ATA 2010DYNAMICS of the MILKY WAY

Ken Freeman, ANU & UWA

Galaxies are collections of stars, gas, dust and dark matter

Masses are between about 106 and 1012 M. The Milky Way is a disk galaxy and is near the upper end of the mass range.

Introduction

NGC 2997 - a typical disk-like spiral galaxy

NGC 891

A spiral galaxyseen edge-on

Note the smallcentral bulge andthe dust in theequatorial plane

Disk galaxies

Surface brightness distribution I(R) = Io exp(-R / h)

Io is the central surface brightness, typically around150 pc-2

h is the scale length: 4 kpc for a large galaxy like the MW

Ratio of stars/gas varies : for the MW stars 95%, gas 5% of the visible matter.

Flat rotating disk-like systems, often with spiral structure

Dark/visible mass ratio is about 10-20

The nearby spiral galaxy M83 in blue light (L) and at 2.2 (R)

The blue image shows young star-forming regions and is affectedby dust obscuration. The NIR image shows mainly the old stars andis unaffected by dust. Note how clearly the central bar can be seenin the NIR image

Rotation of spirals

Mostly don’t rotate rigidly - wide variety of rotation curve morphology depending on their light distribution. Here are a couple of extremes - 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 ? (always ask this questionfor any stellar system)

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.

Our GalaxyBelieved to be much like NGC 891, with weak barlike M83. Rotational velocity ~ 220 km/s

Our Galaxy at 2.4

Schematic picture of our Galaxy, showing bulge, thin disk, thick disk, stellar halo and dark halo

Start by showing a numerical simulation of galaxy formation.

The simulation summarizes our current view of how a disk galaxylike the Milky Way came together from dark matter and baryons,through the merging of smaller objects in the cosmologicalhierarchy.

MOVIE

• much dynamical and chemical evolution• halo formation starts at high z• dissipative formation of the disk

Simulation ofgalaxy formation

• cool gas • warm gas • hot gas

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• z ~ 13 : star formation begins - drives gas out of the protogalactic dark matter mini-halos. Surviving stars will become part of the stellar halo - the oldest stars in the Galaxy

• z ~ 3 : galaxy is partly assembled - surrounded by hot gas which is cooling out to form the disk

• z ~ 2 : large lumps are falling in - now have a well defined rotating disk galaxy.

You saw the evolution of the baryons. There is about 10 xmore dark matter in a dark halo, underlying what you saw:it was built up from mergers of smaller sub-halos

Movie synopsis

Course Objectives

To study the dynamics of the Milky Way. Most of its visible mass is in stars, so the dynamical theory is mostly stellar dynamics

Following this basic descriptive introduction, I will go straight tothe lectures on the theoretical dynamics. This will give youmaximum opportunity to complete the assignments.

We will then return to more advanced descriptive material onnear-field cosmology: ie what we can learn about galaxy formationfrom studying the detailed properties of our own Galaxy.

Lecture times

2 to 4 pm on

Monday 02, 09, 16 August 2010

ICRAR, UWA - ground floor

Assessment

30% on assignment work, 70% on examination

Assignments: one problem sheet with 5 questions: please hand in at lecture on Fri Sep 18. I use these problems as part of the teaching process, as well as for assessment, so please do them. They require some time and effort.

I encourage you to discuss the problems with others, but the work you submit should be your own. It is very obvious if people collaborate in the submitted work, and it will cost both (all) parties some marks.

There will be a brief tutorial session on the assignment in class

Examination: you will have a 2-hour examination for the 3 combined ATA modules.For this module, you will be asked to do two questions from a choice of three.

Feel free to contact me about the problems or any other aspect of the course: office ICRAR 249phone 6488 4756 email kcf@mso.anu.edu.au

You can find the lecture notes and assignment sheet athttp://www.mso.anu.edu.au/~kcf/ATA

References

Binney & Tremaine: Galactic Dynamics (1987, 2008). The dynamical lectures are partly based on this book, whichis the best book on the subject. It covers far more groundthan we can cover in these lectures.

Binney & Merrifield: Galactic Astronomy (1998). This is a more descriptive book and well worth reading forbackground.

Sparke & Gallagher: Galaxies in the Universe (2007).Ditto : good book, with some theory

13.7 Gyr

Two important timescales

1) The dynamical time (rotation period, crossing timeG where is a mean density. Typically 2 x 108 yr for galaxies

2) The relaxation time. In a galaxy, each star moves in thepotential field of all the other stars. Its equation of motion is where

is Poisson’s equationThe density (r) is the sum of 106 to 1012 -functions.

As the star orbits, it feels the smooth potential of distant stars and the fluctuating potential of the nearby stars

€

˙ ̇ r = -∇Φ

€

∇ 2 Φ = 4π G ρ

Question: do these fluctuations have a significant effect on the star’s orbit ?

This is a classical problem - to evaluate the relaxationtime TR - ie the time for encounters to affect significantlythe orbit of a typical star

Say v is the typical random stellar velocity in the system m mass n number density of starsThen

TR = v3 / {8 G2 m2 n ln (v3 TR / 2Gm)} (see B&T I:187-190)

TR / Tdyn ~ 0.1 N / ln N where N is the total number of stars in the system

In galactic situations, usually TR >> age

eg in the solar neighborhood, m = 1 M, n = 0.1 pc-3

v = 20 km s -1 so TR = 5.10 12 yr >> age of the universe

In the center of a large spiral where n = 10 4 pc -3 andv = 200 km s -1, TR = 5.10 11 yr

(However, in the centers of globular clusters, the relaxation time TR ranges from about 107 to 5.109 yr, so encounters have a slow but important effect on their dynamical evolution)

Conclusion: in galaxies, stellar encounters are negligible: they arecollisionless stellar systems. is the potential of the smoothed-outmass distribution, which makes galaxy dynamics much simpler.

For real disk galaxies, we can calculate the potential of the stars andthe gas from the observed surface density distribution of stars and gas in the disk, and then calculate the expected rotation curve from

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This is not usually a good fit to the observed rotation curve, because most of themass of disk galaxies is in the form of dark matter

Surface Brightness

HI Rotation Curve(out to 11 scale lengths)

Dark matter is important here

If E and Lz are the only two integrals of the motion, then the orbit would visit all points within ints zero-velocity curve.

EL

circular orbitslocus of const rmax

E = E max

A rosette orbit is the vector superposition of these two components: the epicycle + the circular guiding centre motion.

Now take ez

NGC 1300

Define the convective derivative in phase space

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Then we can show that

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for a collisionless system. This is the collisionless Boltzmann equation: the convectivederivative of the phase space density is zero.

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These two equations are coupled: QuickTime™ and a

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Merrifield (1992)

Rotation of the Galaxy

25001250

RR2 (km s -1) 2

-30

-20

-10

< V

> (

km s

-1 )

Stromberg’s asymmetric drift

absorbs

Merging stimulates star formation and disrupts the galaxies. This is NGC 4038/ 9 : note the long tidal arms . The end product of the merger is often an elliptical galaxy.

Disk galaxies interact tidally and merge.

NGC 5907: debris of small accreted galaxyOur Galaxy has a similar structure from the disrupting Sgr dwarf

APOD

The “field of streams” seen in SDSS star counts in the halo of our Galaxy

north galactic pole

l = 180, b = 25

Accretion of small galaxies is more important than major mergers for the evolution of the Milky Way: look now at the two main processes involved in accretion.

Recent HST proper motion measurements for the LMC indicate that the LMC is not in a circular orbit around the Galaxy and may not even be bound to the Galaxy.

The HI Magellanic Stream (Putman 2002),believed to come from interaction of theGalaxy and the Magellanic Clouds. Seen only in HI, not in stars.

The pioneering work on this problem was done by Quinn & Goodman 1986)

Decay ofa prograde

satelliteorbit

The satellite sinksinto the plane of thegalaxy in < 1 Gyr.

The disk providesabout 75% of the torque on the satellite: dynamical friction against the dark halo Provides the rest

Some background to the paper “Panoramic High Resolution Spectroscopy”and galactic archaeology

Chemical EvolutionElements lighter than ~ Be are built in the hot universe, shortly after the big bangElements heaver than Be are built in stars, and ejected back into the interstellar gas by supernovae and AGB stars - many cycles of enrichment give chemical evolution up to the present level of chemical abundance - SN and AGB stars Two main kinds of supernovae: SNII (progenitor M > 8M) produce -elements (O, Mg, Si, Ca,Ti), some Fe-peak elements (V … Zn), and r-process elements (eg Eu) all on timescales ~ 107 years SNIa (lower mass progenitors, probably white dwarf binaries) produce mainly Fe-peak elements but on longer timescales ~ 109 yearsAGB stars over wide range of mass produce s-process elements (Sr, Zr,Ba), again on longer timescales ~ 109 years

If we see stars which are rich in -elements relative to iron, this means that the chemical evolution of the gas from which they formed happened quickly (~ 108 yr), before there was time for the SNIa to generate a lot of iron etc

To measure the abundances of chemical elements accurately, we need high resolution spectra with R > 30,000. Until now, high resolution spectrographs can measure onlyone star at a time. In the near future, we will be able to measure hundreds a a time.

The galactic disk shows kinematical substructure in the solar neighborhood: groups of stars moving together, usually called moving stellar groups (Kapteyn, Eggen)

• Some are associated with dynamical resonances (eg Hercules group): don't expect chemical homogeneity

• Some are debris of star-forming aggregates in the disk (eg HR1614 group). Might expect chemical homogeneity; these could be useful for reconstructing the history of the galactic disk.

• Others may be debris of infalling objects, as seen in CDM simulations: eg Abadi et al 2003 (Arcturus Group, Navarro et al 2004)

Stellar Moving Groups in the Disk

The Hercules group is associated with local resonant kinematic disturbances by the inner bar : OLR is near solar radius

(Hipparcos data) : Dehnen (1999), Fux (2001), Feast (2002)

Sirius and Hyadesstreams - mainlyearlier-type stars

Hercules disturb-ance from OLR -mainly later-type stars

Dehnen 1999(U,V are relative to the LSR)U

V

The abundances ofHercules Group starscannot be distinguishedfrom the field stars. Thisis a dynamical group, notthe relic of a star formingevent.

Hercules group

•o field stars

Bensby et al 2007

Now look at the HR1614 group (age ~ 2 Gyr, [Fe/H] = +0.2). Studied by Feltzing & Holmberg (2000) who argued for its realityas a relic group.

De Silva et al (2007) measured very precise chemical abundancesfor many elements in HR1614 stars, and finds a very smallspread in abundances.

The Wolf 630 group was recently found to be similarly homogeneous in its element abundances

• HR 1614o field stars

The HR 1614 stars (age 2 Gyr)

are chemically homogeneous.

They are probably the

dispersed relic of an old star forming event.

De Silva et al 2007

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

Most spirals (including our Galaxy) have a second thicker disk component . In some galaxies, it is easily seen

The thin disk The thick disk

Our Galaxy has a significant thick disk

• its scaleheight is about 1000 pc, compared to 300 pc for the thin disk

• its surface brightness is about 10% of the thin disk’s.

• it rotates almost as rapidly as the thin disk

• its stars are older than 12 Gyr, and are

• significantly more metal poor than the thin disk (-0.5 > [Fe/H] > -2.2) and

• alpha-enriched

The galactic thick disk• its mass is about 10% of the thin disk’s • it is old (> 12 Gyr) and significantly more metal poor than the thin disk: mean [Fe/H] ~ -0.7 and -enhanced• its rotation lags the thin disk by only ~ 50 km/s

thick diskthin disk

higher [/Fe] more rapid formation

Most disk galaxies have thick disks: (eg Yoachim & Dalcanton 2006)

The Galactic element abundance data are consistent with a time delay between formation of thick disk stars and the onset of star formation in the current thin disk.

The fraction of baryons in the thick disk is typically small(~ 10-15%) in large galaxies like the MW but rises to~ 50% in smaller disk systems

Yoachim & Dalcanton 2006

Baryonic mass ratio: thick disk/thin disk

How do thick disks form ?

• a normal part of early disk settling (Samland et al 2003, Brook et al 2004)

• accretion debris (Abadi et al 2003, Walker et al 1996)

• early thin disk, heated by accretion events - eg the Cen accretion event (Bekki & KF 2003): Thin disk formation begins early, at z = 2 to 3. Partly disrupted during merger epoch which heats it into thick disk observed now, The rest of the gas then gradually settles to form the present thin disk

Disks have a roughly exponential light distribution in R and z:

I(R,z) = Io exp (-R/hR) exp (-z/hz)out to R = (3 to 5) hR, then often truncated

M33 (Ferguson et al)

The truncations are not understood: may be associated with

• the star formation threshold• angular momentum redistribution by bars and spiral waves• the hierarchical accretion process • bombardment by dark matter subhalos (de Jong et al 2007)

Roskar et al (2008) - SPG simulation of disk formation from coolinggas in an isolated dark halo : includes star formation and feedback.The break is seeded by rapid radial decrease in surface density ofcool gas : break forms within 1 Gyr and gradually moves outwardsas the disk grows. The outer exponential is fed by secularly redistributed stars from inner regions (Sellwood & Binney 2002) so its stars are relatively old.

Roskar et al (2008)

stellar surface density

gas surface density

star formation rate

mean stellar age

Roskar et al (2008)

Secular radial distribution of stars via spiral arm interactioninto outer (break) region of truncated disk

Redistribution of stars by orbit swapping will affect the galactic abundance gradient

break

The galactic disk shows an abundance gradient(eg galactic cepheids: Luck et al 2006) ....

Background to the final section ….

Using dispersed star clusters for galactic archaeology: finding fossil remainsof the star forming events which built up our Galaxy

Galaxies like the Milky Way are believed to form by

• the infall of gas which then turns gradually to stars (most of which form in the disk of the Galaxy, in open star clusters which quickly dissolve), and also by • the accretion of smaller galaxies which become absorbed in the larger system.

A major goal is to determine how important these accretion events were in building up the Galactic disk and the bulge.

Our current galaxy formation theory based on Cold Dark Matter predicts a very high level of accretion activity which conflicts with many observed properties of disk galaxies.

By now, the star clusters and the small accreted galaxies have broken up andbe unrecognisable: their debris will be dispersed right around the Galaxy. But …

We can use their chemical signatures over many chemical elements to identify their debris:

• stars from a common cluster have similar chemical signatures, and their chemical properties vary from cluster to cluster

• stars from a small accreted galaxy have chemical patterns that are very different from those we see in the open clusters which formed in the disk.

Using chemical signatures to identify stars having a common origin is called chemical tagging

This will be one of the big things of the next decadein galactic astronomy

Cluster abundance patterns

HyadesColl 261HR1614

De Silva 2007

Zr

Ba

Mn

Ca

Si

Mg

Na

Clusters vs

nearby field stars

HyadesColl 261HR1614

De Silva 2007

Clusters have smallabundance spread:

The mean isdifferent from cluster

to cluster

Galactic Archaeology with HERMES

Simulations show that a chemical tagging programto reconstruct the fossils of the star forming aggregates

that built up our Galaxy needs high resolution spectra of about a million stars

We are building a large multi-object spectrometer (HERMES) for the AAT to do this survey. It will acquire high resolution spectra ofabout 400 stars at a time, and the survey will take about 400 clear nights. Expect to start work in 2012