A supernova is the final, explosive end of a star. From Type Ia to II-P, IIn and Ib/Ic, dial in the ejecta mass, Ni-56 mass, explosion energy and distance, and watch the Arnett analytic light curve, peak absolute magnitude and Phillips ΔM15 relation update in real time.
Parameters
Supernova type
Explosion mechanism and typical ejecta composition
Ejecta mass M_ej
M☉
Total mass blown out. Ia ≈ 1.4, II-P ≈ 10–20
Ni-56 mass M_Ni
M☉
Synthesised ⁵⁶Ni. The dominant control on peak luminosity
Explosion energy E_kin
foe
Kinetic energy (1 foe = 10⁵¹ erg). Ia ≈ 1.5, II ≈ 1.0
Ejecta velocity v_ej
km/s
Photospheric expansion velocity
Distance d
Mpc
Distance to the supernova. 1 Mpc ≈ 3.26 Mly
Photometric band
B: blue, V: visual (default), Bolometric: all wavelengths
Results
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Diffusion time τ_diff (day)
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Peak luminosity (× 10⁹ L☉)
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Absolute magnitude M_V (mag)
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Apparent magnitude m_V (mag)
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Rise time to peak (day)
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Phillips ΔM15 (mag)
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Supernova explosion — ejecta, shock and observer
The Ni-56 core (white) and outer shock front (orange ring) expand, while γ-rays diffuse through the ejecta toward the observer. The bar at top shows the current position on the light curve.
Arnett's (1982) analytic model. τ_d is the photon diffusion time, κ the opacity, M_ej the ejecta mass and v the expansion velocity. γ-rays from the Ni → Co → Fe chain are thermalised in the ejecta and re-emerge as optical light.
Arnett's simplified peak luminosity and its conversion to absolute V magnitude. M_Ni = 0.6 M☉ gives M_V ≈ -19.0, the canonical SN Ia standard-candle value.
Distance modulus and Phillips (1993) relation. ΔM15 is the B-band decline 15 days after peak and is the workhorse for standardising SN Ia.
About the Supernova Light Curve Simulator
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So a "supernova" is when a star explodes? People talk about Type Ia and Type II — what makes them so different?
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The trigger is fundamentally different. Type Ia is a white dwarf — about the mass of the Sun — that accretes matter from a companion star and at the Chandrasekhar limit (≈1.4 M☉) ignites runaway carbon fusion, blowing the entire star apart: a "thermonuclear" explosion. Type II, Ib and Ic come from massive stars (M ≳ 8 M☉) whose iron core can no longer release energy by fusion and collapses under its own gravity. The collapsed core becomes a neutron star or black hole, and a rebound shock blasts the outer envelope off — "core collapse". Same name, two completely different ways for a star to die.
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But Type Ia somehow have a near-constant brightness, right? That's why they're called "standard candles" — why do they line up so neatly?
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That is the magic of SN Ia. The starting condition — a Chandrasekhar-mass white dwarf — is nearly the same every time, so the amount of radioactive Ni-56 synthesised is also very similar (0.4–0.8 M☉). Around peak the light is powered by Ni-56 → Co-56 → Fe-56 decay; its γ-rays thermalise in the ejecta and emerge as optical photons. Arnett's rule gives L_peak ≈ 2×10^43 erg/s × M_Ni/M☉, so M_Ni = 0.6 in the slider yields about 3×10^9 L☉, or absolute V magnitude -19.0. The same wherever in the universe it happens — so you measure the apparent brightness and get the distance back. That is the trick behind the 1998 discovery of cosmic acceleration by Riess, Perlmutter and Schmidt (2011 Nobel Prize).
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Cool! Then what is the "Arnett rule"? The theory box shows τ_d = √(κM/cv).
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It is the analytic model from Arnett (1982): the supernova's optical light is "the Ni-56 → Co-56 → Fe-56 decay energy smeared over a photon diffusion time τ_d". τ_d is the time photons take to random-walk out of the ejecta and depends on opacity κ, ejecta mass M and expansion velocity v. For typical SN Ia parameters (κ ≈ 0.1 m²/kg, M = 1.4 M☉, v = 10⁴ km/s) it is about 20 days — which is also the rise time to peak. A large τ_d delays, lowers and broadens the peak; a small τ_d sharpens it. Type II-P, which collapses while keeping its hydrogen envelope, has M_ej of 10–20 M☉ and the famous 100-day "plateau" coming from hydrogen recombination at constant photospheric temperature.
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And the Phillips ΔM15 relation — what does "standardising a standard candle" actually mean?
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Phillips (1993) found that the peak absolute magnitude of a SN Ia and ΔM15, the B-band decline over the 15 days after peak, are tightly correlated. Brighter SN Ia decline more slowly; dimmer ones decline faster. Applying this correction shrinks scatter to ±0.15 mag, ±7% in distance. Riess and collaborators used this ΔM15-corrected sample at high redshift to discover that the expansion of the universe is accelerating. Today LSST/Rubin Observatory, JWST and the Zwicky Transient Facility (ZTF) detect hundreds of new SN every night and keep refining the relation. Historic landmarks include SN 1987A (LMC, first neutrino detection), SN 2011fe (Pinwheel galaxy, the most-observed SN Ia) and SN 2014J (M82, nearby Ia).
Frequently Asked Questions
For both thermonuclear (Type Ia) and core-collapse (Type II, Ib/Ic) supernovae, the light around peak comes from gamma-rays released when the freshly synthesised Ni-56 decays through Co-56 to Fe-56 and is thermalised in the expanding ejecta. Arnett's empirical rule gives L_peak ≈ 2×10^43 erg/s × (M_Ni / M_sun). For a Ni-56 mass of 0.6 M☉ this becomes L_peak ≈ 3.14×10^9 L_sun, or an absolute V magnitude of about -19.0 — the physical basis for using SN Ia as cosmological distance indicators.
It is the timescale on which photons random-walk out of the optically thick ejecta. Arnett (1982) wrote τ_diff = √(κ M_ej / (c v)), where κ is the opacity, M_ej the ejecta mass and v the expansion velocity. For SN Ia values (M_ej = 1.4 M☉, v = 10^4 km/s, κ ≈ 0.1 m²/kg) this gives τ_diff ≈ 20 days, which is also the typical rise time to peak. Massive II-P supernovae have larger M_ej and slower rise; stripped Ib/Ic objects have smaller M_ej and faster rise.
Phillips (1993) showed that the peak absolute magnitude of a SN Ia is tightly correlated with ΔM15, the decline in B magnitude in the 15 days after peak. Brighter Ia events decline slower; dimmer ones decline faster. Applying this correction standardises SN Ia peaks to ±0.15 mag accuracy and was the key tool behind the 1998 discovery of the accelerating universe (2011 Nobel Prize, Riess, Perlmutter, Schmidt). This tool reports the simplified form ΔM15 ≈ 0.7 - 0.5·(M_Ni - 0.6).
Apparent magnitude m and absolute magnitude M are linked by the distance modulus m - M = 5·log10(d/10 pc). Because SN Ia all peak at roughly M_V ≈ -19.0, measuring m_V immediately gives d — that is what makes them standard candles. A SN Ia is m ≈ 11 at 10 Mpc, 16 at 100 Mpc and 21 at 1 Gpc, directly setting the depth that Hubble, Rubin/LSST and JWST need to reach.
Real-World Applications
Cosmological distance ladder and the Hubble constant: Because SN Ia have nearly the same absolute magnitude (M_V ≈ -19.0), they measure distances from nearby galaxies all the way past redshift z ≈ 1. The SH0ES programme combines Cepheid variables with SN Ia to obtain H_0 ≈ 73 km/s/Mpc, in tension with the Planck CMB value H_0 ≈ 67 — the "Hubble tension" that is the most-discussed open problem of present-day cosmology. A single SN Ia's photometric precision feeds directly into cosmological parameters.
Large time-domain surveys (LSST/ZTF/Rubin): Vera C. Rubin Observatory (LSST) will detect more than 2,000 new supernova candidates every night during its 2025–2035 ten-year run. ZTF has already classified more than 5,000 SN. Statistical analyses of light-curve parameters (rise time, ΔM15, peak magnitude) drive precision cosmology, constrain the dark-energy equation of state w, and uncover unusual SN sub-classes such as SN Iax and super-Chandrasekhar events.
Nucleosynthesis and galactic chemical evolution: Roughly half of the iron in the universe comes from SN Ia, while α-elements such as oxygen and magnesium are mainly forged in core-collapse SN. Changing M_Ni in this tool directly tracks the amount of iron (Ni-56 → Fe-56) returned to the universe. Galaxy formation simulations (IllustrisTNG, EAGLE) take SN Ia and CC-SN rates as primary inputs.
Multimessenger astronomy: SN 1987A was the first SN observed in light, neutrinos, radio and X-rays. Kamiokande and IMB caught 24 neutrinos and confirmed the neutrino burst from core collapse. The next Galactic supernova is expected to yield around 10^4 neutrinos in Super-Kamiokande-Gd, KamLAND, IceCube and JUNO, allowing detailed reconstruction of core-collapse physics.
Common Misconceptions and Pitfalls
The first myth is that "SN Ia peak luminosities are perfectly identical". The intrinsic scatter is actually about ±0.4 mag; only after applying the Phillips relation (ΔM15) and colour corrections (e.g. SALT2) does the scatter shrink to ±0.15 mag. Non-standard "sub-Chandrasekhar" and "super-Chandrasekhar" SN Ia exist and break the standardisation. Cosmological analyses must carefully exclude these or they bias H_0 and w. The simple Phillips form (ΔM15 ≈ 0.7 - 0.5(M_Ni - 0.6)) in this tool is for intuition only; production light-curve fitters such as SALT2 and SNooPy are much richer.
Next, Arnett's model is not universal. Arnett (1982) assumes a spherically symmetric, homogeneous, optically thick photosphere and that the decay energy is smeared by the diffusion time τ_d at peak. This is a good approximation for SN Ia near peak but does not apply to the Type II-P plateau (hydrogen recombination), Type IIn (interaction with circumstellar matter) or the asymmetric, GRB-related Ib/Ic events. In this tool the same framework is applied to all four types, so II-P / IIn / Ibc results should be read as order-of-magnitude only.
Finally, apparent magnitude is not set by distance alone. Real observations include extinction by dust in the host galaxy and the Milky Way (E(B-V)). SN 2014J in the M82 dust lane appeared about 1.6 mag fainter than its intrinsic brightness. High-redshift SN further require K-corrections (mismatch between observed and rest-frame bands), cosmological K-corrections, and intergalactic dust corrections. The distance modulus m - M = 5log(d/10 pc) used here only captures geometric dilution in vacuum.
How to Use
Select supernova type (Ia, II-P, IIn, or Ib/Ic) to establish baseline physics
Adjust ejecta mass (mejNum, range 1–20 M☉) using the slider to model explosion violence
Set Ni-56 mass (mniNum, range 0.4–2.0 M☉) controlling radioactive heating and light curve decay
Modify kinetic energy (energyNum, range 10⁵⁰–10⁵² erg) to simulate shock strength
Input ejection velocity (velNum, range 5,000–30,000 km/s) for photospheric dynamics
Enter distance (parsec) for apparent magnitude calculation
Click Calculate to generate diffusion timescale, peak luminosity, and magnitude predictions
Worked Example
Type II-P supernova with ejecta mass 15 M☉, Ni-56 mass 0.08 M☉, kinetic energy 1.0×10⁵¹ erg, velocity 8,000 km/s at distance 10 Mpc yields: diffusion time τ_diff ≈ 85 days, peak luminosity ≈ 0.3×10⁹ L☉ (absolute magnitude M_V ≈ −16.5), apparent magnitude m_V ≈ 23.8, rise time ≈ 95 days, ΔM15 ≈ 1.1 mag. Increasing Ni-56 to 0.15 M☉ brightens peak by ~0.8 mag and accelerates decay.
Practical Notes
Type Ia: Fix ejecta ~1.4 M☉, vary Ni-56 (0.4–0.8 M☉) to match Phillips relation; higher Ni56 → brighter, slower decline (ΔM15 reduced)
Type II-P: Longer diffusion times (~80–120 days) due to high ejecta; plateau phase duration correlates with ejected mass
Distance uncertainty dominates apparent magnitude error; use parallax or redshift+Hubble constant for accuracy
Velocity affects photospheric temperature; underestimated velocities compress timescales and suppress early UV flux