8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-1 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-2 Galaxy Formation Leading questions for today How do visible galaxies form inside halos? Why do galaxies/halos merge so easily? How do visible galaxies form inside halos? gas density fluctuations and gravity produce: dark matter halos halos much bigger than visible part of galaxy halos rotate slowly < v > /σ 0.3 Halos entirely UNLIKE visible galaxies So what happens? dark matter When new halo just formed: gas is distributed like dark matter gas supported by pressure dark matter supported by random motions Gas can cool by radiation, and can collapse to the center if cooling efficient Dark matter cannot cool! Will not collapse to center Gas cooling is expressed as: cooling rate = n 2 Λ(T) cooling rate is cooling per unit volume element n is number density of gas Λ(T) is cooling function
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-3 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-4 Draw figure of n lum, the number density in luminous material (in units of particles/cm 3 ), versus temperature T. How do t cool and t dyn depend on density and temperature? cooling time thermal energy/volume coolingrate/volume n lumt n 2 lum Λ(T) dynamical time 1/ n lum Cooling mechanisms: bound-bound, bound-free, freefree, electron scattering. The peaks in the cooling function are caused by: T=10 4 = ionization/recombination hydrogen T=10 5 = ionization/recombination helium Hence the dynamical time and cooling time are equal when n lum T 2 /Λ 2 (T) Now draw the line of t cool = t dyn, and put in astronomical objects: galaxies groups and clusters of galaxies T> 10 6 K : thermal bremsstrahlung and Compton scattering Now take a halo with gas inside. Two options: t cool < t dyn, then cooling is efficient, and the gas will collect in the center t cool > t dyn, then cooling is inefficient, and the gas will NOT collect in the center
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-5 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-6 Homework assignment 1) prove M T 3/2 /n 1/2 lum. Use σ2 T and n lum M/R 3. We find gas in galaxies cools efficiently gas in clusters does not! when galaxies cool, the density will increase, while T remains roughly constant. When the gas becomes self gravitating, the T might increase (the circular velocity will increase, hence the temperature v 2 c) when the gas is self-gravitating, it can start to form stars! As a result, the luminous galaxy forms in the center of the halo, and is much smaller than the dark halo
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-7 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-8 How to get disks in spiral galaxies? Hence this occurs when Gas cools down and contracts. Assume that the specific angular momentum j is conserved or 0.3f = 2 f = 5 j = J m = r start < v >= 0.3r start σ dm Gas contracts by factor f: f = r start r end Hence, a cooling gas cloud will settle into a disk when it has contracted by about a factor of 5 or so. Ellipticals and bulges can be made out of pre-existing disks when galaxies merge, or during mergers As specific angular momentum is conserved: j end = r end < v end >= j start = 0.3r start σ dm Hence < v end >= 0.3 r start r end σ dm = 0.3fσ dm The gas rotates faster and faster while the gas contracts contraction is halted when the cooled gas is in circular orbits around the center. For such orbits Homework assignment: 2) Our Milky Way galaxy has a mass which is typical for galaxies. It likely has an isothermal dark matter halo. Calculate the temperature of isothermal gas in the halo of our galaxy if it has a density proportional to r 2, where r is the radius from the center. v = v c = 2 σ dm
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-9 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-10 Why do halos/ galaxies merge so easily? BT 7.1 abbreviated dynamical friction slows down two galaxies meeting each other even galaxies with hyperbolic orbits can merge! Dynamical friction consider massive point mass M, moving in sea of small point masses m the motion of the massive object will produce a wake behind it the wake is an overdensity, and will exert a force which slows down the moving massive object the wake is proportional to GM, hence the gravitational force on the object is proportional to G 2 M 2 The motion of the pointmass and the massive object is simply given by the solution for the two-body problem. m is the mass of small pointmass. M is the mass of big pointmass. v 0 is velocity difference at the start. v 0 = v m v M b is impact parameter. The deviations in velocity are v M, = 2mbv 3 0 G(M +m) 2 [ 1+ v M, = 2mv [ 0 1+ (M +m) b 2 v0 4 ] 1 G 2 (M +m) 2 b 2 v0 4 ] 1 G 2 (M +m) 2 the parallel deviation v M, will always be in the same direction, whereas the perpendicular component will be in a random direction. the friction can be estimated effectively by considering individual interactions between the massive object, and the small point masses Hence, as a result, when the contributions from all particles are taken (by integration), the perpendicular component can be ignored to first order, and the parallel component will dominate. This will slow down the moving mass M.
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-11 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-12 Assume that phase-space density of stars is f( v). M encounters stars with velocities in volume d v m at impact parameters between b and b+db rate = 2πb db v 0 f(v m )d v m Integrate over impact parameters b, then the change in v M is d v M dt = v 0 f( v m )d v m bmax [ 1+ 0 2mv 0 M +m b 2 v0 4 ] 1 G 2 (M +m) 2 2πbdb where b max is the largest impact parameter that needs to be considered. Now calculate the integral, using v 0 = v m v M. We get: d v M dt where = 2πln(1+Λ 2 )G 2 m(m+m)f( v m )d v m ( v m v M ) v m v M 3 Λ b maxv 2 0 G(M +m) Usually Λ very large. Globular cluster in Milky Way: M = 10 6, v 0 100 km/s. Λ = 4.6 10 3, ln(1+λ 2 ) 17. In the following we use ln(1+λ 2 ) 2lnΛ. We ignore the variations of Λ with the velocities v m of the background stars. We assume that the galaxy is isotropic. The resulting integral is valid for encounters with stars in volume element d v m. We have to integrate over all v m to get the total force on M. Notice that the force depends on v m only through the last 3 terms at the right hand side of the equation. Hence we have to integrate these 3 terms over v m : f( v m ) ( v m v M ) v m v M 3d v m The equation simplifies if the distribution function is isotropic. Notice that the equation is equivalent to the equation for the gravitational force at a location r = v M for a density denstribution ρ = f. Newtons theorem states that this is equivalent to the force caused by a pointmass M with mass equivalent to the mass inside r. Hence f( v m ) ( v m v M ) v m v M 3d v m = vm Use ln(1+λ 2 ) 2lnΛ to obtain d v M dt = 16π 2 ln(λ)g 2 m(m+m) Equation (1) f(v 0 m )4πvmdv 2 m vm 3 v M vm f(v 0 m )vmdv 2 m vm 3 v M Only stars moving slower than v M contribute to the force. The drag always opposes the motion.
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-13 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-14 This is the CHANDRASEKHAR DYNAMICAL FRIC- TION FORMULA (BT 7.1) for very large v M, one derives approximately dv M dt = 4πln(Λ)G2 (M +m)ρ m v 2 M Two interesting points: the drag depends on ρ m, but not m itself the larger M, the stonger the deceleration massive objects fall in faster than low-mass objects Dynamical friction for object with mass M in isothermal halo For mass M in orbit in isothermal halo one derives the following. The density in the halo is given by ρ = σ 2 /(2πGr 2 ) = v 2 c/(4πgr 2 ). Fill this in the equation 1 above to derive: dv M dt = 0.428lnΛ GM r 2 Application to Magellanic Clouds (BT 7.1 1(b) The LMC and SMC have distances of 50 and 63 kpc, and masses of 2e10 and 2e9 solar masses. If our galaxy has a massive halo extending to the clouds, then the friction decay time can be estimated in the following way: The force causes the mass M to lose angular momentum per unit mass L dl dt = Fr M = 0.428GM r lnλ At all times L = rv c, and v c is constant. Hence Solution r dr dt = 0.428GM v c lnλ r(t) 2 = 2 0.428 GM v c lnλt+constant Hence, if r(0) = r i, the mass reaches r = 0 at t fric = 1.17r 2 i v c/(gm lnλ) For the clouds this gives: t fric = 1 1010 lnλ approximately: ln Λ = 3 ( r ) 2 ( v c 60kpc 220km/s )( 2 10 10 M tot Hence they will spiral inwards quickly, in a couple of Gyr! This mechanism makes galaxies merge well!! Simulations indicate that the orbits may be elliptical. Since the Clouds are close to peri-galacticon, the average friction time may be higher than the previous estimate. ) yr.
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-15 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-16 The Magellanic Stream (BM 8.4.1 page 530) is gas that escaped from the clouds during their orbit around the galaxy. The stream can be found over 60 degrees in the Southern Sky Homework assignment 3) Calculate the dynamical friction timescale for a globular cluster with mass 1e6 M at a radius of 10kpc from the center of the galaxy. The gas distribution of the magellanic stream and the magellanic clouds magellanic stream projected on the sky
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-17 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-18 Mergers of galaxies (BT 7.4 1(a,b)) Theories of galaxy formation predict that halos grow by the mergers of lower mass halos. What happens to the galaxies inside these halos? Simulations can give us the answer. Below is an example. Merging galaxies quickly form 1 large galaxy. Structure of mergers of non-rotating galaxies generally slowly rotating, oblate density ρ r 3, or r 1/4 profiles - like ellipticals radial gradients not erased: material that was in center in progenitors is likely in center of merger remnant Compare to observations Radial structure A standard example is NGC 7252, which has low luminosity tails, and a luminous, central system.
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-19 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-20 Conclusion: after the merger is over, it will look very much like a normal elliptical! How to recognize mergers? BT 7.4 3 Arp s Atlas of Peculiar Galaxies has many merger remnants. Examples the radial surface brightness can be measured by averaging over circles The photometry follows an r 1/4 law very accurately. These were first thought to be exploding. Now we know they are mergers. Very typical mergers the Antennae
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-21 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-22 BT 7.4 3(a) Stellar populations in mergers typical is: two fuzzy centers from each center, a long, curved, tail Toomre and Toomre (1972) showed that this can exactly be produced in a merger In a plot of U-B against B-V, mergers generally lie away from the relation for normal galaxies. This is caused by bursts of starformation which happened recently. We can predict the velocities along the tail, and compare to observations. Usually good agreement.
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-23 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-24 How are these tails made in mergers? Mergers of rotating galaxies (BT 7.4 2) result depends on sense of rotation of disk: prograde: disk angular momentum pointing in same direction as that of orbit. retrograde: disk angular momentum pointing in opposite direction as that of orbit. Tails are formed by tidal forces. Each disk can produce 1 tail. Why is this? Model the merger as the encounter of two pointmasses, one with a set of rings around it retrograde: the pointmasses in the ring move opposite to that of the merger galaxy. They do not react very strongly, because sense of rotation opposite.
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-25 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-26 see more detail in a slow-motion picture below: The particles in the ring move with comparable angular speed as the intruder galaxy. The system is a forced oscillator, with the frequency of the force term comparable to the natural frequency of the oscillator. Hence a resonance occurs, and a very strong reaction follows. The resulting merger remnants have the following features: prograde: the pointmasses in the ring move in the same sense as that of the merger galaxy. A very strong reaction follows they look like featureless ellipticals, with de Vaucouleurs profiles merger remnants are slowly rotating if initial total angular momentum low
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-27 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-28 How efficient is merging? Frequency of merging BT 7.4 3(b) assume two equal mass galaxies, with orbits of certain energy E and angular momentum L calculate numerically whether they merge or not, and plot in diagram about 11 out of 4000 NGC galaxies are typical mergers the timescale for this merger phase is typically 5 10 8 h 1 yr. if the merger rate is constant, then for every observed merger now, 10 10 /(5 10 8 )=20 happened in the past. past. in total, 11*20 galaxies in NGC catalogue may have undergone merging, or 200. there are 440 ellipticals in the NGC catalogue - comparable to the expected number of mergers all ellipticals may have formed through mergers if merging rate increases towards the past! Mergers are very efficient, even galaxies on hyperbolic orbits can merge!
8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-29 8-5-2015see http://www.strw.leidenuniv.nl/ franx/college/ mf-sts-2015-c9-30 Ripples BT 7.4 3(c) Some ellipticals show ripples in the outer parts ( Malin- Carter shells ). They can also form from major mergers, but a cold component is needed in both cases either cold disk, or cold spherical galaxy Homework assignment These can form from a small galaxy falling into a much bigger one: 4) We can distinguish between elliptical galaxies, which have no disk, and spiral galaxies, which have a disk. If we see a merger remnant with 1 tail, what kind of galaxies were involved in the merger (ellipticalelliptical, elliptical-spiral, or spiral-spiral). Justify your answer. What kind of merger produces two tails? 5) Try to find the equal mass merger with 2 nuclei which is closest to us.