Sedov-Taylor blast wave calculator

The Sedov-Taylor blast wave calculator determines radius R(t) of a strong spherical shock wave generated by a point explosion (supernova, nuclear bomb, gamma-ray burst) expanding in a uniform medium, per the formulation by Soviet physicist Leonid Sedov 1946 and independently by British physicist Sir Geoffrey Ingram Taylor 1950. The self-similar formula: R(t) = ξ_0 · (E · t² / ρ_0)^(1/5), with E total explosion energy in joules, t elapsed time in seconds, ρ_0 ambient medium density kg/m³, ξ_0 dimensionless polytropic constant (γ = 5/3 ideal gas → ξ_0 = 1.1517 Sedov 1946; γ = 4/3 relativistic plasma → ξ_0 = 1.033). Shock velocity: v_shock = dR/dt = (2/5) · R/t. Postshock temperature: T_shock = (3/16) · (μ · m_H / k_B) · v_shock². Three SNR evolution phases:

• free expansion 1,000 years (R = v_ej · t linear, ejecta v_ej = 10,000 km/s)
• Sedov-Taylor adiabatic 100,000 years (R ∝ t^(2/5), 95% of visible evolution)
• pressure-driven snowplow > 100,000 years (R ∝ t^(1/4) radiative cooling). Italian historical applications:

• Crab Nebula M1 SN 1054 observed China + Italy (Schiaparelli) 1054, INAF Brera Milan 1762 (E = 10⁴⁴ J = 10⁵¹ erg, ρ_0 = 10⁻²¹ kg/m³, today t = 970 years → R_Sedov = 1.15 × (10⁴⁴ × (3.06×10¹⁰)² / 10⁻²¹)^(1/5) = 3.5 pc consistent with 5.5 pc observed Crab)
• SN 1572 Tycho Brahe + Galileo Galilei study
• SN 1604 Kepler last galactic
• SN 1987A LMC INAF TNG La Palma 1998 + ESO
• SN 2011fe M101 INAF + TNG first within hours
• Cassiopeia A 11,000 ly INAF (youngest galactic SNR ~340 years)
• Cygnus Loop Veil Nebula INAF 2,400 ly
• Vela SNR 800 ly INAF. Italian nuclear applications:

• Enrico Fermi Rome 1901 - Chicago 1954 Nobel Prize 1938 fission discovery (Rome 1934 with Edoardo Amaldi + Bruno Pontecorvo + Emilio Segrè + Ettore Majorana "Via Panisperna boys")
• Chicago Pile-1 December 1942 first controlled chain reaction (Manhattan Project)
• Trinity test New Mexico 16 July 1945 21 kt TNT = 8.8×10¹³ J (G.I. Taylor 1947 deduced yield from public photographs of spherical shock front exactly applying Sedov-Taylor 1946 formula still classified! - "The Formation of a Blast Wave by a Very Intense Explosion" Proc. R. Soc. Lond. 1950)
• Hiroshima 6 August 1945 Little Boy 15 kt TNT
• Castle Bravo 1 March 1954 Bikini 15 Mt = 6.3×10¹⁶ J H-bomb. Italian X-ray missions SN remnants observation: BeppoSAX 1996-2002 ASI; XMM-Newton ESA 1999 with Italian RGS Reflection Grating (Padua + Bologna spectral resolution R=800 Ne Mg Si S Fe abundances); Chandra NASA 1999 0.5" imaging; NuSTAR 2012 NASA hard X-ray; IXPE 2021 NASA-ASI Imaging X-ray Polarimetry (Cassiopeia A magnetic polarization gas pixel detector INAF Brera + INFN Pisa); Athena ESA 2035 X-IFU calorimeter INAF Palermo 25%

Italian Sedov-Taylor astrophysics tables

(Source: Sedov 1946 + Taylor 1950 Proc. R. Soc. + Landau-Lifshitz "Fluid Mechanics" 1959 + Reynolds 2008 ARA&A + INAF Rome 2002).

Italian Sedov-Taylor calculation examples

• Crab Nebula M1 SN 1054 observed China + Italy July 1054 INAF Brera Milan 1762: E = 10⁵¹ erg = 10⁴⁴ J Type II core collapse SN kinetic energy; ρ_0 = 10⁻²¹ kg/m³ galactic ISM; t = 970 years = 3.06×10¹⁰ s. R_Sedov = 1.1517 × (10⁴⁴ × (3.06×10¹⁰)² / 10⁻²¹)^(1/5) = 1.13×10¹⁶ m = 0.37 pc Sedov pure radius. Observed Crab pulsar PSR B0531+21 with 5.5 pc remnant → mixed free expansion + Sedov-Taylor phase
• SN 1987A Large Magellanic Cloud 50 kpc INAF TNG La Palma 1998 + ESO: E = 10⁴⁴ J, ρ_0 = 10⁻²² kg/m³, t = 38 years. R_Sedov = 0.7 pc. HST + JWST 2023 ring confirmation
• Cassiopeia A 11,000 ly 340 years IXPE NASA-ASI 2021 INAF Brera: E = 2×10⁴⁴ J, ρ_0 = 10⁻²¹ kg/m³. R_Sedov = 1.7 pc consistent with 2.5 pc shell observations
• Trinity atomic bomb test New Mexico 16 July 1945 Manhattan Project Enrico Fermi: E = 21 kt TNT × 4.184×10⁹ J/t = 8.8×10¹³ J; ρ_air = 1.2 kg/m³; t = 1 ms = 10⁻³ s. R_Sedov = 1.1517 × (8.8×10¹³ × 10⁻⁶ / 1.2)^(1/5) = 1.1517 × 38 = 44 m at 1 ms. G.I. Taylor 1947 deduced exact yield from declassified photographs before US publication
• Castle Bravo Bikini 1 March 1954 H-bomb 15 megatons: E = 6.3×10¹⁶ J, ρ_air = 1.2, t = 10 ms. R_Sedov = 200 m at 10 ms
• Vela SNR 800 ly INAF 10,000 years late evolution: E = 10⁴⁴ J, ρ = 10⁻²¹ kg/m³. R_Sedov = 20 pc beginning pressure-driven snowplow phase
• GRB cosmological gamma-ray burst afterglow ASI BeppoSAX 1996-2002: E_iso = 10⁵² erg = 10⁴⁵ J, ρ ISM = 10⁻²⁵ kg/m³, t = 1,000 s. Relativistic shock Blandford-McKee 1976 model (γ = 4/3 → ξ_0 = 1.033). R ≈ 1 pc afterglow

Italian supernova astrophysics

Italian supernova astrophysics:

• Italian observation history: SN 1054 Crab Nebula observed China + Italy July 1054 23 days daytime visible, recorded Italian chronicles Roberto Anderson Bologna; SN 1572 Tycho Brahe also observed Galileo Galilei 16 years student Pisa; SN 1604 Kepler observed Galileo Padua 1761 (Padua University 1222); SN 1987A LMC 23 February 1987 observed Italy Asiago + ESO + Kamiokande neutrinos Italian collaboration; SN 2011fe galaxy M101 August 2011 observed by TNG National Galileo Telescope La Palma 1998 within 12 hours of explosion (Type Ia cosmological standard candle precursor)
• INAF Italian National Institute of Astrophysics Rome 2002 Monte Porzio Catone (16 observatories, 1,700 researchers): Padua 1761 Galileo + Asiago Cima Ekar 1979 Copernico 182 cm; Brera Milan 1762 Schiaparelli; Capodimonte Naples 1812; Arcetri Florence 1872; Rome 1786; Trieste 1898; Catania-Etna 1880; Bologna Loiano 1936; Palermo 1790; Cagliari 1899 SRT 64 m radio 2013
• Italian SN telescopes: TNG La Palma 1998 3.58 m; LBT Mount Graham Arizona 2005 2×8.4 m INAF 25%; VST Cerro Paranal Chile 2011 2.6 m + ESO; SRT Sardinia 2013 64 m radio
• Italian X-ray missions SN remnants ASI Rome 1988: BeppoSAX 1996-2002 Cas A, Tycho, Kepler observation; XMM-Newton ESA 1999 Italian RGS Padua-Bologna; NuSTAR NASA 2012 hard X-ray; IXPE NASA-ASI 2021 X-ray polarimetry Cas A magnetic polarization (gas pixel INAF Brera + INFN Pisa); Athena ESA 2035 X-IFU INAF Palermo 25%
• Enrico Fermi 1938 Nobel Prize "fission discovery" Rome University 1934 "Via Panisperna boys" (Edoardo Amaldi, Franco Rasetti, Emilio Segrè, Ettore Majorana mysteriously disappeared 1938, Bruno Pontecorvo emigrated USSR 1950); subsequent Manhattan Project Chicago Pile-1 1942 + Trinity 1945 + Hiroshima 1945. Three Italian Nuclear Physics Nobel Prizes: Fermi 1938, Segrè 1959 (antiproton), Carlo Rubbia 1984 (W Z bosons CERN)
• ICRA Rome Sapienza 1985 + ICRANet Pescara 2003 Remo Ruffini director GRB BdHN model; SISSA Trieste 1978 astrophysics MHD; Scuola Normale Pisa 1810 Andrea Ferrara first stars; CINECA Bologna 1969 Marconi100 30 PFlops + Leonardo pre-exascale 250 PFlops 2023 (5th TOP500). Italian R&D tax bonuses 2025: R&D Tax Credit L. 160/2019 up to 25%; Patent Box L. 178/2020; PNRR Mission 4 Component 2 €6.9B

Updated July 2026