The science of galaxies — their structure, classification, formation, evolution, dynamics, and the supermassive black holes at their centers.

## Key Points

- Disk diameter: ~26 kpc (~85,000 ly) for stellar disk; gas disk extends further
- Total stellar mass: ~5 x 10^10 solar masses
- Total baryonic mass: ~6 x 10^10 solar masses
- Number of stars: ~100-400 billion
- Sun's orbital velocity: ~220 km/s; orbital period: ~225-250 Myr
- Distance Sun to center: 8.178 +/- 0.013 kpc (GRAVITY collaboration)
- Solid-body rotation in the inner ~1-2 kpc (v proportional to r)
- Roughly flat beyond ~5 kpc (v ~ constant)
- Flat rotation implies enclosed mass M(r) proportional to r, far exceeding visible mass
- This is primary evidence for a dark matter halo with density profile approximately rho proportional to r^-2 (isothermal) at intermediate radii
- Mass: 4.152 +/- 0.014 x 10^6 solar masses (from stellar orbits, GRAVITY/Keck)
- Distance: 8.178 kpc

## Quick Example

```
M_BH ~ 10^8.3 * (sigma / 200 km/s)^4.4 solar masses
```

Galactic Astronomy

The science of galaxies — their structure, classification, formation, evolution, dynamics, and the supermassive black holes at their centers.

---

The Milky Way

Structure

Component	Properties
Thin disk	Scale height ~300 pc; contains young stars (Population I), gas, dust, open clusters; active star formation in spiral arms; metallicity [Fe/H] ~ 0 to +0.3
Thick disk	Scale height ~1000 pc; older stars (8-12 Gyr); lower metallicity [Fe/H] ~ -0.5 to -1.0; kinematically hotter (higher velocity dispersion)
Central bulge/bar	Boxy/peanut-shaped; ~2 kpc half-length bar oriented ~25-30 degrees from Sun-center line; mix of old and intermediate-age stars; high metallicity range
Stellar halo	Extends to >100 kpc; old, metal-poor stars (Population II, [Fe/H] < -1); globular clusters (~150 known); stellar streams from disrupted dwarf galaxies
Dark matter halo	Extends to ~200-300 kpc (virial radius); total mass ~1-1.5 x 10^12 solar masses; contains ~85% of total galaxy mass
Spiral arms	Logarithmic spirals; major arms: Perseus, Sagittarius-Carina, Scutum-Centaurus, Norma-Outer; Sun located in Local Arm (Orion Spur) at ~8.2 kpc from center

Key Numbers

• Disk diameter: ~26 kpc (~85,000 ly) for stellar disk; gas disk extends further
• Total stellar mass: ~5 x 10^10 solar masses
• Total baryonic mass: ~6 x 10^10 solar masses
• Number of stars: ~100-400 billion
• Sun's orbital velocity: ~220 km/s; orbital period: ~225-250 Myr
• Distance Sun to center: 8.178 +/- 0.013 kpc (GRAVITY collaboration)

Rotation Curve

The Milky Way rotation curve is approximately flat from ~5 kpc outward at ~220 km/s:

• Solid-body rotation in the inner ~1-2 kpc (v proportional to r)
• Roughly flat beyond ~5 kpc (v ~ constant)
• Flat rotation implies enclosed mass M(r) proportional to r, far exceeding visible mass
• This is primary evidence for a dark matter halo with density profile approximately rho proportional to r^-2 (isothermal) at intermediate radii

Sagittarius A*

The central supermassive black hole:

• Mass: 4.152 +/- 0.014 x 10^6 solar masses (from stellar orbits, GRAVITY/Keck)
• Distance: 8.178 kpc
• Schwarzschild radius: ~12 million km (~0.08 AU)
• Star S2/S0-2: 16-year orbit, closest approach ~120 AU, v_max ~ 7650 km/s; used to test general relativity (gravitational redshift, Schwarzschild precession both detected)
• Event Horizon Telescope: imaged Sgr A* shadow (2022); ring diameter ~52 microarcsec consistent with GR prediction for 4 million solar mass BH
• Currently quiescent (low accretion rate ~10^-8 solar masses/yr); Fermi bubbles suggest past activity

Stellar Populations

• Population I: young, metal-rich stars in the disk; found in spiral arms, open clusters; OB associations, H II regions
• Population II: old, metal-poor stars in the halo and bulge; globular clusters, subdwarfs; ages 10-13 Gyr
• Population III: hypothetical first-generation zero-metallicity stars; never observed; predicted to be massive (>100 solar masses), short-lived; enriched primordial gas with first metals

---

Galaxy Classification: The Hubble Sequence

Elliptical Galaxies (E0-E7)

• Smooth, featureless light profiles; classified by apparent ellipticity: E_n where n = 10(1 - b/a)
• Range from nearly spherical (E0) to highly elongated (E7)
• Dominated by old, red stars (Population II); little gas or dust; minimal ongoing star formation
• Stellar motions dominated by random orbits (velocity dispersion), not ordered rotation
• Follow Sersic profiles with high Sersic index (n ~ 4, de Vaucouleurs profile)
• Luminosity range: dwarf ellipticals (M_B ~ -14) to giant cD galaxies (M_B ~ -24) in cluster centers
• Formed primarily through major mergers of disk galaxies (supported by simulations and observations of merger remnants)

Spiral Galaxies (Sa-Sd, SBa-SBd)

• Disk + bulge + spiral arms; classified by bulge prominence, arm winding, and arm resolution into stars/H II regions
• Sa/SBa: large bulge, tightly wound smooth arms
• Sb/SBb: moderate bulge, moderately wound arms
• Sc/SBc: small bulge, loosely wound arms with prominent H II regions
• Sd/SBd: very small or no bulge, fragmented arms
• Barred spirals (SB): ~65-70% of disk galaxies have bars; bars drive gas inward, fueling central star formation and AGN
• Blue disks with active star formation; red bulges with older stars
• Milky Way: SBbc (barred spiral, intermediate winding)

Lenticular Galaxies (S0)

• Transitional between ellipticals and spirals: prominent disk but no spiral arms
• Little gas or dust; minimal star formation
• May form from spiral galaxies that exhaust or lose their gas (ram pressure stripping in clusters, strangulation)

Irregular Galaxies

• No clear symmetric structure; often gas-rich with active star formation
• Irr I (Magellanic type): some structure but asymmetric (e.g., LMC, SMC)
• Irr II: chaotic, often result of interactions
• Common at high redshift; many dwarf galaxies are irregular

---

Galaxy Formation and Evolution

Hierarchical Assembly

• Galaxies form within dark matter halos that grow by merging smaller halos (bottom-up, hierarchical)
• Gas cools and condenses at halo centers; angular momentum conservation produces rotating disks
• First galaxies: small, irregular, gas-rich systems at z > 6; observed by JWST at z ~ 10-14
• Major mergers (mass ratio > 1:3) transform disks into ellipticals; violent relaxation erases ordered rotation
• Minor mergers (mass ratio < 1:10) build stellar halos and thicken disks

Color-Magnitude Diagram

The galaxy population divides into two main sequences:

• Blue cloud: star-forming galaxies; spiral and irregular morphologies; gas-rich; blue colors from young OB stars
• Red sequence: quiescent galaxies; elliptical and lenticular morphologies; gas-poor; red colors from old stellar populations
• Green valley: transitional region; galaxies migrating from blue cloud to red sequence during quenching; relatively unpopulated (fast transition ~1-2 Gyr)

Quenching Mechanisms

Processes that shut down star formation:

Mechanism	Type	Description
AGN feedback	Internal	Jets and radiation from accreting SMBH heat or expel gas; dominant for massive galaxies
Stellar feedback	Internal	Supernovae and stellar winds drive outflows; dominant for low-mass galaxies
Ram pressure stripping	Environmental	Hot intracluster medium strips gas from galaxies falling into clusters (Virgo cluster examples)
Strangulation	Environmental	Hot halo gas prevented from cooling onto galaxy; cuts off fuel supply; slow quenching
Harassment	Environmental	Repeated high-speed encounters in clusters heat disk and strip material
Major mergers	Mixed	Gas consumed in starburst; remainder heated or expelled; builds elliptical remnant
Morphological quenching	Internal	Bulge growth stabilizes disk gas against collapse via increased shear

---

Active Galactic Nuclei (AGN)

The Unified Model

All AGN are powered by accretion onto a supermassive black hole. Observed differences arise primarily from viewing angle relative to a dusty torus:

                      [Blazar / BL Lac]
                           |
                      (jet, face-on)
                           |
    [Seyfert 1 / Type 1 QSO] --- (direct view of broad-line region)
                           |
                     [dusty torus]
                           |
    [Seyfert 2 / Type 2 QSO] --- (torus obscures broad-line region)
                           |
                      (jet, edge-on)
                           |
                    [Radio galaxy]

AGN Types

• Seyfert 1: broad + narrow emission lines; unobscured view of accretion disk and broad-line region (BLR); moderate luminosity; found in spiral hosts
• Seyfert 2: narrow emission lines only; torus blocks BLR; polarized broad lines visible in scattered light (proof of unified model; Antonucci & Miller 1985)
• Quasars (QSOs): high-luminosity AGN (M_B < -23); visible to z > 7; point-like at cosmological distances; powered by accretion rates up to ~10 solar masses/yr
• Radio galaxies: powerful radio jets (FR I: edge-darkened, low power; FR II: edge-brightened, high power); hosted by massive ellipticals
• Blazars: jet pointed directly at observer; extreme variability, superluminal motion, gamma-ray emission; includes BL Lac objects (featureless continuum) and FSRQs (broad lines)
• LINERs (Low-Ionization Nuclear Emission Regions): low-luminosity AGN; common in nearby galaxies; may be low-accretion-rate SMBHs or other excitation mechanisms

Accretion Physics

• Eddington luminosity: L_Edd = 4piGMm_p*c / sigma_T ~ 1.3 x 10^38 (M/M_sun) erg/s
• Radiative efficiency: eta ~ 0.06-0.42 depending on spin (Schwarzschild to maximal Kerr); L = eta * M_dot * c^2
• Thin disk (Shakura-Sunyaev): standard for ~0.01-1 L_Edd; UV/optical thermal emission
• ADAF (Advection-Dominated Accretion Flow): low accretion rates (<0.01 L_Edd); radiatively inefficient; applies to Sgr A*
• Super-Eddington accretion: radiation-trapped; may explain ultraluminous X-ray sources and rapid SMBH growth at high z

---

Supermassive Black Holes

M-sigma Relation

A tight correlation between SMBH mass and host galaxy stellar velocity dispersion:

M_BH ~ 10^8.3 * (sigma / 200 km/s)^4.4 solar masses

• Implies co-evolution of black hole and host galaxy despite vastly different spatial scales (BH sphere of influence ~ pc vs galaxy ~ kpc)
• Maintained by AGN feedback: BH grows until feedback energy couples to and regulates gas supply
• Also correlations with bulge mass (M_BH ~ 0.002 * M_bulge) and bulge luminosity

SMBH Census

• Nearly all massive galaxies harbor central SMBHs (mass 10^6 to 10^10 solar masses)
• Most massive known: TON 618 (~6.6 x 10^10 solar masses); Phoenix A (~10^11 solar masses)
• JWST detections of SMBHs at z > 10 challenge models of seed formation — too massive too early for standard Eddington-limited growth
• Seed formation hypotheses: Pop III remnants (~100 solar masses), direct collapse black holes (~10^4-10^5 solar masses), runaway mergers in dense star clusters

---

Galaxy Interactions and Mergers

Observational Signatures

• Tidal tails: long streams of stars and gas pulled out by gravitational torques (e.g., Antennae galaxies NGC 4038/4039)
• Bridges: material connecting interacting pairs
• Shells and ripples: concentric arcs in elliptical galaxies from minor mergers
• Starbursts: enhanced star formation rates (10-100x normal) from gas compression during interaction
• Tidal dwarf galaxies: self-gravitating structures forming in tidal tails

Key Examples

• Antennae (NGC 4038/4039): prototypical major merger in progress; spectacular tidal tails; intense starburst; distance ~22 Mpc
• Mice (NGC 4676): pair with long tidal tails; early stage of merger
• Cartwheel galaxy: ring galaxy from head-on collision through a disk galaxy
• Andromeda-Milky Way merger: predicted in ~4.5 Gyr; will likely produce an elliptical galaxy ("Milkomeda"); Triangulum (M33) may participate

---

Galactic Dynamics

Density Wave Theory

• Lin & Shu (1964): spiral arms are not material structures but quasi-stationary density waves rotating at a pattern speed Omega_p
• Stars and gas pass through the wave; compression triggers star formation (explains why young stars and H II regions trace arms)
• Pattern speed is slower than disk rotation at the Sun's radius: corotation radius at ~25-30 kpc for Milky Way
• Alternative: transient/recurrent spiral structure from swing amplification; N-body simulations show both mechanisms contribute

Dark Matter Halo Profiles

• NFW profile (Navarro, Frenk & White): rho(r) = rho_s / [(r/r_s)(1 + r/r_s)^2]; universal profile from N-body simulations; cuspy center (rho ~ r^-1)
• Core-cusp problem: observed dwarf galaxy rotation curves prefer constant-density cores; NFW predicts cusps
• Possible resolutions: baryonic feedback (supernovae heat and flatten cusps); self-interacting dark matter; observational systematics

Satellite Galaxies and Missing Satellites

• LCDM predicts ~500 dark matter subhalos >10^7 solar masses around Milky-Way-mass galaxies
• Only ~60 satellite galaxies known (including ultra-faint dwarfs found by SDSS, DES, LSST precursors)
• Missing satellites problem: largely resolved by reionization suppressing star formation in small halos + observational incompleteness
• Too big to fail problem: most massive predicted subhalos are denser than observed satellites; baryonic physics and tidal stripping may resolve
• Planes of satellites: Milky Way and M31 satellites concentrate in thin planes; tension with isotropic prediction from LCDM (debated)

Dwarf Galaxies

• Most numerous galaxy type; stellar mass 10^3 to 10^9 solar masses
• Types: dwarf elliptical (dE), dwarf spheroidal (dSph), dwarf irregular (dIrr), ultra-faint dwarfs (UFDs)
• Ultra-faint dwarfs: L < 10^5 L_sun; highest dark matter fractions (M/L up to ~1000); most dark-matter-dominated objects known
• Important for: dark matter constraints (J-factor for annihilation searches), near-field cosmology, chemical enrichment history

---

Key Instruments and Surveys

• Hubble Space Telescope: deep fields revealed galaxy evolution across cosmic time (Hubble Ultra Deep Field to z > 10)
• JWST: rest-frame optical/IR imaging of galaxies at z > 10; SMBH studies; resolved stellar populations
• Gaia: 3D mapping of ~2 billion Milky Way stars; proper motions, parallaxes, radial velocities; revealed disk substructure, streams, merger history (Gaia-Enceladus/Sausage)
• ALMA: submillimeter; dusty star-forming galaxies, gas dynamics, high-z galaxies
• VLT/MUSE: integral field spectroscopy; spatially resolved galaxy kinematics and chemistry
• Vera C. Rubin Observatory (LSST): 10-year survey starting ~2025; billions of galaxies; time-domain science; dwarf galaxy census

---

Anti-Patterns

• Stating the Hubble sequence is an evolutionary sequence: Hubble explicitly noted it was morphological, not evolutionary; ellipticals do not evolve into spirals or vice versa in sequence order
• Claiming all galaxies have supermassive black holes: Observational evidence is strong for massive galaxies; many dwarfs may lack central SMBHs or have intermediate-mass BHs
• Treating the Milky Way as a typical galaxy: It is relatively massive, has low star formation rate for its mass, possesses unusually massive satellite (LMC), and the Local Group is not a cluster environment
• Confusing AGN luminosity with host galaxy luminosity: At high redshift, quasar luminosity can exceed host by factors of 100+; at low z, Seyferts are often outshone by their hosts
• Presenting galaxy rotation curves as the only dark matter evidence: Rotation curves were historically important but are only one of many independent lines of evidence (CMB, lensing, clusters, BBN)
• Stating that spiral arms are fixed structures of stars: They are density waves or transient features; stars move through arm regions
• Conflating the missing satellites problem with a fatal flaw of LCDM: It is largely resolved through a combination of baryonic physics and improved observations
• Using the Milky Way's age and the universe's age interchangeably: The Milky Way formed ~12-13 Gyr ago but the universe is 13.8 Gyr old; the oldest Milky Way stars are ~13 Gyr old but the galaxy assembled over time
• Ignoring the role of environment in galaxy evolution: Cluster vs field environment dramatically affects morphology, gas content, and star formation rate
• Presenting the unified AGN model as explaining everything: It is a useful framework but has known exceptions and refinements needed (clumpy torus, radiative mode vs jet mode, etc.)