GALAXIES 626 Upcoming Schedule:

Today: Structure of Disk Galaxies Thursday:Structure of Ellipticals Tuesday 10th: dark matter (Emily's paper due) Thursday 12th :stability of disks/spiral arms Tuesday 17th: Emily's presentation (intergalactic metals) GALAXIES 626

Lecture 17: The structure of spiral galaxies NGC 2997 ­ a typical spiral galaxy NGC 4622 yet another spiral note how different the spiral structure can be from galaxy to galaxy Elementary properties of spiral galaxies Milky Way is a “typical” spiral

radius of disk = 15 Kpc thickness of disk = 300 pc

Regions of a Spiral Galaxy • Disk • younger generation of stars • contains gas and dust • location of the open clusters • Where spiral arms are located • Bulge • mixture of both young and old stars • Halo • older generation of stars • contains little gas and dust • location of the globular clusters Spiral Galaxies

The disk is the defining stellar component of spiral galaxies.

It is the end product of the dissipation of most of the baryons, and contains almost all of the baryonic angular momentum

Understanding its formation is one of the most important goals of galaxy formation theory. Out of the galaxy formation process come galactic disks with a high level of regularity in their structure and scaling laws

Galaxy formation models need to understand the reasons for this regularity Spiral galaxy components 1. Stars • 200 billion stars • Age: from >10 billion years to just formed • Many stars are located in star clusters 2. Interstellar Medium • Gas between stars • Nebulae, molecular clouds, and diffuse hot and cool gas in between 3. Galactic Center – supermassive Black Hole 4. Dark Matter • The total mass of the far exceeds the mass with stars and interstellar medium put together • Hidden, invisible or missing component The matter in the spiral galaxies emits different kinds of radiation..... Stars: Halo vs. Disk • Stars in the disk are relatively young. • fraction of heavy elements same as or greater than the Sun • plenty of high­ and low­mass stars, blue and red • Stars in the halo are old. • fraction of heavy elements much less than the Sun • mostly low­mass, red stars • Stars in the halo must have formed early in the Milky Way Galaxy’s history. • they formed at a time when few heavy elements existed • there is little interstellar gas in the halo • star formation stopped long ago in the halo when all the gas flattened into the disk The interstellar gas Disk structure

Empirically, the surface brightness declines with distance from the center of the galaxy in a characteristic way for spiral galaxies.

For spiral galaxies, need first to correct for: • Inclination of the disk • Dust obscuration • Average over spiral arms to obtain a mean profile

Corrected disk surface brightness drops off as: ­R/h I  R=I  0  e R where I(0) is the central surface brightness of the disk, and hR is a characteristic scale length. In practice, surface brightness at the center of many spiral galaxies is dominated by stars in the bulge. Central surface brightness of disk must be estimated by extrapolating inward from larger radii.

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radius Typical values for the scale length are: 1 kpc h 10 kpc  R In many, but not all, spiral galaxies the exponential part of the disk seems to end at some radius Rmax, which is typically 3 - 5 hR.

Beyond Rmax the surface brightness of the stars decreases more rapidly - edge of the optically visible galaxy.

The central surface brightness of many spirals is ~ constant, irrespective of the absolute magnitude of the galaxy! I 0 »21.65 mag arcsec­2 B  

Presumably this arises from physics of galaxy and / or star formation… Rotation of spirals

Mostly don’t rotate rigidly ­ wide variety of rotation curves depending on their light distribution. The one on the left is typical for lower luminosity disks, while the one on the right is more typical of the brighter disks like the Milky Way What keeps the disk in equilibrium ?

Most of the kinetic energy is in the rotation

in the radial direction, gravity provides the radial acceleration needed for the ~ circular motion of the stars and gas

in the vertical direction, gravity is balanced by the vertical pressure gradient associated with the random vertical motions of the disk stars. Motion under gravity Motions of the stars and gas in the disk of a spiral galaxy are approximately circular (vR and vz << vφ).

Define the circular velocity at radius r in the galaxy as V(r). Acceleration of the star moving in a circular orbit must be provided by a net inward gravitational force: V 2 r  =­ F r  r r

To calculate Fr(r), must in principle sum up gravitational force from bulge, disk and halo. For spherically symmetric mass distributions:

• Gravitational force at radius r due to matter interior to that radius is the same as if all the mass were at the center. • Gravitational force due to matter outside is zero.

Thus, if the mass enclosed within radius r is M(r), gravitational force is: GM r  F =­ r r2

(minus sign reflecting that force is directed inward) Bulge and halo components of the Galaxy are at least approximately spherically symmetric - assume for now that those dominate the potential.

Self-gravity due to the disk itself is not spherically symmetric…

Note: no simple form for the force from disks with realistic surface density profiles… Rotation curves of simple systems

1. Point mass M: GM V r =  r Applications: • Close to the central black hole (r < 0.1 pc) • `Sufficiently far out’ that r encloses all the Galaxy’s mass 2. Uniform sphere: If the density ρ is constant, then: 4 M r = pr3 ρ 3 4 pGρ V r = r 3 Rotation curve rises linearly with radius, period of the orbit 2πr / V(r) is a constant independent of radius.

Roughly appropriate for central regions of spiral galaxies. 3. Power law density profile: If the density falls off as a power law: −α r ρr =ρ 0 r  0  …with α < 3 a constant, then:

4 pGρ r α 0 0 α V r = r1− /2  3−α For many galaxies, circular speed curves are approximately flat (V(r) = constant). Suggests that mass density in these galaxies may be proportional to r-2. 4. Simple model for a galaxy with a core:

Spherical density distribution: V 2 H 4 pGρr = r2 a2  H

• Density tends to constant at small r • Density tends to r-2 at large r Corresponding circular velocity curve is:

a H r V r =V 1− arctan H r a   H  Resulting rotation curve Navarro, Frenk and White profile

Numerical simulations of the formation of dark matter halos by Navarro, Frenk and White (1997) suggest that the dark matter has a single `universal’ profile irrespective of mass: d ρr  c = ρ 2 crit r /r 1r /r  s s ρ δ …where crit, c and rs are all constants which can be calculated if we know the redshift at which a halo forms.

Slope of NFW profile is -1 in center, -3 at large radius. Circular velocity rotation curves for NFW profile Measuring galaxy rotation curves Consider a galaxy in pure circular rotation, with rotation velocity V(R). Axis of rotation of the galaxy makes an angle i to our line of sight.

If we measure the apparent velocity in the disk at an angle φ, measured in the disk, then line of sight (radial) velocity is: V R ,i V V R sin i cos f r  = sys   where Vsys is the systemic velocity of the galaxy. If we measure Vr across the galaxy, and can infer the inclination i, then obtain the full rotation curve V(R).

Even if the galaxy is not resolved, measuring the amount of emission as a function of the line of sight velocity gives a measure of the peak rotation speed in the galaxy Vmax: W »2V sin i max Can use the Doppler shift of any convenient spectral line to measure the line of sight velocity: λ V obs r =1 λ c emit

Optical: for nearby galaxies use Hα spectral line to measure rotation curves. Distant galaxies use spectral line of oxygen. Measures rotation of the stars.

Radio: traditional measure of rotation curves. Use 21cm line of hydrogen. Measures rotation of the neutral hydrogen gas disk.

Major advantage: detectable gas disk extends further out than detectable stellar disk. Examples of spiral galaxy rotation curves

Typically flat or even rising out to many scale lengths of the exponential disk. If all the mass in these galaxies was provided by stars and -1/2 gas, expect that V(R) would drop as R at R > few x hR.

Existence of flat (or even rising) rotation curves at these radii imply additional unseen mass - dark matter.

Rotation curve measurements on their own only indicate that the dark matter must be:

• Dynamically dominant at large radii (required proportion of dark matter ~50% in Sa / Sb galaxies, 80-90% in Sd galaxies). • Have a more extended distribution than either the stars or the gas. Note: no evidence for dark matter on the scale of the Solar System, or in the nearby Galactic disk. The evidence for dark matter is clear for galaxies with 21 cm HI rotation curves that extend far out, to R >> 3 h. maximum disk decomposition for NGC 3198:

M/LB = 3.8 for disk

observed Why are spiral disks so uniform?

Why do the observed galaxies occupy such a a small fraction of possible structural configurations: size, surface brightness, shapes, etc.. •Stability? •Initial Conditions? •Feed­back during the formation? Present Structural Parameter Relations for Disk Galaxies Disk Size vs Mass/Luminosity

• Galaxy size scales with luminosity/stellar mass

• At given luminosity/size: Disks fairly broad (log normal) Disks SpShperoheirodsids distribution

1/3 • Rd~M* Shen et al 2003 SDSS • Constant central surface brightness Another way of seeing the uniformity: Tully-Fisher relation Plot the maximum circular velocity of spiral galaxies against their luminosity in a given band:

Find that L and Vmax are closely correlated

Smallest scatter when L is measured in the red or the near-infrared wavebands e.g. in the H band centered at 1.65 µm:

3.8 V L »3´ 1010 max L H 196 km/s  H ,solar

LµV 4 Roughly, max

Important use as extragalactic distance indicator:

• Measure Vmax, eg from radio observations of HI • Infer L in a given band from the Tully-Fisher relation, and convert to absolute magnitude • Measure the apparent magnitude • Use: d m−M=5 log 10 pc  …to estimate distance Origin of the Tully-Fisher relation In part, Tully-Fisher relation reflects simple gravitational dynamics of a disk galaxy... Estimate the luminosity and maximum circular velocity of an exponential disk of stars. Luminosity Empirically, disk galaxies have an exponential surface brightness profile: −R/h I  R=I 0 e R

…with central surface brightness I(0) a constant. Integrate this across annuli to get the total luminosity: ¥ −R/h Lµ∫ 2 p RI 0e R dR 0 Can integrate this expression by parts, finding: LµI 0 h2   R i.e. for constant central surface brightness, luminosity scales with the square of the scale length.

Circular velocity If the mass in the stars of the exponential disk dominates the rotation curve, then the enclosed mass within radius R will be proportional to the enclosed luminosity: R −R' /h M  R µL R µ∫ 2 p R' I 0e R d R' 0 Approximately, use formula for spherical mass distribution to get V(R): V 2  R GM  R = R R2 This gives, h h R R −R/h −R/h V 2  R µ − e R−e R ´ h [ R R ] R

Dependence on R always occurs via the combination R / hR

Function in square brackets

peaks at R ~ 1.8 hR Conclude that: V µ h max  R

Eliminate hR using previous result: LµV 4 max

…the Tully-Fisher relation! Problems with this `explanation’

This argument shows that it is plausible that a relation akin to the Tully-Fisher law should exist.

Does not really explain the exact form:

• Flat rotation curves imply that enclosed mass is not mostly stars (except very near the center). For the same argument to work for dark matter, need to additionally assume that M/L = constant.

• Derivation makes use of I(0) = constant, which is not an obvious fact. What determines sizes of stellar disks?

Angular momentum Arising from halo size and spin parameter λ Dark halo and its adiabatic contraction do matter

Conversion of gas to stars

Internal re­distribution of angular momentum Bar instabilities?

Still too hard a problem for the simulations as we discussed previously Look­back observations and disk formation Disk evolution with redshift: What might we expect? • Sizes from Initial Angular Momentum 1/3 ­ R (M ) ~ M λ ­4/3 (z) 2/3 exp * * x md jd x H

• When did the presently existing disks form? – 1/3 of all stars at z~0 are in disks – 40% of all stars (now) have formed since z~1 (mostly in disks) – Majority of the Milky Way disk stars have formed in the last 7Gyrs z~1  z~0 is the most important epoch for building today’s stellar disks

– Note: higher SFRs at z>0  higher surface brightness(?) Disk Evolution to z~1

t ns co = µ v How did the surface brightness of disk galaxies evolve since z~1? For luminous b r i g

galaxies, the mean h

Freeman “law” t e surface brightness r

has dropped by 1 mag 1mag over the last 7Gyrs

MV<­20 Evolution of the mean surface mass density of disks since z~1

10 M*>10 Mo Redshift Evolution of the Tully­Fisher Relation Expected change in surface brightness from the observed stellar population changes Size­evolution from z~2.5 to z~0

At a given (V­band) luminosity, galaxies were about 2.5x smaller at z~2.5 than now.

At a given stellar mass, they were only 1.4x smaller than now.

Galaxies at high­z were bigger H2/3(z) than the naïve halo­scalings lead us to expect! Summary

• Disks at high­z (0.5­2.5) seem to live on the σ same locus in the M*,R,( ) plane

• Evolution of this locus in the LV,R plane, reflects changes in stellar mass­to­light ratio

This argues for galaxies evolving along those relations.

(?) disks grow “inside out”, along R(M) ~M1/3

If disks were to grow in mass along with ­1 ­2/3 their halos, Rd(M) ~ H (z) or H (z), we would have expected them to be smaller at high­z than observed. End