Astronomy 422

Lecture 23: Early Universe

Exam 3 ch 28-30

Chapter 28: Active galaxies and Sunyaev-Zeldovich Effect• Know formulas 28.1-3 (basics about radiation)• Skip ch 28.4 about grav. lensing BUT do the last few pages on Lyalpha forest/damping etc (and see lecture notes)

•  Superluminal motion formulas

•  Know what the S-Z effect is and how it is used Chapter 29: Newtonian Cosmology

• Know formulas 29-3,4,5,6,7,8• e.g. how Hubble parameter relates to scale factor

• 29.15, 18 and a simple derivation using escape velocity

• these are definitions of parameters like the density parameter, know them

• Know 29.10/65/108/110: These are all Friedmann's equation expressed in slightly different ways. What is the difference, what do they mean?

Exam 3 continued

Chapter 30 – Early UniverseKnow what the successes and problems are with the Hot Big Bang cosmological model.

Know what inflation is, and how it solves 4 major problems with the Hot Big Bang model.

Know what the Planck time is and the history of the universe after that including major events like: inflation, radiation dominated, matter dominated, CMB decoupling/recombination, epoch of re-ionization

Know what the matter-antimatter asymmetry is.Know about the origin of structure.

Astro 422 Presentations:

Thursday April 28: 9:30 – 9:50 _Isaiah Santistevan__________ 9:50 – 10:10 _Cameron Trapp____________ 10:10 – 10:30 _Jessica Lopez____________Tuesday May 3: 9:30 – 9:50 __Chris Quintana____________ 9:50 – 10:10 __Austin Vaitkus___________ 10:10 – 10:30 __Kathryn Jackson__________Thursday May 5: 9:30 – 9:50 _Montie Avery_______________ 9:50 – 10:10 _Andrea Tallbrother_________ 10:10 – 10:30 _Veronica Dike_____________ 10:30 – 10:50 _Kirtus Leyba________________________

Key concepts:

The Early Universe: A summaryStructure formationEnd of the Universe

The Early Universe: conditions

•  We know the the conditions & expansion rate of the universe today.

•  If we run the expansion backwards we can predict the temperature & density of the Universe at anytime in its history using basic physics

– we can study how matter behaves at high temperatures & densities in laboratory experiments

•  Current experimental evidence provides information on conditions as early as 10–10 s after the Big Bang. Theories take us back to as little as as 10–43 s.

GUT Era (10–43 < t < 10–36 sec)

•  The universe contained two natural forces:

–  Gravity–  Grand Unified Theory (GUT) force

•  electromagnetic + strong (nuclear) + weak forces unified

•  Lasted until t~10–38 sec old–  at this time, the universe had

cooled to 1029 K–  the strong force “froze out” of the

GUT force

Inflation (10–36 < t < 10–34 sec)–  the energy released by this caused

a sudden and dramatic inflation of the size of the universe

Electroweak Era (10–34 < t < 10–11 sec)

• The universe contained three natural forces:

– gravity, strong, & electroweak

• Lasted until t~10–10 sec– at this time, universe had cooled to

1015 K– the electromagnetic & weak forces

separated

• Experimentally verified in 1983!– discovery of W & Z bosons– electroweak particles predicted to

exist above 1015 K (80-90 GeV)

Particle Era (10–11 < t < 10–3 sec)

•  The four natural forces were now distinct–  Particles were as numerous as photons.

•  When the universe was 10–4 sec old:–  quarks combined to form protons, neutrons, & their anti-particles

•  At 10–3 sec old, the universe cooled to 1012 K–  protons, antiprotons, neutrons, & antineutrons could no longer be

created from two photons (radiation)–  the remaining particles & antiparticles annihilated each other into

radiation–  slight imbalance in number of protons & neutrons allowed matter

to remain–  Electrons & positrons are still being created from photons

Era of Nucleosynthesis (10–3 sec < t < 3 min)

•  During this era, protons & neutrons started 'fusing'–  but new nuclei were also torn apart by the high temperatures

•  When the universe was 3 min old, it had cooled to 109 K–  at this point, the fusion stopped

•  Afterwards, the baryonic matter leftover in the Universe was:–  75% Hydrogen nuclei (i.e. individual protons)–  25% Helium nuclei–  trace amounts of Deuterium & Lithium

Era of Nuclei (3 min < t < 3.8 x 105 yr)

•  The universe was a hot plasma of H & He nuclei and electrons.–  photons bounced from electron to electron, not traveling very far–  the universe was opaque

•  At t~380,000 yrs:–  universe had cooled to a

temperature of 3,000 K–  electrons combined with nuclei

to form stable atoms of H & He–  photons free to stream across

the universe, decoupling

Era of Atoms (3.8 x 105 < t < 109 yr)

•  The universe was filled with neutral atomic gas.–  Usually referred to as the “Cosmic Dark Ages”

•  Density enhancements in the gas and gravitational attraction by dark matter:

–  eventually form protogalactic clouds–  the first star formation lights up the universe–  which provokes the formation of galaxies

When is the Epoch of Reionization?

Sometime between z = 30 and z = 7Begins at Cosmic Dawn with the formation of first stars & galaxies

Current Best Estimates & Limits

LWA 1 Science Program: Dark Ages

16

The predicted brightness temperature of the 21cm line from the HI gas is displayed as a function of time, redshift & frequency.

Figure 1 from Pritchard & Loeb, 2010 Nature 469 772

LWA1 has two major funded projects in place:• LEDA (PI Greenhill): Constrain Dark Ages signal [LG001]

•  Probe thermal history & Lyα output of 1st stars & galaxies by characterizing HI trough – only means to detect IGM @ z >15

•  New correlator, total power hardware & data reduction pipeline

• Cosmic Dawn (PI Bowman):Constrain final absorption peak -dual-beam technique to minimize foregrounds [LB002]

The Dark Ages through Cosmic Dawn encompasses the formation of the 1st galaxies & black holes. LWA1 offers a unique window into this era.

LEDA

EDGES

Production of ionizing photons determines the difference between dash-dot and solid curves

Case where IGM not reheated prior to reionization. It takes just 10-3 eV per baryon to significantly change this curve.

Lyman-α photonproduction (likely from stars) determines magnitude ofdecoupling from the dashed curve

LEDA: Inference

LWA1 project [LG001]

Era of Galaxies ( t > 109 yr)

The first galaxies came into existence about 1 billion years after the Big Bang.

Accelerating Universe

Accelerating Universe

Structure formation - the big picture

Structure formation is theory of transition from a very homogeneous state in the early universe, as reflected in the CMB, to the structure of galaxies and clusters we observe today.

•  Quantum fluctuations from inflationary era were 'stretched' to cosmic scales

•  Density fluctuations frozen in until matter-radiation equality

•  Density fluctuations grow during matter-dominated era (>10,000 yr ABB) due to gravitational instability

•  Astronomical structures form when fluctuation amplitude becomes large

Gravitational instability

From CMB, we know that at the time of recombination perturbations were about 10-5 of the average density.

Now, it is about 105 (in a galaxy).

How do we get there?

Baryon Acoustic Oscillations

Eisenstein et al. 2004

Theory of structure formation

•  What is the spectrum of initial density fluctuations?

•  How do density fluctuations grow in an expanding universe?–  in dark matter?–  in baryonic matter?

•  How does growth occur for stars and galaxies of primordial gas?–  Did big or little form first?

•  Let's consider growth of perturbations in a static, and then in an expanding universe.

Static spacetime

•  Idealized problem:–  infinite space–  constant density ρ0 everywhere–  consider only gravity

•  What happens?

•  Nothing. A given particle is attracted equally in all directions.•  Now suppose that in a sphere of radius R, there is a constant

additional density ρ0δ <<1.•  What happens?

Dense region contracts further.

Gravitational collapse:

•  Consider a particle on edge of the density perturbation.

•  Gravity on it is sum of background (constant density) plus perturbation.–  Background gives no net force–  Only perturbation matters

•  Extra mass

•  Acceleration

•  How long does it take to shrink by

•  Density contrast doubles in time

Collapse on static background

•  Suppose spacetime is not expanding.

•  We know that at a given redshift, the critical density is

Close to this in early universe.

•  Time scale to collapse is then

Very short at z=1000. This would form structure easily, within a few million years.

•  'Static background' valid for molecular clouds. But universe itself is expanding.

Collapse on expanding background

•  Now we suppose that there is a slight density enhancement, but that the spacetime is expanding.

•  As long as ρ<<1, the density decreases.

•  The density enhancements are proportional to R(t), =1/1+z(assuming matter domination)

•  As a result, the growth of the perturbations is much slower. From models, the first structures may be expected at around z=10-20.

Non-linear collapse

•  Now suppose that we reached a point where ρ~1

•  The overall expansion becomes unimportant, and the collapse will be in free fall.

•  First, consider dark matter, no non-gravitational interactions.–  Collapse cannot proceed indefinitely!–  When random motions become comparable to orbital speeds, a

quasi-equilibrium is reached.

Next step: gas physics

•  If all matter were non-interacting, elementary particles, nothing would happen.

–  achieve relaxed configuration–  sit there indefinitely

•  But, normal matter interacts:–  gas collides, radiates–  cooling causes sinking in potential

•  This means normal matter can achieve much higher densities –  once density is high enough, stars can form

The first stars

•  How would the first star in a large volume differ from today's stars?–  no metal enrichment (only H, He, little Li, Be)–  Little cooling

•  This implies that the Jeans mass remains high.

•  Winds, pulsations are less effective–  driven by metal line opacities!

•  First stars could be very massive 102-3 Msun

•  Possible quasi-stars with105 Msun

From small to large

•  In the standard picture of primordial fluctuations, there is a larger δ on smaller scales

–  The first structures therefore form on small scales

•  BUT: temperature prevents structure to form at a too small scale–  compromise: 105 Msun–  globular clusters?

•  Small fluctuations are strongest on top of big fluctuations

•  Therefore, hierarchical structure formation–  small structures form early–  big structure forms late–  small halos merge to big

Consequences and predictions

•  One prediction relates to the number of 'small' halos to 'big' halos.–  MW should have hundreds–  ….oops?

•  Why so few dwarf galaxies? Maybe if too small, first star blows away all gas, just BH and dark matter

–  would still have dark matter halos–  possibly seen with lensing!

•  If BH are formed at centers of all halos, would expect many mergers of BH when halo merge…. gravitational waves?

Structure formation summary:•  The evolution of structure depends on the cosmological parameters

(ie, the amount and type of matter and energy and the expansion rate)

•  The evolution of large-scale structure in the Universe is governed by gravity.

•  All structures today formed by gravitational amplification of the small fluctuations that we think were generated by inflation.

•  We think our Universe is dominated by cold dark matter.

•  In Universes dominated by cold dark matter (CDM), structure forms hierarchically, i.e., small things form first, and merge to form larger things.

•  Structure on various scales in CDM is nearly self-similar (substructure in galaxies looks like substructure in clusters)

1) The Primordial Era

2) The Stelliferous Era

3) The Degenerate Era

4) The Black Hole Era

5) The Dark Era

The Five Ages of the Universe

1. The Primordial Era: 10-50 - 105 y

Something triggers the Creation of the Universe at t=0

2. The Stelliferous Era: 106 - 1014 y

Now = 14 billion years ~ 1010 y

How Long do Stars Live?

A star on Main Sequence has fusion of H to He in its core. How fast depends on mass of H available and rate of fusion. Mass of H in core depends on mass of star. Fusion rate is related to luminosity (fusion reactions make the radiation energy).

lifetime α

mass (mass) 3

Because luminosity α (mass) 3,

lifetime α or 1 (mass) 2

So if the Sun's lifetime is 10 billion years, the smallest 0.1 MSun star's lifetime is 1 trillion years.

mass of core fusion rate

mass of star luminosity α

So,

How Long do Galaxies Live?

Only as long as they can continue to manufacture stars. To do that the galaxy needs gas.

lifetime α

Galaxies with modest star formation rates can shine for perhaps 1 trillion years

Mass of gas star formation rate =

So,10 billion years (for MW)

3. The Degenerate Era: 1015 - 1039 y

Most stars leave behind a white dwarf

Mass between 0.1 and 1.4 M_sun

The Degenerate Era: 1015 - 1039 y

Some failed protostars never got hot enough to ignite hydrogen fusion:

Brown Dwarfs

Mass < 0.08 M_sun

Brown dwarfcollisions can createoccasional warmspots in an increasingly cool universe

The Degenerate Era: 1015 - 1039 y

The Degenerate Era: 1015 - 1039 y

Neutron stars:

Cold and no longer pulsating

Mass ~ 1.5 M_sun

The Degenerate Era: 1015 - 1039 y

Black holes

Stellar mass black holes

Supermassive black holes

Galaxy evolution: dynamic relaxation during the Degenerate Era

Galaxies continue to merge to form large meta-galaxies (entire local group merges into a single galaxy); spirals merge --> ellipticals

Massive remnants sink to the center of the galaxyLess massive remnants get ejected from the galaxy (all the brown dwarfsare gone by 1020 y).

What happens to Solar systems like ours?

Inner planets are fried during end of stelliferous eraPlanets are gradually stripped away during stellar encounters in the degenerate era

1017 1015 1012 y

Dark Matter

Annihlation of WIMPs (Weakly Interacting Massive Particles)?- In the halo of the galaxy- In the cores of white dwarfs (power ~ 1015 Watts, 10-9 L_sun)

Surface temperature ~60 KSteady energy source for ~1020 y

Proton Decay

Predicted lifetime of protons (and neutrons) is 1034 y- In white dwarfs (power ~ 400 Watts, 10-22 L_sun)

Surface temperature ~0.06 KComposition changes to frozen HStar expandsSlow decay over ~1036 yEventual disintegration into photons

Neutron stars, planets, dust, all face the same fate.

4. The Black Hole Era: 1040 - 10100 y

Black holes inherit the Universe- mostly in the form of stellar mass black holes

Some electrons, positrons, neutrinos and other particles remain

Planets, Stars and Galaxies are all long gone

4. The Black Hole Era: 1040 - 10100 y

Black holes eventually start to decay by Hawking Radiation

Hawking radiation continued:

Effective Temperature ~ 1/mass

Universe cools with time, so that after 1021 y, the Universe is cooler than a 1 solar mass black hole (10-7 K)

After 1035 y, even 1 billion solar mass black holes have begun to evaporate.

Final stage of black hole radiation is explosive with 106 kg of mass converted into energy

After 10100 y, even the most massive black holes are gone.

NB: If acceleration (non-zero cosmological constant) is assumed then Universe expands and cools much faster.

5. The Dark Era: > 10101 y

Only some elementary particles and ultra-long-wavelength photons remain inside a vastly expanded Universe.

Density is unimaginably low. Our observable Universe now has a size of 1078 cubic meters. In the Dark Era there will be one electron every 10182 cubic meters.

Heat death - nothing happens, no more sources of energy available

Or ….

1. The Primordial Era: 10-50 - 105 y

Something triggers the Creation of a child Universe

Child Universe

Living on borrowed energy:

mc2 = 1/2 m vesc2

Energy of expansion is about equal to energy in matter

Ω = 1