Lecture Four: Scaling Relations Late Type Galaxies… Masses of Spiral

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

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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

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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

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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

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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 in Brightness Surface Mean 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!!

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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.

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/

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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.

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Typical Sloan Galaxy Spectrum The Sloan Digital Sky Survey

SDSS is an ambitious and influential survey. Over eight years of operations (SDSS- I, 2000-2005; SDSS-II, 2005-2008), it obtained deep, multi-colour images covering more than a quarter of the sky and created 3-dimensional maps containing more than 930,000 galaxies and more than 120,000 quasars. SDSS data have been released to the scientific community and the general public SDSS-III, a program of four new surveys using SDSS facilities, began observations in July 2008, and will continue through 2014. http://www.sdss.org/

R=2000

35 36 Very large consortium!! SLOAN - Quasars

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SLOAN - high redshift quasars SLOAN - quasar luminosity fn

quasar redshift distribution Resulting i-band luminosity function determining how many quasars there are at high redshift

Fan et al. 2004 AJ, 128, 515 Richards et al. 2006 AJ, 131, 2766 Fan 2006 New Astronomy Reviews, 50, 665

39 40 SLOAN - also stars! New dwarf galaxies from SDSS the field of streams CVn II Com

CVn I Boo IIIKoposov 1 Willman 1 Boo I Leo II UMa I Boo II Leo V Segue 1 Leo I Leo T Ursa Minor Leo IV UMa II Sextans Draco Her Koposov 2 Canes Venatici dwarf

Sagittarius stream B o l=180 l=0o, b=0o l=-180o

Sagittarius stream A Sagittarius Bootes Segue 3 Segue I Carina

Leo IV & V LMC Segue 2 Pisces II SMC

here is a map of individual stars seen in SDSS field of view - colour coded by Fornax distance. Sagittarius stream is very prominent. Also many new very faint galaxies Sculptor found - called “ultra-faint” galaxies.

Belokurov et al. 2007 ApJ, 658, 337 from Vasily Belokurov, SDSS data release 8 41 42

SLOAN - adding to Local Group What are they? Lines of constant surface Canes Venatici I Bootes Canes Venatici II Coma Bernices brightness

dSph D = 220kpc D = 60kpc D = 150kpc D = 44kpc Absolute magnitude Absolute Rh = 220pc Rh = 140pc Rh = 70pc Rh = 550pc

MV = -5.8 MV = -4.8 MV = -3.7 MV = -7.9 ??

Globular Clusters

http://www.ast.cam.ac.uk/~vasily/ Half-light radius Belokurov et al. 2007, ApJ, 654, 897

43 44 SLOAN - Supernovae survey SLOAN - Systematic characterisation of During SDSS-II, a time-domain survey, involving repeat imaging of the same region of sky every other night, weather permitting. The primary scientific motivation was to detect and measure light curves for galaxies several hundred intermediate-redshift (0.05 < z < 0.35) Type Ia supernovae

Imported Author 1 Yesterday, 12:26 large scale structure in the northern equatorial slice of the SDSS main galaxy redshift sample. The slice is 2.5 degrees thick, and galaxies are color-coded by luminosity.

provide new constraints upon dark energy and insights into the systematics of SNe Ia as calibrated standard candles and cosmological distance indicators. Frieman et al. 2008 AJ, 135, 338 Sako et al. 2008 AJ, 135, 348

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huge survey

With the large samples from SDSS and 2dF Galaxy Survey a more quantitative SLOAN insights into galaxies approach to galaxy classification has had to be developed, necessitated by the need to analyse huge samples automatically. What is lost in the detail is more than properties... made up by the HUGE statistics of galaxies of different properties. The early Sloan releases created samples of ~200 000 galaxies. The last release What are the gains of studying the detailed properties of 200 000 brings this number up to ~900 000 which has not changed substantially the picture galaxies or even 900 000 galaxies all in one go in a consistent fashion? with the smaller sample.

47 48 SLOAN - luminosity functions

Blanton et al (2003) ApJ, 592, 819

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Is it a Schechter Function?

~150 000 galaxies in the Local Universe

z redshift Blanton et al (2003) ApJ, 592, 819

51 52 SLOAN - Luminosity Function Luminosity functions in different ﬁlters

many faint galaxies

~150 000 galaxies in the Local Universe

few bright galaxies

Answer: not quite – but very close! z=0.01 – 0.2 is 2.5 Gyr Evolution is important Note large excess at large mass/luminosity – likely to be Blanton et al (2003) ApJ, 592, 819 either cD galaxies OR photometric problems Blanton et al (2003) ApJ, 592, 819

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Mass Functions Mass Functions convert from luminosity to mass using spectral synthesis methods

Panter et al. 2004 MNRAS 355 764

Evolution is important: z=0.01-0.2 is 2.5 Gyr

Panter et al. 2004 MNRAS 355 764

55 56 SLOAN -Bimodality Bi-model Colour Distribution blue dominate faint magnitudes

RED SEQUENCE

BLUE SEQUENCE

Using a simple merger model, they show that the differences between the two functions are consistent with the red distribution being formed from major galaxy mergers.

Baldry et al (2004) ApJ, 600, 681 u-r u-r Baldry et al. 2004 ApJ, 600, 681 red most luminous

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Luminosity functions A result of mergers?

N-body simulations suggest that the geometries and the motions of stars, similar to those observed in elliptical galaxies, can be produced by galaxy mergers (Barnes 1988; Barnes & Hernquist 1992).

Thus it is possible that mergers are the cause of the bimodality, with the red distribution deriving from major merger processes and the blue distribution deriving from more quiescent accretion (with only minor mergers at most)

Baldry et al. 2004 ApJ, 600, 681 Baldry et al. 2004 ApJ, 600, 681

59 60 Mass functions Overall properties data models (merging)

Baldry et al. 2004 ApJ, 600, 681 Blanton et al (2003) ApJ, 594, 186

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SLOAN - general properties A sequence in concentration luminosity index Sersic surface brightness u-g u-g g-r r-I i-z SB Sersic Abs Mag u-g u-g g-r r-I i-z SB Sersic Abs Mag color u-g g-r r-I i-z SB Sersic Abs Mag u-g g-r r-I i-z SB Sersic Abs Mag number density luminosity density surface Sersic color brightness index luminosity

Blanton et al. 2003 ApJ, 594, 186 63 64 A sequence in concentration A sequence in concentration luminosity luminosity index index Sersic Sersic surface surface brightness brightness color color