Dark Matter, Dark Energy & the Fate of the Universe Flashcards
Stars & ISM clouds are
visible matter
Existence of unseen matter
inferred from its gravity effects on visible matter. Orbital velocities of visible objects can be observed & measured
Kepler’s Law
Normally, the orbital speed drops as distance from a single central mass increases.
Same orbital speeds even for stars far away from galactic centre
Most of galaxy’s mass lies beyond our Sun
Same orbital speeds even for stars far away from galactic centre
Galactic mass NOT only at centre & most of it is located into halo and extends far out from it
Where is the dark matter in our galaxy?
This mass gives off very little light → dark matter
Total amount of dark matter could be 10× the total mass of all stars in the disk!
Visible matter in disk only a small fraction of total mass!
Radius of dark matter halo may be 10× as large as galaxy’s halo of stars
To determine the amount of dark matter in a galaxy
→ compare galaxy’s mass with its luminosity
Measuring luminosity → easy if its distance can be determined
Total mass of other spiral galaxies also determined
Measure orbital speeds as far from the galaxy’s centre as possible
Stars are rarely found at great distances from galactic centre
Doppler shift of the 21 cm radio emission line of H gas clouds in the receding & nearing arms of the galaxy tells us how fast the clouds are moving towards or away from us
Rotation curves of galaxies are flat at large distances from centres
Similar to our galaxy dark matter distributed far beyond disk & halo
Other spiral galaxies also have at least 10× as much mass in dark matter as they do in stars
In typical spiral galaxies, 90% of matter is dark matter
Different techniques must be used for elliptical galaxie
Very little H gas no detectable 21 cm emission line Must observe motions of stars
Mass-to-Light Ratio in dark matter in galaxy
Amount of dark matter in galaxy can also be quantified by its mass-to-light (M/L) ratio:
Mass: in [MSun] units
Visible luminosity (from apparent brightness): in [LSun] units
Milky Way: mass to light ratio
M/L = 6 if deduced from visible matter inside Sun’s orbit, but of about 50 if ALL matter of entire galaxy is considered
Other spiral galaxies have M/L ratios of ~50 or more
The large M/L ratios (≥50 MSun/LSun) obtained from measurements for elliptical galaxies also indicate that, just as spirals, they contain far more dark matter than visible one
and also predominantly located in the halo.
Dark matter in galaxy clusters discovered by Fritz Zwicky in 1930s.
Assumed galaxies orbit about cluster centre
Measured orbital speed of galaxies (redshifts) & their distance from centre
Calculated cluster mass with Kepler’s law Huge M/L ratios found (>100MSun/LSun) More sophisticated measurements today confirmed his finding
2 other independent ways to determine cluster mass:
Measure temperature & hot gas distribution between galaxies
Observe how clusters bend light (gravitational lenses)
Measure temperature of intracluster medium between galaxies
Gas heated to ~10…100 m K → temp. of intracluster gas depends on the mass of the clusters
Being so hot → emits X-rays & is nearly in gravitational equilibrium, i.e. outward pressure balances gravity’s inward pull → cluster mass can be estimated from temperature of hot gas
50× more dark matter than the combined mass of the stars in the cluster’s galaxies
Gravitational lensing
A massive cluster of galaxies bends light like a lens distant object behind cluster can be seen
Multiple distorted, magnified & brightened images of the background source can be generated
Gravitational lensing (continued)
Distortion strength reveals mass.
Lens bending angle depends on mass
A different theory of gravity is used: masses distort the space-time “fabric” of the Universe
All previous methods to find mass depended on Newton’s law of gravity
Cluster masses measured by 3 independent methods all agree
Conclusion: Clusters of galaxies hold huge amounts of dark matter
Most galaxy clusters have >100 MSun/Lsun → contain far more dark matter mass than stars
At least some of dark matter can be ordinary matter:
Protons, neutrons (baryons) & electrons Only thing unusual is that it is dim Called baryonic matter
The rest must be extraordinary matter Made of particles we have yet to discover Known as nonbaryonic matter
Our galactic halo has lots of dark baryonic matter:
Low-mass M dwarfs, brown dwarfs
Black holes & Jovian-sized planets
Too faint to be seen at large distances Also known as “MAssive Compact Halo Objects” MACHOs
Still, the number of MACHOs is not large enough to account for all Milky Way’s dark matter
Neutrinos from the Sun are nonbaryonic matter
Weakly interacting particles → interact with other particles through gravity & weak force.
Very low mass & high speed → easily escape galaxy’s gravity. Can account for only a very small % of dark matter observed.
Others are “Weakly Interacting Massive Particles” = WIMPs
WIMPs are still theoretical & have NOT yet been discovered
Massive enough and/or in large enough numbers to exert gravitational influence.
They do not emit light or are bound to any light-emitting charged matter.
They do/will not collapse into a galaxy’s disk/body.
Hence, they will remain gravitationally bound in a galaxy’s halo.
Gravitational attraction overcomes the expansion of the Universe at close range
Galaxy’s velocity deviates from Hubble’s law. Universe expands but individual galaxies attract one another
Structure probably began with slight enhancements in matter density during the early Universe.
Regions collapsed into protogalactic clouds forming galaxies.
Individual galaxies fell in towards one another to form clusters.
Individual clusters now congregating to form superclusters.
Collapses against expansion facilitated by dark matter
even today, dark matter’s gravitational pull must be the primary force holding the large-scale cosmic structures together.
Cosmic structures studied by galaxy surveys.
Once required years of effort just to map location of a few 100s galaxies (measure redshift to deduce distances) Recent technology measures 100s of galaxies in a single night of telescopic observation
Hubble’s law primarily used to measure galaxy distances
Hubble expansion dominates beyond 300 m l.y. from Earth
Galaxy distribution maps can be constructed
Galaxy distribution map reveals large scale structures much bigger even than clusters of galaxies! →
superclusters, and some are even LARGER !!!
Galaxies are not randomly scattered but arranged on a
scale of 100s m l.y. in gigantic chains, sheets & walls surrounded by empty regions called voids
Chains come from the initial regions
s of density enhancement
Voids come from the initial
regions of density depletion
Galaxies appear evenly distributed on a 1 b l.y. scale
On very large scales, the Universe looks much the same everywhere → in agreement with the Cosmological Principle
The structures we see today mirror the original distribution of dark matter in the early stage of the Universe
How will the Universe end ?
Gravity pull between galaxies slows down Hubble expansion.
Critical density is the average mass density for its gravity pull to
equal the kinetic energy of expansion.
Critical density is the average mass
density for its gravity pull to equal the
kinetic energy of expansion.
IF existing total mass has density < critical density
Universe expands forever
If existing total mass has density > critical density
Universe will stop expanding & contract The current density of the Universe is very-very close but still below critical density
Current kinetic energy of the universe given by
H0
Hence, the critical density is found to be
10–29 g/cm3 → ~5 H atoms/m3
Visible matter contributes only
~0.5% of the critical density necessary to halt the Universe’s expansion
Dark matter in individual galaxies & galaxy clusters has
~10…50× the mass in stars → but it should be ~200× to stop the expansion
Overall density of matter (both baryonic & non-baryonic dark matter) of Universe = ~25% of critical density
This suggests Universe will expand forever! Unless much more dark matter beyond cluster boundaries exist (not probable as this would be causing large deviations from Hubble’s law, which are not observed)
Recent observations of white dwarf supernovae in very
distant galaxies yielded unexpected results.
Look-back time (distance) from standard candles
Redshift (recession velocity) gives the Universe’s expansion rate
Redshift (recession velocity) smaller than expected at measured look-back time.
Universe expanding slower in the past
Implies that Universe’s expansion is accelerating!
There must be an unknown force that repels the galaxies: Dark energy
We do NOT know why the Universe is accelerating
tremendous amounts of energy required! We have NO idea what dark energy might be!!!
Hypothetical energy which permeates space & has strong negative pressure.
Effect of such pressure is qualitatively similar to an opposing force to gravity at large scales.
Explains expansion at an accelerating rate & accounts for significant portion of missing mass in the Universe.
From observing distant galaxies
Farther out we look, the farther back in time we see → as early as 1…2 b years old
However, light could not move freely before Universe was ~380,000 years old
Earlier conditions & expansion rate of universe deduced from running expansion backwards with mathematical models.
Temperature/density predicted with basic physics Study matter at high temperatures/densities in laboratory Conditions as early as 10–10 s after Big Bang can be obtained
Early Universe conditions
Universe extremely hot during 1st few seconds but cools as it expands.
At such extreme temperatures, photons can transform into matter (& vice versa)!
According to E = mc2 Early universe filled with radiation (remnant heat of the Big Bang) & subatomic particles.
2 particles created when 2 photons collide
Total energy more than 2× subatomic particle mass (p+, n, e–)
Particles of matter & antimatter
Reaction also runs in reverse → matter-antimatter annihilation
Matter/radiation continually converts into each other during the very first few moments.
Constant total mass-energy
Laws of physics can be used to calculate the proportions of radiation & matter at various moments in Universe’s early history → the only problem: incomplete understanding of laws of physics: could have been different under those extreme conditions!
Each Era in Universe’s very early history
distinguished from the others by some major change in the physical conditions as the Universe cooled
Planck Era (t < 10–43 s)
The first 10–43 s → until Universe cooled to 1031 K.
Universe consisted entirely of 31 K
radiation (very small, dense &
hot).
Substantial energy fluctuations from point to point
rapidly changing gravitational field that must have randomly and severely warped space-time. • Planck Era (t < 10–43 s)
Unable to describe this Era.
Our science can only adequately describe conditions after this Era.
Do we use quantum mechanics or general relativity?
Need to unify them in order to more adequately describe the conditions and phenomena of that Era.
All four natural forces (strong, weak, electromagnetic & gravitational) were probably unified in this Era in a single “superforce”
GUT Era (10–43 s < t < 10–38 s)
Until Universe cooled to 1029 K. Only 2 natural forces: Gravity & Grand Unified Theory (GUT) force
Our current understanding of physics allows us to know only a bit more about this Era than about the Planck Era
At its end, the strong force froze out of the GUT force
enormous amount of energy released
a dramatic inflation (expansion by a factor of 1030) occured in only 10–36 s: the size of an atomic nucleus grew to the size of our Solar system !
• Electroweak Era (10–38 s < t < 10–10 s)
Universe cooled to 1015 K when reached the age of 10–10 s.
GUT force splits into 2: strong & electroweak with gravity they form now the 3 natural forces
Intense radiation still filled the space spontaneous production of matter-antimatter elementary particles but all convert back to photons immediately
As many particles as photons
Electroweak condition experimentally verified in 1983.
• Particle Era (10–10 s < t < 10–3 s)
All 4 forces now distinct
T ↓ to 1012 K too cool for the spontaneous exchange matter ↔ energy to continue
At t = 0.1 ms, photons turned into quarks, which combined to form protons (p+), neutrons (n), e–, neutrinos (ν) & perhaps WIMPs.
Since matter obviously is present in today’s Universe
p+ must have outnumbered antiprotons (p– )
Today photons outnumber p+ by about 109:1
in early Universe there were 1+109 p+ for each 109 p–
The Era of nucleosynthesis (10–3 s < t < 5 min.)
p+ & n started fusing into heavier nuclei. But formed nuclei also torn apart by (the still) very high T
At t = 5 min. (T = 109 K), density in expanding universe dropped significantly & fusion stopped.
When fusion stopped:
~75% of the ordinary (baryonic) matter = p+
~25% of the ordinary (baryonic) matter = fused into He nuclei
Also traces of deuterium & Li nuclei in leftover baryonic matter
The Era of nuclei (5 min. < t < 380,000 years)
Universe now a hot plasma of H nuclei (p+), He nuclei & e– :
Fully ionized nuclei moved independently of e–
Photons did not travel very far before bumping into an e–
the Universe was opaque
Cooled to 3,000 K after 380,000 years:
Nuclei captured e– to form stable H & He
The Universe became transparent Photons free to stream across universe → the Cosmic Microwave Background (CMB) we see today
The Era of atoms (380,000 years < t < 109 years)
Universe holds neutral atoms, plasma & lots of photons
Density enhancements in gas & gravity attraction by dark matter eventually form protogalactic clouds. 1st stars formed: light up Universe & trigger galaxy formation
Era of Galaxies (t > 1b years
1st galaxies appeared ~1b years after Big Bang
This is the current Era of the Universe
Galaxies are still forming to this day and will continue for quite some time in the future
A good scientific model makes verifiable predictions.
The Big Bang model has gained wide scientific acceptance because it makes 2 predictions that have been verified experimentally since 1960s:
Radiation that began to flow into the suddenly transparent Universe at the end of Era of nuclei should still be present today → The Cosmic Microwave Background (CMB)
The He content of the Universe (& that of other light elements) must be that resulted from the Era of nucleosynthesis
• Radiation left over from the Big Bang
Universe immersed in a sea of radiation after Big Bang → unleashed only at the end of the Era of nuclei, when the Universe was only 380,000 years old.
Universe cooled enough (3000 K) for H & He atoms to form
The Universe became transparent
Photons free to stream across universe → the Cosmic Microwave Background (CMB) we see today
The CMB predicted by Big Bang theory was accidentally
discovered in 1965.
Appeared to come from every direction Had a perfectly thermal spectrum at 2.73 K → expected temperature due to Universe’s expansion
Origin of CMB
Radiation originally identical with that of a 3,000 K blackbody.
However, the Universe expanded 1,000 times until now!
Cosmological redshift turned this radiation into microwaves Perfect thermal radiation spectrum peak corresponds to T ~2.73 K.
Density of the Universe
Measurements in the 90s showed that the CMB is NOT perfectly uniform
Temperature variations of the 380,000 year-old universe reflect density variations that acted as a genetic code for the Universe’s structure today → the ‘seeds’ of structure formation during the Era of nuclei
The CMB indicates exactly how hot the Universe was and how much He it should have made
• How was cosmic helium created?
During the Era of nucleosynthesis, when T ≥1011 K → p+-to-n nuclear particle conversions were reversible
When T↓ <1011 K → nuclear conversions favored p+
n = more massive than p+
p+-to-n conversion requires energy
n-to-p+ conversion releases energy → unhindered by Universe cooling
The He nuclei created then were very short-lived
Split apart by the intense γ radiation that filled the Universe at that time
Long-lasting He nuclei formed only when the Universe was ~1 min. old & cooled enough to contain much less γ radiation
How much cosmic helium was created?
12 H nuclei for every He nucleus made
The final p+-to-n ratio must have been ~14:2, i.e. the Big Bang model predicts Universe must have had (at the end of the Era of nucleosynthesis) a composition of 75% H & 25% He ≡ 3:1 mass ratio of H:He
Milky Way has
~28% He & no galaxy has <25% He.
Fusion in stars only produced ~10% of He observed
The estimation of the mass/concentration of other elements, like deuterium, etc., also match the practical measured values
Excellent agreements with Big Bang model, confirming its validity!
Abundances of light elements
When the first stable & long-lived He nuclei formed, the Universe was already too cold for enabling fusion of other elements.
Only very few reactions between p+, deuterium (2H) nuclei, tritium (3H) nuclei, 3He & 4He were possible
3H + 4He → 7Li
These had minor contributions because 2H & 3H were very rare Before cooling of the Universe shut off fusion entirely, only trace amounts of Li & Be were produced Most of Be & all B were created later, by high-energy splitting up of heavier elements fused in stars
We saw earlier that formation of deuterium was necessary for the production of He nuclei.
The fusion stopped before all deuterium could be used up
The amount of deuterium in Universe today indicates the density of baryons (p+ & n ) at the end of the Era of nucleosynthesis.
Presently 1 in 40,000 H atoms has a deuterium nucleus
Density of ordinary (baryonic) matter = ~4% of critical density
Overall density of Universe
~25% of critical density
The Universe contains about
6× more extraordinary (nonbaryonic) matter than ordinary (baryonic) matter Most of the extraordinary matter is believed to consist mainly of WIMPs
Inflation explains several key features of today’s Universe:
1) Although CMB shows that the density of the Universe at the end of the Era of nuclei was not perfectly uniform (variations of ~0.01%), the overall smoothness is remarkable → Inflation explains why distant reaches of the Universe look so similar wherever we look
Regions presently very distant (i.e. which can’t have possibly exchanged light or any information) still have the same temperature & density because they were in contact prior to inflation
Inflation explains why
ρOrdinaryMatter + ρDarkMatter + ρDarkEnergy < ρCrit
⇔ ρMatter + ρDarkEnergy < ρCrit ⇔ Ωm + Ωv < 1 where
Ωm = ρMatter/ρCrit and Ωv = ρDarkEnergy/ρCrit i.e. total density of the Universe → very close to critical density ρUniverse < ρCrit
This equation was preferred instead of ρUniverse ≅ ρCrit which does not indicate clearly which of the 2 terms is bigger
The overall geometry of the Universe should be very flat (perfectly flat only if EXACT equality would occur in the relation above)
General relativity says that matter can curve spacetime.
Curvature of universe can vary from place to place… …but the Universe as a whole has the same overall shape → flat, closed or open
Spacetime curvature can result from
imbalance in the expansion kinetic energy & pull of gravity.
If density was 10% more, Universe would have collapsed long ago
If density was 10% less, expansion would have spread all matter too thin & galaxies had never formed
Detailed studies of the CMB suggest that the overall geometry of the Universe is
remarkably flat.
Gravity’s pull ALMOST balances the expansive kinetic energy
TOTAL density of our Universe is very close to critical density
Calculations show that the largest temperature
differences in the CMB should typically be
between sky patches separated by ~1° for a flat universe.
Angular separation <1° if the Universe were open
Angular separation >1° if the Universe were closed
Largest temperature differences observed at
1° angular separation. Deduced from CMB map of WMAP satellite
Various experiments (e.g. Boomerang) done in 2000-2001
confirmed the presence of the largest ripples, which extend about 1o across the sky. Hence, it provided convincing evidence that the overall Universe geometry is “flat”
These experiments also showed that there is a series of preferred scales over which
the temperature fluctuations occur: harmonics peaks were found at the angles predicted by inflation theory
The first peak reveals a specific spot size for early universe sound waves, just as the length of guitar string gives a specific note. The second and third peaks are the harmonics
Why are the Boomerang and WMAP Data Important?
The size of a constant-temperature region is fixed by the size of the horizon at the time of last-scattering (The horizon = the distance over which a photon can travel during the age of the Universe). The apparent angle over which the region is spread depends on the geometry of the universe
The experiments showed average angular separation of ~1o Universe is almost flat
Why is the geometry of the Universe so flat?
Effect of rapid inflation flattened spacetime
Inflation stretched any initial curvature to near flatness Curvature is only noticeable on scales much larger than observable universe
Inflation —> Total matter-energy density < critical density of our Universe.
Consistent with measured matter density & dark energy powering the accelerating expansion of our universe
Dark energy can account for the shortfall in the density of dark matter
Einstein’s theory of relativity → Energy must be able to curve space-time just like mass!
Dark energy → associated with a large-scale repulsive force → can therefore compensate for the shortfall in the matter density and make the Universe flatter that it would otherwise be
Density of ordinary matter is
~4.5% of critical density → measurements of deuterium in the Universe
Total matter density is
~27% of critical density.
Extraordinary dark matter makes up to ~23% of critical density → In line with measurements of mass in galaxy clusters
Flat geometry
total mass-energy < critical density.
Flat geometry & matter density < critical density
repulsive dark energy accounts for remaining 73% of mass-energy & expansion is accelerating. In line with white dwarf supernovae observation
~13.75 b years old at current microwave temperature of
2.73 K. Agreement with Hubble’s constant & age of oldest stars observed
Why is the night sky black if the universe is infinite & filled with stars? Should see a star in every direction we look The sky should be ablaze with light
Possible solutions to this conundrum: 1) The Universe has a finite number of observable stars Hence it would NOT be possible to see a star in every direction we look…
…they are different distances, with luminosities ∝ 1/d2 2) The Universe is changing over time … in such a way that it prevents us from seeing an infinite number of stars Since modern observations have shown a (more or less) uniform distributions of galaxies at very large scales (remember the Cosmological Principle ?!) The Universe may contain an infinite number of stars, but… …since the Universe began at a particular moment with the Big Bang… We can see only the stars that lie within the observable Universe, i.e. inside our cosmological horizon
