Kinematics of a Boxy/X-shaped Milky Way Bulge Model Yujing Qin 1 , Juntai Shen 1 , Zhao-Yu Li 1 , Shude Mao 2 , Michael Rich 3 , Martin C. Smith 1 and Chao Liu 1 1 Shanghai Astronomical Observatory, CAS 2 National Astronomical Observatories, CAS 3 UCLA October 24, 2013
The peanut/X-shaped Milky Way bulge The Milky Way bulge is . . . peanut-shaped due to its bar nature, formed mainly via internal processes, associated with a vertical X-shaped structure . Nataf et al. (2010); McWilliam & Zoccali (2010); Saito et al. (2011); Wegg & Gerhard (2013), etc. McWilliam & Zoccali (2010)
The peanut/X-shaped Milky Way bulge Next decade: Great harvest of data & giant leap in the MW dynamics How do we understand the forthcoming results?
Model: Simulation Simulation from Shen et al. (2010) exponential disk of 10 6 particles in a rigid isothermal halo bar forms rapidly and thickened via the buckling instability structure gets stablized after ∼ 2 . 4 Gyr
Model: Comparison with observation Excellent match with BRAVA observation (Howard et al. 2008, 2009) Shen et al. (2010) / solid lines: model; dots: BRAVA observation
Model: The X-shape in this model The X-shaped structure in this model Li & Shen (2012)
Model: The X-shape in this model The double-peaked distance distributions in this model Li & Shen (2012)
Model: Geometric configuration We adopt the same geometric configuration as Shen et al. (2010) Near side Far side V sun R bar ~ 4 kpc GC 20° Sun D GC = 8.55 kpc Bar (Top View) Ω p,bar ~ 40 km/(s∙kpc)
Identification of density peaks: Gaussian KDE method Peaks are identified with Gaussian Kernel Density Estimators l=2.00,b=6.00 0.45 0.40 0.35 adaptive kernel size σ based 0.30 on number statistics 0.25 tail-cut kernel function to 0.20 avoid neighbouring lumps 0.15 robust against spiky 0.10 histograms 0.05 0.00 4 5 6 7 8 9 10 11 12 13 Distance [kpc]
Identification of density peaks: Peak Separation Separation of two peaks across the bulge region: Separation [kpc] 2.25 2.00 5 nearly constant at the 1.75 same latitude Galactic latitude [deg] 1.50 1.25 0 increases towards higher 1.00 latitude b 0.75 0.50 5 vanishes below | b | ∼ 2 ◦ 0.25 5 0 5 Galactic longitude [deg]
Identification of density peaks: Peak Separation
Identification of density peaks: Distance to the Midpoint Midpoint distance of two peaks across the bulge region: Mean Distance [kpc] 8.90 longitudinal gradient, 5 8.80 the east (left) side is Galactic latitude [deg] 8.70 closer to the sun 8.60 0 close to D GC at l ∼ 0 ◦ 8.50 8.40 qualitatively consistent 5 8.30 with the bar angle 8.20 5 0 5 Galactic longitude [deg]
Kinematics at two sides V los of two sides at ( l , b ) = (0 , 6) Zero point of mean Positive (receding) line-of-sight velocity line-of-sight velocity 0.16 Near 0.14 Far Far 0.12 Number density [ 10 3 ] Near 0.10 0.08 Negative (approaching) 0.06 Zero point of mean line-of-sight velocity line-of-sight velocity 0.04 0.02 0.00 400 300 200 100 0 100 200 300 400 Positive (east) Negative (west) Velocity [km/s] longitude longitude Sun (Top view)
Kinematics at two sides µ ⋆ l (= µ l cos b ) of two sides at ( l , b ) = (0 , 6) “Negative” (westward) 0.16 longitudinal proper motion µ l Near 0.14 µ l Far 0.12 Far Number density [ 10 3 ] Near 0.10 0.08 “Positive” (eastward) 0.06 longitudinal proper motion 0.04 Longitudinal proper motion of the Galactic center: 0.02 V sun /D GC = -5.43 mas/yr 0.00 Positive (east) Negative (west) 14 12 10 8 6 4 2 0 2 4 longitude longitude µ l [mas/yr] Sun (Top view)
Kinematics at two sides µ b of two sides at ( l , b ) = (0 , 6) stable vertical structure, 0.16 (almost) zero µ b Near mean latitudinal proper motion 0.14 µ b Far 0.12 Far Number density [ 10 3 ] Near 0.10 0.08 stable vertical structure, 0.06 (almost) zero mean latitudinal proper motion 0.04 0.02 0.00 Positive (east) Negative (west) 8 6 4 2 0 2 4 6 8 longitude longitude µ b [mas/yr] Sun (Top view)
Mean µ ⋆ l , µ b and V los Mean radial velocity and its difference between two sides Near side Far side Difference Mean V los in the Near Side [km/s] Mean V los in the Far Side [km/s] Difference in V los [km/s] 80 80 80 60 60 60 5 5 5 40 40 40 Galactic latitude [deg] Galactic latitude [deg] Galactic latitude [deg] 20 20 20 0 0 0 0 0 0 -20 -20 -20 -40 -40 -40 5 5 5 -60 -60 -60 -80 -80 -80 5 0 5 5 0 5 5 0 5 Galactic longitude [deg] Galactic longitude [deg] Galactic longitude [deg] V los basically features cylindrical rotation no prominent minimum in ∆ V los related to the X-shape, different from the claim in Gardner et al. (2013)
Mean µ ⋆ l , µ b and V los Mean µ ⋆ l and its difference between two sides Near side Far side Difference Mean µ l in the Near side [mas/yr] Mean µ l in the Far side [mas/yr] Difference of Mean µ l [mas/yr] -5.80 -3.90 2.40 -5.90 5 5 5 -4.05 2.20 Galactic latitude [deg] Galactic latitude [deg] -6.00 Galactic latitude [deg] -4.20 2.00 -6.10 0 -4.35 0 0 1.80 -6.20 -4.50 -6.30 1.60 -4.65 5 5 5 -6.40 1.40 -4.80 -6.50 1.20 5 0 5 5 0 5 5 0 5 Galactic longitude [deg] Galactic longitude [deg] Galactic longitude [deg]
Mean µ ⋆ l , µ b and V los Mean µ b and its difference between two sides Near side Far side Difference Mean µ b in the Near side [mas/yr] Mean µ b in the Far side [mas/yr] Difference of Mean µ b [mas/yr] 0.24 0.30 0.30 0.16 0.20 5 5 5 0.20 0.10 0.08 Galactic latitude [deg] 0.10 Galactic latitude [deg] Galactic latitude [deg] 0.00 0.00 0.00 0 0 0 -0.10 -0.10 -0.08 -0.20 -0.20 -0.16 -0.30 -0.30 5 5 5 -0.40 -0.24 -0.40 -0.50 -0.32 5 0 5 5 0 5 5 0 5 Galactic longitude [deg] Galactic longitude [deg] Galactic longitude [deg] diagonal µ b at both sides (bar rotation?)
Dispersions of µ ⋆ l and µ b Proper motion dispersions for Near + Far σ l (Near+Far) σ b (Near + Far) σ l (Near + Far) σ b (Near + Far) 2.85 3.00 2.70 2.85 5 5 2.55 Galactic latitude [deg] Galactic latitude [deg] 2.70 2.40 2.55 2.25 0 0 2.40 2.10 2.25 1.95 2.10 1.80 5 5 1.95 1.65 Mean ∆ σ l = 0.33 (Model - Obs) Mean ∆ σ b = 0.29 (Model - Obs) 1.80 Dispersion: 0.13 Dispersion: 0.10 5 5 10 5 0 5 10 10 0 10 Galactic longitude [deg] Galactic longitude [deg] Mean ∆ = 0 . 33 mas / yr Mean ∆ = 0 . 29 mas / yr matches the observed trend (Rattenbury et al. 2007, boxes) model prefers slightly higher values than observations (∆ σ ∼ 0 . 3 mas / yr )
Dispersions of µ ⋆ l and µ b Cross-correlation factor σ l ⋆ b /σ ⋆ l σ b and dispersion ratio σ ⋆ l /σ b σ l ⋆ b /σ ⋆ l σ b (Near + Far) σ ⋆ l /σ b (Near + Far) b /σ l σ b (Near + Far) σ l /σ b (Near + Far) σ l 0.15 1.28 5 5 0.10 1.24 Galactic latitude [deg] Galactic latitude [deg] 0.05 1.20 0.00 1.16 0 0 -0.05 1.12 -0.10 1.08 5 5 -0.15 1.04 Mean ∆[ σ l b /σ l σ b ] =-0.09 (Model - Obs) -0.20 Mean ∆[ σ l /σ b ] = 0.00 (Model - Obs) Dispersion: 0.12 Dispersion: 0.05 1.00 10 5 0 5 10 10 5 0 5 10 Galactic longitude [deg] Galactic longitude [deg] Mean ∆ = 0 . 09 Mean ∆ = 0 . 00 shows nice agreements in σ ⋆ l /σ b with Rattenbury et al. (2007) roughly matches the trend in cross-correlation factors
Correlations between µ ⋆ l , µ b and V los Correlations near the peaks µ b vs. V Helio (Near) 8.00 Overall 6.00 Peak Distant Is there any coherent motion inside 4.00 the X-shape? 2.00 µ b [mas/yr] 0.00 Helpful to understand the orbital structure of the X-shape -2.00 -4.00 (see our papre in prep.) -6.00 -8.00 200 100 0 100 200 V Helio [km/s]
Pattern speed of the X-shape from ∆ µ ⋆ l ? ’angular speed of the bar’ /X-shape from ∆ µ ⋆ l ? 5∆ µ ⋆ l , GC + D GC ∆ µ ⋆ l l Ω ≈ µ ⋆ Sgr A ∗ + ≈ µ ⋆ (1) 10 ln ∆ I RC ∆ R ΔR ≈ Separation (Side View) Sun GC R = D GC
Pattern speed of the X-shape from ∆ µ ⋆ l ? ’angular speed of the bar’ /X-shape from ∆ µ ⋆ l ? Lat. Separation ∆ µ ⋆ l (Peak) Ω (Peak) ( mas yr − 1 ) ( km s − 1 kpc − 1 ) ( deg . ) ( kpc ) 4.00 1.07 2.37 120 . 14 ± 37 . 55 4.50 1.28 2.38 105 . 36 ± 30 . 05 5.00 1.53 2.48 96 . 07 ± 24 . 75 5.50 1.63 2.52 92 . 92 ± 22 . 90 6.00 1.81 2.58 87 . 89 ± 20 . 36 6.50 2.02 2.49 80 . 12 ± 18 . 04 7.00 2.16 2.40 75 . 36 ± 16 . 66 probably NOT , neither pattern speed of the X-shape ( ∼ 40 km s − 1 kpc − 1 in this model), nor angular speed of cylindrical rotation ( > 200 km s − 1 kpc − 1 here)
Summary We gave predictions on the kinematics of the X-shaped component toward the galactic center with a self-consistent N-body model, we studied the double-peak feature in the distance distributions across the bulge region; we predicted the detailed proper motion and radial velocity across the bulge field, the results are broadly consistent with existing observations. The recently proposed method to measure the pattern speed of the bar/X-shape from ∆ µ l and peak separation may not work well.
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