BarsGalaxy and galactic system mergers Stefans Quintet impulse approximation dynamical friction 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 M87 in Virgo as an example of a giant elliptical (cD) 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)

N-body calculations by J. Barnes, time between frames ~orbital period.

Tidal forces applied at the beginning of the simulation

Spontaneous growth of the pattern from noise by SWING

About 1/2 of all galaxieshave a bar.

Bar formation may be a by-product of a self-defenceby a disk galaxy against theapproaching gravitationalinstability.

A Milky Way-like galaxywith non-linear waves(as opposed to ‘linear’, that is sinusoidal of very small amplitude; this term has nothing to do with the shape ofthe 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.

sun

MW

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 ~1e6 Kby the motion of galaxy B through the inter-galactic gas in the group.

X-raysand optical

visible

B

GALAXY MERGERS

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

NGC4676mice galaxies

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 relativemotion 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, thetemperature T must be of order T~1e7 K.Conversely, such a high temperature is measured in X-rays, because the photon energy are ~1 keV, which corresponds to T~1e7 K. From this observed T we can then derive the virial estimate of the mass M which bindsthe cluster: GM/R ~ kBT. 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.

TkE Bk 21

221 V

Bk

VT

2

BIMA radio-telescope array image of M81+M82+NGC3077shows gas bridges connecting theinteracting galaxies

While the optical imagesuggests separate galaxies,

Interaction of galaxies in pair and groups as a trigger of spirality

Cf. Fig. 5.34 in textbook

The future: Milky Way - Andromeda collision (several Gyr from now)simulation by John Dubinsky (CITA; McKenzie 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 thatof deflection (gravitational scattering) of stars from the host/target by theperturber 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 starfrom 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).

V

-dV/dt

0

The dynamical friction decelerates an object travelling througha 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:dV/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 theparticles 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: dV/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 thestellar system. Let’s understand thisa little better.

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; vM = V)

Cf. Problem 5.17 in S&G

erf(x) = error function, an integral of Gaussian curve(Maple, Mathematica…)

Notice F~ -M*M

(B&T 1987)

Applications of dynamical friction

Applications of dynamical friction

Applications of dynamical friction

OLD VIEW:SMC and LMCbound since long ago

NEW VIEW:SMC and LMCbound very recently(?)http://arxiv.org/abs/astro-ph/0606240v2

Is the SMC Bound to the LMC? The HST Proper Motion of the SMC

Nitya Kallivayalil (CfA), Roeland P. van der Marel (STScI), Charles Alcock (CfA) Jul 2006

Abstract: We present a measurement of the systemic proper motion of the Small Magellanic Cloud (SMC) made using the Advanced Camera for Surveys (ACS) on the HST. We tracked the SMC's motion relative to 4 background QSOs over ~2 years. We combine this new result with proper motion of the LMC & investigate the orbital evolution of both Clouds over the past 9 Gyr. The current relative velocity between the Clouds is 105+-42 km/s. Our investigations of the past orbital motions of the Clouds in a simple model for the dark halo of the Milky Way imply that the Clouds could be unbound from each other. However, our data are also consistent with Clouds bound to each other for ~ Hubble time.

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 ratherthan small groups like the Local Group.

In the centers of dense clusters live the enormous cD-type galaxies likeM87. They are significantly brighter than L* = 2e10 Lsun

(L* corresponds to an absolute magnitude MB = -20 mag.)

De Vaucouleurs’ formulais a purely empirical formula,there is no physical derivationor 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)

M87 in the Virgo cluster (also: M84, M86)

[such giant, central elliptical galaxies are given type designation cD]

M87 sports a one-sided jetof relativistic electrons and plasma. It comes from a very small “central engine” region,probably a black hole.

The one-sidedness of such jetsis an illusion: the jet is actually two-sided (bipolar) anddirected almost directly towardand away from us. Only the approaching side appearsbright due to a relativistic boosting (a.k.a. gamma-factor).A fast-moving object (atom, electron) radiates mostly in thedirection of motion, and little in the opposite direction.

Can any object move faster thanlight? NO. Not according to physics.

This trick of nature is connected with special relativity theory andthe relativistic gamma factor, butit really just follows from thegeometry of the problem involving a small angle (orientation of the jet to the line-of-sight) and a finite speed of light.Read about it on p. 330 of thetextbook!

Relativistic effects, as alreadymentioned, boost the jet luminosity by a large factor, while dimming the image of the receding jet to a point where we can’t see it at all!

An explanation of apparent superluminal motions in BL Lac objectsand quasars’ jets

Apparent speed of blob S8 is 3 times c (!)Was Einstein wrong?Do we see tachions?

V dt cosO

more precisely, for

21 )/(

max

cV

VVobs

2

cV

The explanation is relatively simple: time delays plus trig

Demonstrate that: