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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
Buta
,et a
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87
• 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