Spiral Galaxy

Anatomy of a spiral

A spiral galaxy is a layered system. From the centre outward:

• Nucleus. A small dense region at the centre, often hosting a supermassive black hole. Sagittarius A* in the Milky Way is 4.3 × 10⁶ M_sun.
• Bulge. A spheroidal swarm of old red stars, kinematically distinct from the disk. Like a small elliptical embedded at the centre. Mass ~ 10⁹ – 10¹⁰ M_sun.
• Bar (in SB galaxies). A central elongated stellar structure threading the bulge. Drives gas inward and may trigger central starbursts and AGN activity. Roughly half of nearby disk galaxies are barred.
• Disk. A thin (~ 300 pc) rotating layer of stars, dust, and cold gas. Stellar populations span all ages with active ongoing formation. Exponential surface-brightness profile with scale length ~ 3 kpc for a Milky-Way-like galaxy.
• Spiral arms. Trailing density-enhancements in the disk, traced by young blue stars, HII regions and dust lanes. Two main grand-design arms and many spurs in flocculent or multi-arm spirals.
• Thick disk. An older, more dispersed disk component thicker than the thin disk (~ 1 kpc), populated by intermediate-age stars.
• Stellar halo. A diffuse cloud of very old, low-metallicity halo stars and globular clusters extending to tens of kpc.
• Dark-matter halo. A roughly spherical halo of cold dark matter ~ 10× the stellar mass, extending out to ~ 200 kpc and producing the flat rotation curve.

The Sa, Sb, Sc sequence (and SB)

Hubble's 1926 scheme distributed disk galaxies along a sequence ordered by three correlated properties: bulge-to-disk ratio, spiral-arm tightness, and resolved star-forming features. The same axis classifies both ordinary (S) and barred (SB) spirals.

Class	Bulge / disk	Arm winding	Star formation	Example
Sa / SBa	Large bulge	Tightly wound	Modest	NGC 1302, NGC 2841
Sb / SBb	Intermediate	Moderate	Active	Milky Way (SBb/SBbc), M31
Sc / SBc	Small bulge	Loosely wound	Vigorous	M33, M101, NGC 3344
Sd / SBd	Almost no bulge	Very open	Very vigorous	NGC 7793
Sm / Irr	None	Irregular	High	Large Magellanic Cloud

The Hubble sequence is descriptive, not evolutionary: Hubble himself did not claim galaxies move along it. Modern interpretations connect bar formation, mergers, and gas accretion to position on the sequence.

Why arms exist — the density-wave picture

The naive expectation — that an initial spiral perturbation would wind up tighter and tighter as the disk rotates differentially — fails fast. Arms in the Milky Way at the Sun's radius would have wrapped through 5 full turns in 10 Gyr; observed spirals show only 1–2 turns. The resolution proposed by C. C. Lin and Frank Shu in 1964 is that spiral arms are not material features but density waves — quasi-stationary patterns in the disk that rotate at a single pattern speed Ω_p, slower than the local material rotation Ω(r).

Gas approaching the arm from behind is compressed by ~ a factor 2–3 in surface density, triggering gravitational collapse and star formation. Young blue stars and HII regions appear inside the arm. As individual stars age and drift downstream of the arm, they redden — explaining the observed colour gradient across a spiral arm: dust lanes on the trailing edge, then HII regions, then young blue stars, then redder older populations downstream.

Barred spirals add a separate dynamical phenomenon: the bar is a real material feature (a stellar orbit family aligned along an elongated potential) that drives gas inward, can fuel central starbursts and AGN, and often connects to outer spiral arms. Bars can form spontaneously from disk instabilities; they can be destroyed by central mass accumulation and reform later.

The Milky Way in particular

• Class. Barred spiral SBb or SBbc. The bar was confirmed by infrared imaging from COBE in the 1990s and refined by surveys like GLIMPSE in the 2000s.
• Diameter. ~ 100 000 light-years (~ 30 kpc) for the visible stellar disk.
• Bar length. ~ 5 kpc semi-major axis, oriented ~ 27° from the Sun-Galactic-centre line.
• Mass. Stellar mass ~ 5 × 10¹⁰ M_sun; total mass within 50 kpc ~ 5 × 10¹¹ M_sun; halo mass possibly 10¹² M_sun.
• Number of stars. Estimated 100–400 billion.
• Rotation speed at the solar circle. ~ 220–240 km/s, with the Sun at R_0 = 8.3 kpc on a 240 Myr orbit.
• Number of spiral arms. Four major (Sagittarius, Scutum-Centaurus, Perseus, Norma) plus several minor spurs, including the Local Arm where the Sun resides.
• Black hole. Sagittarius A* at 4.3 × 10⁶ M_sun (measured from S-star orbits, EHT-imaged 2022).

Flat rotation curves and dark matter

If a spiral galaxy's mass were dominated by the visible stars and gas, rotation speed should fall off beyond the disk edge as v(r) ∝ r^(−1/2), the Keplerian decline. Instead, 21-cm HI and Hα observations of spiral galaxies overwhelmingly find flat or even slightly rising rotation curves out to many disk scale lengths. Vera Rubin's 1970s systematic survey was the decisive empirical demonstration that something invisible must dominate the outer mass — what we now call dark matter.

The simplest explanation is a roughly spherical dark-matter halo with density profile ρ(r) ~ r^(−2) at intermediate radii (yielding v ∝ const), tapering at large radii. NFW (Navarro-Frenk-White) profiles from cosmological simulations have ρ ∝ 1/[r(1 + r/r_s)²], close to the observed shape but with a central cusp that conflicts with the inferred density cores of dwarf galaxies — the "core-cusp problem" — one of the lingering tensions in galaxy formation.

The Tully-Fisher relation

For spiral galaxies, the optical luminosity L and the maximum disk rotation speed v_max obey L ∝ v_max^4 to remarkable accuracy (scatter ~ 0.4 mag in the I-band, less in the infrared). Brent Tully and Richard Fisher discovered the correlation in 1977. The 4th-power exponent emerges from a virial argument: v² ∝ M/R for self-gravity, M ∝ L (for fixed mass-to-light), and the Faber-Jackson-like assumption that surface brightness is roughly constant give L ∝ v^4.

Operationally, you measure v_max from a 21-cm HI line width or a Hα rotation curve, apply the Tully-Fisher relation calibrated locally with Cepheid distances, and read off a distance modulus. The result is a standard rung of the extragalactic distance ladder, complementary to surface-brightness fluctuations and Type Ia supernovae.

Worked example — Milky Way mass at the solar circle

Take the rotational speed at the Sun, v = 220 km/s, at galactocentric radius R = 8.3 kpc. Newtonian central-force balance gives the enclosed mass:

M(R) = R v² / G = (8.3 × 3.086 × 10¹⁹ m) × (2.2 × 10⁵ m/s)² / (6.674 × 10⁻¹¹) ≈ 9.3 × 10⁴⁰ kg ≈ 4.7 × 10¹⁰ M_sun.

So the mass inside the Sun's orbit is roughly half the total stellar mass of the Galaxy. Move out to 50 kpc, where v is still ~ 220 km/s (flat curve), and you get an enclosed mass of nearly 6 × 10¹¹ M_sun. The visible stellar mass alone cannot account for this — dark matter supplies the rest.

Brief history

William Herschel mapped a flattened disk of stars containing the Sun by counting in different directions in the 1780s. Lord Rosse's 1845 drawings of M51 first showed clear spiral structure in what was then called a "nebula." Edwin Hubble in 1924 used Cepheid variables in M31 to establish that the spiral nebulae are external galaxies. Vera Rubin in the 1970s established the flat rotation curve and the dark-matter inference. Lin and Shu in 1964 supplied the density-wave theory of spiral structure. Modern surveys — SDSS, Pan-STARRS, Gaia — now measure spiral-galaxy properties for millions of systems and the Milky Way's own structure to a few percent.

Common pitfalls

• Treating the Hubble sequence as evolutionary. Sa does not "evolve" into Sc. Position on the sequence reflects formation conditions (gas fraction, environment, merger history), not age.
• Picturing spiral arms as rigid features rotating with the disk. They are density waves; material flows through them. Same gas atom may cross several arms in a Gyr.
• Confusing the Milky Way's bar with the disk. The bar is a separate kinematic structure within the inner disk, ~ 5 kpc long; it is not the disk's symmetry axis.
• Reading flat rotation curves as proof of MOND or modified gravity. Standard ΛCDM with NFW dark-matter halos reproduces flat curves; MOND is an alternative that does not require dark matter but has its own difficulties.
• Assuming all spirals are barred. About half are. The fraction depends on observation wavelength: bars are easier to spot in the near-infrared, where dust extinction is small.
• Counting arms naively. Many spirals are flocculent (many short fragments) rather than grand-design (two clean arms). Both are valid spiral morphologies.