Formation and evolution of the cosmic web

Transcription

1 Formation and evolution of the cosmic web aurorasimionescu.wordpress.com/teaching Aurora Simionescu ISAS/JAXA

2 Course Evaluation One short essay (around 2-4 pages) exploring in more detail one of the topics presented in class. Suggested essay themes will be provided at the end of each lecture. Choose only ONE topic; essays due after the end of the course (due date TBA). Your goal: tell me something I did not know before reading your essay. (70%) Active participation in class (0%) Textbooks: Extragalactic Astronomy and Cosmology, Peter Schneider High Energy Astrophysics, Malcolm Longair

3 Lecture I The expanding Universe

4 Discovery of the cosmic expansion v=h*d H=500 km/s/mpc, Hubble 1929 (current value ~70 km/s/mpc)

5 How do we measure the velocity? Doppler Effect c c source is static: observer sees wavelength λ c v c source is moving: observer sees wavelength λ = λ*(1+v/c) if v<<c Vesto Melvin Slipher was the first to observe the shift of spectral lines of galaxies in 1912

6 How do we measure the distance? Charles Messier catalogued catalogued all extended nebulae producing a list of 10 objects by 1784 (final list today has 110) But for ~140 years () it was not known how far the Messier objects were. They could be gas clouds in our own galaxy, as well as other very distant copies of the Milky Way M20 M108

7 Henrietta Swan Leavitt (1908) one of the women human "computers" hired by Edward Charles Pickering to measure and catalog the brightness of stars as they appeared in the Harvard College observatory's photographic plate collection discovered that for a certain class of variable stars called Cepheids there is a relation between the luminosity and the period

8 Absolute distance measurements using Cepheids brightness=luminosity/(4π*distance 2 ) luminosity inferred based on period > knowing luminosity and brightness, we can measure distance

9 191: Ejnar Hertzsprung uses Cepheids to measure distance to the Small Magellanic Cloud as 7,000 light years (current value 199,000 ly) 192: Edwin Hubble discovers variable star in Andromeda Andromeda nebula using the 100-inch Hooker telescope at Mount Wilson Observatory 1924: Edwin Hubble determines distances to Andromeda and the Triangulum nebulae as 900,000 and 850,000 light years: much too far to be a part of the Milky Way These must be other galaxies (current distance values 2.5 million and 2.7 million light years)

10 It has been less than 100 years since we discovered that there are other galaxies apart from the Milky Way. The general theory of relativity was published before we were sure that other galaxies exist. Although astronomy is one of the oldest professions, extragalactic astronomy is one of the youngest fields of science.

11 performed a systematic study of how fast galaxies are moving away from us

12 The fascinating life of Milton Humason dropped out of school at the age of 14 became a "mule skinner" taking materials and equipment up the mountain while Mount Wilson Observatory was being built became a janitor at the observatory in 1917; volunteered as a night assistant in 1919, George Ellery Hale made him a Mt. Wilson staff member recognising his dedication and technical skill got his PhD in 1950 from Lund University; retired in 1957

13 Discovery of the cosmic expansion v=h*d H=500 km/s/mpc, Hubble 1929 (current value ~70 km/s/mpc)

14 Progress in measuring cosmic expansion Hubble Space Telescope Key Project (2001): 72+/-7 WMAP (2011) 70.2+/-1.4 Planck (2015) /- 0.46

15 What does cosmic expansion mean? Imagine an elastic band: L L L L L Now, someone stretched it out to double its initial size: 2L 2L 2L 2L 2L d=l v= L/t d= 2L v= 2L/t d=l v=l/t d= 4L v= 4L/t We recover v d

16 But the Universe is NOT expanding away from any privileged point that remains fixed in space If you live in galaxy A Y X A B C 2v v v 2v If you live in galaxy B Y X A B C v 2v v v

17 D intuitive equivalent to cosmic expansion ( expanding raisin bread model ) But, in the Universe, there is no dough the space itself is growing

18 Relativistic Doppler effect c v c λ = (c+v)t with v positive for receding source [all quantities measured in observer s frame] in relativity we must now in addition consider time dilation: 0 = (c+v)t 0 p 1 v2 /c 2 = p 1+ p 1 0 p p β=v/c

19 The concept of redshift p Redshift (z) is defined as p 0 =(1+z) 0 = p *recall that in the non-relativistic limit, λobs=λ0(1+v/c) therefore z=v/c The recession velocity v of a galaxy has two components: (1) Hubble flow (velocity due to the expansion of space) (2) Peculiar velocity (galaxy is moving through space) the expansion velocity v=h*d, thus if d is small, the expansion velocity is small and peculiar velocities may dominate in the distant universe, the Hubble flow velocity becomes large and peculiar velocities are insignificant in comparison; therefore redshift is often used to indicate the distance of an object rather than quoting it in Mpc Note that z can become (much) larger than 1 p

20 physical distance (e.g. km or Mpc) Mathematical description of expanding universe to account for expansion with time, it is useful to transform to comoving coordinates r=a(t)x coordinate distance (any arbitrary units; e.g. size on a paper in cm) a(t) is called the scale factor We are free to choose, for convenience, a=1 at the present (i.e. units of x is Mpc in local Universe)

21 Mathematical description of expanding universe If nothing is moving with respect to our coordinate grid (x does not change with time) r=a(t)x v=dr/dt=(ȧ/a)r Hubble s law: v= Hr, thus H=ȧ/a Of course things are moving through space, so in reality v=dr/dt=(ȧ/a)r+u with u being the peculiar velocity and (ȧ/a)r the Hubble flow Redshift is due to the fact that the photon wavelength expands as the space expands: λ(a)=aλobs; Remembering the definition of redshift: λobs=λemitted*(1+z) Therefore, a=1/(1+z)

22 Over 2 million galaxies in a region 100 degrees across centered toward the Milky Way Galaxy's south pole. The homogeneous and isotropic Universe Locally, the Universe clearly has structure, but when averaged over very large spatial scales, it becomes well approximated as uniform: isotropic (the same in all directions) and homogeneous (the same at all places).

23 Equations of motion of uniform matter-dominated universe Now, consider the evolution of a spherical volume of radius L(t)=L0a(t) (if we choose small L then GR corrections become small and we can use Newtonian dynamics). Expansion will slow down because of gravitational pull of matter inside sphere: V =4 L d 2 L dt 2 = GM L 2 = m + u c 2 with respect to a point in time where we know the density to be ρ0 m (t) = 0 a 0/a(t) so, in a matter dominated Universe, we obtain m 0 0 ä = 4 G 0a 0 1 a 2 (deceleration must be non-zero) Integrating once with respect to time (multiply both sides by 2ȧ): a 2ȧä = d(ȧ 2 )/dt = 4 G 0a 0 ȧ 2 = 8 G 0a 0 2ȧ a 2 = 8 G 0a 0 d( 1/a)/dt 1 a kc 2 integration constant

24 Equations of motion of uniform matter-dominated universe ȧ 2 = 8 G 0a 0 1 a kc 2 The meaning of k: RHS must be greater than zero. If k > 0, then there is a maximum value of a at which the expansion turns around and collapse begins. This is a closed Universe. If k < 0, expansion rate eventually tends to a constant determined by the value of k - an open Universe. If k = 0, expansion slows but never reverses - a flat Universe. Einstein - de Sitter Universe: For k=0, a t 2/ And we can define the critical density (such that k=0) and remembering that H=ȧ/a scale factor a Note The Hubble constant is not a constant

25 In-class exercise: The Hubble constant at the present time is 70 km/s/mpc (1) If the Universe is empty, what is its age? (2) In an Einstein - de Sitter (matter dominated, critical density) Universe, what is the time since the Big Bang? [The answer to #2 is true of any kind of matter that gravitates, both baryons and dark matter] ȧ 2 = 8 G 0a 0 c,0 = H2 0 8 G 1 a kc 2 1/H0=14Gyr 2/H0=9.2Gyr

26 All of the stars in a globular cluster formed at roughly the same time, thus they can serve as cosmic clocks. The older the cluster, the less massive the biggest hydrogen burning star in it can be. The oldest globular clusters contain only stars less massive than 0.7 solar masses, suggesting that they are between 11 and 18 billion years old.

27 Equations of motion of uniform expanding universe with a cosmological constant ä = 4 G m a ä a = for matter dominated Universe; adding radiation: a 4 G ( m + u r /c 2 ) matter density (baryons+dark matter): proportional to a - radiation energy density: number of photons decreases as a -, but wavelength also increases as a so that this term decreases as a -4

28 The radiation-dominated era In 1964, Arno Penzias and Robert Wilson accidentally discover the signal from this background radiation. George Gamow (see also work of Ralph Alpher and Robert Herman) had predicted in 195 that radiation left over from the Big Bang should fill the whole Universe with a temperature of 7K. Its discovery supports the model in which the Universe started with a hot Big Bang, and provides further evidence for an isotropic Universe.

29 Cosmic microwave background basics 400 photons per cubic centimeter. In this room A few percent of TV static. There are 1 billion photons for every baryon in the Universe. We see the surface of last scattering when Universe became transparent to light. CMB temperature is the same within +/-0.005K; those variations are due to the absolute velocity of the Earth through the Universe, v = 627 +/- 22 km/s (Kogut et al. 199, COBE). Once that is taken out, the temperature is the same within 1 in 100,000. If we do not live in a special place and the Universe is isotropic to all other observers then it must be homogeneous

30 The radiation-dominated era When matter and radiation were compressed at very high densities, matter was first in the form of a quark soup (quark-gluon plasma); the radiation density was much higher than the matter density, so the dynamics of the expansion was driven by radiation (photons). As expansion continued and temperatures dropped, quarks combined to protons and neutrons and the universe became filled with hydrogen plasma. The Universe was still opaque to light and as the universe expanded further, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral hydrogen atoms ( epoch of recombination ). These atoms could no longer absorb the thermal radiation, and so the universe became transparent (~80,000 years after Big Bang). After recombination, matter and radiation evolve independently. The radiation left over from this epoch follows a black-body distribution whose effective temperature drops as the universe expands.

31 Evolution of the temperature of the Universe The Planck function Bν specifies the radiation energy of blackbody radiation that passes through a unit area per unit time, per unit frequency interval, and per unit solid angle. The number density dnν of photons in the frequency interval between ν and ν+dν is: dn d D 4 B ch P D 82 1 c exp hp k B T 1 1 At two different points in time (t2 later than t1), an observer measures a different photon frequency due to the expansion of space: ν = ν/(1+z), thus dν is changed accordingly, 0 and dn ν has diminished by (1+z), where 0 C 1+z=a(t2)/a(t1). 0 dn 0 0 D dn =.1 C z/ d 0 d=.1 C z/ D C z/ C z/ 2 c exp hp.1cz/ 0 k B T 1 1 D c exp hp 0 k B T 2 1 ; Once established, a black body distribution is conserved by the expansion of space, with an evolving temperature T(z)=T0(1+z). At recombination, z=1100, so T~000K.

32 CMB density From Stefan-Boltzmann law: CMB D a SB T 4 2 k 4 B 15 c T 4 ' 4: c,0 = H2 0 Compared to the critical density: 8 G r r m = m,0, cr,0 r = r,0 we define, cr,0 T 4 2:7 K CMB ' 2: h 2 and including neutrinos in addition to photons, r ' 1:68 CMB 4: h 2 g cm In class exercise: what was the scale factor of the Universe, a, at matterradiation equality, as a function of Ωm?

33 Equations of motion of uniform expanding universe with a cosmological constant ä = 4 G m a deceleration must be non-zero Einstein added a cosmological constant term to force ä to be 0 when it was believed that the Universe was static (before discovery of expansion) General relativity allows for integration constant Λ in

34 Equations of motion of uniform expanding universe with a cosmological constant ä a = matter density (baryons+dark matter): proportional to a - a 4 G ( m + u r /c 2 )+ / radiation energy density: number of photons decreases as a -, but wavelength also increases as a so that this term decreases as a -4 cosmological constant: does not depend on a at all Useful to define a radiation density and a cosmological constant density as r = u r /c 2 and = /8 G a ȧ 2 = 8 G m a 2 kc 2 then more generally becomes: ȧ a 2 = H 2 = 8 G( m+ r + ) kc 2 a 2 Friedmann equations

35 Three stages of the Universe Early universe (small a): radiation dominated As a increases, ρr decreases the fastest (as the 4th power of a). At some point, ρr becomes smaller than ρm which decreases only as the rd power of a. As a increases further, ρm decreases as the third power of a while ρλ does not change. No matter how small ρλ is initially, because it does not decrease with a, it will become dominant for large a. scale factor a

36 Expansion dominated by matter vs. cosmological constant (any kind of) matter m (t) = 0 a 0/a(t) = /8 G 1 8 ȧ a 2 = H 2 = 8 G( m+ r + ) kc 2 a 2 cosmological constant ȧ a 2 = H 2 = 8 G 2 exponential increase

37 Effect of cosmological constant on age of Universe From numerical solutions to: ȧ a 2 = H 2 = 8 G( m+ r + ) kc 2 a 2 r r m = m,0 cr,0, =,0 cr,0 Solves problem of age of Universe compared to oldest globular star clusters (1.8 Gyr)

38 The homogeneous Universe: take-home points On large scales (hundreds of Mpc), the Universe is uniform (isotropic&homogeneous) The Universe is expanding. Expansion velocity measured p via Doppler effect as a redshift (z) of the spectra: 0 1+ =(1+z) 0 = p 0 1 The rate of expansion and age of the Universe depend on the contents of the Universe. The scale factor a=1/(1+z) evolves as (Friedmann eqns): ȧ a 2 = H 2 = 8 G( m+ r + ) ä a = 4 G a baby universe: radiation dominated ( m + u r /c 2 )+ / kc 2 a 2 teenager universe: matter dominated adult/senior universe: cosmological constant dominated The Universe is filled with a microwave background radiation left over from the last time matter interacted with light. It follows a Planck distribution with T=2.7K and increasing in the past T(z)=T(1+z). p p

39 Suggested essay topics 1) Explain in more detail how Cepheids are used for distance determination. What are the different types of Cepheids? How were Hubble s measurements of distances to Andromeda and the Triangulum galaxy revised, and what drove the changes in the measurements of the Hubble constant over time? 2) Explain the role of neutrinos during the radiation-dominated phase of the Universe. At what temperature does neutrino decoupling happen, and what was then the age and scale factor of the Universe? How many neutrinos per cubic centimeter of space are there from the cosmic neutrino background?