The Balance of Dark and LuminousMass in Rotating GalaxiesStacy McGaughUniversity of MarylandKITP, UCSB, 5 October 2006starsgasbaryonsdarkmatterVflatsum of DM + baryons conspire to give isothermal potentialinterpretations differ...Primary Sample74 galaxies with detailed mass models60 have high precision velocity data All have extended rotation curves from 21 cm velocity fieldsGalaxies span all disk Hubble Types Sa to Irr (mostly later types)Span wide range of physical parameters:Rotation velocity:Baryonic Mass:Disk Scale Length:Central Surface Brightness:(σV/V < 0.05)54 ≤ Vf< 300 km s−13 × 108< Md< 3 × 1011M!0.5 ≤ Rd≤ 13 kpc19.6 ≤ µ0≤ 24.2 B mag arcsec−2compilations - Sanders (1996); McGaugh & de Blok (1998);Sanders & McGaugh (2002); McGaugh (2005, 2006)Data have many sources:original sources - Begeman (1987)Broeils (1992)de Blok (1997)Verheijen (1997)Jobin & Carignan (1990)Begeman, Broeils, & Sanders (1991)de Blok, McGaugh, & van der Hulst (1996)Sanders & Verheijen (1998)McGaugh, de Blok, & Rubin (2001)Verheijen (2001)and many others...Supplemented by Extreme Dwarf Sample8 galaxies with resolved, extended HI rotation curvesVery low mass & velocity:Rotation velocity:Baryonic Mass:17 ≤ Vf≤ 51 km s−14 × 106< Md< 8 × 108M!(McGaugh 2005)Newton saysV2 = GM/R.Equivalently,Σ = M/R2V4 = G2MΣThereforeDifferent Σshould meandifferent TFnormalization.μ = -2.5 logΣ +CTF Relation Tully Fisher residualsZwaan et al. (1995)Sprayberry et al. (1995)Tully & Verheijen (1997)McGaugh & de Blok (1998)Courteau & Rix (1999)McGaugh (2005)Pizagno et al. (2005)Dutton et al. (2006)Gnedin et al. (2006)UGC 128NGC 2403as seen on skyNGC 2403UGC 128same physical scaleVpRpVpRpNGC 2403: Begeman (1987); Fraternali et al. (2001) : HI dataBlais-Ouellette et al. (2004); Daigle et al. (2006) Hα Fabry-PerotUGC 128: van der Hulst et al. (1992); Verheijen & de Blok (1999) : HI dataKuzio de Naray et al. (in prep.) Hα IFURp≈ 2.2Rdindistinguishable in TF:same Mass, same Vbut very differentbaryon distributionStellar Mass TF Baryonic TF (stars + gas)Search for signature of disk in TF residuals:velocity residuals as a fcn of scale length residualsV2b|Rp∝ ΣbNo Residuals from TF rel’nRequires fine balance between dark & baryonic massMcGaugh (2005) Phys. Rev. Lett. 95, 171302Renzo’s Rule:“For any feature in the luminosity profile there is a corresponding feature in the rotation curve and vice versa.”(Sancisi 2004, IAU 220, 233)The distribution of mass is coupled to the distribution of light.Quantify by defining the Mass Discrepancy:D =V2V2b=V2Υ!v2!+ V2g74 galaxies> 1000 points(all data)60 galaxies> 600 points(errors < 5%)radiusorbitalfrequencyaccelerationDifferent choices of Stellar Mass-to-Light RatiogN∝ ΣD(gN) =V2Υ!v2!+ V2gThe mass discrepancy - acceleration relationMcGaugh 2004, ApJ, 609, 652DDV = D1/2VbUGC 11455: Spekkens & Giovanelli (2006): HI + Hα dataIndependent from calibrating dataDΥI!= 1.1 M!/L!±0.2ResidualsLine: Bell et al. (2003)DRenzo’s rule works even for LSBs! - e.g., NGC 1560:Sellwood & McGaugh 2005, ApJ, 634, 70V200= 80c = 4.9initial halomd= 0.01RdRs= 0.12halo compressionbaryonsinitial halocompressed haloOne universal fcn + one free parameter per galaxy (M*/L)is more efficacious than multi-parameter disk-halo fits.i.e., there is a single effective force law in disk galaxies.What does this?CDM: doesn’t fall out naturally. Feedback? Scatter?Why does the baryonic tail wag the dark matter dog?MOND: most natural interpretation of rotation curves.TeVeS, BSTV: can test with gravitational lensing.Other forms of DM?SIDM, WDM... ignore baryons!(Just making a core is not good enough.)Other ideas...ConclusionsPiazza & Marinoni (2003) PRLBlanchet (2006) gr-qc/0609121It’s all about the