Dark Matter Halo of the Milky Way Dynamical

Dark Matter Halo of the Milky Way • Dynamical Mass inside Sun’s orbit: • “Oort limit” => Dark Matter not in disc • Spherical DM halo model : • Enclosed mass : • Flat rotation curve : V = V 0 (Enclosed mass M( R ) diverges) • Local density of DM halo : AS 2001 Galactic Astronomy

MACHOs and WIMPs • Rotation curve V( R ) = > Mass distribution of DM halo : • Two types of DM (Astrophysics vs Particle Physics) : • MACHOs (MAssive Compact Halo Objects) • • Black holes Neutron stars Brown dwarfs Planets m > 3 Msun ( typically 10 -30 Msun ) m ~ 1. 4 Msun m < 0. 08 Msun m ~ 10 -3 to 10 -5 Msun • WIMPs (Weakly Interacting Massive Particles) • Neutrinos ( mass too low, also too “hot”, V ~ c > Vesc ) • Super-symmetric particles ? Axions ? ? • ( WIMP hunt ongoing with deep mine detectors, LHC ) AS 2001 Galactic Astronomy

How to find MACHOs? Microlensing • Gravitational lens: MACHO background star sun • Einstein : light rays bend when passing by a mass V • Bend angle : AS 2001 q r m Galactic Astronomy

Point Mass Gravitational Lens Strong Negative Spherical Aberration ! RE RE Observer’s View: on axis : Einstein Ring AS 2001 Radius RE Galactic Astronomy

Point Mass Gravitational Lens r+ r- Observer’s View off axis : 2 distorted images AS 2001 at r+ and r- Galactic Astronomy

Gravitational Optics f • Focal length f : Parallel rays in r q I O • Einstein Ring radius RE : object lens Maximum RE at x = 0. 5 AS 2001 Galactic Astronomy image

Perfect Alignment : Einstein Ring • Perfect Alignment : • Object appears as a ring of • radius RE around the lens RE Ring image of background star • For a MACHO half-way to Galactic Centre : d = R 0 , x = 0. 5 • Too small to resolve, even with HST’s 0. 05 arcsec resolution. AS 2001 Galactic Astronomy

MACHO bending too small to resolve We can see galaxy-galaxy lensing: RE = few arcsec for galaxy-galaxy lensing Shows that these galaxies also have a Dark Matter halo AS 2001 Galactic Astronomy

Gravitational Lensing by a Galaxy Cluster RE = few arcmin for lensing by a galaxy cluster Probes the Dark Matter halo of the Galaxy Cluster AS 2001 Galactic Astronomy

AS 2001 Galactic Astronomy

MACHO Lightcurve Observations AS 2001 Galactic Astronomy

Imperfect Alignment : Two Images q • Star appears shifted by q 1 • Bend angle : q = q 1 + q 2 q 1 q 2 object O r r 0 I lens • Quadratic equation now gives 2 roots for the positions of 2 images AS 2001 Galactic Astronomy image

Two Images : Magnification A( u ) • 2 images on opposite sides of lens. • Major/minor image outside/inside RE • Image positions : r 0 r+ • • RE r- Azimuthal width stretched by factor : Radial width squashed by factor : Surface brightness conserved Magnification factor A(u) is ratio of image areas : AS 2001 Galactic Astronomy

Lensing Lightcurves : Einstein 1936 Plane of the Sky source rmin lens r 0 Lightcurve A(t) = A+(t) + A-(t) A(u) = 1. 34 at u = 1 / u as u => 0 AS 2001 Galactic Astronomy

Einstein Timescale => MACHO mass • Einstein Timescale : • Time to cross radius of Einstein ring • For V ~ 200 km/s and d ~ 10 kpc • Black holes : ~ months Stars : ~ weeks Jupiters : ~ days Earths : ~ hours AS 2001 Galactic Astronomy

Microlens Planet Search Lightcurves • Large (brief) signal from small planets • Ratio of durations => mass ratio q=m/M • Jupiters – few days • Earths – few hours • Time offset => separation in RE units AS 2001 Galactic Astronomy

Probability of Lensing • How many MACHOs are “close” to line of sight to G. C. ? RE ( r ) Star near Galactic Centre us x = r / R 0 • MACHOs / volume ( power-law halo model ) : • Probability of lensing ( with u < 1 so A > 1. 34 ) : Probability ~ 5 x 10 -7 ( independent of MACHO mass m ) • Need to examine >107 stars to see one MACHO lens. AS 2001 Galactic Astronomy

MACHO Hunting Sightlines • • Need large number ( > 107 ) source stars. Need long sightline for MACHOs to pass Need dedicated wide-field mosaic CCD cameras Baade’s Window -- disc stars (+ MACHOs? ) ~ 2000 / yr Magellenic Clouds – halo stars (+ MACHOs? ) few / yr Event numbers and timescales consistent with stars No large excess of events due to MACHOs Baade’s Window SMC LMC AS 2001 Galactic Astronomy

MACHOs are not enough WIMPS needed (still hunting) (or some alternative to Einstein Gravity) • Upper limits on MACHO contribution to DM Halo : 100% Macho Fraction of DM Halo 10% 1% t. E : AS 2001 MACHOs here RULED OUT by microlensing 10 -5 hours 10 -4 10 -3 days 10 -2 0. 1 1. 0 M / Msun weeks Galactic Astronomy

DM Halo : Summary of Main Points • Flat rotation curve : V( R ) = V 0 • => Enclosed mass : M( R ) ~ V 02 R / G = 1011 (R/R 0) Msun • Oort limit => DM is not in the disc. • DM halo density profile : r( R ) ~ r 0 ( R / R 0 )-2 • • • MACHOs or WIMPs ? Gravitational microlensing rules out MACHOs Still searching for WIMPs … or … some Alternative Gravity Theory e. g. MOND (Modified Newtonian Dynamics) predicts V 2( R ) = a 0 G M( R ) / R a 0 ~10 -10 m/s 2 AS 2001 Galactic Astronomy

Dark Matter : MACHOs AND WIMPs • Gravitational lensing simulator http: //www. astrophysicsspectator. com/topics/generalrelativity/Gravitational. Len s. Point. Sim. html • Gravitational “Lens Toy” : https: //slowe. github. io/Lens. Toy/ • Simulation of Gravitational Lens passing over Hubble Deep Field : https: //www. youtube. com/watch? v=y. PANV 8 fof-I AS 2001 Galactic Astronomy

Thanks for Listening AS 2001 Galactic Astronomy

Online End-of-Module Student Evaluation Survey • Please take a moment (before 11 May) to fill in the online end-of-module evaluation survey (on MMS) for AS 2 x 01 • (https: //mms. st-andrews. ac. uk) • (and your other modules). • Your feedback helps us improve the course for future cohorts. AS 2001 Galactic Astronomy

Online Student Evaluation Survey QR code AS 2001 Galactic Astronomy