Schmidt-Kennicutt star formation law calculator

The Schmidt-Kennicutt law calculator determines the star formation rate per unit area ΣSFR from a galaxy from its gas surface density Σ_gas, per the original formulation by Dutch astronomer Maarten Schmidt 1959 ApJ "The rate of star formation" (vol. 129, p. 243) Caltech, empirically calibrated by Robert C. Kennicutt 1998 ApJ "The global Schmidt law in star-forming galaxies" (vol. 498, p. 541) Steward Observatory Arizona. The classic formula: ΣSFR = A · (Σ_gas / Σ_0)^N, with ΣSFR SFR per unit area in M_sun/year/kpc², Σ_gas gas surface density (HI + H2 + He) in M_sun/pc², A = 2.5×10⁻⁴ coefficient, Σ_0 = 1 M_sun/pc², N = 1.4 ± 0.15 "Kennicutt-Schmidt index" (universal slope). Modern extensions:

• Bigiel et al. 2008 ApJ molecular law (ΣSFR ∝ Σ_H2 with N=1, linear in dense H2)
• Krumholz-McKee-Tumlinson 2009
• Lada-Lombardi-Alves 2010 density threshold Σ ≈ 116 M_sun/pc²
• SFR depletion time τ_dep = Σ_gas / ΣSFR ≈ 2 Gyr (universal star formation efficiency 1-2% per dynamic time). Physics: SFR ∝ ρ_gas / t_dyn with t_dyn = √(R³/GM) dynamical time. Gravitational instability Toomre Q < 1 trigger collapse + H2 cooling 100 K + supernovae radiative feedback. Cosmological applications:

• galaxy evolution (gas reservoir → stars chemical enrichment)
• cosmic SFR Madau-Dickinson 2014 (cosmic SFR peak z=2-3 "cosmic noon" 10× current)
• feedback regulation AGN + supernovae
• chemical evolution Mg/Fe O/Fe. Italian astrophysical applications:

• ALMA Atacama Large Millimeter Array Chile + INAF Padua 1761 (resolved Σ_gas H2 + ΣSFR galaxy maps)
• Survey VST KIDS Cerro Paranal Chile 2011-2019 INAF Capodimonte 1812 1,500 deg² weak lensing dark matter + SF
• JWST 2021 NIRSpec Italian first galaxies INAF Schmidt-Kennicutt z>5 (Roberto Maiolino Cambridge ex-INAF Arcetri)
• M82 NGC 3034 starburst INAF SFR 10× higher cosmic noon
• Barred M83 NGC 1300 INAF Capodimonte
• Andromeda M31 INAF Trieste 1898 low SFR passive disk
• SRT Sardinia Radio Telescope 64 m Cagliari 2013 INAF HI 21 cm gas surface density. Italian radio measurements: SRT Sardinia 2013 64 m HI 21 cm; VLA NRAO + EVLA Italian collaboration; ALMA Atacama 66 antennas CO 1-0 H2 surface density; JWST 2021 NIRSpec MIRI Hα Hβ optical; Spitzer Herschel ESA infrared dust SFR

Schmidt-Kennicutt galaxy tables

(Source: Schmidt 1959 ApJ 129, 243 + Kennicutt 1998 ApJ 498, 541 + Bigiel et al. 2008 ApJ molecular law + Madau-Dickinson 2014 ARA&A cosmic SFR + INAF Rome 2002 + ALMA Atacama Chile).

Italian Schmidt-Kennicutt examples

• Milky Way solar disk 8.3 kpc INAF Padua 1761 + GAIA ESA 2013: Σ_gas = 10 M_sun/pc² (HI 5 + H2 2 + He 3) disk average. Schmidt-Kennicutt: ΣSFR = 2.5×10⁻⁴ · 10^1.4 = 6.3×10⁻³ M_sun/yr/kpc² ≈ 0.006. Total integrated MW SFR 15 kpc area 700 kpc² → 4 M_sun/yr (consistent with 1-2 M_sun/yr Hα + IR observations). Depletion time τ_dep = 10/0.006 = 1,700 Myr = 1.7 Gyr
• M82 NGC 3034 'cigar' starburst 12 Mly INAF Brera 1762: Σ_gas = 1,000 M_sun/pc² extremely dense central kpc. Schmidt-Kennicutt: ΣSFR = 2.5×10⁻⁴ · 1,000^1.4 = 4 M_sun/yr/kpc² but observed 10 M_sun/yr/kpc² → starburst factor 2-3× above SK. Total SFR 10-15 M_sun/yr (vs MW 1-2). Confirmed Chandra X-ray + Spitzer IR + ALMA CO
• Andromeda M31 INAF Trieste 1898 + GAIA ESA 2013: Σ_gas = 5 M_sun/pc² gas-poor passive disk. ΣSFR = 1×10⁻³ M_sun/yr/kpc² → total SFR 0.5 M_sun/yr (low passive evolution + future MW collision 4.5 Gyr trigger starburst)
• ULIRG Arp 220 merger 78 Mpc JWST 2021 ALMA INAF: Σ_gas = 10⁴ M_sun/pc² (gas merging-compressed central kpc). Schmidt-Kennicutt: ΣSFR = 1,000 M_sun/yr/kpc² ULIRG extreme, total SFR ~200 M_sun/yr. τ_dep = 10⁴/1,000 = 10 Myr (rapidly depletes)
• Cosmic noon z=2 main sequence cosmic SFR peak Madau-Dickinson 2014 INAF + JWST 2021: Σ_gas = 500 M_sun/pc² average (z=2 gas-rich vs current z=0). ΣSFR = 10 M_sun/yr/kpc². 10× higher cosmic SFR density vs current value. z=2 galaxies in cosmic noon star formation peak universal
• SRT Sardinia Radio Telescope 64 m Cagliari 2013 INAF + ALMA Atacama Chile: HI 21 cm + CO 1-0 maps Σ_gas resolved 100 pc nearby galaxies M51 M83 NGC 6946 NGC 628 (THINGS + HERACLES + PHANGS-ALMA surveys)

Italian star formation astrophysics

Italian star formation astrophysics:

• INAF Italian National Institute of Astrophysics Rome 2002 Monte Porzio Catone (16 observatories, 1,700 researchers): Padua 1761 Galileo + Asiago 1979 Copernico 182 cm; Brera Milan 1762 Schiaparelli; Capodimonte Naples 1812 VST KIDS dark matter; Arcetri Florence 1872 Galileo Solar Telescope; Rome 1786; Trieste 1898 Planck CMB hardware Andromeda; Catania-Etna 1880; Bologna Loiano 1936 M51 starburst; Palermo 1790; Cagliari 1899 SRT 64 m radio 2013 HI 21 cm
• Italian star formation telescopes: TNG La Palma 1998 3.58 m INAF; LBT Mount Graham Arizona 2005 2×8.4 m INAF 25% (LUCI MOS Hα emission galaxies); VST Cerro Paranal Chile 2011 2.6 m INAF Capodimonte + ESO; SRT Sardinia 2013 64 m radio (HI 21 cm); ALMA Atacama Chile 2013 66 antennas (Italian INAF Padua 5%, CO 1-0 H2 maps) + APEX precursor
• Italian IR missions ASI Rome 1988: Herschel Space Observatory ESA 2009-2013 far-IR PACS+SPIRE (Italian INAF + INFN); Spitzer Space Telescope NASA 2003-2020 mid-IR; JWST 2021 NIRSpec Italian Hα Hβ optical first galaxies SFR z>5; Euclid ESA 2023 ASI 25% 15,000 deg² weak lensing 25 mln galaxy spectroscopy 6 years; BeppoSAX 1996-2002 ASI X-ray AGN starburst M82 NGC 1068
• Italian Physics Nobel Prizes: Marconi 1909, Fermi 1938, Segrè 1959, Carlo Rubbia 1984, Riccardo Giacconi 2002. Andrea Ghez UCLA + Reinhard Genzel MPE 2020 Sgr A*
• Andrea Ferrara Scuola Normale Pisa 1810 first galaxies cosmic dawn SFR z>6 Population III; Roberto Maiolino Cambridge ex-INAF Arcetri 1872 JWST first galaxies + AGN feedback; SISSA Trieste 1978 astrophysics galaxy chemical evolution; ICRA Rome Sapienza 1985 Remo Ruffini AGN; CINECA Bologna 1969 Marconi100 30 PFlops + Leonardo pre-exascale 250 PFlops 2023 (5th TOP500) hydrodynamic galaxy formation simulations. 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