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1 Galaxy Classification 2 Spirals 3 Ellipticals 4 Comparison 5 Multiwavelength 6 Spiral Rotation and Arms 7 Barred Spirals 8 Dwarf Galaxies 9 Galaxy Luminosity Function 1. 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: The Zoo: Sloan Digital Sky Survey http://www.galaxyzoo.org/ Four main types of galaxies – Hubble proposed a scheme for classifying galaxies in his 1936 book, The Realm of the Nebulae Ellipticals (20%)(E) Lenticulars (SO or SB0) S01, S02, S03 – strength of dust absorption, S01 has none SB01, SB02, SB03 – prominence of bar Spirals (77%)– normal (S) (SA) or barred (SB) Sa – Sc depending on bulge/disk ratio, tightness of spiral arms, and gas content Irregulars (3%)(do not fit into above category) 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 an 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 2 Spiral Galaxies 2.1 Classification de Vaucouleurs introduced several important features: Continuity of barred and non-barred spirals (through mixed types SA-SAB-SB) Continuity of spirals into irregulars Sc-Scd-Sd-Sdm-Sm-Im (m means Magellanic, the LMC being the prototype): Rings. Galaxies are divided into those possessing ring-like structures (denoted ‘(r)’) and those without rings (denoted ‘(s)’). So-called ‘transition’ galaxies are given the symbol (rs). Hoag’s object: (183Mpc) 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. ▪ ▪ ▪ ▪ Sa - tightly-wound, smooth arms, and a bright central disc Sb - better defined spiral arms than Sa Sc - much more loosely wound spiral arms than Sb Sd - very loose arms, most of the luminosity is in the arms and not the disc Normal spiral galaxies are designated S* or SA*. 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. Logarithmic Spirals: The "*" is chosen from a, b or c, and was originally classified on the basis of the pitch angle of the spiral arms: The derivative r'(θ) is proportional to the parameter b. In other words, it controls how "tightly" and in which direction the spiral spirals. In the extreme case that b = 0, the spiral becomes a circle of radius a. Conversely, in the limit that b approaches infinity the spiral tends toward a straight line. o Note that late-type spiral galaxies (Sc's) also tend to have: smaller bulges more "grand design" spiral structure M65 Sa : Triangulum, 900kpc, M33, SA(s)cd: M51a and M51b – whirlpool SA(s)bc + SB0pec, 7 Mpc M31, 780kpc, Andromeda SAb 2.2 Irregular Irregular galaxies come in two types: • Irr I which are in some sense a logical extension of the Hubble tuning fork, having characteristics "beyond" those of class Sc - high gas content, dominant presence of a young population. Irr I galaxies may show bar-like structures and incipient spiral structure like the Large Magellanic Cloud, below. Such galaxies are sometimes referred to as "Magellanic Irregular" galaxies. NGC1427a: The LMC Large Magellanic Cloud • Irr II which are galaxies which defy classification because of some form of disturbance. M82, shown below, is undergoing an intense period of star-formation. 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 Msun o . 2.3 Spiral Properties 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). About 90% 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 Surface Brightness. At large radii, face-on disk galaxies typically have exponential luminosity profiles; the log of the surface brightness falls as a linear function of radius, or The total luminosity of an exponential disc profile I(R) = Io exp(-R/Ro) is given by 2I o Ro2 , where I0 is the (extrapolated) surface brightness at the center of the disk, and R0 is the disk's exponential scale length. At smaller radii, the luminosity profile may deviate either above or below the exponential line; the former are known as `Type I' profiles, the latter as `Type II' ( Barred Spirals). Observations of edge-on disks show that most of the luminosity comes from a rather thin component which is reasonably well-fit by 2 I(z) = where z I(z=0) sech2 (z/2zo) . sech(z)=2/[exp(z)+exp(-z)]. Colours. The integrated colours of disk galaxies reveal trends with morphological type; S0 and Sa galaxies are red, while Sc and Sd galaxies are blue. These trends reflect different rates of star formation; broadband colors are sensitive to the average star formation rate over the last 108 years. 2.4 Barred spirals A large fraction of disk galaxies have bars: narrow linear structures crossing the face of the galaxy. In barred S0 galaxies the bar is often the only structure visible in the disk. In types SBa and later the bar often connects to a spiral pattern extending to larger radii (e.g. NGC 1300). Viewed face-on, bars typically appear to have axial ratios of 2. The surface brightness within the bar is often fairly constant. Some bars appear to be ‘squared off’ at the ends. The true 3-D shapes of bars are difficult to determine, but many appear to be no thicker than the disks they occur in; if so then bars are the most flattened triaxial systems known Bars in edge-on galaxies are hard to detect photometrically; however, kinematic signatures of barred potentials have been used to infer their presence in some edge-on systems. What is noteworthy is that such edgeon bars appear to be associated with boxy or peanut-shaped bulges. M58 SBb: 3 Elliptical Galaxies When you have seen one elliptical galaxy, you have pretty much seen them all. Here is a picture of one such system, the nearby elliptical M32: 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. So, elliptical galaxies are designated "E#," where # refers to their apparent flattening: o # = 10(1 - b/a) M89: E0 M59 E5 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 Disky: normal and low luminosity ellipticals, which have nearly isotropic random velocities but are flattened due to rotation. 3-D shapes – ellipticals are predominantly triaxial ellipsoids: Oblate: A = B > C (a flying saucer) Prolate: A > B = C (a cigar) Triaxial A > B > C (A,B,C are intrinsic axis radii) 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) It was once thought that the shape of ellipticals varied from spherical to highly elongated. The Hubble classification of elliptical galaxies ranges from E0 for those that are most spherical, to E7, which are long and thin. It is now recognized that the vast majority of ellipticals are of middling thinness, and that the Hubble classifications are a result of the angle with which the galaxy is observed. In between the ellipticals and the spirals are the S0s which have o very large bulges o weak disks o no spiral structure Surface Brightness. Many normal bright (Mv < -17) elliptical galaxies and the bulges of spirals have a projected luminosity distribution that follows a de Vaucouleurs. (or R1/4) law. The surface brightness, I, of the bulge of the galaxy (measured in units of L pc-2) shows a radial dependence according to: where Re is the radius of the isophote containing half the total luminosity, and Ie is the surface brightness at Re. This is often referred to as a r1/4 law – and the distribution is sometimes called a de Vaucouleurs profile. Note that this law is a purely empirical fit with no physical basis. However, any theory of elliptical galaxy formation must reproduce it. Cores of Ellipticals • Seeing corrections are important; moreover, it's generally not possible to make corrections without some assumptions about the underlying luminosity distribution • Few E galaxies actually have flat luminosity profiles at small radii; instead, the profiles rise inward to the last measured point . • Cores may exhibit unusual kinematics; for example, about a quarter of all elliptical galaxies have cores which appear to counter-rotate with respect to the rest of the galaxy . • Although such `kinematically decoupled' cores are generally not photometrically distinct, several E galaxies with decoupled cores have features in their line-strength profiles coincident with the kinematically decoupled regions . • A few nearby E galaxies have nuclear star clusters with densities much higher than the cores they reside in; some of these nuclei may be rotating, disk-like systems. Shapes of Ellipticals • Projected axial ratios range from b/a = 1 to ~0.3, but not flatter (Schechter 1987). • Apparent ellipticity is generally a function of projected radius, with a wide range of profiles. • Isophotal twists are common. Because it is highly unlikely that intrinsically twisted galaxies could be dynamically stable, such twists are generally interpreted as evidence for triaxiality . • Elliptical galaxies are not elliptical; isophotes may depart significantly from perfect ellipses. A Fourier analysis of isophotal radius in polar coordinates implies that most E galaxies are either `boxy' or `disky' . Kinematics of Ellipticals • The rotation velocities of bright E galaxies are much too low to account for the flattenings we observe; fainter E galaxies, however, rotate at about the rates implied by their shapes (Davies 1987). • E galaxies may exhibit minor-axis rotation; more generally, the apparent rotation axis and the apparent minor axis may be misaligned. While in most galaxies these misalignments are modest, a few galaxies appear to rotate primarily about their minor axes. Larger galaxies have fainter effective surface brightnesses. Mathematically speaking: effective radius, and As (Djorgovski & Davis 1987) where Re is the is the mean surface brightness interior to Re. , we can substitute the previous correlation and see that and therefore: meaning that more luminous ellipticals have lower surface brightnesses. More luminous elliptical galaxies have larger central velocity dispersions. This is called the Faber-Jackson relation (Faber & Jackson 1976). Analytically this is: . Shells & Other `Fine Structures' • The surface brightnesses of E galaxies do not always decline smoothly with radius. When a smooth luminosity profile is subtracted from the actual surface brightness, `shells' or `ripples', centered on the galaxy, are seen. • The fraction of field E galaxies with shell-like features is at least 17% and possibly more than 44%. • The colours of shells indicate that they are composed of stars. In many cases the shells are somewhat more blue than the galaxies they occupy. • Shell systems have a variety of morphologies; some galaxies have shells transverse to the major axis and interleaved on opposite sides of the center of the galaxy, while other galaxies have shells distributed at all position angles . • Profile subtraction sometimes reveals other kinds of structures in E galaxies, including embedded disks, linear features or `jets' (not the jets seen in AGNs!), `X-structures', etc.. Gas & Dust in Ellipticals • When examined with sufficient resolution, 25% to more than 40% of E galaxies show features due to dust absorption. • The dust lanes seen in E galaxies imply that the absorbing material is distributed in rings or disks. Dust lanes may be aligned with either the major or minor axes, or they may be warped. • E galaxies contain modest amounts of cool and warm gas, although not as much as is found in S galaxies. A few E galaxies have extended disks of neutral hydrogen. • X-ray observations indicate that many ellipticals contain 10^9 to 10^10 solar masses of gas at temperatures of ~10^7 K; this hot gas typically forms a pressure-supported `atmosphere' around the galaxy. Tidal Features • Elliptical galaxies in rich galaxy clusters often exhibit luminosity profiles which fall below a de Vaucouleurs law at large radii. Such downturns are often attributed to tidal truncation in the mean field of the cluster (K82). • In contrast, E galaxies with close companions often have luminosity profiles which rise above a de Vaucouleurs law at large radii. These features may be plausibly blamed on tidal interactions. • E galaxies in closely interacting systems sometimes exhibit outer isophotes which are visibly egg-shaped and/or offset with respect to the centers of their galaxies. Again, tidal effects are strongly implicated (K82, Borne et al. 1988). • On very deep exposures, some E galaxies are seen to have `plumes' or `tails', while others (e.g. NGC 5128) show rather irregular luminosity distributions. Tail-like features may be signatures of major mergers involving one or more dynamically cold disk galaxies (Schweizer 1987). 4 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 The Colour-Magnitude Diagram: Colour: Large automated imaging surveys are better at defining a galaxy's colour rather than morphology. it is more natural to describe a galaxy as being on the ‘red sequence’ or ‘blue sequence’ rather than being an ‘early type’ or ‘late type’. This interpretation also has the advantage that galaxy colours are directly related to the star formation, dust and metal-enrichment history of the galaxy and can thus be more readily interpreted in theoretical models The bimodal distribution of red and blue galaxies as seen in analysis of Sloan Digital Sky Survey data[2] and even in de Vaucouleurs' 1961 analyses of galaxy morphology. Three features: the red sequence, the green valley the blue cloud. The red sequence includes most red galaxies which are generally elliptical galaxies. The blue cloud includes most blue galaxies which are generally spirals. In between the two distributions is an underpopulated space known as the green valley which includes a number of red spirals. Unlike the comparable HR diagram for stars, galaxy properties are not necessarily completely determined by their location on the color-magnitude diagram. The diagram also shows considerable evolution through time. Colour (U-R) versus stellar mass relations for different environments. Panel (a): void-like environments while Panel (f) cluster-like environments. [Conclude: Hubble sequence applies to other properties.] 5 Multiwavelength Views of Galaxies Our view of is greatly affected by the observing wavelength – the infrared penetrates deeper than optical radiation. M101, a nearby Sc galaxy: The Whirlpool: M51…below Chandra (X-ray) and ISO (mid-IR): The x-ray image (left) highlights the energetic central regions of the two interacting galaxies. Much of the diffuse glow is from multimillion degree gas. Many of the point-like sources in the x-ray image are due to black holes and neutron stars in binary star systems. Mid-IR light (right) is well-suited to studying star formation and tracing dust in spiral galaxies. This image not only shows the galaxy cores and spiral arms, but nicely illustrates the knots of star formation occurring in the arms of M51. M104: (SAa, 9 Mpc) Spitzer's infrared view of the starlight, piercing through the obscuring dust, is easily seen, along with the bulge of stars and an otherwise hidden disk of stars within the dust ring. NGC253 at infrared,optical and X-ray wavelengths M81 at optical wavelengths and using the 21cm wavelength HI tracer of atomic hydrogen gas. The spiral structure is clearly shown in this image, which shows the relative intensity of emission from neutral atomic hydrogen gas. In this pseudocolor image, red indicates strong radio emission and blue weaker emission. 6 SPIRAL ROTATION Basic components of Spirals reviewed: Disks: metal rich stars and ISM, nearly circular orbits with little random motion, spiral patterns Bulge: metal poor to super-rich stars, high stellar densities, mostly random motion – similar to ellipticals Bar: present in 50 % of disk galaxies, long lived, flat, linear distribution of stars Nucleus: central (<10pc) region of very high mass density, massive black hole or starburst or nuclear star cluster Stellar halo: very low surface brightness (few % of the total light), metal poor stars, GCs, low-density hot gas, little/no rotation Dark halo: dominates mass (and gravitational potential) outside ~10kpc, nature unknown? Luminosity profiles: (1D): Exponential disk: I(r) = I0 exp(-r/rd) rd= disk scale length, typically ~2-6 kpc Light falls off sharply beyond Rmax ~3-5rd In the central regions, also see light from the bulge Bulge follows the r1/4-law, like ellipticals Vertical disk structure: The surface brightness perpendicular to the disk is also described by a exponential or better by a sech law I(z) = I(0) exp(-|z|/z0) I(z) = 0.25 I(0) sech2 (-z/2z0) …… recall sech(z)=2/[exp(z)+exp(-z)] z0 is the scale height of the vertical disk Different populations have different scale heights. In the Milky Way: Young stars & gas ~ 50pc Old thin disk ~ 300-400 pc (older stars, like the sun) Thick disk ~1 – 1.5 kpc (older, metal-poor stars) Best interpretation of many of these is a trend in star formation history Early type spirals formed most of their stars early on (used up their gas, have older/redder stars) Late type spirals have substantial on-going starformation, didn’t form as many stars early-on (and thus lots of gas left) Spirals are forming stars at a few Msun per year, and we know that there is ~a few x 109 Msun of HI mass in a typical spiral Rotation curves of other galaxies On the left, a spiral galaxy image, with spiral arms delineated by HII regions. On the right, the light from 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. We can measure rotation curves via: HI mapping: 21cm emission from atomic hydrogen Via optical spectroscopy: Optical absorption lines from the stellar component or Optical emission lines from hotter gas. ◦ More luminous galaxies have higher rotation velocities, later type galaxies have slower rise in velocity rotational velocity is constant, so that means M r beyond limits of stellar disks, which are showing an exponential drop off in light (and thus mass) anyway! Tully-Fisher Relation: Tully & Fisher (1977) found that L Vmax where ~ 4 The Tully-Fisher relation for spiral galaxies, (and the Faber-Jackson relation for ellipticals), follow from the dynamics if we assume constant mass-to-light ratio and surface brightness. Plot the maximum circular velocity of spiral galaxies against their luminosity in a given band: Find that L and Vmax are closely correlated Tully-Fisher relation Smallest scatter when L is measured in the red or the near-infrared wavebands m Vrot /R=GMm/R 2 2 2 so M is proportional to Vrot R • the observed flux or Luminosity L of a galaxy ◦ can be determined photometrically ▪ eg. simply integrating the surface brightness to determine the total flux or Luminosity from the galaxy. ◦ which is a function of the (visible) mass (more massive - more stars - more emission) Assuming all galaxies have the same M/L ratio and the same surface brightness, then the relation L is proportional to Vrot4 In part, Tully-Fisher relation reflects simple gravitational dynamics of a disk galaxy (see problem 5.10 in textbook). Estimate the luminosity and maximum circular velocity of an exponential disk of stars. Luminosity Empirically, disk galaxies have an exponential surface brightness profile: I(R) I(0) exp[-R / hR] …with central surface brightness I(0) a constant. Integrate this across annuli to get the total luminosity: L 2R I(0) exp[R/ hR] dR Can integrate this expression by parts, finding: L I(0)hR2 2 i.e. for constant central surface brightness, luminosity scales with the square of the scale length. Spiral Structure The most obvious feature in a spiral galaxy is its spiral structure: o Here, for example, is M101 with clear ‘grand design’ spiral arms: Flocculent spiral: NGC 4414 Structure is made up from young, bright stars Because disk galaxies rotate differentially, the orbital period is an increasing function of radius R. Thus if spiral arms were material features then differential rotation would would soon wind them up into very tightly-coiled spirals. The expected pitch angle of material arms in a spiral galaxy like the Milky Way is only about 0.25 degrees. In fact, pitch angles measured from photographs range from about 5 degrees for Sa galaxies to 20 degrees for Sc galaxies (Kennicutt 1981). The most likely implication is that spiral arms are not material features. First ingredient for producing spiral arms is differential rotation. For galaxy with flat rotation curve: V(R) constant (R) V R Angular R1 velocity Any feature in the disk will be wrapped into a trailing spiral pattern due to differential rotation. o o Open spiral structure cannot be maintained in this way. This problem is usually known as the winding dilemma In the 1950's it was thought that magnetic fields could be the mysterious generators of spiral structure. 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? 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 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 o Properties of spiral arms can be explained if they are not rotating with the stars, but rather density waves: • Spiral arms are locations where the stellar orbits are such that stars are more densely packed. • Gas is also compressed, possibly triggering star formation and generating population of young stars. • Arms rotate with a pattern speed which is not equal to the circular velocity - i.e. long lived stars enter and leave spiral arms repeatedly. …..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 • Pattern speed is less than the circular velocity material travels around undisturbed elliptical orbits, but sometimes many orbits come close together, so the density increases. The only remaining question is why orbits arrange themselves in correlated ellipses. o the answer is self organization: This feedback loop can also generate the bars in SB galaxies o 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 (frequency of radial oscillations) and m is an integer (the # of spiral arms) o Define the epicyclic frequency via: 2(R) 1/R 3 d/dR R22 o For a point mass gravitational field, . 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 7. 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. 8. Dwarf Galaxies Dwarf Elliptical Faint, M > -18, 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!! There are probably lots of these, in the Local Group there are >30! 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…..however: 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 9. Galaxy Luminosity Function Count the number of galaxies as a function of luminosity (or absolute magnitude) Useful for: Understanding galaxy formation (distribution by luminosity implies distribution by mass – how many galaxies of a given type and mass were formed Galaxy evolution models – either must reproduce observed LFs (hierarchal formation models) or assume them (and work backwards in time). Can also measure evolution in LFs vs. redshift! Galaxy Properties Schechter (1976) found that (L)dL = *(L/L*) exp{-L/L*}d(L/L*) (L)dL = number of galaxies per unit volume with luminosities between L and L+dL Where L* = 1.9 x1010h72-2 Lsun is a characteristic luminosity cutoff, is the powerlaw slope at the faint end, * is the normalization (# galaxies/Mpc3) This function is a power law for L< L* , but cuts off rapidly for L > L* Usually measured in magnitude: (M)dM = (0.4 ln10)x * x 10 0.4(+1)(M*-M) x exp{-10 0.4(M*-M)}dM * = 0.45 x10-2h723 Mpc-3 Schechter Function by galaxy type and environment Field – dominated by Spirals, faint end dIrr Clusters – many more E/S0 galaxies, faint end dE, more dwarfs than in field Approximate Schechter values: M* ~ -20.5 (in B), depends on H0 L* ~ 2 x 1010 L (~Milky Way) ~ -1 to –1.5 , often take -1 . 2 5 Normalization is uncertain! Integrating the Luminosity Function n* = 8 x 10-3 Mpc-3 L* = 1.4 x 1010 Lsun …where Lsun = 3.9 x 1033 erg s-1 is the Solar luminosity. Illustrative 1. Total Number of Galaxies: If we integrate the Schechter function, we get the total number of galaxies (per Mpc3), we find: N = ∫0 (L)dL = * L* (+1) Where is the gamma function, (j+1)=j! when j is an integer If <-1, (+1) is undefined (!), and N is infinite!! 2. Total Luminosity of Galaxies: We can also integrate to find the total luminosity total lum = ∫0 L (L)dL = * L* (+2), which diverges if < -2 so the total amount of light is finite! (Phew!!) Dominated by galaxies with L ~ L* for typical value of . Mass function of galaxies For stars, measurements of the luminosity function can be used to derive the Initial Mass Function (IMF). For galaxies, this is more difficult: • Mass to light ratio (M/L) of the stellar population depends upon the star formation history of the galaxy. • Image of the galaxy tells us nothing about the amount and distribution of the dark matter. More difficult measurements are needed to try and get at the mass function of galaxies.