The Stellar Velocity Ellipsoid and Multi-component Stability of...

Kyle B. WestfallKapteyn Astronomical Institute, Groningen, Netherlands

The Stellar Velocity Ellipsoidand Multi-component Stabilityof Galaxy Disks

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Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

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Outline

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David R. Andersen (HIA)

Matthew A. Bershady (UW)

Thomas P. K. Martinsson (Leiden)

Robert A. Swaters (NOAO)

Marc A. W. Verheijen (Kapteyn)

Kyle B. Westfall (Kapteyn)

The DiskMass Survey Team

• The Stellar Velocity Ellipsoid (SVE)• What is it?• Extragalactic Measurement Approach• Our Data• A Stepwise Approach • A Holistic Model• A Tests of Accuracy• Comparison with the literature

• Disk (in)Stability and Star-formation



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The Stellar Velocity Ellipsoid

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• Ideally, we want f (x,v).- This distribution is complex in

the Milky Way.

• Extragalactic measurements require some simplifying assumptions.

• Characterize f (x,v) by its velocity-dispersion tensor.

• The SVE is its 3D surface.

Vx

Vy

Vz

Dehnen (1998)



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SVE Assumptions

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SVE Assumptions

• Galaxy is steady-state, axially symmetric.

• No strong streaming motions.

• Eigenvectors of velocity-dispersion tensor aligned with {R,θ,z}. (No vertex deviations)

• First-order dynamical equations hold:- Epicycle Approximation (EA)

- Simplified Asymmetric Drift Equation (AD)

- Circular-speed from a gas-pressure correction (Dalcanton & Stilp 2010)

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A “Simple” Approach

•Gerssen, Shapiro Griffen, Noordermeer, et al.- 2D Kinematics (N long-slit positions/IFU)

- Rotation curve (EA) gives one axial ratio

- σmaj, σmin difference gives the other

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σ LO

S

θ (deg)

Ger

ssen

& S

hapi

ro G

riffe

n (2

012)

σ2LOS = (σ2R sin2θ + σ2θ cos2θ) sin2i + σ2z cos2i



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Observational Data

• Sample size: 40 Sa-Sd galaxies• Integral-field Spectroscopy of all

(WIYN,CAHA)• Optical NIR/Imaging of all

(KPNO 2.1m, SDSS, 2MASS)• Mid-IR imaging of all

(Spitzer)• Far-IR imaging of 10

(Herschel)• 1- & 3-mm Radio Synthesis of 5

(IRAM, CARMA)• 21-cm Radio Synthesis of all

(Westerbork, VLA, GMRT)

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UGC 4368

DiskMass Survey“Phase-B” Sample



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Observational Data

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• Sample size: 30 Sa-Sd galaxies• Integral-field Spectroscopy of

all (WIYN,CAHA)• Optical NIR/Imaging of all

(KPNO 2.1m, SDSS, 2MASS)• Mid-IR imaging of all

(Spitzer; 24µm→ICO→ΣH2)• Far-IR imaging of 10

(Herschel)• 1- & 3-mm Radio Synthesis of 5

(IRAM, CARMA)• 21-cm Radio Synthesis of all

(Westerbork, VLA, GMRT)

DiskMass Survey “Phase-B” Sample

UGC 4368



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A Stepwise Approach

• Disk-plane geometry- Circular rotation + TF

• Azimuthally average kinematics- Impose axial symmetry

• EA+AD leads to SVE



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UGC 4368 • Disk-plane geometry- Circular rotation + TF

• Azimuthally average kinematics- Impose axial symmetry

• EA+AD leads to SVE

A Stepwise Approach



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A Holistic Model

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UGC 4368

Analytic➡ Parametrized forms

➡ V*, σR, α=σz/σR, σg, Σg➡ Epicycle Approximation

➡ β=σθ/σR➡ Asymmetric Drift

➡ Vc➡ Gas Pressure Effects

➡ Vg

Bayesian➡ Parameter values and errors

sampled from the Bayesian posterior



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UGC 4368

Analytic➡ Parametrized forms

➡ V*, σR, α=σz/σR, σg, Σg➡ Epicycle Approximation

➡ β=σθ/σR➡ Asymmetric Drift

➡ Vc➡ Gas Pressure Effects

➡ Vg

Bayesian➡ Parameter values and errors

sampled from the Bayesian posterior

A Holistic Model

δAD= Vg2-V✴2

σ✴2

δGP= Vc2-Vg2

σg2



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Tests against an N-body modelwith Elena D’Onghia & Carlos Vera-Ciro

A Test of Accuracy



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A Test of AccuracyTests against an N-body model

with Elena D’Onghia & Carlos Vera-Ciro



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A Test of Accuracy

Bulge Effects

σ Rσ θ

σ zσ z

/σR

σ θ/σ

R Particle Data

Fit

Tests against an N-body modelwith Elena D’Onghia & Carlos Vera-Ciro



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SVE vs. Hubble Type

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From RC3: Unbarred (S)

Barred (SB)

Weakly barred (SA)



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• Single component fluid disk

• Correction for a collisionless fluid

• Disk thickness corrections

• Two-component disk solution

The Stability Criterion

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(Too

mre

196

4)(R

omeo

&

Wie

gert

2011

)



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The Stability Criterion

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The marginalized two-component stability at 1.5 scale lengths is QRW = 2.0 ± 0.9.



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Star-Formation Law(s)

• Trends with SFR qualitatively consistent with theory

- ΣSFR anti-correlated with QRW (Li et al. 2006)

- SFE proportional to √Σ✴ (Ostriker et al. 2010)

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Shi+2011



ConclusionsWe have developed a holistic, Bayesian approach to modeling the SVE in the disks using our two-dimensional data.- The approach fairs very well when tested against an

“observed” N-body simulation.

- We find results consistent with previous measurements, but find that the trend of α=σz/σR with Hubble type is not trivial.

- We find the marginalized two-component stability is QRW = 2.0 ± 0.9 at 1.5 scale lengths.

- We find disks with larger star-formation activity have lower QRW and higher Σ✴, consistent with theoretical predictions.

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The Stellar Velocity Ellipsoid and Multi-component Stability of...

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