Cosmic Distance Ladder Spiral/Elliptical Galaxy Kinematics Beena Meena Astro 8400 Cosmic Distance Ladder 15 Mpc to 200 Mpc Upto 15 Mpc Spirals “The Essential Cosmic Perspective”, Bennett et al Elliptical: Faber-Jackson Relation 4/20/20 Beena Meena - Astro 8400 2 Galaxy Rotation: Basics Km/sec https://pages.uoregon.edu/jimbrau/BrauImNew/Chap24/6th/24_11Figure-F. jpg 4/20/20 Beena Meena - Astro 8400 3 Galaxy Rotation from HI (λ 21cm) line CreDit: JRob’s prospectus Note: Line wiDth needs to be correcteD for inclination: WiDth/sin(i) 4/20/20 Beena Meena - Astro 8400 4 The Tully - Fisher Relation “A new method of determining distance to galaxies”, Tully, R.B; Fisher, J.R., A&A, 1977, A&A, 54, 661 Line width∝ Absolute Magnitude (Brighter galaxies rotate faster) 4/20/20 Beena Meena - Astro 8400 5 Original Tully Fisher Relation (TFR) “A new method of determining distance to galaxies”, Tully, R.B; Fisher, J.R., A&A, 1977, A&A, 54, 661 • Photometric measurements (M81 & M101) : CepheiD Distances • Note: Absolute MagnituDe M∝ D • RaDio observation: 91 m NRAO • Apparent Mag. (m): Optical (B) • FinD Best fit: Calibration • Apply to distant galaxies 4/20/20 Beena Meena - Astro 8400 6 TFR for distance measurement 1) Distance Modulus µ = m – M Luminosity ΔV(0): H1 line wiDth correcteD for inclination mpg : Photographic magnituDe Slope (⍺) Log(L) 2) Hubble Constant H0 = V/D Preliminary Value = 80 km s−1 Mpc−1 ΔV(0) 4/20/20 Beena Meena - Astro 8400 7 Progress: TF Relationship • MoveD on from visible to other bandpasses • Tully Fisher Relation is tighter in I band −1 −1 • H0 = 71 +/-7 km s Mpc Sakai et al., ApJ 529, 698 (2000) 4/20/20 Beena Meena - Astro 8400 8 Advanced TF Relation (by Tully) Tully et al. , AJ , 2013, 146, 4 Cosmicflows2 • Cosmicflows3: 17,669 entries • Photometry at 3.6 µm Observation: Spitzer Space Telescope • CepheiD, Tip of the ReD Giant Branch (TRGB), Type Ia supernova (SNIa): Distance Calibrations −1 −1 • H0 = 76.2 +/-2.7 km s Mpc 4/20/20 Beena Meena - Astro 8400 9 More recent Results: • Lelli Federco et al., MNRAS,2019 484,3 • A const. M/L ratio breaks at Low Luminosity galaxies • IncluDe gas mass so total mass = Stellar mass + gas (Baryonic mass) • Baryonic Tully –Fischer relation (from McGaugh et. al. 2000, 533,2 ) • Slope (⍺) = 3.85 ± 0.09 Sheii, J. R. et al., AAS 2020, 4,4 “Tully Fischer for southern galaxies with HIPASS anD WISE” −1 −1 Hubble Const. H0 = 73.3 ± 1 km s Mpc Range of Distance measurements: upto z = 1.4 Lorenzo et al., A&A,2010, 521,A27 4/20/20 Beena Meena - Astro 8400 10 Limitations & Source of Errors • Does not consiDer mass from Dark Matter: Halo(?) • Constant M/L ratio for a range of luminosity • Errors Due to measurement of inclination (5% uncertainties in inclination amounts to 9% error in line width: cosmicflow2, Tully et al 2013) • More: Uncertainties in measurement of apparent magnituDe 4/20/20 Beena Meena - Astro 8400 11 Elliptical Galaxies • Prolate (Rugby ball) shape • Generally composeD of olDer, low-mass stars • Minimal star formation • HarDly rotating: Can’t use Tully Fischer • Stellar velocity Dispersion M87: WikipeDia 4/20/20 Beena Meena - Astro 8400 12 Faber–Jackson relation • PresenteD by astronomers SanDra M. “Velocity dispersions and mass-to-light ratios for elliptical galaxies”, Faber, S. M.; Jackson, R. E. Faber anD Robert Earl Jackson in 1976 1976,ApJ, 204, 668 • Similar to TF L ∝ σˠ Velocity Dispersion(σ) σ = Stellar velocity dispersion ˠ ∼ 4 4/20/20 Beena Meena - Astro 8400 13 FunDamental Plane (FP) • To minimize the scatter in Faber Jackson • Djorgovski, S.; Davis, Marc 1987 coineD the term FunDamental Plane: • (Lum)⍺(RaDius)β(vel. Dispersion)ˠ = Const. • Any one of the three parameters may be Dn = Diameter measured at estimated from the other two. 20.75 mag per square arcseconD Dressler et al., 1987, ApJ 313, 42 4/20/20 Beena Meena - Astro 8400 14 (FP) (somewhat) Recent Results: Ellipticals S0 Galaxies ReDuceD Scattering from 25% (Dresseler et al. 1987) to 20% for each galaxy BernarDi et al.,2002, AJ 123, 2159 4/20/20 Beena Meena - Astro 8400 15 Summary • Distance LaDDer Rung 5: Galaxy Kinematics Best within ≈ 200Mpc • Spiral-> Tully Fisher : L ∝ (ΔV)⍺ ; ⍺ ∼ 3 to 4 • Elliptical -> Faber Jackson: L ∝ σˠ or FunDamental Plane 4/20/20 Beena Meena - Astro 8400 16 Thank you! 4/20/20 Beena Meena - Astro 8400 17.