Bars Galaxy and galactic system mergers Stefans Quintet

Bars Galaxy and galactic system mergers Stefans Quintet impulse approximation dynamical friction in Maxwellian velocity field applications: dissolution of globular clusters in Andromeda future merger with LMC and SMC and our Galaxy Elliptical galaxies: photometry M 87 in Virgo as an example of a giant elliptical (c. D) galaxy - jets, black hole, superluminal motions etc.

BARS

Simulations of spiral structure formation in a 3 -component galaxy model (yellow=bulge stars, blue=disk stars, red=halo) Tidal forces applied at the beginning of the simulation Spontaneous growth of the pattern from noise by SWING N-body calculations by J. Barnes, time between frames ~orbital period.

About 1/2 of all galaxies have a bar. Bar formation may be a by-product of a self-defence by a disk galaxy against the approaching gravitational instability.

MW sun A Milky Way-like galaxy with non-linear waves (as opposed to ‘linear’, that is sinusoidal of very small amplitude; this term has nothing to do with the shape of the wave!). SPH (Smoothed Particle Hydrodynamics) model of gas disk response to the Milky Way’s force field including a stellar bar. Notice the non-linear response of gas: shock waves form, as opposed to a smooth and gradual density structure with a smaller density contrast in the stellar disk. Basic difference in response is due to velocity dispersion of 7 km/s in gas vs. 35 -45 km/s in stars.

Stephan’s Quintet is a small group of galaxies in the constellation Pegasus. The galaxies are not only close on the sky but are physically close in space. So close, in fact, that they interact gravationally with each other. A new Chandra X-ray observatory data details the results of this interaction. The image below (upper left) is a composite of an X-ray image (shown in blue), superimposed on an optical image showing the locations of the Quintet galaxies, which are marked A, B, D, E & F on the lower right image). The X-ray image shows a "blue glow" produced hot gas in a bow shock in front of the "intruder" galaxy B. The gas in the bow shocked is heated to ~1 e 6 K by the motion of galaxy B through the inter-galactic gas in the group. X-rays and optical B visible

GALAXY MERGERS NGC 4676 mice galaxies See links to work done at Canadian Inst. For Theoretical Adtrophysics (CITA) on St. George campus http: //orca. phys. uvic. ca/~patton/openhouse/movies. html http: //www. cita. utoronto. ca/index. php/index_items/nature_of_dark_matter

Estimate of the temperature T of gas after virialization (thermalization): The mean energy per particle (ion or electron) and per one dimension, in a thermalized gas (gas which relaxed to Maxwellian equilibrium) is equal The colliding gas flows in a cluster have a specific kinetic energy of relative motion equal to which is also of order potential energy of the cluster (by the virial theorem). Temperature of the shocked gas will thus be of order Typical velocities in the center of a clusters reach V~500 km/s. Then, the temperature T must be of order T~1 e 7 K. Conversely, such a high temperature is measured in X-rays, because the photon energy are ~1 ke. V, which corresponds to T~1 e 7 K. From this observed T we can then derive the virial estimate of the mass M which binds the cluster: GM/R ~ k. BT. That mass usually is significantly, for instance ten times larger, than the estimate based on the visible matter (stars and gas). The gravitational potential well and the high velocities seen in the galactic groups and clusters predominantly due to dark matter.

Interaction of galaxies in pair and groups as a trigger of spirality While the optical image suggests separate galaxies, BIMA radio-telescope array image of M 81+M 82+NGC 3077 shows gas bridges connecting the interacting galaxies Cf. Fig. 5. 34 in textbook

The future: Milky Way - Andromeda collision (several Gyr from now) simulation by John Dubinsky (CITA; Mc. Kenzie supercomputer, 512 cpus, 10 days)

Another view… the merger remnant becomes nearly elliptical

The Antennae Galaxies (also known as NGC 4038 / NGC 4039) are a pair about 20 Mpc away in the constellation Corvus. They were both discovered by Friedrich W. Herschel in 1785

J. Dubinski (CITA)

Movie of galaxy formation and mergers

Why do collisions often end in mergers and not just fly-by’s? (cf. Fig. 5. 37 and description in the book) Dynamical friction provides the braking force. Its basic physics is that of deflection (gravitational scattering) of stars from the host/target by the perturber body. The perturber may either be a point mass or a compact stellar system, all of which stars will be considered to move together. Let us denote the mass of the perturber as M, and that of a star from the target galaxy as m. The relative velocity of m and M at infinity is V, both before and after encounter (due to energy conservation). We treat all the encounters as independent scatterings, in the limit of weak encounter (trajectory only slightly bent). While it is sometimes easiest to talk and draw only the relative motion of the bodies m and M, we must be careful not to forget about the fact that the lighter body (m) undergoes a stronger deflection than the more massive one (M), in proportion to the ratio M: (M+m) vs. m: (M+m).

The dynamical friction decelerates an object travelling through a sea of stars (perhaps a target galaxy in a merger). The impulse approximation predicts an inverse quadratic dependence of the friction force on the velocity of relative motion: d. V/dt = -const. (…)/V^2. This is because, for any given impact parameter b, the time of interaction is ~1/V, V is large, and the interaction brief and weak. However, the situation may be quite different, if our chosen test particle travels around a center of some system together with the particles providing the dynamical friction. Then, our integration should not assume that all the stars encountered arrive from one direction. Rather, we should arrive in the limit of V --> 0 at a final result where the test particle is NOT subject to any friction force except the isotropic random kicks from the passing compact objects: d. V/dt --> 0 as V-->0. This is a very different dependence, which looks like across the range of V like this: Here, is the velocity dispersion in the -d. V/dt stellar system. Let’s understand this a little better. 0 V

How dynamical friction from a stream of particles with Maxwellian velocity distribution affects a body of mass M

(an explicit formula w/derivation can be found in Binney & Tremaine 1987; v. M = V) (B&T 1987) Cf. Problem 5. 17 in S&G erf(x) = error function, an integral of Gaussian curve (Maple, Mathematica…) Notice F~ -M*M

Applications of dynamical friction

Applications of dynamical friction

Applications of dynamical friction

Elliptical galaxies Ellipticals are not as simple as their projected shape suggests. Most are triaxial ellipsoids (3 different axial extents) They are not in a relaxed, Maxwellian state (Trelax >> age of the universe. ) They are most common in dense clusters of galaxies rather than small groups like the Local Group. In the centers of dense clusters live the enormous c. D-type galaxies like M 87. They are significantly brighter than L* = 2 e 10 Lsun (L* corresponds to an absolute magnitude MB = -20 mag. )

De Vaucouleurs’ formula is a purely empirical formula, there is no physical derivation or understanding of ubiquity.

But it works here!

Tricks played by projection

Most galaxies in Virgo are spiral, except in the center which is dominated by ellipticals and giant ellipticals - a sure sign of environmental influences (probably mergers)

M 87 in the Virgo cluster (also: M 84, M 86) [such giant, central elliptical galaxies are given type designation c. D]

M 87 sports a one-sided jet of relativistic electrons and plasma. It comes from a very small “central engine” region, probably a black hole. The one-sidedness of such jets is an illusion: the jet is actually two-sided (bipolar) and directed almost directly toward and away from us. Only the approaching side appears bright due to a relativistic boosting (a. k. a. gamma-factor). A fast-moving object (atom, electron) radiates mostly in the direction of motion, and little in the opposite direction.