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    disk to 20 25 kpc Scale length h R 3 5 kpc Distance where density drops to 1 e of original disk exponential ie Two primary components Thin Disk dominant visible component Young stars Fe H 0 5 to 0 3 Vertical scale height z 100 300 pc e r z Depends on spectral type age Based on data from Mihalas and Binney 1981 Galactic Astronomy Structure and Kinematics M thin 6 10 10 M M gas dust 0 5 10 10 M Thick Disk Primarily old er stars Fe H 0 5 mainly z 1 2 kpc not well constrained M thick 0 2 0 6 10 10 M Thus can model disk as superposition of these o 0 02 pc 3 for 4 5 M V 9 5 Bulge inner R 3 kpc spheroidal component Generally older stars but some young ones Fe H 1 1 Weak bar present M thick 10 10 M Stellar Halo outer R 40 kpc spheroidal component Old pop II stars Fe H 4 to 0 5 Very little to no rotation orbits have random i o r 3 5 inner halo Slightly flattened c a 0 6 at R 20 kpc M

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/mw.html (2016-02-13)
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    may be SBb Sc SBc Open spiral arms Pitch angle 18 20 Very small if noticeable bulge L bulge L disk 0 05 eg M33 M101 M61 SBc S0 Galaxies Lenticular galaxies lens shaped Transitional case between E and Sa SBa Smooth light distribution Disk present with no spiral structure Gas dust in some cases No recent SF Classification S0 or SB0 Also subclasses no dust S0 1 S0 2 S0 3 dust present barely discernable bar SB0 1 SB0 2 SB0 3 strong bar present Examples of lenticulars NGC 5866 NGC 3115 Irregular Galaxies Unsymmetric systems Typically lower L systems than E Sa Sc Two classes both now superceded Irr I some hint of spiral structure gas rich eg LMC SMC Irr II irregular systems with a smoother gas poor appearance rare eg M82 starburst galaxy Hubble classification has been modified over the years de Vaucouleurs 1959 Introduced additional spiral classes Sd Sm Im m Magellanic To replace some Sc and all Irr I objects All have lower L than Sa Sc galaxies Also added subclasses based on where spiral arms originated r from an inner ring eg ESO 269 57 s s shaped Sandage from previous Hubble work 1961 Irr II galaxies Sm Im Amorphous classes van den Bergh 1960 DDO System Added luminosity classes based on arm quality length I strong well defined sprial arms most luminous galaxies M B 21 to 22 V chaotic small arms least luminous spirals late types M B 15 to 17 General trend in L M B V with luminosity class But large for a given luminosity class 0 5 1 0 mag not a precise distance indicator Many other classification schemes exist eg Elmegreen Elmegreen 1982 1987 arm classes similar to DDO system Types of spiral galaxy Grand design spirals

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/gal.html (2016-02-13)
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    watts or ergs s 10 7 erg s 1 1 W area m 2 or cm 2 solid angle physical unit is steradian but in astronomy often use squared arc units squared arc second squared arc minute Recall flux power area and thus the operational definition of surface brightness is I flux solid angle flux what astronomical detectors measure solid angle area on the sky apparent size of astronomical object An extended object is generally measured as a pixellated image pixel area pixel flux f i pixel surface brightness I i f i Total flux Shrinking the pixels to an infinitesimal size where the solid angle d is given by Surface brightness is independent of distance I flux solid angle But and where the Area is the component of the physical area of the galaxy perpendicular to the line of sight That is Thus where L and A are intrinsic properties of the source However this is only an approximation for the local universe z 1 At high redshifts I 1 z 3 Two powers of 1 z come from aberration that opens the beam solid angle one from time dilation in the rate of reception of photons and one from the loss of energy per photon Quite often in astronomy use convenient units L specified in L solar luminosity units Area for galaxies convenient unit is pc 2 or kpc 2 hence the units of I are L kpc 2 or L pc 2 but to use these units we must know the distance to the object being measured Observed flux what we measure F I cos d cos component parallel to NORMAL d solid angle sin d dφ In general assume isotropic radiation I I φ F I φ cos sin d dφ Now consider a circular source

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/sb.html (2016-02-13)
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    us the SB distribution Convert to via calibration to standard system i 2 5 log I i gal C With CCD images usually I per pixel converted to per sq Surface Brightness Profiles 1D profile vs r Usually plot as a function of radius r major or minor But often use the geometric mean radius r where r radius of circle with same area as ellipse of axes a b Profile shape of resolved objects larger than that of a stellar image point spread function Innermost regions flattened out by seeing limits resolution See Figure 23 28 in text So what information can we get from SB profiles Brightness luminosity L Colours variation with r Colour gradients Variations in age metallicity dust all Shape Related to formation Presence of bulges bars or nuclei Related to subsequent evolution Evidence for mergers shells Presence of dust Fitting Functions de Vaucouleurs r 1 4 profile Good fits to many E galaxies some bulges only early types Empirical law no physical basis Form a b r 1 4 works quite well 3 33 set to define r e below where r e effective radius r inside which 1 2 of total light is enclosed ie F r r e 1 2 F total I e SB at r e Observationally Plot vs r 1 4 straight line Fit to SB profile get e and r e de Vaucouleurs profile very good 2 parameter fit But not always eg cD galaxies show excess over r 1 4 see example Similarly Integrating I r over an extended object with parameters I e r e yields F total 7 21 r 2 e I e where r 2 e is the surface area inside r e and I e is I at r e SB profiles of

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/sphot.html (2016-02-13)
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    the total kinetic energy of the system The first term on the RHS where I is the total moment of interia of the system Thus we get The term on the LHS is often called the virial of Claudius As we are considering a gravitational system the virial is simply related to the total potential energy of the entire system U leaving If the system as a whole is not

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/virialthm.html (2016-02-13)
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    resolved galaxy get v at different r rotation curve HI observations Spin flip transition of HI 21 1cm 1420 Mhz See HI contour map In many cases galaxies unresolved for HI observations Get spread in spectral line due to range v present Faster V rot wider line Double horned structure measure linewidth Get maximum or dominant V rot from this method For resolved nearby galaxies Can trace out V vs r for gas at different points assume circular motion Can get further out in HI than in H optical disk HII regions So what can this information tell us Can get masses of galaxies M r R Assuming circular motions of the gas V rot or If all mass contained within a radius R M constant for r R implies V rot r 1 2 Keplerian falloff eg planets in the solar system Observed rotation curves flat to edge of data no Keplerian falloff seen Thus for V 2 rot constant M r r Beyond the observed limit of the data dark halo Thus M tot difficult to get Why Discussion Possible ideas to get a handle on M tot Extent of dark halo 100 200 kpc Density profile For a spherically symmetric system with density r Mass dM of concentric shells dM 4 r 2 dr r We know from before and Thus for observed rotation curves r 2 But is the dark halo spherical But inner regions don t require dark halo Normally model dark halo with following Thus for r r c r r 2 and for r r c o constant as we have seen Can model rotation curve with Exponential disk constant M L Bulge contribution Dark halo w form similar to above Dark halo contribution primarily at large r Some trends with Hubble type and L ASIDE What of inner regions Rapid rise of V with r Rigid body rotation at small r The Tully Fisher Relation Linewidth luminosity relation L V rot M a b log V rot L extinction corrected V rot inclination corrected Important distance indicator more later Physical reasoning Not complete From the virial theorem 2K U 0 Assumption 1 M L constant L M Assumption 2 o and thus L o constant L r 2 Substitute or a slope of 10 M a 10 log V rot Reality slope of TF relation not 10 Varies with bandpass B 6 I 8 H 10 Simple reasoning not quite correct Most assumptions are not valid Variations in both M L and I o o Star formation feedback also not accounted for Scatter in TFR also varies with least in I H in IR TF better distance indicator Extinction less at IR Smoother SB profiles in IR i easier to determine Sampling dominant longer lived stellar population in IR older RED stars B mainly young hot stars transient population Some dependance on slope zeropoint with Hubble type Recent results show only a small effect The Tully Fisher relation for spiral galaxies Mass

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/sp.html (2016-02-13)
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    L 4 As with TF this is not the end of it L 4 lots of scatter but slope ok 2nd parameter What is this 2nd parameter effective radius r e 3 parameters I e r e define a PLANE Observationally See Figure 23 31 in text note scatter about FJ relation FJ was used as a distance indicator but not as good as TF why Kormendy relation and FJ law are 2 parameters projections of FP 3 parameters onto 2 axes What do we expect Differences between observed and expected M L variations If differences purely due to M L Systematic differences in stellar populations Not clear yet BUT What if c 1 varies too c 2 constant Again any model of galaxy formation requires explaining FP As we said for TF Graphs of the fundamental plane Faber Jackson relation and Kormendy relation D n relation not in text Dressler et al 1987 Use of D n diameter inside which B 20 75 not an isophotal diameter Tighter relation with than FJ law D n 4 3 Why D n includes L and r e yet another projection more edge on than FJ law of the FP D n relation important distance indicator for E galaxies as we shall see Question How would we use the FJ law or D n as a distance indicator Why do we use D n now and not FJ Graphs comparing FJ and D n Many E galaxies appear flattened due to rotation As can be large for E s need a similarly large v r to appreciably flatten galaxy via rotation for an ideal oblate rotator with isotropic velocity distribution Rotation Parameter Define the rotation parameter For most luminous E galaxies Not rotationally supported Pressure supported v not random preferred direction s Suggestive of triaxial shape of galaxies Line of sight velocity dispersions for some E galaxies For many lower L ellipticals but NOT dE s 18 M B 20 5 Primarily rotation supported If rotation important in an elliptical usually oblate For dwarf ellipticals Also not rotationally supported Again velocity anisotropy primary reason Rotation parameters of low L E s and dE s Some important notes Some E s show minor axis rotation Some kinematically distinct cores Dynamics of core rest of galaxy Mergers Some E s show dust lanes accreted through mergers not aligned with principal axes Further note that bulges are also rotationally supported They have colors like E s but in detail are quite different Traditional thought Bulges Ellipticals Not quite as we are observing Elliptical Fits There is still more that photometry can tell us Not all ellipticals are perfect ellipticals in shape With CCD photometry able to study deviations from ellipticity as the residual between the true isophote r and the best ellipse r E r r r E We can approximate the residual as a fourier series note text is confusing on this where is measured from the major axis The first few terms will

    Original URL path: http://www.astro.queensu.ca/~courteau/Phys216/e.html (2016-02-13)
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    1 M yr Multicomponent disk different structures and ages Retrograde motion of some halo stars v rot 0 in halo Some dynamical clumps of stars in halo moving groups Age differences 2 3 Gyr in some GC s not from this rapid collapse No Fe H r relation for GC s What would you expect from ELS However this was an important paper on galaxy formation and still is Any other models Searle Zinn 1977 Bottom up scenario of Milky Way formation General idea MW forms from aggregation of smaller 10 6 8 M dwarf galaxy sized protogalactic fragments more chaotic Each may have already formed stars GC s Dwarf galaxies evolved from fragments that did not become part of larger galaxies Fragments perhaps supergiant molecular clouds SGMC s Sagittarius Dwarf galaxy This model can explain Retrograde halo stars moving groups Differing chemical enrichment histories of disk s bulge And of course there is much evidence to show that this process has already happened at some level However still no treatment of dark matter Note Both of these models represent 2 extremes True galaxy formation is more complex than either and it is likely a combination of both But these models a good start Bulge formed first from initial collapse like ELS old low Fe H Or some stars formed later by accreted gas stars old and younger stars Thick disk Due to early merger of small satellite Thin disk formed after that Accretion from gas in our own halo High Velocity Clouds or gas ejected from MW General Picture A general picture of galaxy formation Here are some basic well supported ideas Early Universe Big Bang and Inflation Primordial matter density fluctuations Density spectrum few high mass many low mass Growth of structure due to gravitational instability Hierarchical model

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