The mass distribution in spiral galaxies - ESO

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Two different methods to determine the masses of spiral galaxies. 1. Using kinematical data. 2/12. 2. ] [ h d. VVV. +. = d opt. R. R. 2.3. = d d. RV. M. 2. 2. = ...
The mass distribution in spiral galaxies Irina Yegorova SISSA, Trieste, Italy In collaboration with Paolo

Salucci, Alessandro Pizzella, Niv Drory

Outline: •The disk mass of spiral galaxies •Radial Tully-Fisher relation (RTF) • Satellites of spiral galaxies

M(R)

V rot2 R = G

Two different methods to determine the masses of spiral galaxies 1. Using kinematical data

V = [V + V ] 2 d

2 1/ 2 h

Ropt = 3.2 Rd

M = 2V Rd 2 d

UGC 8460

2. Using photometrical data The method is based on the comparison of multicolor photometry from SDSS to a grid of stellar population synthesis models (Niv

Drory, Max-Planck, Garching)

The data: ugriz bands from the Sloan Digital Sky Survey (SDSS) (Data Release 4) JHK bands from the 2 Micron All Sky Survey

log Mpho = (-0.4 ± 1.27) + (1.02 ± 0.12) log Mkin

Mass-to-light ratio vs color and luminosity

1 log M D ≅ (log M pho + log M kin ) 2

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 determining Distances 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

Physical basis of the TF-relation From the equation of centrifugal equilibrium we get:

V

2 0

GM = γ Rc

total dark

matter M dark α = M lum

mass

V0 – representative velocity, M - total mass, Rc – characteristic radius of luminous matter γ - structural parameter depending on the shape of the mass distribution

M = M

prameter

dark

+ M

lum

surface density parameter M lum µ0 = R c2

The first equation can be written in this form:

M lum = V [γ ( 1 + α) G µ0 ] 4 0

2

2

2

−1

This equation can be written in the form of the Tully-Fisher relation:

L = V [ γ (1 + α ) G µ 0 ( M 4 0

2

2

2

lum

M = Msun − 2.5 log( L / Lsun )

/ L )]

−1

Samples: 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

UGC2405 250

Vmax

200

V

150

100

50

0 0.0

0.5

1.0

1.5

R/Rd

2.0

2.5

3.0

1. Mathewson sample: R 2. Courteau sample: R 3. Vogt sample: R

R/Ropt; bin=0.2 R/Rd; R/Rd;

bin=0.2 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.

1st sample: TF-relation for 967 galaxies -24

-23

-22

0.2R/Ropt 0.4R/Ropt 0.6R/Ropt 0.8R/Ropt 1.0R/Ropt 1.2R/Ropt

Mi

-21

-20

-19

-18

-17

-16 1.0

1.2

1.4

1.6

1.8

log V

2.0

2.2

2.4

2.6

1st sample: TF-relation for 967 galaxies

Slope of the TF-relation MB = ai + bi log V(Ri)

Gap in the slopes of 2 samples:

L = V [ γ (1 + α ) G µ 0 ( M 4 0

2

No dark matter

2

1+ k x

L

4 M x = − 2 .5( ) log V; 1+ k

k=0.1 for I band k=0.3 for R band

2

=V

lum

/ L )]

4

M lum ~ Lk L

function of the band

The slope of TF-relation is related to k

−1

Physical meaning of the slope 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.

L ~ V (1 + α ( R , L )) 4 0

M dark =α M lum

α decreases with L α increases with R

dark

matter

−2

parmeter

this has influence on the slope

Scatter of the TF-relation

TF-relation using Vmax -24

-22.5

-23

-22.0

-22

-21.5 -21.0

-20

MR

Mi

-21

-20.5

-19 -20.0

-18 -19.5

-17 -19.0

-16 1.4

1.6

1.8

2.0

2.2

2.4

2.6

logVmax

slope=-7,579; scatter=0,328; number of galaxies=843

1.9

2.0

2.1

2.2

2.3

2.4

2.5

log Vmax

slope=-5.54; scatter=0.49; number of galaxies=83

Probing dark matter halos of spiral galaxies with their satellites 1.5 - 2 satellites per host galaxy •Zaritsky (1993): 45 primaries – 69 satellites Kitt Peak 2.3 m •Sales & Lambas (2004): 1498 primaries – 3079 satellites 2dFGRS 3.9 m •T. Breinerd (2004) 3 samples: 1351 primaries – 2084 satellites, 948 primaries – 1294 satellites, 400 primaries – 658 satellites SDSS 2.5 m

We are studying 7 isolated spiral galaxies at z = 0.03 - 0.09

+

Satellites

+

= 58 h

Rotation curves

SDSS J154040.56-000933.5 z=0.078

7 primaries 77 satellites identified Primary galaxy

z

SDSSJ134215.02

0.029 0.046 0.083 0.085 0.075 0.077 0.038

SDSSJ145211.01 SDSSJ152621.67 SDSSJ153221.6 SDSSJ154040.5 SDSSJ154904.29 SDSSJ221957.2

N of sat. (SDSS) 4 4 4 5 7 2 4

N of sat. (found) 8 7 17 19 11 8 7

SDSS J145211.01+044053.6

SDSS J145211.01+044053.6

SDSS J145211.01+044053.6

Main results: •The kinematical and spectro-photometrical methods coincides •We found a Radial Tully-Fisher (RTF): 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. The small scatter in the RTF-relation. This implies that galaxies have similar physical characteristics.

• Satellites seems a good tracer of matter distribution in spirals