Gravitational Lensing

Transcription

1 Gravitational Lensing

2 Examples of Lens Systems Galaxy Clusters about 1 arcminute about 1 arcsecond Galaxies

3 More examples

4 Clusters of galaxies as lenses Many examples are known, but strong lensing is still quite rare. T. Johnson (U Michigan)

5 Gravitational Lensing is similar to the more familiar optics Glass Water Air

6 Tests of Light Deflection Early expeditions: 1912, 1914 (failed), 1919 (success!) These days: use radio emission from quasars Also: light travel time from spacecraft behind Sun has been measured

7 A Brief Introduction to Lensing Goal: find posi)ons of images on the sky How? use Fermat s Principle - images are formed at the local minima, maxima and saddle points of the total light travel )me from source to observer posi)on on the sky total travel )me

8 A Brief Introduction to Lensing Plane of the sky Elliptical lens Off-axis source Circularly symmetric lens Off-axis source Circularly symmetric lens On-axis source

9 A Brief Introduction to Lensing Elliptical lens Off-axis source Circularly symmetric lens Off-axis source Circularly symmetric lens On-axis source

10 All the Information about Images is contained in the Arrival Time Surface Posi%ons: Images form at the extrema, or sta)onary points (minima, maxima, saddles) of the arrival )me surface. Time Delays: A light pulse from the source will arrive at the observer at 5 different )mes: the )me delays between images are equal to the difference in the height of the arrival )me surface. [Schneider 1985] [Blandford & Narayan 1986] Magnifica%ons: The magnifica)on and distor)on, or shearing of images is given by the curvature of the arrival )me surface; magnifica)on ~ 1/curvature

11 Einstein s 1936 paper Today: lensing of stars by stars in our Galaxy, lensing of galaxies and quasars by galaxies lensing of galaxies by clusters of galaxies, etc. B A

12 assuming the delay is small compared to the total light travel time. ton flying from the source additional delay of the photon comes from travelling angingan direction and comthrough curved spacetime at the lens. This gravitational on change the would increase time delay tgrav (x is related to the mass distribution of the lens. coming through s, ys ). generally mthe the relation geometryisof deflec- written as a two-dimensional Poiselling in a Citizen Science expression, Context avoiding 3 son equation, but an alternative calculus, is as follows. The value of tgrav through (x, y) equals its (y y ), s average value on the(3) circumference of a small circle centred atto(x, plus a constant times the mass within that cirred they), total light travel 3 cle. The constant is 2G/c times the cosmological expansion factor (1 + zl ). Thus oton comes from travelling he lens. This gravitational 2G tgrav (x, y) = (x, y )i + (1 + zl ) 3 M (x, y ). (4) ass distribution ofht the lens. grav c s a two-dimensional PoisWe have used (x,calcuy ) to denote the circumference of a circle, xpression, avoiding (x,(x, y )y)toequals indicate through its the integrated mass within the cirv and relates this expression to the better-known e cle. of a Appendix small circleacentred explicit form for thecirgravitational time delay. he mass within that The lightexpansion travel time of a virtual photon is therefore he cosmological longer by Arrival time surface, " or time delay surface no mass in the lens 2G = tgeom + tgrav + zla ) single M (x, y image ). t(x, (4)y) is c3 than it would at havethe beenmin. with no lens present. formed e circumference of a circle, (5) Real photons take paths that make t(x, y) extremal, that is, having rated mass within the cira minimum, maximum or saddle point (Fermat s principle). ssion to the better-known some massonin the The proportionality factors in (2) and (3) depend time delay. the redshifts cosmological parameters, and areimages given in are three rtual photon isand therefore Appendix A. + tgrav (5) 2.2 Arrival-time contours o lens present. Real pho- Kung+2015 more mass in the lens five images are formed: 2 min, max & 2 saddle lens formed: min, max & saddle

13 Wavefronts & multiples images Fort & Mellier (1994) R. Schmidt (Heidelberg)