how galaxy formation works –These particles do not feel the electromagnetic force nor the strong nuclear force; they feel only gravity and the weak force –They can’t radiate energy away and thus can’t collapse Why Believe in WIMPs?

What have we learned? What is the evidence for dark matter in galaxies? –Rotation curves of galaxies are flat, indicating that most of their matter lies outside their visible regions What is the evidence for dark matter in clusters of galaxies? –Masses measured from galaxy motions, temperature of hot gas, and gravitational lensing all indicate that the vast majority of matter in clusters is dark

What have we learned? Does dark matter really exist? –Either dark matter exists or our understanding of our gravity must be revised What might dark matter be made of? –There does not seem to be enough normal (baryonic) matter to account for all the dark matter, so most astronomers suspect that dark matter is made of (non-baryonic) particles that have not yet been discovered

Structure Formation Our goals for learning: What is the role of dark matter in galaxy formation? What are the largest structures in the universe?

The gravity of dark matter is what caused protogalactic clouds to contract early in time

WIMPs can’t contract to the center because they don’t radiate away their orbital energy. This explains the rotation curves of galaxies.

Dark matter is still pulling things together After correcting for Hubble’s Law, we can see that galaxies are “flowing” toward the densest regions of space, which is where the dark matter is denser.

Maps of galaxy positions reveal extremely large structures: superclusters and voids on a scale of millions of light-years LARGE SCALE STRUCTURE

Models show that gravity of dark matter pulls mass into denser regions – so the universe grows lumpier with time [Universe began smooth with a high degree of symmetry–it has a very low entropy–as time progressed (under gravity) it becomes disordered and entropy increases. This may provide the “arrow of time”.] Time in billions of years Size of expanding box in millions of lt-yrs

Models show that gravity of dark matter pulls mass into denser regions – universe grows lumpier with time

Structures in galaxy maps look very similar to the ones found in models in which dark matter is WIMPs. [Note however that on scales of BILLIONS of light-years everything looks the same!]

What have we learned? What is the role of dark matter in galaxy formation? –The gravity of dark matter seems to be what drew gas together into protogalactic clouds, initiating the process of galaxy formation What are the largest structures in the universe? –Galaxies appear to be distributed in gigantic chains and sheets that surround great voids

The Fate of the Universe Our goals for learning: Will the universe continue expanding forever? Is the expansion of the universe accelerating?

Does the universe have enough kinetic energy to escape its own gravitational pull? The fate of the universe depends on the amount of dark matter

We can calculate how much mass (or density) is needed to stop the expansion. Amount of dark matter is ~25% of this “critical” density suggesting that the fate is eternal expansion.

But, observations show that the expansion appears to be speeding up! This means that there must be something working against gravity! Dark Energy?

Estimated age depends on both dark matter and dark energy

Brightness of distant white-dwarf supernovae tells us how much universe has expanded since they exploded

Brightness of distant white-dwarf supernovae tell us how much the universe has expanded since they exploded. Dark matter and normal matter create gravity and should slow down expansion. Dark energy is like a coiled up spring releasing energy. The Evidence for Dark Energy Distance (d) from Hubble’s Law and the distance from luminosity of White Dwarf Supernovae don’t agree, yet both are solid methods. H 0 must have been smaller in the past! White Dwarfs supernovae are fainter than expected! V=H 0 d

The Accelerating Universe is best fit to supernova data. Einstein’s Cosmological Constant – a repulsive energy associated with the vacuum of empty space, is a strong candidate for the Dark Energy

What have we learned? Will the universe continue expanding forever? –Current measurements indicate that there is not enough dark matter to prevent the universe from expanding forever Is the expansion of the universe accelerating? –An accelerating universe is the best explanation for the distances we measure when using white dwarf supernovae as standard candles