1. DM in the Galaxy James Binney Oxford University TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A

2. ½ DM = ½ - ½ B Constraints on ½ The disk, inner & outer The disk, inner & outer The bar/bulge The bar/bulge Which dark halo? Which dark halo? Microlensing data Microlensing data Conclusions Conclusions

3. The disk Rotation curve Rotation curve At R<R 0 tangent v ! v c (modulo R 0, £ 0 and effects of bar & spiral arms) At R<R 0 tangent v ! v c (modulo R 0, £ 0 and effects of bar & spiral arms) From ¹ of Sgr A*, £ 0 =240 § 1(R 0 /8kpc) (Reid & Brunthaler 04) From ¹ of Sgr A*, £ 0 =240 § 1(R 0 /8kpc) (Reid & Brunthaler 04) Take R 0 =7.6 (Eisenhauer+05) ) £ 0 =229 km/s Take R 0 =7.6 (Eisenhauer+05) ) £ 0 =229 km/s

4. Outer disk For R>R 0, with only data @ b=0 need distances to tracers For R>R 0, with only data @ b=0 need distances to tracers Distance errors can suggest rising v c Distance errors can suggest rising v c Merrifield (92): if z(R), using extent in b at fixed W=v los /sin l can get v c (R) and z 1/2 (R) Merrifield (92): if z(R), using extent in b at fixed W=v los /sin l can get v c (R) and z 1/2 (R) Revisited by Olling & Merrifield (98-01) Revisited by Olling & Merrifield (98-01) Kalberla+ (07) apply to new data (LAB) ! Kalberla+ (07) apply to new data (LAB) ! v c gently rising to 20kpc v c gently rising to 20kpc evidence for a ring 13<R<18.5 kpc, M ' 2.5 £ 10 10 M ¯ evidence for a ring 13<R<18.5 kpc, M ' 2.5 £ 10 10 M ¯ Problems: (i) warp, (ii) can’t determine f(v z ) away from Sun Problems: (i) warp, (ii) can’t determine f(v z ) away from Sun Binney & Dehnen (97)

5. Local disk density Near Sun v rand ! Near Sun v rand ! ½ (R 0,0) = 0.1 § 0.01 M ¯ pc -3 (Holmberg & Flynn 00; Creze et al 98) ½ (R 0,0) = 0.1 § 0.01 M ¯ pc -3 (Holmberg & Flynn 00; Creze et al 98) Counting stars and gas (Flynn+ 06) ) § d ' 49 M ¯ pc -2,   = 1.2 § 0.2 M ¯ /L ¯ (no DM) Counting stars and gas (Flynn+ 06) ) § d ' 49 M ¯ pc -2,   = 1.2 § 0.2 M ¯ /L ¯ (no DM) Stellar motions at Galactic poles ! § (R 0,1.1kpc) = 71 § 6 M ¯ pc -2 (Kuijken & Gilmore 91; Holmberg & Flynn 04) Stellar motions at Galactic poles ! § (R 0,1.1kpc) = 71 § 6 M ¯ pc -2 (Kuijken & Gilmore 91; Holmberg & Flynn 04) Difference attributable to dark halo Difference attributable to dark halo

6. Photometry of disk Use NIR to (a) beat dust absorption, (b) be sensitive to mass-bearing stars Use NIR to (a) beat dust absorption, (b) be sensitive to mass-bearing stars COBE/DIRBE data provide unique overview – but 0.7 o resolution COBE/DIRBE data provide unique overview – but 0.7 o resolution 2MASS star counts allow more detailed work (Robin+03) 2MASS star counts allow more detailed work (Robin+03) Data consistent § (R) / exp(-R/R d ) Data consistent § (R) / exp(-R/R d ) R d ' 2.5 kpc R d ' 2.5 kpc Using § (R 0 )=49M ¯ pc -2 get M d = 4 £ 10 10 M ¯ ! £ 0 =156 km/s (only 1/2 measured acceleration & falling) Using § (R 0 )=49M ¯ pc -2 get M d = 4 £ 10 10 M ¯ ! £ 0 =156 km/s (only 1/2 measured acceleration & falling)

7. The bulge For contribution to £ 2 use GM/R 0 = (92.5 km/s) 2 For contribution to £ 2 use GM/R 0 = (92.5 km/s) 2 M = 1.4 § 0.6 £ 10 10 M ¯ (Launhardt et al 01) M = 1.4 § 0.6 £ 10 10 M ¯ (Launhardt et al 01) ! £ 0 = 181 km/s ! £ 0 = 181 km/s The dark halo has to provide The dark halo has to provide V c =(229 2 -181 2 ) 1/2 =140 km/s V c =(229 2 -181 2 ) 1/2 =140 km/s

8. Which dark halo? Dark halos ~ 1 param family (NFW to Neto+07) Dark halos ~ 1 param family (NFW to Neto+07) ½ (r)= ½ 0 /[(r/a)(1+r/a) 2 ] ½ (r)= ½ 0 /[(r/a)(1+r/a) 2 ] ½ (r 200 )=200 ½ c ½ (r 200 )=200 ½ c c=r 200 /a c=r 200 /a Log(c) ' 2.121 - 0.1 log(M 200 ) § 0.1 (Neto+07) Log(c) ' 2.121 - 0.1 log(M 200 ) § 0.1 (Neto+07) Then observables fns(M 200 ) Then observables fns(M 200 ) From v c need From v c need M 200 = 2.5 £ 10 12 M ¯ a=36.1 kpc M 200 = 2.5 £ 10 12 M ¯ a=36.1 kpc V c (max)=228 km/s ½ DM (R 0 )=1.1 £ 10 7 M ¯ kpc -3 V c (max)=228 km/s ½ DM (R 0 )=1.1 £ 10 7 M ¯ kpc -3 So DM contributes 2.2 £ 1.1 =24.2 M ¯ pc -2 to § (1.1kpc) (cf 22 § 6 from v rand ) So DM contributes 2.2 £ 1.1 =24.2 M ¯ pc -2 to § (1.1kpc) (cf 22 § 6 from v rand )

9. Density at large r Random Vs of satellites Random Vs of satellites Proper motions essential: v los ! v r, v t ! r ¹ Proper motions essential: v los ! v r, v t ! r ¹ Need also d º /dr for population Need also d º /dr for population Wilkinson & Evans (99): M(50kpc)=(5.2 to 1.9) £ 10 11 M ¯ Wilkinson & Evans (99): M(50kpc)=(5.2 to 1.9) £ 10 11 M ¯ Battaglia+(05): ¾ los falls 100 to 50 km/s at r>50 kpc; suggest low end Battaglia+(05): ¾ los falls 100 to 50 km/s at r>50 kpc; suggest low end NFW gives M(50kpc) = 5.7 £ 10 11 M ¯ NFW gives M(50kpc) = 5.7 £ 10 11 M ¯

10. Shape of dark halo? Without baryons, halos generically triaxial Without baryons, halos generically triaxial Baryons drive towards axisymmetry Baryons drive towards axisymmetry Uncertain predictions Uncertain predictions Should be able to probe with tidal streams Should be able to probe with tidal streams Conflicting results to date Conflicting results to date SDSS should transform the situation SDSS should transform the situation

11. Microlensing Measures mass in stars only Measures mass in stars only ¿ = P(lensed) ~ 10 -6 towards GC and ~10 -7 outwards ¿ = P(lensed) ~ 10 -6 towards GC and ~10 -7 outwards So need rich target starfields – bulge and Magellanic clouds So need rich target starfields – bulge and Magellanic clouds Major problems: “blending” & intrinsic stellar variability Major problems: “blending” & intrinsic stellar variability

12. LMC lensing –Given blending, best interpreted as upper limits –<20% of ¿ expected if DM stellar; excludes masses down to 10 -7 M ¯ – ¿ LMC =1 £ 10 -7 (Alcock+00, Bennett 05); 1.5 £ 10 -8 (EROS: Jetzer 04) – ¿ possibly compatible with known stars (Evans & Belokurov)

13. Bulge microlensing Consider only lensing of clump giants (V<18) Consider only lensing of clump giants (V<18) Basel model (based on IR photometry, kinematics & dynamics of gas and stars) Basel model (based on IR photometry, kinematics & dynamics of gas and stars) Strongly non-axisymmetric © required; hard to generate non-circular motions of required magnitude Strongly non-axisymmetric © required; hard to generate non-circular motions of required magnitude So model has no DM ! ¿ -map and durations So model has no DM ! ¿ -map and durations Durations consistent with reasonable stellar mass function Durations consistent with reasonable stellar mass function If NFW added, must reduce predicted ¿ If NFW added, must reduce predicted ¿ Very tight budget, zero room for obs ¿ to be over- estimated Very tight budget, zero room for obs ¿ to be over- estimated

14. Fine structure ~20% of mass in substructures ~20% of mass in substructures Low prob of our being in one Low prob of our being in one Key question: depth of troughs in “smooth” background Key question: depth of troughs in “smooth” background Way beyond resolution of existing N- bodies Way beyond resolution of existing N- bodies

15. Conclusions Rotation curve of MW well determined inside R 0 Rotation curve of MW well determined inside R 0 At R À R 0 situation confused At R À R 0 situation confused At R<R 0 MW baryon-dominated At R<R 0 MW baryon-dominated Near Sun data consistent with expected DM halo Near Sun data consistent with expected DM halo At R ¿ R 0 non-circular motions constrain contribution of axisymmetric component; microlensing ¿ only slightly overpredicted when all matter stellar, but probably room for cosmologically favoured dark halo At R ¿ R 0 non-circular motions constrain contribution of axisymmetric component; microlensing ¿ only slightly overpredicted when all matter stellar, but probably room for cosmologically favoured dark halo