The mass distribution in spiral galaxies

Transcription

1 The mass distribution in spiral galaxies Irina Yegorova SISSA, Trieste, Italy In collaboration with Paolo Salucci, Alessandro Pizzella, Niv Drory

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

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4 M(R) = V 2 rot G R

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6 Two different methods to determine the masses of spiral galaxies 1. Using kinematical data V = [ V d Vh ] 1/ 2 Ropt = 3. 2R d M = 2 V 2 d R d

7 UGC 8460

8 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

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

10 Mass-to-light ratio vs color and luminosity log 1 M D (log M pho + 2 log M kin )

11 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)

12 New method of determining Distances to galaxies R.B.Tully and J.R.Fisher, A&A, , 1977

13 TF-relation has two important applications: 1. It is used to obtain cosmological distances M = m - 5logD It can be used for studying the dynamical properties and the evolution of galaxies

14 Physical basis of the TF-relation From the equation of centrifugal equilibrium we get: G M = γ V 2 0 total R c 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 dark + M lum dark matter prameter surface density α M M dark lum = µ 0 = 2 M lum R c parameter

15 The first equation can be written in this form: M lum 4 [γ 2 ( 1 0 = V + α) G µ ] L This equation can be written in the form of the Tully-Fisher relation: 4 [ γ 2 (1 + α ) 2 2 µ (M / )] 0 0 lum = V G L 1 M = M sun 2.5log( L / Lsun)

16 Samples: 1 st sample: 967 spiral galaxies Mathewson (1992) 2 nd sample: 304 spiral galaxies Courteau (1997) 86 galaxies selected for analysis 3 sample: 329 spiral galaxies Vogt (2004) 81 galaxies selected for analysis

17 UGC Vmax V R/Rd

18 1. Mathewson sample: R R/Ropt; bin= Courteau sample: R R/Rd; bin= 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.

19 1 st sample: TF-relation for 967 galaxies R/Ropt 0.4R/Ropt 0.6R/Ropt 0.8R/Ropt 1.0R/Ropt 1.2R/Ropt -21 M i log V

20 1 st sample: TF-relation for 967 galaxies

21 Slope of the TF-relation M B = a i + b i log V(R i )

22 Gap in the slopes of 2 samples: L 4 [ γ 2 (1 + α ) 2 2 µ (M / )] 0 0 lum = V G L No dark matter M x L 1+ k = x 4 = 2. 5( ) log V; M lum k ~ L 1+ k L V 4 1 k=0.1 for I band k=0.3 for R band function of the band The slope of TF-relation is related to k

23 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 4 (1 + α ( R, L )) 0 2 M M dark lum = α dark matter parmeter α decreases with L α increases with R this has influence on the slope

24 Scatter of the TF-relation

25 TF-relation using Vmax M i logv max M R log V max slope=-7,579; scatter=0,328; number of galaxies=843 slope=-5.54; scatter=0.49; number of galaxies=83

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27 Probing dark matter halos of spiral galaxies with their satellites 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

28 We are studying 7 isolated spiral galaxies at z = = 58 h Satellites + Rotation curves

29 SDSS J z=0.078

30 7 primaries 77 satellites identified Primary galaxy z N of sat. (SDSS) SDSSJ SDSSJ SDSSJ SDSSJ SDSSJ SDSSJ SDSSJ N of sat. (found)

31 SDSS J

32 SDSS J

33 SDSS J

34 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