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    Planck spectra At low frequencies the Planck function is a power law This is called the Rayleigh Jeans Approximation B has a peak at o h o 2 83 kT or The peak depends only on the temperature Exponential cutoff for h h o This is called Wien s limit Some images Types of EM radiation and their sources Electromagnetic spectrum The depth of the atmosphere through which EM radiation can travel Another one Energy level diagram for hydrogen emission lines Emission lines for some gases Kirchhof s laws of emission and absorption Planck spectra for stars of different colour Absorption lines in a Planck spectrum General absorption by clouds Rotational broadening of a line Absorption spectra for stars of different spectral type Relative flux as a function of wavelength for different spectral types Relative strengths of lines for different spectral types Astrophysical Transitions Atomic Transitions for Hydrogen Line Transition Wavelength L α 1 2 1 1215 67 L β 1 3 1 1025 72 L γ 1 4 10 792 54 Lyman limit 1 10 911 8 0 H α 2 3 1 6562 80 H β 2 4 1 4861 32 H γ 2 5 1 4340 46

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/spectro.html (2016-02-13)
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    Question based on this LF what would you surmise on the total number of galaxies in a given volume Consider total number of galaxies in a given volume For 1 diverges infinite number of low L galaxies There must be a faint end cutoff somewhere M V 8 or so UNCLEAR However many values of in this part of LF Can be uncertain difficult to determine Why The total luminosity

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/glf.html (2016-02-13)
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    but not of any galaxy perhaps globular clusters Question Where did the intracluster material come from The Coma Cluster HST image Nearest rich cluster of galaxies 100 Mpc Roughly spherical in shape relaxed cluster Diameter 4 5 6 8 Mpc Over 10 000 galaxies mostly dE s Luminous galaxies Less than 10 are spirals the rest are E S0 Morphology Density Relation see below E S0 especially in core regions 2 giant cD galaxies in central regions common in rich dense clusters Compare with Virgo The Morphology Density Relationship Denser clusters fewer Sp galaxies more E S0 galaxies Dressler 1980 ApJ 236 351 E S0 galaxies in high density regions more in rich clusters S Irr galaxies in lower density regions groups outer parts of clusters very few in rich clusters Perhaps increased interactions in richer clusters Perhaps E galaxies preferentially formed in rich clusters Which Both Not clear yet Other examples of cluster galaxy evolution Higher z clusters More blue vs red galaxies than observed locally Butcher Oemler effect More episodes of star formation in past Observe more spirals interacting galaxies in rich clusters at high z Importance of mergers in galaxy evolution It is clear that we are seeing a marked evolution of galaxies in the cluster environment Question Can you think of some mechanisms where this happens In a hierarchical universe larger scales form last Thus clusters are among last entities to form Cluster Masses To derive masses of galaxy clusters a few ways Virial Mass If a cluster is virialized 2K U 0 relaxed we can use the size and of the cluster to get a mass estimate as with elliptical galaxies Problem some clusters are irregular Outer regions still falling in substructure not virialized Confusion for cluster size and velocity field Recall where is 5 for a uniform spherical distribution actual value depends on details of orbits Thus Note more robust mass estimators are used Some typical masses of clusters Poor clusters 500 800 km s d 1 3 Mpc M 10 14 h 1 M or more Rich clusters 800 km s d a few Mpc M 10 15 h 1 M A historical note Zwicky 1933 Coma too high for observed galaxies Unseen matter Dark matter in galaxy clusters Intracluster gas Hot 10 7 to 10 8 K gas throughout clusters called intracluster medium High T X rays 1 to 10 keV photons Where does this energy come from Thermal Bremsstrahlung process braking radiation At these temperatures H is ionized and most everything else plasma Galaxy clusters readily emit X rays some clusters found via X ray surveys Luminosity density from bremsstrahlung in a pure H gas l d 5 44 10 39 4 n e 2 T 1 2 e h kT d where l energy per unit volume per unit time n e density of free electrons T gas temperature Total luminosity density of gas in cluster Assume an isothermal sphere with radius R and of pure H Example the Coma

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/cluster.html (2016-02-13)
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    A more massive object will feel a greater effect also Example a massive star cluster or small galaxy in a galactic halo will slowly spiral lose kinetic energy towards the galaxy centre But how long will this take Consider a globular cluster in a circular orbit a distance r from a galaxy within the dark matter halo of the galaxy Recall for DM halo MW v v c 220 km s assume same for GC Angular momentum L m v r mvr for circular orbit As F d works against motion of GC TORQUE If v GC constant How long does it take to go from r i to r 0 Example A massive M 5 10 6 M globular cluster in a circular orbit about the Milky Way Inside what galactocentric distance r will such GC s C 76 have spiralled into the MW nucleus in a Hubble time age of the universe expect all GC s of this mass within 4 kpc to have spiralled in by now Bottom line t df is small for small r or v large M Perhaps some galactic nuclei have incorporated massive GCs M31 double nucleus due to dynamic friction Important implications of dynamical friction GC s orbiting galaxies Formation of some nuclei Some not all dE nuclei GC s Galaxy mergers Decrease in orbital KE due to DF orbital decay Formation of giant cD galaxies in cluster centres Galactic cannibalism Accretion of small galaxies by larger ones Eventual fate of LMC SMC certainly for Sgr dE Note that the timescales here make assumptions about the dark matter halo Question How do you think the presence or absence of dark matter affects galaxy interactions What about high speed encounters eg Cartwheel ring galaxy Timescales so short stars cannot react to interaction ie no wake Impulse approximation Here stars do not move much during encounter U essentially unchanged related to mass distribution Consider total energy E of the system s Virial Theorem 2K U 0 2K U 2E During encounter K f K K E f K U E i K After 2K U 2 K i K U 2K i U i 2 K 2K i U i 0 2K U 2 K NOT in virial equilibrium System eventually re establishes virial equilibrium K f E f E i K E i K K i K Net KE lost by system s How Some KE to motion of individual stars Escape of highest v stars evaporation System s may re adjust slightly so that some K U Change in distribution of stars change of shape puffing up Tidal stripping Consider the interaction between a large galaxy mass M and a smaller galaxy with mass m and radius R Near side of m Far side of m Assuming R r 1 Stars tidally removed by forces from large galaxy forming streamers and tails on the merging galaxies eg Antennae Tidal tails gas or stars can have SF going on A numerical simulation of

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/merg.html (2016-02-13)
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    High z Galaxies are probably more gas rich Toy model for gas fraction evolution Z form 3 M 0 3 Λ 0 7 Model Gyr f b z 0 Sa 3 0 05 Sb 5 0 1 Sc 10 0 3 Under threshold models for star formation e g Quirk 1972 Kennicutt 1989 these gas rich galaxies may be nearer to the critical threshold for star formation e g semi analytic modeling by Kauffmann 1996 z 0 z 2 5 Gas concentrates at high densities and is more prone to local gravitational collapse high z interactions may be much more efficient at driving global disk wide starburst activity We may be seeing this in the very knotty appearance of high redshift galaxies HST medium deep survey image and multiwavelength images of high z galaxies Bunker et al 2000 Griffiths et al 1995 What about inflows and nuclear starbursts Are high z disks any more or less stable than low z disks Hints Out to z 1 there seems to be only mild evolution of luminous disk galaxies e g Driver et al 1995 Vogt et al 1997 Lilly et al 1998 N body Steinmetz and Navarro 2000 and semi analytic Kauffmann 1996 Baugh et al 1996 models suggest that bulges of luminous spirals are assembled by z 1 1 5 or so At higher redshift there is some observational evidence for a decrease in B D ratio At higher redshift there is also indications that the observed galaxy population is more compact figure from Marleau Simard 1998 data from Cohen et al 1996 Steidel et al 1996 Zepf et al 1997 Lowenthal et al 1997 So where does that leave us z 0 5 galaxies evolve towards more quiescent interactions But spectacular exceptions exist 0 5 z 1 disks more

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/evolution.html (2016-02-13)
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    3 0 3 pc Perryman et al 1998 A A 331 81 CMD of Hyades List of m M o for Hyades over 60 years How does is compare with moving cluster Pleiades also used calibrated with parallaxes but it s further away Also possible systematic error Hipparcos m M 0 3 from other methods Always have to be careful Globular Clusters No nearby globulars no parallaxes Use local subdwarfs metal poor stars to make a known MS Fit to cluster MS distance Much recent controversy Recent subdwarf p from Hipparcos suggests old GC distance scale too small Clusters up to 0 2 mag further Problems Not many subdwarfs Secondary Distance Indicators These are techniques that require local calibration ie parallax MS fitting etc Higher rungs in distance ladder Usually luminous objects Many methods More than listed here Standard Candles Cepheids RR Lyraes Planetary Nebula Luminosity Function Globular Cluster Luminosity Function Supernovae Ia Tip of the Red Giant Branch Surface Brightness Fluctuations Novae Dynamical methods Tully Fisher spirals D n Relation ellipticals Cepheids Luminous pulsating variable stars Evolved high mass stars cross instability strip of the HR diagram See Figure 14 6 in text Follow a Period Luminosity PL relation M V 2 to 6 5 Very reliable indicator often used to calibrate other methods Useable to 20 30 Mpc with the HST Cepheid in action Basic idea Observe period P average m of Cepheid Get M V L from PL relation Distance The PL relation Actually a PLC relation but reduced to PL relation Often debated Usually calibrated using LMC Cepheids what problem might arise Scatter in PL relation dependent IR less scatter but sky brightness higher Slope well determined Cepheids in clusters Zeropoint what we need for distance Advantages Solid physical basis well understood Very characteristic light curve Small dispersion in PL relation reliable candle Disadvantages Require many observations Extinction problems Cepheids in spirals Spirals usually in outer regions of clusters Calibration usually tied to d LMC Metallicity effects changes in internal structure Also W Virginis stars pop II Cepheids Have PL relation but fainter by 1 5 mag factor of 2 in distance Early confusion LMC distance moduli note the range of values HST Key Project One primary goal of HST galactic distances from Cepheids nearby galaxies only See HST Key Project flow chart Project observe 18 galaxies in V I filters Find study Cepheids Fit observed PL relation to that of the LMC Get d based on m M o 18 5 about 50 kpc for the LMC and E B V 0 10 for LMC Project complete final results almost all published But this will not be the final word RR Lyraes Also pulsating variables but Evolved old low mass low Fe H stars In globular clusters galactic halos Lower luminosity M V 0 3 0 8 than Cepheids Do not follow a PL relation Most have P 0 4 0 6 days Advantages Similar to Cepheids Halos globular clusters less dust Disadvantages Low L

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/eds.html (2016-02-13)
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    elliptical galaxies Highly luminous variable AGN Luminosity can vary by a few orders of magnitude in short timescales days No thermal component only power law continua No absorption nor emission lines in their cores None have radio lobes some have jets emitted directly from the active core BL Lac produced when active core observed almost directly down the jet towards the central opening of the accretion disk Cool picture Gamma ray image of blazar 3C 279 Quasars QUASARs radio loud Quasi Stellar Radio Sources QSOs radio quiet Quasi Stellar Objects Of all quasi stellar AGNs 90 are QSOs QSOs resemble mostly Sey Is bright power law continua and broad emission lines Some absorption lines CIV and MgII associated with QSO itself QSO s have very high luminosities Some with L 10 13 15 L 3C 273 L few 10 12 L Most luminous objects in the universe Most luminous quasars are 10 5 times more energetic than the Milky Way Excess UV light relative to stars of similar colours quite blue in appearance U B 0 4 surveys yield mostly quasar candidates 3C 3rd Cambridge catalog of radio sources 1957 Most without optical counterparts A few stellar looking counterparts showed unusual spectra 3C 273 spectrum strongly red shifted H lines M Schmidt 1963 v r 44 000 km s Suggestive of large distances cosmological Many more found since then 5000 Most with large z 3C 273 quite close actually 2000 a few with z 5 QSO s often variable over small time scales hours or days Energy emitted from a small region t 1 hr R 1 07 10 9 km z 0 15 3 5 10 5 pc or 7 AU HST CFHT Hi Res images showed they are surrounded by material host galaxy Bottom line QSO s are

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/agn.html (2016-02-13)
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    absorption systems and high z galaxies b QSO Pairs Rarely closer than few arcminutes scales few hundred kpc Cross identification can be difficult due to crowding at high z and the large separation A study of QSO pairs with transverse separation 1 2 h 1 Mpc Sargent et al 1982 concluded that there is too little coherence across the plane of the sky to account for the large pancakes predicted by the HDM model However less densely populated C IV forests suggested large structure Coherent absorption in the Lyman forest may be missed due to cross identification difficulties Gaseous structures with large coherence usually come from large column density systems Eventually evidence was found for large structure in lower density clouds at lower redshifts In all studies spherical clouds were assumed However spherical clouds of the sizes and densities measured would be highly ionized and the total baryon count would overfill the universe The simplest explanation which allows for a denser and more neutral gas at such large transverse sizes is that the Lyman clouds are flattened All of the above cloud parameters argue against the typical Lyman forest originating in potential wells of already formed galaxies Pie diagrams for galaxies and absorbers Cosmological Significance of the Lyman Forest Hydrodynamic Simulations of the Lyman Forest By early 1990 s numerical hydrodynamic cosmological simulations became capable of quantitative predictions of IGM and the high z Lyman forest from initial conditions of a given structure formation model Lyman forest is completely described by the Hubble constant gas density temperature perculiar velocity neutral fraction along LOS The correspondence between Lyman forest absorbers and physical properties of the underlying structure can be examined by predicting the above quanities for simulated QSO LOS Basic properties of the Lyman forest turn out to be only weakly dependent on the cosmological model The Nature of Lyman Absorbers A generic picture has emerged from these studies Column Density Structure log N HI 14 sheet like structure with length scale few hundred kpc like small Zeldovich pancakes log N HI 14 filament structure extending over Mpc distances with thickness 40 100 kpc log N HI 16 invariably spherical This confirms and earlier result that a large fraction of baryons 80 90 resides in low column density Lyman forest 14 log N HI 15 5 The density temperature diagram from simulations reveals signifcant departures from thermal photoionization equilibrium in all but the highest density gas The relation is steeper at lower densities because of expansion cooling for low density clouds adiabatic compression and shock heating for higher density clouds The low temperatures due to adiabatic cooling and the expansion due to low density in the voids ensure that line broadening is dominated by bulk motion for column densities log N HI 13 HI column density contours Density temperature diagram of the Ly forest Matching the Observations Simulations have been very successful in matching overall observed properties of the absorption system Broad wings in weak lines expected from bulk motion broadening

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/lyman.html (2016-02-13)
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