The differential Tully-Fisher relation for spiral
galaxies
Irina Yegorova
SISSA, Trieste, Italy
Outline:
•Observations of spiral galaxies
•The standard Tully-Fisher relation
•Differential Tully-Fisher relation
Evidence of dark matter comes from:
WMAP
X-Ray
gravitational lensing
rotation curves
blue shift
red shift
The Tully-Fisher (TF) relation is an empirically established correlation between the luminosity L of a spiral galaxy and its rotational velocity V (Tully-Fisher, 1977)
New method of determiningDistances to galaxies
R.B.Tully and J.R.Fisher,A&A, 54. 661-673, 1977
TF-relation has two important applications:
1. It is used to obtain cosmological distances
M=m - 5logD - 25
2. It can be used for studying the dynamical properties and the evolution of galaxies
M M M mass total lumdark
lum
dark
M
M α
prametermatter dark
2c
lum0 R
Mμ
parameterdensity surface
Physical basis of the TF-relation
From the equation of centrifugal equilibrium we get:
M
V20
cR
G V0 – representative velocity, M - total mass, Rc – characteristic radius of luminous matter - structural parameter depending on the shape of the mass distribution
10
22240 1M ]μGα)([γVlum
10
22240 )]/M()1([ LGVL lum
The first equation can be written in this form:
This equation can be written in the form of theTully-Fisher relation:
)/log(5.2 sunsun LLMM
Differential Tully-Fisher relation
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
50
100
150
200
250
V
R/Rd
UGC2405
Vmax
1st sample: 967 spiral galaxies Mathewson (1992)
2nd sample: 304 spiral galaxies Courteau (1997) 86 galaxies selected for analysis
3 sample: 329 spiral galaxies Vogt (2004) 81 galaxies selected for analysis
Samples:
1. Mathewson sample: R R/Ropt; bin=0.2
2. Courteau sample: R R/Rd; bin=0.2
3. Vogt sample: R R/Rd; bin=0.2
Ropt=3.2Rd, where R_d is the disk exponential length-scale, for Freeman (exponential) disk this corresponds to the 25 B-mag/arcsec^2 photometric radius.
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
-16
-17
-18
-19
-20
-21
-22
-23
-24
Mi
log V
0.2R/Ropt
0.4R/Ropt
0.6R/Ropt
0.8R/Ropt
1.0R/Ropt
1.2R/Ropt
1st sample: TF-relation for 967 galaxies
1st sample: TF-relation for 967 galaxies
2nd sample: TF-relation for 86 galaxies
1.4 1.6 1.8 2.0 2.2 2.4
-19.0
-19.5
-20.0
-20.5
-21.0
-21.5
-22.0
-22.5
-23.0
1.2 1.4 1.6 1.8 2.0 2.2 2.4
-19.0
-19.5
-20.0
-20.5
-21.0
-21.5
-22.0
-22.5
MR
log V
R/Rd=0.7
MR
log V
R/Rd=0.3
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4
-19.0
-19.5
-20.0
-20.5
-21.0
-21.5
-22.0
-22.5
-23.0
MR
log V
R/Rd=1.3
1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
-19.0
-19.5
-20.0
-20.5
-21.0
-21.5
-22.0
-22.5
MR
log V
R/Rd=1.7
1.9 2.0 2.1 2.2 2.3 2.4-18
-19
-20
-21
-22
-23
MR
log V
R/Rd=2.3
1.9 2.0 2.1 2.2 2.3 2.4
-19.0
-19.5
-20.0
-20.5
-21.0
-21.5
-22.0
-22.5
-23.0
MR
log V
R/Rd=2.9
Slope of the TF-relationMB = ai + bi log V(Ri)
Gap in the slopes of 2 samples:
10
22240 )]/M()1([ LGVL lum
The slope of TF-relation is related to k
k=0.1 for I bandk=0.3 for R band
No dark matter
function of the band
V;)k
(.M x log1
452
41 VL kx
klum L~L
M
Physical meaning of the slope
240 )),(1(~ LRVL
The slope of the TF-relation steadily rises with distance due to the fact that the fractional amount of the dark matter in galaxies changes with the radius.
M
M
lum
dark
increases with R
decreases with L
parmetermatter dark
this has influence on the slope
Scatter of the TF-relation
TF-relation using Vmax
slope=-5.54; scatter=0.49; number of galaxies=83
slope=-7,579; scatter=0,328; number of galaxies=843
1.4 1.6 1.8 2.0 2.2 2.4 2.6-16
-17
-18
-19
-20
-21
-22
-23
-24
Mi
logVmax
1.9 2.0 2.1 2.2 2.3 2.4 2.5
-19.0
-19.5
-20.0
-20.5
-21.0
-21.5
-22.0
-22.5
MR
log Vmax
Main results:1. We found the new method Differential TF relation.
2. The slope decreases monotonically with the distance, while the scatter increases with distance. This implies the presence of a non luminous mass component (DM) whose dynamical importance, with respect to the stellar disk (baryonic matter) increases with radius.3. We found small scatter in the TF-relation. This implies that galaxies have similar physical characteristics.4. Minimum of the scatter 0.15 (1st sample), 0.24 (2nd sample), 0.29 (3 sample) at 2.2R/Rd at the position of the maximum
disk contribution
We are planning to do mass modeling for these galaxies to reproduce the observable slope and scatter in the TF-relation
Work in progressWork in progress