The Smithsonian Institution to the left and as imaged with a gravitational lens to the right
(computer model only -- the calculation assumed viewing from the Natural History Museum with a lens about the
mass of Saturn, so no experiments were actually conducted!)
K1 Lensing and lensing terminology
Classes of gravitational lensing
In general relativity, the presence of matter (energy density) can curve
spacetime, and the path of a light ray will be deflected as a result. This
process is called gravitational lensing and in many cases can be described in
analogy to the deflection of light by (e.g. glass) lenses in optics. Many useful
results for cosmology have come out of using this property of matter and light.
Lupe: Einstein verzerrt im BH
For many of the cases of interest one does not need to fully solve the
general relativistic equations of motion for the coupled spacetime and matter,
because the bending of spacetime by matter is small.
Quantitatively the matter bending space is moving slowly relative to c, the
speed of light and the "gravitational potential"
induced by the matter obeys |F|/c2 << 1.
The lens or the lensing object may be a star,
a dark object, a galaxy, or any mass inhomogeneity that curves space locally.
Behind it is the source or the lensed object: a star, a QSO, or a galaxy,
an image of which we observe through the curved space of the lens.
If the lens and the source are on a nearly straight line from us, one has the case of
strong lensing which produces several (an odd number of) distorted pictures of the source,
giant arcs and caustics.
In the case of an exactly straight-line geometry,
the caustics form a symmetric Einstein cross which collapses to an Einstein ring
when the radius of the lens is small.
Microlensing corresponds to the case when the
resolution is smaller than the radius of the Einstein ring. The image is then seen magnified
during the time the lens passes in front of the source.
Screen-lensing denotes the case
when the source is distant, but the lens is within our halo. Self-lensing denotes the case
when both the source and the lens are in the same distant galaxy. If the lens and the source are not
on a straight line joining us, no caustics are formed, only elliptical deformations of the image
of the source. This is called weak lensing, an important tool to study the large-scale
distribution of gravitating matter.
Ellipticity and shear can enhance the magnification.
The most extreme bending of light is when the lens is very massive and the source is close enough
to it: in this case light can take different paths to the observer and more than
one image of the source will appear.
Q0957+561 - Die Erste Linse mit Quasar.
Lupe: Daten dazu vom CASTLES Survey.
The first example of a double image was found in 1979, of a quasar (0957+561). The number of lenses
discovered has been used to estimate the volume of space back to the sources.
This volume depends strongly on cosmological parameters, in particular the
If the source varies with time, the multiple images will vary with time as well. However, the
light doesn't travel the same distance to each image, due to the bending of
space. So there will be time delays for the changes in the images. These time
delays can be used to calculate the hubble constant H0.
A few systems with these time delays have been found and are under study. Much
of the subtlety in this work lies with constructing the model of the mass
distribution forming the lens.
In some special cases the alignment of the source and the lens will
be such that light will be deflected to the observer in an "Einstein ring."
One of these was observed in 1998 and is reported here.
More often than a ring, the source may get stretched out and curved, and form a
tangential or radial arc. A lot of mass is needed to cause an arc to appear, so
that properties of arcs (numbers, size, geometry) can often be used to study
massive objects like clusters. One can also, given a set of images, try to reconstruct the lens
Large separation lensed quasars
To find large separation lensed quasars, a project was started
to search for large separation lenses in the quasar sample of
the Sloan Digital Sky Survey and - so far - one was found.
The newly discovered SDSS J1004+4112 is a fascinating lens system.
It illustrates how large separation lenses can be used to probe the
properties of clusters and test models of structure formation.
The full SDSS sample is expected to contain several more large separation
lenses. The complete sample of lenses, and the distribution of their
image separations, will be extremely useful for understanding the
assembly of structures from galaxies to clusters. More immediately,
the discovery of a quasar lensed by a cluster of galaxies fulfills
long-established theoretical predictions and resolves uncertainties
left by previously unsuccessful searches.
HCM 6A — Discovery of a redshift z = 6.56 galaxy lying behind the cluster Abell 370
z ~ 10 (Keck)
More Discoveries by Subaru Telescope
| — |
||Authors: Chary, R-R; Stern, D; Eisenhardt, P.|
||Journal-ref: ApJ 635 (2005) L5-L8 [astro-ph/0510827 ]|
||Title: Spitzer Constraints on the z=6.56 Galaxy Lensed by Abell 370|
We report on Spitzer IRAC observations of the spectroscopically
confirmed z=6.56 lensed Lya emitting source HCM 6A which was found behind
the cluster Abell 370. Detection of the source at 3.6 and 4.5 microns,
corresponding to rest-frame optical emission, allows us to study the stellar
population of this primeval galaxy. The broadband flux density at 4.5 microns
is enhanced compared to the continuum at other wavelengths, likely due to the
presence of strong Ha in emission.
The derived Ha line flux
corresponds to a star-formation rate of around
140 M yr-1, more than an
order of magnitude larger than estimates from the ultraviolet continuum and
Lya emission line. The dust extinction required to explain the
discrepancy is A_V of about 1 mag. The inference of dust at such high
redshifts is surprising and implies that the first epoch of star-formation in
this galaxy occurred at z ~ 20.
The first spectroscopically confirmed galaxy at z > 6 was HCM 6A (z = 6.56), discovered by Hu et al. (2002)
in a narrowband imaging survey of lensing galaxy cluster fields and confirmed through the detection of
The source is magnified by the foreground cluster Abell 370 by a factor of 4.5 and appears to
be fragmented into two components separated by < 2'' in the North-East/South-West direction.
The Lya line and UV continuum luminosity correspond to a star-formation
rate (SFR) of 2-9 M yr-1.
This does not include any corrections for dust, since the existence of dust
and absorption are quite uncertain from the purely rest-frame ultraviolet data previously
obtained for HCM 6A.
Übertrifft Abell 2218 mit z = 5.58.
(Hu et al.)
The spectrum of HCM 6A from a 4-hr exposure made with the LRIS spectrograph using the 400 line/mm grating.
The emission line is at 9187 Å. The solid line
near the axis shows the median continuum flux above the line, and gives a
break strength consistent with the broadband measurements. The solid line
above the emission shows the 50% width of the narrowband filter, whose
profile is shown overlaid on the fluxed nightsky spectrum, plotted at 1% strength above the object spectrum.
Enlarged plots of the object's emission feature and 1% of the nightsky background spectra taken with the 400
line/mm grating are shown in the inset, where the asymmetry of the line profile can be clearly seen.
The object HCM 6A was found in a narrowband imaging survey using a 118 Å bandpass filter centered
at 9152 Å in the LRIS camera on the 10 m Keck II Telescope.
emitters were identified by the equivalent width
of the emission and the absence of lower wavelength flux in ultradeep
Hu, Esther M., Cowie, L. L., McMahon, R. G., Capak, P., Iwamuro, F., Kneib, J.-P., Maihara, T., & Motohara, K.
2002, ApJ, 568, L75
"A Redshift z = 6.56 Galaxy Behind the Cluster Abell 370"
Cluster redshifts are z = 0.37 for A370, 0.41 for A851, and 0.231 for A2390.
(Ref.: Hu et al. 2002 [astro-ph/0203091 ])
HCM 6A is the first galaxy to be confirmed at redshift z>6, and has
W_(observed)=190 Å, flux = 2.7 × 10-17 erg cm-2 s-1.
Spectra obtained with LRIS confirm the emission line and the continuum break across the line,
and show an asymmetric line profile with steep fall-off on the blue side.
Deep Subaru near-infrared CISCO images in J, H and K' which extend
the sampled continuum to longer wavelengths give a consistent estimate of
the continuum flux density in these line-free regions of 2.6 ×
10-30 erg cm-2 s-1 Hz-1.
The line width and strength,
asymmetric profile, and very deep spectral break are only consistent
with the interpretation of the line as a redshifted Lya feature.
From the detailed lensing model of this cluster, we estimate a lensing
amplification of 4.5 for this galaxy, which is located slightly over
an arcminute from the center of the cluster, for an unlensed flux of
6.5 × 10-18 erg cm-2 s-1.
The presence of such a galaxy suggests that the reionizing epoch is beyond z=6.6.
Cy 2201-3201: An Edge-on Spiral Gravitational Lens
RCS0224-002 / L* Lyman-break Galaxy (z~5)
RCS0224-002 (zl = 0.9) — L* Lyman-break galaxy (zs = 4.88)|
||Authors: A.M. Swinbank, R.G. Bower, G.P. Smith, R.J. Wilman, I. Smail, R.S. Ellis,
S.L. Morris, J.-P. Kneib|
||Journal-ref: MNRAS 376 (2007) 479 [astro-ph/0701221 ]|
||Title: Resolved Spectroscopy of a Gravitationally Lensed L* Lyman-break Galaxy at z~5|
By combining HST imaging with optical (VIMOS) and near-infrared
(SINFONI) integral field spectroscopy we exploit the gravitational potential
of a massive, rich cluster at z=0.9 to study the internal properties of a
gravitationally lensed galaxy at z=4.88.
Using a detailed gravitational lens
model of the cluster RCS0224-002 we reconstruct the source-frame morphology of
the lensed galaxy on 200pc scales and find an ~L* Lyman-break galaxy
intrinsic size of only 2.0x0.8kpc,
a velocity gradient of <60km/s and
implied dynamical mass of
1.0x1010M within 2kpc.
We infer an integrated
star-formation rate of just
12 ± 2M/yr from the intrinsic [OII] emission line
The Ly-alpha emission appears redshifted by +200 ± 40km/s with respect
to the [OII] emission. The Ly-alpha is also significantly more extended than
the nebular emission, extending over 11.9x2.4kpc. Over this area, the Ly-alpha
centroid varies by less than 10km/s.
By examining the spatially resolved
structure of the [OII] and asymmetric Ly-alpha emission lines we investigate
the nature of this system.
The model for local starburst galaxies suggested by
Mass-Hesse et al. (2003) provides a good description of our data, and suggests
that the galaxy is surrounded by a galactic-scale bi-polar outflow which has
recently burst out of the system. The outflow, which appears to be currently
located >30kpc from the galaxy, is escaping at a speed of upto ~500km/s.
Although the mass of the outflow is uncertain, the geometry and velocity of
the outflow suggests that the ejected material is travelling far faster than
escape velocity and will travel more than 1Mpc (comoving) before eventually
One of the most important observational breakthroughs in recent years was the discovery that a significant
fraction of high-redshift galaxies are surrounded by “superwinds”– starburst and/or AGN driven
outflows which expel gas from the galaxy potential, hence playing no further role in the star-formation history
of the galaxy. This phenomenon is beginning to be understood by theorists as the missing link in galaxy
formation models which are otherwise unable to match the shape and normalisation of the luminosity function.
These feedback processes may also offer natural explanation as to why only 10% of baryons cool to
form stars (the Cosmic Cooling Crisis; White & Rees 1978; Balogh et al. 2001).
However, important questions remain unanswered. Evidence for these superwinds is usually based on
observations which compare the nebular emission line properties with the
rest-frame UV emission and absorption lines. such as Lya,
Ha and UV ISM absorption lines.
A Gravitationally Lensed L* Lyman-break Galaxy at z~5|
Image credit: HST / SINFONI / Swinbank et al.
Left: True colour HST V I-band image of the core of the lensing cluster RCS0224-002 at z=0.78.
The contours mark the high-redshift critical curves (curves of infinite magnification) from the
gravitational lens model described in §3. We also overlay the field of view of the SINFONI IFU (shown by the
white box) which was used to map the [Oii] l3727 emission.
The cluster galaxies which we are able to spectroscopically identify
are labelled CG1-6. R1 is the radial counter-image of the z=4.88 arc and R2 is the z=1.05 radial
arc from Sand et al. (2005). Serendipitous background galaxies are labelled A1 and A2 (VIMOS) and 1–4
Right: V R(I+Lya) colour image of the cluster core generated from the VIMOS
The inner and outer curves show the z=4.88 caustic and critical curves respectively. The center of the
cluster (0,0) is at a =02:24:34.255 d =-00:02:32.39 (J2000)
and we haverotated and aligned the HST and VIMOS data such that North is up and East is left in both panels.
Velocity offsets of several hundred km/s have been measured, suggestive of large scale outflows comparable to
starburst driven winds often observed in low-redshift Ultra-Luminous Infra-Red Galaxies (ULIRGs) in the local
Universe (Martin 2005).
However, the current data lack spatial information, which is vital if we are to understand if material
escapes into the Inter-Galactic Medium (IGM) or whether the outflowing material eventually stalls, fragments and
drains back onto the galaxy, potentially disrupting the disk and causing further bursts of star-formation.
K3.1 Large Separation Lensed Quasar SDSS J1004+4112
Lensed Quasar with Quadruple Images
SDSS J1004+4112 — image separation: 14.''6|
||Authors: J. Fohlmeister, C.S. Kochanek, E.E. Falco, J. Wambsganss, N. Morgan, C. W. Morgan,
E. O. Ofek, D. Maoz, C. R. Keeton, J. C. Barentine, G. Dalton, J. Dembicky, W. Ketzeback, R. McMillan,
||Journal-ref: ApJ 662 (2007) 62 [astro-ph/0607513 ]|
||Title: A Time Delay for the Largest Gravitationally Lensed Quasar: SDSS J1004+4112|
We present 426 epochs of optical monitoring data spanning 1000 days from
December 2003 to June 2006 for the gravitationally lensed quasar SDSS
J1004+4112. The time delay between the A and B images is 38.4+/-2.0 days in the
expected sense that B leads A and the overall time ordering is C-B-A-D-E. The
measured delay invalidates all published models. The models failed because they
neglected the perturbations from cluster member galaxies. Models including the
galaxies can fit the data well, but strong conclusions about the cluster mass
distribution should await the measurement of the longer, and less substructure
sensitive, delays of the C and D images. For these images, a CB delay of
681+/-15 days is plausible but requires confirmation, while CB and AD delays of
>560 days and > 800 days are required. We clearly detect microlensing of the
A/B images, with the delay-corrected flux ratios changing from B-A=0.44+/-0.01
mag in the first season to 0.29+/-0.01 mag in the second season and 0.32+/-0.01 mag in the third season.
Observations and Theoretical Implications of the Large Separation Lensed Quasar SDSS J1004+4112
(Oguri et al. ApJ 605, 2004)
Since the discovery (Walsh, 1979) of the first gravitationally lensed quasar Q0957+561,
about 80 strong lens systems have been found so far.
All of the lensed quasars have image separations smaller than 7'',
and they are lensed by massive galaxies (sometimes with small boosts
from surrounding groups or clusters of galaxies). The probability that
distant quasars are lensed by intervening galaxies was originally
estimated by Turner (1984) to be 0.1%--1%, assuming that galaxies
can be modeled as singular isothermal spheres (SIS).
Redshift distribution of quasars identified by the
spectroscopic pipeline in the SDSS. Dashed vertical lines show the
redshift cut 0.6 < z < 2.3 used for the statistical analysis.
This prediction has been verified by several optical and radio lens surveys, such as
The lensing probability is sensitive to the volume of the universe, so it can be used to place interesting
constraints on the cosmological constant Lambda.
- the Hubble Space Telescope (HST) Snapshot Survey,
- the Jodrell Bank/Very Large Array Astrometric Survey, and
- the Cosmic Lens All Sky Survey [CLASS](Myers, 1995).
In contrast, lenses with larger image separations should probe a
different deflector population: massive dark matter halos that host
groups and clusters of galaxies. Such lenses therefore offer valuable
and complementary information on structure formation in the universe,
including tests of the Cold Dark Matter (CDM) paradigm.
So far the observed lack of large separation lensed quasars has been used to infer that, unlike galaxies,
cluster-scale halos cannot be modeled as singular isothermal spheres.
The difference can probably be ascribed to baryonic processes: baryonic infall and
cooling have significantly modified the total mass distribution in galaxies but not in clusters.
As a result, large separation lenses may constrain the density profiles
of dark matter halos of cluster more directly than small separation lenses.
Alternatively, large separation lensed quasars may be used to place
limits on the abundance of massive halos if the density profiles are specified.
Better yet, the full distribution of lens image separations may provide
a systematic diagnostic of baryonic effects from small to large scales in the CDM scenario.
The fact that clusters have less concentrated mass distributions than
galaxies implies that large separation lensed quasars should be less
abundant than small separation lensed quasars by one or two orders of
magnitude. This explains why past surveys have failed to unambiguously
identify large separation lensed quasars.
For instance, CLASS found 22 small separation lenses but no large separation lenses
among ~15000 radio sources. Although several
large separation lensed quasar candidates have been found,
they are thought to be physical (unlensed) pairs on the basis of individual observations
or statistical arguments. Recently Miller (2004) found 6 candidate lens systems with image
separations > 30'' among ~ 20000 quasars in the Two-degree Field (2dF)
quasar sample. Given the lack of high-resolution spectra and deep
imaging for the systems, however, it seems premature to conclude that
they are true lens systems. We note that because the expected number
of lenses with such large image separations in the 2dF sample is much
less than unity, these systems would present a severe challenge to standard models if confirmed as lenses.
The A--B time delay should
be on the order of weeks or months, so it should be very feasible
to measure it, provided that the source has detectable variations.
Measuring the A--B delay would be very useful because it would
determine the temporal ordering, and thereby robustly determine the
image parities. In addition, it would allow a good estimate of the
long C--D delay and indicate whether attempting to measure that delay
would be worthwhile.
To find a first unambiguous large separation lensed quasar, we started a
project to search for large separation lenses in the quasar sample of the Sloan Digital Sky Survey.
This project complements ongoing searches for small separation lenses in SDSS.
The SDSS has completed less than half of its planned observations, but already it contains more than
30000 quasars and is superior to previous large separation lens surveys in several ways. The full SDSS sample
will comprise ~100000 quasars, so we ultimately expect to find several large separation lensed quasars. One of
the most important advantages of the SDSS in searching for large separation lensed quasars is that imaging in
five broad optical bands allows us to select lens candidates quite efficiently.
Recently we reported the discovery of the large separation lensed quasar SDSS J1004+4112 at z=1.73 (2003) in
the SDSS. The quasar itself turned out to be previously identified in the ROSAT All Sky Survey and the
Two-Micron All-Sky Survey, but was not recognized as a lensed system.
Inada (2003) showed that SDSS J1004+4112 consists of four quasar images with the same redshift from the Keck
spectroscopy. The colors of galaxies found by Subaru imaging follow-up observations indicated
the presence of a cluster of galaxies at z=0.68. Moreover, the configuration of the four images was successfully
reproduced by a simple lens model based on a singular isothermal ellipsoid mass distribution.
All these results strongly implied that SDSS J1004+4112 is the first quasar lens system due to a massive
The enormous range of predicted time delays means that constraining the Hubble constant with this system
will be difficult because of large systematic uncertainties in the lens models.
Ref.: Walsh, D., Carswell, R.F., & Weymann, R.J. 1979, Nature 279, 381
— discovery of the first gravitationally lensed quasar Q0957+561
K3.2 SDSS J1029+2623
(Image Separation Dql 22''.5)
SDSS J1029+2623 — zs = 2.197 — zl ~ 0.55 — Dql
||Authors: N. Inada, M. Oguri, T. Morokuma, M. Doi, N. Yasuda, R.H. Becker,
G.T. Richards, C.S. Kochanek, I. Kayo, K. Konishi, H. Utsunomiya, Min-Su Shin,
M.A. Strauss, E.S. Sheldon, D.G. York, J.F. Hennawi, D.P. Schneider, X. Dai, M. Fukugita|
||Journal-ref: ApJ 653 (2006) L97-L100 [astro-ph/0611275 ]|
||Title: SDSS J1029+2623: A Gravitationally Lensed Quasar with an Image Separation of 22.5 Arcseconds|
We report the discovery of a cluster-scale lensed quasar, SDSS J1029+2623,
selected from the Sloan Digital Sky Survey. The lens system exhibits two lensed
images of a quasar at zs = 2.197. The image separation of 22.5" makes it the
largest separation lensed quasar discovered to date. The similarity of the
optical spectra and the radio loudnesses of the two components support the
lensing hypothesis. Images of the field show a cluster of galaxies at zl ~ 0.55
that is responsible for the large image separation. The lensed images and the
cluster light center are not collinear, which implies that the lensing cluster has a complex structure.
The gri composite SDSS image of SDSS J1029+2623 (1.''3 seeing). The quasar images
(blue stellar objects) are indicated by A and B. G1 and G2 (red extended objects) are likely to be member
galaxies of a lensing cluster at z ~ 0.55.
The inset shows an expanded view of component B:
An object ~ 2'' Southeast of component B has quite different color from those of the quasar components.
The discovery of SDSS J1004+4112 with an image separation of 14.''6, the first example of a quasar
multiply imaged by a massive cluster of galaxies, opened a new window for understanding our universe
(Inada et al. 2003; Oguri et al. 2004). Although there are many examples of galaxies (arcs)
lensed by clusters, large-separation lensed quasars have several advantages over arcs as a cosmological probe.
First, the simpler (point-like) structure of quasars and their well-understood redshift distribution should make
the large-separation lensed quasars much cleaner probes of cosmology and structure formation models,
while the statistics of arcs remain contentious.
Second, the time-variability of quasars allows the measurement of time delays among the multiple lensed
images, thereby breaking the mass-sheet degeneracy of lens models given a priori knowledge of the Hubble
This was explored in detail for SDSS J1004+4112 (e.g., Oguri et al. 2004; Fohlmeister et al. 2007).
Our current problem is that the small number of known systems limits their use in statistical analyses,
however, current and future large lens surveys will discover many large-separation lensed quasars
Fohlmeister, J., et al. 2007, ApJ 662, 62
Inada, N., et al. 2003, Nature, 426, 810
Oguri, M., et al. 2004, ApJ 605, 78
Oguri, M., & Keeton, C. R. 2004, ApJ, 610, 663
Oguri, M., et al. 2006, AJ, 132, 999
Wambsganss, J. 2003, Nature, 426, 781
K3.3 The Third Image of SDSS J1029+2623
SDSS J1029+2623 — zs = 2.197 — zl ~ 0.6
— Mvir = 1.2 × 1015M|
||Authors: M. Oguri, E.O. Ofek, N. Inada, T. Morokuma, E.E. Falco, C.S. Kochanek, I. Kayo,
T. Broadhurst, G.T. Richards|
||Journal-ref: ApJ 676 (2008) L1 [0802.0002 ]|
||Title: The Third Image of the Large-Separation Lensed Quasar SDSS J1029+2623|
We identify a third image in the unique quasar lens SDSS J1029+2623, the second known
quasar lens produced by a massive cluster of galaxies.
The spectrum of the third image shows similar emission and absorption features, but has a redder
continuum than the other two images which can be explained by differential extinction or microlensing.
We also identify several lensed arcs. Our observations suggest a complicated structure of the lens
cluster at zl ~ 0.6. We argue that the three lensed images are produced by a naked cusp on the basis
of successful mass models, the distribution of cluster member galaxies, and
the shapes and locations of the lensed arcs.
Lensing by a naked cusp is quite rare among galaxy-scale lenses but is predicted to be common among
large-separation lensed quasars. Thus the discovery can be viewed as support
for an important theoretical prediction of the standard cold dark matter model.
SDSS J102913.94+262317.9 (SDSS J1029+2623;
Inada et al. 2006) is one of two examples of strongly lensed quasars produced by massive clusters of galaxies.
It was discovered in the Sloan Digital Sky Survey Quasar Lens Search (SQLS; Oguri et al. 2006, 2008; Inada et al.
2008), a survey to identify gravitationally lensed quasars from the spectroscopic sample of quasars in the Sloan
Digital Sky Survey (SDSS; York et al. 2000). The image separation of 22.''5 makes it the largest lensed quasar
known to date.
Inada et al. (2006) found that the system consists of two images of a radio-loud quasar at
zs = 2.197 created by a massive cluster of galaxies at z ~ 0.6. The rareness of such quasar-cluster lens systems
(e.g., Ofek et al. 2001; Inada et al. 2003) validates the importance of understanding this
system with extensive follow-up work.
Fig. 1.— Image of SDSS J1029+2623
Several lensed arcs are also seen. Note particularly two
large blue arcs on the east and west sides of galaxies G1/G2, a red arc on the south of object C,
and a blue arc located near galaxy G2.
Fig. 3.— Critical curves and caustics
The square in the lower panel shows the best-fit source position, whereas the three
squares in the upper panel indicate the corresponding best-fit image
positions which are very close to the observed image positions.
Because of the naked cusp in the caustics, this model predicts only three images on the same side of the
lens potential, which explains the unique image configuration of this lens system. (see also Figure 1).
The model is an elliptical Navarro et al. (1997) profile with
Mvir = 1.2 × 1015M,
concentration parameter cvir = 4.9, ellipticity e = 0.44, and
position angle qe = -88°.
However, note that the derived mass and concentration parameter
crucially depend on our assumption of the scale radius, rs = 60''.
Inada, N., et al. 2003, Nature 426, 810
Inada, N., et al. 2005, PASJ 57, L7
Inada, N., et al. 2006, ApJ 653, L97
Inada, N., et al. 2008, AJ 135, 496
Navarro, J.F., Frenk, C.S., & White, S.D.M. 1997, ApJ 490, 493
Ofek, E.O., Maoz, D., Prada, F., Kolatt, T., & Rix, H.-W. 2001, MNRAS 324, 463
Ofek, E.O., Oguri, M., Jackson, N., Inada, N., & Kayo, I. 2007, MNRAS 382, 412
Oguri, M., et al. 2006, AJ 132, 999
Oguri, M., et al. 2008, AJ 135, 512
Lens modelling and Ho estimate in quadruply lensed systems
Gravitational lensing is one of the main tools to obtain
information about the structure and evolution of the universe. In
particular, time delay measurements are a recent primary distances
indicator, furnishing a new method to estimate the Hubble constant
Ho, which determines the present expansion rate of the universe.
PG 1115+080: A Gravitational Cloverleaf |
Credit: CISCO, Subaru 8.3-m Telescope, NAOJ
Actually, in 1964, Refsdal proposed to estimate Ho
from multiply imaged QSOs by the measurements of the delays in the arrive time between light rays
coming from the different images, which follow different optical
paths. It is not difficult to show that the time delay between two
images due to a gravitational lens can be factorized in two
pieces: the first one depends on cosmological parameters and is
inversely proportional to Ho, while the second one is
determined by the lens model only. Thus, having measured time
delays among images of a lensed QSO, once we fix the cosmological
parameters, we can obtain a direct estimate of Ho provided
that the lens model has been recovered from the lensing
constraints, or is known in an other independent way.
Nowadays, there are more than eighty multiple image systems,
but only about ten of them have measured time delays. However,
this number is increasing day by day, and in the future it will be
possible to measure time delays for many other systems.
It is well known hat the most significant uncertainty affecting the estimate of Ho with the Refsdal
method is only related to the mass model used. In the usual approach the model parameters are recovered by
fitting some parametric models to the available constraints through minimization techniques.
Instead, other authors carried out the pixellated lens modelling, that describes the mass distribution by a
large number of discrete pixels with arbitrary densities, so determining the Hubble constant by means of a set
of physical motivated constraints. A compromise between these two approaches consists in the numerical solution
of a set of non linear equations - HERQULES - to develop an algorithm to estimate Ho without the
need to give an explicit expression for the shape function.
|Refsdal, S. ||1964|| MNRAS, 128, 295.
|Refsdal, S. ||1964||MNRAS, 128, 307.
|Refsdal, S. ||1966||MNRAS, 132, 101.
|Schneider, P., Ehlers, J., Falco, E.E.||1992
K5.1 10 time-delay lenses
CLASS Gravitational Lens B1608+656
10 galaxy lenses — h = 0.72|
||Authors: P. Saha, J. Coles, A.V. Maccio, L.L.R. Williams|
||Journal-ref: ApJ 650 (2006) L17 [astro-ph/0607240 ]|
||Title: The Hubble time inferred from 10 time-delay lenses|
We present a simultaneous analysis of 10 galaxy lenses having time-delay
measurements. For each lens we derive a detailed free-form mass map, with
uncertainties, and with the additional requirement of a shared value of the
Hubble parameter across all the lenses. We test the prior involved in the lens
reconstruction against a galaxy-formation simulation. Assuming a concordance
cosmology, we obtain 1/Ho = 13.5 (+2.5/-1.3) Gyr;
Image credit: Saha et al.
Table 1: Lenses and time delays
Ho = 72 (+8,-11) km s-1 Mpc-1, i.e. h = 0.72
If an object at cosmological distance is lensed into multiple images, the light travel time
for individual images differs. For variable sources, the differences are observable as time
delays. The delays are of order
Dt ~ GMc-3 ~ (DΘ)2 H-1
where M is the lens mass and
DΘ is the image separation (in radians). As Refsdal (1964) first
pointed out, the effect provides an independent way of measuring H-1.
Time-delay measurements have made much progress over the past decade and now at least 15 are available.
While Eq. (*) provides the order of magnitude, to determine the precise factor relating
time delays and H one has to model the mass distribution. An observed set of image
positions, rings, magnification ratios, and time delays is generically reproducible by many
different mass models. This results in a large model-dependent uncertainty on the inferred
Hubble parameter, even with perfect lensing data.
To appreciate how serious this model-dependence is, compare the models of B0957+561 by
Kundic et al. (1997) and Bernstein & Fischer (1999):
the results are H = 64 ± 13 and 77 (+29-24) km s-1Mpc-1 respectively, both
at 95% confidence; the more general models in the latter paper yield larger error-bars.
Alternatively, consider the nice summary in Fig. 12 of Courbin (2003) of published H0
estimates and uncertainties from individual lenses.
Among the lenses shown, B1608+656
has all three of its independent time delays measured, B1115+080 has two delays measured,
whereas the others have one each. One would expect these two best-measured lenses to be
the best constrained. Yet B1608+656 has the largest error-bars on H and B1115+080 the
This suggests that in the less-constrained lenses the real uncertainties are
much larger, but have been underestimated because the fewness of constraints did not force
sufficient exploration of model-dependence.
Abstracts: Q0957+561 Quasar
||Authors: R.E. Schild|
||Astronomical Journal 129, 1225-1230 (2005) [astro-ph/0504396]|
||Accretion Disc Structure and Orientation in the Lensed and Microlensed Q0957+561 Quasar
Because quasars are unresolved in optical imaging, their structures must presently be inferred.
Gravitational microlensing offers the possibility to produce information about the luminous
structure provided the Einstein ring diameter of the microlensing particle is comparable
to or smaller than the radiating quasar components.
The long brightness history measured for the Q0957 quasar has been analyzed previously
for information about the microlensing particles, and evidence for the
existence of a cosmologically significant population of planetary mass particles
has been reported.
The microlensing results have also directly determined the sizes of the ultraviolet light
emitting surfaces in the quasar Autocorrelation analysis of the same brightness record has
produced evidence for complex structure in the quasar;
if the quasar suddenly brightens today, it is probable that it will brighten again after
129, 190, 540, and 620 days. We interpret these lags as the result of luminous structure
around the quasar, and in particular we interpret them in the context of the Elvis (2000) model
of the quasar's structure. We find that the autocorrelation peaks imply that beyond the
luminous inner edge of the accretion disc, the biconic structures of the Elvis model must
lie at a radial distance of 2x10^17 cm from the black hole, and 2x10^16 cm above and below
the plane of the accretion disc. The quasar is apparently inclined 55 degrees to the line of
sight. A second possible solution with lower inclination and larger structure is also
indicated but statistically less probable.
existence of a cosmologically significant population of planetary mass particles
Rudolph E. Schild
More: [astro-ph/0409549] Microlensed double-image quasars have sent a consistent message
that the baryonic dark matter consists of a population of free-roaming planet mass objects.
Since the original baryonic dark matter detection from quasar microlensing was first announced
in 1996, substantial strides have been made in confirming the rapid microlensing signature in
the Q0957 system and in other gravitational lens systems. The most rapid event recognized had
a 1% amplitude and a 12-hour duration.
Interpretation of the rapid fluctuations has centered upon 3 offered explanations; microlensing
of fine quasar structure by a population of planet mass astronomical bodies in the lens galaxy,
orbiting bright structures in the accretion disc of the supermassive black hole of the quasar,
or dark clouds swarming around the luminous quasar source. The observations, particularly the
equal positive and negative fluctuations, seem to strongly favor the cosmological population of
planetary mass objects in the lens galaxy.
Of the several ideas advanced for the origin of such a population, the most appealing seems to
be their birth at the time of recombination 300,000 years after the Big Bang.
||Authors: R. Gil-Merino, G.F. Lewis|
||A&A 437 (2005) L15 [astro-ph/0505372]|
||Interpreting microlensing signal in QSO 2237+0305: Stars or planets?
The multiply imaged, gravitationally lensed quasar, QSO 2237+0305, has been the subject
of recent optical monitoring campaigns, with its light curves displaying uncorrelated variability
attributed to gravitational microlensing by masses in the foreground galaxy.
Ref. [astro-ph/0503018] Einstein Cross, QSO2237+0305
Based on these light curves, it has been claimed that the dominant microlensing
population must be a population of free-floating Jupiter-like objects; such a conclusion
is not new, with several similar claims in the literature.
Historically, however, it has been shown that such conclusions are flawed,
with an incorrect interpretation of the complex caustic network that arises
at significant optical depth. This paper examines this more recent claim,
illustrating that it too is flawed.
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