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Spiral Galaxy Rotation Curve The Milky Way rotation curve: Although the enclosed mass, M(r), continues to grow apparently without limit, the enclosed luminosity, L(r), tends to a finite limit as we reach the edge of the luminous material in the galaxy. There must therefore be significant amounts of dark matter which continue to contribute to M(r) out to very large radii. o Out to the furthest point measured, typical galaxies have a luminosity of L ~ 1010 L , and a typical enclosed mass of M ~ 1011 M . The "mass-to-light ratio" M / L is hence ~ 10 solar units. ~ 90% of the material in the galaxy is dark! Example: The Sun moves at about 220 km s-1 in a circular orbit around the centre of the Galaxy, like almost all the stars near the Sun. We can assume that all the matter is at the Galactic centre, a not too bad approximation. Let the speed be V0 , the mass of the Galaxy be MG and the distance of the Sun from the Galactic centre be R0. Then the centrifugal force due to rotational speed must balance the gravitational force due to the mass of the Galaxy. GMG/R02 = V02/R0 where G is the gravitational constant. Hence MG = V02 R0/G Substituting values of 8 kpc and 220 km s-1 for the Sun and G = 0.00430 M (km s-1)2 / pc, we get MG = 1011 M . However, measurements of the rotation of the outer edge of the Milky Way show that the stars out there also rotate at 220 km s-1, out to about 20 kpc. Thus, within a radius of 20 kpc we get a mass of MG = 2x1011 M If the light distribution of the Galaxy were proportional to the mass distribution, then the two mass estimates above would imply that the amount of light emitted by the 8 kpc region would be the same as the region from 8 - 20 kpc... whereas measurements show that the 8 kpc region emits about 10 times more light than the 8 - 20 kpc region. The major conclusion is that the distribution of emitted light is not necessarily the same as the underlying distribution of matter. Rotation curves of other galaxies On the left, a spiral galaxy image, with spiral arms delineated by HII regions. On the right, the light a narrow strip running along the major axis of the galaxy has been spread into a spectrum, between about 6500 and 6800 Angstroms. The rotation of the galaxy is seen in the emission lines from H alpha at 6563 Angstroms (the brightest line), as well as other fainter lines in this region due to [NII]. HII regions appear reddish in this image because of the prominence of the H alpha line in the red region of the spectrum. The Local Group The biggest and brightest Local Group members are the Milky Way Galaxy and the brightest Messier objects: M31 (Andromeda) and M33. Next in line would be M32 and the two Magellanic Clouds (the LMC and SMC). The Clouds are big and close, so we have good detailed studies of them. The rest are smaller objects, either irregular galaxies or dwarf ellipticals. M31: LMC: SMC : In fact, it seems that our own galaxy undergoes a gravitational interaction with the LMC and SMC. NGC 6822 (``Barnard's Galaxy'') and IC 1613: Two other more distant and less luminous irregular galaxies that have been extensively studied with large telescopes. They are providing new insights for both the distance scale and the evolution of galaxies. Both have Cepheid variables, still the best way of determining distances within the nearest 10 million light-years, and both have current star-formation activity. NGC 6822 (left) and IC 1613 – both are Irregular galaxies The Local Group – dominated by the two giant spirals, Andromeda (M31) and our own Milky Way. In addition to Messier 33, an intermediate mass Sc galaxy, there are 15 ellipticals and 13 irregular galaxies in the cluster, including the Magellanic Clouds, our Galaxy's satellites, Messier 32 and NGC 205, satellites of Andromeda. The group has a size of about 3 million ly., and has a total mass of 5 x 1012M What is the criterion for inclusion in the Local Group? Proximity. If we grant membership to all galaxies within 4 million light-years, we have about 30 members. This shows the 3-dimensional distribution of Local Group galaxies Clusters On the larger scale we have galaxy clusters such as the Virgo Cluster, about 50 million light years away, that is the nearest regular cluster of galaxies. Our Local Group is an outlying member of a "supercluster" of galaxies of which the Virgo Cluster is the dominant member. The Virgo Cluster The Virgo Cluster with its some 2000 member galaxies dominates our intergalactic neighbourhood, as it represents the physical centre of our Local Supercluster (also called Virgo or Coma-Virgo Supercluster), and influences all the galaxies and galaxy groups by the gravitational attraction of its enormous mass. The Virgo Cluster has slowed down the escape velocities (due to cosmic expansion, the `Hubble effect') of all the galaxies and galaxy groups around it, causing an effective matter flow towards itself (the so-called Virgo-centric flow). Eventually many of these galaxies have fallen, or will fall in the future, into this giant cluster which will increase in size due to this effect. Our Local Group has experienced a speed-up of 100-400 km/sec towards the Virgo cluster. Detail of Virgo cluster: The Hercules Cluster (below), about 650 million light-years distant. This cluster is loaded with gas and dust rich, star forming, spiral galaxies but has relatively few elliptical galaxies, which lack gas and dust and the associated newborn stars. Colours in the composite image show the star forming galaxies with a blue tint and ellipticals with a slightly yellowish cast. In this cosmic vista many galaxies seem to be colliding or merging while others seem distorted - clear evidence that cluster galaxies commonly interact. Over time, the galaxy interactions are likely to affect the content of the cluster itself. Researchers believe that the Hercules Cluster is significantly similar to young galaxy clusters in the distant, early Universe and that exploring galaxy types and their interactions in nearby Hercules will help unravel the threads of galaxy and cluster evolution. The Hercules Cluster Distant Clusters. The Hubble Space Telescope has provided the first opportunity to look back into the early universe at clusters. Billions of years ago, clusters contained many more spiral galaxies than they do today. CL 0024+1654 is a large cluster of galaxies located 5 billion light-years from Earth. It is distinctive because of its richness (large number of member galaxies), and its magnificent gravitational lens. The blue loops in the foreground are lensed images of a spiral galaxy located behind the cluster. The CL 0024+1654 Cluster – note the gravitational lensing The rich galaxy cluster, Abell 2218, is a spectacular example of gravitational lensing. The arc-like pattern spread across the picture like a spider web is an illusion caused by the gravitational field of the cluster. The cluster is so massive and compact that light rays passing through it are deflected by its enormous gravitational field. Hubble Deep Field: Probably the deepest image ever taken was by the HST over about 150 consecutive orbits (about 10 days) from December 18 through 30, 1995 on a single piece of sky located at 12h 36m 49.4000s +62d 12' 58.000" (near the Big Dipper). Distance to Galaxies – The Hubble Law Cepheids., and went on to observe Cepheids in other galaxies as well and so obtain distances to them. Redshifts. In the 1920s, Hubble determined the distance to the Andromeda galaxy by finding a Cepheid variable star there. Hubble and collaborators began a systematic study of nearby galaxies which included measuring both their distance (Cepheids etc) and radial velocity. They soon noticed a remarkable trend: virtually all the galaxies they observed were moving away from our galaxy (redshifted) and the recession speed increased with distance. Hubble's first dataset included only a few dozen galaxies which were < 2 Mpc away but his basic conclusion has not changed as more and more galaxies at larger distances have been observed. We live in an expanding Universe. Due to the Big Bang, the universe is expanding. Hubble found that there was a direct linear relation between distance and redshift: the further a galaxy was from us, the faster its recession velocity. This relation, which has come to be known as Hubble's Law, is written v = Ho D where v is the recession velocity, D is the distance to the galaxy, and Ho is the constant of proportionality known as Hubble's Hubble found H0 ~ 500 km/s/Mpc !! Hubble’s original data: Figure: A redshift versus magnitude plot reveals a linear relationship between recession velocity and distance. For relatively nearby objects, Hubble's law itself becomes a way to determine distances. Suppose you had a galaxy in which you found an emission line of sodium, which has a rest wavelength of 590 nm, shifted to 620 nm. What is the distance to that galaxy using Hubble's Law? First, compute the redshift: z = ( - o) / o = (620 - 590) / 590 = 0.05 For speeds much less than the speed of light, z = v/c, hence this galaxy is receding at a speed that is 5 percent the speed of light, or 0.05 x 3 x 105 = 1.5 x 104 km s-1. Using a value of the Hubble constant of 70 km s-1 Mpc-1 we can now solve for the distance in Megaparsecs: 1.5 x 104 / 70 = 214 Mpc. The Doppler formula we have been using to relate the redshift z to the velocity v is appropriate only for velocities much less than the speed of light (i.e., nearby galaxies). The formula z = v / c implies that you can't have redshifts greater than one because that would give you a velocity greater than the speed of light, something not permitted by the laws of physics. In fact, redshifts larger than 1 are possible, and are observed. For example, if an object has a velocity near the speed of light we have to use the "relativistic Doppler shift formula" c v z 1 c v 2 which is derived from special relativity. You can see by the presence of the (c-v) in the denominator of the fraction that as v gets close to c the redshift becomes increasingly large. (z = c would yield an infinite redshift). This means the Hubble law at high redshift becomes Two galaxies have been moving apart for something like 13 Gyr (assuming that they were one time very close together – such as at the moment of the Big Bang). Another way of looking at this is to see that: and Ho is essentially an inverse Hubble time. But there is sufficient mass in the Universe which slows down the expansion - so our assumption that M87 and the Galaxy have been moving apart at a constant speed since the expansion began is probably false. Galaxy Classification External galaxies occur in a wide variety of shapes and sizes. In the first systematic attempt to quantify their morphology, Hubble produced his "tuning fork" diagram in the 1920s: Galaxies on the left are designated "early type galaxies," and those toward the right are called "late types." These labels arise because Hubble believed that this diagram represents and evolutionary sequence. We now believe otherwise. A detailed description of Galaxy classifications can be found at: http://nedwww.ipac.caltech.edu/level5/Haynes/Haynes_contents.html Four types of galaxies – Hubble proposed a scheme for classifying galaxies in his 1936 book, The Realm of the Nebulae Ellipticals (E) Lenticulars (SO or SB0) S01, S02, S03 – strength of dust absorption, S01 has none SB01, SB02, SB03 – prominence of bar Spirals – normal (S) or barred (SB) Sa – Sc depending on bulge/disk ratio, tightness of spiral arms, and gas content Irregulars (does not fit into above category) Elliptical Galaxies An elliptical galaxy shows no spiral structure and can vary from almost round (what Hubble called E0) to almost cigar shaped (called E7). This classification is based on our perspective from Earth and not on the actual shape. M89: E0 M59 E5 Elliptical galaxies are designated "E#," where # refers to their apparent flattening: o # = 10(1 - b/a) o o o o o Apparently round ellipticals are E0s The flattest ellipticals observed are E7s. Do not have perfect elliptical isophotes – typical deviations of a few % Deviations from ellipses can be classified as disky or boxy(peanut) Boxy galaxies tend to be more luminous, slower rotators o o o o o o o o o o 3-D shapes – are ellipticals predominantly: Oblate: A=B>C (a flying saucer) Prolate: A>B=C (a cigar) Triaxial A>B>C (a football) (A,B,C are intrinsic axis radii) Want to derive intrinsic axial ratios from observed Find that galaxies are mildly triaxial: A:B:C ~ 1:0.95:0.65 (with some dispersion ~0.2) Triaxiality is also supported by observations of isophotal twists in some galaxies (would not see these if oblate or prolate) o o For normal bright ellipticals (Mv < -17) the surface brightness falls off from the centre according to the empirical formula cD’s are massive bright ellipticals at the centers of galaxy clusters In between the ellipticals and the spirals are the S0s which have o very large bulges o weak disks o no spiral structure Spiral Galaxies As a fiducial, the Milky Way Radial Scale Length of 3-4 kpc Blue Luminosity of ~ 1.5 x 1010 L Absolute blue magnitude, -20.7 Total Mass of ~1011 – 1012 M Depending on how much dark matter there is Spiral galaxies have outstretched, curving arms suggestive of a whirlpool or pinwheel. Hubble distinguished different sub-classes according to the tightness of the arms and the size of the nucleus. He called these Sa, Sb, and Sc. In terms of the arms, Sa is the tightest wound while Sc is the most open. Normal spiral galaxies are designated S?. Barred spiral galaxies are designated SB?. Definite spiral structures are seen in some 61% of galaxies. These structures often extend throughout most of the galaxy’s visible disk, which have scale lengths to 15 kpc or more. Although individual galaxies often show irregularities in the light distribution within the spiral patterns the underlying spiral geometry is highly regular. o The "?" is chosen from a, b or c, and was originally classified on the basis of the pitch angle of the spiral arms: o Note that late-type spiral galaxies (Sc's) also tend to have: smaller bulges more "grand design" spiral structure M65 Sa : M33 Sc: About ¾ of galaxies in the field are spirals Most spirals are found in the field (in groups) Spiral galaxy scale lengths run from ~1 kpc (dwarfs) to ~50 kpc Absolute magnitudes ranging from –16 to –23, that’s a factor of ~1000 in luminosity! Masses ranging from 109 to 1012 M Barred Spirals Barred spirals show the same spiral structure as normal spirals, and also a prominent bar through the nucleus. The spiral arms emerge from the end of the bar. The sub-classifications are the same as for normal spirals. M58 SBb: Dwarf galaxies Faint, M > -18, Dwarf Ellipticals, dwarf spheroidals, dwarf irregulars There are probably lots of these, in the Local Group there are >30! Dwarf Spheroidal, Leo I : Leo I Low Surface brightness galaxies (LSB) Very difficult to detect! Need dedicated surveys Recent automated CCD surveys suggest there may be more LSB galaxies than all the other types of galaxy put together Peculiar Galaxies In particular, interacting galaxies Many cataloged by Arp in 1966 NGC 4676 – The Mice Arp 188 The Tadpole: Irregulars Certain galaxies lack either an obvious spiral structure or nuclear bulge, appearing instead as a random collection of stars with no obvious order. These are designated "Irr" for "irregular." Make up a few % of the field galaxy population Generally smaller, sizes of a few kpc Absolute magnitudes of –13 to –20 Masses of 108 to 1010 M o . Galaxy constituents: Spiral galaxies contain: o stars (population I and II) , gas, dust Elliptical galaxies contain: o stars (population II only – (i.e. old) stars) Irregular galaxies are harder to classify. They usually contain: o stars (population I (young stars) – in other words there are significant amounts of gas in the galaxy which is being transformed into young stars – with ages as short as a few million years) and some population II) , star-forming regions , gas (a higher proportion than in spirals) The Large Magellanic Cloud at optical wavelengths Mass M Absolute mag Luminosity L M/L (M / L =1) Diameter (kpc) Stellar population Ellipticals 105 - 1013 -9 -> -23 3 x 105 - 1011 100 Spirals 10 – 4 x 1011 -15 -> -21 108 – 2 x 1010 2 – 20 Irregulars 108 – 3 x 1010 -13 -> -18 107 - 109 1 1 – 200 II and old I 5 - 50 I in arms, II and old I overall Yes 1 – 10 I, some II 83 4 Presence of Almost none dust Total fraction 13 % 9 Yes E Colour Red S0 Sa Red Sb Sc Blue Sd Irr Blue Stellar Old Old + Old + Intermediate Population Intermediate Intermediate + + Young Young Star Form zero low higher high Rate HI (gas) Zero/ low modest high highest low dust Zero/ Higher highest Lower low (less metals) Dynamics Bulge/halo Disk dominated, so dom. rotation Lecture 3: Views of Galaxies Our view of galaxies is greatly affected by the observing wavelength – the infrared penetrating more deeply that optical radiation, and the HI emission tracing atomic gas, which may be quite differently distributed to the stellar populations: NGC253 at optical and infrared wavelengths M81 at optical wavelengths and using the 21cm wavelength HI tracer of atomic hydrogen gas Spiral Structure The most obvious feature in a spiral galaxy is its spiral structure: o Here, for example, are M101 and M100, with clear ‘grand design’ spiral arms: Flocculent spiral: Structure is made up from young, bright stars Over time, differential motions cause the spiral arms to wind up: The stars in a spiral arm cannot always be the same stars: o Very rapidly, spiral structure will wind up very tightly. There are different types of spiral arms o “Grand-Design” – two well-defined spiral arms (10%) o Multiple-arm spirals (60%) o Flocculent spirals – no well-defined arms at all, “ratty” (30%) Are spiral arms leading or trailing? What is the nature of the arms? So, open spiral structure cannot be maintained in this way. o This problem is usually known as the winding dilemma The solution to this dilemma was finally sorted out by Lin & Shu in 1963. o Their solution was to assume that: Stars follow slightly elliptical orbits The orientations of these orbits are correlated: o o o As is apparent from the above figure, this arrangement produces a spiral density wave: spiral arms are caused by a density perturbation that moves along at a speed different from the speed of the objects within it. The density wave resists the spiral’s tendency to wind up and causes a rigidly rotating spiral pattern material travels around undisturbed elliptical orbits, but sometimes many orbits come close together, so the density increases. So, young bright stars should lie in front of the highest density regions High densities also compress the magnetic fields, which produces a maximum in the radio continuum emission in regions of highest density. So, bright stars should appear "down stream" from the peak in the radio continuum emission. This effect is, indeed, observed, and so the density wave theory is vindicated! In the inner parts of disks, stars are moving faster than the pattern speed and overtake the density wave. In the outer parts, stars move more slowly than the pattern speed, and the spiral arms over take the stars o o o o o o The only remaining question is why orbits arrange themselves in correlated ellipses. o the answer is self organization: o This feedback loop can also generate the bars in SB galaxies Such a runaway process is called a dynamical instability o Note that this process only works if there is enough mass in the disk for the perturbations to modify the gravitational field In early-type spirals (Sa's) where most of the mass is in the bulge not the disk, the instability will be partly suppressed. This suppression explains the anti-correlation between bulge size and strength of spiral structure. Spiral arm pattern is amplified by resonances between the epicyclic frequencies of the stars (deviations from circular orbits) and the angular frequency of the spiral pattern o Spiral waves can only grow between the inner and outer Linblad resonances (p = -/m ; p = + /m ) where =the epicyclic frequency and m is an integer (the # of spiral arms) o o Self propagating star-formation: o Stars outside this region find that the periodic pull of the spiral is faster than their epicyclic frequency, they don’t respond to the spiral and the wave dies out o Resonance can explain why 2 arm spirals are more prominent Note that density wave theory does not explain flocculent spirals. Those can be explained by self-propagating star formation: o Star forming regions produce supernovae, which shocks the gas, which triggers more star formation, etc, etc, etc o Differential rotation stretches out the regions of star formation into trailing, fragmentary arms o No global symmetry (as observed) o Barred Galaxies e.g. NGC 1300: Half of all disk galaxies show a central bar which contains up to 1/3 of the total light Bars are almost as flat as surrounding disks. S0 galaxies can have bars – a bar can persist in the absence of gas Bar patterns are not static, they rotate with a pattern speed, but unlike spiral arms they are not density waves. Stars in the bar stay in the bar. The asymmetric gravitational forces of a disk allow gas to lose angular momentum (via shocks) compressing the gas along the edge of the bar. The gas loses energy (dissipation) and moves closer to the center of the galaxy. Elliptical Galaxies When you have seen one elliptical galaxy, you have pretty much seen them all. So, here is a picture of one such system, the nearby elliptical M32: By studying absorption-line spectra of ellipticals, we can investigate their internal dynamics and masses. Many elliptical galaxies have a projected luminosity distribution that follows a de Vaucouleurs (or R1/4) law, which states that the surface brightness, I, of the bulge of the galaxy (measured in units of L pc-2) shows a radial dependence according to: 1 4 I (r ) r log10 3.3307 1 I r e e where Ie and re represent the surface brightness at a radius Ie. This is often referred to as a r1/4 law – and the distribution is sometimes called a de Vaucouleurs profile. re has in the past been used to represent the radius within which one half of the bulge’s light is emitted. So, a plot of surface brightness in magnitudes versus radius to the quarter power for such a galaxy will appear as a straight line. Note that this law is a purely empirical fit with no physical basis. o However, any theory of elliptical galaxy formation must reproduce it. Dwarf Galaxies Low-luminosity: 106 – 1010 L Low-mass: 107 – 1010 M Small in size, ~few kpc Often low surface brightness, so they are hard to find! Why are dwarf galaxies important?? Majority of galaxies are dwarfs!! Dwarf galaxies may be remnants of galaxy formation process: “proto-dwarf” gas clouds came together to form larger galaxies (hierarchical formation) Dwarf galaxies are currently being “absorbed” by larger galaxies Dwarf galaxies are relatively simple systems, not merger products Different types of dwarf galaxies Dwarf ellipticals (dE): Note that these are structurally very different from luminous E’s. Gas-poor, old stellar population. Note that many dE’s have nuclei (dE,N). Dwarf spheroidals (dSph): Gas-poor, diffuse systems. Low luminosity (low surface brightness end of dE’s. Dwarf irregulars (dIrr): Extreme end of late type spirals. Active, on-going star-formation but low surface brightness (like dSph’s). Gas-rich. Note that there are no dwarf spirals!! In the Local Group, we can study the resolved stellar population (color magnitude diagrams) to determine the star formation histories of dwarf galaxies Dwarf ellipticals are generally old (stars formed > 10 Gyr old), but some may have had more recent (a few Gyr ago) weaker episodes of star formation Dwarf irregulars tend to have quasi-continuous star formation (perhaps interspersed with bursts). Lower luminosity dIrr’s more likely to have a bursty history Environmental effects may play a role (e.g., tidal stripping removing gas from dSph’s) No two galaxies have the same star formation history Dwarfs do not contain dark matter. Collisions and Mergers Approximately 0.3% of galaxies are currently in the process of merging. When two galaxies collide, they initially create long tidal tails and plumes, but ultimately settle down to systems which look very like normal elliptical galaxies. Could this be how the ellipticals formed? Below is a sequence of images of various real galaxies which we see at progressively later stages in the merger process The system shown below, NGC7252, is a system at a very late stage of merging – this is shown in successively deeper images of the system – which appears with the short integrations, to be a single galaxy. NGC7252 above provides the "smoking gun" which shows that mergers between galaxies can produce elliptical galaxies. This HST Image below is of the ‘Cartwheel galaxy’, and is a particularly impressive example of what can happen when two galaxies collide face-on. It is likely that the Milky Way will collide and merge with the Andromeda Galaxy in about 3 billion years from now. Clusters of Galaxies Galaxies are not distributed at random in the sky - most are found in clusters: o Poor clusters contain ~ 10 - 100 galaxies of all types (spirals, ellipticals & irregulars). See, for example the local group. o Rich clusters contain ~ 100 - 1000 galaxies Mostly ellipticals Often dominated by 1 or 2 giant ellipticals (designated "cD" galaxies) near their centres. Here, for example, is a picture of the centre of the Coma cluster, the nearest rich cluster of galaxies, which is dominated by two giant ellipticals: Clusters are supported against collapse by the random motions of the galaxies: (c.f. the motions of stars within elliptical galaxies) o So, we can estimate their masses using the same formula as for elliptical galaxies, o For a rich cluster, the sizescale r ~ 1 Mpc and typical random velocities, v ~ 1000 km s-1, giving a mass estimate of M ~ 2 x 1014 M . A typical rich cluster contains ~ 1000 galaxies each with the luminosity of the Milky Way (~ 1010 L ). So the mass-to-light ratio of the whole cluster is M / L ~ 20 solar units. ~ 95% of the material in a cluster of galaxies is dark! o o cD Galaxies and Cannibalism How do the giant "cD" galaxies found at the centres of some clusters form? Perhaps by repeatedly merging with other cluster members. Why do these mergers occur at the centre of the cluster? o Because dynamical friction makes galaxies lose kinetic energy: The motion of a galaxy creates an enhanced "wake" of galaxies behind it The excess gravitational pull of this wake slows the motion of the galaxy --- it is a frictional force. The net effect of this force is to make a galaxy slowly spiral in toward the centre of the cluster (the point of lowest energy). Once there, it will merge with all the galaxies that have proceeded it. Evidence for this scenario comes from the large number of "multiple nuclei" seen in cD galaxies: o o o These secondary condensations of light leftover mergers – M31 is another example: