! Dark Matter and the Universe Topic 1 Dark Matter, Dark Energy and the Cosmology Revolution! What is the real structure of our Universe and how do we know it is so? ! Contents of Topic 1 This ﬁrst Topic provides an introduction to the Dark Matter Problem, putting it in the context of current understanding of the composition of the Universe and covering some of the essential Cosmology and tools needed to study it. ‣ What do we mean by Dark Matter and why bother? ‣ Composition of the Universe & the Cosmology Revolution ‣ What could the Dark Matter be? ‣ Cosmology and tools for Dark Matter? ‣ The Cosmological Principle, Isotropy and Homogeneity ‣ The Big Bang ‣ Hubble’s Law and Redshift ‣ Critical Density ρc and the Density Parameter Ω0 ‣ The geometry of space and Inﬂation What! is Dark Matter and Why Bother?! ‣ The name Dark Matter attests to the fact it doesn’t give off light. Yet it provides the gravitational pull to hold together the galaxies and clusters we see in the Universe today.! ‣ We see the effects of Dark Matter everywhere – it bends light, it makes gas move at great velocity, without it galaxies would ﬂy apart.! ‣ It must be something other than bright stars, but what?! !‣ So we should bother very much about Dark Matter! . It is a dominant material in our Universe and yet we do not know what it is made of. It most likely will lead us to completely new physics. ‣ The term Dark Matter simply means material that is Non-Luminous. The! Composition of the Universe ‣ In more detail current results give us the Mass-Energy Composition of the Universe approximately as follows: ! ! ‣ Note again! the small fraction of visible atoms! ‣ Note how Dark Matter and Dark Energy dominate! The! Composition of the Universe ‣ The little bit of the matter in the Universe we really know about can be broken down as follows: ! ! !
‣ Interesting fact: Neutrinos contribute about the same mass- energy content to the Universe as do all the stars. The! Composition of the Universe ‣ In more detail if we look at individual galaxies we see how Dark Matter dominates galaxies but Dark Energy has the biggest inﬂuence in the Universe as a whole. ! ! Observable! Universe Galaxies
Ordinary Matter Ordinary Matter Dark Matter Dark Matter Dark Energy Dark Energy The Composition of the Universe ! ‣ These results are relatively recent - we are living through a period of cosmology and particle physics revolution.! ‣ For the ﬁrst time in history we have a good picture of the Universe - called the Inﬂationary Big Bang Model or the Standard Model of Cosmology.! ‣ We also have a good picture of the fundamental particles and forces - the Standard Model of Particle Physics.! ‣ The merging of these areas of science, Astrophysics, Cosmology and Particle Physics, are giving us new and powerful insights, forged around the new disciplines of Particle Astrophysics and Particle Cosmology. ! ‣ However, big questions remain…:! ! The Cosmology Revolution! ‣ So we have two important models but there are gaps. Big Questions in Remain! ‣ A few of these questions are as follows: 1. How did the structure of the Universe we observe form?! 2. What is the Dark Matter?! 3. Could there be more than one kind of Dark Matter?! 4. Why is the Dark Matter distributed the way it is?! 5. Could the Dark Matter be new fundamental particles?! 6. What is the Dark Energy?! ! ! What! does the Term Dark Matter Mean? ! ‣ “ Dark Matter ” means any Non-Luminous material that shows its presence by its gravitational inﬂuence.! ‣ Here’s an old example:! ! ! Calculate the Earth’s Mass two ways! ! typical ‣ Earth’s circumference - 40,075 km! rock ‣ Typical rock density - 2.8 g/cm3! ‣ Use this to estimate the mass - ANS (1)………
‣ Newton says F = GmM/r2 = ma! gravity ‣ g = 9.8 m/sec2, G = 6.67 x 10-11m3/(kg sec2)! ‣ Use this to estimate the mass - ANS (2)……….. ! Dark Matter in the Universe ! ‣ In the previous calculation we get a factor ~x2 discrepancy due to the gravitational effect of the hidden high density “dark matter” core of the Earth. But how do we know there is hidden matter throughout the Universe? ! ‣ Later Topics will cover many of the techniques used by Cosmologists, here is a summary: 1. Observation of Rotational Curves of Galaxies! 2. Observation of Gravitational Lensing! 3. Observation of Hot Gas in Galaxy Clusters ! 4. Computer simulations of Cluster Evolution! 5. Analysis of Large Scale Structure ! 6. Analysis of the Cosmic Microwave Background ! ‣ All these show us that Dark Matter pervades the Universe Dark Matter and Structure Formation ! ! ‣ A particularly interesting result comes from computer simulations which model Structure Formation in the Universe. It is impossible to get a match to the observed structure, with voids and clumps, without accounting for Dark Matter.! ‣ This example simulation is from the EAGLE group. So What Could the Dark Matter be? ! ‣ When considering Dark Matter it turns out we can think two ! broad classiﬁcations: Baryonic Dark Matter (normal matter but non-luminous) ! ! Some examples to be covered in later Topics are:! (1) Dim Stars (<0.1M⊙)! (2) Hydrogen Ice! (3) Black Holes! ! Non-Baryonic Dark Matter (new fundamental particles) ! ! Some examples to be covered in later Topics are:! (1) Weakly Interacting Massive Particles (WIMPs)! (2) Axion Particles! (3) Other exotic particles! What is Dark Matter Most Likely to be? ! ‣ It turns out that it’s hard to avoid the conclusion that Dark Matter is weakly interacting Non-Baryonic “cold” particles, fundamentally new physics in action in the Universe. ‣ An amazing bit of new evidence for this is from observation of the Bullet Cluster - two galaxy clusters merging:
Blue - Dark Matter inferred Bullet by gravitational lensing Cluster Red - normal baryonic matter traced by the x-ray emission from hot gas ‣ We will return to the Bullet Cluster in later Topics ‣ The blue is DM reconstructed from Gravitational Lensing. The red is normal matter. The DM has carried on moving through the merger, the baryonic matter has slowed down. The Universe in Summary so Far ! ‣ So we now know the Cosmic Recipe. Mostly the Universe is invisible “Dark Matter” (~25%) and “Dark Energy” (~70%). The remainder is normal atoms (baryons) that are also hidden (~4%), plus the small amount of visible material such as the stars (~0.5%), H and He. The Earth and inhabitants are made of the rarest stuff of all: heavy elements (~0.01%). ‣ The best idea for the Dark Matter is that it is so-called Cold Dark Matter (CDM) made of non-baryonic particles. Cold means slow moving, non-relativistically. Theories based on this can account for all the large scale features we see including the heat radiation of the Big Bang and the large scale distribution of galaxies. ‣ But we still don’t really know what the Dark Matter and Dark Energy are. There is lots of work to do. Cosmology and Tools for Dark Matter ! ‣ To continue our study we will need some basic knowledge of cosmology and to be familiar with relevant tools and parameters. Only then can start to make progress in understanding Dark Matter. We need to know about:
The Cosmological Principle! The Big Bang Concept and Observational Evidence for it! Hubble’s Constant and Red Shift ! Angles and Distances in Astronomy ! The Critical Density Parameter! The Geometry of Space and Cosmic Inﬂation The Cosmological Principle ‣ The average density of galaxies is ﬁxed throughout the Universe and does not change with distance or direction. ! ! ‣ So an observer anywhere !in the Universe sees approximately the same thing. No place is special, and there is no edge or centre.
‣ We know the Universe is expanding and since the expansion occurs evenly at every point in space, galaxies are separating from each other at about the same pace, giving the Universe a nearly uniform density and structure. Thus the Universe appears smooth at large distance scales. A Homogeneous and Isotropic Universe ‣ Thus the Universe is said to be homogeneous & isotropic: - Uniform with respect to position (homogeneous), ! - Uniform with respect to viewing angle (isotropic).
‣ In the left image we have an Isotropic Universe - i.e. if you stand at the centre and look in every direction, the Universe will look the same. On the right is a Homogeneous Universe. This means that if you stand in any one place and look around, the Universe looks the same. The Big Bang ‣ The Universe is observed to be expanding with all galaxies receding from each other due to the expansion of space itself. The recession is not due to their own “peculiar” motion.
Imagine what happens to the dots on a balloon being blown up - a 2 dimensional analog of the 3D Universe.
‣ If the Universe is expanding now, it's logical to assume it was smaller before - i.e. that all galaxies and stars started from a hot, high density plasma, the Hot Big Bang comprising a soup of fundamental particles and energy. ! ‣ The term Big Bang is a very bad name as there is no explosion into space. It is space itself that is expanding! !Big Bang Observational Evidence ‣ The! two main bits of observational evidence for the Big Bang: (1) Galaxies are receding - the Universe is expanding! (2) The cosmic microwave background radiation (CMBR) ‣ The CMBR is a pervasive microwave radiation, the same in all directions, that can only have arisen when the Universe became transparent 300,000 years after the Big Bang. ‣ The CMBR has an almost perfect blackbody form with T = 2.7 K. ‣ Very small variations in the intensity of the CMBR from different directions can tell us a lot about dark matter. We will return to this in later Topics. The Universe is Expanding ‣ Edwin Hubble discovered that the Universe is expanding using the 100 inch Hooker Telescope on Mt. Wilson (1929): ‣ He showed that galaxies move away from each other at velocities v proportional to their separation d Some typical measurements of recessional velocity vs. distance to different galaxies. ‣ You can visit the telescope and see his coat locker! Hubble’s Law ‣ Hubble’s Law, often called the velocity-distance relation, relates the distance d to a galaxy and its recession velocity: Hubble Constant
v = H0d
distance to a galaxy for small red shift z
‣ H0 is the Hubble Constant. The value, with error of ~5%, much improved by the WMAP results, is 72 km s-1 MPc-1
‣ Note that sometimes the constant ho is used, related to the Hubble Constant by H0 = h0 x 100 km s-1 Mpc-1, where values of 0.5 < h0 < 1 are typical used (e.g. 0.72). Redshift ‣ We can use Hubble’s Law to ﬁnd the distance to a distant object provided we know the objects’ recession velocity v. ! ‣ We can ﬁnd v by making observations of the light arriving from the object because as this distance scale changes, the wavelength of the light stretches in response. This is the Doppler Shift. ! ‣ What we actually measure is the Redshift of spectral lines. The redshift can be deﬁned as:
‣ Taking account of relativity and assuming v < c yields also: and hence Redshift ‣ However, time evolution of the expansion of the Universe means this expression for z is only approximate, it works only for nearby objects where z < ~0.05.
For very nearby objects z < 0.05
‣ For objects further away we have to note that the Universe is evolving with time, that the rate of change may also be evolving. For objects having redshifts up to z < 0.75 we can use the following second order result:
For objects z < 0.75
‣ Here q0 is the Deceleration Parameter. A value q0 = -0.2 is now used - negative because the expansion rate is increasing with time (a manifestation of Dark Energy). Distance and Angles ‣ In Cosmology often angles are measured rather than distances, related as follows: θ
R d ‣ For small angles (< ~0.02 radians) to calculate d knowing R make the approximation that the shortest leg of the very skinny triangle above is actually a small arc of a circle. In this case, if θ is an angle in Radians, then d = Rθ. ‣ To convert from degrees to radians, multiply by 2π/360. ‣ Solid angles are measured in Steradians. Imagine that an observing ‘eye’ is at the centre of a spherical shell of radius 1m. The total solid angle of the whole sky all around the observer is 4π Steradians. The solid angle of an object is the area on the unit sphere that it covers. Critical Density ρc
‣ In cosmology the Critical Density ρc is a parameter often deﬁned as the average density of matter required for the Universe to just halt its expansion, after an inﬁnite time. ‣ Consider the motion of a galaxy of mass m at the edge of a spherical region radius r. According to Hubble’s Law its velocity is v = Hor and the kinetic energy T = mv2/2. ‣ If the region has mass M then the potential energy at the edge is U = -GMm/r.! ‣ The total energy is E = T + U = mv2/2 - GMm/r ‣ If the Universe has mean density ρ then M = (4πr3/3)ρ. The value of ρ that gives E = O is called the Critical Density ρc.
‣ Hence: ρc = 3Ho2/8πG Density Parameter Ω ‣ It is useful to express the density as a fraction of the density required for the critical condition by using the so called Density Parameter Ω = ρ/ρc, ρ being the measured density. ‣ Note that as the Universe is expanding the value of ρ and hence Ω might change with time. So it is usual to give a subscript 0 when referring to the current time: Ω0 = ρ0/ρc,0. ‣ So the condition Ω = 1, or Ω0 = 1 for the current time, means we have the condition of critical density. If on the other hand we ﬁnd Ω > 1 then the Universe will eventually collapse. ‣ The different types of matter (or energy) in the Universe all contribute to Ω, e.g. components like Ωbaryons, Ωneutrinos etc. all add together to give the total Ω. ‣ Meanwhile there has always been a theoretical preference for Ωo = 1 because this also gives us a “Flat Universe”. Ω and the Geometry of Space ‣ What do we mean by a “Flat Universe”? Flat Universe: Space has Euclinean geometry. Sum of angles in triangle = 180˚. Universe will barely expand to a stop. very special case!
Open Universe: Space has negative curvature. Sum of angles in triangle < 180˚. Universe will expand forever.
Closed Universe: Space is curved back into itself. Sum of angles in triangle > 180˚. Universe will stop expanding and collapse into itself: Big Crunch Ω0 and Dark Matter ‣ So measurements of ρ0 and Ω0 are vital in cosmology as they can tell us about the composition of the Universe and its eventual fate. But how does this relate to Dark Matter? ‣ A typical current estimate now gives Ω0 = 1.02 ± 0.02 indicating that the Universe is very close to critical density. ‣ The critical density now for an H0 of 70 kms-1Mpc-1 (h0 =0.7) is calculated to be ρc,0 = 1.2 x 10-26 kg/m3. ‣ But the density of baryons estimated from luminous matter (stars etc) and the rest appears to be 5.0 x 10-28 kg/m3.
So Ωbaryons = 5.0 x 10-28 / 1.2 x 10-26 ≈ 0.04 ‣ So if the total from all measurements is Ω0 = 1 then 96% of the Universe is not visible and probably not baryons either! We have a big Dark Matter problem! Dark Matter, Inﬂation & the Big Bang ‣ So where might the missing material have come from? ‣ The answer may lie in the solution to one problem with Big Bang Theory - why is the Universe so smooth and isotropic on large scales? This is called the Horizon Problem. ‣ The CMBR in particular illustrates the problem. These photons emerged ~400,000 yrs after the Big Bang when only parts of the Universe as large as 300,000 light-years (~1˚ in today's sky) could be causally connected, yet the CMBR is very smooth over the whole sky, with T = 2.7K.
In this image of the CMBR there are a million causally disconnected regions (no info/light can reach the others): how come they all agreed to have the same Temperature to 1 part in 100,000? Dark Matter, Inﬂation & the Big Bang ‣ The answer is Cosmic Inﬂation. This proposes a very rapid expansion of the Universe at age t = 10-37 -10-32 s during which the Universe grows by a factor of x 1040-10100!
‣ The ﬁeld that drove this expansion decayed by 10-37 s producing a Universe the size of a marble in the form of a Primordial Soup of particles that including the baryons but also possibly DARK MATTER PARTICLES! Summary of Topic 1 ! A guide for the exam ‣ The Universe contains both luminous and dark components - understand the broad types and quantities of material and basic evidence for them. ! ‣ The principles of cosmology and the Big Bang are needed to study Dark Matter and the Universe - understand the cosmological principle, basics of structure in the Universe, the concept of the Big Bang and Inﬂation, evidence for them, the importance of the CMBR and the geometry of space. ! ‣ Dark Matter study needs certain tools - understand the Hubble Law, Redshift, Critical Density & Density Parameter.! ‣ The Critical Density can be derived from basic principles - understand how to derive this in terms of the Hubble Constant. ! Terms to know from Topic 1 ! A guide for the exam ‣ Dark Matter, Dark Energy, Neutrinos ‣ Inﬂationary Big Bang Model, Standard Model of Cosmology, Standard Model of Particle Physics ‣ Particle Astrophysics, Particle Cosmology ‣ Critical Density, Density Parameter ‣ Structure Formation, Cosmic Recipe ‣ Baryonic Dark Matter, Non-Baryonic Dark Matter ‣ Cold Dark Matter (CDM), Big Bang, Cosmic Microwave Background (CMBR) ‣ Flat Universe, Open Universe, Closed Universe ‣ Cosmological Principle, Isotropic and Homogeneous Universe ‣ Hubble’s Law, Hubble Constant, Redshift, Doppler Shift, Deceleration Parameter ‣ Radians, Steradians ‣ Horizon Problem, Inﬂation, Primordial Soup Equations from Topic 1 ! Equation reminders for the exam
F = GmM/r2 = ma
v = H0d
For very nearby objects z < 0.05
For very objects z < 0.75
d = Rθ
ρc = 3Ho2/8πG Questions on Topic 1 ! to help with the exam revision ‣ Explain the signiﬁcance of the bullet cluster observation regarding the nature of dark matter. ‣ The Universe comprises what 4 main components and in what proportion? ‣ What is a parsec? ‣ Why is the parameter h0 used? ‣ What is the difference between an Isotropic Universe and a Homogeneous Universe? ‣ Derive an expression for the Critical Density in terms of the Hubble Constant. ‣ What is the deceleration parameter and why do we have this and not an acceleration parameter? ‣ What observational evidence leads us to postulate Inﬂation theory? ‣ What is a Baryon? What are the two classes of dark matter? write out 4 candidates for baryonic dark matter.