Lecture 31:The Age & Fate of the Universe

Astronomy 1143 – Spring 2014Astronomy 1143 – Spring 2014

Key Ideas:Expansion history of the Universe

•Calculate the time since the Big Bang•Hubble time gives an approximate answer•Current best estimate 13.798 +/- 0.037 Gyr

Test w/Ages of Oldest Stars – Hydrogen burning

Fate of an Accelerating Universe:•Expands forever at an ever-increasing rate•Star formation will end, protons may decay, black holes will evaporate, other quantum effects may become important•Ends in a cold, dark, disordered state.

Back to the Beginning

The Universe is expanding now.

In the past:• Universe was smaller.• Galaxies were closer together in space.

If we go back far enough in time:• All galaxies (matter) in one place.

How far back = “Age of the Universe”

Road Trip Analogy

You leave Columbus by car for Florida, but leave your watch behind.

How long have you been on the road?• Your average speed = 100 km/h• Your odometer reads: distance = 230 km

Time since you left: T = distance speed• T = 230 km 100 km/h = 2.30 hours

The Hubble Time: T0

Hubble’s Law says• A galaxy at distance d away has a recession

speed, v = H0d

If locally, v is its average speed, then:• T0 = d / v

• but since, v = H0d, T0 = d / H0d = 1 / H0

Hubble Time: T0 = 1 / H0

Estimate of the Age of the Universe

Example

H0=72 km/s/Mpc What is the Hubble Time?

First issue: units!

But…Cosmic expansion is not expected to be constant over all times. But galaxies still need to get to their current distances.

If faster in the past than 72 km/s/Mpc:• Galaxies would take less time to get to their current

distances

• T0 would overestimate the age of the Universe.

If slower in the past than 72 km/s/Mpc:• Galaxies would take more time to get to their current

distances

• T0 would underestimate the age of the Universe.

So, How Old is it Really?

Need two hard-to-measure numbers:

Hubble Parameter, H0:

• How fast the universe is expanding now.

Density Parameter, :• How the matter & energy density affected the

expansion rate in the past.

• Can include an term that enhances the expansion rate

Needed to determine the expansion history.

Best Estimate of the Age:

13.798 ± 0.037 GyrTo calculate this number, we need to know many other properties of the Universe, such as H0, m, and .

We can test whether our measurement makes sense by looking at the ages of objects in the Universe. They should all be younger than 13.798 Gyr..

Testing the Finite Age of the Universe

Ages of the Oldest Stars• We can determine how long stars should be

burning H into He in their cores• Longer for lower masses• When stars run out of hydrogen, their outward

appearance changes dramatically as they evolve into red giants

• Measure masses of stars that are turning into red giants – get their ages

Stars cannot be older than the Universe

Globular Clusters

Results

Accurate measurements have been made for ~30 globular clusters

Ages from 11-13 Gyr

Biggest uncertainties• Distance to cluster• Amount of dust between cluster and us• Composition of stars in cluster• Improvements with Gaia!

Oldest star clusters -- younger than Universe

Epochs of the UniverseIn the distant past, the Universe was radiation-

dominated• First 72,000 years

Then the Universe is matter-dominated• Next 10 billion years • Density of matter dominates the budget of the

Universe

Now & in the future, the Universe is dark-energy-dominated• All-pervading dark energy is most important

Epochs of the Universe

Current State of Universe

We are living in a great time in the Universe for life

• Lots of stars

• Lots of planets

• Lots of light

• Enough stars have died to create metals to form planets and us

• Not so much time has past that all the gas has been used up and all stars are dead

Still have gas to make stars in the Galaxy today

Fading Out

10 trillion years

10 million years

Sometime in the future….

White dwarfs, neutron stars, black holes

Epoch of Star Formation

The Present Day (t 14 Gyr):• Most stars are metal rich, and make more

metals ejected in supernova explosions.• Next generation starts with a little less Hydrogen

and few more metals.

Some fraction of the star’s matter gets locked away in stellar remnants:

• White dwarfs, neutron stars & black holes.

The Once & Future Universe

As the Universe expands:• Expansion continues forever at a faster rate• Space between galaxy clusters widens• Universe cools down at a faster rate

Details of the future Universe depend upon• Stellar Evolution• Gravity• Quantum Mechanics

End of Star Formation

After t=1012 years:Successively more matter is locked up in stellar remnants, depleting the free gas reserves.

Cycle of star birth & death is broken:• Nuclear fuel is exhausted• Red dwarfs burn out as low-mass white dwarfs• Remaining matter is locked up in black dwarfs,

cold neutron stars, and black holes

The last stars fade into a long night…

Solar System “Evaporation”

After t=1017 years:

Gravitational encounters between stars are rare, but disrupt orbiting systems:

• Planetary systems get disrupted by stellar encounters and their planets scattered.

• Wide binary systems are broken apart.• Close binary stars coalesce into single

remnants.

Dissolution of Galaxies

After t=1027 years:• Stellar remnants within galaxies interact over

many many orbits.• Some stars gain energy from the interaction and

~90% get ejected from the galaxy.• Others lose energy and sink towards the center.

The last 10% coalesce into Supermassive Black Holes.

Will Dark Energy Help Tear Galaxies Apart?

One of the many things we don’t know about dark energy is whether it has

• constant energy density for all time (cosmological constant)

• increasing or decreasing energy density with time (quintessence)

If it is a cosmological constant, Universe will continue to accelerate, but gravity will be important. If the energy density increases with time, then dark energy could overwhelm gravity

Right now, the dark energy seems fairly constant

Dissolution of Matter?

After t=1033 years:• Some particle models predict that protons are

unstable.• Protons decay into electrons, positrons, to

neutrinos.• All matter not in Black Holes comes apart.

Current experimental limits suggest that the proton decay time may 1032 years.

If protons don’t decay

101500 years from now – matter quantum tunnels to become iron

years from now – iron quantum tunnels to become neutron stars – black holes

Regardless – Universe will become very cold, very thin and very uninteresting.

Black Holes Aren’t PermanentVirtual particles (particle/anti-particle) pairs are

constantly being created and then immediately annihilate.

If they are formed near a black hole’s event horizon, however, then one particle can go into the black hole while the other is released

Black hole is emitting particles – Hawking radiation

Energy must come from somewhere – mass is lost by the black hole

Hawking Radiation

Evaporation of Black HolesHigher energy is radiated as the black hole mass decreasesAfter t=1067 years:

• Remaining stellar-mass black holes evaporate by emitting particles and photons via Hawking Radiation.

After t=10100 years:• Supermassive Black Holes evaporate one-by-

one in a last final weak flash of gamma rays.

End of the epoch of organized matter

PositroniumPositronium is formed when an electron and positron orbit each other, bound by electric forces

Eventually will release energy, get close and annihilate

t~1083 years

Size~1045Mpc

Cannot happen unless the imporance of dark energy decreases…

The Big ChillAfter black holes have all evaporated:

• Universe continues to cool off towards a Radiation Temperature of absolute zero.

• If protons decay, only matter is a thin, formless gas of electrons, positrons, neutrinos.

• Only radiation is a few increasingly redshifted photons.

The end is cold, dark, and disordered...

Some say the world will end in fire.Some say in ice.From what I’ve tasted of desireI hold with those who favor fire.But if it had to perish twice,I think I know enough of hateTo say that for destruction iceIs also greatAnd would suffice.

Robert FrostFire and Ice (1920)