... typically^1.1

The names give an indication of the corresponding wavelength region, B FOR BLUE, V FOR VISUAL, R FOR RED, U FOR UV (IN THE DIRECTION OF THE UV-THAT IS), I FOR IR.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... extended^1.2

Very nearby stars can be resolved with special techniques.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... energy/time/area/steradian.^1.3

A solid angle is usually expressed in steradians, or arc sec$^2$, see http://whatis.techtarget.com/definition/0,,sid9_gci528813,00.html.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... independent^1.4

This is only true for relatively nearby galaxies. On cosmological distance the SB decreases with distance because of the redshift.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...arcsec\ ^2.1

An arcsec is a 60th of an arc minute, or 1/3600th of a degree. Now we can do much better!

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... radians^2.2

We've used the fact that this angle is very small.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... find^2.3

The amount of dust is not the same everywhere: there are regions where the absorption is much stronger, not surprisingly called dark clouds, and some directions along which the absorption is much less, a well known direction is called Baade's window.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Roto-vibrational^3.1

Most transitions you know, which occur in the visible and UV-part of the spectrum, are electronic transitions: in emission, they occur because an electron changes from a higher energy state to a lower one, e.g. from $n=2\rightarrow 1$ for the hydrogen Lyman-$\alpha$ transition, and from $n=3\rightarrow 2$ for the hydrogen H$\alpha$ transition. And in absorption, they go the other way around. But molecules also have excited levels due to their rotation or vibration. Since these are also quantum-mechanical the energy levels are quantised. And transitions between them correspond to rotational or vibrational transitions. Since the energy-levels are lower they correspond to longer wavelengths - typically mm and cm: in the radio.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... interferometers.^3.2

One way to think of this is to realise in good `mirror' the departure from the ideal shape should not be larger than some small fraction of the wavelength of the radiation you plan to observe. So for optical telescopes, it should be of the order of 500nm, say, but for radio-waves, fractions of a mm, and up to a m. There is a down-side. The resolution you get, when making diffraction limited observations, is of order $\lambda/D$, where $\lambda$ is the wavelength, and $D$ the diameter of the telescope. And so, radio-telescopes have to be much bigger to obtain a similar resolution. In an interferometer, instead of building one giant dish - which would be very expensive, and difficult to move - one builds many smaller dishes, put far apart, and combines their output. The result is that the effective $D$ is not the size of a dish, but rather the biggest distance between them. What you loose, is that the collecting area is only the sum of the sizes of all dishes, not $D^2$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... mission^3.3

http://astro.estec.esa.nl/Hipparcos/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...GAIA^3.4

http://astro.estec.esa.nl/GAIA/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Helium^3.5

The Big Bang produced hydrogen, helium, and trace amounts of more massive elements

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Silicon^3.6

And they produced the stuff we are made of

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... stars^3.7

The Sun is thought to be a third generation star.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... regions.^4.1

Many molecules in the earth's atmosphere, for example water, absorb infrared light in their molecular bands, which is why it is difficult to perform infrared observations from the ground. Some IR observatories have moved to the South pole, where there is much less water vapour.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... at^4.2

One of the more famous HII regions is the Orion nebula, M42.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... spectra.^4.3

The strongest line from a Planetary Nebula is O[III], which is a forbidden transition. This means that the quantum mechanical probability is zero, and such lines are not observed in laboratory environments. The reason that the line does occur is because a collision with another particle makes the transition possible. But because the transition is forbidden, once the photon is produced, it has no trouble escaping the nebula.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...$\alpha$^4.4

Recall that transitions to $n=1$ are called the Lyman series and to $n=2$ the Balmer series. Furthermore, a transition $n+k$ to $n$ are `counted' with the Greek alphabet, and so $n=3\rightarrow n=2$ is called H$\alpha$, $n=4\rightarrow n=2$ is H$\beta$, $n=2\rightarrow n=1$ is Lyman$\alpha$, $n=3\rightarrow n=1$ is Lyman$\beta$, etc.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... (anti-aligned).^4.5

Two bar magnets can of course have any angle between them. But for quantum mechanical spins, this is impossible, and they are either fully aligned, or fully anti-aligned, with nothing in between! So the analogy only goes so far.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... interactions.^4.6

Interactions between the spin and the orbital angular momentum of the electron also result in slightly different energy levels and transitions.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... transitions.^4.7

Energy can be stored in rotation of the molecule. In a quantum mechanical description, the amount you can store is quantised. Rotational transitions are transitions between different rotation speeds of the molecule.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... CO.^4.8

In different books, you'll find slightly different numerical pre-factors in the definition of the Jeans length and Jeans mass.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... by^4.9

An even better way would be to find the dispersion relation that relates the speed of a wave to its wavelength.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... rotation^5.1

The inner parts go around faster than the outer parts, so differential rotation, as opposed to say solid body rotation.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...fig:Oort)^5.2

We are describing the motion of stars in the plane of the disk, hence the galactic coordinate $b=0$

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... (LSR)^5.3

Note that this is not an inertial reference frame!

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... and^5.4

This only works when $\vert l\vert<\pi/2$, i.e. toward the centre, since in the outer parts there is no unique orbit that you can associate with a given velocity.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... galaxies.^5.5

There is a third way out: may be gravity does not behave as expected on these large scales, or for these small accelerations. This is not so easy to dismiss as you might think: we have no measurements on other scales, for example in the solar system, or in the laboratory, that can test the small acceleration regime that applies on galactic scales. The theory of Modified Newtonian Dynamics (MOND) is able to provide very good fits to measured rotation curves with a small modification of gravity that cannot be probed in other regimes.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... contrast^5.6

the relative difference in density at given $r$ from the centre, within vs outside of the arm

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... other.^5.7

The tidal force exerted by the moon causes the tides in the earth's oceans.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... velocities^6.1

The quoted velocity is wrt to the centre of mass velocity of the MW. Do not confuse these with Oort's high velocity stars, which are typically low mass, low metallicity stars in the Galactic Halo. The velocities of Oort's stars are of order 200 km s$^{-1}$. The present high velocity stars are typically $A$-type stars, presumably born in the disk, that have acquired their high velocity following a super nova explosion.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... speed^6.2

Stars travelling at the local escape speed are just able to leave the potential well and escape to infinite.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... ^6.3

$R_\odot$ is the radius of the circular orbit around the MW, at the position of the Sun - the solar galacto-centric radius.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... means^6.4

Remember: we've only derived a lower-limit to the MW mass, hence a lower-limit to the mass-to-light ratio.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... MW^6.5

What one measures is the radial velocity wrt to the Sun. Since the Sun is on a (nearly) circular orbit around the MW, one needs to correct the measured heliocentric velocity to obtain the radial velocity of Andromeda wrt the MW.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... accurate^6.6

From properties of the micro-wave background radiation.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... MW^6.7

Equation (6.11) has no unique solution for $\theta$, since it describes motion in a periodic orbit. On its first approach, $\theta$ should be the smallest solution to the equation.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... so^6.8

Recall that the luminosity of stars scales with their mass quite steeply, $L\propto M^\alpha$, with $\alpha\approx 5$, and hence $M/L\propto M^{1-\alpha}$. See your notes on stars, p. 34.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... profile^7.1

rather, a characteristic distribution function, the density of stars in six-dimensional position and velocity space.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... alive^7.2

Recall that massive stars have short lifetimes.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... bremsstrahlung^7.3

German for `braking radiation'.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... cools.^7.4

Also the ions collide of course, but since they are much more massive than the electron, their acceleration is far smaller, and hence their radiation is negligible.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... numbers^8.1

A handy approximate relation is $1{\hbox{\rm km}}/s\approx 1\pc/{\hbox{\rm Myr}}$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... time^9.1

If $v$ is the typical velocity of a galaxy in a cluster of galaxies, and $R$ is the radius of the cluster, then the crossing time $T_{\rm cr}=R/v$, i.e. it is the typical time a galaxy takes to cross the cluster once.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... clusters^9.2

Except in the inner parts of some cooling flow clusters

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... value^9.3

Recall that the sun contains a mass fraction of 0.02 of metals.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... gas^9.4

Recall that the nucleus of a Deuterium atom differs from that of ordinary Hydrogen in that it has a proton and a neutron.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Remember^10.1

It is unfortunate that absolute magnitude and mass are both denoted by $M$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... A^11.1

The redshifting of the spectral lines is due to the expansion of the Universe. By measuring the expansion rate, one can convert redshift to distance, assuming a cosmological model.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... 3C 48^11.2

The C stands for Cambridge - this is the third Cambridge radio-survey.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... series^11.3

The Balmer series is the series of electronic transitions in an atom which starts with the H$\alpha$ line ( $n=3\rightarrow n=2$), then H$\beta$ ( $n=4\rightarrow n=2$) etc.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... distance^11.4

The `velocity' of such distant objects is not a real velocity in the sense that something is moving. The velocity results from space expanding, and it is often better to not convert this to velocity at all - just use the cosmological model to find the relation between the redshift $z=\Delta\lambda/\lambda$ and distance.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... current^11.5

March 2003. The text book we're using, OC, states we know 5000 of them. And that we know `several' with redshift greater than 4. This just shows you how rapidly this field is evolving.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... idea^11.6

You may argue we should use special relativity. In fact, we need general relativity to make proper sense of this.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... minutes^11.7

To do this properly, we need to take (special) relativistic effects into account. But if you do everything properly, you get a similar answer to what we found.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... object^11.8

Actually, annihilation of matter-anti-matter is even better!

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... schemes^11.9

i.e. theories that try to explain QSO activity in terms of a single model - accretion onto a SMBH.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... I^11.10

I will follow a nice review paper by Luis Ho, see
http://nedwww.ipac.caltech.edu/level5/March01/Ho/Ho.html for the full text.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... as^11.11

I just state the result and don't expect you to derive it.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... spectra^11.12

Recall the need to go to the IR: there is a lot of absorption by dust toward the MW centre but IR-light undergoes far less absorption.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... motion^11.13

Whereas stars can freely move through one another, gas motion must be ordered not to produce shocks.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... centre^11.14

Don't get confused with evidence for dark matter from flat rotation curves. Here we are looking close to the centre, whereas for rotation curves we were looking at large distances, $\sim 20{\hbox{\rm kpc}}$ from the centre.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... maser^11.15

A maser is a laser that operates in the mm regime.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... Wambsganss^12.1

see http://www.livingreviews.org/Articles/Volume1/1998-12wamb

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... If^12.2

I took this part, including the figures, from W Evans' 2003 review, see astro-ph/0304252

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... collaboration^12.3

http://wwwmacho.mcmaster.ca/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.