Astrophysics

1. Astrophysics • 18 lecture introduction -10 lectures on cosmology -8 lectures on stellar evolution one guest lecture by Matthew Young on Pulsars • Power point slides plus one lecture from a PDF • Two minor, one major assignment: see handout • Slides will be put on web • Text Carroll and Ostlie: Modern Astrophysics • Contact me whenever necessary: ext 2736, mob 0409687703,dgb@physics, rm4-67, basement lab, Gingin 95757591 This course includes material from lectures at many major universites and institutes including Chicago, Fermilab, Stanford, Sheffield. Authors include R Kolb, Mohr, W.Hu, V Kudryavtsev,

2. Course Outline See handout Cosmology: 10 lectures Stellar Evolution: 8 lectures Excursion: Wed 16 March: barbeque, cosmology and astronomy field night. Time: leave UWA 4.30pm: bus and car pool. Return by 11pm. Major Assignment: Dark Energy, Black hole binary systems and Intermediate mass black holes. astrophysics lectures 1and 2

3. Major Assignment The major assignment asks you to writean investigation on one of three topics based on recent research dark energy and the missing mass intermediate mass black holes. ( eg 1000 solar mass near galactic centre) stellar mass black hole binary systems (predicted, none discovered, many expected in gravitational wave signals) The investigation should be based on recent discovery papers. In your investigation you must demonstrate that you have read and understood at least 3 research letters. Show how they relate to each other. Use Nature, Astrophysical Journal Letters, Science and arXiv Astro-ph or gr-qc preprints. astrophysics lectures 1and 2

4. Looking into the past Telescopes are time machines Looking into the past we see a universe that is Hotter: - thermal background radiation rising in temperature Denser: -galaxies are closer together Expanding:-Everything is receeding astrophysics lectures 1and 2

5. History of the Universe astrophysics lectures 1and 2

6. Cosmology and Dark Matter • First 2 lectures Hubble law Critical density Density parameter Mass to light ratio Dark Matter in solar system Dark Matter in galaxies Dark Matter in clusters of galaxies and superclusters Conclusions astrophysics lectures 1and 2

7. Introduction First hints for ‘dark matter’ (1844): It was noticed that planet Uranus had moved from its calculated position by 2 arc minutes. F. W. Bessell found the strange motion of the star Sirius. By 1846 the planet Neptune was discovered (no longer a dark matter). In 1862 the faint companion to Sirius (Sirius B - a white dwarf) was discovered. astrophysics lectures 1and 2

8. wavelength at the point of observation l - l wavelength at the point of emission. obs em l em z 1 v / c v + = ≈ 1 v / c c - 1 z + Redshift z = In terms of the velocity of the receding object red shift is given by: astrophysics lectures 1and 2

9. v H0 r = The Hubble Law 1 parsec = 3.25 ly. Stellar parallax from earth orbit. Cepheid variables standard candles In 1929, based on the observation that the universe is expanding it was further realised, by Hubble, that the expansion velocity v is proportional to distance away from the observer (Earth) r: astrophysics lectures 1and 2

10. - 1 - 1 H 100 km s Mpc . 0 H0 v r z ≈ c c Hubble’s Law H0 is the Hubble constant - the rate of expansion at the present time. = The precise value of H0 was disputed for many years. Today cosmologists agree H0 ~ 70 km s-1 Mpc-1 h = h = 0.70 ± 0.05 Hubble thought H0 was 540 km s-1 Mpc-1 astrophysics lectures 1and 2

11. d This requires the famous Newtonian result: a particle inside a spherical mass distribution feels no gravitational force. b) For a particle outside a spherical mass distribution the gravitational force is as if all the matter were concentrated at central point. e.g. 1) The force exerted on the Earth by the moon depends on the mass of the moon and not on its density profile. 2) The gravitational acceleration of the earth falls to zero as you approach the core. Critical density Mass m r contributing mass astrophysics lectures 1and 2

12. 2 3 H0 rc = 8 G p 3v2 rc = 8p G r 2 rc Critical Density Consider the motion of a galaxy of mass m at the edge of a spherical region of mass M and radiusr : T = mv2/2 Kinetic energy U = -GMm/r Potential energy at the edge of a sphere E = T + U = mv2/2 - GMm/r Total energy The mass of the sphere can be calculated from its volume and mean density M = 4p r3r / 3 The critical density of the Universe is the density which gives E = 0 critical density From known H0we can compute the value of the critical density: rc(t0) = 1.88 h2. 10-26 kg m-3 (i.e. small) 6 H atoms per m3 astrophysics lectures 1and 2

13. r0 W0 = rc Density Parameter W0 The density parameter W0 is the ratio of the true density of the Universe at the present time to the critical density: density parameter 0 < W0 < 1 r0 < rc Open Universe: r0 = rc W0 = 1 Flat Universe: r0 > rc Closed Universe: W0 > 1 Note that we can use the density parameter to quantify components of the density due to particular types of material in terms of the ratio to the critical density, i.e. Wrad, Wmatter, Whalo, etc. astrophysics lectures 1and 2

14. empty open flat closed Fate of the Universe The Friedmann Equations Open Universe: will expand forever Flat Universe: will expand forever (but the expansion rate slows to zero at infinite size) Closed Universe: will end in a Big Crunch W=0 W<1 W=1 W>1 The fate of the Universe, as well as many other things, depend on the density (density parameter). Can we measure it? astrophysics lectures 1and 2

15. q0 = 1 empty 2c a = 2p max H open t L= 0 H0 flat 2 closed t0= 3H0 Age Size and Lifetime of Closed Universes For closed solutions the size of the Universe will reach a maximum decelleration parameter qo also we can calculate the lifespan of the Universe - the time from birth to recollapse, e.g. for q0 = 1. astrophysics lectures 1and 2

16. ~ 1 W A crude estimate of the density A crude estimate comes form considering the typical mass of a galaxy ~ 1011MSun, and typical galaxy separation ~ 1 Mpc. Check for yourself that this gives a density close to the critical density. astrophysics lectures 1and 2

17. g = 0.51 MSun MSun erg/s LSun LSun M L Mass to light ratio Mass to light ratio can help us to find the density or W0. There are stars which are intrinsically faint, such as white dwarfs, brown dwarfs. There are also dead stars, such as neutron stars and black holes. Important to distinguish between objects which are intrinsically dim and those which are dim because they are very distant. We can define the mass to luminosity ratio for a given system (galaxy, cluster of galaxies, any part of galaxy) relative to the Sun. We define the mass to light ratio as: whereh = 1for the Sun = h astrophysics lectures 1and 2

18. Mass to light ratio Characterise the average density in various regions of the Universe in terms of mass-to-light ratio. and contribution to the density parameter. Note M/L is proportional to h. Two examples: i) h <<1 :a system is composed of massive , young and luminous main sequence stars; i) h >>1 : a system with old white dwarfs and hidden (dark) matter. Measurement of M/L depends on location: Solar neighbourhood: count up the luminosity of all stars etc and determine masses from orbital motions. In galaxies measure total galaxy luminosity and use rotation curves or virial theorem (see later) to estimate total mass. astrophysics lectures 1and 2

19. Dark Matter in the Galaxy Consider motion of the stars perpendicular to the Galactic plane. Assume this motion is independent of the conventional circular motion around the Galactic centre. astrophysics lectures 1and 2

20. Dark Matter near the Sun - the Oort limit The velocity in z-direction vz decreases as z increases due to the gravitational attraction to the Galactic plane. It is impossible to measure vz or gz (the gravitational force per unit mass). But assuming the big number of oscillations made around the plane and mapping the distributions of stars away from the plane, it is possible to estimate the average gravitational force. In general we have: gz = g0 (z / z0) where g0and z0 are measurable constants of acceleration and length. astrophysics lectures 1and 2

21. The Oort limit The acceleration due to gravitational attraction is thus: dgz / dz = - 4 p G r where r is the average density of gravitating matter. Thus near the Sun (Oort limit - 1932, 1965): r = g0/ 4 p G z0 Oort estimated this as 0.2 MSun/pc3. Recent estimates give the total density of 0.15 MSun/pc3 (0.3 GeV/m3) and 0.08 MSun/pc3 for stars and gas only. Hence about 1/2 or 1/3 is missing matter. But this is at a very specific point (near the Sun). astrophysics lectures 1and 2

22. M100 spiral 0 . 005 ~ W stars 0 . 01 W = visible baryons Density in stars and other luminous matter We can estimate the mass contribution from stars in galaxies. We add up the mass of stars, making use of the known relationship between stellar luminosity, temperature and mass. Within the optical radius of galaxies this yields a non-dynamical estimate for the mass density. This provides a lower limit for the baryonic density. It can be extended slightly by integrating over the total background luminosity of the Universe, but it still yields a value no more than: astrophysics lectures 1and 2

23. The galaxy "M51". Messier 51 is also known as NGC 5194 and sometimes called the Whirlpool galaxy. The distance to M51 is about 9 Mpc Density estimated from galactic dynamics Rotation curves of spiral galaxies The first real evidence for substantial dark matter came in 1970 with Freeman’s observation of the rotation curves of Galactic halos. He showed that the 21 cm line of neutralhydrogen did not show the expected Keplerian decline beyond the optical radii of these galaxies. What would we expect if all the mass of a galaxy were accounted for by the visible mass? astrophysics lectures 1and 2

24. 2 GM ( r ) v GM ( r ) v circ = = circ r 2 r r Rotation curves of spiral galaxies Assume that stars, gas and dust move in circular orbits around galaxy. At large distances the gravitation field would be as if all the mass were concentrated in the centre Centripetal force is balanced by gravity: =gr Keplerian decline v ~ r -1/2 is not observed Doppler shift can be due to several motions: i) motion of the whole galaxy away/towards us; ii) random motions of the clouds; iii) rotation of the galaxy. This can be separated to find the rotation curve: we can measure v0 + vcirc and v0 - vcirc . This applies to galaxies seen edge on or at an angle. astrophysics lectures 1and 2

25. Rotation curves of spiral galaxies In almost all galaxies the velocity is found to be constant with radius. astrophysics lectures 1and 2

26. Rotation curves of spiral galaxies astrophysics lectures 1and 2

27. 300 200 /kms-1 HI (layer) HI (Tangent) HI (Petrovkaya) HII (regions) PNs 100 0 LUMINOUS MATTER 0 5 10 15 20 actual density (Galactic disk) R/kpc mean spherical density ~0.3 GeV cm-3 mean density (g cm-3) 10-20 10-21 DARK MATTER 10-22 mean spherical density 10-23 10-24 10-25 LMC ~30 kpc Sun 10-26 10-27 0 10-28 distance from galactic centre (cm) 10-29 1.1023 2.1023 Rotation curve of the Milky Way Milky Way astrophysics lectures 1and 2

28. Rotation curves of spiral galaxies From the observations we can try to model the density distribution: The easiest model is to assume the galaxy is spherical (we don’t need to assume that the hidden mass is distributed like the visible mass): astrophysics lectures 1and 2

29. We can use: where M(r) is the mass within radius r. GM ( r ) g = r 2 r 2 r r 0 0 ( r ) r = 2 2 ( r r ) + 0 (maximal) 0 . 1 W ≈ halo Rotation curves of spiral galaxies In this case we can determine the mass distribution uniquely. The solution is not much different for the more realistic case of a flattened spheroid. The best fit mass density distribution is: ro,roare constants This yields a typical total mass to light ratio in the halo (lower limit is for visible part of galaxy): hhalo~ 10 -100 A similar result is obtained when considering orbiting pairs of galaxies. astrophysics lectures 1and 2

30. M87 Elliptical (maximal) 0 . 1 W ≈ halo Density estimates for elliptical galaxies To determine the mass of elliptical galaxies we need to use the virial theorem because there is not much rotation. Alternatively we can use X-rays in halos or pairs of galaxies. All this gives: hhalo~ 10 -100 astrophysics lectures 1and 2

31. Density of clusters from bulk motions 2 1 GM a 2 T M v = < > V = - 2 R Estimates by the virial theorem In any system of gravitating bodies changes in size are determined by the balance between gravitational attraction and the motions of the bodies. For orbit, mv2/r=GmM/r2Hence twice the kinetic energy T is equal to the negative of the gravitation potential energy V. (Correction factor a) Example: Coma 2 T V 0 + = 0 . 5 2 . 0 a = - Cluster mass Mean galaxy velocity 2 v R hclusters~ 200 < > M = G a 0 . 2 W ≈ clusters astrophysics lectures 1and 2

32. Problems with clusters • We have to be sure that the galaxies are actually in the cluster (redshift). • Exclude large fluctuactions (fast moving galaxies). • Carefully treat close clusters moving near each other. • Account for total velocity (not just vz). • Be sure that this is a cluster (not a random coincidence) and that the cluster is not contracting or flying apart. • Take into account cosmological evolution (galaxy formation). astrophysics lectures 1and 2

33. Estimates from x-ray observations Example: Coma 0 .3 W ≈ cluster The properties of the hot gas that emit x-rays can be used to determine the mass and density profile of the dark matter, even though they may not themselves have the same density profile. The temperature maps can be used to determine the mass needed to prevent the hot gas and galaxies from escaping the clusters. One of the best examples is the analysis for the Coma cluster. The result is: hclusters≈ 300 astrophysics lectures 1and 2

34. Estimates from x-ray observations Chandra X-ray Observatory images (left, X-rays from hot gas) and Hubble Space Telescope images (right, massive central regions bend light from distant galaxies) of the giant galaxy clusters Abell 2390 and MS2137.3-2353. The clusters are located 2.5 and 3.1 billion light years from Earth, respectively. astrophysics lectures 1and 2

35. Gravitational lensing A relatively new technique of measuring the Dark Matter is to use the gravitational deflection of light rays by the cluster. This distorts the image of background objects giving arc-like features which are magnified images of distant galaxies behind the cluster. astrophysics lectures 1and 2

36. 0 .3 W ≈ cluster Density estimated from gravitational lensing hclusters≈ 300 a distant galaxy lensed by a nearer galaxy cluster astrophysics lectures 1and 2

37. Map of a galaxy cluster using gravitational lensing showing the Dark Matter distribution Tyson et al. Density estimated from gravitational lensing astrophysics lectures 1and 2

38. HST deep field 0 . 8 0 . 5 W = ± supercluster Density from supercluster dynamics The total mass of superclusters is obtained from deep redshift galaxy surveys, again using virial techniques. Comprehensive surveys of infra-red and other galaxies have gone out to distances in excess of 200 Mpc. From large-scale velocities, it is possible using linear theory to estimate the homogeneous mass density. hsuperclusters= 800±500 astrophysics lectures 1and 2

39. Density from supercluster dynamics astrophysics lectures 1and 2

40. W 0 . 3 ≥ DM 1 W = 0 Density from theory - structure and inflation There are no current working models of structure formation that do not require dark matter with: Inflation, the model that may explain the Universe in its early stages when it undergoes rapid expansion, predicts that the Universe is flat. In the simplest form this tells us: However, we could have a lower density of matter if we assume the presence of dark energy, which is favoured by recent observations of distant type Ia supernovae (cosmological constant). astrophysics lectures 1and 2

41. TheoreticalExpectation 1 Large Scale Structure Clusters of Galaxies Non-baryonic DM problem 0.1 Galaxy: All Mass  Nucleosynthesis Baryon Limits 0.01 Baryonic DM problem Galaxy: Visible Mass 0.001 Solar Neighbourhood 100 0.0001 0.01 1 10000 Scale (Mpc) Conclusions There is a missing mass (dark matter) in the Universe; It is seen at all scales from galaxies to superclusters; It is also predicted by the theory (simulations of the structure evolution, inflation). astrophysics lectures 1and 2