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Astro 6590: 2008Lecture #3:

More on galaxy spectra (and more later, too)Overview of structure of the Milky WayStellar metallicity indicatorsThin disk, thick disk, bulge, bar, nucleus, haloBasics of chemical enrichment Closed-box model G-dwarf problemIntro. to galaxy photometry; surface brightness profilesR1/4 law; King model; Sersic profile

Next class: Elliptical galaxies overview

Homework #1 due todayHomework #2 is posted: Part A due Mon; Part B due Wed

Galaxy spectra

• Redshift

• Velocity dispersion/rotational velocity

• Star formation rate

• AGN activity

• Abundances

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Observing galaxy spectra

The observed spectrum of a galaxy, made up of a large # of *s, (assumed here, for simplicity, to be identical) can be described as

G(u) = ∫ dvlos F(vlos) · S(u – vlos)where u = c ln λ is the wavelength expressed in logarithmic units

S is the spectrum of the star in the same unitsF(vlos) describes the distribution of the stellar line-of-sight

velocities within the portion of the galaxy observed.

Note: this is a convolution integral. In practice, it is therefore possible to extract F(vlos) from an observed G(u) if a suitable template stellar spectrum S is available.

But need “suitable” spectrum => mix of types

Understanding spectra as evolution

Bruzual & Charlot, 1993 ApJ 405, 5382003 MNRAS 344, 1000

Basic assumptions:• Galaxies can be treated as closed systems• Chemical enrichment is not important after stars form• The SFR is either a burst or a smooth function of time,

independent of stellar mass; it determines the spectral and luminosity evolution of the galaxy

• The IMF is a simple function of the stellar mass (independent of galaxy age)

• The effect of dust and gas on the observed spectra can be treated separately

We will look at B&C again later

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Models vs. Data: Ellipticals

• Best-fitting age model and composite elliptical spectrum

• Fairly good fit over entire spectral range

• Note UV-rising branch, highlighting importance of accurate AGB modeling

• ELLIPTICALS: The oldest objects formed stars within 1-2 Gyr of the BB and have had little SF since. “RED AND DEAD”

• Instantaneous burst models

BC93 Fig. 5

Spectral evolution

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Milky Way OverviewB&T

Classic picture of MW formation

Eggen, Lynden-Bell and Sandage 1962: collapse of the Milky Way• Link to this paper found on A6590 web site• Will be basis of homework/discussion next week

•Basic picture: collapse of rotating, spherical, gaseous halo•First stars form in halo => oldest stars, globular clusters, Pop II•Use kinematics and metallicities to infer model

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Galactic Rotation Relations

Vobs = V(R) cosα - V(R ) cos(90º-l )= V(R) cosα - V(R ) sin l

At any longitude, Vobs(d) depends on the rotation curve

characteristics.

… more details on this next weekNotice that we observe the max. Vr from an object at the tangent point along any l.o.s.

Spiral structure in the MW

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Infrared & radio view: unobscured

Larger (~mm), cold dust grains

10 to 30850-2000Submm/mm

Global structure of the Galaxy; HI clouds

HI: 100-1000

eg, 21 cm lineRadio

Cold dustCentral regions of galaxiesVery cold molecular clouds

10 to 10025 to 350FarIR

Planets, comets, asteroidsDust warmed by starlightProtoplanetary disks

90 to 7505 to 25MidIR

Cooler red stars. Red giants, dust transparent

740 to 52000.8 to 5NearIR

Radiation source/locationTempK

λμm

Band

HI map of galactic plane velocity field

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Use Doppler Shift to Map Radial VelocityIn Various Directions

• Starting point: Map intensity of neutral hydrogen along Galactic plane for various Galactic longitudes.

• From this, it has been shown that the neutral hydrogen appears to be concentrated in the spiral arms of the Milky Way.

Ambiguities in Mapping Structure•Assuming circular model of rotation of gas

Probably OK, but only approximate.• Range of phenomena near the Galactic plane. • Ambiguity in the overall flux density profile.

H. Karttunen et. al., Fundamental Astronomy.

Intensity

Galactic Center

Sun

Radial Velocity

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Structure in the Milky Way Plane• Existing maps are still coarse. • The MW clearly has spiral structure. • Additionally, we see the Sagittarius

Dwarf Galaxy very close on the far side.

Most recent HI survey reference:“The Leiden/Dwingeloo Survey of Galactic Neutral Hydrogen”

Dap Hartmann, Thesis, Leiden, 1994 (in Physics Library)Several other surveys underway (SGPS, CGPS, G-ALFA)

HI structure

HI and H2 in the MW

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MW HI Map: z vs. Radius

Verschuur & Kellerman, P. 348The MW HI layer is warped!

“Sombrero effect”

Many galaxies are warped: why?

Rotation curve of Milky Way

Will discuss estimates of MW mass and DM later…

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NGC 4762 - a disk galaxy with a bright thick disk (Tsikoudi 1980)

Most spirals (including the MW) have a second thicker disk component, believed to be the early thin disk heated by an accretion event. In some galaxies, it is easily seen :

The thin disk The thick disk

Thin and thick disks

MW thin and thick disks

• hR = 2 to 4 kpc, both for the thin (hz ~ 0.3 kpc) and the thick disk (hz ~ 1.5 kpc)

• Beyond R=15 kpc, the disk density is rapidly declining. The brightness distributions of other galaxies show similar downturns.

Using the MW spherical polar coordinate R,Φ,z, we can approximate the density n(R,z,S) of stars of spectral type S by a double exponential of form:

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Exponential in R and z : scaleheight ~ 300 pc, scalelength 3-4 kpc (!) velocity dispersion decreases from ~ 100 km/s near the center

(similar to bulge) to ~ 15 km/s at 18 kpc

Lewis and Freeman 1989

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1.5

1

R (kpc)

log

(vel

ocit

y di

sper

sion

)

Velocity dispersion of the thin disk

Freeman 1991; Edvardsson et al 1993; Quillen & Garnett 2000

• Velocity dispersions of nearby F stars

• Thick disk is discrete component

old disk

thickdisk

appears atage ~ 10 Gyr

Kinematics of the MW thick disk

We will discuss u,v,w next week

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Vertical velocity w.r.t. sun (W) as a function of stellar age:stars are born in a thin disk with small W; old stars are in a thick disk.

-10 km/s

(Pop II objects)

(1) Thick disk of high-metallicity globular clusters (left-hand panel) is made of objects on low-inclination, nearly-circular orbits the system has some prograde rotation.

(2) Spherical system (right panel) has completely disorganized motions, no rotation on average; some clusters have prograge, some retrograde motion, Orbits are highly inclined.

thick disk

spherical systemConnection between kinematics & geometry

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optical view 2MASS (2 micron all-sky) survey

• image made from star counts(not a direct image)

• total of 250 million *s in 2MASS.

Infrared view of the MW central regions

What are the instrument specs for 2MASS?

2MASS View of the Milky Way

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• 20% of Galaxy’s light from the bulge, R~1 kpc• Stars: few Gyr old, metal-rich unlike the metal-poor stars of the

halo; inner halo is also more round and does not show rotation • Bulge rotates in prograde sense, like the Sun, but slower: ~

100 km/s • A slight asymmetry of the bulge and additional kinematic data

show that the Milky Way has a central bar extending to R=2-3 kpc. It is a Sbc galaxy or SABbc( r)

.

Bulge

2MASS view of the MW

Heavy element (metal) abundancesAstronomical convention defines metals as all elements heavier than H, He X + Y + Z = 1where X, Y, and Z are mass fractions of hydrogen, helium and metals respectively. The typical values of these are 0.7, 0.3, and 0.005-0.05 respectively. The mass fraction Z is referred to as the metallicityof the object in question, and is usually measured as the ratio Z/Zwhere Z = 0.02 is the metal mass fraction of the Sun.

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Heavy element (metal) abundance measuresThe effect of changing Z on a star can be gauged by its effect on the luminosity of the star. The luminosity depends on many factors, including the temperature and pressure in the stellar interior. The ideal gas equation of state serves as a convenient approximation for these relationships:

where P is the pressure at the center of the star, ρ is the density of the gas,μ is the mean molecular weight, and T is the temperature. Varying Z most directly changes the value of μ . As μ changes, the T and P must also change to compensate. This, therefore, changes the luminosity of the star. Other effects may arise due to changes in radiative opacity in the stellar interior, owing to a change in μ . On the whole, a star is redder when its Z is high, and bluer when its Z is low.

We see therefore, that changing the metallicity of a star can lead to considerable changes in its radiative properties. These changes, in turn, govern its evolution over its lifetime.

Heavy element (metal) abundance measuresMost chemical abundance measurements are carried out using the

absorption lines of the element iron, because they are easy to pick out among the literal forest of spectral lines generally observed. We can define a measure of the metallicity of star thus:

where [Fe/H] is the metallicity of the star expressed as a logarithmic ratio between the relative abundance of iron seen inthe star (first term), and the relative abundance of iron in theSun (second term).

• This ratio is a convenient way to compare the metallicities of different stellar populations.

• The Sun's [Fe/H ] ratio is taken by convention to 0.00.• [Fe/H] ratios generally range from -3.00 (very metal poor) to

+2.00 (very metal rich). more on this later today…

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The UV color excess as a metallicity indicator

• By definition, for A stars: (B-V) = 0 = (U-B)

• In the U,B,V system

RV ≡

=

≈ 3.0

τVτB - τV

AVE(B-V)

•Now define the ultraviolet color excess

δ(U-B) = (U-B)obs – (U-B)expSee: B&M Box 5.4

UV color excess as a metallicity indicator

• Color excess may also be contributed by different Z• Why? Presence of dark spectral lines in any photometric band

will reduce flux emitted in that band

• Line blocking• Blocking coefficient ελ ≡ 1 -

• As Z ↑, *s become fainter in (B-V)even fainter in (U-B)

• Since total flux must be emitted, energy blocked in lines must be redistributed in λ and escape from cont. between lines

⇒ raise continuum⇒“backwarming” of atmosphere; simulates higher Teff

• Ultraviolet color excessδ(U-B) = (U-B)obs – (U-B)exp

∫ Fλ dλ

∫ Fλc dλ

λ+Δλ

λ-Δλ

λ+Δλ

λ-Δλ

Expected of a normal Zstar of same (B-V) or Teff

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UV color excess (cont)• Line blocking versus backwarming

• Blocking dominates in U, slightly exceeds in B, less important in V• Increase Z => add lines => increase (U-B) and (B-V), decrease V

A Hyades * of the same Teff has colors that differ by an amount Δ(B-V) and Δ(U-B) from those of the subdwarf. The effect of adding metal lines to the subdwarf’s atmosphere while holding Teff = const. is to move the observed colors along the “blanketing vector”.

• Both (U-B) and (B-V) are different

Hyades * has Z ~ 0

UV color excess (cont)• Line blocking versus backwarming

• Blocking dominates in U, slightly exceeds in B, less important in V

• Increase Z => add lines => increase (U-B) and (B-V), decrease V

A Hyades * of the same Teff has colors that differ by an amount Δ(B-V) and Δ(U-B) from those of the subdwarf. The effect of adding metal lines to the subdwarf’satmosphere while holding Teff = const. is to move the observed colors along the “blanketing vector”.

•Both (U-B) and (B-V) are different

Hyades * has Z ~ 0

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Stellar populations in the MW

The galactic bulge is rotating, like most other bulges: Kuijken & Rich (2002)

HST proper motions

Rotation (Beaulieu et al 2000)K giants from several sourcesand planetary nebulae (+)

Velocity dispersion of innerdisk and bulge are fairly similar- not easy to separate inner diskand bulge kinematically

Bulge ends at |l| ~ 12o

Bulge rotation and dispersion

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Dinescu et al 2003

3D kinematics of 7 globularclusters in the bar/bulge

Their velocities show:• All of them are confined to

the bulge region• the metal-poor clusters (o) are

part of the inner halo• the metal-rich clusters include

• a bar cluster • clusters belonging to a

rotationally supported system

Bulge globular clusters

Near the center of the bar/bulge is a younger population,

on scale of about 100 pc : the nuclear stellar disk(M ~ 1.5 x 109 M_sun)

and nuclear stellar cluster(~ 2 x 107 M_sun )in central ~ 30 pc.

(Launhardt et al 2002)

~ 70% of the luminosity comesfrom young main sequence stars.

Young stars in the GC

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The center of the Galaxy (nucleus) is a very exotic place, with the Sag A* radio source, surrounded by a torus (R=7 pc) of molecular gas, which flows in at a rate of 0.001-0.01 M /yr and formed dozens of massive stars within the last 3-7 Myr.

A fairly dark and inactive, ‘starved’ black hole (m= 2-3 x 106 M ) lurks in the center (white dot).

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Galactic Nucleus

2MASS view of the G.C.

We will discuss the G.C. later

Basics of chemical evolution• H and He were produce early in the history of the Universe, while

all other elements (except for a very small fraction of Li) wereproduced through nucleosynthesis in stars.

• Metals are found in very similar (though not identical) proportions in all *s. => the small differences reveal clues about the material from which the *s were made.

• Z ≡ fraction by mass of heavy elementsZ⊙ ~ 0.02Most metal poor *s in MW have < 10-5 Z⊙

• Metal abundance of the ISM gas and of subsequent generations of *s should increase with time (assuming no gas infall from outside)

• Expect a relation between ages and Z of *s• On avg, older *s contain less Fe than younger ones• Partially true for Solar neighborhood

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Chemical evolution in galaxies

Only high mass stars count

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Terminology for nucleosynthesis

Motion in the (Z,N) plane due to radiactive decay

Atomic number A ≡ Z + N

Nuclide: point in the (Z,N) plane

e.g. 16O => A=16, Z=8 so (Z,N)=(8,8)

Only a few points in the (Z,N) plane correspond to bound nuclear states => stability band, roughly || to, but centered just above N=Z line.

α-nuclides: 20Ne, 24Mg, 28Si, 32S, 36A, 40Ca Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu⇒ Stable isotopes with similar binding energy⇒ Formed in late evolutionary stages when core v. hot

“stability valley”: move along the stability band along a line A=Z+N=constant; absolute value of binding enery per nucleon first increases, then decreases. Deepest point in the valley is Fe

Atomic nucleus: bound state of Z protons and N neutrons

Terminology for nucleosynthesis (2)

Motion in the (Z,N) plane due to radiactive decay

Atomic number A ≡ Z + N

Nuclide: point in the (Z,N) plane

e.g. 16O => A=16, Z=8 so (Z,N)=(8,8)

Only a few points in the (Z,N) plane correspond to bound nuclear states => stability band, roughly || to, but centered just above N=Z line.

α-nuclides: iron-peak nuclides:s-process nuclides: “slow” => 88Sr, 89Y, 90Zr, …140Ce, 208Pb…

⇒ Lie along valley floor at higher A up from Fe peak ⇒ Require Fe-peak elements already present in C,O zone⇒ Form by slow neutron neutron capture

r-process nuclides: “rapid” => 80Se, 81Br, 84Kr, …127I, 196,198Pt…⇒ Lie on neutron-rich side of valley floor just above s-

process nuclides.⇒ Form in similar way, but by rapid neutron capture

Atomic nucleus: bound state of Z protons and N neutrons

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Element production overview

Element production in SNe

SN IISNe are prime source of both Fe-peak and r-process nuclei.

SNe winds may play an important role in

effective yield. Maeder 1992, A&A

254, 105.

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Stellar yields

Element abundances in the solar neighborhood

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“Closed box” model• First ones: Tinsley (1980)• For now: skip details about gas ejection/winds, etc.• Stick to simplest model• Assume there is one-zone and instantaneous recycling

=> Ignore delay bet. formation and ejection by massive *s• Assume gas is well mixed and has same Z everywhere• Assume that no gas escapes or is added (initially)• Assume that all elements heavier that He maintain same

proportion relative to one another• Define:

For the “closed box” then: dMg = - dMsSee: BM Ch 5

“Closed box” model• Start with a mass of stars M* which has Z ≡ Mh/Mg; let *s form.• After the massive stars have died off, dM* remains in low mass *s

and remnants

• Mass in heavy elements produced by this generation of *s is:p dM*

where p is the yield of the stellar generation. It depends on the IMF and the details of nuclear burning.

• The fraction of heavy elements locked up in low-mass *s and remants is Z dM*

• The mass of heavy elements Mh in the IS gas changes as the metals produced by the high mass *s are returned.

The rate of change in the metal content of the gas mass is:dMh/dt = p dM* /dt – Z dM*/dt

dMh/dt = (p – Z) dM*/dt

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“Closed box” modelThe rate of change in the metal content of the gas mass is:

dMh/dt = p dM* /dt – Z dM*/dt

dMh/dt = (p – Z) dM*/dt

Mass conservation implies: dMg/dt + dM*/dt = 0

The change in metallicity of the gas is:dZ/dt = d(Mh/Mg)/dt

= dMh/dt∗1/Mg - Mh/Mg2 ∗ dMg/dt= 1/Mg∗(dMh/dt – Z dMg/dt)

So thatdZ/dt = -p/Mg dMg/dt

If the yield p does not depend on Z, integrate to obtain the metallicity Z at time t

Z(t) = Z(0) – p ∗ ln[Mg(t)/Mg(0)]

The metallicity of the gas grows with time, as new stars are formed and the gas is consumed

Metallicity distribution of the starsThe mass of the stars that have a metallicity less than Z(t) is then:

M*[

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The G-dwarf problem• Observations of *s in the disk give the yield, p,

Z(today) ~ Z(0) – p ln [ Mg(today)/Mg(0)]

• Avg in the disk near the Sun: Zg(today) ~ 0.7 Z⊙• Initial mass of gas: Mg(0) = M*(today) + Mg(today)

M*(today) ~ 40 M⊙/pc2 and Mg(today) ~ 10 M⊙/pc2

• Assuming that Z(0) = 0, => p ~ 0.43 Z⊙• The prediceted mass in metal-poor stars (Z = 0.25 Z⊙) in the Solar

Neighborhood relative to the mass in *s with Zg(today) is:

M*(< 0.25 Z⊙)/ M*(< 0.7 Z⊙) = [1 – e -0.25 Z /p]/[1 – e -0.7 Z /p] ~ 0.54

In a closed box model, HALF of all stars in the disk near the Sun should have Z< 0.25 Z⊙

But, only 2% of F-G dwarfs in the Solar Nbhd are that metal-poor.

This discrepancy is called the “G-dwarf problem”

⊙ ⊙

Alternatives to the “closed box”?The G-dwarf problem => in the disk, a “closed” box doesn’t work.Its assumptions:

• Initial gas was metal free: Z(0) = 0• Get a better prediction if Z(0) = 0.15 Z⊙• Pop III pollution?

• Gas was chemically homogeneous (well mixed)• Gas has has been lost through winds of *s or SNe

• “leaky box” model: chemically enriched gas lost• Gas has been accreted; accreted gas has lower Z

• “accreting box” model: pristine gas added

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Components of the Milky Way

Quantitative morphologyLevels of symmetry:

1. spherical: glob. clusters, E0 galaxies (some round by projection)2. axial: natural result of rotation => disk

- basic shape for most galaxies3. triaxial: (less recognized); results in strongly anisotropic velocity

distributions.

Fundamental planes of galaxy properties (are there more?)1. Form: morphology, color, star formation rate, specific angular

momentum2. Scale: luminosity, linear size, mass

Question: Is the shape of a galaxy, in the absence of active perturbations, dominated by:

1. present equilibrium conditions?2. initial (or early) conditions?

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Surface brightness

• Units: L⊙/pc2• Nearby, S.B. is independent of D• Often, use magnitudes to denote flux at given point in image

μλ(x) = -2.5 log10 Iλ(x) + constλ• For V-band => constV = 26.4 mag/arcsec2 which corresponds to

1 L⊙/pc2 andIV = 100.4(26.4-μ) L⊙,V/pc2

Units are [mag/arcsec2]

I(x) = F/α2 = L/(4πd2)∗(d/D)2 = L/(4πD2)

Surface brightness measured in mag/arcsec2 (μI, μB, μR, etc.)

is independent of distance since light falls as 1/d2, but the area subtended by 1 sq arcsec increases as 1/d2.

• however, cosmological dimming of 1/(1+z)4 causes higher z galaxies to have lower surface brightnesses

Photometric Properties of Galaxies

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μB

Much of the galaxy structure is fainter than the sky which must be accurately subtracted.

Night sky at 22.7• SB profiles are produced by

azimuthally averaging around the galaxy along isophotes of constant brightness.

• Must understand viewing geometry.• Seeing effects on SB profiles -

unresolved points spread out due to effects of our atmosphere, etc.

• makes central part of profile flatter

• makes isophote rounder

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Galaxy photometry

Where does the image above come from?

•Fitting isophotes: in practice• Fixed center• Smooth variation in

PA, ellipticity

Surface brightness profile => I(r) in L⊙pc-2 μ(r) in mag arcsec-2

SDSS Sky Server

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Photometry and the structure of galaxiesWhat can we infer about the 3-d luminosity density j(r) in a transparent galaxy from its projected surface-brightness distribution I(R)?

If I(R) is circularly symmetric, j(r) may be spherically symmetric:

We’ll talk more about E’s next time

Popular surface brightness fitting functions

deVaucouleurs profile or R1/4 - law

Hubble-Oemler profile

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King profileFlat as r → 0

c = log =rt r(I=0)rc r(I=½Io)

Comparisons; effects of seeing

• Need to account for seeing • Need accurate sky subtraction

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Sérsic + Exponential profilesI(R) = I(Re) exp {-b[ (R/Re)1/n – 1]}

GALFIT is a galaxy/point source fitting algorithm that fits 2-D parametrized, axisymmetricfunctions directly to images. See: Peng et al. 2002, AJ 124, 266 orhttp://users.ociw.edu/peng/work/galfit/galfit.html

n=1 exponential

n=4 deVauc