Photometric and dynamical modelling of the Milky Way bar

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Photometric and dynamical modelling of the Milky Way bar

Shude Mao

Tsinghua University/NAOC

April 14, 2015@Taiwan Collaborators:

Yougang Wang, Richard Long, Juntai Shen, Liang Cao, …


!  Observed properties of barred galaxies

"  The Milky Way bar

#  Photometric modelling

$  Dynamical modelling

%  Summary and Future Outlook



! Overview: Hubble sequence of galaxies

•  2/3 of spiral galaxies host bars, especially in infrared

•  Understanding of the Milky Way bar is key to understanding

other barred galaxies in the Universe


Barred galaxies in the Universe

•  Bars are straight – rigid angular pattern speed

& no winding up due to differential rotation!

•  Bars often host dust lanes & vigorous star formation at the end of bars

NGC 1300


Rings in Barred galaxies

IC 5240

27000 ly

•  Barred galaxies often show rings of star formations

•  IC 5240 has an outer ring (~4 kpc) at the end of bar


Rings in Barred galaxies

Radius ~1000 ly

Rings are thought to be associated with resonances

in barred galaxies.


Boxy/peanut-shaped barred galaxies

•  edge-on barred galaxies often exhibit boxy or peanut shapes

•  They follow more complex kinematics



Peanut-shaped galaxy NGC 128

•  Located in a group of five galaxies.

•  External tidal origin (Li, Mao et al. 2009) or internal secular evolution?

NGC 128


X-shaped Structure

NGC 4710 by Hubble


X-shaped structure

NGC 128

•  X-shaped structure may be related to

resonant orbits


Summary: barred galaxies

•  Barred galaxies are very common '  Straight ( rigid rotation.

'  Dust lanes (gas streaming motions).

'  Rings of star formation (resonances).

•  Edge-on bars

'  exhibit as boxy, peanut-shaped or X- shaped galaxies.

'  Kinematics are more complex.

•  They likely form via internal secular (long-

term) evolution.


" The Milky Way bar

2MASS NIR images of the MW: disk + bulge


COBE map of the Milky Way bar

•  Milky Way from the space satellite COBE.

•  The asymmetric shapes implies the presence of a bar.

Dwek et al. (1995)


Top-down view of the Galaxy


Offset: 24000 ly


Robert Hurt (SSC/JPL/


The Milky Way is a beautiful SBc type galaxy


•  Bar basic parameters:

&  Bar angle

&  Bar tri-axial lengths

•  How many bars?

&  boxy/peanut bar

&  Long, thin bar

&  Super-thin bar

•  Needs tracer

populations: RR Lyrae stars, red clump giants

# Photometric modelling of the

Milky Way bar



Color Magnitude Diagram close to the Sun


•  Red clump giants are metal-rich

horizontal branch stars

•  Small intrinsic scatter in

luminosity (~0.09mag)

•  Good standard candles!

blue red




•  Observed RCG width is larger in the bulge due to the extension of the bulge.

•  Careful studies of RCGs provide a 3D map of the bar.

Bulge Color-magnitude diagrams




OGLE-III sky coverage

– 5 –

2. Data

OGLE-III observations were taken with the 1.3 meter Warsaw Telescope, located at the Las Campanas Observatory. The camera has eight 2048x4096 detectors, with a combined field of view of 0.6 ⇥ 0.6 yielding a scale of approximately 0.26


/pixel. We use observations from 263 of the 267 OGLE-III fields directed toward the Galactic Bulge, which are almost entirely within the range 10 < l < 10 and 2 < |b| < 7 . We do not use 4 of the fields, BLG200, 201, 202, and 203; located toward (l, b) ⇡ ( 11 , 3.5 ), due to the much higher di↵erential reddening and disk contamination toward those sightlines. The photometric coverage used in this work is shown in Figure 1. Of the 263 fields used, 37 are toward northern latitudes. More detailed descriptions of the instrumentation, photometric reductions and astrometric calibrations are available in Udalski (2003a), Udalski et al. (2008) and Szyma´ nski et al. (2011). OGLE-III photometry is available for download from the OGLE webpage



Fig. 1.— Coverage of the OGLE-III Galactic bulge photometric survey used in this work, overplotted on an optical image of the same area. Galactic coordinate system shown. Red squares denote OGLE-III fields used in this work, and yellow squares denote fields not used.

We also make use of data from the Two Micron All Sky Survey (2MASS, Skrutskie


Longitude (degrees)

Latitude (degrees)

OGLE-III fields Cover ~ 100 square degrees


Residual map Other surveys

2 Wegg et al.



40 20 0 20 40

10 5 0 5 10



40 20 0 20 40

10 5 0 5 10

logN(12.25<K0<12.75) [deg2]

3.2 3.5 3.8 4.1 4.4 4.7 5.0

Figure 1. In the top figure we show the surveys used in this study. We use, in order of preference, VVV in red, UKIDSS in green, and 2MASS in blue. Grey regions are those without data of sufficient depth i.e. close to the plane without VVV or UKIDSS data where 2MASS is insufficient. In the lower figure we show the surface density of stars in the Ks-band in the extinction-corrected magnitude range 12.25 < K0<12.75. Asymmetric number counts in l close to the plane are a result of non-axisymmetry due to the long bar. The star counts are smoothed with a Gaussian kernel ofs = 0.1 . Extinction is corrected using the H K colour excess as in equation (1) (i.e. K0⌘ µK+MK,RC) and data outside the colour bar range are plotted at its limit.

dynamically; the suggested length ratio is low and therefore the mutual torques are strong. It has instead been suggested that rather than two distinct bars, the long bar is the in-plane extension of the central three-dimensional boxy/peanut structure structure (Martinez- Valpuesta & Gerhard 2011; Romero-G´omez et al. 2011). One of the motivations for this study is to help resolve this controversy.

Throughout we use the terminology that the bar outside the bulge region at |l| > 10 is the long bar, regardless of the details of thickness, bar angle, or alignment with the barred bulge.

Our primary indicator of bar structure are RCGs which are core helium burning stars and provide an approximate standard candle (Stanek et al. 1994). We combine several surveys to have the widest view and the greatest possible scope on the bar density distribution.

In the Ks-band we use data from (i) the United Kingdom Infrared Deep Sky Survey (UKIDSS) Galactic Plane Survey (GPS, Lucas et al. 2008), (ii) the VVV survey (Saito et al. 2012) and, (iii) to extend the study further from the galactic plane than previous studies, we augment this with 2MASS data (Skrutskie et al. 2006). We homogenise the analysis of the surveys using a common photometric system and identify RCGs statistically in magnitude distributions rather than in colour-magnitude diagrams since this has worked well in the bulge (e.g. Nataf et al. 2013; Wegg & Gerhard 2013).

We verify our results where possible using data at 3.6µm and 4.5µm, which is significantly less affected by extinction, taken from the Galactic Legacy Mid-Plane Survey Extraordinaire (GLIMPSE) survey on the Spitzer space telescope (Benjamin et al. 2005). Be- cause this data only covers |b| . 1 we use the Ks-band as our primary data, but the GLIMPSE data remains very important for cross checks, particularly of dust extinction.

This work is organised as follows: In section 2 we describe the data and construction of magnitude distributions for the stars in bulge and bar fields. In section 3 we fit the red clump stars in these magnitude distributions and discuss the features of these fits.

In section 4 we examine the vertical structure of the fitted red clump stars in longitude slices, and in section 5 we derive densities which fit and best fit the observed magnitude distributions. We discuss our results and place them in context in section 6, and finally conclude in section 7.

2 MAGNITUDE DISTRIBUTION CONSTRUCTION A number of steps are required to combine the surveys (UKIDSS, VVV, 2MASS, GLIMPSE) and bands (H, Ks, 3.6µm, 4.5µm) and construct consistent magnitude distributions: The surveys must be transformed to the same photometric system, extinction corrected, and to compare bands and convert to distances we require the char- acteristic magnitudes and colours of RCGs.

2.1 H and Ks-band data

The first step in construction of the magnitude distributions is to transform all the surveys to the same photometric system. We choose to convert the UKIDSS and VVV surveys to the 2MASS system using the methods and transformations described in appendix A.

2.1.1 Extinction Correction

Extinction is then corrected for on a star-by-star basis assuming that all stars are red-clump giants (RCGs). We primarily work with the RCG Ks-band distance modulus,µK, where we calculate the Ks-band extinction from the H Ksreddening:


Extinction Correction

z }| {


E(H Ks)[(H Ks) (H Ks)RC]

| {z }


MKs,RC, (1)

c 2015 RAS, MNRAS000, 1–18

Views of the Milky Way combining three surveys

•  Vista Variables in the Via Lactea (VVV)

•  United Kingdom Infrared Deep Sky Survey (UKIDSS)

•  2MASS

Wegg, Gerhard &

Portail (2015)

•  Vista Variables in the Via Lactea (VVV, Saito et al.

2012; red)

•  the United Kingdom Infrared Deep Sky Survey (UKIDSS, Lucas et al. 2008; green)

•  2MASS (Skrutskie et al. 2006; blue)



Red clump giants luminosity function

For each field, we can obtain

•  luminosity function

(number as a function of brightness)

•  integrated number counts Rattenbury, Mao et al. (2007)


Number counts of red clump giants – 45 –

Fig. 20.— TOP: Surface density of RC stars toward the Galactic bulge ⌃


, as a function of direction. Values are normalized to the surface density toward Baade’s window (l = 1 , b = 3.9 ) of 45,100 RC stars deg


. BOTTOM: Distance modulus dispersion of bulge RC stars as a function of direction, after application of a 20



•  Regular elliptical contours close to the plane

•  Fit smooth tri-axial ellipsoidal models, such as

& ρ = ρ 0 exp(-r 2 /2), Gaussian model

& ρ = ρ 0 exp(-r), exponential model,

&  where r 2 =(x/x 0 ) 2 +(y/y 0 ) 2 +(z/z 0 ) 2

Nataf et al.



•  Tri-axial “exponential” density model

preferred over Gaussian (Cao, Mao et al.


&  x 0 :y 0 :z 0 =0.68kpc: 0.28kpc: 0.25kpc.

&  Close to being prolate (cigar-shaped).

&  Bar angle ~ 30 degrees (statistically very well constrained).

Photometric model of the MW


•  Most fields exhibit a single peak.

•  Double peaks are only prominent at large b.

Double peaks in RCG counts


12 13 14 15 0

200 400 600


12 13 14 15 (+3,-8)

12 13 14 15 (+5,-8)

12 13 14 15 (+7,-8) 200


(-1,-8) (-2,-8) (-4,-8) (-6,-8)

Figure 3. Luminosity functions for the red clump region of fields at various longitudes, for latitude b = −8. The bright red clump component is particularly strong on the positive longitude side, while the faint component is stronger on the negative longitude side.

12 13 14 15 0

200 400 600


12 13 14 15 (+3,+8)

12 13 14 15 (+5,+8)

12 13 14 15 (+7,+8) 200

400 600

(-1,+8) (-2,+8) (-4,+8) (-6,+8)

Figure 4. Luminosity functions for the red clump region of fields at various longitudes, for latitude b = +8. The bright red clump component is particularly strong on the positive longitude side, while the faint component is stronger on the negative longitude side.

Figures1and2suggest that the double clump might be due to the presence of two populations at two different distances. A magnitude difference of ∼0.4 at ∼8 kpc would correspond to a distance difference of ∼1.5 kpc.

We note here for the first time that in the outer bulge, along the minor axis, bright and faint RCs coexist, as if the near and far side of the bar both extend toward the minor axis.

Figure 1 demonstrates that the horizontal branch RC in the field at b = −6is significantly broader than the one of Baade’s Window at b = −4.

If the double-peaked RCs are due to the distances of the two populations, the observations immediately appear inconsistent with a single tilted bar. It is, therefore, important to ask

whether the double-peaked RCs could have resulted from stellar evolution, or due to effects other than distance.

A few points can be addressed by looking at these figures.

First of all, the double clump is real. It is not an artifact of bad photometry, such as a bad match of mosaic data, because it is present in several independent catalogs. We have checked that it is present in each of the eight chips of the WFI mosaic.

Second, the two peaks cannot be due to the RGB bump, nor the asymptotic giant branch (AGB) bump, falling close to the RC because in that case the two would also occur in Baade’s Window.

Also, as we will see in Figures 3and4, the relative strength of the two RC peaks changes dramatically with longitude, while

l=-1° b=8°


Mcwilliam & Zoccali (2010); Nataf et al. (2010)




X-shaped structure in the Milky Way


•  At high latitude fields, double peaks

•  Low latitude fields exhibit a single peak


The Milky Way’s Bar Outside the Bulge 13



Fitted Model N-body model + Besançon Disk

5 0 5

l= 40 l=





= l 04


+ Thin Bar Component

l= 40 l=





= l 04


+ Super-Thin Component

l= 40 l=





= l 04


5 0 5

1 0 1

5 0 5 5 0 5

8.0 8.5 9.0 9.5

7.5 8.0 8.5 9.0

log10SurfaceMassDensity M/kpc2 ]log10SurfaceMassDensity [M/kpc2][

Figure 14. The three upper panels show the view from the north Galactic pole of the surface mass density of the best fitting two component model described in 5.3. The lower panels show the same model observed side-on. We also add the Besanc¸on model disk density described in Robin et al. (2003) since the disk of the N-body model alone is insufficient. The left hand panels show the N-body model together with the Besanc¸on model disk. The central panels additionally include the 200pc thin bar component. The right hand panels additionally include the 40pc super-thin bar component. The bar length was measured from these images using the methods described in subsection 5.5.

We add one additional bar length measurement, Lmod. We take the difference between the face-on major and minor axis surface density profiles along the bar and fit an exponential to the long bar region. We then define the bar length as the point at which the density falls to 1/e of the exponential profile. In the case of an analytic exponential bar with a Gaussian cutoff, like our parametric long bar functions, this corresponds to defining the bar length as Ro+so.

All these methods were applied to face-on images of our densit- ies to which we added the density of the disk in the Besanc¸on model.

We show these face-on images in Fig. 14 and the resultant bar half lengths are given in Table 2. All our stated bar lengths are the half length, defined as the distance from the galactic centre to the bar end.

Before considering the bar length measurement we first return to the data near the bar end. In Fig. 15 we show histograms stacked in Galactic latitude as a function of longitude. We show both the positive and negative longitude sides to demonstrate the peak at positive longitudes is non-axisymmetric. To make the plot clearer we also subtract an exponential in µK which can be thought of as representing the background of non-RCGs. The bar is clear and well localised to l < 26 . At l > 30 while non-axisymmetry still appears it is much less significant and fainter than would be expected for the bar. In the region 26 < l < 30 the non-axisymmetric excess weakens, broadens and becomes fainter. We therefore presume that the bar ends in this region, possibly transitioning into the spiral arms. If we convert these longitudes of the bar end to a bar length assuming that the bar lies at a ⇡ 27 and that projection effects are negligible we would recover a bar half length between 4.4 and 4.8kpc.

We produced a similar plot to Fig. 15 showing just the N-body model and it is clear that the bar ceases to be significant at too low longitude. In contrast plotting the one component long bar model it is clear that the bar extends beyond the data in longitude to where

there is no non-axisymmetry in the data. For this reason we disregard the bar length measurements of these models in Table 2.

Instead the two component model is a significantly better fit to the stacked data near the bar end in Fig. 15. We show it compared to the data together with variations in which the bar was artificially lengthened and shorted by adjusting the outer cutoff by 0.5kpc. The model with an artificially shortened bar is insufficient particularly beyond l = 25 . In contrast the model with an artificially lengthened bar predicts excessive non-axisymmetry beyond l = 30 when the positive and negative latitudes have similar counts at the distance of the bar.

Because the two component model appears to reasonably fit the stacked data in Fig. 15 we consider the measurements of this model to be our fiducial bar half length. These measurements lie in the range 4.73 5.23kpc. We have repeated this process on the other N-body models finding that the variation between models is smaller than the variation between methods of measuring bar length. The one component bar length appears longer, however it is evident from Fig. 12 that this model fits poorly in the region beyond l > 30 . Therefore taking the average and standard deviation of these measurements we consider our fiducial estimated bar half length for the Milky Way to be (5.0 ± 0.2)kpc.


6.1 Continuity Between Box/Peanut Bulge and Long Bar Two lines of evidence in this work support that bar and bulge appear to be naturally connected: the angle between the Box/Peanut (B/P) Bulge and Long Bar is small, and the scale height along the bar decreases smoothly.

We find in this work that the long bar has bar angle in the rangea = (28 33) consistent with recent determinations of angle found at |l| < 10 in the B/P Bulge (e.g. Wegg & Gerhard 2013).

We find this angle by fitting the magnitude distributions through c 2015 RAS, MNRAS000, 1–18

(i)  The bar extends to l ∼ 25◦ at |b| ∼ 5◦

from the Galactic plane, and to l ∼ 30◦

at lower latitudes.

(ii)  The long bar has an angle to the line- of-sight in the range (28 − 33)◦ ,

consistent with studies of the bulge at |l|

< 10◦.

(iii)  (iii) The scale-height of RCG stars smoothly transitions from the bulge to the thinner long bar.

(iv)  (iv) There is evidence for two scale

heights in the long bar. We find a ∼ 180 pc thin bar component reminiscent of the old thin disk near the sun, and a ∼ 45 pc super-thin bar component which exists predominantly towards the bar end.

(v)  (v) Constructing parametric models for the RC magnitude distributions, we find a bar half length of 5.0 ± 0.2 kpc for the 2-component bar, and 4.6 ± 0.3 kpc for the thin bar component alone.

(vi)  the Milky Way contains

(vii)  a central box/peanut bulge which is the vertical extension of a longer, flatter bar, similar as seen in both external galaxies and N-body models.

More complexities in the outer part

Wegg, Gerhard &

Portail (2015)

•  The Galaxy may not only contain a central boxy/peanut tri-axial bar.

•  The outer part may

contain a long, thinner bar with similar bar


•  Are they dynamically



•  Kinematic data

•  Dynamical modelling techniques

$ Dynamical modelling of MW bar



Radial velocity fields of BRAVA

•  Radial velocities of 8500 red giants.

•  Radial velocity accuracy ~ 5 km/s.

•  More data available from other surveys (ARGOS).

Kunder et al. (2012)




Velocity dispersion

BRAVA Radial velocity data

-1.5(1.5 kpc




longitude latitude





+3.7 year +8.9 year

•  Two decades of microlensing surveys enabled proper motions to be measured for millions of stars (~few mas/yr).

•  HST observations enable proper motions to even higher accuracy (~ 0.2-0.6 mas/yr)

Proper motions of stars with HST

Kozlowski, Wozniak, Mao et al. (2006)


Galactic dynamics

•  Stars in galaxies are collisionless.

•  stars move in collective gravitational field with effects of star-star scattering

negligible over the Hubble time.

•  Galaxies are a sum of stars on different



•  In a Keplerian

potential, Force ~ 1/r 2

•  all orbits are closed ellipses

Orbits in spherical potentials

Loop orbit

Rosette orbit

•  Rosette orbits for a potential, Force ~ 1/r

•  eventually fills an



Orbits in 3D Stackel tri-axial potentials

short-axis (z-)

tube orbits major-axis (x-)

tube orbits box orbits

•  (Kunder et al. 2012)

From Barnes


Resonant Orbits in 3D triaxial potentials

Pretzel orbits

4:3 resonance Fish orbits

3:2 resonance

From Barnes


Chaotic orbits

•  Chaotic orbits diverges in the phase space.

•  How do we find chaotic orbits is not an easy issue!

(Wang, Athanassoula & Mao 2015, in preparation).




Orbital families in rotating bars:

x1 and x2 families of closed orbits

As viewed in the co-rotating frame


Contopoulos & Grosbol (1989)


Gas motions in a rotating bar


Bar major axis

x1 x2

Athanassoula (1992)


Typical regular orbits


Banana or Pretzel

X-shaped structure

Y ???





Z 2:1 Z

Provided by Yougang Wang


Many orbits are in fact chaotic!

Chaotic orbits


•  Schwarzschild method: orbit-based

&  Choose Φ(x), integrate orbits, fit data by weighting orbits.

•  Made-to-Measure method: particle-based

&  Choose Φ(x), integrate orbits, fit data by

changing particle weights.

Methods of orbit superposition


Schwarzschild method

•  Find the right mix of orbits to fit density and kinematics.

•  May suffer from degeneracy & stability issues.


Orbit individual particles, superimpose orbits


End of run, weight orbits to reproduce observations


Use linear / quadratic programming to determine weights


Well established, to determine black hole/galaxy masses

orbits box

long axis tube

short axis tube

+ chaotic orbits










* *



In a given potential

•  N (~10 6 ) particles are orbited

ij N



ij i los, N


i j


w v w

= v

δ δ

i=1, N j-th


•  Adjusts the weights on- the-fly to fit obs. Data

•  More flexible than

Schwarzschild method

•  Cross-check on model degeneracy


Made-to-Measure Method

(Syer & Tremaine 1996)


De Lorenzo 07, 08; Morganti &

Gerhard 12;


Dehnen 09;


Long & Mao 10, 12; Zhu et al. 14


Hunt et al. 12


Numerical Model of the Milky Way Bulge


•  Shen et al. (2010) starts with an exponential disk plus a dark matter halo.

•  Bar and buckling

instabilities form boxy/

peanut-shaped bulges.

•  We use this as the initial condition and adjusts

the particle weights to better match the





70 km/s/kpc 0


Best-fit bar pattern speed: 40 km/s/kpc Bar angle: 30 deg


Reproducing BRAVA radial velocity

Long, Mao, Wang & Shen (2012)



Constraints on the Galactic bar parameters

•  Fit both surface brightness and BRAVA radial velocities well.

•  bar pattern speed: 40 km/s/kpc, angle: 30 degrees.

•  not well constrained! Need more data!

Long, Mao, Wang & Shen (2012)

Bar angular speed

Model c hi^2

Bar angle


Effects of bars on

local velocity substructures?

Spiral arms + bar


Radial velocity tangential v elocity

Solar vicinity

Effects of the MW bar on the solar neighbourhood

Quillen et al. (2011)


Velocity substructures from LAMOST

•  We selected 13000 F&G dwarfs from LAMOST and 2MASS surveys

&  S/N>20, 100pc<z<500pc

•  Biggest sample in similar volume

&  With fainter and more distant stars

•  We use the extreme de-convolution method

&  Can better identify large-scale structures than

the wavelet method used previously

Xia, Liu, Mao et al. (2014)


Ripple 1 (1:1 ? )

Ripple 2 (2:1 ? ) New




'  Resonance due to bar or spiral arms?

'  larger DR1

sample to study radial,

metallicity dependence

Tangential v elocity

Radial velocity

Dehnen (2000)


Summary & open questions

•  Photometric modelling indicates

&  a short, exponential boxy/peanut bar with a

bar angle ~  30  degrees.

&  There  may  be  other  thinner,  longer  bars  in  the   outer  part.

•  Both the Schwarzschild and Made-­‐to-­‐Measure   methods  can  be  used  to  fit  the  data.

•  Open questions

&  How long is the bar (5kpc)?

&  How fast does the bar rotate (30 km/s/kpc)?

&  Are different components distinct in

kinematics and chemical abundances?


Future outlook

•  Lots of new data to come

&  Photometric data: OGLE-IV and VISTA


&  Kinematic data: ARGOS, APOGEE-II, OGLE

(proper motions), GAIA.

•  Much theoretical work yet to be done

&  Needs to explain new chemo-dynamical

correlations (Ness et al.) in particular.

&  Stability and degeneracy issues need to be

further explored.




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