Modern observational astronomy: from stars to galaxies Universidad Nacional de Colombia, Bogota,...

Modern observational astronomy:Modern observational astronomy:from stars to galaxiesfrom stars to galaxies

Universidad Nacional de Colombia, Bogota, Agosto 2005Universidad Nacional de Colombia, Bogota, Agosto 2005

VII – Disk galaxies & Group environmentDr. Michael Hilker (Sternwarte Bonn)

Dr. Michael Hilker (Sternwarte Bonn)

Spiral Galaxies are complex systems:Spiral Galaxies are complex systems:• wide range in morphological appearance

• wide range in stellar populations old, intermediate, young and currently forming ongoing chemical enrichment

• wide range in stellar dynamics “cold” rotationally supported disk stars “hot” mainly dispersion supported bulge and halo stars

• significant inter stellar medium (ISM)


Morphological classification byde Vaucouleur

Three axes:

•stage (early-late)•family (bar)•variety (rings)

used in the ReferenceCatalogue of BrightGalaxies: RC1 (1964), RC2 (1976), RC3 (1991)


Spectra ofspiral andstarburstgalaxies

compare to spectraof early-typestars

emissionlines are from gas(H II regions)


Photometry of disk galaxiesPhotometry of disk galaxies


Photometric effects of dust

No transparent galaxy: absorption and scattering!

Depending on inclination to line-of-sight, affects: surface brightness profile + apparent magnitude causes selection effects in galaxy samples


Basic Components and their 3-D shapes (1)Basic Components and their 3-D shapes (1)

Disks: metal-rich stars and ISM nearly circular orbits with little (~5%) random motion spirals patterns

• mostly flat circular disks (can be very thin)• deviation from circular due to slightly oblate/triaxial dark matter potentials• HI disk is often warped (but starlight almost always flat)

in 3-D:

Apparentaxial ratios:

q = b/abulge influencesmeasurements


Early-type spiral galaxy with a warped disk


The vertical structure of disksThe vertical structure of disksThe vertical structure of disk galaxies can be measuredfrom the photometry of edge-on spirals.

Two laws have been used to fit the data:

z0 is the scale heigth of the disk, I(z0) = 1/e I(0)

I(z) = I(0) exp(-|z|/z0)

I(z) = I(0) sech2(-|z|/2z0) sech(z) = 2/[exp(z) + exp(-z)]

In the Milky Way there are several components of different scale height and velocity dispersion:

• gas and dust z0 ~ 50 pc; z ~ 10 km/s

• young thin disk z0 ~ 200 pc; z ~ 25 km/s

• old thick disk z0 ~ 1.5 kpc; z ~ 50 km/s


edge-on Sd spiral

edge-on irregular

ESO342 VLT


Basic Components and their 3-D shapes (2)Basic Components and their 3-D shapes (2)

Bulge: metal-poor to super metal-rich stars high stellar density with steep profile vrot/ ~ 1

in 3-D:• probably similar to low-luminosity ellipticals• 0 < < 0.7• ~ oblate spheroids, flattened by rotation• ~ 25% have very boxy isophotes

“peanut” shape

relatedto a bar?


Bulge-disk decompositionBulge-disk decomposition

bulge

disk

de Vaucou-leurs law

exponential law


Further examplesFurther examples

Definition of bulgefraction:

or bulge-to-disk-ratio:

B/T =Re

2Ie

Re2Ie + 0.28Rd

2Id

B/D =Re

2Ie

0.28Rd2Id

Boroson(1981)


A distance spiral in the Ultra Hubble Deep Field


Basic Components and 3-D shapes (3)Basic Components and 3-D shapes (3)

Bar: long-lived, flat, linear distribution of stars associated with dust lanes and star formation associated with rings and spiral pattern

in 3-D:• axis ratio in disk plane range from 2.5 to 5• isophote twists suggest nested bars common: bars within bars• are probably flat (barely seen in edge-on spirals)

surface brightnessalong the bar’s appa-rent major axis andminor axis

early-type late-type


ellipticity

surfacebrightness

triaxial bulge


Basic Components and 3-D shapes (4)Basic Components and 3-D shapes (4)

Nucleus: central (< 10pc) region of very high density dense ISM and/or starburst and/or star cluster massive black hole

Stellar halo: very low surface brightness; ~few % of light metal-poor stars, GCs, low density hot gas little/no rotation

Dark halo: dominates mass (+ potential) outside ~10 kpc mildly flattened and/or triaxial nature unknown


Stellar and gas kinematicsStellar and gas kinematicsof disk galaxiesof disk galaxies


Bulge kinematicsBulge kinematics

Light from surrounding disks contaminates the observationand dust obscuration further complicates the analysis.But: with the knowledge of the inclination of the disk one can define one of the principal axis of the bulge• bulges seem to be flattened by rotation

• bulges fall on the same fundamental plane as ellipticals

• bulges with boxy isophotes rotate cylindrically (axisymmetric or bar?)

Disk kinematicsDisk kinematics

Stars in disks follow approximately circular orbits with littlerandom motion. Thus, one can obtain rotation curves.• rotation curves have similar properties to those obtained for gas

• in some disks gas and stars are counter-rotating

• in some there even exist two counter-rotating stellar disks


Spectrum of K0 giant star (S)and the center of the lenti-cular galaxy NGC 2549 (G)

Mg b

The features in the galaxy areredshifted and broadened

The cross-correlation functionbetween the galaxy and starspectra radial velocity

longslit on major axis

spectrum atone position

velo-citydisper-sion

Convolution of stellar spectrumwith Gaussian model LOSVD


When taking a spectra with a longslit across a galaxies,one has not only the spectral information at one point,but at all positions along the slit. If X is the position along the slit, one can calculate the line-of-sight velocity distribution (LOSVD), F(X,vlos) for each X.

If one normalizes F(X,vlos) by the total intensity of lightat each point X, one obtains PV(X,vlos) = I(X) x F(X,vlos).This is proportional to the phase density of stars if theyare all of similar type.

A plot of the function PV(X,vlos) is known as a position-velocity diagram, or PV diagram. A cut through thisfunction at constant X yields the LOSVD at this point, while integrating this quantity over vlos yields the surfacebrightness at this point.

Position-velocity diagramsPosition-velocity diagrams


Random motions inthe bulgeSignature of therotationally-supporteddisk

Stellar position-velocity diagram for the major axisof the edge-on S0 galaxy NGC 7332

The greyscaleindicates thedensity ofstars


A kinematic map of the central region ofM104

Mean line-of-sight velocity

Line-of-sight dispersion

Skewness

Disk: rapid rotation

low dispersion due to streaming motions

skewed LOSVD: concentrationof stars close to the circular speed, and tail towards systemicvelocity

Bulge: random motions dominate and cause a high dispersion


Stellar position-velocity diagram for the major axis of the Sa galaxy NGC 3593

Counter-rotatingsmall stellar disk


Observations by aperture-synthesis telescopes or Fabry-Perot interferometer (for H) yield a 3-dimensional data cube, with the frequency and the x,y position as coordi-nates. It can be displayed as a series of channel maps,dividing narrow ranges in frequencies (= radial velocities)

Kinematics of the interstellar mediumKinematics of the interstellar medium

The interstellar medium in disk galaxies can be mappedby the observation of emission lines of H, CO, the well-known 21-cm line of HI, and others.The CO and HI lines are emitted in the sub-millimeter and radio regime. First observations were performed withsingle-dish instruments, resulting in a poor angular reso-lution.Only with the upcoming of aperture-synthesis telescopesexternal galaxies could be mapped with an angularresolution in the arcsecond regime.


Getting the velocity fieldGetting the velocity fieldof a spiral galaxy:of a spiral galaxy:25 channel maps (velocityslices) of the 21-cm line forthe Sc galaxy NGC 5033.asymmetry of profiles warped disk in NGC 5033re

cedin

g side

systemic velocity

approaching side


HI gas inNGC 7331

gas surfacedensity

and

contours ofconstant

gas velocity


Observing geometry for disk galaxies

Rotating disk viewed from above The observer’s line of sight makes angle i with the disk’s rotation axis z

Radial velocity: Vr(R,i) = Vsys + V(R) sin i cos

Circular velocity: Vc(r) = r (r), with (r) the angular speed

Line-of-sight velocity: Vlos(r ) = r (r) sin i


A typical galacticcircular-speed curve

Spider diagram of circular-speed curve when viewing thesystem at inclination 30o and horizontal major axis• the contours have constant line-of- sight velocities• inside: solid body rotation• outside: closed contours because of declining rotation curve

solid-body rotation: vc ~ r

declining

closed


Rotation curve V(R) in a ‘dark halo’ Spider diagram of Vr for a diskpotential in units of VHalo = Vmax observed 30o from face-on. Contours are marked in units of VHalo sin 30o

rising

openmajor

minor

Kinematic minor axis: line of systemic velocityKinematic major axis: perpendicular to the local constant velocity-contours

in the case of flat circular disk: coincide with optical axeswarped or elliptical disk: distinct optical axes


Circular speed curves are important because from it one can deduce the mass M(r) interior the radius r. From the light curve, one would expect a Keplerian decline of therotationcurve, but:

missingmass:dark

matter


The 21-cm circular-speedcurve of the Sc galaxyNGC 3198

r-band brightness profile

calculated curve with(M/L)r = 3.8 (M/L)r,

Most of the galaxy’smass lies beyond R25


Observed and modeled rotation curve of NGC 7331

points: HI gas, dotted: CO gas for bulge and disk a mass-to-light ratio has to be assumed

dark matter


Rotation curves of spiral galaxies


A tilted ringmodel of

M83

The observedspider diagram

Kinematic warpsKinematic warps

M83 in theB-band


A strongly warped disk seen from nearly-edge on

Some lines of sight cut the warped disk twice the line-profile is liable to be multi-peaked

Our closest neighbors, M31 and M33, exhibit this phenomenon


A warped HI disk in NGC 4013


The amplitude of the rotation velocityis correlated with the absolute magnitude of the galaxy: Ltot ~ Vmax

with = 4more luminous galaxies have higher circular velocitiesThis correlation is known as theTully-Fisher relationIt can be used as distance indicator

MB = -10.2 log Vmax+2.71


The Tully-Fisher relation can be derived from the followingconsiderations:Most spirals possess nearly flat rotation curves beyond a certain radius.This implies that the mass contained within a radius r is given by

Mr = (V2r)/G derived from (mV2)/r = (GMrm)/r2

For the entire galaxy (r R, Mr M) it holds:

M = (VmaxR)/G where Vmax is measured in the flat part of the rotation curve

2

If the mass-to-light ratio has the same value for all spirals (M/L = CML = const.), then

L = 1/CML .(VmaxR)/G2

42

If we further assume that all spirals have the same surface brightness(Freeman’s law), L/R2 = CSB = const., then we can write the luminosity:

L = 1/(CMLCSB) .(VmaxR)/G2 = CVmax

with C containing all the constants.

4

In absolute magnitudes the relation then is: M = -10 logVmax + const.


Nearby galaxy groupsNearby galaxy groups


Distribution of nearby groups within 5 Mpc radius

Supergalactic plane from the top and ... .... from the side

Karachentsov et al. (2002)


Two nearby galaxy groups

M51 group M81 group

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.




M81Galaxy type: Sb

Largest galaxyOf the UrsaMajor Group


HI distribution in theM81 group andposition of tidaldwarf candidates

Makarova et al. (2002)


Examples for interacting spirals

M51


HI in the M51 system


Stellar and gaseous tidaltails displaced to each other


About half of all galaxies in the universe are found ingroups. Groups are generally dominated by late-typegalaxies (i.e. gas-rich spirals).

Stars and gas react differently to galaxy interactions:• gas clouds can collide and can trigger intense star formation• also gas can be stripped-off from galaxies when those enter a dense intergalactic medium

• stars can be regarded as collisonless, they ‘only’ feel the gravitational forces of the interaction• depending on the speed of the encounter, stars and gas can be thrown out in more or less extended tidal tails

Galaxy groups are dynamically young environments.The group velocity dispersion often is of the same orderas the orbital speeds of stars in the member galaxies.Thus strong interactions are taking place in most groups.

Some facts on galaxy groups and interactions to rememberSome facts on galaxy groups and interactions to remember



Modern observational astronomy:Modern observational astronomy:from stars to galaxiesfrom stars to galaxies

Universidad Nacional de Colombia, Bogota, Agosto 2005Universidad Nacional de Colombia, Bogota, Agosto 2005

VIII – Ellipticals & Galaxy ClustersDr. Michael Hilker (Sternwarte Bonn)


Elliptical Galaxies• mostly have old stellar populations and few gas

• are located in galaxy clusters and groups

• it is believed that some (or most?) were created by the merging of spirals

M87 in the Virgo Cluster

M49

M59


Spectrum of an elliptical galaxy

comparable with spectra of K and M stars


Some isophotes

of ellipticals

roundelongated& twisted

“disky ” “boxy “

The surface brightness profile is measured along the major axis


Fitting functions forFitting functions forsurface brightness profilessurface brightness profiles

of ellipticalsof ellipticals

logarithmic R1/4

de Vaucouleurs law:

Some properties: Ltot = 7.22 Re2 Ie (total luminosity)

I(0) = 103.33 ~ 2000 Ie (central surface intensity)

<I(<Re>)> = 3.61 Ie (mean surface intensity)

Re: effective radius = half-light radius Ie: effective surface intensity at Re


The de Vaucouleurs law is a special case of a more general Sersic law:

Properties: b =1.999 n - 0.327 (N>1) 0.5 Ltot = I(<Re) n=4, b=7.67 de Vaucouleurs law n=1, b=1.67 exponential profile

Lower luminosity Es (MB~-19) have steep slopes (n<4)Higher luminosity Es (MB~-22) have shallower slopes (n>4)

There also exist physically motivated models, like the isothermal model and King profiles. They describe aself-gravitating system with Boltzman distribution in energy(potential + kinetic). Violent relaxation at the formation ofgalaxies can lead to this Boltzman distribution.(good fits to globular clusters, but only moderate fits to some ellipticals)


Centers of ellipticalsCenters of ellipticalsThe nuclear regions ofellipticals are not well fit by most profiles. A newfunction, the “Nuker”profile, can describe theslope of cusps or cores inthe central region.R >> Rb: outer power law defined by R << Rb: inner cusp or core defined by sets the sharpness of the transition near Rb

“Nuker”profile

cusp

core


The (deprojected) luminosity density of 40 early-type galaxies

~ j(r)

Gebhardt et al. 1996

two classes of ellipticals??


Deviation from elliptical isophotes (1)Deviation from elliptical isophotes (1)


Deviation from elliptical isophotes (2)Deviation from elliptical isophotes (2)

The isophote can be expressed as a Fourier series:

is the mean radius a1, b1 define the ellipse center

a2, b2 define the eccentricity and a3, b3 are useful diagnostics of position angle dust (asymmetries)

a4 defines the boxiness or diskiness, a4 < 0 : boxy a4 > 0 : disky

( ) ( )


Correlations with boxy-/diskynessCorrelations with boxy-/diskyness

boxy disky boxy disky

boxy disky boxy disky


Deprojecting galaxy images (1)Deprojecting galaxy images (1)

What will be the 3-dimensional luminosity density j(r) in a transparent galaxy with projected surface-brightness distribution I(R)?Note: for constant M/L ratio, j(r) tracks the spatial mass density.

observerz

R r z2 = r2 - R2 dz = r dr / (r2 - R2)1/2

For circular symmetry in projection on space:

Abel integral equation

with solution:)


Deprojecting galaxy images (2)Deprojecting galaxy images (2)A fitting function for an observed surface-brightness profilethat corresponds to a simple analytical form of j(r) is the modified Hubble law:

Problem: total luminosity diverges as log R for large R

Solution: Dehnen laws (including Hernquist and Jaffe laws) see Binney & Merrifield, p.181

Hubble-Reynolds law:

Some remarks for spherical models (simple power law of index ):

I(R) ~ R- j(r) ~ r --1

I(<R) ~ R2-a Mass(<r) ~ r2-a

central surface intensity

radius at half I(0)


TriaxialityTriaxialityIf I(R) is not circularly-symmetric, the galaxy cannot bespherically symmetric, but might be axisymmetric.

Is the line of sight within the galaxy’s equatorial plane,one can find solutions for the deprojection, but normallythe galaxy will be inclined. Then the image containsinsufficient information to reconstruct the 3-dimensionalluminosity density j(r).

ellipse equation: x2/a2 + y2/b2 + z2/c2 = r2

Triaxial shape: a > b > c

But even more complicated, many galaxies are notaxisymmetric, but triaxial (it has three orthogonal symmetryplanes). Projected onto the sky, the isophotes havedifferent ellipticities and can be twisted, depending onthe orientation of the body and its axis ratio.


Projection effects whenseeing an oblate, elongated elliptical not from face-on

Isophotal twist as a consequenceof triaxiality. Two concentric, coaxial ellipsoids are shown(a prolate ellipsoid insinde an oblateellipsoid).

Oblate ellipsoid: a = b > c “flying saucer”Prolate ellipsoid: a < b = c “cigar”


The stellar kinematics of elliptical galaxiesThe stellar kinematics of elliptical galaxies

Major-axis kinematics: since ellipticals are getting very faint in the outer parts, large telescopes, efficient spectrographs and long exposuretime are needed to study the large-scale kinematics of Es.

The LOSVD in an elliptical is generally close to a Gaussian,so they are suited for the analysis by the Gauss-Hermitetechnique.

General findings:• kinematical parameters are symmetric (or antisymmetric) about the center simple equilibrium models can explain their current dynamical state• the mean velocity changes sign as we pass through the center rotation about their minor axes, flattening the system but amount of rotation is not enough to account for rotational flattening only!!


Shape parameters of velocity distribution profiles

3: skewness departure from symmetry in the LOSVD

4: kurtosis symmetric departures from a Gaussian

long tail to positive velocitieslong tail to negative velocities

rect

ang

ul a

r d

ist r

ibu

t io

nce

ntr

ally

-pea

ked

dis

trib

uti

on


Major-axis kinematics for four giant ellipticals


The rotation in ellipticals seems to be correlated to theskewness parameter, h3

The observed skewed LOSVD can be produced by thesum of two components, a non-rotating broad distributionand a rapidly-rotating narrow distribution.

Ellipticals harbor a rotationally-supported disk component.The size of this component relative to the whole galaxydictates the “diskyness” of the galaxy and its kinematicsalong the major axis.

The kurtosis parameter, h4, tends to be positive within theeffective radius of most ellipticals and zero or negativeoutside this radius. The reason for this transition is not clear.


Rotation measure vs. luminosity and boxy-/diskyness


Detection of dark halosDetection of dark halosAs in spiral galaxies, the velocity dispersion profile of ellipticals seems to stay flat out to large radii. This shouldpoint to the contribution of a dark matter halo.

However, in ellipticals, primarily tangential stellar orbits can mimic a flat or even increasing velocity dispersion profile although the true tangential and radial velocity dispersion of the stars is decreasing with radius. There exists an ambiguity between the distribution of stellarorbits and the distribution of mass in ellipticals.

R A

Bdominating

Rdominating

Luckily, one can see fromthe shape of the LOSVDs in ellipticals that there isno strong anisotropy seen:

= R

massive DM halo exists


Orbits in the x,y plane of a triaxial potential

loop orbit,avoids thecenter

box orbit,passingthroughthe center

chaotic orbit,producedwhen a cen-tral spheri-cal poten-tial is added

surface ofsection:values of(x,vx) forall threeorbits when orbitcrossesy=0 withvy>0


Simulations of spiral-spiral mergers by Barnes et al. (1996, 1998)

The identification of orbits in a strongly triaxial merger remnant

Box orbit. Main orbit family, consistent with triaxial den-sity distributions.

X-tube orbit. Loop aroundthe major axis. Only familypresent in prolate potentials.

Z-tube orbit. Loop aroundthe minor axis. Only familypresent in oblate potentials.

Pretzel orbit. 4:3 resonancein a deeppotential.

Fish orbit. 3:2 resonancein a deeppotential.












SAURON

NGC 5813

recon-structedsurfacebrightnessimage

and stellarvelocityfieldshowing adecoupledcore

Mg b map

H mapsbefore andafter sub-traction ofemissionlines

Note thegaseousfilaments


Correlations among global parameters of elliptical galaxiesCorrelations among global parameters of elliptical galaxies

Shape parameters:

• ellipticity: • boxy-/diskyness: a4/a• rotation rate: (v/)*

Shape-independent parameters:

• luminosities: LX (in various bands X)

• effective radius: Re

• effective surface brightness: Ie, e

• mean colors: B-V, etc.• linestrength indices: Mg2, Fe, etc.

• central velocity dispersion: 0

Correlation between parameters provide importantconstraints on theories of galaxy formation.


2-parameter correlations (1)2-parameter correlations (1)Color-magnitude relation:more luminous ellipticals areslightly redder

Mg2 vs. velocity dispersion:

galaxies with deeper poten-tials have stronger Mg2

Color vs. Mg2 relation:

the redder the galaxy thestronger Mg2

Color and Mg2 track metallicity (and age)Luminosity and 0 track total galaxy mass

deeper potentials form stars more effectivelyand hold ISM longer, thus allowing metals to

build up more rapidly

dEs

S0s

Es


2-parameter correlations (2)2-parameter correlations (2)

Size & luminosity vs. surface brightness (Kormendy) relation:

<Ie> correlates with Re: Re ~ <Ie> -0.83+/-0.08

<Ie> correlates with Ltot: Ltot ~ <Ie> -2/3

larger more luminous galaxies are fluffier with lower densities

Luminosity vs. velocity dispersion (Faber-Jackson) relation:

e correlates with Ltot: Ltot ~ *n with 3 < n < 5

more luminous galaxies have higher velocity dispersions (remember Tully-Fisher relation for spirals)



Correlations with boxy-/diskyness (2)Correlations with boxy-/diskyness (2)

Property boxy (a4<0) disky (a4>0)

Luminosity high: MB < -22 low: MB > -18

Rotation rate slow/zero: (vr/)* < 1 faster: (vr/)* ~ 1

Flattening velocity anisotropy rotational

Rotation axis anywhere photometric minor axis

Velocity field anisotropic nearly isothermal

Shape moderately triaxial almost oblate

Core profile cuspy core steep power law

Core density low high

Radio luminosity radio loud and quiet radio quiet 1020 - 1025 W/Hz < 1021 W/Hz

X-ray luminosity high low

Idea: formation via … … hierarchical mergers … monolithic dissipative and random accretions collapse


The 2-parameter relations have a considerable real scatter,a tighter correlation can be found among 3 parameters:• a tilted plane of points in 3-D volume, which projects onto 2-D planes as the correlations seen before

The 3-parameter fundamental planeThe 3-parameter fundamental plane

• the Dn - relation (Dressler et al. 1987) F-P relation edge-on

Dn ~ e1.4 Dn: diameter (in kpc) where <Se> = 20.75 B mag/arcsec2

Three choices of parameter sets have been studied:

• log Re, <e>, log e (Djorgovski & Davis 1987)

log Re = 0.36 <e> + 1.4 log e + const

• Kappa space: 1, 2, 3 (Bender et al. 1993)

1 = 2-1/2 log(e2 Re) ~ log M (M = mass)

2 = 6-1/2 log(e2 Ie

2/ Re) ~ log [Ie (M/L)1/3] 3 = 3-1/2 log(e

2/ Ie/ Re) ~ log (M/L)


Projections of the fundamental plane

Faber-Jackson relation


The 3-parameter fundamental planeThe 3-parameter fundamental plane

What are the physicals meanings of the found relations?

The F-P is based principally on virial equilibrium

the M/L ratios and dynamical structures of Es are very similar

weak trend for M/L to increase with mass

limit on the ranges of ages and metallicities: ages ~ 10-13 Gyr, Z ~ 2-4 Zsolar

no dependence on environment internal properties robust


Hercules

ComaVirgo

Different cluster types

spiral-poorintermediate

spiral-richlose

cD clusterdense


The galaxy cluster MS1054-0321



Abell 2218 (z = 0.17)


The galaxy luminosity functionThe galaxy luminosity function

The luminosity function (M) describes how the relativenumber of galaxies varies with their luminosity.The quantity (M)dM is proportional to the number ofgalaxies in the magnitude range (M, M+dM).

The luminosity function (LF) contains information about:• primordial density fluctuations• processes that destroy/create galaxies• processes that change one type of galaxy into another• processes that transform mass into light

For which galaxy samples a LF have been measured?

• for field galaxies (averaged over a large sample)• for cluster galaxies (or groups)• for specific Hubble types in different environments


In clusters: the Schechter function In clusters: the Schechter function

Schechter’s data for13 clusters and theanalytic representationof the luminosity function

absolute magnitude vs. log (number)

similar to field LF, butsteeper faint end

faint bright


The Schechter function(2) The Schechter function(2) The analytical representation of the observed LF is as follows,as a function of:

luminosity:

magnitude:in logarithmic form:

The parameters are: steepness (slope) of faint end

M*, L* characteristic magnitude/luminosity (where the luminosity falls steeply off) M*

B ~ -19.7 + 5 log (h)

h = H0/(100 km/s/Mpc) c (or 0, n*) normalization, ~ 0.02 h3 Mpc-3


The Schechter function(3) The Schechter function(3) divided into two parts: (1)

(2)

(1) a power law (~ L) dominates at low luminosities ~ -1.5 “steep” faint end slope ~ -0.5 “flat” faint end slope

(2) an exponential cutoff ( ~ e-L) dominates at high luminosities, i.e. very luminous galaxies are rare

The integration over luminosity gives:

the total luminosity density then is (for = -1.0): ~108 LBo Mpc-3

and the total mass density (for M/L~10): ~109 h Mo Mpc-3 ~ 0.004


The LFs of the major galaxy types are different from each other, but relatively indepen-dent of environment

Spirals (Sa-Sc): Gaussian, ~ 1.4 mag

Lenticulars: Gaussian, ~ 1.1 mag

Ellipticals: skewed Gaussian

dwarf ellipticals: Schechter function, ~ -1.3

dwarf irregulars: Schechter function, ~ -0.3

The relative proportions of each galaxy type varies be-tween cluster and field


Dressler (1980)

spirals

ellipticals

lenticulars

low density high

Morphology-density relationPossibly relevant phy-sical processes that explain the relation:

• high densities inhibit the formation of spirals

• spirals may be stripped of gas to make S0s

• spirals experiencing “harrassment” can resem- ble S0s (heating of disk)

• spiral mergers may create S0s and/or Esdeprojected


HI in the Virgo ClusterHI deficiency -stripping of spiralHI gas

probably due to rampressure as the galaxy moves through the intra-cluster medium (ICM)

Definition:

HI deficiency =(M - <M>)/<M>

<M>: mean HI mass for galaxies of the same Hubble type

M : actual HI mass


LX

radius

HI deficiency increases …… towards the center of clusters… with increasing X-ray luminosity

However, the efficiency of stripping is rather weak, since … CO is not removed (denser and deeper in galaxy potential) … only the outer HI is stripped



Date post:	17-Jan-2016
Category:	Documents
Upload:	james-roberts
View:	212 times
Download:	0 times

Modern observational astronomy: from stars to galaxies Universidad Nacional de Colombia, Bogota,...

Documents