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An Introduction to Gravitational Lensing Ian Browne, Jodrell Bank Observatory (Thanks to Andy Biggs and Neal Jackson for pictures and slides)

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Outline Introduction to the basics of lensing Lensing configurations plus pictures Radio lens surveys – CLASS Time delay and results for

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Lensing Basics Radiation is deflected in gravitational fields Just as for conventional lenses, images will form at extrema in the light travel time surface (Fermat). Normally there will be just one deflected image but, for sufficiently deep gravitational potentials, multiple images form.

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Lensing and Time Delays Images seen in directions perpendicular to the wavefronts Wavefronts from the same event in the object arrive at different times

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Lensing geometry For a point mass the deflection is given by (b is the impact parameter) There is a simple geometric relation between the angles that must apply if there are multiple images – known as the lens equation. Images are formed at angles where the deflection equation and the lens equation are satisfied simultaneously

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Bend angle diagram

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Lensing astrophysics (Galaxy-mass lensing) Not just a cosmic curiosity!! Counting lens systems gives a mass-biased census of the universe not the usual luminosity-biased one. The best way of locating compact dark objects. The number of lenses depends on the cosmological geometry (particularly the cosmological constant) Time delays give us a distance measuring technique; i.e. the Hubble constant (H 0 ).

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Lensing by galaxies At cosmological distances galaxies deflect radiation by about an arcsecond. The mass is distributed => the deflection depends on impact parameter and reflects the mass distribution. About 1 in 600 quasars are sufficiently lined up with an intervening galaxy to be lensed. Some galaxies contain dust and therefore may hide the images they produce in the optical. –One reason why radio searches are best

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Typical Image configurations There is a range of image configurations. Depends on the complexity of the mass distribution and impact parameter. –2-image (doubles) –4-image (quads) –6-image –Einstein rings (There should be an odd number of images but the odd one is de-magnified and not detected.)

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Images Circular symmetry => doubles Elliptical mass distributions => doubles or quads. Depends on impact parameter Perfect alignment gives Einstein ring (or Einstein cross) More complex mass distributions => higher multiplicities. (6-image system known)

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CLASS Lens Systems

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Properties of images Magnified and distorted Surface brightness preserved –Beware absorption/scattering in lens Achromatic –Beware of absorption/scattering in lens Polarization not changed –Beware of Faraday rotation/depolarization in the lens

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Finding lens systems If intrinsic structure of object is simple, then multiple imaging is easy to recognize; e.g. in quasars and compact radio sources. For extended radio sources, and even galaxies, it’s often difficult to be certain of lensing. N.B. It’s a rare event -- ~1 in 600 Need resolution better than 1 arcsec.

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Radio lens searches Radio searches are best! –Resolution better –The radio sky is sparsely populated –Lensing of compact sources is easy to recognize –Compact sources are variable –Dust in the lens does not hide images

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Motivation for lens searches To find a “Golden lens”, one suitable for measuring the time delay (or delays) and hence the Hubble constant. To obtain reliable lens statistics in order to learn about cosmology. To learn about the mass distributions of intermediate redshift galaxies. To look for incidental propagation effects –Best constraint on any change of the fine structure constant with time comes from H1 and molecular lines in a lens system (Murphy et al, astro-ph/ ).

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Radio Lens Surveys MG (MIT/Greenbank) – VLA. No pre- selection of tagets. JVAS – VLA. Pre-select flat spectrum objects CLASS – VLA. As JVAS Southern surveys (VLA or AT)

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CLASS (Cosmic Lens All-Sky Survey) (Jodrell, Caltech, Dwingeloo, NRAO) Flat spectrum sources S 5GHz >30mJy selected from GB6 and NVSS. Observe with VLA at 8.4GHz (0.2” resolution) Follow up candidates at higher resolution with MERLIN and VLBA snapshots (~ 20/day) Complete from 0.3 to 15 arcsec and flux ratios <10:1

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More about CLASS ~16,500 sources observed with VLA Complete sample of ~10,500 ~ 300 candidates followed up with MERLIN at 5GHz ~50 with VLBA at 5GHz With JVAS has found 22 lens systems Lensing rate in well defined sample 1:600

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Results from CLASS Amongst 22 systems there are roughly equal numbers of doubles and quads Lensing rate 1:600 Median separation ~1arcsec –Smallest 0.33 and largest 4.5 arcsec The search is virtually complete

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MERLIN images of CLASS Lenses

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Hubble’s Constant Light travel time –Geometric & gravitational – angular diameter distances H 0 Require –Source and lens redshifts –Good lens model –Time delay –Cosmological model ( 0, 0 )

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B Identified as a lens in JVAS (1992) Two images (A,B) of flat-spectrum core –Very small separation (335 mas) Golden Lens? –Both redshifts known –Image substructure (core-jet) –Einstein ring –Background source variable –Cosmological dependence weak (low z)

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VLA 15 GHz

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VLBA 15 GHz MERLIN/VLA 5 GHzHST I-band

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Time Delay Measurement VLA monitoring –3 frequencies (5, 8.4 and 15 GHz) –Polarization + total intensity –~50 observations over 3 months Time delay analysis – 2 /CCF/DCF/D 2 –Monte Carlo simulations for errors – = 10.5±0.4 days

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Polarization Position Angle 15 GHz

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Lens Modelling Attempt to map images to same source –More images – more constraints Usually assume isothermal power-law H 0 = 69 kms -1 Mpc -1 –Statistical error: +13/-19 kms -1 Mpc -1 –Systematic error: 15%? –Lens galaxy position poorly known

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Other times delays Total of 7 measured Three from CLASS – – VLA – – VLA, MERLIN,optical – VLA

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Scattering in ? The angular sizes of the radio images are strongly frequency dependent. –~1mas at 15GHz –~30mas at 1.6GHz Surface brightness of images is not conserved.

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VLBA 15 GHz MERLIN/VLA 5 GHzHST I-band

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Image Core-Jet Structure CJ1 ACJ1 B

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VLBA Imaging (13, 18, 21 & 50 cm)

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Scattering? Frequency dependence does not go as wavelength squared except over restricted frequency range. Difficult to model as lensing effect Scattering is default explanation The lens is a spiral with rich ISM

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Future work Find and study more lens systems –Reaching the limits of present radio instrumentation – maybe possible to increase numbers by ~10 but most will be mJy sources. Better high resolution mapping of existing systems to refine mass models, etc. –Lots of work to be done Multi-frequency observations to study propagation effects – e.g. scattering, Faraday rotation, free-free absorption More and better time delays. Look for superluminal motion in the images. None found yet. Spectral line VLBI of absorption systems to get lens kinematics and velocity dispersions. Use the magnification of lenses to gain extra resolution –E.g. weak CSOs

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The End

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Scatter-Broadening ( ) 2 images + Einstein ring V. bright ~ 4 Jy at 8.4 GHz 2 dependence - SW image Scattering in lensing galaxy Galaxy closer to SW image

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