zel1

8/6/2019 zel1

1/19

409RESONANCE May 2011

GENERAL ARTICLE

Ya B Zeldovich (1914 1987)Chemist, Nuclear Physicist, Cosmologist

Varun Sahni

Keywords

Ya B Zeldovich, cosmology,

black holes, expanding universe,

cosmic web.

Varun Sahni did his PhD

in Moscow State Univer-

sity under the supervision

of Ya B Zeldovich and A A

Starobinsky.

He is a professor at

IUCAA with interests in:

the early Universe, gravity

waves, dark matter and

dark energy, quantum

field theory in curved

space-time and the

formation of large scale

structure in the Universe.

1 Bourbaki was the pseudonym

collectively adopted by a group

of twentieth century mathemati-

cians who wrote several influen-

tial books under this pseudonym

on advanced mathematical con-

cepts.

Ya B Zeldovich was a pre-eminent Soviet physi-

cist whose seminal contributions spanned many

elds ranging from physical chemistry to nuclear

and particle physics, and nally astrophysics and

cosmology. This article attempts to convey some

of the zest with which he did science and the im-

portant role he played in fostering and mentoring

a whole generation of talented Soviet scientists.

Introduction

Yakov Borisovich Zeldovich was exceptionally talented.His active scientic career included major contributionsin elds as diverse as chemical physics (adsorption andcatalysis), the theory of shock waves, thermal explo-sions, the theory of ame propogation, the theory ofcombustion and detonation, nuclear and particle physics,and, during the latter part of his life: gravitation, astro-physics and cosmology [1].

Zeldovich made key contributions in all these areas, nur-turing a creative and thriving scientic community inthe process. His total scientic output exceeds 500 re-search articles and 20 books. Indeed, after meeting him,the famous English physicist Stephen Hawking wrote\Now I know that you are a real person and not a group

of scientists like the Bourbaki"1

. Others have comparedhis enormously varied scientic output to that of LordRaleigh who, a hundred years before Zeldovich, workedon elds as varied as optics and engineering.

Remarkably Zeldovich never received any formal uni-versity education! He graduated from high school in St.Petersburg at the age of 15 after which he joined the

8/6/2019 zel1

2/19

410 RESONANCE May 2011

GENERAL ARTICLE

Pioneering work on

nuclear fission and

fusion.

Institute for Mechanical Processing of Useful Minerals(`Mekhanabor') to train as a laboratory assistant. Thedepth of Zeldovich's questioning and his deep interestin science soon reached senior members of the scienticcommunity and, in 1931, the inuential soviet scientistA F Ioe wrote a letter to Mekhanabor requesting thatZeldovich be \released to science". Zeldovich defendedhis PhD in 1936 and, years later, reminiscenced of the\happy times when permission to defend [a PhD] wasgranted to people who had no higher education".

Despite his never having been formally taught (or per-haps because of it!) Zeldovich developed a very originalstyle of doing science, and became, in the process, an ex-ceptional teacher. It is also interesting that in his earlyyears Zeldovich had been an experimentalist as well asa theoretician, and this closeness to complementary as-pects of science guided him throughout his later life.

Nuclear and Particle Physics

It is quite remarkable that Zeldovich ventured into a

totally new eld { Astrophysics { around 1964 whenhe was nearing 50. By then Zeldovich had already de-veloped a very considerable reputation in elds rangingfrom physical chemistry (there is a `Zeldovich number'in combustion theory) to nuclear physics. Indeed, hav-ing done pathbreaking work on combustion and detona-tion, Zeldovich moved to nuclear physics in the 1930'swriting seminal papers demonstrating the possibility ofcontrolled ssion chain reactions among uranium iso-topes. This was the time when fascism was on the rise

in Germany, and, in an eort for national survival, theSoviet Union was developing its own atomic program ofwhich Zeldovich (then in his mid 20's) quickly becamea key member. According to Andrei Sakharov, \fromthe very beginning of Soviet work on the atomic (andlater thermonuclear) problem, Zeldovich was at the veryepicenter of events. His role there was completely

8/6/2019 zel1

3/19


GENERAL ARTICLE

2 Space does not permit me to

elaborate on Zeldovichs other

seminal work in this area whichincluded the possibility of muon-

catalyzed fusion (1954), his work

on weak interactions i ncluding

his brilliant hypothesis on the

existence of parity violating neu-

tral currents (1959), his remark

(1957) about the existence of a

toroidal dipole moment (which

has since spawned an active

research area) and his predic-

tion about the existence of the K

meson (1958) which was subse-

quently discovered. The reader

is referred to [1] for more details.

exceptional" [2]. One might add that Zeldovich's ear-lier work on combustion paved the way for creating theinternal ballistics of solid-fuel rockets which formed thebasis of the Soviet missile program during the `great pa-triotic war' and after [3]. Sadly, much of Zeldovich'swork during this period remains classied to this day.

After the war Zeldovich went on to do pioneering workin several other aspects of nuclear and particle physicsincluding 2:

In 1952 and 1953 Zeldovich proposed laws for theconservation of lepton and baryon charges.

In 1955 Zeldovich and Gershtein suggested the con-servation of the weak vector current. This ideawas independently discovered some years later byFeynman and Gell-Mann and played a key rolein the development of the theory of weak inter-actions. Zeldovich (1959) also suggested the ex-istence of neutral currents which violated parity

conservation. He showed that parity violation inweak interactions should lead to the rotation of theplane of polarization of light propogating in a sub-stance not containing optically active molecules.This prediction was subsequently conrmed.

In 1959 Zeldovich suggested a method of contain-ment (storage) of slow neutrons via total internalreection from graphite. This method is now reg-ularly used to measure the neutron electrical mo-ment.

Zeldovich also studied the possible existence oflong-lived nuclei with a large isotopic spin. Hesuggested the possibility of observing an isotopeof 8He, soon after which this isotope was, in fact,discovered!

8/6/2019 zel1

4/19


GENERAL ARTICLE

3 By this time Zeldovich was a

very well-known figure in Soviet

science and had won several

major laurels including three gold

stars, the Lenin Prize and a fel-

lowship of the prestigious Soviet

Academy of Science.

Astrophysics and Cosmology

Instead of resting on his laurels (had he so desired Zel-dovich could have easily landed a `comfortable' job head-ing a premier research laboratory or institute), Zeldovichdecided to change course midstream and, from about1964, devoted his phenomenal abilities to problems inastrophysics3. A change of track can be precarious ifmade later in life when ones scientic tastes and habitshave usually become set. Indeed, each scientic disci-pline has its own nuances the mastering of which can

take considerable time and eort, and history is repletewith examples of scientists { exceedingly capable in theirchosen eld { making grave errors of judgement whenmoving to another.

It is therefore quite remarkable that Zeldovich not onlyplunged deeply into astrophysics, he virtually revolutio-nized the eld, becoming in the process one of the found-ers of relativistic astrophysics and physical cosmology.

Below is an imperfect attempt to summarize some of Zel-

dovich's seminal contributions to astrophysics and cos-mology.

1. In 1963 Zeldovich and Dmitriev showed that the totalenergy of a system of particles interacting via gravity(in a universe expanding according to Hubble's law v =HR) evolved according to the simple formula

dE

dt= (2K + U)H; (1)

where E = K + U is the total energy of the system

with K and U being its kinetic and potential energyrespectively. (This relation was independently suggestedby Layzer (1963) and Irvine (1961) and is frequentlyreferred to as the Cosmic Energy Equation.) _E = 0 oncematter decouples from cosmological expansion. In thiscase, (1) reduces to the virial equation 2K+U = 0 whichcan be used to investigate the amount of dark matter

8/6/2019 zel1

5/19


GENERAL ARTICLE

4 Smaller mass black holes would

have evaporated by emitting

Hawking radiation and disap-

peared.

Zeldovichsuggested that

black holes might

glow and be

detectable

since they

accreted matter.

associated with gravitationally-bound systems such asclusters of galaxies.

2. Zeldovich was intrigued by black holes and spenta considerable amount of eort in understanding theirproperties. In 1962 Zeldovich published a paper in whichhe showed that a black hole could be formed not onlyduring the course of stellar explosions, as was then widelybelieved, but by any mechanism which compressed mat-ter to suciently high densities. This opened up the pos-sibility of the formation of microscopically small black

holes in the early Universe. Were they to survive un-til today, the smallest black holes would have masses ofabout 1016 grams, roughly that of a large mountain4.There has also been some speculation that microscopicblack holes may be the dark matter that everyone issearching for! (This was Zeldovich's rst paper on Gen-eral Relativity. It was also the last work that he dis-cussed with his teacher, Lev Landau, before the latter'stragic car accident in 1962.)

3. In 1964 Zeldovich suggested that a black hole may be

detected by its inuence on the surrounding gas whichwould accrete onto the hole. (The same result was inde-pendently obtained by E Salpeter in the USA.) In 1966Zeldovich also suggested (with Guseinov) that one couldlook for a black hole in binary star systems through thehole's inuence on the motion of its bright stellar com-panion. These papers helped create a paradigm shift inwhich black holes were elevated from their earlier sta-tus of `impossible to observe passive objects' to objectswhich created very signi cant astrophysical activity in

their vicinity.Thus Zeldovich's early work led to what is currently athriving area in astrophysics, with numerous observa-tional programmes being dedicated to the discovery ofblack hole candidates in our own galaxy as well as indistant galaxies and QSO's.

8/6/2019 zel1

6/19


GENERAL ARTICLE

Zeldovich and

Starobinsky

demonstrated that in arapidlyexpanding

universe the vacuum

was unstable and

spontaneously

gave birth to particles

and antiparticles .

4. Zeldovich remained deeply interested in black holesand, in 1971, turned his attention to the issue of par-ticle production and vacuum polarization in the stronggravitational elds that one would expect to encounternear black holes and during the early infancy of theuniverse. Zeldovich (1971) and his student Starobinsky(1973) showed that under certain conditions a rotatingblack hole could loose energy via the production of aparticle{antiparticle pair. These papers were precursorsof a whole body of later work including Stephen Hawk-ing's famous paper on evaporating black holes publishedin 1975.

5. In tandem with their study of quantum eects nearblack holes, Zeldovich and Starobinsky began a system-atic investigation into quantum eects which occur dur-ing the early stages of the universe when it was expand-ing very rapidly. Quantum eld theory informs us that,far from being empty, the vacuum is actually seethingwith activity in the form of virtual particle{antiparticlepairs in the constant process of creation and destruction.

From the uncertainty principle Et ~

we know thatsuch pairs (of mass 2m) come into existence for a veryshort time t ~=2mc2. If an electric eld is applied tothe vacuum then, for a suciently large value (Ecr), thework done (W) on the virtual pair can become equalto the total rest mass 2mc2:

W = cjeEcrj ' 2mc2 ; (2)where the Compton length c = ~=mc provides an esti-mate of the separation between particle and antiparticle.

The critical eld value Ecr ' m2

c3

=jej~at which the vac-uum becomes unstable to particle{antiparticle produc-tion is called the Schwinger limit, after Julian Schwingerwho discovered it in 1951. (Ecr 1016 volt=cm for elec-trons.)

Zeldovich and Starobinsky showed that a similar eectoccurs if the universe is expanding rapidly. In this case

d

8/6/2019 zel1

7/19


GENERAL ARTICLE

5 The present-day universe ex-

pands according to Hubbles law

v = Hr, where the Hubble pa-

rameter H is a scalar quantity

whose value depends only upon

time but not upon spatial direc-

tion. During anisotropic expan-

sion, the expansion rate is dif-

ferent along the three spatial

directions so that Qi

= Hijrj, with

the Hubble parameter being pro-

moted to a tensor.

the role of the electric eld is played by the gravita-tional eld which, in Einstein's general relativity, is anexpression of space-time curvature. A rapidly expand-ing universe literally tears a virtual particle{antiparticlepair apart giving rise to spontaneous particle creationfrom the vacuum. Near the big bang the universe ex-pands very rapidly, (its rate of expansion being given bythe Hubble parameter H = _a=a), and copious particleproduction from the vacuum is expected when the ex-pansion rate becomes of the order of the particle mass(H

m).

In an inuential paper published in 1971, Zeldovich andStarobinsky showed that particle production from thevacuum becomes extremely signicant if the universeexpands anisotropically5. In this case the copious en-ergy density of particles released from the vacuum farexceeds that of any pre-existing matter in the universe!Furthermore, the newly created particles (and their an-tiparticles) backreact on the universe through the semi-classical Einstein equations, Gik = 8GhTiki, isotropis-ing its expansion. The mechanism proposed by Zel-dovich and Starobinsky provided an interesting meansof making the properties of the universe similar to whatwe observe today.

It is well known that the most general solutions to theEinstein equations will be both inhomogeneous and aniso-tropic. Even if one were to restrict oneself to homoge-neous models (whose spatial properties did not dependupon the precise location of the observer), a universewhich expanded at dierent rates along dierent direc-

tions was, in a sense, much more likely than our ownisotropic universe. This dilemma was substantially ame-liorated by the work of Zeldovich and Starobinsky sincecopious particle production (and vacuum polarization)would ensure that a universe whose expansion was ini-tially anisotropic soon isotropized and began to resem-ble our own!

8/6/2019 zel1

8/19


GENERAL ARTICLE

6 The possibility of massive neu-

trinos playing the role of dark

m at t er w as p o in t ed o ut b y

Cowsik and McClelland (1973)

and independently by Marx and

Szalay (1972). However it is cur-

rently believed that neutrinos

account for only a small fraction

of the total dark matter density in

the universe.

Even a tiny mass ofthe neutrino is

sufficient to make it

an important player

in the cosmological

scenario .

6. In 1966 Zeldovich and Gershtein showed that, if neu-trinos were massive, then they could very easily be thedominant matter component in the universe. The reasonhas to do with the fact that the theory of weak interac-tions predicts a relic abundance for neutrinos of roughly100 particles per cubic centimeter (per species). (Bycomparison the cosmic microwave background contains 400 photons per cubic centimeter, also of relic origin.)If neutrinos were massive then, for a large enough mass,their density could easily exceed that of visible mat-

ter in the universe! Zeldovich and Gershtein placed alimit on the mass of the muonic (and electronic) neu-trino from cosmological considerations. Their result,m() < 400 ev cm

3, was considerably lower than lab-oratory bounds at the time, and convincingly demon-strated that the universe could be used as a particlephysics laboratory.

Subsequently Schwartzmann, a student of Zeldovich, sho-wed how the number of neutrino species could be con-strained from observations of the helium abundance in

the universe. (The reason is simple: a larger numberof neutrinos speeds up cosmic expansion and, in so do-ing, alters the primordial nucleosynthesis of light ele-ments taking place during the rst few minutes of thebig bang.) These early papers by Zeldovich and his stu-dents proved to be prescient in dening a vibrant neweld, Astroparticle Physics, in which the early universeplays the role of a particle-physics laboratory. In the1970's, the existence of a large amount of dark matterin galaxies was discovered observationally. Zeldovich's

earlier work demonstrated that relic non-baryonic par-ticles left over from the big bang could easily play thisrole! Non-baryonic dark matter is currently believed toconstitute roughly a third of the total matter density inthe universe { signicantly more than the 4 con-tributed by baryons and electrons6.

8/6/2019 zel1

9/19


GENERAL ARTICLE

7

(i) Zeldovichs paper (withKhlopov) demonstrating that the

abundance of t HooftPolyakov

monopoles was unacceptably

large appeared in 1978, a year

before the famous paper by

Preskill which highlighted the

same problem but within the

framework of grand unified theo-

ries. (ii) Cosmic strings created

during a grand unified phase

transition will have a radius much

smaller than that of a proton, an

enormous length ( upto a million

light years) and a very high den-

sity: a kilometer long cosmic

string can be as massive as the

earth! These enormously long

one-dimensional objects should

not be confused with the much

smaller superstrings.

Cosmic stringscan seed galaxy

formation in the

universe.

7.Zeldovich returned to the issue of relic abundances afew years later in a seminal work on eld theory. Cos-

mology, like other disciplines, has frequently been inu-enced by developments in neighboring elds. An exam-ple is provided by eld theories including those in whichthe ground state is degenerate so that the system cansettle into dierent ground states in dierent regions ofspace. (In ferromagnetism, at temperatures below theCurie point, the magnetization vector can point in anygiven direction. The phase transition in this case is ofsecond order.)

Zeldovich investigated cosmological consequences of pha-se transitions which could have occured in the earlyuniverse when its temperature was exceedingly high.He demonstrated that theories with degenerate groundstates predicted a relic abundance of `new objects', calledtopological defects, which can be zero-dimensional (suchas magnetic monopoles), one-dimensional (such as cos-mic strings), or even two-dimensional domain walls. Top-ological defects arise during an early phase transition

once the universe has cooled below a critical value. Theirproperties are similar to the defects seen in laboratoryphysics such as vortices in a superuid and ux tubesin a superconductor. Zeldovich, Kobzarev and Okun(1974), and independently Kibble (1976), appreciatedthe enormous impact that stable topological defects couldhave within a cosmological setting. Zeldovich and hiscolleagues demonstrated that whereas monopoles andwalls were disastrous for cosmology, cosmic strings mightbe useful since they would act as `seeds' onto which mat-ter accreted resulting in the formation of galaxies and

other gravitationally-bound systems7.

8. In 1967 Zeldovich applied himself to the puzzle ofthe cosmological constant `'. Originally introduced byEinstein in 1917, the cosmological constant has the un-usual property that its pressure is negative and equal, inabsolute terms, to its density (P = ). Hence, while

8/6/2019 zel1

10/19


GENERAL ARTICLE

The CosmologicalConstant naturally

arises within the

framework of

quantum field

theory.

the density in normal forms of matter declines in an ex-panding universe, the density in remains frozen to aconstant value = =8G. After its inception the cos-mological constant had fallen into disrepute since it didnot seem to be required by observations. Even Einsteindistanced himself from it, calling the -term `my biggestblunder'.

Zeldovich radically changed this perspective by persua-sively arguing that, within the context of quantum eldtheory, the prospect of a non-zero value for the -term

should be taken extremely seriously. The reason is thatthe quantum polarization of the vacuum results in avacuum energy which, quite remarkably, has the pre-cise form of a cosmological constant: hTki i = ki =8G.(The equation of state P = is, in fact, Lorenz invari-ant and remains the same in any coordinate system. Sothe properties of the vacuum do not change from one co-ordinate system to another, which is indeed a desirableproperty.) A positive cosmological constant can resultin an accelerating universe, and by strongly supporting

the -term, Zeldovich paved the way for future advancesincluding cosmic ination in the 1980's and dark energyin this century [4]. These new results suggest that theuniverse accelerated both in its remote past (ination)and at present (dark energy). Thus current observationsappear to require a form of matter whose properties aretantalizingly similar to that of the -term and one is re-minded of Zeldovich's prescient statement, regarding ,made almost half a century ago [5] \the genie has beenlet out of the bottle, and it is no longer easy to force it

back in".9. The discovery of the cosmic microwave background(CMB) in 1964 resulted in Zeldovich becoming an ar-dent believer in the hot big bang model of the universe(originally proposed by another gifted Russian physi-cist George Gamow). During 1968{1971, working witha dedicated team of students and researchers (including

8/6/2019 zel1

11/19


GENERAL ARTICLE

8 This took place about 100,000

years after the big bang, when

the temperature of the universe

had dropped to 4000 oK. Prior to

this the universe had been

opaque to the passage of light.

9 Additionally, if the phases of

I(k) are randomly distributed,

then the spatial distribution of

the gravitational potential I(x)

has the properties of a Gaussian

random field.

Doroshkevich, Novikov and Sunyaev), Zeldovich showedhow the CMB could be used to probe the properties ofthe early universe. His work in this eld focussed on sev-eral key issues including that of the cosmological recom-bination of hydrogen from free protons and electrons8,the nature of angular uctuations in the CMB, and howthese could be linked to uctuations in matter. He alsoaddressed the problem of cosmological nucleosynthesisin the hot early universe.

The Zeldovich Approximation and the Cosmic

Web

Zeldovich himself felt that his main contribution to cos-mology was in the understanding of how gravitationalinstability develops in the universe from small initialvalues.

A realistic model of galaxy formation clearly requirestwo essential ingredients:

(i) A description of the initial uctuations in the distri-bution of matter which might later form galaxies.

(ii) A theory describing the growth of these uctuationsunder the inuence of gravity or other forces.

In 1972 Zeldovich published a paper which subsequentlyproved to be rather prescient. In it he discussed how`seed' uctuations (which later gave rise to galaxies)could have a scale invariant spectrum. Mathematicallythis meant that the fourier amplitudes of the spatiallyuctuating gravitational potential had the form j(k)j2 /k3, so that

R

j(k)

j2d3k =

Rdlog k. In other words,

each logarithmic interval contributed an equal amountof power to the gravitational potential responsible formoving matter into galaxies9. (The scale invariant spec-trum was independently discovered by E Harrison.) Adecade after it was initially proposed on phenomenolog-ical grounds, the scale invariant spectrum was shownto be a generic prediction of inationary models of the

8/6/2019 zel1

12/19


GENERAL ARTICLE

early universe, where its origin was quantum mechani-cal. The presence of uctuations in the CMB detectedby the COBE satellite in 1992 marked a turning pointin our understanding of the universe since it showedthat the infant universe had not been featureless andsmooth, but had tiny uctuations (approximately 1 partin 100,000) imprinted on it. The (fourier) spectrum ofthese uctuations turned out to have the `scale-invariantform' suggested by Zeldovich and Harrison more thantwo decades earlier. (These tiny uctuations in matterbecome galaxies several billion years later, after being

amplied by gravitational instability.) This milestonediscovery made by COBE was awarded the Nobel Prizein Physics in 2006.

An important property of the universe is that it is gravi-tationally unstable. This means that small initial uctu-ations in the density of matter grow and become larger.A theoretical analysis of density uctuations had beencarried out in the 1940's by the eminent Soviet physi-cist Evgeny Lifshitz. Lifshitz had shown that in anexpanding universe density perturbations grow at therather modest rate / t2=3. This is very much slowerthan the exponentially rapid `Jeans instability', /exp(

p4Gt) which occurs in a static universe. The

reason for the dierence is that cosmic expansion movesparticles away from one another while gravity pushesthem together. Since the two inuences oppose eachother, gravitational instability becomes weaker if theuniverse expands. Although Lifshitz's treatment wasrigorous it had a fundamental limitation. In order tosolve the complicated equations of general relativity Lif-

shitz had to assume that perturbations were linear, i.e., 1, where = ()= is the perturbation in the cos-mic density relative to its mean value . Although thisapproach was exceedingly useful in the context of theearly universe which was quasi-homogeneous, it brokedown at more recent times since density perturbations

8/6/2019 zel1

13/19


GENERAL ARTICLE

10 The pancake is a popular and

tasty Russian dish. One could

equally well substitute pizza,

chapati or dosa, depending upon

ones, favourite cuisine!

11 The comoving coordinate r

is a convenient quantity be-

cause, in the absence of per-

turbations, its value does not

change as the universe ex-

pands. It is related to the physi-

cal coordinate x by means of

the transf ormation r = x/a(t).

The Zeldovich approximation

in physical coordinates has the

form x = a(t)[q + v(q) Gl] .rand

q respectively represent the

Eulerian and Lagrangian coor-

dinate of a particle in fluid dy-

namics.

at the present epoch are exceedingly large, the densitycontrast associated with a galaxy being close to a million( 106).Zeldovich set about rectifying this situation by propos-ing, in 1970, a remarkably simple and elegant approx-imation which could be used to follow a perturbationfrom its initially linear form into the fully nonlinearregime when 1. Along the way Zeldovich up-set a widely prevailing world view according to whichthe assembly of the rst large astrophysical objects in

the universe was spherical in nature. According to thispoint of view, the spherical globular clusters that or-bit our galaxy were the rst objects to condense out ofan expanding quasi-homogeneous gas of neutral hydro-gen. Zeldovich toppled this deeply ingrained notion bydemonstrating that gravitational instability was muchmore likely to proceed in an anisotropic manner result-ing in the formation of two-dimensional sheet-like ob-jects which he called `Pancakes'10.

The Zeldovich approximation proposes that the nal co-

ordinate of a particle is related to its initial coordinateby the transformation

r = q + v(q) ; (3)

where is the density contrast predicted by linear the-ory and v(q) is the initial velocity eld of a pertur-bation11. (v(q) = 0 if particles remain at rest with re-spect to the background cosmic expansion, in which caser = q.) If the particle ow is irrotational then, undersome assumptions, one can relate the velocity eld to

the linearised gravitational potentialv(q) = r : (4)

In turn is related to the primordial density perturba-tion and the mean density of matter in the universe,, through the Poisson equation

r2 = 4Ga2 : (5)

8/6/2019 zel1

14/19


GENERAL ARTICLE

Figure 1. Caustics of light

in a pool of water.

The cosmic webseen in the

distribution of

galaxies is similar

to caustics

of light which form

in a pool of water.

We noted earlier that / t2=3. Introducing a new timecoordinate T = / t2=3 allows us to rewrite (3) as

r = q + v(q)T : (6)

We have thus shown that the Zeldovich approximationis equivalent to the simple inertial motion of particles!An essential feature of inertial motion from random ini-tial conditions is the intersection of particle trajectories

leading to the formation of singularities in the densityeld. A similar eect is seen in the propogation of lightas it passes through a medium such as a plate of glassor water. After passing through the plate, neighboringlight trajectories intersect to form caustics where theintensity of light is exceedingly bright (Figure 1).

Indeed, the Zeldovich approximation bears a very sim-ple analogy to the propogation of light rays in geomet-rical optics! Consider a light ray which enters a (two-dimensional) glass plate at the point q =

fq1; q2

g. If the

thickness of the plate is h = h(x; y) then, after passingthrough the plate, the light ray will be deected by anangle ~s(q), which determines the direction of the ray af-ter it passes through the plate [6]. The two-dimensionalcoordinates of the light ray after it has emerged fromthe plate will depend upon ~s as well as the location ofthe screen z, so that

8/6/2019 zel1

15/19


GENERAL ARTICLE

Figure 2. Caustics of light

on a screen.

Adapted from [6].

R(z; q) = q + sz ; (7)

where

si = (n 1)@h(q)

@qi(8)

and n is the refractive index of the plate.

A screen kept some distance away from the plate willsee an inhomogeneous distribution of light (Figure 2).Varying the location of the screen one will see caustics,

regions where light trajectories have interesected causingthe brightness of light to suddenly shoot up. If we denotethe brightness of light by , it is easy to show that

(z; q) =0

[1 z(q)][1 z(q)] ; (9)

where 0 is the initial intensity of light and (q) and(q) are the principal curvatures of the surface of theplate h = h(q). In other words (q) and (q) are eigen-values of the tensor @2h=@qi@qk. Clearly the optics rela-

tion (7) is identical to the Zeldovich approximation givenby (6). The similarity between optics and gravitationalinstability is striking! The role of the plate thickness h isplayed by the gravitational potential , and the location

8/6/2019 zel1

16/19


GENERAL ARTICLE

The cosmic web is

a percolatingcellular structure

consisting

of clusters and

superclusters of

galaxies separated

by giant voids.

of the screen z is analogous to the cosmic time coordi-nate T. In optics (gravitational instability) the intensityof light (density of matter) becomes extremely large atcaustics where nearby light (matter) trajectories inter-sect. From (9) we nd !1 when z' 1 (assuming > ). A similar result holds in the Zeldovich approx-imation when we replace z by T. In this case the law ofmatter conservation results in the following expressionfor the density

(x; t) =0

[1

T (q)][1

T (q)][1

T (q)];

T / t2=3 ; (10)where ; ; are the eigenvalues of the three-dimen-sional deformation tensor @2=@qi@qk and is the inho-mogeneous primordial gravitational potential responsi-ble for moving particles in (3), (4) and (6). Thus the Zel-dovich approximation predicts that matter moving un-der the inuence of a perturbing gravitational potential(q) will get focussed into caustics, at locations speci-ed by the eigenvalues of @2=@qi@qk. Whether a given

volume element contracts or expands depends upon thespecic values of the eigenvalues (q); (q); (q), in agiven region of space and especially on their sign. If, atthe point q one of the eigenvalues, say (q), is positive,then, since T / t2=3 is a monotonically increasing func-tion of time, a time will come when 1 T = 0. From(10) we nd that the denominator in this expression willvanish as the density of matter aquires very large (for-mally innite) values. This signals the formation of acaustic at q. Such a region will be the birthplace of a

pancake.Intersections of fully grown pancakes will form lamentsand intersections of laments will result in clumps. Mat-ter will have a multistream ow within pancakes, movingalong them towards laments, and then moving along l-aments to converge into clumps. The formation of caus-tics will be accompanied by the formation of immense

8/6/2019 zel1

17/19


GENERAL ARTICLE

Figure 3. The development

o f the Cosmic Web is

shown in a hydrodynamic

N-body simulation from z

= 6 (leftmost cube) to z= 0

(rightmost cube) via z = 2

(middle cube). A near fea-

t u re l e ss d e n si ty f ie l d

evolves to produce fila-

mentary and sheet-like su-

perclusters which perco-

late through the box-vol-

ume. These are separated

by large voids.

[Reproduced from Current Sci-

ence, Vol.88, No.7, 10 April

2005.].

Figure 4. The Sloan Great

Wall situated at the red-

shift z ' 0.08 is shown in

the upper panel of the fig-

ure. Forcomparison,a rela-

t ively n earer stru ctu re

known as the CfAgreatwall

is also shown. The linear

extent of the Sloan GreatWallis about 500 Megapar-

sec, which is roughly twice

as large as the CfA Great

Wall.

[Reproduced from Current Sci-

ence, Vol.88, No.7, 10 April

2005.].

underdense regions, or voids, from which matter getsdrained into pancakes and laments. Thus the Zeldovichapproximation predicts that, as the universe expands,

the matter in it becomes concentrated along planar andlamentary `superclusters', and that neighboring super-clusters are separated by `voids' { vast empty regionsvirtually devoid of the presence of matter (Figure 3).It is remarkable that precisely such a supercluster-voidnetwork of galaxies, now commonly referred to as theCosmic Web, has been discovered by large galaxy sur-veys almost 30 years after it was rst predicted to existby Zeldovich [7]. The supercluster which currently holdsthe record for being the largest contiguous object in the

universe is close to a billion light years across and hasbeen dubbed the Sloan Great Wall since it was discov-ered by the Sloan Digital Sky Survey (SDSS) (Figure4).

8/6/2019 zel1

18/19


GENERAL ARTICLE

Suggested Reading

[1] Selected works ofYa kov Borisovich Zeldovich, Princeton UniversityPress,

Vol.1&2, 1992.

[2] A Sakharov, A man of universal interests, Nature, London, Vol.331,

p.671, 1988.

The ionized gas ingalaxy clusters

distorts the Cosmic

Microwave

Background.

In his later years, Zeldovich, together with students Doro-shkevich and Shandarin and the eminent Soviet mathe-matician Vladimir Arnold, developed a rigorous mathe-matical understanding of gravitational clustering in theuniverse involving sophisticated mathemetical methodswhich included catastrophy theory and percolation anal-ysis. Work in this direction continues to this day [8].

The Cosmic Web is spectacular. The `atoms' of this webare galaxies, which gravitationally bind together to formclusters of galaxies (a `rich' cluster can contain several

thousand galaxies) and the much larger superclusters.In 1972, Zeldovich and Sunyaev published a seminal pa-per in which they showed that photons from the cosmicmicrowave background would scatter o the hot plasmatrapped in the deep potential wells of clusters. Thiswould alter the brightness of the CMB when viewed inthe direction of a cluster. Since its prediction almostfour decades ago, the Sunyaev{Zeldovich eecthas beenobserved in many galaxy clusters and promises to pavethe way for a deeper understanding of our universe on

the very largest scales, perhaps even throwing light onthe elusive nature of dark energy [9].

I hope that this short article has managed to conveyZeldovich's enormous contribution to science in generaland to astrophysics and cosmology in particular. Hislegacy and style of work are enormously inspiring andthe directions and vistas opened by him continue to bevery actively explored by a new generation of physicists.Some personal reminiscences of Prof. Zeldovich are con-tained in my second article on him in this issue of Res-

onance, p.462.

8/6/2019 zel1

19/19


GENERAL ARTICLE

[3] V L Ginsburg, Yakov Borissovich Zeldovich, Biographical Memoirs of

Fellows of the Royal Society, Vol.40, pp.431441, 1994.

[4] Ya B Zeldovich, Resonance, Vol.16, No.5, pp.480484, 2011.

[5] Ya B Zeldovich, The cosmological constant and the theory of elementary

particles, Sov.Phys.Usp., Vol.11, pp.381393, 1968.

Republished in Gen.Rel.Grav., Edited by Varun Sahni and Andrzej

Krasinski, Vol.40, pp.15571591, 2008.

[6] S F Shandarin and Ya B Zeldovich, Rev. Mod. Phys., Vol.61, p.185, 1989.

[7] J R Gott et al, Astrophys. J., Vol.624, p.463, 2005 [astro-ph/0310571].

[8] V Sahni and P Coles, Phys. Rep., Vol.262, No.1, 1995.

[9] Biman Nath, Resonance, Vol.16, No.5, pp.428436, 2011.

Address for Correspondence

Varun Sahni

Inter-University Centre for

Astronomy & Astrophysics

Post Bag 4, Ganeshkhind

Pune 411 007, India.

Email: [email protected]

Date post:	07-Apr-2018
Category:	Documents
Upload:	pratik-dabhade
View:	226 times
Download:	0 times

zel1

Documents