Course:ASTR303/Syllabus

Chapter 1

Section 1.1

• Explain the relationship between flux and luminosity.
  • Luminosity is the total energy output of a body per unit time measured, for example, in Watts ($W$). Flux is the energy output through a unit area per unit time, such as Watts per square meter ($W/m^{2}$). A star's flux is its luminosity divided by the area of the sphere the energy passes through ($F=L/4\pi d^{2}$).
• Explain how stars are classified.
  • Stars are primarily classified using the strength of their Balmer lines, the categories being O,B,A,F,G,K, & M with O stars being the hottest and M stars being the coolest. Furthermore these classes have been divided into subclasses ranging from 0 (the hottest) to 9 (the coolest). The categories L and T have been added due to the discovery of very cool stars.
• Distinguish an early-type from and late-type star from their spectra.
  • Early-types are bright and young OBA stars with strong He, C and H lines.
  • Late-types are typically KMLT stars which contain absorption lines of molecules in their spectra.
• Explain the progression of spectral lines from hot to cold stars.
  • O – temperatures over 30 000 K, He-II and C-III lines strong, H lines weak.
  • B – lower remperatures than O, stronger H lines, lines of He-I.
  • A – temperatures below 11 000 K , strongest H lines and lines of singly ionized metals.
  • F – weaker H lines than A, and lines of neutral metals.
  • G – temperatures below 6000 K, strong Ca-II lines and CH band, neutral metal lines stronger than in hotter stars.
  • K – lines of neutral metals and of molecules like TiO.
  • M – temperatures below 4000 K, deep bands of TiO and VO and neutral metal lines
  • L – temperatures below 2500 K, weaker lines of TiO and VO, lines of neutral metals and prominent lines of Sodium.
  • T – temperatures below 1400 K, deep lines of water & methane.

• Distinguish a giant from a dwarf from their spectra.
  • A dwarf star has a smaller radius than a giant, which means the atoms near the surface of a dwarf star are closer to each other. The energy levels of atoms will be affected by the electric fields of nearby ions and electrons. As a result, the absorption lines are widened.(See Fig. 1.2. on P.7)
• Explain why giant and dwarf spectra differ.
  • Giants have big radii and small surface gravity so their lines are more narrow than dwarf stars.
• Contrast the life of a low-mass star from a high-mass star.
  • For massive stars, with M > 8M⊙, they become blue or yellow giants which burn Helium and heavy elements after leaving main sequence(Burning sequence: He → C → Ne → Mg → . . . → Fe). When Fe is burning, it absorbs energy instead of releasing energy. So the core collapses to form a degenerate Neutron Star, and the outer layers fall in and bounce off (type II Supernova). If the star is massive enough, it will become a black hole.
  • For intermediate mass, 2M⊙ → 6∼8M⊙, their cores start to burn Helium without being degenerate. Stars become bluer. When Helium at core is gone, they get red again(asymptotic giant branch). The outer layers are lost due to stellar superwind(planetary nebula). The only thing left is a White Dwarf with M < 1.4M⊙.
  • For low mass stars with 0.6M⊙ < M < 2M⊙, they become cool and red when Hydrogen is depleted in the core(subgiant phase). After the temperature outside the core rises high enough, Hydrogen starts to burn in surrounding shell(red giant). Gradually, Helium falls into the core, so the core gets denser and temperature rises(degenerate - star behaves like a solid or a liquid). Once the core temperature reaches about 108 K, Helium fuses into Carbon. The energy released from the He→C reaction can not change the density of the degenerate core, so the burning is explosive(Helium flash). When Helium is used up, the core contracts and the outer envelop swells(asymptotic giant branch - Helium and Hydrogen burning in shells). Then the envelops are lost due to stellar superwind. So the Carbon core is exposed as White Dwarf with M∼0.6M⊙ (planetary nebula).
  • For stars below 0.6M⊙, they have not left the main sequence since the beginning of the universe.
• Explain the major stages in the lives of stars.
  • Protostellar stage: A cloud of gas collapse by gravity. The gas is heated and it radiates energy, so gravitational energy counterbalances the energy lost by radiation.
  • Main Sequence: The temperature in the core increases and hydrogen starts to burn into helium. The pressure at the center is enough to stop the contraction and the star is brighter now.
  • Subgiant phase: The core burns all the hydrogen. The core becomes denser and the outer layers expand. The star becomes cool and red.
  • Red giant phase: In this stage, hydrogen starts to burn in surrounding shells, it makes the star brighter. The core starts to burn helium into carbon because its temperature is higher. When helium and hydrogen start to burn in next shells the star goes to the asymptotic giant branch. The star is more luminous and cooler. In this step, gas from outer layers can be lost as stellar wind.
  • The end: It depends on the star mass. For massive stars they could finish as supernova explosions, neutron stars or implode as black holes.
• Discuss why the advanced burning stages of a high-mass star are so short.
  • This kind of star is usually called Wolf-Rayet star. They are very hot with characteristic strong emission lines of Helium, Carbon, and Nitrogen coming from a fast stellar wind; the outer layers were blown off long time ago. Star with M∼50M may never become a red supergiant because their mass were lost so rapidly.
• List some ways that a companion can affect a star's evolution.
  • If there is a binary stars system and one of them is a white dwarf then this one can absorb hydrogen gas from the companion until it gets so dense that it has to explode to helium creating a classical nova or if the white dwarf takes more matter of the other star then it can explosive burn carbon and oxygen to create a Type Ia supernova.
• Calculate the magnitude of a star given its flux.
  • Let $m_{1}$ = the apparent magnitude of the Sun, $F_{1}$ = the flux of the Sun, $F_{2}$ = the flux of the star.
  • By using the equations below, we can get the apparent magnitude $m_{2}$ and the absolute magnitude $M_{2}$ of the star.
• Convert the apparent magnitude of a star to an absolute magnitude and vice versa.
  • The absolute magnitude($M$) and apparent magnitude($m$) of a star are related by the formula: $M=m-5\log _{10}(d/10)$. This is derived from the fact that the absolute magnitude is defined as the magnitude the star would appear to have from a distance of 10 parsecs. The flux at that distance can be calculated from the flux at Earth, and then substituted into the magnitude comparison formula $m_{1}=m_{2}-2.5\log _{10}(F_{1}/F_{2})$. This results in the first formula.
• Explain why astronomers use bands, list the important bands.
  • Hydrogen gas absorbs most of the far-ultraviolet wavelengths(below 912A).
  • Earth’s atmosphere blocks out light at wavelengths below 3000A, or longer than few microns.
  • Night sky emits light due to human light pollution.
  • UX, B, V, R, I, J, H, K, and L.
• Explain why astronomers use magnitudes.
  • They are somewhat archaic, but they are still useful because comparative measurements between stars are far more accurate than absolute measurements, due to factors such as atmospheric absorption.
  • Our current technologies allow us to do relative measurements much more precisely than absolution ones.
• Explain what is the bolometric correction
  • It is the amount that must be subtracted from a star's absolute magnitude in the V band in order to account for its magnitude across all wavelengths.

Section 1.2

• Distinguish the different parts of the Milky Way by morphology, colour, spectra, kinematics, stellar and gas composition.
• Explain why the spectral lines observed from interstellar species often are difficult to see in the laboratory.
  • The gas density in laboratory is too high, an atom in excited state will collide with other particles before it emits photon.
• Explain why spectra over a wide range of wavelength are useful.
  • Depending on materials and conditions (such as temperature and density), lines will will be emitted at very different parts of the spectrum.
• Calculate the extinction of a source in terms of the optical depth, explain how the extinctions at different energies are related and what causes extinction.
  • $m_{\lambda }$: the apparent magnitude with absorption; $m_{\lambda ,0}$: the apparent magnitude without absorption; $F_{\lambda ,0}$: the flux without absorption.
  • $A_{\lambda }=m_{\lambda }-m_{\lambda ,0}=-2.5\log _{10}({\frac {F_{\lambda ,0}e^{(-\tau _{\lambda })}}{F_{\lambda ,0}}})$
  • $A_{\lambda }=2.5\log _{10}(e)\tau _{\lambda }$
• Relate the different astronomical coordinate systems and explain where each is useful.
  • Equatorial: To find coordinates of stars in our sky.
  • Sun-centred Galactic Coordinate System: To give the positions of stars as we see them in relation to the Milky Way.
  • Cylindrical Polar Coordinate System: To calculate motions near the sun relative to the Milky Way.

Section 1.3

• Explain how it is determined that galaxies lie outside the Milky Way
  • Before the 1920s, astronomers thought galaxies were nebulae because they appeared fuzzy in their telescopes. Edwin Hubble, using a 100 telescope was able to find variable stars in M31. He showed that the ligh brightness of these stars changed like Cepheid variable stars within our Galaxy. He determined that the stars of M31 were the same type, with the same luminosities and calculated the distance (at least 300kpc from Milky Way), so M31 had to be a galaxy. This system is still used today. -I hope my english wasn´t so bad!
• Distinguish the different types of galaxy by morphology, colour, spectra, kinematics, environment, demographics, stellar and gas composition. What are early and late-type galaxies?
  • Ellipticals have little rotation, and mostly random stellar orbits. These are 'early-type' galaxies.
  • Spirals and barred spirals have a central bulge (sometimes with bar) with a rotating disk of stars about it. Dense parts in the disk form spiral arms. These are 'late-type' galaxies.
  • Lenticular galaxies have a bulge and a rotating disk, but haven't got spiral arms. These fall between early and late-type galaxies. They're right on time.
• Explain how observations of galaxies differ from that of stars, e.g. how do you determine how big a galaxy is?
  • We know that galaxies are not point sources of light as stars. They are extended sources. In addition, turbulence in Earth's atmosphere has negative effects on the image we see from a galaxy. These differences make astronomers use the surface brightness of a Galaxy: $I(x)={\frac {F}{\alpha ^{2}}}$. It is the amount of light per square arcsecnd on the sky in a particular point x. Since $\alpha =D/d$, we can see that the surface brightness can be writen: $I(x)={\frac {L/4\pi d^{2}}{D^{2}/d^{2}}}$. So, I(x) doesn´t depend on the distance we are from the galaxy.
  • To meausure the size of a galaxy, astronomers define the Isophotes: Contours of constant surface brightness on a galaxy image. So, they measure their sizes within a fixed isophote because galaxies don´t have sharp edges.
• Explain the luminosity function and the Schechter function.
  • The Luminosity function $\Phi (M_{V})$ describes the number of stars per $pc^{3}$ there are for a given luminosity and a certain region of space. The Schechter function is like a luminosity function for galaxies.
  • The SCHECHTER function: $\Phi (L)\Delta L=n_{*}({\frac {L}{L_{*}}})^{\alpha }exp({\frac {L}{L_{*}}}){\frac {\Delta L}{L_{*}}}$. This function gives you the number of galaxies per $Mpc^{3}$ between luminosity L and $L+\Delta L$. $n_{*},\alpha$ & $L_{*}$ are constant determined by the observations. We can see if L>>$L_{*}$, then the number of galaxies with L luminosity dicreases fast because of the negative exponencial part of the function. I was wondering something about this function: How could Schechter find this expresion? I mean, the number of different kind of galaxies by luminosity in the universe has to be random, right? So, how can a function predict something like that and fit so good?

Section 1.4

• Explain how the fact that the velocity of a galaxy is proportional to its distance show that the universe is expanding.
• Show how this linear proportionality shows that the expansion has no centre.
  • We see galaxies moving away from us with speed proportional to distance. It could make us think that we are the centre of the expansion. But it's wrong. It's only a partial perception of the situation. Any galaxy moves away from us in the same way we move away from it, it means if we were in that galaxy, we would see the Milky Way moving away from us with speed proportional to the distance.
• Show an expansion without a centre implies the Hubble law (the converse of above).
• Explain why the history of the universe is important to the study of galaxies.
  • There are some reasons that show why it is important:
    • The Hubble time and the age we have estimated for the oldest stars are very similar. It tells us the galaxies can be no older than the Universe.
    • It's important to understand how galaxies came into existence, that's why we need to know how long took to form the earliest stars studying the history of the Universe. The atmosphere of old stars (low mass) in galaxies give information from the primary universe. Since we have studied the stellar evolution and we have a model, we can know how long ago these stars began their lives on the main sequence.
• Explain what the redshift of a galaxy tells us.
  • Since the universe is expanding, the redshift that is measured for a galaxy can be extrapolated back into the past so we can relate the redshift of the galaxy with the time after the Big Bang when the first light of the galaxy was emitted. For instance, with the redshift of the galaxy we can know the age of it.
• Explain what is the critical density.
  • If the average density of our universe is smaller than the critical density, the universe will keep expanding forever. - Open universe
  • If the average density of our universe is equal to the critical density, the rate of expansion will slow to zero but the universe will not collapse. - Flat universe
  • If the average density of our universe is greater than the critical density, the universe will collapse eventually due to gravity. - Closed universe

Section 1.5

• Explain what is the Big Bang.
  • The Big Bang is a model for the origin of the Universe. The main idea of this model explains that at the beginning, the cosmos was matter at a very high temperature which expanded rapidly. This hot early Universe let create particle-antiparticle pairs. It depended on the temperature of the Universe what kind of particle was created by collisions of photons. When the temperature was appropiate, elementary particles could form nuclei of simplest elements.
• Outline the evidence for the Big Bang.
  • Since the universe is expanding as Hubble found out, then it must be a point with infinite density at a time in the past, which suggests a Big Bang to be the driving force of the expansion.
  • The energy of cosmic background radiation is much larger than the energy in any other spectral regions. The only reasonable explanation is a Big Bang.
• Explain how the chemical elements are produced in the Big Bang.
  • Free neutrons will decay into a proton, an electron, and an anti-neutrino. The protons can then combine with electrons to form Hydrogen. Neutron forms deuterium with a proton at $10^{9}K$. Deuterium can combine with other particles to form Helium 4. The Universe expanded too rapidly to form heavy elements, so there are only traces of boron and lithium were found.
• Explain why the recombination epoch is so important to our understanding of cosmology.
  • The radiation that we receive from the time when the atoms of Hydrogen recombined is called Cosmic Microwave Background and is important because based on this we can know the motion of the galaxy in relation to the rest of the Universe. Thus, we can calculate the peculiar velocity of the Milky Way, which is its speed over the Cosmic Microwave Background and also, the energy of this cosmic background, gives us a proof of the Big Bang.

Chapter 2

Section 2.1

• Explain how we measure distances to nearby stars.
  • The distance to nearby stars can be found using measurements of trigonometric parallax. As the Earth orbits the Sun, nearby stars will shift in position with respect to further, background stars. If we measure the parallax angle that the star moves across the sky in one year (in arcseconds), the distance to the star (in parsecs) is simply the inverse of the parallax. This relationship works because of the approximation $\tan(\theta )=\theta$ for small angles, and parallax angles are always small.
• Explain how we measure the luminosity function.
  • The luminosity function is the ratio of the absolute V-magnitude of stars over the volume of space in which stars of this magnitude are observed.
• Explain how to convert the luminosity function of stars to the initial mass function.
  • That is only an idea, but I think it could be work: First of all, we need to convert the luminosity function to the INITIAL luminosity function using the equation 2.4 in the opossite way ($\Phi$-->$\Psi$). Then, we can use the equation 1.6 that relates the luminosity of a star with its mass ($L\approx L_{o}({\frac {M}{M_{o}}})^{\alpha }$) to write the mass as a function of the luminosity ($M=M(L)$). So, if we know the number of stars which have been born with an specific luminosity (it is $\Psi (L)$), by eq 1.6 we can know the equivalent mass, so, we know the number of stars which have born with an specific mass (it is $\xi (M)$).

Section 2.2

• Outline how is the scale of the Galaxy as a whole determined.
• Outline how we know the distance to the LMC and why it is important.
  • In 1987, there was a supernova observed in the LMC. 85 days later, narrow emission lines from nearby heated gas became visible to us. This heated gas forms a tilted ring surrounding the star that exploded. Assuming that the ring is circular, we can measure its radius in arcseconds. Since we know it took 85 days longer for the light to reach the ring, and then the emission lines to reach us, than for the supernova light to reach us directly, we can measure the radius of the ring in light-days as well, and from this work out the distance to the supernova (and to the LMC).
• Explain what is spectoscopic parallax and how it works.
  • Spectoscopic parallax is a technique applied to measure the distance of distant stars using its spectrum.
  • First, the apparent magnitude and the spectral type of the star must be obtained. Then we can get $M_{v}$ of the star from table 1.4 in the textbook. By using $M=m-5\log _{10}(d/10pc)$, we have the distance to the star.
• Describe the vertical structure of the Galactic disk.
  • There is an important parameter that we need to know to describe the vertical structure of the galactic disk: the scale height $h_{z}$. It's a parameter that we use to estimate how much does the density of stars change if we move in the z-direction. If the value of $h_{z}$ is big, it means that the density falls slowly when we increase the height above the disk. This parameter depends on the type of star we are studying. The main structure is the thin disk and the thick disk.
  • The gas and dust is confined to the thin disk. Also we find A stars live mainly here, we can see it from fig. 2.8. The thin disk is still forming stars, and we find heavy elements which are part of them.
  • The scale height for G and K stars is greater than A stars, so we can find G and K stars far away from the midplane of the galaxy. Also older stars have larger scale heights and vertical velocities. The thick disk no includes O,B or A stars. The spectra of thick-disk stars shows a smaller fraction of heavy elements.
• Determine the distance to a star cluster using isochrones.
• Explain why the distances to star clusters are more accurate than from individual stars.
  • In a star cluster, we can plot out the stars on a Hertzsprung-Russell diagram and compare them to a theoretical H-R diagram on which we can tweak the assumed age, distance, and metallicity in order to most closely match the cluster's diagram. Also, if we know that all the stars are lumped together, and whatever distance methods we're using give the same distance for the different stars in the cluster, we're probably on the right track.

Section 2.3

• Describe the motion of stars and gas in the galactic disk.
• Derive the radial velocity relative to the local standard of rest of material orbiting about the galactic center.
• Explain what is the local standard of rest.
  • It's defined as the average motion of stars near the Sun, after correction for the asymmetric drift. It's about $R_{0}=8.5kpc$ and $V_{0}=220km/s$.
• Explain what is the asymmetric drift.
  • It's the speed relative to a circular orbit in the disk at the Sun´s position.
• Derive the tangential motion relative to the local standard of rest.
• Explain how the Oort constants measure the motion of material around the Galaxy.
• Explain how the rotation curve provides evidence for dark matter.

Section 2.4

• Explain how gas affects the Galaxies properties.
  • Without gas, the Milky Way would be a S0 galaxy (Lenticular galaxy->It has a central elliptical buldge and a rotating disk with no spiral arms) because gas gives the spiral pattern to our galaxy. Futhermore, hot young stars are formed there, so, without gas our disk would be lack of these stars.
• Outline some difficulties in observing gas that do not plague stellar observations.
  • The first thing is that gas is not divided in units like stars. In addition, it's dificult to determine the mass of gas because is not related to his temperature or any other quantity that we could know independently of its distance.
• Outline some things that affect the dynamics of gas that do not affect stars.
• Describe the distribution of molecular and atomic gas in the Galaxy.
  • Molecular Gas: Most of the molecular gas is concentrated in a ring of radius 4kpc. It spreads along a thin layer. We can see that in the front cover of the book, molecular Hydrogen image of Milky Way. The densest is concentrated in spiral arms, where young stars are located.
  • Atomic Gas: It spreads to much larger radii than molecular gas (more than 4kpc), and along a thicker layer. We can find atomic gas in the buldge of the Galaxy too, where there is a gas-rich region which is forming stars.
• Distinguish the interpretation of observations of an optically thick versus optically thin spectral line.
• What are high velocity clouds?
  • These clouds could be material from the disk that has been thrown up abouve the midplane of our galaxy by supernovae or winds from hot massive stars and now is falling back. There are also clouds that come from beyond the Milky Way.
• Describe the multiphase ISM.
• Explain how star formation affects the gas.
• Explain how is atomic gas heated if the star light is sufficiently blue to ionize hydrogen.

Chapter 3

Section 3.1

• Show that the potential within a spherical shell is constant and the potential outside the sphere is <m>-GM/r</m> where <m>r</m> is the distance to the centre of the sphere.
  • Newton proved two useful theorems about the gravitational field: 1.The gravitational force inside a spherical shell of uniform density is zero. 2.Outside any spherically symmetric object, the gravitational force is the same as if all its mass had been concentrated at the center. We are going to use these two theorems and the fact $f=-\nabla \phi$, where f is the gravitational field. Inside the spherical shell, by theorem 1 we have $f=0=-{\frac {d\phi }{dr}}$, so the potential must be $\phi =K$. Outside the spherical shell, by theorem 2 we have $f=-{\frac {GM}{r^{2}}}=-{\frac {d\phi }{dr}}$. If we integrate the last equation, assuming that the potential goes to zero when r goes to infinity, we get $\phi =-{\frac {GM}{r}}$. We can compute the value of K applying continuity conditions in r=a (spherical shell of radius a).
• Does the equation 3.1 say that the force between two point masses follows an inverse cube law?
  • Absolutely not. Equation 3.1 states: ${\frac {d}{dt}}(mV)=-{\frac {Gm_{1}m_{2}}{r^{3}}}R$. Where capital letters are VECTORS. So, R is the distance vector between 1 & 2. We can rewrite $R_{unit}$ as $R_{unit}={\frac {R}{||R||}}$, where ||R||=r. It is, the vector R normalized. Our new $R_{unit}$ is a vector which have the direction between 1 & 2 and its modulus is 1. Now, the equation 3.1: ${\frac {d}{dt}}(mV)=-{\frac {Gm_{1}m_{2}}{r^{2}}}R_{unit}$. Now, the equation seems more familiar to us.

• Identify and describe Newton's two theorems which describe the gravitational field of a spherical mass (i.e. galaxies, stars, or clusters)
  • The first theorem states that the gravitational force inside a spherical shell of uniform density is zero. This theorem shows that

by the inverse-square law, all objects located on the surface of a sphere exert equal forces on a central object like a star that lies within that sphere. These forces then cancel each other out, showing that there is no force on the star so the potential must be constant within the shell.

• • The second theorem states that outside any spherically symmetric object, the gravitational force is the same as if all its mass had

been concentrated at the center. This is shown for a uniform spherical shell so that any spherically symmetric object built from those shells can also apply the same rule. Contributions of potential from small patches of the shell are added up to find the potential outside the sphere. The same thing is done inside the sphere and both potentials are shown to yield -G*M/r therefore the potential is the same as if all the mass of the sphere had been concentrated at its center.

• • Give physical significance to the virial theorem, as would pertain to the internal motions of an isolated star cluster, or an individual star.

Section 3.2

• Contrast the effects of nearby and distant stellar encounters on the path of a star.
  • Stars are considered to have passed within a "strong-encounter radius" if the change in potential energy is at least as great as the starting kinetic energy. Essentially this just means the stars passed close enough that there is a very significant change in their velocities, both in magnitude and direction. A distant weak encounter considers the effect on the path of a particular star from another star much further away than the strong-encounter radius. This tends to be just a very slight tug, and its strength is inversely proportional to the speed at which the star whose path we're considering is moving.
• Explain relaxation time.
  • I think it's approximately how long it takes for a star's direction of motion to end up totally perpendicular to its original path, based on the description at the end of p.127, beginning of p.128, but I may not be interpreting that correctly. Relaxation time is the time over which energy is equally distributed within a cluster.
• Explain why stellar encounters are not important for the Galaxy but are important for stellar clusters.
  • When we study strong and weak encounters in a system, we find two parameters $t_{s}$ and $t_{relax}$. $t_{s}$ is defined as the time in which one star has one strong encounter. The relaxation time $t_{relax}$ is the time over which energy is equally distributed within the system, after many weak encounters. So if we compute $t_{s}$ and $t_{relax}$ for a star like the Sun in our neighborhood we find that the values we obtain are greater than the age of the Universe. But if we compute these parameters for a open cluster, we see that the encounters become important relative to the cross time, it means that encounters are important for the cluster evolution.
• Outline how a cluster of stars evaporates.
  • If we think about the stars in a two-body collisions, the stars exchange energy and momentum depending on their masses, process known as two-body relaxation and this exchange follows a Maxwellian distribution, which means that the velocities of the stars will change toward the most probable way of sharing energy. As the velocities follow this distribution, two-body relaxation causes the stars to move faster than the escape speed so they escape from the cluster and after a time of relaxation other stars also get greater energies than the escape energy so they leave the cluster too and this way the cluster evaporates.
• Explain mass segregation.
  • If we assume that all stellar velocities in a cluster have about the same magnitude, then the more massive stars have greater momentum. This means that in a stellar interaction, a more massive star will give up kinetic energy to a less massive star, which decreases the velocity of the former and increases the velocity of the latter. Over time, this results in a greater spread in locations in the lower-mass stars, while the high-mass stars clump together in the centre.
• Describe how relaxation drives the evolution of a globular cluster.

Section 3.3

• Derive the effective potential from a given spherical mass distribution.
• Calculate the epicyclic frequencies for a given spherical mass distribution.
• Explain why stars in the solar neighbourhood on average lag behind the local standard of rest.
• Relate the epicyclic frequencies and the shape of the epicycles to Oort's constants.

Section 3.4

• Explain what is the distribution function.
  • It describes the density of positions and velocities of stars. (If it's the one I think it is)
• Explain how the Boltzmann equation provides an estimate of the density of the Galactic disk.
• Relate the distribution function to the density distribution.
• Explain Lioville's theorem.
• Explain why integrals of motion are useful when using the CBE.

Chapter 4

• List the major galaxies of the Local Group.
  • M31: It's a Sb galaxy. It's the most luminous of the Local Group. Its center contains a possible black hole and a stellar cluster.
  • Milky Way: It's a Sbc galaxy. It's 50% less luminous as M31, but it contains about 2/3 of M(HI) in M31. Its bulge is smaller than M31 bulge.
  • M33: It's a Sc galaxy. It's much less luminous than M31 and Milky Way, and it's smaller too. It has a tiny bulge. The spiral arms are more open than those in M31.
  • LMC: It's a SBm galaxy. LMC has about 10% of the Milky Way's luminosity. It has only one stubby spiral arm.
  • SMC: Could be classified as irregular galaxy. It's ten times fainter than LMC. A bridge of gas connects the LMC with SMC.
• Describe the minor galaxies of the Local Group

Section 4.1

• Describe how galaxies affect each other's growth using the Magellanic clouds as an example.
• Describe what Leavitt did.
• Compare and contrast dwarf spheroidal galaxies with irregular galaxies and globular clusters.
• Describe how tides affect dwarf galaxies.

Section 4.2

• Outline the main characteristics of Andromeda
  • Andromeda is a Sb galaxy, bigger than Milky Way: about 50% more luminous, its scale lenght is 6-7kpc, V(R)=260Km/s. The bulge is also larger than Milky Way's bulge. Bulge stars are rich in heavy elements, and we can find ionized gas, HI and dust there. The center harbor 2 main objects: a possible black hole and a stellar cluster. M31 is a cannibal galaxy, and we can see that metal-rich halo stars probably arrived as M31 merged with another galaxy. There is a ring of fire where stars are forming. The gas we find is neutral Hydrogen, HI clouds in the "ring of fire". Clouds in gas disk orbit circular and molecular gas represents an small fraction. The outer parts are not flat but bent into an 'S' shape. It's common in spiral galaxies.
• Outline the main characteristics of M33

Section 4.3

• Describe the ELS model for the birth of the Milky Way.
• Elaborate on the role of energy and angular momentum conservation in the formation of galaxies.
• Describe the results of closed-box and open-box models for the build-up of metals in a galaxy.
• Define the yield.

Section 4.4

• Contrast dwarf ellipticals, spheroidals and irregulars.
• Describe the role of gas supply in the evolution of dwarf galaxies.

Section 4.5

• Outline the future of the Local Group.
• Estimate the timescale for the end of LG as we now know it.

Chapter 5

• List the main features of disk galaxies.

Section 5.1

• Describe how CCDs work.
  • CCD (Charge-coupled device) is the current 'workhorse' detector for astronomical imaging and spectroscopy. It is based on the photoelectric effect. Light incident on a semiconductor (usually silicon) produces electrons. These electrons are trapped in potential wells produced by numerous small electrodes (pixels). There they accumulate until the total number is read out by charge coupling the detecting electrodes to a single read-out electrode. So, you can register the distribution of light because the charge (# of electrons) in each pixel is proportional to the intensity of light (# of photons).
• List some other astronomical imaging devices.
  • Array detectors, which can be used for shorter wavelengths than CCDs
• Describe how the resolution of the CCD affects what we can measure.
• Describe mathematically how the surface brightness is distributed in a disk galaxy.
  • The surface brightness I(R) in the stellar disk often follows approximately an exponential form: $I(R)=I(0)exp(-R/h_{R})$. Where $h_{R}$ is the scale lenght. It's important to say that the scale lenght is different for different bands. For example, in B band, $h_{R}$ is about 20% longer than I band because the disks become redder toward the center. We can study mathematically how surface brightness distributes above and below the dust lane we find in the disk. It follows too a exponential form: $I(R,z)=I(R)exp(-|z|/h_{z})$, where $h_{z}$ is the scale height.
• Describe how the colour and absolute magnitudes of disk galaxies correlates with galaxy type.
• Contrast UV, visible and IR images of nearby disk galaxies.
  • IR images help us to investigate the old stellar populations because hot young stars emit relatively little of near IR light. The spiral arms appear smoother and less prominent. At UV we can see the light from hottest stars. It gives us a snapshot of the star formation. We can find bright light along the spiral arms, it means that clumps of massive stars have been born there. UV and optical wavelengths can be absorbed easily by dust.

Section 5.2

• Describe how an interferometer works.
  • We know that the difraction limit for a single telescope of diameter D is: $\alpha ={\frac {\lambda }{D}}$. It means that sources that are closer than this angle in the sky will appear blended together. To improve it we use array of smaller telescopes. To see how it works we think of radio waves as oscillating electric and magnetic fields. For a wavelength $\lambda$, the voltage induced at the focus of radio telescope is V proportional to $cos({\frac {2\pi ct}{\lambda }})$. The key is that we observe with more than one radiotelescope (eg 2 radiotelescopes: $V_{1}$ and $V_{2}$), so the waves from a source at elevation $\theta$ travel an extra distance $dcos\theta$ and the signal in the second will be delayed by a time ${\frac {dcos\theta }{c}}$ relative to radiotelescope 1. We multiply signal 1 and 2 in a correlator and filter them to remove the rapid oscillations. The result is a fringe patter whose signal is S proportional to $cos({\frac {2\pi dcos\theta }{\lambda }})$. You can distinguish sources separated only by ${\frac {\lambda }{dsin\theta }}$. It has the resoluting power of a large single dish of $D=dsin\theta$.
• Describe how to measure the amount of neutral gas in a galaxy.
• Explain why the surface density of neutral hydrogen is similar for most disk galaxies even those with low surface brightnesses.
• Explain the origin of 21 cm radio emission and radio continuum emission.

Section 5.3

• Explain the spider diagram.
  • When observing a disk galaxy at some angle from face-on, because of the differential rotation we can represent the galaxy as an ellipse with lines of constant radial velocity (relative to the Sun) drawn across. These form a shape that reminds astronomers of spiders. Or perhaps spider webs?
• Outline the evidence for dark matter in spiral galaxies.
  • There is an expected rotation curve for a disk potential made up of visible matter, which starts high and drops off towards large radii, and there is an expected potential for a halo of mysterious invisible matter, which starts off low at low radii but becomes large at large radii. When we add these together, we get a potential that rapidly rises out to a particular radii, and then remains essentially flat. This is the potential we actually observe in most spiral galaxies, and variations in it give us indications of visible to dark matter ratios in different types of spirals.
• Derive the double horned profile of the 21cm line in edge-on spiral galaxies.
• Explain what the Tully-Fisher relation tells us about the mass-to-light ratios of spiral galaxies.
  • The rotation speed of a galaxy increases with its luminosity, at about $L\propto V_{max}^{4}$

Section 5.4

• Explain how the various properties of spiral galaxies correlate with each other: star formation, colour, gas content, luminosity, mass, spiral arms, bulge-to-disk ratio, mass, rotational velocity.

Section 5.5

• Explain why a spiral pattern would tend to wrap up quickly.
  • The inner stars in the disk have higher angular velocity than the outer stars, so the further out into the disk you look, the further behind the stars will fall in what used to be a group. This could form a spiral pattern, but it would be twisted up completely before long, because of the variation in speeds.
• Contrast grand-design spirals with flocculent spirals.
  • In grand-design spirals the arms can be traced from the centre way out towards the edge, often wrapped very far around the galaxy, without being broken. Flocculent spirals have a general spiral direction and are pretty-looking, but if you look at any particular spiral arm it's just a little piece that dies out quickly. There are many of these at various radii.
  • floc-cu-lent: having or resembling tufts of wool

Section 5.6

• Describe the bulges of the Milky Way and M31 galaxies
  • both bulges contain more metal than their disks, they also contain less gas than their dicks except at the very centre of the bulge
  • galaxies become redder toward the center, so bulges are slightly redder than the inner disk
  • stars in their bulges are at least a few gigayears old
• Describe what Sérsic's Formula tells us about light distribution in elliptical galaxies.
  • Sérsic's Formula $I(R)=I(0)e^{-({\frac {R}{R_{0}}})^{\frac {1}{n}}}$ for n=4 (elliptical galaxies) implies that surface brightness of a galaxy should continue to increase towards the center.

Chapter 6

• List the main features of elliptical galaxies.
  • Appear round; smooth light distribution; lack clumps of young blue stars; patches of dust; rich in stellar hot gas; no disks;
  • Luminous ellipticals have triaxial shape and low rotation speed. They are strong X-ray sources
  • Less luminous ellipticals rotates rapidly, and have dense stellar cusps at centers.

Section 6.1

• Describe ellipticity,ϵ and the Hubble type, En.
  • Ellipticity is defined as ϵ=1-b/a where a is the semi-major axis, and b is the semi-minor axis of an ellipse. The Hubble type, En, is a method of classification of elliptical galaxies by their ellipticity, where n=10(1-b/a). For example, n=0 signifies a perfectly circular galaxy, it's type is E0.
• Rewrite Sersic's formula to find light distribution of elliptical galaxies.
• Describe cD galaxies.
  • They are the most luminous of all galaxies, and contain the most stellar mass. cD galaxies are found at centers of galaxy groups and clusters only. Their light distribution is proportional to $R^{1/4}$ out to the effective radius. Thereafter, the light distribution changes, and becomes higher than what the formula predicts. This is occurs due to an 'outer enevelope of extra light.' The surface brightness of cD galaxies is low, and this is due to galactic collisions which increase the motion of stars in the galaxies making them less tightly bound.
• Compare and contrast the dimmest ellipticals.
  • Compact ellipticals have significant rotation, whereas dwarf ellipticals (dE) and dwarf spheroidals (dSph) do not. dSph are less luminous than dEs, but both types have larger cores than midsized ellipticals. Central brightness is lowest in least-luminous dE and dSph.
• Compare and contrast "disky" and "boxy" elliptical galaxies.
  • If the isophotes of an elliptical galaxy are approximated by an ellipse, the difference between the actual isophote and that ellipse can be futher approximated as $\Delta r=a_{4}cos(4\theta )$. If the coefficient $a_{4}<0$, the galaxy is "boxy", and a galaxy with $a_{4}>0$ is called "disky".
  • Disky Ellipticals
    • Rotate faster than boxy galaxies.
  • Boxy Ellipticals
    • Emit strongly in the X-rays and radio spectrum.

Chapter 7

Section 7.3

• Why does the 'fundamental plane' relationship between core size and central brightness cause problems for the idea that most elliptical galaxies formed through mergers?
• What is the importance of finding a 4000 Angstrom break in the spectra of high redshift galaxies?