An Introduction to Gravitational Lensing

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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 0218357

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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 (H0).

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Lensing by galaxies

• At cosmological distances galaxies deflect
  radiation by about an arcsecond.
• The mass is distributed gt 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 gt doubles
• Elliptical mass distributions gt doubles or
  quads. Depends on impact parameter
• Perfect alignment gives Einstein ring (or
  Einstein cross)
• More complex mass distributions gt higher
  multiplicities. (6-image system known)

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1938666
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CLASS Lens Systems
1600434
1608434
2045265
1933503
1359154
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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,
  its often difficult to be certain of lensing.
  N.B. Its 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/0101519).

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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 S5GHz gt30mJy 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
  lt101

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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 1600

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Results from CLASS

• Amongst 22 systems there are roughly equal
  numbers of doubles and quads
• Lensing rate 1600
• 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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Hubbles Constant

• Light travel time
• Geometric gravitational
• ?? ? angular diameter distances ? H0
• Require
• Source and lens redshifts
• Good lens model
• Time delay
• Cosmological model (?0,?0)

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B0218357

• 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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MERLIN/VLA 5 GHz
HST I-band
VLBA 15 GHz
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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/D2
• Monte Carlo simulations for errors
• ?? 10.50.4 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
• H0 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
• 0218357 VLA
• 1600434 VLA, MERLIN,optical
• 1608656 --VLA

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Scattering in 0218357?

• 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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MERLIN/VLA 5 GHz
HST I-band
VLBA 15 GHz
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Image Core-Jet Structure
CJ1 A
CJ1 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 (1830-211)

• 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