What are the Contents of the Universe? Taking an Inventory of the Baryonic and Dark Matter Content of the Universe

Layout of the Course Sept 4: Introduction / Overview / General Concepts Sept 11: No Class -- Science Day Sept 18: Age of Universe / Distance Ladder / Hubble Constant Sept 25: No Class Oct 2 Distance Ladder / Hubble Constant / Distance Measures Oct 9: Dist. Measures + SNe science + Baryonic Content Oct 16: Baryonic + Dark Matter Content of Universe Oct 23: Dark Matter Content of Universe Oct 30: Cosmic Microwave Background Nov 6: Large Scale Structure / Baryon Acoustic Oscillations Nov 13: Clusters / SZ Nov 20: Dark Energy / Cosmic Shear Nov 27: Dark Energy Missions / Review for Final Exam Dec 11: Final Exam This Week

Review Material from Last Week

What is the Baryonic mass density of the universe? (summary) Ωstars = 0.002 Ωcold = 0.0003 gas, HI Ωcold = 0.0003 gas, molecular hydrogen Ωionized = 0.02 hydrogen Ωtotal = 0.0226

Multi-phase Diagram from Cosmological Hydrodynamical Simulation Showing where the Baryons Are Predicted to be: gas in galaxy clusters WHIM ICM warm, hot intergalactic medium diffuse IGM cold halo gas SF gas van der Voort et al. 2011 (was a student of Joop Schaye here)

Missing baryons were thought to possibly be in MACHOs (massive compact halo objects) i.e., white dwarfs, neutron stars, black holes, Jupiter mass sources (investigated extensively in mid 1990s)

How did people search for MACHOs? -- observe millions of stars in the Large Magellanic Cloud... -- wait for some star to brighten because compact object passes in front of it -- a few events are found in such experiments, but seem to be consistent with self lensing BRIGHTNESS -- no evidence contributes significantly to baryonic matter density TIME

But where does this number Ωbaryon = 0.04 come from?

Big Bang Nucleosynthesis Nuclear fusion in early Big Bang (though we can also derive it using the CMB observations)

Here again is an approximate history of the universe BIG BANG Synthesis of Elements 10-14 Age of Recombination 0.0003 AS 4022 Cosmology First Stars 0.2 First Galaxies Billions of Years (Gyr) 0.4 0.7 Normal Galaxies Now 1 2 3 13.7

How do heavier elements build up? (occurs during first 2-5 minutes of p + n universe) build Nuclear fusion reactions responsi-

Stable mass gaps in the periodic table 9 Be 7 Li 6 Li 4 He 2 H 3 He No stable nuclei 1 H The lack of stable elements with masses 5 and 8 make it more difficult for cosmic nucleosynthesis to progress beyond Lithium and even Helium.

How do abundances depend on time? Fraction of Mass Density Light-element abundances as a

But what does this teach us about the matter density in baryons?

Abundance of heavier elements synthesized depends on baryon density Reaction Rate Density of Baryons Note: The time scale during which nucleosynthesis can occur is almost independent of the baryon density -- since the energy density of the universe dominated by radiation at early times Baryon density

Abundance of heavier elements synthesized depends on baryon density Reaction Rate Density of Baryons He 4 is much more stable species -- therefore if sufficient baryons are present, it will form Notice that fraction of He 4 increases in proportion to density of baryons Baryon density

Abundance of heavier elements synthesized depends on baryon density IMPLICATION: If we can determine what the abundance of the above elements is relative to hydrogen, we can determine the baryon density in the universe at early times... Baryon density

So this gives us the framework -- but what does it imply?

So how can we go out and determine what the abundance of these heavier elements is relative to hydrogen? The challenge is that the universe has not been held in a constant state, there are stars, and they destroy some elements and create others...

Challenge is that: D readily destroyed in stars from fusion He 4 readily produced from fusion Li 7 readily destroyed in stars from fusion may be created by cosmic-ray spallation in the interstellar medium He 3 produced by burning deuterium destroyed to produce He 4

How might we determine the primordial abundances then? For deuterium: Observe some gas cloud in early universe where stars have not yet formed and look for absorption by hydrogen and deuterium: - Lyman-alpha clouds Primordial gas cloud quasar Very bright sources like quasars needed so we infer the presence of rare elements in gas clouds through weak absorption features

What do these spectra look like? Quasar Spectrum Verify that the gas cloud shows no evidence for being polluted by heavier elements (this ensures deuterium abundance not affected) Tytler & Burles

What do these spectra look like? Quasar Spectrum Need to be sure this isn t just another cloud of cold gas at different redshift Tytler & Burles

How might the observations look different with another deuterium abundance? different deuterium abundances

What results have been found for deuterium? For deuterium: [D/H] ~ 3 x 10-5

How might we determine the primordial abundances then? For He 4 Recombination lines from HII regions in low metallicity galaxies Measure abundance ratios of many elements He, O, N, H

How might we determine the primordial abundances then? For He 4 mass fraction of baryons Extrapolate to metallicity of 0 in He 4 to infer primordial abundance Metallicity

How might we determine the primordial abundances then? For Li 7 observed by absorption in the atmospheres of cool, metal poor population II halo stars but difficult to infer since it can both be destroyed and created inferring its abundance also difficult due to uncertainties in modeling the atmosphere of stars

How might we determine the primordial abundances then? For Li 7 10 12 (Li/H) Again extrapolate to metallicity of 0 to infer primordial abundance Metallicity

How might we determine the primordial abundances then? For He 3 Has been found in some galactic HII regions In principle, not burned in outer layers of stars -- though convection in stars could mix outer layers will inner layers. Somewhat model dependent, so not especially reliable

What is bottom line putting together constraints? Boxes show constraints on abundances relative to hydrogen Best Fit Baryon Density Bh 2 = 0.019 ± 0.0024 B = 0.037 ± 0.009 Most useful constraint is from deuterium abundances given steep dependence on Ωbh 2

Worthwhile, noting that this gives us another strong piece of evidence for big bang Maybe helium just formed during fusion in stars?

Here is the evidence: Helium abundance Oxygen abundance =>

Helium could not just have formed from fusion in stars (since one would expect other heavier elements to be produced)

Evidence for Big Bang 1. Age of Stuff in Universe ~ 1/H0 Radioactive Decay, White Dwarf Cooling, Globular Clusters Expansion Rate of Universe ~13 ± 1 Gyr ~13.8 Gyr 2. Helium Abundance of Universe cannot be explained by fusion in stars, but easily explained as happening in Big Bang, but

Baryonic mass density Ωstars = 0.002 Ωcold = 0.0003 gas, HI Ωcold = 0.0003 gas, molecular hydrogen Ωionized = 0.02 hydrogen Ωtotal = 0.0226 vs. Ωbaryons = 0.04 (from BBN)

This week: How can establish the dark matter content of universe directly from observations? First of all, what is dark matter?

Dark Matter: Baryonic dark matter: black holes, compact objects (not typically what one refers to as dark matter ) Hot dark matter (HDM): low-mass particles such as neutrinos (since they have low mass, they can erase small scale density fluctuations) Cold dark matter (CDM): much heavier particles such as WIMPs. Since these particles are much heavier, this matter tends to preserve density smallscale density fluctuations)

This week: How can establish the dark matter content of universe directly from observations? Second of all, what is the evidence for dark matter?

Evidence from the Rotation Curves of Galaxies

Dark matter in galaxies -- One technique for estimating the mass inside a circularly symmetric rotating object is from the rotation speed GM( r) r 2 force per unit mass = v2 rot(r) r 2 acceleration r = radius, v = rotation speed, M(<r) = mass inside radius r, G = gravitational constant

Dark matter in galaxies -- One technique for estimating the mass inside a circularly symmetric rotating object is from the rotation speed GM( r) r 2 r = radius, = v2 rot(r) r 2 v = rotation speed, M(<r) = mass inside radius r, G = gravitational constant r r M( r) = v2 rotr G

Dark matter in galaxies -- How are galaxies observed to rotate? -- The rotation rate of galaxies can be measured by letting light pass through a slit along the axis of a galaxy and taking a spectrum -- It is easiest if we observe a spiral galaxy edge-on. Otherwise we need to apply an inclination angle correction

Dark matter in galaxies -- Rotation velocities of spiral galaxies increase rapidly from their centers to their outer radii roughly constant, independent of radius -- Rotation velocities tend to asymptote towards some constant value r r M( r) = v2 rotr G M( r) r.

Dark matter in galaxies -- By contrast, light in galaxies decreases exponentially with v radius: const. = M, I(r) =I 0 exp( r/h) roughly constant, independent of radius h = scale length of galaxies -- Integrating up the total light in a galaxy to some radius r0: I 0 r0 2πr exp( r/h) dr 0 h 2 h(r + h)exp( r/h) -- Equals a constant at large radii -- The implication is that the light and also baryons in galaxy are restricted to very center

Dark matter in galaxies -- This restriction of the baryonic mass to the center of galaxies is in contrast to the monotonic increase seen in the gravitational mass roughly constant, independent of radius -- So if gravity works the same on large scales as small scales, then there must be some other matter in universe we do not see!

Dark matter in galaxies -- In many case, one can measure the velocity of rotation out to very large radii by observing the HI gas (neutron hydrogen) through the 21 cm -1 line HI gas observed through 21 cm -1 line Star Light HI gas often extends much further than stars

Evidence from the Observations of Colliding Galaxy Clusters

Mass in clusters Evidencebudget from the Observations of Colliding Clusters name galaxy is aamisnomer! FirstThe a few words to clusters orient you little more about what a galaxy cluster is ~2% mass in galaxies ~13% in the hot, ionized intra-cluster plasma Galaxy clusters areitregions of the universe that have (baryon that didn t make to the galaxies) ~85% dark mattercollapsed (due to gravity) Approximate mass budget: ~2% galaxies ~13% in a very hot ionized gas ~85% in dark matter Most of the baryons are in the ionized gas!

Evidence from the Observations of Colliding Clusters Reason it is useful can be seen from the following simulation : Cluster #1 Cluster #2 -- dark matter from the colliding clusters pass right through each other -- ionized gas from the colliding clusters run into each other forming a shock this presents us with a situation where the light (from baryons) and mass (from dark matter) are in different places

Evidence from the Observations of Colliding Clusters -- how can we use the observations to see that baryons do not provide most of the mass Bullet Cluster Clowe et al. 2006 x-ray baryons -- x-ray light shows us where the ionized gas (i.e., baryons) is -- gravitational lensing shows us where the mass is (mostly dark matter) lensing dark matter -- ionized gas from the colliding clusters run into each other forming a shock -- dark matter from the colliding clusters pass right through each other

The Bullet Cluster Credit: Papovich for layout See Clowe et al. 2006 Orange: stars Red : X-ray gas Blue : Mass from lensing measurements

Now let us estimate the total amount of dark matter in the universe:

Context As we measure the mass in dark matter, we ll see how the measured M/L (mass to light) ratio for the universe increases to larger scales (indicating the greater importance of dark matter at such scales!) Sun: M/L = 1 (by definition) Universe: M/L = 1400ΩM h 2 ~ 200 (ΩM/0.3)(h/0.7) 2

Let s start by estimating the apparent amount of dark matter in galaxies

Dark matter in galaxies -- What is the total gravitational mass inferred in galaxies from this type of analysis and how does it compare with the light? i.e. what is the apparent mass to light ratio in galaxies? (M/L)galaxy ~ 10-20 Msolar/Lsolar i.e. how does it compare to typical stellar populations? (M/L)stars ~ 1-3 Msolar/Lsolar Total Dark Matter >= 10 x [mass in stars] ΩDM >= 10 x Ωstars >= 10 x (0.002) ΩDM >= 0.02

Now let s move to a bigger system: a cluster of galaxies

How can we infer this amount of mass in dark matter? We need to be able to determine the mass of a galaxy cluster (and see what is missing)

Weighing Galaxy Clusters (from the motions of galaxies in a cluster) Virial Theorem: For systems that have collapsed gravitationally and relaxed, we expect: Kinetic Energy = 1/2(Potential Energy) Implication for galaxy clusters: if galaxies move around inside galaxy clusters at a very fast speed, then the mass of a cluster must be very high

Weighing Galaxy Clusters (from the motions of galaxies in a cluster) By doing spectroscopy of many galaxies inside a cluster, we can measure Doppler shifts and hence the scatter in the average velocity along line of sight. However, there is no reason that the direction we observe a cluster is special, so the random motions in the two other directions is likely similar vx 2 + + = 3 v 2 = v 2 y v 2 z v 2 This implies the following kinetic energy: E kin = 1 2 m i v 2 i = 3 2 M v 2 i

Weighing Galaxy Clusters (from the motions of galaxies in a cluster) Now, for the potential energy: E pot = GM 2 R cl Relating the potential energy to the kinetic energy, we can solve for the mass: v 2 R cl M = 3 G For typical velocity dispersions v ~ 1000 km s -1 and cluster radii ~1 Mpc, we derive M ~ 10 15 Msolar

Weighing Galaxy Clusters (from the motions of galaxies in a cluster) For typical velocity dispersions v ~ 1000 km s -1 and cluster radii ~1 Mpc, we derive M ~ 10 15 Msolar The total amount of stellar mass in galaxies themselves in clusters is typically ~10 13 Msolar Therefore, the total baryonic mass in galaxies is much less than that inferred to exist from the velocities of the galaxies i.e. what is the apparent mass to light ratio in clusters? (M/L)cluster ~ 100-200 Msolar/Lsolar vs. 10-20 Msolar/Lsolar for galaxies (dark matter even more important)

Context Measured M/L ratios indicate the increasing importance of dark matter on largest scales! Sun: M/L = 1 (M/L)galaxy ~ 10-20 Msolar/Lsolar (M/L)cluster ~ 100-200 Msolar/Lsolar Universe: M/L = 1400ΩM h 2 ~ 200 (ΩM/0.3)(h/0.7) 2

Weighing Galaxy Clusters (from the motions of galaxies in a cluster) The observation that the velocities of individual galaxies in clusters suggested a total mass much greater than that seen in galaxies was originally suggested by Fritz Zwicky in 1933 (based on observations of Coma cluster)! Fritz Zwicky (1898-1974)