Outline The DiskMass z Survey Team The Stellar Velocity - - PowerPoint PPT Presentation

Kyle B. Westfall

Kapteyn Astronomical Institute, Groningen, Netherlands

The Stellar Velocity Ellipsoid and Multi-component Stability

• f Galaxy Disks

σz σθ σR

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Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE Assumptions

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Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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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Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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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σLOS θ (deg)

Gerssen & Shapiro Griffen (2012)

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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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)

6 UGC 4368

DiskMass Survey “Phase-B” Sample

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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A Stepwise Approach

• Disk-plane geometry
• Circular rotation + TF
• Azimuthally average

kinematics

• Impose axial symmetry
• EA+AD leads to SVE

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

9

UGC 4368

• Disk-plane geometry
• Circular rotation + TF
• Azimuthally average

kinematics

• Impose axial symmetry
• EA+AD leads to SVE

A Stepwise Approach

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

A Holistic Model

10 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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

A Holistic Model

10 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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

11 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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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

A Test of Accuracy

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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

A Test of Accuracy

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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A Test of Accuracy

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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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A Test of Accuracy

Bulge Effects

σR σθ σz σz/σR σθ/σR

Particle Data Fit Tests against an N-body model with Elena D’Onghia & Carlos Vera-Ciro

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE vs. Hubble Type

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From RC3: Unbarred (S) Barred (SB) Weakly barred (SA)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE vs. Hubble Type

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From RC3: Unbarred (S) Barred (SB) Weakly barred (SA)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE vs. Hubble Type

14

From RC3: Unbarred (S) Barred (SB) Weakly barred (SA)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE vs. Hubble Type

14

From RC3: Unbarred (S) Barred (SB) Weakly barred (SA)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE vs. Hubble Type

14

From RC3: Unbarred (S) Barred (SB) Weakly barred (SA)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE vs. Hubble Type

14

From RC3: Unbarred (S) Barred (SB) Weakly barred (SA)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

SVE vs. Hubble Type

14

From RC3: Unbarred (S) Barred (SB) Weakly barred (SA)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

• Single component fluid disk
• Correction for a collisionless fluid
• Disk thickness corrections
• Two-component disk solution

The Stability Criterion

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(Toomre 1964) (Romeo & Wiegert 2011)

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

The Stability Criterion

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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

σz σθ σR

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

Thursday, October 24, 2013

Dynamics of Disk Galaxies 24 Oct 2013, 서울

Conclusions

We 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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감사합니다

Thursday, October 24, 2013