Galaxies Introduction Elliptical galaxies Spiral galaxies Scaling relations

Galaxies • Introduction • Elliptical galaxies • Spiral galaxies • Scaling relations • Central black holes • Luminosity functions • Spectra

Introduction Classification: the Hubble sequence spirals ellipticals lenticulars barred spirals

Introduction - 2 • The Hubble classification is morphological and influenced by projection effects (2 D view, not 3 D) • Elliptical galaxies belong to classes En (n = 0, …, 7) where b a • Ellipticity is not necessarily an intrinsic property of the galaxy (a cigar or a disk could be classified E 0, depending on the viewing angle)

Introduction - 3 • Spiral galaxies are classified Sa, Sb, Sc, Sd depending on the importance of the bulge with respect to the disk and the characteristics of the arms • Intermediate classes (Sab, Sbc, Scd) are also introduced • Barred spirals have a similar classification: SBa, SBab, SBb, … • Galaxies not fitting in that scheme are classified irregulars

Introduction - 4 Mass / luminosity ratio (ϒ or Y) • Generally given in solar units → Y = 1 for the Sun • Depends on the spectral band (ex: YV = M/LV) • Extrapolated to bolometric luminosity using spectral models • Applies to stars, star clusters, galaxies, galaxy clusters • Ex: massive stars: Y < 1 gas-rich spiral galaxies: Y ~ 1 – 10 elliptical galaxies: Y ~ 10 – 100 galaxy clusters: Y ~ 300 Why Y > 1 in most galaxies ?

Introduction - 5 • Most massive stars (→ most luminous) evolve faster (M ≈ ct but L decreases) → Y increases when galaxy ages (and mostly when star formation slows down) • Hot stars ionize gas around them (HII regions, high L for very low M) → reinforce the variation of Y with age • Stellar remnants have a very high Y • and dark matter an infinite Y…

Introduction - 6 Color • The color of an object is measured by a color index (ex: B–R = m. B – m. R) • After correction for dust reddining (if necessary), it is an intrinsic property of the object B • An object with a large color index is called red, an object with a low (or negative) color index, blue red object blue objects R

Introduction - 7 Metallicity • Content in elements from carbon and heavier • Iron is often considered representative • Applies to stars, interstellar matter, galaxies • Depends on the chemical history of matter (previous stellar generations) → generally not homogeneous in a galaxy • Higher metallicity → redder object (since more absorption lines in the blue)

Introduction - 8 Magnitudes • For a point-like object: • For an extended object: – either one measures the integrated magnitude – either one measure the magnitude per unit of solid angle where Isurf is the flux received per unit solid angle (μ in mag/arcsec 2)

Introduction - 9 Virial theorem • For an isolated system in dynamical equilibrium: 2 EK + EP = 0 (in absolute value, kinetic energy = ½ potential energy) • Estimate of the mass of a cluster (of galaxies): R = mean distance between 2 galaxies → EP ~ −GM 2/2 R (*) V = mean velocity of galaxies → EK ~ ½ MV 2 (* /2 in order not to count twice the energy associated to a pair of galaxies)

Elliptical galaxies (early-type galaxies) Sub-types – g. E (giant elliptical) – E (elliptical) ESO 325−G 004 (g. E) – c. E (compact elliptical) – d. E (dwarf elliptical) (surface brightness of d. E lower than c. E) M 32 (c. E) NGC 205 (d. E)

Elliptical galaxies - 2 – c. D galaxies: supergiant ellipticals (c) with extended halo → appear diffuse (D) located at the center of some rich clusters Image: NGC 3311 (c. D) and NGC 3309 (g. E) at the center of Hydra I cluster Note the presence of thousands of globular clusters around these galaxies

Elliptical galaxies - 3 – S 0 galaxies: lenticulars (intermediate between spirals and ellipticals) ≈ spirals without spiral arms Image: NGC 2784

Elliptical galaxies - 4 – d. Sph galaxies: dwarf spheroidals, very low surface brightness → observable only in the local group (maybe the most frequent galaxies, but very hard to observe) Image: NGC 147

Elliptical galaxies - 5 Luminosity profile • The surface brightness decreases from the center to the outskirts according to a simple empirical law (de Vaucouleurs law): or: Re = effective radius (contains half the emitted light) Ie = surface brightness at the effective radius (r 1/4 law)

Elliptical galaxies - 6 • For c. D galaxies, there is an excess brightness at large radii compared to the r 1/4 profile → c. D ≈ g. E + extended luminous halo • The extended halos of the c. D galaxies could be the remains of many small galaxies `swallowed´ by the giant elliptical • The de Vaucouleurs law can be generalized to elliptical isophotes where ae and be are the major and minor semi axes

Elliptical galaxies - 7 Composition • old stars, little gas → no more star formation • sometimes dust bands (remains from absorbed spirals? ) Centaurus A NGC 7049

Elliptical galaxies - 8 Ellipticity • Why have ellptical galaxies kept their shape and did not all become spherical? • Rotation as in spirals? • Rotation flattening significant if vrot ~ σv where However, vrot << σv + triaxial galaxies → rotation can not explain the observed ellipticity → shape is a testimony of history The center of the Virgo cluster

Elliptical galaxies - 9 Stability of the ellipsoidal shape • Collisions between stars tend to increase the symmetry of the system • The time needed for this `relaxation´ can be estimated by: trelax = characteristic time for direction change due to collisions tcross = crossing time of the system N = number of stars in the system • With tcross ~ 108 years and N ~ 1012 → trelax ~ 1018 years >> age of the Universe → ellipsoid is stable

Elliptical galaxies - 10 Departures from ellipsoidal shape • Generally: isophotes ≈ concentric ellipses • But: − ellipticity ε not always constant with radius − major axis orientation may vary: isophote twisting • Twisting can be a projection effect if ε varies (apparent direction of major axis seems to vary more if ε → 0)

Elliptical galaxies - 11 Shells and waves • Complex structures sometimes visible at low surface brightness • Signs of complex evolution, probably linked to merging of galaxies Image: NGC 474

Spiral galaxies (late-type galaxies) Sub-types – spirals: Sa, Sb, Sc, Sd (+ intermediates Sab, Sbc, Scd) – barred spirals: SBa, SBb… (+ intermediates SBab, SBbc…) M 74 NGC 1365

Spiral galaxies - 2 • Sub-classes a, b, c correspond to differences in: Sa Sb Sc large (~0. 3) medium (~0. 13) small (~0. 05) winded up (~6°) (~12°) open (~18°) smooth intermediate granular color (B−V) red (~0. 75) (~0. 64) blue (~0. 52) gas fraction (Mgaz/Mtot) low (~0. 04) average (~0. 08) high (~0. 16) importance of bulge (Lbulbe/Ltot) opening of arms (θ) structure of arms bulge θ arm • Barred spirals (± as numerous as spirals) have a similar classification

Spiral galaxies - 3 Sa M 104 « Sombrero »

Spiral galaxies - 4 Sab Sb M 81 M 63

Spiral galaxies - 5 Sbc Sc / Sd NGC 3184 NGC 300

Spiral galaxies - 6 SBb M 91 M 95

Spiral galaxies - 7 SBbc SBc NGC 1300 M 109

Spiral galaxies - 8 `intermediate´ (embryo of a bar) M 83

Spiral galaxies - 9 Luminosity profile • The (mean) surface brightness of the disk decreases with distance from the center according to an exponential law: or: • μ 0 not directly measurable (center inside the bulge) → extrapolation • μ 0 nearly constant in `normal´ galaxies: (Freeman law) • The surface brightness of the bulge follows the same law as elliptical galaxies

Spiral galaxies - 10 Rotation curves • If the galaxy is not seen face-on: where i = inclination (angle between the galactic plane and the plane of the sky) - vrad measured by spectroscopy (Doppler effect) - i determined by assuming that the disk is circular (apart from spiral arms…)

Spiral galaxies - 11 • The rotation velocity in the outer parts is too high for the estimated mass (stars + interstellar matter) → one postulates the existence of a dark matter halo

Spiral galaxies - 12 • Modelling: one assumes circular orbits in the disk (+ spherical halo) where M(R) = mass included inside the radius R One estimates the amount of `normal´ (luminous) matter Mlum from L(R) and an estimated M/L ratio → gives a predicted rotation curve → the amount of dark matter Mdark is what we need to add to explain the rotation curve:

Spiral galaxies - 13 • The different components are modelled separately (disk, bulge, halo, central black hole) R z r The gravitational potential F(R) is defined by Parameters Mdisk, a, ρ0, R 0… are adjusted to fit the observations

Spiral galaxies - 14 Composition 1. Stars: Later type → more young stars → more massive stars → bluer color M 81 (In agreement with the reduced importance of the bulge, redder and containing older stars) NGC 300

Spiral galaxies - 15 2. Gas: Later type → larger proportion of gas (necessary for star formation) 3. Dust: Mass of dust ~1% mass of gas If dust heated by hot stars → emission in far IR (FIR) → mainly in late -type spirals M 104 in false colors: blue = visible (HST) red = FIR (Spitzer)

Spiral galaxies - 16 Structure 1. Spiral arms: Higher contrast in blue but arms also seen in red → imply all components of disk but excess of young stars Density waves (amplitude ~10 – 20%) that propagate at a speed different from that of matter Perturbation amplified by dynamic evolution Various theories to explain their appearance: chaotic phenomenon, tidal effect from a companion, triggering of star formation by differential rotation…

Spiral galaxies - 17 2. Bar: Stable over several rotation periods Triggered by instability in the disk NGC 6050 and IC 1179

Scaling relations Scaling relation = • relation between several characteristic properties of a class of objects • determined empirically in the nearby Universe • that can be applied to remote objects for which the determination of one of these properties would necessitate the knowledge of distance Ex: δv independent of d L depends on d → allows to estimate the distance of these remote objects

Scaling relations - 2 Tully – Fisher relation (spiral galaxies) vmax = maximum rotation velocity (in the `plateau´ – measured e. g. by the 21 cm H line) L = integrated luminosity α = exponent varying with wavelength (α increases with λ) • nearby galaxies: spatially resolved spectrum • remote galaxies: integrated spectum W

Scaling relations - 3 Interpretation:

Scaling relations - 4 Interpretation (2): Since L is roughly proportional to M*, Tully-Fisher links M* and v 4 However, in some galaxies (less massive ones, which have the lowest star formation rate), Mgas should be taken into account One gets indeed a better correlation between log vmax and log(Mdisk = M*+Mgas) than with M* alone → suggests that the M/L ratio (and thus the fraction of dark matter) is ± constant in a large range of galactic masses (disk-halo conspiracy) M* Mdisk

Scaling relations - 5 Faber – Jackson relation (elliptical galaxies) σ0 = velocity dispersion in the center of the galaxy L = integrated luminosity Dispersion around the relation larger than for Tully-Fisher → suggests that (at least) another parameter plays a role

Scaling relations - 6 Fundamental plane (elliptical galaxies) • One seeks a relation between 3 parameters in order to reduce the dispersion • It is empirically found that where Re = effective radius (contains half of the luminous flux) and = mean flux inside Re → suggests to seek a relation between , Re et σ0

Scaling relations - 7 I

Central black holes Black hole = solution of the general relativity equations for a `point mass´ • escape speed vesc: • Schwarzschild radius: RS = R for vesc = c • black hole = object for which R < RS • all sufficiently massive galaxies seem to contain a central supermassive black hole (SMBH, M ~ 105 – 109 MO)

Central black holes - 2 Detection in inactive galaxies • Dynamical effect can be measured in a region where black hole (BH) potential dominates R 0 = radius of the sphere in which the black hole potential dominates σ0 = velocity dispersion at the center of the (elliptical) galaxy or of the bulge (in a spiral) • Angular resolution needed: → possible in nearby galaxies with the best instruments

Central black holes - 3 • Increase of velocity dispersion σ or of the rotation velocity vrot in the central region (R < R 0) • No direct proof that it is due to a black hole but no alternative solution (huge mass in a limited volume) image of the galactic center spectrum x spectrograph slit λ

Central black holes - 4 Correlations • Estimates of the SMBH mass in a sample of galaxies → study of correlations with galactic properties → one observes a correlation between the mass of the black hole and the mass of the bulge: MSMBH / Mbulge ~ 0. 002 → joint evolution? or result of galactic mergers?

Central black holes - 5 Sagittarius A* • At the center of our Galaxy: compact star cluster centered on the radio source Sgr. A* • The proper motions and radial velocities of ~1000 stars in that cluster could be measured (inside 10 arcseconds around Sgr. A*) → imply the presence of a mass M = (3. 6± 0. 4) 106 MO in R < 0. 01 pc (2000 AU) centered on Sgr. A*

Luminosity function = number of objects as a function of their luminosity • Φ(L) d. L = number of galaxies per unit volume, whose luminosity is between L and L+d. L • Total density: • There is a similar function in (absolute) magnitude: • One can define a luminosity function for each class of galaxies (or for any object); it can also vary with time

Luminosity function - 2 • Difficulties: – measurement of L depends on distance (often estimated from the redshift z) – need for representative samples → large volume (but not too large as the function evolves with time…) – L depends on the chosen filter and shift with z (k-correction) – Malmquist bias → difficulty to determine Φ at low L → need to build a volume-limited sample and not a magnitudelimited one

Luminosity function - 3 Schechter luminosity function: L* = characteritic luminosity (exponential decrease for L > L*, power law for L < L*) Φ* = normalisation factor (Φ*, L*, α depend on filter) → good empirical approx. of the global luminosity function L* ~ 1010 h– 2 LO Φ* ~ 10– 2 h 3 Mpc– 3 α ~ – 1

Luminosity function - 4 • Each class of galaxies has its own luminosity function: – spirals on narrow L domains – ellipticals dominate at high L – low L dominated by Irr and d. E • Different distributions in the field and in clusters: Ex: – Irr / d. E ratio at low L – (Sa+Sb) / (SO+E) at high L

Luminosity function - 5 Color-magnitude diagrams • Simpler classification (does not need morphological studies) → bimodal distribution: a `luminous and red´ peak; another `fainter and bluer´ peak • Φ different for `red´ and `blue´galaxies → Schechter ≈ coïncidence • at a given L, always 2 peaks in the color distribution

Luminosity function - 6 • The central color (the mode) of each peak shifts towards the red when luminosity increases • The M/L ratio is larger for the red population (fewer young, very luminous stars) • Above ~ 2 – 3 × 1010 MO, `red´ galaxies dominate • Below, `blue´ galaxies dominate

Galactic spectra • In UV, visible, near IR: the spectrum of galaxies is dominated by emission from stars (+ gas emission lines) → spectrum of a galaxy = superposition of stellar spectra (with Doppler effects → shift + broadening of lines) Fλ λ(Å) Spectrum of an elliptical galaxy

Galactic spectra - 2 • Stellar evolution rather well understood • Stellar spectra computed from stellar model atmospheres → the galactic spectrum can be computed if one knows the number of stars as a function of their mass, chemical composition, evolution stage • these parameters can be computed from the initial mass function (IMF) and the star formation rate (SFR) NGC 1672

Galactic spectra - 3 Initial mass function • IMF φ(m)dm = fraction of stars having, at birth, a mass between m and m+dm Normalisation: with mi ≈ 0. 08 MO ms ≈ 100 MO Reference IMF (Salpeter): φ(m) ~ m– 2. 35 (overestimates very low masses)

Galactic spectra - 4 Star formation rate • SFR ψ(t) = rate of star formation (in MO/year): ψ(t) depends of the history of the galaxy considered Metallicity • Z(t) = proportion (in mass) of chemical elements from carbon and over (thus synthesized in stars) • The initial Z of a star is that of the interstellar medium in which it forms (enriched by previous stellar generations) • Z gives a 1 st approximation to the chemical composition

Galactic spectra - 5 Spectral energy distribution • SED Sλ, Z (t) = energy emitted by a sample of stars with metallicity Z and age t, per unit wavelength and time Stellar populations synthesis • Flux emitted by a galaxy: Integration goes back in time from t΄ = 0 (present time) to t (birth of the galaxy)

Galactic spectra - 6 Sλ, Z (t–t΄)(t) = spectrum emitted at time t, taking into account the chemical evolution of the galaxy and the stage of evolution of the stars → computed from stellar evolution and atmospheres models On the basis of the adopted IMF, one computes the population density along the isochrones → Sλ, Z (t–t΄)(t) = sum of all spectra on an isochrone

Galactic spectra - 7 • Spectra of a stellar population born in a single event t billion years ago (t = 0. 001 → 13) 106 years: dominated by massive stars (UV) 107 years: fast decrease of UV light and increase NIR (red supergiants) 108 years: UV nearly disappears and NIR stable (red giants) 109 years: dominated by red giants 4– 13× 109 years: very slow evolution 13× 109 years: slight increase UV (post-AGB stars and very hot white dwarfs) 4000 Å break: after 107 years, opacity H ↔ H–, useful to determine redshift and galaxy type

Galactic spectra - 8 • Detailed spectra not always available → color indices (shorter observing time, many simultaneous observations…) • Integrate spectra in the filter passbands → theoretical color indices – fast reddening for young populations – M/L increases with age since M constant and L decreases (much stronger effect in visible compared to near-IR) → LK ± good indicator of mass

Galactic spectra - 9 • Influence of the star formation rate Single age populations may be well suited for stellar clusters but not for most galaxies → take the SFR evolution into account `Classical´model: tf = time of startup τ = characteristic time for star formation H(t) = 0 if t < 0, = 1 if t > 0 (Heaviside function) → sudden start followed by exponential decrease caused by progressive gas exhaustion

Galactic spectra - 10 • The predicted color strongly depends on the characteristic time for star formation τ If τ is very long, the reddening with time is lower since new, blue, massive stars continue to form To explain the colors of E/SO galaxies, one needs τ < 4× 109 years → basically no more star formation for the last 4 to 5 billion years (but this does not take galactic collisions into account)

Galactic spectra - 11 • Contributions of the different components: – stars: continuum + absorption lines – gas: emission lines – dust: extinction + reddening (light absorbed more strongly in the blue and UV and re-emitted in IR)

Galactic spectra - 12 • Evolution along the Hubble sequence (from ellipticals to late-type spirals): – SED bluer for later types – 4000 Å break gets weaker – strength of absorption lines decreases – emission lines increase (HII regions around young stars) – spectra of E and SO nearly identical (old stars)

Galactic spectra - 13 • Modelling: – adjust composite stellar populations via SSP models (Single Stellar Population) of given Z and t

Galactic spectra - 14 • Main absorption lines in the visible: atm. Fe (5270) break à 4000 Å Na. I D (5895) Mg. I b (5174) Hβ (4861) bande G (4300) Ca. II H et K (3934 -3969) Hα (6563)

Galactic spectra - 15 • Main emission lines in the visible: Hα (6563) [OII] (3727) Hβ (4861) [OIII] (4959 -5007) [NII] (6548 -6583) [SII] (6717 -6734)

Galactic spectra - 16 Study of the gas content • Reddening Dust absorbs radiation → heats up → emits in FIR where Iλ = intrinsic flux Fλ = observed flux f(λ) = reddening curve c measures the importance of reddening f(λ) depends on the types of dust grains f(λ)

Galactic spectra - 17 • Balmer decrement Depending on the emission mechanism, theoretical intensity ratios for some lines can be computed (in particular for the Balmer series of hydrogen) One often uses the Hα to Hβ intensity ratio (Balmer decrement) E n = 5 n = 4 The theoretical intensity ratio varies from 2. 85 (HII region) to 3. 1 (AGN) Comparison of observed and theoretical ratios → estimate of reddening Hα Hβ Hγ n = 3 n = 2 n = 1

Galactic spectra - 18 • Ionization source The comparison of some emission line intensities allows to distinguish between the different excitation and ionization sources Intensity ratios of neighboring lines are particularly interesting as they are nearly independent of reddening Ex: [OIII]/Hβ, [NII]/Hα

Galactic spectra - 19 • Estimate of the SFR Many indicators in different spectral ranges, calibrated from stellar population models – UV flux ↔ massive and very young population, but very sensitive to reddening – visible and NIR: intensity of some emission lines ↔ ionizing flux ↔ hot stars – FIR: thermal emission from dust heated by massive hot stars – radio: emission from supernova remnants All these indicators being indirect, one tries to combine several of them to reduce the uncertainties

Galactic spectra - 20 Examples of SFR indicators: Birthrate parameter = present SFR / average past SFR Measures the present rate of activity compared to past one `starburst´ galaxy: b > 2 – 3