VIEWS: 0 PAGES: 34 POSTED ON: 11/21/2013
The Milky Way The Milky Way (our galaxy) is a fairly typical spiral galaxy • About 2 x 1010 stars • Flat-ish disc of stars: ~300 pc thick, ~30 kpc diameter • Bright, roughly spherical central bulge • Spiral “arms” or orbiting stars • Huge “halo” containing old stars (Globular Clusters) Spiral Density Waves Spiral arms are not “solid” but rotating density waves caused by mis-alignment of slightly elliptical orbits Star formation occurs in higher-density regions Other Galaxies Not all galaxies are Spirals like our own. In 1925 Hubble produced a classification sequence called the “Hubble Sequence” or “Tuning Fork Diagram ” Basic types: • Elliptical – sub-grouped by ellipticity • Spiral – sub-grouped by dominance of bulge • Barred-spiral – like spirals but with elongated bulge • Irregulars – everything else! Sizes vary from few 1000 stars to > 1011 stars. Note: This is not an evolutionary sequence! Hubble Sequence Galaxy Types cont. Ellipticals generally contain old stars and very little dust or gas. Light is dominated by Red Giants. The largest and smallest galaxies are elliptical. The bulges of spirals and barred-spirals are similar to ellipticals, but the spiral arms contain more dust and gas and contain new stars. The light of the arms is, therefore, dominated by hot, massive blue stars . Clusters of Galaxies Just as stars group together to form clusters, so do galaxies. Clusters of galaxies vary in size from a handful of galaxies to several thousand . We live in a small cluster called the Local Group . CL002+1654 Hubble’s Law As noted in Distance Estimation section, galaxies appear to be moving away from us and the speed of the recession is proportional to their distance . This was discovered by Edwin Hubble in 1929 (See the website for a brief history) Apparent recession due to the Expansion of the Universe Although Hubbles’ original measurements were rather inaccurate (not his fault!), the result has held. Hubble’s Law cont. Recession Velocities Recession velocities measured using doppler shift in galaxy spectra Redshift Redshift z is given by: Where l is the observed wavelength, l0 is the rest-frame wavelength and Dl = l – l0 For small z: Where v is the recession velocity and c is the speed of light Hubble’s Law Hubble’s relationship is, therefore: Where d is the distance to the galaxy and H0 is called Hubble’s Constant . The exact value for H0 is subject to debate! The latest value (from WMAP results) is: 71 km/s/Mpc Note the weird units! Cosmology The discovery of the expansion of the Universe, coupled with Einsteins development of General Relativity marked the beginning of Cosmology Cosmology is based on the assumptions that: • Structure (ie galaxies, stars etc) are negligible on large enough scales: Æ The universe is Homogeneous ÆOur position in the universe is not special Æ Assumption of Isotropy Without these assumptions, cosmology would get nowhere! The Scale Factor In this simple universe, we can represent any distance by a dimensionless number multiplied by a universal Scaling Factor which changes with time. The distance between two points s then becomes s=xR(t) where x is the dimensionless distance (a constant for any two points) and R(t) is the Scale Factor. Recession Velocity From this, the recession velocity is given by: where This demonstrates the linear nature of Hubble’s Law, but note that the Hubble “constant” actually varies with time! Age of the Universe If H0 were a true constant, the age of the Universe would be given by 1/H However, the gravitational effect of all the mass in the Universe will tend to slow down the expansion. Therefore the 1/H0 value will be an upper limit to the age. The rate of change of R(t) is governed by the average density of the universe. If the density is low, the universe will expand for ever. If it is high, the expansion will eventually be stopped and reversed. The Cosmological Parameter that governs this is W0 The Density Parameter - W0 W0 is defined as: Where r0 is the current density of the universe and rc is the critical density – the density that sits on the border between an infinitely expanding universe and a re-collapsing one. So: • W0 < 1 gives infinite expansion – called an Open Universe • W0 = 1 on the balance point - a Flat Universe • W0 > 1 re-collapse will occur - a Closed Universe The Density Parameter - W0 The fate of the universe So, what is W0? The obvious way to estimate W0 is to add up all the mass we can see and divide it by the volume we are looking at! This gives W0 ~ 0.003 If this was all there was, the universe would expand for ever. However, there is evidence for a lot of matter that we cannot see making W0 much larger (close to 1) This is the so-called Dark Matter Evidence for Dark Matter The idea that most of the mass in the Universe is something we cannot see is a bold one! Without a lot of evidence, it is going to be very difficult to accept. However, the nature of Dark Matter is such that we can only see its gravitational effects. One example is the rotation curves of galaxies Rotation Curves The rotational velocity V of an object at radius R from an object of mass M is given by Also, the gravitational mass of a galaxy at a particular orbital distance is the mass inside that orbit. Example Rotation Curve V µ R constant density V = const. M µ R Flat rotation curve, so mass must be increasing even outside the “visible” galaxy. Cosmological Constant When all the extra matter is included, W0 ~ 0.2-0.3 However, the theory of Inflation (where the universe expands very fast in its early history) predicts W0 = 1 Current models provide the extra “density” by adding a constant to the solution for R(t) This is the Cosmological Constant L0 Sometimes called a “vacuum energy density” or “dark energy ”, this term produces a repulsive force which opposes gravity and is µ distance. Evidence from Sn Ia “Standard candle” distances. Best Estimate for W0 Current best estimate for W0 come as a result of the WMAP microwave background measurements (see later): W0 from normal matter = 0.04 W0 from dark matter = 0.23 W0 from L0 = 0.73 W0 total = 1.0 Flat Universe Standard Hot Big Bang Model If the universe is expanding, then it follows that by going back in time, we move towards a moment when the universe is infinitely dense This singularity, from which the universe is expanding is the so-called Big Bang. The Big Bang model is a theory for the formation, development and future history of the universe. As with any theory, it includes assumptions and is developed by testing it. Big Bang - Assumptions • The universe is homogeneous and isotropic: The Cosmological Principle Gravity dominates on large scales (i.e. General Relativity is correct) The same laws of physics apply though all time and space Without assumptions such as these, no theory can even get started. Some attempts are begin made to test them, but it is very difficult. Big Bang - Tests The Big Bang theory is considered to be a very successful one. This is mainly because it explains three very important observational facts (tests): • The expansion of the Universe • The relative abundances of light elements • The cosmic microwave background. We have already discussed the expansion (Hubble’s Law etc). What about the other two? Primordial Nucleosynthesis For the first 10-15 minutes, the temperature of the universe is very high – high enough to produce light elements by nuclear fusion. The theory of Primordial Nucleosynthesis combines our understanding of nuclear physics with the Big Bang model to predict the relative abundances of the light elements: Deuterium (21H), Helium-3 (32He), Helium-4 (42He), Lithium -7 (73Li) These predictions can be tested by studying metal-poor galaxies (i.e. those where stellar-processing has had very little effect) Predictions match observations exactly Cosmic Microwave Background In the early stages of the universe, the temperature was high enough to keep all matter fully ionized. Photons scattered on all the free electrons and electrons collided with ions. This kept matter and radiation in equilibrium However, once the temperature of the universe dropped to ~3000K, neutral Hydrogen could form – this was about ½ million years after the Big Bang. At this point, the number of free electrons dropped dramatically, and the photons became free to move independently of matter: Era of Decoupling CMB cont. Therefore, at decoupling the universe was filled with radiation with a blackbody temperature of ~3000K. Since then expansion has caused the radiation to “cool”. Big Bang theory, therefore, predicts a “sea” of photons filling the universe now with a blackbody temperature of ~3K. A 3K blackbody peaks at ~1mm wavelengths, so it is very difficult to observe. However, in 1965 Penzias and Wilson accidentally discovered the radiation (a Nobel prize was to follow) Since then, several satellites and other experiments have produced detailed maps and spectra of the CMB. CMB Spectrum from CoBE Fit to spectrum – giant errorbars CMB maps Be the time of Decoupling, some structure had started to form (by gravitational magnification of small fluctuations) So, when photons became “free”, some had larger gravitational wells to climb out of than others. So, some will have been gravitationally redshifted . Therefore, some parts of the CMB will be slightly “cooler” than others By producing a map, we can measure the size and relative density of the fluctuations at this very early point in the universe This can then be used to devise further tests for the Big Bang model. WMAP Map WMAP satellite recently produced newer results (Feb.2003). Higher resolution and less noise. Still supports Big Bang model Cosmology - Summary Current evidence favours a slightly modified Hot Big Bang model of the Universe: • Universe started in a singularity ~13-14 billions years ago • Expanded since then, forming structure by gravitational instability magnifying tiny initial fluctuations • Expansion slowed by combination of “normal” matter, dark matter and “dark energy” • Evidence from: expansion, light element abundances, CMB (among others) • Still a number of questions… Cosmology - Questions Some of the major outstanding questions: • What is the Dark Matter? • How do we get from the structure in the CMB to the galaxies, stars, planets etc that we see today? • What about the very earliest stages of the Big Bang? (new physics required) • What was there “before” the Big Bang? (this is more philosophy than physics!) Remember: Theories cannot be proved right, only proved wrong!
Pages to are hidden for
"Handout"Please download to view full document