Type Ia supernovae · distance · expansion history
A Type Ia supernova can briefly rival the light of its host galaxy. Correct its light-curve width and colour, compare apparent with standardized luminosity, and it yields a distance. Repeat that measurement across redshift and the changing expansion rate appears in the Hubble diagram.
The transient · Type Ia
The circled point is the supernova itself, observed by Swift on 22 January 2014. False colour maps mid-UV to blue, near-UV to green, and visible light to red.
What is a supernova?
A supernova is observed first as a new point source that brightens and fades over weeks or months. Years later, telescopes may resolve the ejecta and shocks as a remnant. The gallery above deliberately shows both stages.
Ia
A carbon–oxygen white dwarf in a binary system undergoes runaway nuclear burning and is disrupted. The light curve is powered principally by the radioactive decay chain 56Ni → 56Co → 56Fe. Type Ia spectra lack hydrogen and show strong silicon near maximum light.
They are standardizable, not perfectly standard: broader, slower-declining light curves are intrinsically brighter, and colour carries luminosity and dust information.
II / Ib / Ic
A massive star exhausts nuclear fuel, its core collapses, and the outer layers are expelled. SN 1987A, Cassiopeia A, and the Veil Nebula are core-collapse examples included to show the anatomy of ejecta and blast waves—not the Type Ia distance sample used below.
From photons to expansion history
Repeated images measure flux versus time in several bands; spectroscopy supplies classification and redshift.
f(t, λ) → mB, x1, c, zLight-curve shape and colour corrections reduce object-to-object luminosity variation.
mBcorr = mB + αx1 − βc + …The difference between corrected apparent magnitude and standardized absolute magnitude gives distance modulus.
μ = mcorr − M = 5 log10(dL/Mpc) + 25The redshift-dependent shape of μ(z), not a sky image, constrains the expansion history and Ωm.
μ(z) ↔ H(z), Ωm, ΩΛExperiment below
After profiling over an unknown magnitude zero-point, how strongly does the redshift-dependent shape of this subset prefer a low-density flat ΛCDM model over an Ωm = 1 matter-only universe?
Interactive analysis
Distance–redshift relation
Observed distance moduli with diagonal uncertainty bars, compared with the selected flat ΛCDM curve and an offset-profiled matter-only curve.
Posterior predictive check
Included observations are scaled by their effective diagonal uncertainty. The shaded band marks ±1σ and dashed lines mark ±2σ.
Profile best Ωm
—Δχ² = 1 interval: —Matter-only separation
—Δχ²; diagonal-only diagnosticCurrent fit
—χ² / included light curveProfiled offset
—absorbs H0–magnitude scaleDeceleration parameter
—at z = 0Parameter inference
The orange line is this lab’s diagonal-error subset profile. The blue band marks the published Pantheon+ SNe-only Ωm benchmark.
Interpretation
Waiting for the first analysis run.
Calculation
The luminosity distance is evaluated numerically with ΩΛ = 1 − Ωm and no radiation term.
dL = (1 + z)c/H0 ∫ dz′/E(z′)The released diagonal distance-modulus error is combined with the selected intrinsic scatter.
σ²eff,i = σ²diag,i + σ²intAt every Ωm, the additive magnitude offset is solved analytically, isolating curve shape from absolute scale.
ΔM̂ = Σwi(μi − μmodel,i) / ΣwiThe interval is the grid crossing at Δχ² = 1 under independent Gaussian diagonal errors.
χ² = Σ[(μi − μmodel,i − ΔM̂)/σeff,i]²Data used in this browser
The official distance table is sorted by zHD; 180 evenly spaced row indices preserve the full 0.00122–2.26137 redshift span. The source file is checksum-pinned and can be rebuilt with the included acquisition script.
CIDzHDMU_SH0ESMU_SH0ES_ERR_DIAG| Object | zHD | μ | σdiag | Included | Residual | Standardized |
|---|
Selected literature