Spectral Energy Distribution

The idea: one curve, many wavelengths

Take a single astronomical object — a star, a galaxy, a quasar, a dusty protoplanetary disk — and measure how bright it is in every band you can: radio, microwave, far-infrared, mid-infrared, near-infrared, optical, ultraviolet, X-ray, gamma ray. Plot those brightnesses against wavelength (or frequency). The resulting curve is the object's spectral energy distribution, or SED. It is, in a real sense, a single object's entire electromagnetic budget laid out on one axis.

The power of the SED is that its shape is diagnostic. You do not need to resolve individual spectral lines to learn an enormous amount. Where the curve peaks tells you the dominant temperature. A second bump at longer wavelengths betrays cooler dust. A long, straight, scale-free section that refuses to turn over is the fingerprint of a non-thermal engine. The wholesale shift of fixed features toward the red gives the redshift. One curve carries temperature, luminosity, dust mass, star-formation rate, stellar mass, and distance — which is why nearly every modern survey, from the infrared satellite IRAS to JWST, is fundamentally an SED-measuring machine.

Why we plot νF_ν against log frequency

An SED is almost always shown as νF_ν (equivalently λF_λ) on the vertical axis versus the logarithm of frequency (or wavelength) on the horizontal. The reason is physical bookkeeping. The flux density F_ν is energy per unit frequency; multiplying by ν and plotting against log ν makes the quantity energy per logarithmic frequency interval:

ν F_ν = energy emitted per unit log(ν)
∫ F_ν dν = ∫ (ν F_ν) d(ln ν)

That means the area under any segment of the νF_ν curve is proportional to the actual power the object radiates in that band, and the height of the curve directly shows where the energy comes out. The peak of νF_ν is "where this object shines." A region that looks flat in F_ν can be radiating enormously different power per decade once you account for the log axis — so νF_ν is the honest representation. Note that the νF_ν peak of a blackbody lands at a shorter wavelength than the F_ν peak (≈ 3670 µm·K vs 5100 µm·K in the Wien displacement constant) precisely because of that extra factor of ν.

The thermal backbone: blackbodies and Wien's law

The simplest SED is a single blackbody. A body in thermal equilibrium at temperature T radiates the Planck spectrum:

B_ν(T) = (2hν³/c²) · 1 / (exp(hν/kT) − 1)        [per unit frequency]
B_λ(T) = (2hc²/λ⁵) · 1 / (exp(hc/λkT) − 1)        [per unit wavelength]

The location of the peak is set by temperature alone — Wien's displacement law:

λ_peak · T = 2.898 × 10³ µm·K      (using B_λ)
T = 6000 K  →  λ_peak ≈ 0.48 µm   (blue-green, the Sun)
T = 30 K    →  λ_peak ≈ 97 µm      (far-infrared, cold dust)
T = 2.725 K →  λ_peak ≈ 1.06 mm    (microwave, the CMB)

On either side of the peak the Planck curve has two limits worth knowing on sight. At low frequency (hν ≪ kT) it follows the Rayleigh-Jeans law, B_ν ∝ ν², a gently rising slope. At high frequency (hν ≫ kT) it follows the Wien tail, B_ν ∝ ν³ exp(−hν/kT), an exponential cliff. The presence of that exponential cutoff is the unmistakable signature of a thermal source: real photospheres and dust do not radiate appreciably far above their thermal peak. When an SED instead keeps going as a straight power law past where any reasonable temperature should have cut it off, the emission is not thermal.

Reading a galaxy's SED component by component

A real galaxy's SED is a superposition of several physical components, each occupying its own wavelength territory. Learning to recognise them turns the curve into a parts list.

Wavelength band	Dominant emitter	Typical T / mechanism	What it measures
Radio (cm–m)	Synchrotron + free-free	Non-thermal / 10⁴ K plasma	Supernova rate, AGN jets
Far-IR (50–500 µm)	Cold dust	~15–40 K blackbody (modified)	Dust mass, obscured SFR
Mid-IR (5–50 µm)	Warm dust + PAH features	~100–300 K + line bands	Star-forming regions, AGN torus
Near-IR (1–5 µm)	Old stars (1.6 µm bump)	~3000–4000 K photospheres	Stellar mass
Optical (0.4–1 µm)	Main-sequence stars	~4000–10000 K	Stellar populations, ages
UV (0.1–0.4 µm)	Young massive stars	~10⁴–4×10⁴ K (O/B)	Unobscured SFR
X-ray	Hot gas, accretion, XRBs	10⁶–10⁸ K / Comptonisation	AGN, hot halo, binaries

The crucial insight is that energy is conserved across the SED: ultraviolet light absorbed by dust does not vanish, it reappears in the far-infrared. A galaxy that looks dim in the UV because it is dust-choked will be correspondingly luminous in the far-IR. This energy-balance constraint is what lets modern SED-fitting codes — MAGPHYS, CIGALE, Prospector — solve simultaneously for the unobscured and obscured star-formation rate by demanding that the energy absorbed in the UV/optical equals the energy re-emitted in the IR.

Power laws: the non-thermal engines

When a source is powered by relativistic particles rather than a hot surface, its SED looks completely different. Synchrotron radiation from electrons gyrating in a magnetic field, and inverse-Compton scattering of low-energy photons up to high energies, both produce broad power laws:

F_ν ∝ ν^(−α)        α = spectral index
S(ν) for an electron population N(E) ∝ E^(−p)
   gives synchrotron α = (p − 1)/2      (typically α ≈ 0.7 for SNRs)

These are scale-free: a power law has no characteristic frequency, so it can stretch across ten or more decades without turning over. That is the giveaway. A blazar, an active galactic nucleus with its jet aimed at us, shows a famous double-humped νF_ν SED — a low-frequency synchrotron hump (radio to X-ray) and a high-frequency inverse-Compton hump (X-ray to TeV gamma rays). An ordinary quasar shows the "big blue bump," a thermal accretion-disk component peaking in the rest-frame ultraviolet near 10⁵ K (matching the T ∝ M^(−1/4) disk scaling for a 10⁸ M☉ black hole), riding on top of a flatter non-thermal continuum. The interplay of thermal bumps and power-law plateaus across an AGN SED is precisely how observers disentangle the accretion disk, the dusty torus, the corona, and the jet.

Quantified examples: where real objects peak

The following sources span fourteen decades in temperature and luminosity, yet each is summarised by a recognisable SED shape. Luminosities are bolometric (integrated over the whole SED) unless noted.

Object	Characteristic T / index	SED peak (νF_ν)	Bolometric L	SED shape
Sun (G2 V)	5772 K	~0.5 µm	3.83 × 10³³ erg/s	Single blackbody + lines
Cold ISM dust	~18 K (β ≈ 1.8)	~160 µm	—	Modified blackbody
T Tauri disk	star + ~10–1500 K dust	optical + IR excess	~1 L☉	Stellar + flat IR plateau
Starburst (M82)	~40 K dust dominant	~60–80 µm	~3 × 10¹⁰ L☉	Far-IR dominated
ULIRG (Arp 220)	~45 K, 95% in IR	~60 µm	~1.4 × 10¹² L☉	Almost pure far-IR
Quasar (3C 273)	disk ~10⁵ K + jet	UV bump + flat	~10⁴⁶ erg/s	Blue bump + power law
Blazar (Mrk 421)	synchrotron + IC	two humps (X-ray, TeV)	~10⁴⁵ erg/s	Double-humped power law
CMB	2.72548 K	~1.06 mm	—	Perfect blackbody

The CMB deserves special mention: the COBE/FIRAS instrument measured its SED in 1990 and found it to be a blackbody at 2.725 K to better than 1 part in 10⁴ — the most precise blackbody ever observed in nature, and a foundational confirmation of the hot Big Bang. At the other extreme, an ultraluminous infrared galaxy like Arp 220 (77 Mpc away, L ≈ 1.4 × 10¹² L☉) emits roughly 95 percent of its prodigious luminosity in the far-infrared, completely hidden from optical view — a fact you could never guess without measuring its SED across the dust bump.

SED fitting and photometric redshifts

In practice you rarely have a continuous SED; you have brightnesses measured through a handful of broadband filters — say the ugrizy optical bands plus near- and mid-IR. SED fitting takes a library of model templates (stellar population synthesis spectra, dust emission models, AGN templates), redshifts and reddens them, convolves each with the instrument filter curves, and finds the combination of parameters whose synthetic photometry best matches the data. The outputs are physical: stellar mass, age, star-formation history, dust attenuation A_V, and the bolometric luminosity.

The same machinery delivers a distance. Galaxy SEDs carry several fixed features: the 4000 Å break (the pile-up of metal absorption lines below 4000 Å in old stars), the Lyman break at 912 Å (the wall where neutral hydrogen absorbs everything bluer), and the 1.6 µm stellar bump. As redshift z increases, every feature moves to a longer observed wavelength by the factor (1+z):

λ_observed = λ_rest × (1 + z)
4000 Å break at z = 1  →  observed at 8000 Å (z-band)
Lyman 912 Å break at z = 7  →  observed at 7300 Å
photo-z accuracy with good multi-band data: Δz/(1+z) ≈ 0.03–0.05

By finding the redshift that best aligns template features with the observed colours, surveys assign photometric redshifts to millions of galaxies far too faint for spectroscopy. The Lyman-break "dropout" technique — a galaxy that vanishes in bands below the redshifted Lyman break but appears in redder ones — is how the highest-redshift galaxies are found; JWST has used dropout SEDs to identify candidates beyond z ≈ 13, when the universe was under 350 million years old.

The dust SED is not a pure blackbody

Cold interstellar dust does not radiate as an ideal blackbody. Grains are inefficient emitters at long wavelengths, so the far-IR/submillimetre SED is a modified blackbody (greybody) with an emissivity that rises with frequency:

S_ν ∝ ν^β · B_ν(T_dust)        β ≈ 1.5 – 2.0 (dust emissivity index)
T_dust ≈ 15 – 40 K for the diffuse and star-forming ISM

The dust mass follows from the long-wavelength (Rayleigh-Jeans) flux, where the SED is optically thin, because there M_dust ∝ S_ν D² / (κ_ν B_ν(T)). This is why submillimetre facilities like ALMA and the now-retired Herschel and SCUBA-2 are dust-weighing machines: a single 850 µm flux on the cold tail of the SED, with a temperature from the peak, yields a dust mass. There is a notorious degeneracy here — a colder dust temperature mimics a higher dust mass at fixed flux — which is why sampling both sides of the far-IR peak matters so much.

Where SEDs do the heavy lifting

• Classifying young stellar objects. The slope of the near-to-mid-IR SED defines the Lada classes: Class 0/I protostars have rising IR SEDs (envelope-dominated), Class II T Tauri stars show an optical photosphere plus a flat IR excess (disk), and Class III stars have only a tiny excess (disk dissipated). The SED slope literally tracks the stages of star and planet formation.
• Measuring obscured star formation. Roughly half of all the starlight ever emitted has been absorbed by dust and re-radiated in the infrared — the cosmic infrared background. You cannot count this star formation in the UV; you must integrate the far-IR bump of the SED.
• Disentangling AGN from star formation. A hot dusty torus around an accreting black hole adds a mid-IR bump (~3–30 µm) that star-forming dust alone cannot produce. SED decomposition separates the AGN and host contributions to the bolometric luminosity.
• Brown dwarf and exoplanet characterisation. A directly imaged planet or brown dwarf is characterised almost entirely by its SED: the peak gives effective temperature (hundreds to ~2000 K, peaking in the near-IR), and molecular absorption bands (water, methane, CO) carve the broadband shape that defines the L, T, and Y spectral classes.
• Cosmological surveys. Vera C. Rubin Observatory's LSST and Euclid will measure SEDs (through photometry) for billions of galaxies, deriving photometric redshifts that underpin weak-lensing and large-scale-structure cosmology. The science return rests on how well the SED templates and photo-z calibration hold up.

Common misconceptions and edge cases

• "The SED peak is always the temperature." Only for a single optically thick thermal component. A composite SED has multiple peaks, and a power-law source has no thermal peak at all. Reading a temperature off the peak of a synchrotron source is meaningless.
• "F_ν and νF_ν peak at the same place." They do not. Because of the extra factor of ν, the νF_ν peak of a given blackbody sits at a shorter wavelength than the F_ν peak. Always check which axis you are reading before quoting a peak wavelength or a temperature.
• "You measured it in one band, so you know the luminosity." The bolometric luminosity is the integral over the whole SED. A galaxy bright in the optical but dust-choked can have most of its luminosity in the unobserved far-IR; quoting an optical luminosity as "the" luminosity can be off by an order of magnitude.
• "Redshift just dims and reddens everything uniformly." Redshift stretches the SED in wavelength by (1+z) and dims it; the observed-frame band you measure samples a bluer rest-frame band for higher-z objects. Comparing objects at different redshifts requires a "K-correction" to a common rest-frame band — forgetting it biases every colour and luminosity.
• "Cold dust and lots of dust look the same." On the long-wavelength tail, lowering the dust temperature and raising the dust mass both raise the flux, so they are partly degenerate. Breaking that degeneracy requires sampling both the rising and falling sides of the far-IR peak — a single submillimetre point is not enough.
• "A featureless straight SED is boring." The opposite — a clean, decades-long power law with no thermal turnover is the strongest possible evidence for a non-thermal, relativistic engine: a jet, a pulsar wind, or a supernova remnant accelerating particles.