Defining the Milky Way Rotation Curve using Open Clusters

Transcription

1 Aufbau der Galaxis II SS2013 Defining the Milky Way Rotation Curve using Open Clusters Kieran Leschinski

2 Overview Galactic Rotation 101 The Tangent Point Method using HI clouds Rotation Curve using Open Clusters Results; old and new Curious coincident

3 Galactic Rotation 101 Two ways to support a galaxy against gravitational collapse: 1) Pressure due to random stellar motions Requires spherical symmetry (Ellipticals, Globulars) 2) Centripital force, ie rotational Flinging - Requires codirectional rotation in a plane (Spirals) ω Cen - M104 - Hubble Heritage Team

4 Why is the rotation curve important?

5 Why is the rotation curve important?

6 Measuring the Rotation Curve Known Quantities: Galactic londitude, l Observables: Distance and velocities, d, Vr, Vt Spectral doppler shift: Vobs,r = Adsin(2l) Proper motion: Vobs,t = Adcos(2l) + Bd Derivables: Oort's constants, A, B and ω0, dω0/dr0 Angular velocity: ω0 = A B Slope of Angular Velocity: dω0/dr0 = A B

7 Rotation Curve using HI clouds R0 = 8.5 kpc Clemens et al., 1985 ApJ 295, 422

8 HI Tangent point method Validity R < Ro R 0 or 180 VT = V0 sin(l) + Vlos

9 HI Tangent point method Assumptions Flat rotation curve angular speed decreases with distance Cloud with highest velocity is located at the tangent point, ie V=VT Sources of Error Variation in HI velocity up to 20km/s due to spiral arms Impossible to know exact distances from HI

10 Using Open Cluster Velocities JHK False colour image from the VISTA survey -

11 Advantages of using Open Clusters Easy to determine distance from the Sun Many data points allow determination of mean cluster velocity Proper and Radial Motions already available for many stars known Open Clusters Not limited to inside R0 J Hron, 1987

12 Determining mean velocity of a Cluster (J. Hron, 1986) Dcluster = Σwidi Σdi Σwivr,i Vcluster,r = Σvr,i W weighting is equal to the number of spectra for each star

13 Determining the Galactic Rotation Curve Iterative process needed to compensate for Solar Motion 1) Preliminary rotation (R, v) using literature values for (u0,v0,w0) rv(lsr,u0,v0,w0) R0sin(l)cos(b) = v/r v/r0

14 Determining the Galactic Rotation Curve Iterative process needed to compensate for Solar Motion 1) Preliminary rotation (R, v) using literature values for (u0,v0,w0) rv(lsr,u0,v0,w0) R0sin(l)cos(b) = v/r v/r0 2) Determine accurate values for (u0,v0,w0) and hence accurate LSR (R0,v0) rv(obs) = u0cos(l)cos(b) v0sin(l)cos(b) w0sin(b) 2(A(R-R0)+α(R-R0)2)sin(l)cos(b) + K

15 Determining the Galactic Rotation Curve Iterative process needed to compensate for Solar Motion 1) Preliminary rotation (R, v) using literature values for (u0,v0,w0) rv(lsr,u0,v0,w0) R0sin(l)cos(b) = v/r v/r0 2) Determine accurate values for (u0,v0,w0) and hence accurate LSR (R0,v0) rv(obs) = u0cos(l)cos(b) v0sin(l)cos(b) w0sin(b) 2(A(R-R0)+α(R-R0)2)sin(l)cos(b) + K 3) Rotation curve relative to LSR (R0,v0) rv(lsr,u0,v0,w0) R0sin(l)cos(b) = v/r v/r0

16 Rotation Curve for R=[5.5, 13.5] kpc Rotation curve is well constrained outside R0 R=5.5kpc R=13.5 kpc J Hron, 1987

17 Rotation Curve for R=[5.5, 13.5] kpc Rotation curve is well constrained outside R0 R=5.5kpc R=13.5 kpc Clemens 1985, J Hron, 1987

18 Most recent Galactic Rotation Curve Lotkin and Popova (2012) Catalogue of 434 Open Clusters for R=5kpc to R=15kpc Up to 40% rejection outliers in Clusters' sample Used HI to constrain curve for inner galaxy. No single statistical distribution to quantify outliers means: Outliers are random ω0 = 24.5 km/s/kpc

19 Most recent Galactic Rotation Curve Lotkin and Popova (2012) Their conclusion: Rotation curve NOT increasing in outer regions. Previously seen rise explained through influence of random errors 2σ error corridor All clusters Selected clusters

20 More recent Galactic Rotation Curve Bobylev (2007) R-Ro < 2.5 kpc R-Ro < 5 kpc Concluded earlier by Bobylev et al (2007) when comparing clusters inside 2.5 kpc and 5 kpc of R0 (R0=7.4kpc) Second order rotation term (-4α=R0(dω/dR)Ro) plays a significant role

21 How things have changed over time In the last 20 year, the constants have been getting smaller

22 Conclusions Open Cluster help to constrain the outer galactic rotation curve Only young cluster are useful to determine rotation curve Open clusters confirm v0 220 km/s Recent surveys are disputing the rise in rotational velocity at R > 15 kpc

23 Back of the envelope calculation Assuming only the v0 component is constant and u0 and w0 oscillate around R0=8.5 kpc, where was the Sun born relative to the current LSR? Distance travelled by Sun from birth place u0 = 10 km/s tsun = 5 Gyr x π x 107 s/yr = 5π x 1016 s dsun = 10 km/s x 5π x 1016 s = 5π x 1017 km LSR -u0=10km/s = 5π x 1017 km / 3 x 1016 kpc/km = 52 kpc Circumfrence of LSR circle 2πR0 = 6.28 x 8.5 kpc = 53 kpc

24 References: Clemens, D; 1985; Massachusetts-Stony Brook Galactic plane CO survey - The Galactic disk rotation curve; ApJ vol. 295, p , Hron, J; 1987; Kinematics of young open clusters and the rotation curve of our Galaxy; AandA, vol. 176, no. 1, p Lotkin, A and Popova M; 2012; Rotation curve of the Galaxy from the motions of open star clusters; AApTr, vol 27, p Frinchaboy, P and Majewski, S; 2005; Determination of the Galactic Rotation using Open Star Clusters: Preliminary Results; arxiv:astro-ph/ v1 31 Aug 2005 Bobylev, V et al; Galactic Rotation Parameters from Data on Open Star Clusters; Astronomy Letters, 2007, Vol 33, No 11, p Homna, M and Sofue, Y; 1997; Rotation Curve of the Galaxy; PASJ Vol 49, p Blitz, L and Fich, M; 1982, Catalog of CO Radial Velocities towards Galactic HII Regions; ApJ Sup 49, p Oort, J; 1927; Additional notes concerning the rotation of the galactic system; BAN Vol 4, p 91 Oort, J; 1927; Investigations concerning the rotational motion of the galactic system etc.; BAN Vol 4, p 79 Morgan, H and Oort, J; A new determination of the precession and the constants of galactic rotation; BAN Vol 11, p 379 For individual picture references, please see individual slides

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