Download pptx

Spiral galaxies without Lambda
Cold Dark Matter
Piotr Skindzier
Jagiellonian University
15 March, Moriond 2013
Suported by The National Science Centre grant nr. K/PBP/000391
1
VHEPU Moriond 2013
Outline
 Introduction
 Disk Model
 Vertical Gradient
 Summary
2
VHEPU Moriond 2013
Introduction
3
VHEPU Moriond 2013
Disk model
 2  0
 2  4 (  )
 2  0
To determine rotational velocity at a given radius one needs the surface mass density
be given also everywhere outside that radius
And vice versa, the surface mass density is related to the rotation curve by the formula
4
VHEPU Moriond 2013
Self consistent iteration
5
VHEPU Moriond 2013
Disk model - result
6
Name
NGC 7793
NGC 1365
NGC 6946
NGC 4736
UGC 6446
distance [Mpc]
3.38
18.6
6.0
4.7
18.6
morphological type
SAd
SBb
SAbc
Sab
Sd
LB[1010Lʘ]
0.3
9.81
1.64
1.3
0.218
MH+He[1010Mʘ]
0.12
2.36
0.97
0.067
0.434
MGal[1010Mʘ]
1
1.02
1
33.4
30.9
31.9
7.14
8.55
11.5
2.68
1.5
MGal/LB
3.33
3.4
3.33
3.4
3.15
3.25
4.35
5.21
7.01
2.06
6.88
(MGal-MGas)/LB
2.93
3
2.93
3.16
2.91
3.01
3.49
4.35
6.15
2.01
4.89
VHEPU Moriond 2013
Vertical gradient
George H. et al. AJ 647:1018-1029
7
VHEPU Moriond 2013
Vertical gradient - model
 2  0
 2  4 (r , z )
 2  0
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:
8
VHEPU Moriond 2013
Vertical gradient - result
Rotation curve for NGC 891 for Δz=0.6kpc
Name
distance [Mpc]
morphological type
MGal[1010Mʘ]
dVz [km/s] - measured
z – range of observation [kpc]
r – range of observation [kpc]
dVz [km/s] - calculated
9
Milky Way
SBbc
11.2
-22±6
(0.22, 2.62)
(3, 8)
-21±4.2
VHEPU Moriond 2013
NGC 891
9.5
Sb
10
-17.5±5.9
(1.2, 4.8)
(4.02, 7.03)
-19,9±2.4
Vertical gradient velocitie for NGC 891
NGC 2403
3.24
SBc
5.22
-12
(0.4, 4)
(1.3, 19.7)
-10±4
NGC 4559
9.7
SBc
4.82
-10
(0.2, 4)
(1.3, 19.7)
-7.2±2.4
NGC 4302
16.8
Sc
5.05
-31±19.8
(0.4, 2.4)
(2.5, 6)
-22.7±8.4
NGC 5775
24.8
SBc
9.65
-8±4
(1.2, 3.6)
(0, 12)
-12±4.3
Summary
 To explain rotation of spiral galaxies we do not need Lambda
Cold Dark Matter
 To explain vertical gradient of rotation velocity in spiral
galaxies we do not need Lambda Cold Dark Matter
 Lambda Cold Dark Matter can be introduce in our model but
it do not dominate dynamic of stars and gas in spiral galaxies
10
VHEPU Moriond 2013
''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
11
VHEPU Moriond 2013
12
VHEPU Moriond 2013
Vera C. Rubin et al. „Rotation of Andromeda Nebula from a spectroscopic survey of
emission region” 1970ApJ...159..379R
13
VHEPU Moriond 2013