: Mod. I (L.Secco): Mod. II (G.Galletta): Mod. II (G.Galletta)

Galaxy dynamics - Mod. II (G. Galletta)

Motions in the milky Way: Velocity ellipsoid near the Sun. Oort formulae.

Mass distribution of stars in galaxies: Surface brightness laws of galaxies. Freeman, De Vaucouleurs and Sersic laws. Deduction of the main parameters from the observations.

The tridimensional shape of galaxies. Statistical methods. Inclination of a galaxy: principal planes and methods to find inclination and line of the nodes. Polar ring and other reference planes. Twisting of the isophotes. Twisting of the isophotes.

Rotation curve of a galaxy. Mass estimate with simple models

Observing galaxies at other wavelenghts: HI and CO lines. Observing techniques in our and other galaxies.

Estimate of the gas mass inside a galaxy by means of HI, CO and IR observations.

The sequence

• Module I is divided into two Parts:

• I Part- starts nowand ends before Easter

• II Part- startsat the end of May-beginning• II Part- startsat the end of May-beginningof June and ends at about 15 June.

• INSIDE THE GAP: MODULE II

About contents:

what is the location of Mod.I contents inside the history of contents inside the history of

Universe?

• Phase 0=TOE; Phase1=GUT;

• Phase2=E-W unification

-43 -370

3

2

1

-11 -5

a

-37

Log t (sec)

+19 +15 +2

Log E (GeV)

250 MeV

Hadrons have been formed at:

Quarks----->Hadrons

phase-transition

at about 10^-5 sec.

We’ll see it inside the environment ofinteraction trends

As density and temperature decreasedecrease

matter transforms

from plasma toward neutral matter

From a mixture of matter and radiation impossible to

disintangle

we move gradually to a decoupling between matter and radiation.

Recombination

Radiation needs a very long time to interact with matter

so that matter and radiation get two different temperatures:

breaking of thermodynamical symmetry

Breaking of thermodynamical symmetry

t_exp

t

t_exp

t_inter

t_rec

That allows gravity to act on the matter freelymatter freely

without something like viscosity due to radiation.

After recombination the Universe is engaged to structure itself at a

macroscopic level.macroscopic level.

Here is the location of our Course!

A very interesting interplay between the micro and macro

structure formations:• The micro allowthe macro ones but inside

these latests, e.g. inside stars in galaxies, the complexityof micro-structuresmaycomplexityof micro-structuresmayincrease.

The macro structure formation appears as a Thermodynamic

challenge:challenge:

it drives to an apparent violation of the II Thermodynamical Principle,

we have to consider.

The very small initial density fluctuations may increase thanks

to Jeans’ Instability.

Jeans’Gravitational Instability

Density perturbation occurs inside Hubble expansion.

At the maximum expansion phase:

t_max, t_max,

t the perturbation stops to

follow the Hubble flow. It becomes

a proto-structure which begins to collapse under

its auto-gravity

It has to reach an equilibrium configuration. What kind of

equilibrium and in which way ?

The equilibrium is virial equilibrium. The way is the violent relaxation.

It occurs the transition from the maximum expansion phase

toward virialization,via the violent relaxation mechanism which distributes the total energy by

conserving its total amount.

Landau damping oscillations

What is the role of Dark Matter inside which the baryonic matter

is embedded?

Where the double structure built up of Where the double structure built up of ordinary matter (=baryons) and DM will

land ?

The fate of a baryonic perturbation on a given mass scale

changes under the sucking effect due to the DM potential well which helps it to reach the end of linear regime.

Where the double structure does land at virialization?land at virialization?

Analogy with stars:

MS is an one -dimensional structure embedded inside a two -dimensional embedded inside a two -dimensional

one.

The dimensionality of FP is two inside a three dimensional space.

( heuristic case)

Faber –Jakson law

Main books 1. J. Binney, S. Tremaine, 2008, II Edition,

Galactic Dynamics, Princet. University Press.

2. Coles, P., Lucchin, F., 1995, Cosmology, The Origin and Evolution of Cosmic Structure, ed. Origin and Evolution of Cosmic Structure, ed. J.Wiley e Sons.

3. Longair: Galaxy Formation, 1998, ed. Springer.

4. Galaxy Formation and Evolution, H.Mo, F. van den Bosch and S.White, 2010, ed. Cambridge University Press.

Moreover

5. I.S. Sokolnikoff : Tensor Analysis, ed. J.Wiley &Sons, 1964

6. J.B. Hartle : Gravity, An Introduction to Einstein’s General Relativity, ed. Addison Wesley, 2003

Some more references are in the Lecture NotesLecture Notes

Lecture Notes, 2015

• Secco L., Bindoni D.: Galaxy Dynamics-ed.5

• Secco L.: Monography: On the Fundamental Plane-ed.5

• Secco L.: Monography: Cosmological Scenarios-ed.5• Secco L.: Monography: Cosmological Scenarios-ed.5

Exam

• N.2 written tests: the first at obout 15 April,

immediately after Easter, on the first Part;

• the last at the end of the Course (about 15 June), on the last Part.June), on the last Part.

• If both are positive, examination is passed

• To improve the graduation + oral discussion.

• N.1 final, common, oral exam on the whole course content.