Tully-Fisher relation spiral galaxy calculator

The Tully-Fisher relation calculator determines the absolute magnitude M_B, luminosity L (in solar units) and baryonic mass M_bar of a disk galaxy from the maximum disk rotation velocity V_rot, per the empirical relation by R. Brent Tully (Institute for Astronomy Hawaii) and J. Richard Fisher (NRAO Green Bank) published in 1977 in Astronomy & Astrophysics vol. 54, p. 661 ("A new method of determining distances to galaxies"). The fundamental relation reveals tight correlation between spiral galaxy luminosity and rotational velocity: L ∝ V_rot⁴ (B-band classical). The inverse logarithmic form used as distance estimator: M_B = -10·log₁₀(V_rot/220 km/s) - 19.5, with V_rot disk rotation velocity in km/s measured from HI 21 cm profile width (radio surveys ALFALFA Arecibo, WALLABY ASKAP), M_B absolute magnitude B-band (Johnson photometric filter 440 nm), M_sun_B = +5.48 solar B-band absolute magnitude, hence L/L_sun = 10^((5.48 - M_B)/2.5). Underlying physics: in circular gravitational equilibrium V_rot² = G·M_dyn/R; assumptions of approximately constant mass-to-light ratio M/L and uniform surface density Σ imply L ∝ V_rot⁴ (Aaronson-Huchra-Mould 1979).

The K-band modern form (Verheijen 2001 ApJ 563, 694) M_K = -10.5·log₁₀(W₂₀/2) - 22 with W₂₀ HI profile width at 20% peak reduces scatter (infrared K 2.2 µm less sensitive to dust extinction and young stellar populations). The Baryonic Tully-Fisher Relation (Stacy McGaugh 2000 ApJ 533, L99) M_baryonic = A · V_rot⁴ with constant A ≈ 50 M_sun·s⁴/km⁴ includes stellar + cold HI + molecular H₂ mass and extends from gas-dominated dwarf galaxies to giant spirals, providing one of the most stringent tests of ΛCDM dark matter versus MOND modified gravity Milgrom 1983. Applications:

• Distance Hubble ladder spiral galaxy distances via V_rot from HI 21 cm
• H_0 measurement SBF + Cepheid calibration (Madore-Freedman)
• galaxy mass M_dyn = V_rot²·R/G
• ΛCDM vs MOND test via BTF
• Tully-Fisher z<2 evolution intermediate redshift
• Virgo cluster distances
• cosmological surveys 2MASS Tully-Fisher and WALLABY ASKAP. Italian applications:

• VST KIDS survey INAF Capodimonte 1812 + ESO Cerro Paranal Chile 2011-2019 1,500 deg² galaxy structure and weak lensing
• Asiago Copernico 182 cm INAF Padua 1979 optical spectroscopy H_alpha rotation curves
• TNG La Palma 1998 INAF 3.58 m LRS H_alpha disk spectrography
• SRT Sardinia 64 m 2013 INAF HI 21 cm radio survey, complementary to Noto 32 m INAF VLBI
• LBT Mount Graham Arizona 2005 INAF 25% 2×8.4 m integral-field spectroscopy
• Euclid ESA 2023 ASI 25% 25 mln galaxy spectro 6 yrs 15,000 deg² including disk-rotation samples
• JWST 2021 NIRSpec Italian contribution galaxy rotation z>2 cosmic noon

Italian Tully-Fisher galaxy table

(Source: Tully & Fisher 1977 A&A 54, 661 + Verheijen 2001 ApJ 563, 694 K-band + McGaugh 2000 ApJ 533 BTF + Sofue & Rubin 2001 ARA&A 39, 137 rotation curves + INAF Rome 2002 Monte Porzio Catone).

Italian Tully-Fisher calculation examples

• Milky Way V_rot = 220 km/s INAF Padua 1761 + Asiago Copernico 182 cm 1979: V_rot = 220 km/s (Sun orbits Sgr A* at 220 km/s, Reid-Brunthaler 2004 VLBA), applying M_B = -10·log₁₀(220/220) - 19.5 = -10·0 - 19.5 = -19.5 mag. Luminosity L = 10^((5.48-(-19.5))/2.5) = 10^(24.98/2.5) = 10^9.99 = 2.0×10¹⁰ L_sun. Dynamical mass within 15 kpc M_dyn = V²·R/G ≈ 1.7×10¹¹ M_sun. Baryonic BTF McGaugh 2000: M_bar = 50·220⁴ = 50·2.34×10⁹ = 1.17×10¹¹ M_sun (consistent stars 6×10¹⁰ + cold HI 7×10⁹ + H₂ 2×10⁹)
• M31 Andromeda V_rot = 265 km/s INAF Trieste 1898: M_B = -10·log₁₀(265/220) - 19.5 = -20.3 mag. L = 4.0×10¹⁰ L_sun. M_bar BTF = 50·265⁴ ≈ 2.5×10¹¹ M_sun. M31 distance 778 kpc Cepheids (Riess 2019) consistent with inverse Tully-Fisher
• M33 Triangulum V_rot = 120 km/s INAF Bologna Loiano 1936: M_B ≈ -17.7 mag dwarf spiral SAcd. L = 4×10⁹ L_sun. M_bar = 50·120⁴ = 1.04×10¹⁰ M_sun
• NGC 3198 V_rot = 150 km/s VST KIDS INAF Capodimonte 2011: M_B = -17.84 mag. Classic flat rotation curve van Albada 1985 first dark matter spiral evidence
• LMC Large Magellanic Cloud V_rot = 70 km/s SRT Sardinia 64 m 2013: M_B ≈ -18.5 mag (LMC outlier irregular barred SBm off classical TF relation)
• NGC 4258 (M106) V_rot = 208 km/s VLBI Noto 32 m INAF: water maser VLBI distance anchor 7.576 ± 0.082 Mpc geometric distance Pesce 2020. M_B = -19.26 mag. Tully-Fisher first-rung distance ladder calibrator
• NGC 1300 barred spiral V_rot = 185 km/s VST KIDS INAF: M_B = -18.75 mag. Hubble SBbc prototype barred galaxy

Italian Tully-Fisher astrophysics

Italian spiral galaxy astrophysics:

• INAF Italian National Institute of Astrophysics Rome 2002 Monte Porzio Catone (16 observatories, 1,700 researchers): Padua 1761 Galileo + Asiago Copernico 182 cm 1979 optical spectroscopy H_alpha rotation curves; Brera Milan 1762 Schiaparelli; Capodimonte Naples 1812 + VST Cerro Paranal Chile 2011 2.6 m INAF Capodimonte + ESO survey KIDS 1,500 deg² disk-rotation; Arcetri Florence 1872 Galileo cosmology; Rome 1786; Trieste 1898 Planck CMB H_0 tension; Catania-Etna 1880; Bologna Loiano 1936 AGN dwarf spirals; Palermo 1790 Athena X-IFU 2035; Cagliari 1899 + SRT Sardinia 64 m 2013 radio HI 21 cm rotation curves
• Italian Tully-Fisher telescopes: TNG Galileo La Palma 1998 INAF 3.58 m LRS DOLORES NICS H_alpha disk curves; LBT Mount Graham Arizona 2005 INAF 25% 2×8.4 m LUCI MOS multi-object integral-field; VST Cerro Paranal 2011 INAF Capodimonte + ESO 2.6 m KIDS 1,500 deg² weak lensing galactic structure; SRT Sardinia Radio Telescope 2013 INAF 64 m radio HI 21 cm; Noto 32 m Sicily INAF VLBI maser AGN distance NGC 4258
• ASI Rome 1988 space missions: Euclid ESA 2023 ASI 25% 6 yrs 15,000 deg² 25 mln galaxy slitless spectro Italian NISP NIR photometer hardware; Athena ESA 2035 X-IFU calorimeter INAF Palermo 25%; JWST 2021 NIRSpec Italian contribution Roberto Maiolino Cambridge ex-INAF Arcetri galaxy rotation z>2 cosmic noon; LSPE/STRIP CMB ground-based INAF Trieste + INFN Pisa B-mode primordial; LiteBIRD ESA 2032 INAF + ASI CMB B-mode; AGILE ASI 2007 + AMS-02 ISS 2011; BeppoSAX 1996-2002 ASI
• Italian Physics Nobel Prizes: Marconi 1909, Fermi 1938, Segrè 1959, Carlo Rubbia 1984, Riccardo Giacconi 2002
• ICRA Rome Sapienza 1985 + ICRANet Pescara 2003 Remo Ruffini AGN black holes; SISSA Trieste 1978 Andrea Lapi galaxy formation; Scuola Normale Superiore Pisa 1810 Andrea Ferrara cosmic dawn first disks; CINECA Bologna 1969 Marconi100 30 PFlops + Leonardo HPC pre-exascale 2023 250 PFlops 5th TOP500 worldwide N-body cosmological simulations IllustrisTNG-300 Magneticum Eagle disk galaxy formation. Italian R&D tax bonuses 2025-2026: R&D Tax Credit L. 160/2019 up to 25%; Patent Box L. 178/2020 50%; Industria/Transizione 5.0 Tax Credit DL 39/2024 up to 35%; PNRR Mission 4 Component 2 €6.9B research

Updated July 2026