Six new galactic orbits of globularSix new galactic orbits of globularSix new galactic orbits of globularSix new galactic orbits of globularclusters in a Milkyclusters in a Milky--WayWay--like galaxylike galaxy

Christine Allen, Edmundo Moreno, & BChristine Allen, Edmundo Moreno, & Báárbara Pichardorbara PichardoChristine Allen, Edmundo Moreno, & BChristine Allen, Edmundo Moreno, & Báárbara Pichardorbara PichardoInstituto de Astronomía, UNAMInstituto de Astronomía, UNAM

G l ti bit f l b l l t ( ith t b )G l ti bit f l b l l t ( ith t b )Galactic orbits of globular clusters (without bar)Galactic orbits of globular clusters (without bar)

•• Keenan, Innanen & House (1973), Keenan & Innanen (1975)Keenan, Innanen & House (1973), Keenan & Innanen (1975)Keenan, Innanen & House (1973), Keenan & Innanen (1975) Keenan, Innanen & House (1973), Keenan & Innanen (1975) computed orbits for M67, NGC 188, computed orbits for M67, NGC 188, ΩΩ Cen and NGC 2420.Cen and NGC 2420.

•• Allen & Martos (1988) provided orbits for 13 globular clusters in Allen & Martos (1988) provided orbits for 13 globular clusters in li ti t ti lli ti t ti la realistic potential.a realistic potential.

•• Allen & Santillán (1993) computed orbits for a further 6 clusters.Allen & Santillán (1993) computed orbits for a further 6 clusters.•• Absolute proper motions are now available for 48+6 clustersAbsolute proper motions are now available for 48+6 clustersAbsolute proper motions are now available for 48 6 clustersAbsolute proper motions are now available for 48 6 clusters•• Galactic orbits in an axisymmetric potential have been Galactic orbits in an axisymmetric potential have been

computed (Dinescu et al. 1998, Casetticomputed (Dinescu et al. 1998, Casetti--Dinescu et al. 2007)Dinescu et al. 2007)W t d th i bit i l ti t ti l th t i l dW t d th i bit i l ti t ti l th t i l d•• We now study their orbits in a galactic potential that includes a We now study their orbits in a galactic potential that includes a bar and spiral arms(Allen, Moreno & Pichardo 2006, 2007)bar and spiral arms(Allen, Moreno & Pichardo 2006, 2007)

A model for the galactic bar (Pichardo et al 2004)A model for the galactic bar (Pichardo et al 2004)A model for the galactic bar (Pichardo et al. 2004)A model for the galactic bar (Pichardo et al. 2004)

Underlying potential of Allen & Santillán (1991), with a Underlying potential of Allen & Santillán (1991), with a bar of:bar of:bar of:bar of:

mass: 70% of the bulge mass (1 x 10mass: 70% of the bulge mass (1 x 101010 Mo)Mo)l h kl h klength: 3.5 kpclength: 3.5 kpcaxial ratio: 10:3.5:3axial ratio: 10:3.5:3angular velocity: 60 km/s/kpcangular velocity: 60 km/s/kpcg y / / pg y / / p

(Freudenreich 1998, model S)(Freudenreich 1998, model S)

Allen, Moreno &Allen, Moreno &,,Pichardo 2006,Pichardo 2006,ApJ 652, 1150ApJ 652, 1150

Allen, Moreno &Allen, Moreno &Pichardo 2006Pichardo 2006Pichardo 2006,Pichardo 2006,ApJ 652, 1150ApJ 652, 1150

J=EJ=E--ΩΩhh

CasettiCasetti--Dinescu et al. (2007) obtained absolute proper motions for 6 Dinescu et al. (2007) obtained absolute proper motions for 6 new clustersnew clusters

They calculated orbits in an axisymmetric galaxy …. hoping effect of They calculated orbits in an axisymmetric galaxy …. hoping effect of bar would be negligiblebar would be negligible

But: their clusters reside well within region of influence of barBut: their clusters reside well within region of influence of bar

So we calculated orbits in the axisymmetric and in the barred model. So we calculated orbits in the axisymmetric and in the barred model. yyWe also included spiral armsWe also included spiral arms

The axisymmetric orbits can then be compared and effects of The axisymmetric orbits can then be compared and effects of y py pdifferent models assesseddifferent models assessed

Allen Moreno &Allen Moreno &Allen, Moreno &Allen, Moreno &Pichardo 2008,Pichardo 2008,ApJ, in pressApJ, in press

AS Bar AS BarAS Bar AS Bar

J=EJ=E--ΩΩhh

J=EJ=E--ΩΩhh

Bar, last 5 GyrBar, last 5 Gyr

A model for the spiral arms (Pichardo et al. 2003, updated)A model for the spiral arms (Pichardo et al. 2003, updated)

Spiral locus approx. log, smoothly joining a straight bar Spiral locus approx. log, smoothly joining a straight bar Two arms, with pitch angle of 15.5º (Drimmel 2000), extending Two arms, with pitch angle of 15.5º (Drimmel 2000), extending

t t 12 kt t 12 kout to 12 kpcout to 12 kpcLocal ratio of radial force of arms vs. disk: 5%Local ratio of radial force of arms vs. disk: 5%(implies mass ratio of 3%)(implies mass ratio of 3%)(implies mass ratio of 3%)(implies mass ratio of 3%)Angular velocity: 20 km/s/kpcAngular velocity: 20 km/s/kpc

AS AS + bar AS AS + bar AS+spir AS+spir+barAS+spir AS+spir+bar

AS AS + bar AS+spir AS+spir+barAS AS + bar AS+spir AS+spir+bar

Tidal radii:Tidal radii:

NGC 5139 Rt at pericenters

Averagedoverorbit

(a): AS(b): bar(b): bar

Full: ASEmpty: bar

AS barTidal radii vs limiting radii (with observational uncertainties)

Mackey & van den Bergh 2005Mackey & van den Bergh 2005

Total destruction ratesTotal destruction rates

crosses: rcrosses: rminmin < 3kpc< 3kpc

Summary and conclusionsSummary and conclusions

G l ti bit h b bt i d f 48 6 l b lG l ti bit h b bt i d f 48 6 l b l•• Galactic orbits have been obtained for 48 + 6 globular Galactic orbits have been obtained for 48 + 6 globular clusters in a galaxy with a bar and with spiral arms.clusters in a galaxy with a bar and with spiral arms.

•• They are studied and compared with the orbits in twoThey are studied and compared with the orbits in twoThey are studied and compared with the orbits in two They are studied and compared with the orbits in two axisymmetric potentials.axisymmetric potentials.

•• Differences between potential models (AS) are smaller than Differences between potential models (AS) are smaller than th d t b ti l t i tith d t b ti l t i tithose due to observational uncertainties.those due to observational uncertainties.

•• Orbits of “outer” clusters (Rp > 5 kpc)Orbits of “outer” clusters (Rp > 5 kpc)almost unaffectedalmost unaffected by by bar.bar.bar.bar.

•• Those of “inner” clusters (Rp < 5 kpc) Those of “inner” clusters (Rp < 5 kpc) do change do change with bar.with bar.

Summary and conclusions (cont.)Summary and conclusions (cont.)y ( )y ( )

•• Changes: Changes: larger z, larger excursions in R, more chaoslarger z, larger excursions in R, more chaos..•• In general bar causes In general bar causes no net global changes in E, h.no net global changes in E, h.•• But: bar sometimes But: bar sometimes changes sense of rotationchanges sense of rotation of cluster.of cluster.

S i l h it ti bl ff t bitS i l h it ti bl ff t bit•• Spiral arms have quite a noticeable effect on orbits.Spiral arms have quite a noticeable effect on orbits.•• Bar Bar compatiblecompatible with observed limiting radii of globular clusters.with observed limiting radii of globular clusters.•• Observed and computed radii disagree Recently acquired?Observed and computed radii disagree Recently acquired?•• Observed and computed radii disagree …. Recently acquired?Observed and computed radii disagree …. Recently acquired?•• Clusters with Clusters with problematic tidal radiiproblematic tidal radii in the AS case fare in the AS case fare betterbetter

with a bar.with a bar.

Summary and conclusions (cont.)Summary and conclusions (cont.)y ( )y ( )

•• Calculated destruction rates are sensibly smaller than those Calculated destruction rates are sensibly smaller than those bt i d f d l ( P t )bt i d f d l ( P t )obtained from models (see Poster).obtained from models (see Poster).

Bar slows down destruction ofBar slows down destruction of cluster by bulge So bar helpsby bulge So bar helps•• Bar slows down destruction of Bar slows down destruction of cluster by bulge. So, bar helps by bulge. So, bar helps survival of clustersurvival of cluster..

Some clusters are in peril: even with the bar Pal 5, NGC 6144, NGC 6362, NGC 6522, NGC 6528 will be destroyed within the next 1010 years Without the bar also NGC 5857 NGC 6121next 1010 years. Without the bar also NGC 5857, NGC 6121

Thank you and good day!Thank you and good day!

AS + spiral AS + bar + AS + spiral AS + spiral AS + bar + AS + spiral AS +bar +AS +bar +spiral spiralspiral spiral