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PHY323:Lecture 7 with Gravitational Lensing

•Strong Gravitational Lensing •Theory of Gravitational Lensing •Weak Gravitational Lensing •Large Scale Structure

Experimental Evidence for Dark Matter V Homework I

Deadline Mon 14th March

Attempt all the questions If you get stuck with any of the questions please see me or e-mail and I will help

You should get 100% I will return scripts after marking with feedback n.spooner@sheffield.ac.uk office: E23 , extension 2-4422 What is Gravitational Lensing? In a system where lensing occurs there is a: source: where the light comes from, can be a , a , etc. lens(es): which deflect(s) the light by an amount related to its mass/energy observer: sees a different amount of light than otherwise because the lens has bent and thus the travel paths of the light

(1) a geometric time delay and note also we get: (2) a gravitaional time delay Types of Gravitational Lensing A very powerful technique that can be used to detect and measure non-luminous mass on scales of , clusters, but also smaller objects. Three types of lensing:

(1) Strong Lensing see for instance http:// (2) Weak Lensing astro.berkeley.edu/~jcohn/lens.html (3) Micro Lensing The distinction between these regimes depends on the positions of the source, lens and observer, and the mass and shape of the lens (which controls how much light is deflected and where)

Strong: rare but gives strong local constraints on the potential. Weak: difficult to quantify, but will occur in every cluster of galaxies. Micro: smaller objects such as MACHOs in our own Galaxy Strong Gravitational Lensing Strong Lensing: 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.

Example 1: Galaxy notes Cluster Abell 370

HST image Additional Note on Abell 370

google HST gravitational lensing images

While imaging the cluster of galaxies Abell 370, astronomers had noted an unusual arc to the right of many cluster galaxies. Although curious, one initial response was to avoid commenting on the arc because nothing like it had ever been noted before. In the mid-1980s, however, better images allowed astronomers to identify the arc as a prototype of a new kind of astrophysical phenomenon -- the effect of entire cluster of galaxies on background galaxies. Today, we know that this arc actually consists of two distorted images of a fairly normal galaxy that happened to lie far behind the huge cluster. Abell 370's gravity caused the background galaxies' light -- and others -- to spread out and come to the observer along multiple paths, not unlike a distant light appears through the stem of a wine glass. In mid-July, astronomers used the just-upgraded to image Abell 370 and its gravitational lens images in unprecedented detail. Almost all of the yellow images pictured above are galaxies in the Abell 370 cluster. An astute eye can pick up many strange arcs and distorted arclets, however, that are actually images of more distant galaxies. Studying Abell 370 and its images gives astronomers a unique window into the distribution of normal and dark matter in galaxy clusters and the universe. Strong Gravitational Lensing Strong Lensing: produces clear magnified images of background objects e.g. of distant galaxies behind a cluster A powerful Probe of Dark Matter in Galaxy Clusters. Example:

notes Distortion (ringsAbell or Clusters multiple images) caused by gravitationalAn all-sky lens catalog of 4073 rich clusters of galaxies, each arc-like objects having at least 30 members within the magnitude range m3 to m3+2 Strong Gravitational Lensing Example: Galaxy Cluster 0024+1654 336 h-1 kpc, 1 arc min. Elliptical Einstein rings are clearly observed in this Hubble image The ring of blue disks are images of a background galaxy. The angular radius of the ring is 30 arc seconds. An average galaxy yields about 0.5 arc second of deflection, that deflection being proportional to the square root of the mass, so there should be 602, or approx 103 galaxies of mass are within the ring. But we only see about 100 galaxies, so there is a factor of 10 more matter than in the galaxies ! Strong Gravitational Lensing Strong Lensing: can be sufficient to reconstruct quite detailed maps of dark matter distributions in clusters, as below.. Working backwards from the strong lensing allows the dark matter to be mapped - it shows that bulk of a cluster is dark Example: Galaxy Cluster CL0034-1654

[From Tyson et al., Astrophys. Journ. 498, L107-L110, 1998 May 10] Notes e.g. sketch in “3D” the form of the matter distribution in a galaxy cluster like CL0034-1654 a found by GL Strong Gravitational Lensing Strong Lensing: can produce clear rings or multiple images due to concentrated mass Example: Einstein Rings

notes Gravitational Lensing Theory (1) Deflection of a Light Beam

angle that light beam is deflected

b is called the impact parameter for the incoming trajectory. Gravitational Lensing Theory (2) Bending of light around the Sun Worked Example Estimate the angle of deflection for the following two cases: (1) Bending of light by an object of mass 1kg at b = 1m; ANS: given in lecture (2) Bending of light around the edge of the Sun: ANS: given in lecture APPARENT ORIGIN

ACTUAL ORIGIN OBSERVER ON Effect first observed by MOON EARTH Eddington et al., 1919. SUN Gravitational Lensing Theory (3) Bending of Light by a Galaxy ‘Quick & Dirty’ result: Consider the bending of light by a galaxy predominated by dark matter. BACKGROUND CLUSTER LIGHT SOURCE M US R

Now assume that the deflected beam passes through the dark halo of the galaxy, so that its closest approach is within the region where the rotation curve is flat. Then Bending of Light by a Galaxy Now the impact parameter is roughly the radius of closest approach, and we therefore write b=R. So you get:

Most things cancel and you end up with

Incredibly, in this approximation, the deflection depends only on the virial velocity of the galaxy. Assuming a virial velocity equal to that of our own galaxy, you get

...per galaxy. This is independent of the distance of closest approach of the galaxy. NOTE THE HUGE ASSUMPTION that the light ray passes through the galactic halo. This is not true for spread out clusters - see example later. Notes e.g. prove that for a typical galaxy we expect GL bending of about 0.5 arcsec Gravitational Lensing Theory (4) The Massive Objects as Gravitational Lenses Bending of light in gravitational fields can make lenses out of massive objects NO LENS

LENS SOURCE US LENSING OBJECT Strong or close lens, expect a ring of light, or a ring of images in the presence of the lens - the so-called Einstein Ring. When not resolved, expect increased intensity. Radius of the Einstein Ring Worked Example Radius of the Einstein Ring Show that the opening angle of the Einstein ring is proportional to the square root of the mass enclosed, if the lensing galaxy is half way between us and the source.

Approximate Calculation when DSL=DLE=D

ANS: given in lecture Extra Note Consequences for Estimate Formula Note that in the last formula, the opening angle varies as the square root of the mass if all the mass is at the same distance from the observer, but in the previous estimate we said one arcsecond per galaxy. The estimate method is flawed, in that it assumes that all deflections are in the same plane. In fact, the galaxies are distributed over 3d, and 2d of this is the plane of the cluster as seen from earth. Compromise estimator method, take the angular deflection and divide by 0.5 arc seconds. Square it, and this is an estimate of the number of galaxies you would need to cause that angular deflection. Very rough - don’t try unless I tell you to... N = number of milky-way-like galaxies causing lensing. Distances and Reminder Strong and weak gravitational lensing involves large distances measured using of typically more than about 0.5. Thus we must use the second order Hubble relation (see Lecturte 2):

learn this equation q0 is called the deceleration parameter, which takes account of evolution of the expansion rate, the value being q0 = - 0.2. Worked Example A spectrum of the Einstein ring shows an emission line at 1200 Å. The same line observed in the laboratory is at 800 Å. How far is the source from Earth?

ANS: given in lecture But.... Note that Gravitational Lenses have a Bad Spherical Aberration. Lens you might buy:

Lens you might throw in the bin: Weak Gravitational Lensing In many cases the lens is not strong enough or concentrated in one place enough to form multiple images or arcs.

However, the source can still be distorted: (1) stretched (shear) (2) magnified (convergence).

If all sources were well known in size and shape, one could just use the shear and convergence to deduce the properties of the lens. However, usually one does not know the intrinsic properties of the sources, but has information about the average properties. The statistics of the sources can then be used to get information about the lens. Weak Gravitational Lensing

Galaxies in general aren't perfectly spherical, but if one has a collection of galaxies one doesn't expect them all to be lined up. Thus, if a set of galaxies is lensed, statistically, there will be some overall shear and/or convergence imposed on the distribution, which will give information about the intervening lens(es). Weak lensing inversion Weak Lensing: Most often the lens is too weak to create rings and arcs but the background galaxies are still sketch a typical DM distorted profile density contour for a cluster that might This distortion can be extracted from show up in weak lensing statistical analysis when many galaxies are observed Weak Lensing

Can you see the shear direction of the weak lensing?

So weak lensing also requires dark matter? Weak vs. Strong Lensing Micro Lensing Non-luminous small massive objects can be found by ‘Micro-lensing’ much more next lecture

Massive Object

Star in nearby galaxy Earth

Microlensing observations are used to search for MACHOs (massively compact halo objects), such as small black holes or brown dwarfs, as being a dominant dark matter component Extra Note - MicroLensing In some cases the lensing is of an image that is so small or faint that one doesn't see the multiple images-- the additional light bent towards the observer just means that the source appears brighter. (The surface brightness remains unchanged but as more images of the object appear the object appears bigger and hence brighter.) This lensing can have effects in many measurements, as sources which would have otherwise been too dim become visible. This can be helpful, as when one wants to view objects that would otherwise be too far away. It can also be a problem, for example when one is trying to measure all objects brighter than a certain amount in a certain region and lensing introduces objects by magnifying objects enough to bring them into the sample Conclusion on Clusters and GL So there is evidence for LOTS of dark matter in Galaxy Clusters. A bigger fraction than in halos of individual Galaxies The halos must be so big (100 kpc or more) that their halos merge in a cluster to form an overall density of dark matter. Remember, Galactic dynamics imply that halos contain about 10 times as much dark matter as visible matter. Gravitational Lensing indicates that there is about a hundred times as much dark matter as visible matter in this galaxy cluster. Lensing experiments do not require understanding of any galactic or intergalactic dynamics. Only is required to get the gravity right. Strong and weak lensing analyses lead to the same conclusions about the dark matter composition of galaxy clusters. This agreement persuaded many astrophysicists of the reality of dark matter Dark Matter in Super Clusters Finaly, on scales of very large structure it is impossible to build good models of the cosmos, voids and streams, clusters and super clusters, without this dark matter.

It is now known that there are also superclusters or “great walls” and other large structures as large as 50 photo in lecture Mpc. These have been mapped in 3 dimensions through redshift measurements. The high velocity streaming in these is consistent with even greater masses. Extra Note Dark Matter in Super Clusters The largest scale on which the mass density has been measured with any precision is that of superclusters. A supercluster is an aggregate of several clusters of galaxies, extending over about 10 Mpc. Our local supercluster is an extended distribution of galaxies centered on the Virgo cluster, some 10-20 Mpc distant, and our galaxy together with the Andromeda galaxy forms a small group (the Local Group) that is an outlying member of the Virgo Supercluster. The mass between us and Virgo tends to decelerate the recession of our galaxy, as expected according to Hubble’s Law by about ten percent. This effect is seen as a deviation from the uniform Hubble Expansion of the galaxies and provides a measure of the mean density within the Virgo Supercluster. One again finds a ratio of mass-to-luminosity equal to 300 over this scale, which amounts to about 20Mpc.