Kinematics of a Boxy/X-shaped Milky Way Bulge Model Yujing Qin 1 , - - PowerPoint PPT Presentation

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Kinematics of a Boxy/X-shaped Milky Way Bulge Model Yujing Qin 1 , - - PowerPoint PPT Presentation

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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

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SLIDE 1

Kinematics of a Boxy/X-shaped Milky Way Bulge Model

Yujing Qin1, Juntai Shen1, Zhao-Yu Li1, Shude Mao2, Michael Rich3, Martin C. Smith1 and Chao Liu1

1 Shanghai Astronomical Observatory, CAS 2 National Astronomical Observatories, CAS 3 UCLA

October 24, 2013

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SLIDE 2

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)

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SLIDE 3

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?

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SLIDE 4

Model: Simulation

Simulation from Shen et al. (2010) exponential disk of 106 particles in a rigid isothermal halo bar forms rapidly and thickened via the buckling instability structure gets stablized after ∼ 2.4 Gyr

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SLIDE 5

Model: Comparison with observation

Excellent match with BRAVA observation (Howard et al. 2008, 2009) Shen et al. (2010) / solid lines: model; dots: BRAVA observation

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SLIDE 6

Model: The X-shape in this model

The X-shaped structure in this model Li & Shen (2012)

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SLIDE 7

Model: The X-shape in this model

The double-peaked distance distributions in this model Li & Shen (2012)

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SLIDE 8

Model: Geometric configuration

We adopt the same geometric configuration as Shen et al. (2010) Sun 20° DGC = 8.55 kpc Bar GC Vsun Ωp,bar ~ 40 km/(s∙kpc) Near side Far side (Top View) Rbar ~ 4 kpc

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SLIDE 9

Identification of density peaks: Gaussian KDE method

Peaks are identified with Gaussian Kernel Density Estimators

4 5 6 7 8 9 10 11 12 13 Distance [kpc] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

l=2.00,b=6.00

adaptive kernel size σ based

  • n number statistics

tail-cut kernel function to avoid neighbouring lumps robust against spiky histograms

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SLIDE 10

Identification of density peaks: Peak Separation

Separation of two peaks across the bulge region:

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Separation [kpc]

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

nearly constant at the same latitude increases towards higher latitude b vanishes below |b| ∼ 2◦

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SLIDE 11

Identification of density peaks: Peak Separation

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SLIDE 12

Identification of density peaks: Distance to the Midpoint

Midpoint distance of two peaks across the bulge region:

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean Distance [kpc]

8.20 8.30 8.40 8.50 8.60 8.70 8.80 8.90

longitudinal gradient, the east (left) side is closer to the sun close to DGC at l ∼ 0◦ qualitatively consistent with the bar angle

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SLIDE 13

Kinematics at two sides

Vlos of two sides at (l, b) = (0, 6)

400 300 200 100 100 200 300 400 Velocity [km/s] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Number density [103 ]

Near Far Sun Positive (east) longitude

Far Near

Negative (west) longitude Negative (approaching) line-of-sight velocity Positive (receding) line-of-sight velocity Zero point of mean line-of-sight velocity Zero point of mean line-of-sight velocity

(Top view)

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SLIDE 14

Kinematics at two sides

µ⋆

l (= µl cos b) of two sides at (l, b) = (0, 6)

14 12 10 8 6 4 2 2 4 µl [mas/yr] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Number density [103 ] µl Near µl Far Sun Positive (east) longitude

Far Near

Negative (west) longitude “Positive” (eastward) longitudinal proper motion “Negative” (westward) longitudinal proper motion

(Top view)

Longitudinal proper motion

  • f the Galactic center:

Vsun/DGC = -5.43 mas/yr

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SLIDE 15

Kinematics at two sides

µb of two sides at (l, b) = (0, 6)

8 6 4 2 2 4 6 8 µb [mas/yr] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Number density [103 ] µb Near µb Far Sun Positive (east) longitude

Far Near

Negative (west) longitude stable vertical structure, (almost) zero mean latitudinal proper motion stable vertical structure, (almost) zero mean latitudinal proper motion

(Top view)

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SLIDE 16

Mean µ⋆

l , µb and Vlos

Mean radial velocity and its difference between two sides Near side

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean Vlos in the Near Side [km/s]

  • 80
  • 60
  • 40
  • 20

20 40 60 80

Far side

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean Vlos in the Far Side [km/s]

  • 80
  • 60
  • 40
  • 20

20 40 60 80

Difference

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Difference in Vlos [km/s]

  • 80
  • 60
  • 40
  • 20

20 40 60 80

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)

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SLIDE 17

Mean µ⋆

l , µb and Vlos

Mean µ⋆

l and its difference between two sides

Near side

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean µl in the Near side [mas/yr]

  • 4.80
  • 4.65
  • 4.50
  • 4.35
  • 4.20
  • 4.05
  • 3.90

Far side

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean µl in the Far side [mas/yr]

  • 6.50
  • 6.40
  • 6.30
  • 6.20
  • 6.10
  • 6.00
  • 5.90
  • 5.80

Difference

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Difference of Mean µl [mas/yr]

1.20 1.40 1.60 1.80 2.00 2.20 2.40

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SLIDE 18

Mean µ⋆

l , µb and Vlos

Mean µb and its difference between two sides Near side

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean µb in the Near side [mas/yr]

  • 0.40
  • 0.30
  • 0.20
  • 0.10

0.00 0.10 0.20 0.30

Far side

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean µb in the Far side [mas/yr]

  • 0.32
  • 0.24
  • 0.16
  • 0.08

0.00 0.08 0.16 0.24

Difference

5 5 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Difference of Mean µb [mas/yr]

  • 0.50
  • 0.40
  • 0.30
  • 0.20
  • 0.10

0.00 0.10 0.20 0.30

diagonal µb at both sides (bar rotation?)

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SLIDE 19

Dispersions of µ⋆

l and µb

Proper motion dispersions for Near + Far σl (Near+Far)

10 5 5 10 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean ∆σl = 0.33 (Model - Obs) Dispersion: 0.10

σl (Near + Far)

1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 3.00

Mean ∆ = 0.33 mas/yr σb (Near + Far)

10 5 5 10 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean ∆σb= 0.29 (Model - Obs) Dispersion: 0.13

σb (Near + Far)

1.65 1.80 1.95 2.10 2.25 2.40 2.55 2.70 2.85

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)

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SLIDE 20

Dispersions of µ⋆

l and µb

Cross-correlation factor σl⋆b/σ⋆

l σb and dispersion ratio σ⋆ l /σb

σl⋆b/σ⋆

l σb (Near + Far)

10 5 5 10 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean ∆[σl

b/σlσb]=-0.09 (Model - Obs)

Dispersion: 0.12

σl

b/σlσb (Near + Far)

  • 0.20
  • 0.15
  • 0.10
  • 0.05

0.00 0.05 0.10 0.15

Mean ∆ = 0.09 σ⋆

l /σb (Near + Far)

10 5 5 10 Galactic longitude [deg] 5 5 Galactic latitude [deg]

Mean ∆[σl /σb]= 0.00 (Model - Obs) Dispersion: 0.05

σl /σb (Near + Far)

1.00 1.04 1.08 1.12 1.16 1.20 1.24 1.28

Mean ∆ = 0.00 shows nice agreements in σ⋆

l /σb with Rattenbury et al. (2007)

roughly matches the trend in cross-correlation factors

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SLIDE 21

Correlations between µ⋆

l , µb and Vlos

Correlations near the peaks

200 100 100 200 VHelio [km/s]

  • 8.00
  • 6.00
  • 4.00
  • 2.00

0.00 2.00 4.00 6.00 8.00 µb [mas/yr]

µb vs. VHelio (Near) Overall Peak Distant

Is there any coherent motion inside the X-shape? Helpful to understand the orbital structure of the X-shape (see our papre in prep.)

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SLIDE 22

Pattern speed of the X-shape from ∆µ⋆

l ?

’angular speed of the bar’/X-shape from ∆µ⋆

l ?

Ω ≈ µ⋆

Sgr A∗ +

5∆µ⋆

l

10ln∆IRC ≈ µ⋆

l,GC + DGC∆µ⋆ l

∆R (1) Sun (Side View) R = DGC ΔR ≈ Separation GC

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SLIDE 23

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) (deg.) (kpc) (mas yr−1) (km s−1kpc−1) 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−1kpc−1 in this model), nor angular speed of cylindrical rotation (> 200 km s−1kpc−1 here)

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SLIDE 24

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

  • bservations.

The recently proposed method to measure the pattern speed of the bar/X-shape from ∆µl and peak separation may not work well.