Galaxy Rotation: How we know

AS41310/28/2014D. Clemens

Outline• Ways to detect that galaxies rotate• Measuring rotations of external galaxies• Our problematic location within the Milky Way• Clues from the nearby stars• Success from Radio Astronomy: HI• Sampling the cold ISM: CO (for H2)• Outer Galaxy probes: gas+stars• New(er) Milky Way probes: APOGEE, Gaia• Mass models, dark matter, galaxy assemblage

Evidence that Galaxies Rotate• Optical spectroscopy of

galaxies– Large-aperture

observations reveal absorption lines that are too broad to be from single stars• Would imply impossibly

high surface gravities• Must be due to Doppler

shifting of many stars with a range of radial velocities (RVs) wrt us

• Velocity dispersion of that galaxy (gravitational potential)

– Emission lines from large-apertures don’t necessarily trace velocity dispersion• Emission regions don’t span

galaxy uniformly• Elliptical galaxies don’t

generally have emission lines

• Multi-Object or IFU (Integral Field Unit) RV observations– Velocity dispersion from

scatter in RVs (MOS)– Velocity dispersion from

IFU images

http://www.usm.uni-muenchen.de/people/saglia/praktikum/galspectra/node3.html

• Multi-object fiber-feed – 2dF• http://www.2dfquasar.org/Spec_Cat/gfx/2dFpic3.jpg• One fiber per galaxy• Good for measuring galaxy RVs and cluster RV dispersions

• Lots of spectra• taken

simultaneously• See atmosphere

as well as stellar/galaxy absorptions, emission lines

• Most in this image are earth’s atmospherehttp://astrobites.org/wp-content/uploads/2014/02/MOS.jpg

• Integral Field Unit (3 types shown) – feeding light to multiple spectrographs

• Resolve individual galaxies to elucidate RVs http:

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All Measure Velocity Dispersions

• Alternatively – put spectrograph slit along spiral galaxy axis (long axis)– If spiral galaxy shows a long-axis, it has some

inclination (no E7 spirals!)– If inclination angle can be deduced (from apparent

axis ratio a/b, say), can correct apparent RVs to disk circular velocities

– As a function of offset from the galaxy center, too– Holland, Ford, Rubin (1970s)

https://www.astro.virginia.edu/class/whittle/astr553/Topic05/t5_rotcurv_rubin.gif

• Convert wavelength shift to RV, correct for inclination– Mostly due to HII region emission, so spiral arms

well-represented– “Fold” curve of velocity vs offset about center

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• Lots-o-galaxies – similar ‘Rotation Curves’• Rapid rise from center• Then flattening

http://ned.ipac.caltech.edu/level5/Bothun2/Figures/rcurves.gif

Wrong Answer! (or so they/we thought)

• Add up light from luminous matter (stars)

• Compute mass enclosed to some radius

• Predict circular rotations at each radius

• Too little!• Need more matter

– dark matterBegeman, Broels and Sanders (1991)

What about our Milky Way Galaxy?

• We are in a lousy location – inside the disk, far from the center– Can’t see (at optical wavelengths) very far along

directions in the disk (~ 1 kpc).– The Sun is highly likely to be participating in the local

circular orbits of stars about the Galactic Center• Moving reference frame (Ugh)

– Maybe measure ‘Differential Rotation’ locally?• “Flat Rotation Curve” + increasing radii = differential rotation• Speed the same, distance isn’t

Jan Oort and his constants

Galactic LongitudeL

Radial VelocityOf Nearby stars

Radial Velocity of distant stars

Tangential Velocity of distant stars

0 0 0 >0

90 0 <0 0

180 0 0 <0

270 0 >0 0

360 0 0 >0

In equation form…•

Where is the angular frequency (• Also: • Can measure RV, TV for stars near the sun at

distance d• Expand to first order:

= • For small d, • Then, ; where

• Similarly, , where

• The “A” and “B” are the “Oort Constants” and can be measured from the run of RV and TV with Galactic longitude (L) for stars with known distance:

http://upload.wikimedia.org/wikipedia/commons/0/0b/Oortmeasure.jpg

• Can measure A and B from stars locally• Can also rearrange definitions of A and B to find:

And

• So, from observations, we can get 0 and its radial derivative

• The values obtained will characterize one particular rotation curve, and so (perhaps) select THE rotation curve for the Milky Way disk

• From (A-B), get R0 = 10kpc; 0 = 250 km/s

Enter Radio Astronomy• Radio wavelengths don’t suffer

the extinction seen at optical and near-infrared wavelengths

• Can ‘see’ through the entire Galactic disk

• Great! No, wait… I don’t see stars…

• ‘Clouds’ of gas (‘atomic’ if HI, ‘molecular’ if H2 – or its tracer CO)

• Complex emission spectral lines along each line of sight that goes through multiple clouds

Stack up spectra versus Longitude

Find the “Tangent Points” vs L

http:

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• Then, remap Tangent Velocities with L projection of 0 to reveal circular velocity dependence on R

• OK, but also trying to find Milky Way spiral arms – they are associated with star formation, which HI isn’t

• Survey in CO and repeat tangent analysis

• UMASS-Stony Brook CO survey of the 1980s

CO traces H2, which traces Star Formation Potential

Dame, Hartmann, & Thaddeus (2001) ApJ, 547, 792

Run of RV with L

http://inspirehep.net/record/789176/files/f1_dame.png

Covert RV vs L to (R)

Rotation curve + full CO survey = remap H2 distribution as ‘face-on’ view

Criticisms

• Dips unphysical – too fast for Keplerian

• R0, 0 now different than assumed (Reid+)

• Circular rotation assumption likely not fully correct– Spiral arms have kinematic

perturbations

• Tangent analysis doesn’t work in outer galaxy– Had to adopt other, weaker,

methods

• Others have updated with modern data

• 13CO less optically-thick than 12CO– Better at isolating clouds

and arms– Galactic Ring Survey

(Jackson+06)

HII Region Discovery Survey (Bania+)

HII Regions trace spiral arms best

http:

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Galactic Rotation: Back to the Stars• APOGEE – multi-

fiber high-resolution near-infrared spectroscopy of stars in the Milky Way– Spectral types,

luminosity classes, RVs

• GAIA – direct parallaxes, RVs for up to 1 billion stars in the Milky Way

Analysis = Bayesian (a story for another day…)

2012

Mass Models, Dark Matter, Galaxy Assemblagehttp://milkyway.cs.rpi.edu/download/images/gal_rotation_curve.png

http://www.stsci.edu/~inr/thisweek1/thisweek/cloudstream.jpg