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

The Stellar Velocity Ellipsoid σ z 2 and Multi-component Stability of Galaxy Disks σ θ Kyle B. Westfall Kapteyn Astronomical Institute, Groningen, Netherlands σ R Thursday, October 24, 2013

Outline The DiskMass σ z Survey Team • The Stellar Velocity Ellipsoid (SVE) • What is it? • Extragalactic Measurement Approach David R. Andersen (HIA) • Our Data Matthew A. Bershady (UW) • A Stepwise Approach • A Holistic Model Thomas P. K. Martinsson (Leiden) • A Tests of Accuracy Robert A. Swaters (NOAO) • Comparison with the literature σ θ Marc A. W. Verheijen (Kapteyn) • Disk (in)Stability and Star-formation Kyle B. Westfall (Kapteyn) σ R 2 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

The Stellar Velocity Ellipsoid Dehnen (1998) σ z • Ideally, we want f ( x , v ). V y - This distribution is complex in the Milky Way. • Extragalactic measurements require some simplifying assumptions. • Characterize f ( x , v ) by its σ θ V z velocity-dispersion tensor. • The SVE is its 3D surface. σ R V x 3 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE Assumptions σ z σ θ σ R 4 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE Assumptions σ z • 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) σ θ - Circular-speed from a gas-pressure correction (Dalcanton & Stilp 2010) σ R 4 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A “Simple” Approach σ 2LOS = ( σ 2R sin 2 θ + σ 2 θ cos 2 θ ) sin 2 i + σ 2z cos 2 i σ z σ LOS Gerssen & Shapiro Griffen (2012) θ (deg) • Gerssen, Shapiro Griffen, σ θ Noordermeer, et al. - 2D Kinematics ( N long-slit positions/IFU) - Rotation curve (EA) gives one axial ratio - σ maj , σ min difference gives the other σ R 5 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

Observational Data σ z DiskMass Survey “Phase-B” Sample • 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 σ θ ( Herschel ) • 1- & 3-mm Radio Synthesis of 5 ( IRAM, CARMA ) • 21-cm Radio Synthesis of all σ R ( Westerbork, VLA, GMRT ) UGC 4368 6 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

Observational Data σ z DiskMass Survey “Phase-B” Sample • 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 → I CO →Σ H2 ) • Far-IR imaging of 10 σ θ ( Herschel ) • 1- & 3-mm Radio Synthesis of 5 ( IRAM, CARMA ) • 21-cm Radio Synthesis of all σ R ( Westerbork, VLA, GMRT ) UGC 4368 7 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Stepwise Approach σ z • Disk-plane geometry - Circular rotation + TF • Azimuthally average kinematics - Impose axial symmetry • EA+AD leads to SVE σ θ σ R 8 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Stepwise Approach σ z UGC 4368 • Disk-plane geometry - Circular rotation + TF • Azimuthally average kinematics - Impose axial symmetry • EA+AD leads to SVE σ θ σ R 9 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Stepwise Approach σ z UGC 4368 • Disk-plane geometry - Circular rotation + TF • Azimuthally average kinematics - Impose axial symmetry • EA+AD leads to SVE σ θ σ R 9 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Holistic Model σ z Analytic ➡ Parametrized forms ➡ V * , σ R , α = σ z / σ R , σ g , Σ g ➡ Epicycle Approximation ➡ β = σ θ / σ R ➡ Asymmetric Drift ➡ Vc ➡ Gas Pressure Effects ➡ Vg Bayesian σ θ ➡ Parameter values and errors sampled from the Bayesian posterior σ R UGC 4368 10 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Holistic Model σ z Analytic ➡ Parametrized forms ➡ V * , σ R , α = σ z / σ R , σ g , Σ g ➡ Epicycle Approximation ➡ β = σ θ / σ R ➡ Asymmetric Drift ➡ Vc ➡ Gas Pressure Effects ➡ Vg Bayesian σ θ ➡ Parameter values and errors sampled from the Bayesian posterior σ R UGC 4368 10 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Holistic Model σ z Analytic ➡ Parametrized forms ➡ V * , σ R , α = σ z / σ R , σ g , Σ g ➡ Epicycle Approximation ➡ β = σ θ / σ R ➡ Asymmetric Drift ➡ Vc ➡ Gas Pressure Effects ➡ Vg δ GP = V c2 - V g2 Bayesian σ θ σ g2 ➡ Parameter values and errors δ AD = V g2 - V ✴ 2 sampled from the Bayesian σ ✴ 2 posterior σ R UGC 4368 11 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Test of Accuracy σ z Tests against an N-body model with Elena D’Onghia & Carlos Vera-Ciro σ θ σ R 12 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Test of Accuracy σ z Tests against an N-body model with Elena D’Onghia & Carlos Vera-Ciro σ θ σ R 12 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Test of Accuracy σ z Tests against an N-body model with Elena D’Onghia & Carlos Vera-Ciro σ θ σ R 13 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

A Test of Accuracy σ z Tests against an N-body model σ R with Elena D’Onghia & Carlos Vera-Ciro σ θ σ z Bulge Effects σ z / σ R σ θ σ θ / σ R Particle Data σ R Fit 13 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE vs. Hubble Type σ z Unbarred Weakly Barred From RC3: (S) barred (SA) (SB) σ θ σ R 14 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE vs. Hubble Type σ z Unbarred Weakly Barred From RC3: (S) barred (SA) (SB) σ θ σ R 14 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE vs. Hubble Type σ z Unbarred Weakly Barred From RC3: (S) barred (SA) (SB) σ θ σ R 14 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE vs. Hubble Type σ z Unbarred Weakly Barred From RC3: (S) barred (SA) (SB) σ θ σ R 14 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE vs. Hubble Type σ z Unbarred Weakly Barred From RC3: (S) barred (SA) (SB) σ θ σ R 14 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE vs. Hubble Type σ z Unbarred Weakly Barred From RC3: (S) barred (SA) (SB) σ θ σ R 14 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

SVE vs. Hubble Type σ z Unbarred Weakly Barred From RC3: (S) barred (SA) (SB) σ θ σ R 14 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

The Stability Criterion σ z (Toomre 1964) •Single component fluid disk •Correction for a collisionless fluid •Disk thickness corrections Wiegert 2011) (Romeo & σ θ •Two-component disk solution σ R 15 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

The Stability Criterion σ z σ θ The marginalized two-component stability at 1.5 scale lengths is Q RW = 2.0 ± 0.9 . σ R 16 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

Star-Formation Law(s) Shi+2011 σ z σ θ • Trends with SFR qualitatively consistent with theory - Σ SFR anti-correlated with Q RW (Li et al. 2006) - SFE proportional to √Σ ✴ (Ostriker et al. 2010) σ R 17 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013

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 = σ z / σ R with Hubble type is not trivial. - We find the marginalized two-component stability is Q RW = 2.0 ± 0.9 at 1.5 scale lengths. - We find disks with larger star-formation activity have lower Q RW and higher Σ ✴ , consistent with theoretical predictions. 감사합니다 18 Dynamics of Disk Galaxies 24 Oct 2013, 서울 Thursday, October 24, 2013