Slajd 1

Piotr SkindzierJagiellonian University 15 March, Moriond 2013

Suported by The National Science Centre grant nr. K/PBP/000391VHEPU Moriond 20131Spiral galaxies without Lambda Cold Dark MatterOutlineVHEPU Moriond 20132IntroductionDisk ModelVertical GradientSummary

IntroductionVHEPU Moriond 20133

Disk modelVHEPU Moriond 20134

And vice versa, the surface mass density is related to the rotation curve by the formulaTo determine rotational velocity at a given radius one needs the surface mass density be given also everywhere outside that radiusSelf consistent iteration VHEPU Moriond 20135

Disk model - resultVHEPU Moriond 20136

NameNGC 7793NGC 1365NGC 6946NGC 4736UGC 6446distance [Mpc]3.3818.66.04.718.6morphological typeSAdSBbSAbcSabSdLB[1010L]0.39.811.641.30.218MH+He[1010M]0.122.360.970.0670.434MGal[1010M]11.02133.430.931.97.148.5511.52.681.5MGal/LB3.333.43.333.43.153.254.355.217.012.066.88(MGal-MGas)/LB2.9332.933.162.913.013.494.356.152.014.89Vertical gradient VHEPU Moriond 20137

George H. et al. AJ 647:1018-1029Vertical gradient - modelVHEPU Moriond 20138

Base on the radial force equilibrium and assuming that projection of the orbit on the galactic plane forms a circle or a hyperbolic spiral we can approximate: Here gr(r,z) is a radial component of gravitational acceleration which give:Vertical gradient - resultVHEPU Moriond 20139NameMilky WayNGC 891NGC 2403NGC 4559NGC 4302NGC 5775distance [Mpc]-9.53.249.716.824.8morphological typeSBbcSbSBcSBcScSBcMGal[1010M]11.2105.224.825.059.65dVz [km/s] - measured-226-17.55.9-12-10-3119.8-84z range of observation [kpc](0.22, 2.62)(1.2, 4.8)(0.4, 4)(0.2, 4)(0.4, 2.4)(1.2, 3.6)r range of observation [kpc](3, 8)(4.02, 7.03)(1.3, 19.7)(1.3, 19.7)(2.5, 6)(0, 12)dVz [km/s] - calculated-214.2-19,92.4-104-7.22.4-22.78.4-124.3

Rotation curve for NGC 891 for z=0.6kpcVertical gradient velocitie for NGC 891SummaryVHEPU Moriond 201310To explain rotation of spiral galaxies we do not need Lambda Cold Dark MatterTo explain vertical gradient of rotation velocity in spiral galaxies we do not need Lambda Cold Dark MatterLambda Cold Dark Matter can be introduce in our model but it do not dominate dynamic of stars and gas in spiral galaxiesVHEPU Moriond 201311

''One of the striking conclusion from this models is that the relative contribution of the disk and the halo to the interior mass and circular speed at R0 are very uncertain. ... This degeneracy between the disk and halo parameters has to be resolved by bringing other observation or dynamical argument to bear.' Binney et. all Galactic Dymanics p. 110-118 VHEPU Moriond 201312

VHEPU Moriond 201313

Vera C. Rubin et al. Rotation of Andromeda Nebula from a spectroscopic survey of emission region 1970ApJ...159..379R