tuning fork ellipticals, spirals, irregulars. Hubble Sequence.

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1 Hubble arranged his sequence on a tuning fork diagram. Originally he (incorrectly) hypothesized that galaxies evolved from the Left to the Right of this sequence. Early types Later types Hubble went on in his paper Extra-Galactic Nebulae to propose that galaxies (nebulae) be classified as ellipticals, spirals, and irregulars. This is today known as the Hubble Sequence.

2 Hubble subdivided spiral sequences into Sa, Sab, Sb, Sbc, Sc (Scd, Sd), and SBa, SBab, SBb, SBbc, SBc (SBcd, SBd). Two characteristics dictate this (1) the bulgeto-disk ratio and (2) how tighltly wound the spiral arms are. Spirals with high bulge-to-disk ratios (Lbulge/Ldisk > 0.3) and tightly wound arms are the a subclass. The lower sequence has nuclear bars.

3 Hubble subdivided spiral sequences into Sa, Sab, Sb, Sbc, Sc (Scd, Sd), and SBa, SBab, SBb, SBbc, SBc (SBcd, SBd). Two characteristics dictate this (1) the bulgeto-disk ratio and (2) how tighltly wound the spiral arms are. Spirals with high bulge-to-disk ratios (Lbulge/Ldisk > 0.3) and tightly wound arms are the a subclass. The lower sequence has nuclear bars. Irregulars: galaxies lacking organized structure.

4 Elliptical Galaxies: E s. Galaxies with nearly elliptical isophotes with no clearly defined substructure. - Defined by ellipticity, ε=1 - b/a. a=semimajor axis, b=semiminor axis. 0 < ε< Notation for Morphological Class is En, where n = 10ε. E4 has b/a~0.6. E0 has b/a~1. Spiral Galaxies. Normal Spirals: S s; Barred Spirals: SB s. - In each class, a alphabetic sequence ordered based on brightness of bulge/disk (and tightness of spiral arms, but they are correlated): a (bright bulge, tight arms), ab, b, bc, c, cd, d (faint or no bulge, open arms). - Sa and SBa are Early type spirals. Sd and SBd are late type. - Milky Way is thought to be a SBbc. Irregular Galaxies (Irr s). Galaxies with weak (Irr I) or no (Irr II) structure. - Sometimes classify compared to Magellanic clouds, such as Sdm, Sm, Im. - Large Magellanic Cloud is SBm. S0 Galaxies, also called Lenticular. Transition (?) between spiral and elliptical galaxies. Two types: S0 and SB0. Contain bulge and large disk with no spiral arms.

5 Ellipticals

6 Spirals

7 Spirals

8 Barred Spirals

9 Lenticulars

10 Irregulars

11 Spectral Energy Distributions of Galaxies Normal galaxies have SEDs (flux density per wavelength) that are composites of stellar spectra (Planck functions). Other galaxies have SEDs that depart from these. Including AGN, IR-luminous galaxies, etc.

12 ULIRGS (Ultraluminous IR Galaxies)

13 Spiral Galaxies Compared to Ellipticals, cover smaller range in Absolute Magnitude (-16 > M(B) > -23) and Mass (10 9 M < M < M ). Decreasing bulge-disk luminosity with morphological type: L(bulge)/ L(disk)~0.3 for Sa s to L(bulge)/L(disk) ~ 0.05 for Sc s. Increasing opening angle for Spiral arms with morphological type: ~6 o for Sa s to ~18 o for Sc s. Bars are not uncommon. Frequency is uncertain, possibly as many as 70% of spirals have a bar (including the Milky Way?) Bars redistribute angular momentum of stars, gas, and dark matter. By perturbing oribts, gas can be driven to galaxy centers.

14 Spiral Galaxies - Brightness Profiles The light profile of Spiral Galaxy Disks follows an exponential distribution µ disk (R) =µ R h r The light profile of Spiral Galaxy Bulges follow an r 1/4 distribution µ bulge (R) =µ e R h r 1/4 1 Where μ is the surface brightness in, with μ ~ -2.5 log(i), in units of mag arcsec -2.

15 Rotation Curves of Spiral Galaxies Spiral galaxies do rotate. Measure rotation curve by measuring doppler shifted light from spectral lines as a function of galacticentric distance. Redshifted Wavelength Blueshifted 656 nm (Hα)

16 Rotation Curves of Spiral Galaxies Observations! v ~ constant (r 0 )

17 Rotation Curves of Spiral Galaxies Rubin, Thonnard, & Ford, 1978, ApJ, 225, L107 Vera Rubin (b1928) Responsible for most of the work on the galaxy rotation rate problem.

18 Dark Matter distribution in galaxies. Navarro-Frenk-White (NFW) profile: For Spiral Galaxies, we can extend the relation between Mass and Velocity over the whole galaxy using the maximum rotational velocity, V, at R=size of galaxy: 2

19 Rotation Curves of Spiral Galaxies There is a relationship between the Maximum rotation velocity and the Galaxy s Absolute Magnitude (Luminosity). This relation is now referred to as the Tully- Fisher Relation, after Brent Tully and Richard Fisher who first determined it in They derived: MB = log10 ( vmax ) (Sa) MB = log10 ( vmax ) (Sb) MB = log10 ( vmax ) (Sc) As with other quantities, this relation is tightened when using Infrared magnitudes: MH = -9.50( log10 VR ) Rubin et al. 1985, ApJ, 289, 81

20 Rotation Curves of Spiral Galaxies Rubin et al. 1985, ApJ, 289, 81

21 Rotation Curves of Spiral Galaxies Derivation of the Tully-Fisher Relation. Maximum Rotation rate is related to velocity by: L vmax α with α 4 The Flat Rotation Curve implies M = v2 maxr G L =(M/L) 1 v2 maxr Rewrite this in terms of the M/L ratio: Rewrite the Radius, R, in terms of the mean surface brightness : I = L/R 2 G M 2 1 L = L G 2 I v 4 max

22 Rotation Curves of Spiral Galaxies M 2 1 L = L G 2 I v 4 max If the Mass to Light Ratios and average surface brightness are the same for spiral galaxies, then this gives the Tully Fisher Relation, L ~ v 4. There *is* variation in the mass-to-light ratios and surface brightnesses of Spirals, but they are about the same for Spirals of the same Morphological Classification.

23 Rotation Curves of Spiral Galaxies 21 cm flux vs. Velocity Pierce & Tully (1992)

24 Rotation Curves of Spiral Galaxies MB MR MI MH Pierce & Tully (1992)

25 Luminosity-Metallicity Relation Zaritsky, Kennicutt, Huchra 1994, ApJ, 420, 87 Milky Way Sun Metallicity of stars Sun Metallicity (metal fraction) of gas More luminous galaxies have high metallicities. The more luminous galaxies have had more metal enrichment.

26 More luminous means more mass to first order. Higher-mass galaxies have had more metal enrichment. Mass-Metallicity Relation Tremonti et al. 2004, ApJ, 613, 898

27 Ellipticals

28 Elliptical Galaxies M 87 Giant Elliptical Mass ~ 3 x M Size is ~10 x diameter of Milky Way

29 Elliptical Galaxies - Classifications Normal Ellipticals - includes Giant Ellipticals (ge s), and normal E s. Range in magnitude from -15 < M(B) < -23 (cf. spiral galaxies, which have much smaller range). Diameter s range from kpc. Often includes S0 galaxies. cd Galaxies. (Brightess of the D Ellipiticals in the antiquated Yerkes morphological classification ). Extremely luminous, M(B) > -25, large (R ~ 1 Mpc). Found only in the centers of dense galaxy clusters. Extended light profiles (see below), and high M/L. Dwarf Ellipticals. (de s) Differ from E s in that they have smaller surface brightness, fainter magnitudes (-13 < M(B) < -19), and lower metallicity. Blue Compact Dwarfs (BCDs). Similar in morphological appearnce to E s and de s, but clearly bluer in color, with appreciable gas content. Dwarf Spheroidals. (dsph) similar to de s, have magnitudes down to M(B) ~ -8 mag. Because they are so faint, only found (so far) in local group.

30 Elliptical Galaxies - Classifications

31 Ellipticals - Brightness Profiles The light profile of normal Ellipticals is similar to that of Spiral Galaxy Bulges -- follow an r 1/4 distribution. Also called de Vaucouleur s Profile Surface-brightness profile of NGC 4472 Kim et al. 2000, MNRAS, 314, 307

32 Ellipticals - Brightness Profiles The light profile of normal Ellipticals is similar to that of Spiral Galaxy Bulges -- follow an r 1/4 distribution. Also called de Vaucouleur s Profile Schombert 1986, ApJS, 60, 603

33 Elliptical Galaxies - Dynamics Why are Elliptical Galaxies not Round? What holds them up? Compare rotational velocity, Vrot, to velocity dispersion, σ : What the heck is σ? This is the velocity dispersion, which is the average of radial velocities in a galaxy.

34 Elliptical Galaxies What the heck is σ? This is the velocity dispersion, which is the average of radial velocities in a galaxy. elliptical galaxy (made of lots of stars on radial, keplerian orbits) telescope continuum flux Δλ Absorption line: many stars at different velocities wavelength λ0

35 Elliptical Galaxies - Dynamics Ellipticals with high V/σ Compare rotational velocity, vrot, to velocity dispersion, σ : Ellipticals with lowv/σ Davies et al. 1983, ApJ 266, 41

36 Elliptical Galaxies - Dynamics ATLAS3D: Emsellem et al. 2011, MNRAS, 414, 888 ellipticity

37 Elliptical Galaxies Stars in Elliptical Galaxies are thermalized. Stars are collisionalless partcles on radial orbits. Act like statistical ensemble of particles that interact only via their gravity K = 1 2 Mv2 = 1 2 Mσ2 1 = 3 2 kt If all stars started out in circular orbits, how long does it take for a galaxy to thermalize? Consider the relaxation timescale pair collisions in a system of N stars of total mass M = N m, with extent R, and mean stellar density, n = 3N/(4πR 3 ). Define the relaxation timescale to be the average time it takes a star to change its velocity by 90 o due to pair collisions.

38 Elliptical Galaxies (star 1) Consider a star (star 1)passing another one (star 2), with impact parameter b. Star 1 attains a velocity component perpendicular to the incoming direction of: v (1) Gm 2b aδt b 2 (star 2) v = 2Gm bv Star 1 goes through many collisions, accumulating velocity components. After a time t, the velocity is v = i v (i)

39 Elliptical Galaxies (star 1) (star 2) The expectation value of the perpendicular velocity component is: v = i v (i) =0 because the direction of each kick is random. But, the mean square velocity does not vanish: v 2 = i v (i) v(i) = i v (i) 2 =0 The perpendicular velocity performs a random walk.

40 Elliptical Galaxies To computer the sum over all collisions, convert the sum to an integral where we integrate over all impact parameters b. During time t, all stellar collisional partners with b between b and b+db are locatedin a cylindrical shell of volume element (2πb db)(vt): Note the integral is not defined at b=0 or b=. We have to chose bmin and bmax, in which case the definite integral is proportional to ln(bmin / bmax). Because the stellar system (galaxy) has some extent, we take bmax=r. Because our approximation for v breaks down if it is on the same order as v (the velocity) we choose bmin accordingly: b min =2Gm/v 2 Therefore: b max /b min = Rv 2 /(2Gm)

41 Elliptical Galaxies b max /b min = Rv 2 /(2Gm) Lastly, according to the Virial Theorem, Ug = 2 K, which implies GM/R =G (N m)/r = v 2, in which case bmax / bmin = N. Therefore: We define the relaxation timescale to be the time it takes for the mean square velocity to equal v, the typical velocity of a star in the system: v 2 (t relax ) = v 2

42 Elliptical Galaxies We define the relaxation timescale to be the time it takes for the mean square velocity to equal v, the typical velocity of a star in the system: v 2 (t relax ) = v 2 Therefore: Now, consider, typical galaxies have R/v ~ 10 8 yr and ~ stars. Typical trelax for galaxies is > age of the Universe. Therefore, pair collisions do not play any role in galaxy evolution. We will return to this point when we discuss galaxy formation.

43 Elliptical Galaxies All elliptical galaxies have a relationship between their central radial-velocity dispersion, σ, and their absolute magnitude. This is the Faber-Jackson relation, L ~ σ 4. Dwarf Ellipticals Mass ~ M Diameter ~ 1-10 kpc Normal Ellipticals Mass ~ M Diameter ~ kpc cd Ellipticals Mass ~ M Diameter ~ kpc Sandra Faber b This is a consequence of the Virial Theorem.

44 giant & normal Ellipticals dwarf Ellipticals cd Ellipticals Tighter fit to the data uses the radius (size) of the galaxy. This is the fundamental plane of elliptical galaxies. L ~ σ 2.65 re The effective radius is related to the surface brightness, which is not constant over all types of Ellipticals. You can rewrite the fundamental plane as re ~ σ 1.24 Ie -0.82

45 Fundamental Plane projections Kormendy & Djorgovski 1989, ARAA, 27, 235

46 Where does the Fundamental Plane come from? Consider a cloud of particles of radius R, total mass, M, and initial constant density, ρ0 = M/(4/3)πR 3 The gravitational potential energy on a spherical shell of thickness dr at a distance r is du g = G M r 4πr 2 ρ r dr Integrate over all shells to get total potential energy U g = 4πG R 0 M r ρr dr For constant density, M r = 4 3 πr3 ρ 0 R r dr

47 Where does the Fundamental Plane come from? U g = 4πG R 0 M r ρr dr For constant density, M r = 4 3 πr3 ρ 0 Integral becomes, U g = 4πG Solving gives R 0 U g = 16π2 (4/3πr 3 ρ 0 ) ρ 0 r dr Inserting R dr r 15 Gρ2 0R 5 ρ 0 = M/(4/3πR 3 ) Gives the total gravitational potential energy. U g = 3 5 GM 2 R

48 Where does the Fundamental Plane come from? The total gravitational potential energy. U g = 3 GM 2 5 R The Kinetic Energy is: From the Virial Theorem, 2K + Ug = 0. Therefore: The Luminosity and Surface brightness are related: L =2πR 2 ei e Combining these gives: R e L I e R e L σ 2 I e M = M L 1 σ 2 I e

49 Where does the Fundamental Plane come from? R e L I e R e L σ 2 I e M = M L 1 σ 2 I e To agree with the fundamental plane observation, this must equal: R e M L 1 σ 2 I e σ1.4 I 0.85 e Rewriting in terms of the M/L ratio, using σ ~ M 2 /R and I ~ L/R 2 M L σ0.6 I 0.15 e M 0.3 R 0.3 e R 0.3 e L 0.15 M The effective Radii cancel in the above. Therefore, the fundamental place is reproduced if either : L M 0.2 M L L 0.25

50 Supermassive Blackholes in Galaxies M 87 Giant Elliptical Mass ~ 3 x M Size is ~10 x diameter of Milky Way

51 Supermassive Blackholes in Galaxies M 87 Giant Elliptical Mass ~ 3 x M Size is ~10 x diameter of Milky Way Jet of material emitted by nucleus

52 Supermassive Blackhole in M87 rotational velocity velocity dispersion, σ FWHM / 2.35 Macchetto et al Modeling gives Virial Mass of (3.2+/-0.9) x 10 9 M within r < 0.05 = 3.5 pc. (This density is 1.8 x 10 7 M pc -3. Recall, the solar neighborhood has 0.05 M pc -3.)

53 Supermassive Blackholes in Galaxies

54 Correlation between SMBH Mass and Galaxy Properties Gebhart et al. 2000, ApJ,

55 Correlation between SMBH Mass and Galaxy Properties McConnell, Ma, Gebhardt et al. (2012, Nature, 480, 215) Correlations of dynamically measured black hole masses and bulk properties of host galaxies. (a) Black hole mass, MBH, versus stellar velocity dispersion for 65 galaxies. (b) Black hole mass versus V -band bulge luminosity for 36 early type galaxies with direct dynamical measurements of MBH.