• Elliptical galaxies: typical properties, surface brightness profiles, dust and gas properties, the Faber-Jackson relation and Fundamental Plane
• Further overall statistical properties: The luminosity function, the morphology density relation
• Distance determinations of galaxies
5.1 Classificiation Schemes: The Hubble sequence
1924, Edwin Hubble divided galaxies into different “classes” based on their (optical) appearance.
Why begin here?
•Hubble classification serves as the basic language of the field.
•The morphological sequence reflects a fundamental physical and evolutionary sequence, which offers important clues to galactic structure, formation and evolution.
BUT Appearance of galaxy depends on:• inclination • resolution of image• depth of exposure• wavelength• (redshift)
Hubble Tuning Fork diagram (Hubble 1936, The Realm of the Nebulae)
Ellipticals → Lenticular → Normal Spiral →Irregular and Barred Spiral Evolutionary Sequence ? -- NO!! Early types Late types
For fantastic illustrations see: The Hubble Atlas of Galaxies (Sandage 1961);Carnegie Atlas of Galaxies ( Bedke & Sandage 1994); The Revised Shapley Ames Catalogue (Sandage & Tammann 1981)
Spiral Galaxies
•Disk + spiral arms + bulge (usually)•Subtype a b c defined by 3 criteria:
•Degree of resolution into knots, HII regions, etc.
Barred Spiral Galaxies
•Contain a linear feature of nearly uniform brightness centered on nucleus
•Subclasses follow those of spirals with subtypes a, b and c
Note: hard to differentiate in edge-on galaxies
Elliptical Galaxies
•Smooth structure and symmetric, elliptical contours•Subtype E0 - E7 defined by flattening
•En where n = 10(a-b)/awhere a and b are the projected major and minor axes (doesn’t tell what the 3-D shape is see next sheet)
• BUT NOTE: • many dwarf elliptical galaxies exist: e.g. NGC 147 (dE3), NGC 205 (dE5) and M32 (dE2) in Local Group; very low luminosity, difficult to detect (between E and GC)• dwarf spheroidal galaxies (dSph); Sculptor system discovered by Shapley 1932
Dwarf Elliptical Galaxies (incredible range in mass and luminosity from brightest to faintest elliptical galaxies)
NGC 147 (dE3) : NGC 205 (dE5) : IIIaJ DSS, 40’ x 40’ JHK 2MASS 12’ x 12’ IIIaJ, DSS10’ x 10’ JHK 2MASS 21’ x 21’
M32 (dE2) : Sculptor dSph IIIaJ DSS, 6’ x 6’ JHK 2MASS 8’ x 8’ IIIaJ DSS, 60’ x 60’
Lenticulars or S0 Galaxies
Irregular Galaxies
•No morphological symmetry
•Lots of young, blue stars and interstellar material
•Smaller than most spirals and elliptical galaxies
•Two major subtypes:•Irr I: highly resolved but disturbed spiral-like shapes•Irr II: smooth but chaotic (e.g. M82) with gas filaments
M82NGC 4485 & NGC 4490 NGC 4449
massive irregular
General trends within Hubble sequence E → S0 → Sa → Sb → Sc:• Decreasing Bulge/Disk• Decreasing stellar age• Increasing fractional gas & dust content• Increasing ongoing star formation• Decreasing mass & luminosity
Limitations of the Hubble Classification Scheme
1. Only includes massive galaxies (doesn’t include dwarf spheroidals, dwarf irregulars, blue compact dwarfs)
2. Three different parameters for classifying spirals is unsatisfactory because the parameters are not perfectly correlated.
3. Bars are not all-or-nothing. There is a continuum of bar strengths.
de Vaucouleurs’ Revised Hubble Classification System
(de Vaucouleurs 1958, Handbuch der Phys. 53, 275)(de Vaucouleurs2 1964, Reference Catalog of Bright Galaxies)
Basic idea: retain Hubble system, but add lots of optional bells and whistles
•Mixed types: E/S0, Sab, Sbc
•Mixed barred/normal: SA (unbarred), SB (barred), SAB (in between)
•Inner rings: S(s) (arms out of ring), S(r) (arms in ring), S(rs)
•Outer rings: (R) S
•Extended spiral, irr types: Sm (between spiral and Irr), Im (magellanic), Sd (extreme Sc), Sdm (between Sd and Sm)
•“T-types” scale Added in later editions of the Reference Catalog (de Vaucouleurs2, Corwin 1976)
E0 E/S0 S0 Sa Sb Sc Sd Sm Im-5 -3 -1 1 3 5 7 9 10 (T-type)
No Bar
Bar
Spiralshaped
Ringshaped
Cross section of diagram
Schematic Diagram of Revised Hubble Classification
Limitations:
•E --- Im is not a linear sequence of one parameter•Rings and bars are not independent•Does not take into consideration mass or other important parameters. All based on optical surface brightness morphology.
NGC 6782 (R')SB(r)0/a
No Bar
Bar
Spiralshaped
Ringshaped
Cross section of diagram
Schematic Diagram of Revised Hubble Classification
Limitations:
•E --- Im is not a linear sequence of one parameter•Rings and bars are not independent•Does not take into consideration mass or other important parameters. All based on optical surface brightness morphology.
NGC 6782 (R')SB(r)0/a
No Bar
Bar
Spiralshaped
Ringshaped
Cross section of diagram
Schematic Diagram of Revised Hubble Classification
Limitations:
•E --- Im is not a linear sequence of one parameter•Rings and bars are not independent•Does not take into consideration mass or other important parameters. All based on optical surface brightness morphology.
NGC 6782 (R')SB(r)0/a
No Bar
Bar
Spiralshaped
Ringshaped
Cross section of diagram
Schematic Diagram of Revised Hubble Classification
Limitations:
•E --- Im is not a linear sequence of one parameter•Rings and bars are not independent•Does not take into consideration mass or other important parameters. All based on optical surface brightness morphology.
NGC 6782
Luminosity Classification or “DDO System” (LC I to V w. intermediate LC)van den Bergh (1960) -
In spirals and irregular galaxies, some properties correlate with galaxy mass/luminosity rather than type. The better defined the spiral features (i.e. arm length, continuity and width relative to size) the more luminous (intrinsic).
Sc I - long, well-developed armsSc III - short, stubby armsSc IV - dwarf, spiral galaxy - faint hint of spiral structure
who was at David Dunlop Observatory in Ontario, Canada - hence the “DDO”
Calibration of LC with absolute magnitude
Used by Sandage and Tamman as distance indicator
Automated galaxy classification
Abraham et al. (1994, 1996):Concentration parameter C - fraction of light within ellipsoidal radius 0.3 x outer isophotal radius (1.5 above sky level).Asymmetry parameter A - fraction of light in features not symmetric wrt a 180 degree rotation
Naim, Ratnatunga & Griffiths (1997) use 4 parameters: blobbiness, asymmetry, filling factor and elongation.
Naim et al. (1995) used artificial neural nets to classify galaxies into the numerical T types.
Kennicutt (1992)
Galaxies are shown in order of increasing Hubble type from top to bottom.
Continuum: sharp break and rise after H and K lines (hence brighter in red than blue); dominated by red star light, strong absorption lines;
E and S0 have K-star type spectrum
Flattening of continuum (reduction of red light compared to blue light)
Spirals: F-K stars dominate spectrum
Decrease in strength of absorption lines
Increase in emission lines and strength of emission lines;
A-star dominate spectrum
but also - lots of SF, many O, B stars:- abs. lines of He (typical of O, B stars)- em. lines of ionized gas
H,K G Mg Na
OII OIII H,NII
Hβ
NeII Hγ He SII
Spectra of galaxies from E Im:
Comparative properties of various spiral galaxies and elliptical galaxies:
Dependence of color with Hubble type
→ indicates intrinsic differences for the different morphological types
• therewith of interest to study at different wavelength-ranges• but implies dependency on regarded waveband with prominence of the respective morphological types
5.2 Spiral Galaxies
Photometric properties of spirals
Problem 1: spirals are not transparent, contain varying amounts of dust complicates determination of true shape in 3D and the true magnitude
Problem 2: sky background – the dimly glowing night sky has an average of μsky = 22 B-mag arcsec-2 (light pollution, zodiacal light, unresolved stars of Milky
Way, unresolved galaxies)But modern CCD’s: follow SB profile of galaxy to SB levels of 29 B-mag arcsec-2
it is necessary to do careful sky-subtraction
Typical Surface Brightness profile of spiral galaxy
Recap: some definitions
Units of surface brightness SB (independent of distance) : mag arcsec-2 → if a galaxy has a SB = 20 mag arcsec-2; photons incident on 1 sq. arcsec ↔ equal to star with m = 20
Notation: μB = 20m : surface brightness in the B band of 20 mag arcsec-2
Note: typical central SB of a galaxy in the B-band: μB = 18 mag arcsec-2 (bulge/nucleus)
Typical isophote out to which a galaxy can be traced on e.g. Sky Surveys in the blue (IIIaJ) is 27 mag arcsec-2 (~1% of sky-brightness)
Galaxies do not have sharp edges: definition ofIsophotal radius (or diameter) → radius (or diameter) at which a certain SB is reached
e.g. R25 diameter at SB = 25 μB (if seen f-o and unobscured by dust); (defined and often used, e.g. in the Reference Catalogues (de Vaucouleurs, de Vaucouleurs & Corwin, 1976, 1991)
(Holmberg radius: RH at the isophote of 26.5 mag arcsec-2; older definition, not much used anymore)
Total magnitude: integrated SB across galaxy image (but edge not well-defined) – asymptotical value mT or MT)
Isophotal magnitude: integrated magnitude out to some limiting isophote, e.g. mB25
(a) Disk:
After correction for inclination, dust obscuration and averaging over spiral armsthe SB profile of a spiral disk falls of as an exponential
with I0 …. Central surface brightness of disk hR …. Characteristic scale length
In practice, SB at the center of a spiral is dominated by central bulge or spheroidI0 to be estimated from extrapolations inwards from larger radii
In many (but not all) spiral galaxies,the exponential part seems to end at some radius Rmax which typically is
Rmax = 3 – 5 hR (10-30 kpc)
hR generally is about 20% larger in B than R
Beyond Rmax the SB of the stars decreasesmore rapidly – edge of optical disk
Freeman’s law for normal spiral galaxies (not LSB dwarf-like objects)
Freeman (1970) found: high SB galaxies all have the same central SB
SB0 = 21.7 mag arcsec-2; (SBK ~ 18 mag arcsec-2)
- but note: less in low SB galaxies
e.g. Malin 1 (V ~ 25’000km/s)
μ0,B ~ 25.5 mag arcsec-2 25 times fainter than ‘normal’ spiral galaxies and wellbelow the sky brightness
Recall sky brightness in B on a dark night is 22.7 mag arcsec-2
Malin 1 (discovered 1987):
DSS-image of 8’ x 8’
Strong bulge, weak extended disk withhR ~ 55 kpc (!!)
V-band image with HI-contour overlay(Pickering et al. 1997, AJ)
M(HI) = 6.8 x 1010 Msun
Malin 1 (discovered 1987):
DSS-image of 8’ x 8’
Strong bulge, weak extended disk withhR ~ 55 kpc (!!)
V-band image with HI-contour overlay(Pickering et al. 1997, AJ)
M(HI) = 6.8 x 1010 Msun
(b) Bulge:In the central regions we have an additional light component due to the bulge
Bulge usually follows R1/4 law like ellipticals
SB profiles of spirals require 2 separate fits - one for disk
- one for bulge
For bulges, the central SB is 20-21 mag arcsec-2 (de Souza et al. 2004, ApJS, 153, 411)
(c) Halo Doesn’t contribute much light, so people generally don’t worry about it.
Freeman’s law for disk galaxies
Freeman (1970) found: high SB galaxies all have the same central SB
SB0 = 21.7 mag arcsec-2; (SBK ~ 18 mag arcsec-2
- but note: less in low SB galaxies
The rotation curves of galaxies: SB profiles sample the distribution of luminous matter - but not the distribution of gas or dark
matter
Recall: Observations of neutral hydrogen gas HI (~30 – 100K) using radio telescopes to map HI emission at λ = 21cm (1420.406MHz) the resulting rotation curves are a good measure of the total matter distribution (luminous, gas + dark matter)
When rotation curves are compared with luminosity or Hubble type, a number of correlations are found (see next sheet):
- with increasing luminosity in the B-band, the rotation curves rise more rapidly (from center) and reach higher maximum velocities - within a given Hubble type, galaxies that are more luminous have larger Vmax
Although the maximum rotational velocity within the disk increases for earlier-type galaxies a wide range in Vmax exists for each type, depending on luminosity:
Indication of DM content, which does not always follow the distribution of luminous matter
The maximum rotation velocities for irregular galaxies is significantly lower: about 50 – 70 km/s (suggest that higher rotational velocities –and mass - are required
for well-organized spiral patterns to occur)
-with increasing luminosity in the B-band, the rotation curves rise more rapidly (from center) and reach higher maximum velocities
- within a given Hubble type, galaxies that are more luminous have larger Vmax
Although the maximum rotational velocity within the disk increases for earlier-type galaxies a wide range in Vmax exists for each type, depending on luminosity:
- Sa: 299 km/s (range: 163 – 367 km/s),
- Sb: 222 km/s (range: 144 – 330 km/s),
- Sc: 175 km/s (range: 99 – 304 km/s)
BUT rotation curves are difficult to measure (radio interferometry for HI, or longslit spectroscopy of ionized gas of emission lines Hα, OII or OIII).
Go to single dish radio telescopes and measure velocity width:
Rubin et al. 1985, ApJ 289, 81
What can be learned from single dish observations?
The double peak occurs because a portion of the disk is rotating towards the observer (blueshift) another part is moving away (redshift). The mean is the systemic radial velocity of the galaxy as a whole
- Systemic radial velocity Vsys – generally the central value of linewidth
- Linewidths ΔV (in km/s) - which is indicative of 2x maximal rotation velocity, usually measured at 20% or 50% of the peak flux of the signal
but requires correction for inclination:
i … inclination
Or:
Where ΔV20 is the linewidth measured from the 21cm radio velocity profile at the 20% level of emission from the peak flux, and ΔVrand a random velocity component due to non-circular velocities in the gas (of the order of 5 - 15 km/s)
Other parameters that can be deduced from single dish observations:
- Integrated flux: in Jy km/s
- HI-mass : in Msun with D …. distance in Mpc
Some values for the Tully-Fisher relation
Note: magnitudes need to be corrected for internal extinction effect;
- but whereas high inclinations minimize errors in linewidth corrections (full rotational effect seen in edge-on spirals), these are largest for magnitude corrections (sheet 9, chap. 2)
Tighter relation in the near-infrared: e.g. calibration by Pierce & Tully (1992) for the H-band:
For same linewidth an Sc will be brighter than Sb than Sa
Plot: - log of linewidth (corrected for inclination)- total magnitude (corrected for inclinationand extinction – internal and external)
Very tight correlation(smallest scatter when measure in NIR compared to bluer colors)
distances:- Determine Vmax or linewidth- Infer M for a given band from calibrated relation- Measure apparent magnitude in that bandUse distance modulus
(m-M) = 5 logD - 25 (Mpc)
Very important distance determinator out to about 100 - 200 Mpc (radial velocities 2000 - 4000 km/s) and even higher for clusters of galaxies highly relevant for measuring peculiar velocity/cosmic flow fields
But error for individual galaxy still quite high: about 0.4m in optical to 0.2m in NIR ( about 20% respectively 10% in distance!!)
The Tully- Fisher relation – an important distance indicator
The origin of the Tully-Fisher relation:
- Empirical linear relation between total magnitude and HI-linewidth- Implies: L prop. Vmax
4
What is the underlying physics for this relation?
Recall that for an entire galaxy with radius R and total mass M:
(sheet 15, chap. 4 for r R and Mr M; see also sheets 16 - 18, chap.4)
Assume that the M/L is constant for all spirals (BUT we do know that that does not hold) :
Recall Freeman’s law: all spirals have same central SB (21.7 mag arcsec-2 in B)
Squaring the previous relation for L and substituting R² from central SB relation:
Tightness of relation demands a nearly universal M/L ratio – which remains un-understood! Surprisingly, the slope comes out about right wrt what has been found
Radius Luminosity relation
For early type spirals (Sa – Sc) the radius increases as a function of luminosity
With R25 in units of kpc.
Masses and M/L ratios
The above relation plus the TF relation allows an estimate of mass and M/L within R25
- weak relation only of mass with Hubble type (~109-1012 Msun)
- M/L increases with Hubble type (see Table on sheet 17):
Sa Sb Sc
<M/LB> = 6.2 ± 0.6 4.5 ± 0.4 2.6 ± 0.2
Color and abundance of gas and dust
The above relation indicates that Sc must have a larger fraction of massive MS stars bluer (see sheet 18: <B - V> versus T-type)
Sa Sb Sc Im
<B - V> = 0.76 0.64 0.52 0.4
The colors of Im’s become blueer towards their centers (contrarily to earlier spirals which are redder in their centers – see next section)
still manufactoring stars in their central regions
existence of abundant supply of gas and dust from which stars can be formed
Based on 21cm radiation, H emission and CO (as tracer of H2) it was found that within R25 the
- gas-to-total mass fraction increases from early to late spirals
- the molecular to atomic gas fraction decreases:
Sa Sb Sc Scd
<Mgas/Mtot> = 0.04 0.08 0.1 0.25
<MH2 /MHI> = 2.2 1.8 0.73 0.29
Increase in gas content is as expected based on observations. More molecules in earlier spirals is interpreted as them having deeper gravitational wells (more centrally condensed) in which gas can collect and form molecules.
Molecular gas mass decreases from about 5 x 1010Msun in most massive galaxies to 106Msun in dwarf spirals
The dust mass is usually 150-600 times lower than gas in ISM; dust is primarily responsible for FIR luminosity (some synchrotron and star emission)
IRAS observations found following tendencies between FIR/blue luminosity:
M31 M33 M101 LMC SMC
Sb I-II Sc II-III Sc I SBm III Im IV-V
<LFIR/LB> = 0.07 0.2 0.4 0.18 0.09
Sc’s have the largest FIR luminosity, consistent with them having the most mass in gas and dust
Note: SB (barred spirals) generally have larger FIR emission than their non-barred counterparts
Metallicity and Color gradients in spirals
Apart from overall color dependence on Hubble type, galaxies also exhibit metallicity gradient from central core to outer parts
bulges are generally redder than disks; spheroids are redder in central part than further out
(a) Dependence on star formation
More active SF in disks (increasing as function of T) results in overall bluer color, whereas spheroidal components (bulges) have little gas – overall redder color
(b) Dependence on metallicity (opacity)
The average number of electrons per atom is higher for metal-rich stars higher opacity (more possible orbital transition of electrons)
Higher opacity – light cannot escape as easily radius increases (star puffs up) decrease in surface temperature
higher metallicity higher opacity lower SF temp redder
Bulges are more metal-rich redder. But it is an overall gradient from inner to outer part. This has been measured in our Galaxy. For 4 14 kpc:
And also in our other galaxies
In addition to a metallicity gradient that decreases from the central parts to the outer parts
overall dependence of luminosity with metallicity has been found
holds for spirals and ellipticals both
Chemical enrichment must have been more efficient for luminous galaxies (important for galaxy formation and evolution theories)
dE
Im
Sp
E
Solar
Solar
From Mg absorption lines
From HII-regions (emission)
(a) Example NGC 4258, a nearby spiral at 6 Mpc
Compelling evidence for a supermassive black hole from VLBA observations (100 times resolution of HST)
a group of molecular clouds swirling in an
organized fashion about the galaxy's core
red- and blueshifts of water-vapor spectral
lines
the pattern revealed is that of a slightly warped and spinning disk centered precisely on the galaxy's heart.
The rotation velocities imply the presence of more than 4 10
7 Msun within a region less
than 0.2 pc across.
Supermassive Black Holes
Observations of stellar and gas motions near centers of spirals suggest presence of SMBH, Rotational-velocity measurements can be used to estimate the dynamical mass of a central black hole in the same was as for SgrA* in Galactic Center:
(b) Other strong evidence: M31
Observational evidence up to 2005:
- Asymmetric nucleus, i.e. offset of the brightest point from bulge center and velocity dispersion peak
- Hubble Space Telescope imaging shows:
double nucleus with two bright intensity peaks in a spectrum including Ca II lines (red part of visible spectrum)
(bright nucleus P 1, faint nucleus P 2)
- Rotation curve is approximately symmetric about the faint nucleus P2 !
Estimate of mass of BH: 3 – 10 x 107 Msun (large range)
New observations with HST (Bender et al. 2005, ApJ 631,280):
Third nucleus (P3) within P2 composed
- of population of blue young stars (A to B stars, recently formed)
- very high vel. dispersion (~1100 km/s) ; consistent with rotating circumstellar disk
1.1 – 2.3 x 108Msun
Note: cluster of dark objects excluded; but way beyond BH-mass/luminosity, BH-mass vel.dispersion relation (next sheet)
Determination of central BH mass from velocity dispersion via Virial Theorem (not as precise as kinematic studies)
If a galaxy is in equilibrium, the virial theorem holds, i.e. the time-averaged kinetic and potential energies of stars in the central region (bulge) follow:
For the large number of stars we are regarding, the time average will be the same as the sum over all stars. So, for N stars we have
Assume for simplicity spherical cluster of radius R and N stars, each of mass m M = Nm and divide above expression by N results in:
Generally we can only measure radial velocities (galaxies are too far away to be able to measure proper motions). But the value of the radial velocity should not be different for the perpendicular 2 components (we have no preferred orientation when studying clusters). Therefore the average values
so
Substituting this into the equation at the top, and using the expression for the approximate potential energy of a spherical distribution of total mass M and radius R :
Using M = Nm and solving for the mass a relation between the mass and the vel.dispersion:
R must be selected properly (within sphere of influence of BH). Farther away mass from stars and gas will contribute to total mass within regarded sphere. Look for peak in σ as f(R).
Including this method (next to 3 precise determinations of BH’s for Galaxy, M31 and NGC 4258) gives sufficient numbers of nearby galaxies with central BH estimates to check for correlations of BH mass with galaxy properties
Strong correlation of BH mass with LB and σ of E’s and bulges of spiral (but most recent results for M31 are deviant)
N205,M33 M32 → M87
Existence of fundamental link between feeding of BH and overall mass of galaxy
Specific Frequency of Globular clusters
Abundance of glob. clusters shows an increasing tendency from late type spirals early-type spirals ellipticals cD’s. Implications for galaxy formation theories: more spheroidally dominant galaxies seem to have been more efficient at forming GC during their early histories. Moreover, capturing of globular clusters in merging or cannibalism processes.
Definition of specific frequency of globular clusters:
Where LV is the galaxy’s luminosity ; L15 the reference luminosity corresponding to MV = -15mag.
The mean (and scatter) increases as with decreasing type T:
Harris, ARvA&A 1991
Particularly cD’s which often reside at the centers of massive galaxy cluster have an extraordinary high number of globular clusters.
5.2. Elliptical Galaxies
Ellipticals look like simple objects- round, smooth light distribution (lack of SF regions, obscuring dust patches)- devoid of cool gas (except very centers), no disk (like S0)
But detailed studies show:- huge range of luminosity and light concentration- some rotate, others not (or hardly)- existence of oblate, prolate and triaxial shapes
Recall: 5 main types of elliptical galaxies (sect. 5.1 on morphology and table on sheet 17):
Giant ellipticals (cD): immense, massive and bright galaxies found at the center of rich galaxy clusters with -22 < MB < -25, 1013 < M < 1014Msun, central high SB with extended diffuse envelopes, up to ten’s of thousands of GC (<SN> =15), extreme M/L ratios (~750 Msun/Lsun)
Normal ellipticals (E): centrally condensed objects with high central SB; -15 < MB < -23, 108 < M < 1013Msun, diameters from 1 - 200 kpc, and M/L ratios ranging from 1 – 100 Msun/Lsun; <SN> ~ 5
Dwarf ellipticals (dE): lower SB and metallicity compared to E of similar absolute magnitude; -13< MB < -19, 107 < M < 109Msun, diameters from 1 - 10 kpc; higher <SN> than spirals (~5)
Dwarf spheroidals (dSph): extremely low luminosity, low SB and small: -8 < MB < -15, 107 < M < 108Msun, 0.1-0.5kpc diameter; only known in vicinity of MW; but fairly high M/L (5 -100)
Blue compact dwarfs (BCD): small and unusually blue (<B-V>=0.0 - 0.3) mean A-type spectrum lot of recent SF; -14 < MB < -17; M ~109Msun and D less than ~ 3kpc; have large fraction of gas (15-20% of total mass!!), and lower M/L compared to other E’s
Surface Brightness profiles
The surface brightness distribution follows the so-called de Vaucouleurs’ R¼ - law (first formulated by him for SB profiles of ellipticals in 1948), as seen already for Gal.Bulge
With scale length Re known as the effective radiusdefined such that half the total light of the system is emitted within the interior of Re;
The parameter Ie is the SB at R = Re
→ smooth increase in SB (over 10mag in SB, thus over 10’000 in intensity) from outer edge to center, slightly flattening of at center
Major axis SB-profile for NGC 1700:
Deviations from R¼ law:
(A) profile curves downwards in in μB - R¼ plot for low lum. Ellipticals
Some of the very extreme diffuse dE’s and dSph’s are actually best fitted by an exponential law
I(R) = I0 exp(-R/Rh)
.…But are not rotationally flattened objects as analysis of ellipticities indicates; Ichikawa, Wakamatsu & Okamura 1986(
)B (profile curves upwards in μB - R¼ plot (top) for high lum. ellipticals, cD’s
See Fig. on right for extreme case : - cD at the center of Abell 1413 -- points are observations, -- line is R¼ fit to inner points with – R > 20Re
Dust and Gas in Ellipticals (very little):It was generally thought that ellipticals are free of dust and gas (therefore no star formation)
with few exceptions such as interacting galaxies (acquired gas; e.g. the nearby CenA galaxy )
This holds indeed for
dE and dSph’s:-The low grav. binding energy does not allow these galaxies to retain a significant amount of gas
They are not actively forming stars- They have very low metallicities (similar to glob. clusters)
They must have lost their gas - via SN-driven mass loss - ram-pressure stripping as galaxies pass through gas in clusters
BUT closer examination or large E
Normal and cD galaxies:- some have dust in center, presumably mixed with cold gas- but only 5-10% of normal E have sufficient HI to be detectableSome E’s show peculiarities (often show shells and dust lanes) and can have as much cool gas as normal spirals
NGC 5128 = Cen A
Normal and cD galaxies (cont.):The hydrogen gas manifests itself in different forms:
(a) Hot gas (dominant gas fraction): 1-3 x 107K (radiates in X-ray), is diffuse and extends to >~ 30kpc
From mass loss of older stars older than few Gyrs (from red giant and AGB):
1-2 Msun per yr per 1010 Lsun → large gas reservoir Total gas mass: 108-1010Msun (up to 10-20% of luminous mass) More luminous ellipticals (higher vel. dispersion) have hotter gas
(b) Warm gas (very little):~ 104K observable in H (around PN or HII regions)Total mass of 104-105Msun
(c) Cold gas :~100K - observable as HI in 21cm line → cold gas in luminous E’s : ~ 107-109Msun (compare to Sc: 1010Msun)- CO emission indicate molecular hydrogen H2, also of the order of 107-109Msun
DUST:
Observations indicate that ~50% of ellipticals also do contain some dust, but little in mass contribution (105-106Msun)
Metallicity and Color gradients in ellipticals
Recall from sheet 34 in the discussions of metallicity and colors of spirals:
In addition to a metallicity and color gradient that decreases from the central parts to the outer parts
Central regions are redder and more metal-rich than outer parts of E’s
The same is true for lenticular galaxies
Ell
Sp
overall dependence of luminosity with metallicity
The Faber-Jackson relation (similar to TF – and also very valuable distance indicator)
A relation between central radial velocity dispersion and absolute magnitude MB that holds for dE’s, dSph’s and normal E’s – and also for bulges of spiral galaxies
It is similar to TF relation of spirals: the relation arises from same concept, i.e. assumption of
- virial theorem
- constant <M/L>
- equal average SB
With σ0 being the central radial velocity dispersion
Expressing again the luminosity in solar units and the log(L/Lsun) as a difference in MB:
The Fundamental Plane
Improvement on Faber-Jackson relation (note scatter in plot above) by allowing the exponent to vary between 3 and 5 and introducing a 2nd parameter, the effective radius re
Here galaxies are visualised as residing on a 2-D surface in a 3D space represented with coordinates L, σ0 , re.
The effects of rotation on shapes of elliptical galaxies
Overall result for many (large) Ellipticals: - don’t rotate globally (or very little) - probably not axisymmetric
Most elliptical are ‘not’ purely oblate or prolate rotators with 2 axes, but are triaxial (no preferred axis of rotation)This discrepancy increases for more luminous elliptical galaxies (very low rot.vel)
How is this determined? Rotational velocities are difficult to measure, moreover the intrinsic flatness of E not known (as for disk galaxies); not measurable from ellipticity ε = 1 – b/a
Therefore analysis of Vrot/σ as function of ε ;Vrot … maximum observed rotational velocityσm … velocity dispersion (width of stellar absorption lines)
If the flattening of an elliptical galaxy is due to it being an ideal oblate rotator with an isotropic stellar velocity distribution,
This means that if an ellipticity of e.g. ε = 0.4 were due to pure rotations then Vrot / σ ~ 0.8
Definition of rotation parameter:
One test: determine (Vrot / σ) for given ellipticity assuming it caused by rotation and compare to obs.) the so-called rotation parameter:
→ On average a division is found around the value of (V / σ)* ~ 0.7:
For galaxies with (V / σ)* > 0.7 are considered primarily rotationally supported
- Bright E’s and gE’s have typical rotation parameters of ~0.4hence are pressure supported
Their shapes are primarily due to random stellar motions
- Diffuse faint dE’s have predominantly anisotropic velocity dispersions and are also pressure-supported (Recall: anisotropic means that 2 directions of motions are preferred rather than being completely random in all 3 dimensions, as in isotropic distribution)
- But elliptical galaxies in the range -18.0 > MB > - 20.5 seem to have (V/ σ)* ~ 0.9 and therefore must be largely rotationally supported.
Other (shape) parameters that relate with properties of elliptical galaxies:
According to Bender, & Nieto (1988) many characteristics of ellipticals can be understood in terms of boxiness or diskiness of isophotal shapes of elliptical galaxies
boxy disky
Quantification of deviation from an elliptical shape: write the shape of isophotal contourin polar coordinates as a Fourier series:
a(θ) = a0 + a2cos (2θ) + a4 cos (4θ) + ……
With a being contour radius and θ measure counterclockwise from major axis of ellipsoidfirst term: represents shape of perfect circle2nd term: corresponds to amount of ellipticity3rd term: associated with degree of boxiness: a4 < 0 …. boxy
a4 > 0 … disky
Typically |a4/a0| ~ 0.01 (deviations from perfect ellipses measured to 0.5%), and a4 is generally given as 100a4
Photometry:
Determination of radial surface-brightness profiles → measure SB as function of radius R measured along major axis:R-band isophotes of 4 elliptical galaxies by R. de Jong (Fig. 6.1 in SG)
(a) NGC 5846:
Smooth slightly elliptical isophotes
(c) Zw159-89
Diamond-shaped ‘disky’ isophotes
Note change of orientation of major axes from inner to outer contours
(b) EFAR J16WG:
Quite round inner isophotes, ~horizontal major axis, elliptical outer isophotes, vertical major axis [a4 ~ +0.03]
(d) NGC 4478:
Rectangular ‘boxy’ isophotes [a4 ~ -0.01]
Note: compact contours: are superimposed foreground stars
Other (shape) parameters that relate with properties of elliptical galaxies:
According to Bender, & Nieto (1988) many characteristics of ellipticals can be understood in terms of boxiness or diskiness of isophotal shapes of elliptical galaxies
boxy disky
Quantification of deviation from an elliptical shape: write the shape of isophotal contourin polar coordinates as a Fourier series:
a(θ) = a0 + a2cos (2θ) + a4 cos (4θ) + ……
With a being contour radius and θ measure counterclockwise from major axis of ellipsoidfirst term: represents shape of perfect circle2nd term: corresponds to amount of ellipticity3rd term: associated with degree of boxiness: a4 < 0 …. boxy
a4 > 0 … disky
Typically |a4/a0| ~ 0.01 (deviations from perfect ellipses measured to 0.5%), and a4 is generally given as 100a4
Relations of a4/a0
Boxy ←|→ Disky Boxy ←|→ Disky
Kormendy & Djorgovski 1989, ARvA&A)
Upper left:- Disks tend to be rotationally supported with larger (v/σ)-Boxy: pressure supported(random motions)
Lower left:Core M/L is higher than average for boxy galaxies compared to disky
Lower right:Boxy ones are brighter in radio lum.(though large spread) with small spread in disky galaxiesSame holds in other wavebands
Top right:Ellipticity tends to increase with |a4|Could indicate different origins of ellipticity
All linked: same galaxy type, e.g. ε =0.4some are pressure supported while others are rotationally supported
5.3. The Luminosity Function
What is the overall distribution of the different morphological types we have encountered?E S Im, dwarf galaxies to the most luminous galaxies? Is the distribution universal? How (if) does it vary with the evolution of the Universe?
These questions can be investigated through the study of the luminosity function LF as a function of morphological type, environment,redshift (groups, clusters, field etc.): The galaxy luminosity function is defined analogously to star-LF
Φ(M) dM … is prop. to number of galaxies in the range M to M+dM
Or in luminosity:
Φ(L) dL … is relative number of galaxies in the range L to L+dL
Normalization:
…. Φ* is total number of galaxies per unit volume (Mpc3) in the interval M and M+dM
→ next to optical wavebands, also important for: X-ray, radio fluxes, masses, HI-masses etc.
The range and frequency of different morphological types is sensitive not only to the sample studied, but also to the selected magnitude limit
e.g. Statistics of Hubble types in RSA
Number of galaxies of different Hubble Type in magnitude limited sample (m < 13.4) in Revised Shapley Ames Catalog (RSA)
• reflects the mean of the morphological mix of the RSA
• But only the E/S0 – Sc are fairly represented as these are intrinsically quite bright
• The late type spirals (Sdm, Sm, Im) are underrepresented
• Also the dwarf elliptical galaxies
Magnitude-limited sample of galaxies outside of clusters (in the “field”) are biased towards late-type (Sc) spirals. A typical field sample might consist of 80% S galaxies, 10% S0 galaxies, and 10% E galaxies – but hardly any dwarf galaxies.
BUT: Compare to absolute magnitude distribution of LG members
According to Courteau & van den Berg 1999; including Cetus discovered in 1999 by Whiting, Hau & Irwin
Only 4 of 35 members have MB < - 18 mag!!
The morphology density relation
The percentages of galaxy types in different environments show striking differences:
- Oemler (1974): the elliptical fraction f(E) correlates with the morphology of clusters:- large fraction: regular, symmetric appearance often with cD (like Coma)- small fraction: ratty, irregular (not centrally condensed) distribution
- Dressler (1980): An intermediate density cluster will have 40% Spirals, 40% S0 galaxies, and 20% E A high density cluster will have 10% S, 50% S0, and 40% E.
all of this reflects a nearly universal relation between morphology and local galaxy densitythe so-called
morphology-density relationship (Dressler, 1980)
the fraction of elliptical galaxies decreases as a function local galaxy density. This relation seems universal. It was found to hold over 6 orders of magnitude in number density of galaxies
Back to the determination of the luminosity function:
Despite all of these selection and environmental effects, Schechter (1976, ApJ 203, 297) found a general analytical relation that describes the overall of any selected galaxy sample quite well, and in which the numbers of galaxies have a strong cut-off for galaxies more luminous than a characteristic value M* and monotonic increase for lower luminosities:
The function takes an easier form when working in luminosities rather than magnitudes
L* … is luminosity corresponding to M*, characteristic luminosity above which the number of galaxies falls sharply; it typically is of the order of a bright (MW-like) galaxy
α … sets the slope of the LF at the faint end (α typically is negative)Φ* …sets the overall normalization (number of galaxies per Mpc³)
With Φ*, α and M* to be determined from observations
→ provides reasonable fit to a large variety of galaxy samples / redshift surveys
What does it look like?
Plot from original 1976 Schechter paper
Typical values:
= -1.0 ; MB* = -21.0 … field near MW
= -1.24; MB* = -21.0 … Virgo cluster
Binggeli’s (1987) cartoon of Schechter suppressing the details of “universal” LF:
Is the LF really universal?
Because of morphological density relation and the above dependence of LF on morphological types, we get varying LF’s as a function of environment (Binggeli, Sandage & Tammann 1988, ARvA&A 26, 509)
Division into different morphological types finds very different LF,
-from Gaussian distributions (Sa-Sc, S0, E)
- to open-ended LF (Im, dE):
5.5 The Extragalactic Distance Scale
To map the distribution of galaxies in space (large-scale structure, clustering, structure formation and evolution), we need to measure their distances
Various distance determination methods (listed below) have already been discussed in Chapter 3 to map the distribution of the different components of the Milky Way
Some can either be extended to the nearest galaxies (e.g. Cepheid’s) or can be used to calibrate other distance determination methods (secondary distance indicators) and extend the distance scale measurements to larger (cosmological) distances, the so-called
cosmological distance ladder
Chapter 3:
1. Triangulation stellar parallaxes
2. Spectroscopic parallaxes
3. Wilson – Bappu effect
4. Moving cluster method
5. Baade-Wesselink method
6. Main sequence fitting
7. Cepheids and RR Lyraes
Others:
Tully Fisher relation (this chapter - spirals)
Fundamental Plane (this chapter – ellipticals)
Surface Brightness Fluctuations
SNe – physics and lightcurves
--------
Novae
Glob. Cluster or PN LF
(Brightest galaxies in clusters)
Note: log – log plot Empirical relation:
Calibration problematic as no nearby large E known.
It is often used to determine relative distances, e.g. between clusters of galaxies (all galaxies are assumed to lie at the same distance – that also improves the error as uncertainty for single galaxy is ±0.5mag
The D-σ relation – refinement of Fundamental Plane
The Faber Jackson relation showed considerable scatter (sheet 46) which could be improved by taken effective radius Re into equation - sometimes also SB or μB (Fundamental Plane)
This has led to the definition of the D-σ relation for elliptical galaxies
relates the vel.dispersion
to the diameter as measured at the SB-level of 20.75 B-mag arcsec-2
(note SB distance independent – the so defined diameter D therefore inversely proportional to distance)
Surface Brightness fluctuations
Supernovae (3 methods)
(a) Geometrical (quite precise but possible only for very nearby SN)
for the very nearest SN geometrical considerations based on the observations of the expanding gas-shell will lead to a distance:
If you can observe (resolve) the change of the angular extent θ(t) of photosphere of SN with time:
which determines the tangential velocity if distance is known: vθ = ω d
- Observe the radial expansion velocities from Doppler shifts of spectral lines vej (vr of sphere)
- Assume that expansion is symmetric (radial and tangential velocities are equal)
then the distance can be determined: d = vej / ω
(b) Physical (less precise but applicable to farther distances)
(similar to Baade Wesselink method for pulsating variables): assume that the expanding shell radiates as BB, then the luminosity of SN is given by Stefan Boltzmann equation
R(t) is radius of expanding atmosphere, t is age of SN. By measuring expansion velocity from spectral lines we can determine R(t) = vej t (assuming that the velocity does not change over short time scales we need only one observation)
Determine T from BB spectrum Luminosity absolute magnitude distance (after measurement apparent mag.)
Large uncertainties (15% for M101, 25% for Virgo cluster), because
- photosphere of expanding shell is neither perfectly symmetric nor perfect BB
- interstellar extinction ; in particular for core collapse SN (type II – also Ib and Ic) which are generally found in SF regions (dusty locations within dusty spiral galaxies)
(c) Type Ia Light curves
One of the most important tools are the light curves of SN Ia.
- Reach out to > 1000 Mpc
- have discovered the acceleration of the Universe (and therewith Dark Energy, etc.)
The light curve characterizes the type of SN
Type Ia all have the same intrinsic luminosity at maximum, i.e.
But only 17 ± 3 days until a SN reaches a maximum (recall about 109 increase in luminosity within that period) – so easy to miss maximum.
But there is a well-defined inverse correlation between luminosity reached at maximum and decline rate ( the fainter ones declines more rapidly – see top panel of figure on next page) – which is also used to improve the relation.
In practice a SN will be observed in many wavebands over a period of time. The Multicolor light curve shapes (MCLS) are then compared to a family of parametrized template curves will give max of SN, even if SN has not been caught at its maximum.
Stretch method:
-fits B and V template simultaneously with a single template that has been stretched (or compressed) in time
The stretch factor gives optimized max. luminosity
Error of only 5% in distance (0.1mag in distance modulus)
SN Ia are about 13.3 mag brighter than brightest Cepheid variables
