Lecture Four: Scaling Relations Late Type Galaxies… Masses of Spiral
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Lecture Four: Scaling Relations Measuring galaxy properties contd. One of the main uses of astrophysical surface photometry is for the study of parameter correlations and scaling laws. These contain valuable information about galaxy formation & evolution Kormendy & Djorgovski 1989 ARAA 27 235 Tuesday 11th Feb 1 2 Masses of Spiral galaxies Surface Brightness profiles sample the distribution of luminous matter in a galaxy. This does not necessarily tell us about the mass of the galaxy - due to DARK MATTER. Late Type Galaxies… HI rotation curves allow TOTAL mass determination. Battaglia et al. 2006 A&A, 447, 49 3 4 Rotation Curves of Spiral Galaxies Bosma 1981 Masses of Spiral galaxies correlations : The constant rotational velocities in the outer regions - suggest that mass increases linearly • increasing L rotation curves tend with distance from the centre. In stark contrast to the light distribution, which decreases B exponentially over the same distance. to rise more rapidly with distance from centre and peak at higher This means a rapidly increasing mass-to-light ration (M/L) and a hidden dark matter halo in maximum velocity (Vmax). spiral galaxies (Bosma 1981). • for equal LB spirals of earlier type have larger Vmax. The fact that galaxies of different Hubble types, and therefore different bulge-to-disk luminosity ratios, exhibit rotation curves that are very similar in form if not in amplitude • within a given Hubble type more suggests that the shapes of the gravitational potential do not necessarily follow the luminous galaxies have larger Vmax. distribution of luminous matter. • for a given value of Vmax the rotation curves tend to rise slightly more rapidly with radius for earlier type galaxies. •Vmax is significantly lower in Irrs 5 6 Tully-Fisher: late type galaxies Tully-Fisher with rotation curve A relationship exists between the luminosity of a spiral galaxy and its maximum Three kinds of rotation curves rotation velocity. Good distance indicator! Observed as absolute magnitude and HI profile width Example of global HI profile Vflat not V < V Vflat = Vmax flat max reached? Tully & Fisher 1977 Disk Mass dominates ! Verheijen 2001 7 8 width of global HI profile Trends in M/L with galaxy parameters B B M/L NOT constant! K peak velocity of HI K rotation curve Tightest relation is between M and Vflat K, Absolute mag. K, surface brightness = Relation between the stellar mass (luminosity) and the DM halo mass B B The star formation and the chemical enrichment history determine both the stellar M/L amplitude of flat ratio and galaxy color part of HI rotation curve K K Verheijen 2001 Bell & de Jong 2001 gas-fraction galaxy colour More scatter in B due to stellar pop effects 9 10 Converting luminosity to mass Tully-Fisher with stellar mass IMF (initial mass function) Ψ(m, t), number of stars formed per unit volume at t=0 -α often approximated as a power law: Ψ(m) dm = Ψ0 m LF (luminosity function) currently observed number of stars observed per unit luminosity per unit volume PDMF (present day mass function) number of stars observed today per unit mass per unit volume. This needs to be corrected for the time evolution of the IMF up to the present day, low mass, IMF long lived stars PDMF Star Relations with BRIK colours and assuming a Salpeter IMF are used to convert the Formation magnitude-dependent dust-corrected magnitudes into stellar masses, using the dust- high mass, corrected B-R color as input. short lived History stars Bell & de Jong 2001 Kroupa, Tout & Gilmore 1993 MNRAS, 262, 545 11 12 Tully-Fisher at low masss The slope change in the TF is reconciled when the gas mass is taken into account: M = A * V b Break, for small • d c galaxies b=3.98 ± 0.12 Gas significant, large component in small galaxies BARYONIC TULLY-FISHER McGaugh et al. 2005 13 14 Early Type Galaxies… Families of Ellipsoidal stellar systems… 15 16 Masses of Elliptical galaxies Masses of Elliptical galaxies Elliptical Galaxies: application of virial theorem, assuming Using globular clusters as tracers, the line-of-sight velocity dispersion in Elliptical isotropic stellar distribution galaxies remains remarkably constant out to the limits of observation. This has the same explanation as flat rotation curves in HI. To bind globular clusters with large velocity dispersions at large radii means that the mass within R must increase proportional to R. Large Dark Matter haloes also in Elliptical Galaxies Côte et al. 2003 ApJ, 591, 850 17 18 Shapes of Elliptical galaxies Internal dynamics of Ellipticals Flattening caused by rotation can be tested by measuring the mean velocities and velocity dispersions of the stars through out the body of a galaxy. These measurements can be compared with the rotation and internal velocity dispersions expected if the flattening can be attributed to rotation. Low luminosity Ellipticals and bulges rotate rapidly and have nearly isotropic velocity Solid line: amount of rotation dispersions and are flattened by rotation (solid necessary to black points + crosses). account for observed ellipticity of galaxy relative Bright Ellipticals rotate slowly and are pressure to σ of stars. supported and owe their shapes to velocity anisotropy (open circles) This could be explained by proto-galaxies acquiring angular momentum through tidal torques and then if mergers produce brighter ellipticals the rotation gets scrambled in the It might be thought that the internal dynamics of elliptical galaxies would be relatively process. simple - the surface brightness distributions appear to be ellipsoidal, with a range of Ellipticals rotate too slowly for centrifugal forces flattenings, which it might be thought could be attributed to rotation. to be the causes of their observed flattening. from Davies et al. 1983 19 20 The Faber-Jackson Relation Multi-parameter correlations: Looking for correlations in the observed properties of Elliptical galaxies the Fundamental Plane Faber & Jackson 1976: strong correlation between luminosity (L) and central velocity dispersion (σ): A break through in our understanding of scaling laws came from large homogeneous data sets (from CCDs & long-slit Taking log of both sides, relation in terms of M . A natural consequence of the virial theorem. B spectroscopy), and the application of statistical tools. Plenty of scatter, and the slope of the relation is different than the virial plane - means correlation in a 3D space and we see this space theorem. with three parameters that “see” the correlation from This was assumed to indicate a missing different angles. parameter… and there was originally a lot of debate about what was the missing parameter.. using data from Bender et al. 92 21 22 Ellipticals: Fundamental Plane Projections of Fundamental Plane of Ellipticals & Bulges Radius derived from Tilt to plane leads surface brightness to scatter. profiles, e.g., core or effective radius. Radius Luminosity Faber-Jackson Radius Velocity Dispersion Mean Surface Brightness physical meaning of these measurements links Observed “Cooling Diagram” from galaxy Meanto formationSurface Brightness theory! Velocity Dispersion formation theory (virial temprature vs. density) Radius Plane edge-on plane face-on position of galaxy inMean Surface Brightness this diagram relates to amount of dissipation Velocity Dispersion Combined Velocity Dispersion & surface brightness during its formation. Djorgovski & Davis 1987 23 24 Ellipticals: Fundamental Plane Measuring galaxy properties Radius Velocity Dispersion mean Surface Brightness with Sloan Digital Sky Survey (SDSS) Longair, chapter 3 Blanton & Moustakas 2009 ARAA 47 159 Reading is very important!! 25 26 Studying galaxies A galaxy can consist of hundreds of millions or billions of stars. It can contain considerable quantities of interstellar gas and dust and can be subject to environmental influences through interactions with other galaxies and intergalactic gas. It may be forming stars with a variety of rates. And it will contain dark matter and the dynamics of galaxies are largely dominated by this era of large galaxy surveys.... invisible dark component, the nature of which is unknown. Until recently the properties of galaxies were determined from meticulous morphological studies of samples of bright galaxies - encompassing a vast amount of detail. Now in the era of large surveys [e.g., hundreds of thousands of galaxies in the Sloan Digital Sky Survey (SDSS)] classification has to be simpler as the parameters have to be able to be automatically and consistently measured by computer. What these large surveys lack in detail they more than make up for with statistics. 28 27 28 2DF Galaxy Redshift Survey Millennium Galaxy Catalogue Imported Author Yesterday, 12:26 Reliable redshifts for 220k objects, mainly galaxies, brighter than a magnitude limit of bJ=19.45, cover an area of approximately 1500 square degrees http://www2.aao.gov.au/~TDFgg/ http://www.eso.org/~jliske/mgc/ 29 30 The Sloan Digital Sky Survey SLOAN - hardware The SDSS used a dedicated 2.5-m f/5 modified Ritchey-Chretien altitude- azimuth telescope located at Apache Point Observatory (2788m), New Mexico, USA. It is equipped with two powerful special-purpose instruments. The 120-megapixel camera which can image 1.5 square degrees of sky at a time. A pair of spectrographs fed by optical fibres measured spectra of (and hence distances to) more than 600 galaxies and quasars in a single observation. A custom-designed set of software pipelines kept pace with the enormous data flow from the telescope. Imager: 30 SITe/Tektronix 2048 by 2048 pixel CCDs: r, i, u, z, g filters. Drift scan mode: camera slowly reads CCD as data collected. spectrographs: in a single exposure ~600 spectra of galaxies to the spectroscopic limit of r’ ~ 18.2 over the field of the telescope. R~2000, λ3900-9100Å. 31 32 SLOAN - observing special Sloan filter system shows the strips on the sky observed by Sloan... the underlying contours are extinction from Galactic disk.