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Cluster-Cluster Microlensing as a Probe of Intracluster Stars, MACHOs, and Remnants of the

Cluster-Cluster Microlensing as a Probe of Intracluster Stars, MACHOs, and Remnants of the
Cluster-Cluster Microlensing as a Probe of Intracluster Stars, MACHOs, and Remnants of the

a r X i v :a s t r o -p h /0211222v 3 19 N o v 2002

T O A PPEAR

IN THE

A STROPHYSICAL J OURNAL

Preprint typeset using L A T E X style emulateapj v.14/09/00

CLUSTER-CLUSTER MICROLENSING AS A PROBE OF INTRACLUSTER STARS,MACHOs,AND

REMNANTS OF THE FIRST GENERATION STARS

T OMONORI T OTANI 1

Princeton University Observatory,Peyton Hall,Princeton,NJ 08544-1001,USA

To Appear in the Astrophysical Journal

ABSTRACT

The galaxy cluster Abell 2152is recently found to be forming a cluster-cluster system with another,more distant cluster whose core is almost perfectly aligned to that of A2152.We discuss the detectability of microlensing events where a single star in the source cluster behind A2152is extremely magni?ed by an intracluster compact object in A2152.We show that a search with an 8m-class telescope with a wide ?eld of view,such as the Subaru/Suprime-Cam,can probe intracluster compact objects with a wide mass range of m co ~10?5–1010M ⊙,including ranges that have not yet been constrained by any past observations.We expect that the event rate is biased for the background cluster than the foreground cluster (A2152),which would be a unique signature of microlensing,making this experiment particularly powerful.The sensitivity of this experiment for the mass fraction of compact objects would be 1–10%in the total dark matter of the cluster,which is roughly constant against m co ,with a reasonable telescope time for large telescopes (~10nights).Therefore any compact objects in this mass range can be detected or rejected as the dominant component of the dark matter.About 10events are expected if 20%of the cluster mass is in a form of compact objects with M ~1M ⊙,as claimed by the MACHO collaboration for the Milky Way halo.Other possibly detectable targets include intracluster stars stripped by galaxy interactions,and hypothetical very massive black holes (M 100M ⊙)produced as remnants of the ?rst generation stars,which might be responsible for the recently reported excess of the cosmic infrared background radiation that seems impossible to explain by normal galactic light.

Subject headings:gravitational lensing —dark matter —galaxies:clusters:general —galaxies:clusters:

individual (the Hercules supercluster,A2152)

1.INTRODUCTION

Gravitational microlensing of stars in the Magellanic Clouds (MCs)provides us a unique probe of compact objects that might be a signi?cant part of the dark matter in the Galactic halo (Paczy′n ski 1986),and intensive effort has been made so far (see,e.g.,Narayan &Bartelmann 1995for a review).The MACHO collaboration interprets the microlensing events to-wards MCs as providing evidence for massive compact halo objects (MACHOs)with a mass of ~0.1–1M ⊙in the Galac-tic halo,constituting a signi?cant fraction (~20%)of the total halo mass (Alcock et al.2000).The EROS collaboration,on the other hand,has used their observations to place an upper limit of ~10%on the MACHO mass fraction (Lasserre et al.2000).

When the impact parameter is much smaller than the Ein-stein radius,a very strong magni?cation is expected.By using such strongly magni?ed events,often called pixel lensing (e.g.,Gould 1996),it is possible to do a microlensing experiment with very faint,unresolved stars in distant galaxies.The use of such events has been ?rst discussed for M31(Crotts 1992;Baillon et al.1993),and then for M87in the Virgo cluster (Gould 1995).Such events may also add new information to microlensing events towards MCs (Gould 1997;Nakamura &Nishi 1998;Sumi &Honma 2000).A few experiments towards M31are currently underway (Crotts &Tomaney 1996;Ansari et al.1997;Riffeser et al.2001;Paulin-Henriksson et al.2002;Calchi Novati et al.2002).

There are a few more approaches other than the pixel lensing,which are proposed to constrain MACHOs in clusters of galax-ies.Walker &Ireland (1995)and Tadros,Warren,&Hewett

(1998)considered microlensing of background quasars behind the Virgo cluster.While the optical depth (τ~10?3)is larger than the microlensing experiments towards the MCs (τ~10?7),it is not suf?ciently large because of the small number of avail-able background quasars.The problem is also compounded by the dif?culty of distinguishing microlensing-induced quasar variability from intrinsic mechanisms.Lewis &Ibata (2001)considered to use ?uctuation of surface brightness of galaxies by microlensing to constrain cosmologically distributed com-pact objects,and Lewis,Ibata,&Wyithe (2000)extended this approach to giant gravitationally lensed arcs in galaxy clusters to constrain intracluster MACHOs.However,detection of such ?uctuation would require a long observing time of the Hubble Space Telescope or the Next Generation Space Telescope .

Recent developments of advanced observing facilities enable us to do a deep and/or wide search of microlensing events by ground-based telescopes as well.The Suprime-Cam installed in the prime focus of the 8.2m Subaru telescope combines the sensitivity of 8m-class telescopes with a wide ?eld of view of 30′×30′,and a unique microlensing experiment might be pos-sible by such a facility.

The Hercules supercluster consists of three rich Abell clus-ters of galaxies (A2147,2151,and 2152)at z ~0.04,which seems mildly bound gravitationally,with a total mass of ~8×1015M ⊙(Barmby &Huchra 1998;Blakeslee et al.2001).Each cluster seems not completely stabilized yet showing rather irregular morphologies,and they have relatively high fraction of spiral galaxies (~50%).Recently another,more distant cluster was found just behind A2152at z =0.13,forming a cluster-cluster system with a projected separation of only 2.4′1

Theory Division,National Astronomical Observatory,Mitaka,Tokyo 181-8588,Japan

1

2

(=0.09h?1Mpc at z=0.04)(Blakeslee et al.2001;Blakeslee 2001).Extremely magni?ed stars in the background cluster by microlensing of compact objects in A2152may be detectable by a deep and wide monitoring of this region.Here we give an event rate estimate of such phenomena,supposing a sensi-tivity of8m-class telescopes2with a reasonable telescope time, and show that the sensitivity is good enough to do a unique mi-crolensing experiment for a wide range of the compact object mass.

A similar idea has been studied by Turner&Umemura (1997),but for stars in general?eld galaxies,i.e.,not in clus-ters.They examined only limited population of source stars and lens mass range,with a simple picture of point-mass lens. However,as we will show,caustic-crossing is likely to be more important when the magni?cation is extremely large,and sim-ple point-mass picture does not apply.We will present formu-lations by which one can derive more realistic event rate for a speci?c observation,taking into account caustic-crossing,event time scales,and realistic stellar luminosity function,for a wide range of the lens mass.We will mention that the cluster-cluster system has some advantages compared with a search made for general?elds.

In§2,we present general pictures of expected events and formulations to predict the expected event number.The predic-tion will be made in§3,and some discussions will be given in §4.Then we will present various astrophysical implications that will be obtained by this cluster-cluster microlensing experiment in§5.Throughout the paper we use h≡H0/(100km/s/Mpc)= 0.7.

2.FORMULATIONS

2.1.General Picture:Point-Mass Lens versus Caustic

Crossing

In microlensing experiments towards the Galactic bulge or MCs,where the optical depth is much smaller than unity,gen-erally lensing events can be treated as magni?cation by a sin-gle lens,except for cases where lenses are forming close bina-ries.On the other hand,when optical depth is close to unity such as microlensing of distant quasars by stars in a galaxy on the line of sight,the effects of the various microlenses cannot be considered independently,and complicated caustic networks arise(Wambsganss,Paczy′n ski,&Schneider1990;Narayan& Bartelmann1995).Even if the optical depth is not as large as unity,caustics still exist in the vicinity of the center of the in-dividual lenses,by the external shear induced by nearby point-mass lenses and/or smoothly distributed matter.Therefore the effects of shear could be signi?cant when we consider very large magni?cation events,even ifτ?1.First we should ex-amine which picture is appropriate for the case we will consider here.Assuming typical density pro?les in clusters(discussed in more detail later in§3.1),the optical depthτ=Σ/Σcrit of the lens cluster A2152is0.1–0.2,which is a weighted mean with the density of stars in the source cluster,if all of the cluster mass is in the form of compact objects contributing to microlens-ing.Here,Σis the surface mass density per unit solid angle,Σcrit=(c2/4πG)d S d L/(d S?d L)the critical surface density,and d S and d L the distances to the source and lens clusters,respec-tively.3Therefore microlensing in this system can marginally be considered as the small optical depth case(τco≡f coτ?1), where f co is the mass fraction of the compact lenses.When f co is much smaller than unity,the smallτco approximation be-comes even better.Therefore we assumeτco?1in this paper, and we will consider only microlensing by one individual mi-crolens.Correction by numerical studies to this may be neces-sary in the future in the very central region of the cluster when f co~1.

Whenτco?1,microlensing can be treated as a sum of single point-mass lenses with external shear.The resulting caustics have the shape of an“astroid”,with four cusps at an angular radius2sθE from the location of the lens,where s is the exter-nal shear andθE the Einstein radius(Chang&Refsdal1979, 1984;Schneider&Wei?1986;Mao1992;Kofman et al.1997). The shear is given by the sum of the contributions from nearby compact objects and smooth mass distribution in the cluster,as s=s co+s sm.Typically s co~τco,and its distribution is given by

p(s co|τco)=

τco s co

d S

4GM cl

2

θ2(θ2core+θ2)?3

3 will give formulations to estimate microlensing event rate for

the both limits,and calculate the expected number of events.

Then we examine,for typical events contributing to the event

number,which limit applies in a supposed observation,which

should be dependent on the lens mass considered.

In this paper we consider two modes of observation with total

duration of T obs:(1)a consecutive observation during a night,

typically T obs~6hrs,and(2)a monitoring beyond the time

scale of one night with arbitrary sampling time interval.The

time resolution t res would be minutes for the observing mode

(1)for typical instruments,while it is T obs/N sample for the mode

(2),where N sample is the total number of sampling(i.e.,nights)

during the total observing duration T obs.

2.2.Point-Mass Lens Limit(μ?s?1)

Let f lim,0be the?ux sensitivity limit with an exposure time

t exp,0,for a given telescope.We also assume that the sensitiv-

ity limit scales as f lim=f lim,0(t exp/t exp,0)?1/2.First we consider

the optimal lensing time scale and magni?cation to search for a

microlensing event of a source star whose original luminosity is

L?,for the observing mode(1).The magni?cation required for

detection at a?ux level f lim becomesμ=4π?d2S f lim/L?.For this

magni?cation,the impact parameter between the source star

and the lens must be smaller thanθ<θE/μwhenμ?1,and

the time duration of lensing is given by t lens=t lens,Eμ?1.Here,

t lens,E=θE d L/V is the Einstein-ring crossing time,and V is the

relative transverse velocity between the source and lens pro-

jected on the lens plane.The lensing duration must be longer

than the supposed exposure time to detect an event,and hence

this condition,t lens≥t exp,results in the limiting magni?cation

μlim required,as:

μ>μlim=t exp,0

L?

2

.(3)

For the observing mode(2),the sensitivity is determined by the unit exposure time t u during one night(typically t u~6 hrs),rather than by the lensing time scale that is longer than t u.In this case,the limiting magni?cation is simply given as μlim=4π?d2S f lim,u/L?,where f lim,u=f lim,0(t u/t0)?1/2is the sensi-tivity limit for an exposure of the unit time scale.

We should also examine the?nite source size effect.When the impact parameterθE/μbecomes smaller than the size of source stars,i.e.,r?>r crit≡θE d S/μ,this effect becomes sig-ni?cant,where r?is the size of stars.

To help the reader get a rough image of possible events,we show the values of representative quantities such as t lens,μlim, r?and r crit,for some values of lens mass m co in Table1.The observing mode(1)is assumed.For the treatment of stellar size and other parameters for the cluster-cluster system,see§3.1. These quantities could be very different for different source star luminosity,and this means that only stars in a relatively narrow range of luminosity would contribute to event rate,whose event time scale t lens is matching the practical observing time scale. The optical depth for such extremely magni?ed events is given by?τco=τcoμ?2lim=f co m?1coΣ(θ)πθ2Eμ?2lim,where m co is the mass of compact lens objects,andΣ(θ)is the surface mass den-sity of the lens cluster at the angleθfrom the center.Then the total number of microlensing events detectable in one snapshot of the source cluster is given by

N snapshot(L?)dL?= θcl,S02πθdθS?(θ)φ(L?)dL??τco(θ),(4) for source stars whose luminosity is in a range from L?to L?+dL?,where S?is the mean surface brightness of galaxies in the source cluster4,φthe stellar luminosity function(LF)of source stars normalized by the total stellar luminosity,andθcl,S the maximum angular extension of the source cluster.Here we implicitly assumed that the two clusters are perfectly aligned, which is a reasonable approximation for the A2152system since the projected angular separation of the centers of the two clusters is comparable or even smaller than the typical core size of clusters.For a monitoring with duration T obs,the total ex-pected number of events is then given by integrating over L?, N event= dL?N snapshot(L?)max(1,T obs/t lens).(5) In practice,the integration range over L?must be limited,since the lensing time scale must be reasonable with respect to the ?nite time resolution or duration of observation.(Note that t lens∝m co L2?.)For the observing mode(1),we perform this integration when a condition on t lens,5t res

2.3.Caustic Crossing Limit(μ?s?1)

First we consider the event rate by lenses with a?xed value of shear s,and then we will integrate it over s co with the prob-ability distribution p(s co|τco).It can be shown that the magni-?cation distribution function P(μ)becomes asymptotically the same with that of a point mass lens whenμ?s?1,and be-haves like P(μ)∝μ?3(Schneider1987;Kofman et al.1997). It should be noted that not only the behavior(∝μ?3)but also the angular area in the source plane for magni?cation larger than a givenμbecomes the same as those of point mass lens in the limit ofμ?s?1(Kofman et al.1997).Large magni?ca-tion events should be dominated by caustic-crossing rather than cusps,since P(μ)around the cusps decreases with increasing μas∝μ?7/2,which is faster than the total P(μ)(Mao1992). For a source crossing the caustics around a lens,the projected length of caustics on the source plane is~8sθE.Letθμbe a characteristic width of the region along the caustics where mag-ni?cation is larger thanμ.Then we expect that the area of this region,~8sθEθμshould be equal to the equivalent area for a single point-mass lens,π(θE/μ)2.Then we obtain

θμ~

πθE

V

.(7) These relations indicate that the light curve around the caustic crossing with a constant lens velocity isμ∝t?1/2,as is well known for sources inside the caustics,while magni?cation sud-denly drops when a source crosses and gets outside the caus-tics(e.g.,Schneider&Wei?1986).Since the sensitivity of a telescope also roughly scales as f lim∝t?1/2,the signal-to-noise ratio should be roughly constant against the exposure time in a consecutive monitoring observation.

4It should be noted that S?in this equation is intrinsic surface brightness,while observational estimate of S?is affected by macro lensing of the foreground cluster. See§4.

4

Therefore all stars brighter than a threshold luminosity can be detected by microlensing,when they pass a caustic.For ob-serving mode(1),the magni?ed?ux fμ=μL?/(4π?d2S)must be greater than the?ux limit f lim=f lim,0(tμ/t0)?1/2,and hence we obtain

L?,min(s)>4π?d2S f lim,0 πθE d L,(8) which is independent of tμor the exposure time.In the case of observing mode(2),the sensitivity limit with an exposure of the unit observing time t u should be fainter than the magni?ed?ux of stars with a lensing time scale of the total observing duration, i.e.,tμ=T obs.Then we get

L?,min(s)>4π?d2S f lim,0 πθE d L t u.(9) Ignoring the?nite source size effect,the maximum magni?-cationμmax that can be observed is determined by the minimum time resolution,t res.Replacing tμby t res in eqs.(6)and(7),we obtain:

μmax= 8s t res V.(10)

On the other hand,μmax may be limited by the?nite source size effect.This effect becomes to be visible when the crossing time of stars,r?d L/(Vd S),becomes larger than the time resolution t res.This condition can be written as:

r?>r crit≡

t res V d S

d L

n co(θ)p(s co|τco)ds co T obs(12)

=8s(θ)V T obsτco(θ)p(s co|τco)ds co

c d LS

θ2E

c d LS

θ2E

5 pro?le[ρ∝(cr/R cl,L)?1(1+cr/R cl,L)?2]for the lens cluster with

a typical concentration parameter of c=5(e.g.,Allen,Ettori,&

Fabian2001),we?nd that the microlensing probability is re-

duced by a factor of about2compared with the King pro?le.

Finally,we use the singular isothermal sphere with a softened

core(eq.2),having the same core radius with the King pro?le,

to calculate the shear of smoothly distributed mass.It is par-

tially for computational simplicity,but also a reasonable treat-

ment for intracluster gas.

The LF of source stars must be speci?ed.Here we try two

LFs for disk and elliptical galaxy populations.For disk galax-

ies,we used the I band LF of Mamon&Soneira(1982).For

elliptical galaxies or stellar population in bulges,we use the LF

of our Galaxy bulge presented in Terndrup,Frogel,&Whitford

(1990)showing a cut-off of giant stars brighter than M I=?4,

corresponding to the tip of the red giant branch.The ellipti-

cal/bulge LF has some structure around M I~0due to the red

clump stars.The stellar size as a function of stellar luminos-

ity M I is necessary to check the?nite source size effect.The

approximate radius of stars,r?,is calculated by the bolomet-

ric luminosity and the effective temperature(r?∝L1/2

?,bol T?2eff).

According to Mamon&Soneira(1982),we consider?ve sub-classes of stellar populations,i.e.,two supergiant classes(Ia

and Ib),bright giants(II),giants(III),and main sequence(V), which are dominant in different ranges of M I with an increasing

order,and the borders between these are M I~?8,?6,?4,and 0.The(V?I)versus M I relation for these subclasses is also given in Mamon&Soneira(1982),from which we infer the

spectral type,effective temperature,and bolometric corrections

in Zombeck(1990).The LF,(V?I)color,and stellar radius are shown in Fig.2.

3.2.Results

Here we calculate the expected event rate supposing an observation by Subaru/Suprime-Cam,whose sensitivity is m lim,0,I=26.0(S/N=5)at t exp,0=1hr.In the point-mass lens approximation,we require a signal-to-noise of S/N>10and S/N>5for the observing modes(1)and(2),respectively.The higher S/N is required for the observing modes(1)to assure suf?cient S/N to construct a microlensing light curve.On the other hand,in the caustic-crossing limit,we require a signal-to-noise of S/N>5and S/N>3,respectively.The lower S/N is adopted because the strong magni?cation near the caustic-crossing is expected to increase total effective S/N compared with the point-mass lens limit.(However,when the?nite source size effect is signi?cant,this may not apply.See below.)

In Figures3and4,we show the expected limit on f co ob-tained by an observation using10nights,i.e.,10times repeti-tion of the observing mode(1)with T obs=6hrs and t res=0.1hrs, in the limits of point-mass lens and caustic crossing,respec-tively.Figures5and6are the same,but for the observing mode (2)using10nights,with T obs=10days and N sample=10.In all these four?gures,the limits on f co are shown in the upper pan-els as a function of various lens mass.In the lower panels,we plot the mean of sμ,r?,and M I for events contributing to N event. The calculation in the point-mass lens or caustic-crossing limits is valid only when sμ 1or 1,respectively.Here,the limit on f co is de?ned as the value where the total expected event number,N event is unity.It should be noted that N event∝f co in the point-mass lens limit,while this relation holds only approxi-mately in the caustic-crossing limit,since a change of f co would change the shear s.Equations8,9,13,and14indicate that this relation depends on the shape of LF,and N event∝f co is exactly valid only when N?(L?)∝L?2?,which is a roughly correct ap-proximation in a range of M I ?4.

The point-mass lens approximation is valid only when sμ 1,while the caustic-crossing limit is appropriate only when sμ 1,where x represents a mean of the quantity x over all detectable events.The transition between the two limits occurs at μs ~1,which is at m co~10?5M⊙in the ob-serving mode(1)and at m co~0.1M⊙in the observing mode (2),respectively.At these transition points,both the limits are approximately valid and hence the event rate predictions should agree with each other.Indeed the two predictions agree at the transition lens mass scale,providing a support for the validity of our formulations and calculations.

Most behavior of the f co limit as a function of m co can be understood as follows.A trend easily seen is that typi-cal source star luminosity contributing to event rate becomes smaller with increasing lens mass.In the point-mass limit, the duration of strong magni?cation required for detection is t lens∝t lens,E/μlim∝m co L2?.Since we are supposing10nights duration of observation,and the detectable time scale is lim-

ited by this speci?c time scale.Therefore L? ∝m?1/2

co

.In the caustic-crossing limit,on the other hand,there is the minimum source star luminosity L?,min for detectable events,and hence

L? ∝L?,min∝θ?1/2

E

∝m?1/4

co

.This is why the typical source star luminosity and limits on f co are less sensitive to m co in the caustic-crossing limit,than the point-mass limit.The event rate in the point-mass lens limit scales as

R event∝

dN?( L? )

d log L?

L? 2,(18)

per logarithmic stellar luminosity interval.On the other hand,the event rate in the caustic-crossing limit scales as ∝N?( L? )θ?1E∝N?( L? ) L? 2.These two have the same dependence on L?,and hence the curves of f co limit in Figs. 3–6can be understood as inverted stellar luminosity function per logarithmic interval which is multiplied by L2?.Since dN?/d log L?∝N?(L?)∝L?2?at M I ?4,the limit on f co is roughly constant,but it becomes weaker with decreasing stellar luminosity at M I ?4because of the change of the luminosity function slope.

The?nite source size effect could be signi?cant in the ob-serving mode(1).(Note that the?nite source size effect is not taken into account in the event rate estimates presented here.) Although r?/r crit appears to be much larger than unity in the caustic-crossing limit(Fig.4),this partly comes from the use of small t res=0.1hrs in eq.(11),as mentioned in§2.3.Since the light curve of caustic crossing is f∝t?1/2for a point source, the signal-to-noise ratio does not change much when we change the monitoring time scale of events.If we choose a longer time scale,the?nite source size effect becomes less signi?cant.We will be able to increase t res up to a few hours during a night,and hence the?nite source size effect should not severely suppress the detectable event rate estimated here,especially for larger m co.The?nite source size effect is mostly insigni?cant for the observing mode(2).

To summarize,these results indicate that monitoring of the cluster-cluster system using10nights of a wide-?eld8m-class telescope can probe possible intracluster compact objects,with a sensitivity to the mass fraction in the total cluster mass as f co~1–3%at m co~10?5–108M⊙in the observing mode(1), and f co~3–10%at m co~10?3–1010M⊙in the observing mode

6

(2).The sensitivity in the observing mode(1)might be some-

what reduced by the?nite source size effect,but we expect that it is not signi?cant.

4.DISCUSSION

A weak point of pixel lensing is that there is a degeneracy

of lens parameters due to the lack of information of the source

star luminosity.Even if we assume the transverse lens velocity as V~1000km/s,the lens mass cannot be determined if we

do not know the source luminosity.It is not easy to break this

degeneracy,but it might be possible if the color of microlens-ing events is measured.Elliptical galaxies have only old stellar

populations and there is a sharp cut off of the stellar luminosity

function at the tip of the red giant branch,where the V?I color of stars becomes rapidly redder at almost constant M I on the

color-magnitude diagram(e.g.,Jablonka et al.1999).There-

fore,when a microlensing event with very red color is observed in an elliptical galaxy,it is very likely that the source star has

an absolute magnitude of M I~?4,making the lens mass esti-mate possible.When the?nite source size effect is seen in an

observed light curve,it also gives additional information on the

apparent stellar size,which can be used to break the degeneracy (Gould1997;Sumi&Honma2000).

It is important to discriminate the microlensing events from

other astronomical transient sources.In addition to the fea-tures generally used in microlensing searches,i.e.,characteris-tic light curves and achromatic behavior,there are two expected signatures that are unique for this system:1)more events are expected for stars in the source cluster(z=0.13)rather than in the lens cluster(z=0.04),and2)the event distribution is even more concentrated to the cluster center than the matter distri-bution in clusters,since the lensing probability is proportional to the product of the surface densities of the source and lens clusters.

Another interesting possibility that may be useful for dis-

crimination and breaking the degeneracy is repetition of caus-

tic crossings.When a source star crosses the astroid-shaped caustics of a lens,typically two,and sometimes even more caustic-crossings are expected.The time interval of repetition is roughly given as

t rep~2sθE d L

M⊙ 1/2 s

7

The sensitivity of f co~a few percent in a range of m co~10?5–1010M⊙is suf?ciently good as a probe for the nature of dark matter;we could detect or reject any compact objects in this mass range as the dominant component of the dark matter in galaxy clusters.It should be noted that this mass range?lls up the“desert”of the constraints on?M in the form of com-pact objects:m co~10–105M⊙,which has hardly been con-strained by past observations.Microlensing searches in nearby galaxies or quasar variability have constrained at m co 10M⊙, while millilens searches for radio quasars or echos of gamma-ray bursts constrained at m co 105M⊙(Narayan&Bartelmann 1995;Nemiroff et al.2001;Wilkinson et al.2001,and see Wambsganss2002for the latest review).

Hawkins(1993,1996)claimed that variability seen in high-z quasars is due to the microlensing action of Jupiter-mass compact objects distributed cosmologically,whose density is enough to explain a signi?cant fraction of the dark matter. However,this claim has been questioned by a number of au-thors(e.g.,Baganoff&Malkan1995;Alexander1995).Some observations of strongly lensed quasars have been used to ex-clude this possibility(Schmidt&Wambsganss1998;Wyithe, Webster,&Turner2000),although it also depends on assumed quasar sizes.The latest data of EROS project also seem to have excluded this possibility(Lasserre et al.2000).Anyway, this experiment would provide another independent test for this controversial claim.

If MACHOs exist in the intracluster space with a similar mass fraction(~20%)suggested by the MACHO collaboration (Alcock et al.2001),the cluster-cluster microlensing search should?nd about1–10events.However,it should be noted that the mass-to-light ratio of clusters is much larger than that of the Galactic halo.If the abundance of MACHOs scales with luminous matter,we expect that the intracluster MACHO mass fraction is much smaller than in the Galaxy.Some observa-tions suggest that MACHOs may be white dwarfs(Ibata et al. 2000;Oppenheimer et al.2001),but if20%of the total clus-ter mass is in the form of white dwarfs,and the matter content in the cluster system is the same as that of the whole universe, almost all of the cosmic baryons predicted by the big-bang nu-cleosynthesis[?B~0.02h?2=0.07h?2?M(?M/0.3)?1,Burles &Tytler(1998)]must be locked up in white dwarfs.Such a case would easily violate the constraint coming from the cos-mic background radiation(CBR)in optical and infrared bands (Madau&Pozzetti2000).

On the other hand,there are a few recent reports by inde-pendent groups for detections of the near-infrared CBR(Mat-sumoto2000;Cambrésy et al.2001;Wright2001),and the reported?ux is by a factor of a few higher than the?ux inte-gration of galaxy counts in the same band,which is dif?cult to explain by normal galactic light even if the incompleteness of galaxy surveys and the cosmological surface brightness dim-ming of galaxies are taken into account(Totani et al.2001). Though the discrepancy may be solved if there are some sys-tematic errors in processes of diffuse CBR measurement,e.g.,subtraction of the zodiacal light(Wright&Johnson2001),it

is also possible that the CBR excess is due to exotic extra-galactic sources that are very different from normal galaxies.

If white dwarfs that were formed at very high redshift are re-

sponsible for this excess(I~30nW m?2sr?1),the mass den-sity of white dwarfs and their progenitors would be about2%

and10%of the nucleosynthetic baryons,respectively,assuming

that80%of baryons in progenitors is returned into interstellar space(Madau&Pozzetti2000).Therefore,a plausible fraction

of such white dwarfs in the total cluster mass is only~0.2%.

It is not impossible,but rather dif?cult to detect these objects by the cluster-cluster microlensing experiment,unless a large

number of nights are available.

Another possible source of this excess of CBR is the?rst generation stars at redshift z~10,whose UV and optical

light is redshifted to the near infrared band(Santos,Bromm,

&Kamionkowski2002;Schneider et al.2002;Salvaterra& Ferrara2002).Recent theoretical studies on the formation of

primordial stars strongly indicate that they are very massive

( 100M⊙),and a majority of them might eventually evolve into massive black holes without ejection of any amount of

heavy elements.Then,a major episode of the?rst-generation

star formation is possible before the interstellar matter is pol-luted by metals and normal star formation begins(Schneider

et al.2002).Assuming a conversion ef?ciency from the

rest mass to radiation energy that is similar to normal stars,a mass comparable with the present-day stars[??~0.0024h?1, Fukugita,Hogan,&Peebles(1998)]must have been locked in

the?rst generation stars and then their remnant black holes with M 100M⊙,to explain the CBR excess.If such black holes are

diffusely distributed in intracluster medium,the cluster-cluster

microlensing search might detect them.

It is expected that there is a diffuse population of intracluster

stars that are stripped from galaxies by interactions with other galaxies or intracluster gas.Observations of diffuse optical light,intracluster planetary nebulae,and red giant stars indi-cate that the amount of stellar light from such intracluster stars is10–50%of the total light from galaxies in clusters,though these estimates are still highly uncertain(e.g.,Vílchez-Gómez, Pelló,&Sanahuja1994;Gonzalez et al.2000;Arnaboldi et al. 2002;Durrell et al.2002;Okamura et al.2002).As shown above,about one percent of?M is locked in stars in the uni-verse,and this fraction is probably even higher in clusters of galaxies because of larger fraction of elliptical galaxies.There-fore,if the amount of intracluster stars is comparable with that of stars in member galaxies,the microlensing search of the Her-cules supercluster might detect them,providing a completely independent information for intracluster stars.

The author is deeply indebted to B.Paczy′n ski for many in-spiring conversations.He would also like to thank M.Chiba, E.Komatsu,S.Mao,J.Ostriker,T.Sumi,J.Wambsganss,and M.Kubota for useful information and discussions.He has been ?nancially supported in part by the JSPS Postdoctoral Fellow-ship for Research Abroad.

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T ABLE1

Q UANTITIES FOR S OME R EPRESENTATIVE C ASES

Point-Mass Lens Limit Caustic Crossing Limit

m co[M⊙]θE[μas]M I t lens[hrs]μlim r?[R⊙]r crit[R⊙]M I,maxμmax r?[R⊙]r crit[R⊙]

9

F IG.1.—A schematic diagram for the two different cases of microlensing events:the point-mass lens limit(μs?1,right-hand side),whereμis the magni?cation required for detection and s is the external shear at the lens location.The dot-dashed circles

are the Einstein radius,and the solid circles have radii ofθE/μ,and a source star with a radiusθ?must hit this region for its detection in the point-mass lens picture. On the other hand,the astroid-shaped curves are caustics,extending to~2sθE,and a source star must hit this region for its detection,in the caustic crossing limit.

The corresponding light-curves are shown in the bottom,where the?nite source size effect is assumed to be negligible.(For the condition of signi?cant?nite source size effect,see text.)

10

F IG.2.—The luminosity function(LF),(V?I)color,and radius of source stars as a function of I magnitude.Five different classes of stars[supergiants(Ia and Ib),bright giants(II),giants(III),and main sequence(V)]are assumed to be dominant,depending on the magnitude,as shown in the top panel.The solid line in the top panel is LF in spiral galaxies,while the dashed line is that in elliptical galaxies having old stellar populations.

11

F IG.3.—The sensitivity to the mass fraction f co of compact objects in the total cluster mass,in the limit of point-mass lens approximation(valid only when sμ 1),by10times repetition of consecutive monitoring during a night(6hrs)with observing mode(1).Top panel:the limit on f co as a function of the lens mass, assuming the stellar luminosity function in spiral galaxies(dashed line),in elliptical galaxies(dot-dashed line),and the weighted mean with relative proportions of 30%for spirals and70%for ellipticals(solid line).Bottom panel:the mean values of original absolute I magnitude of source stars(M I),product of magni?cation and shear(sμ),and the ratio of the stellar size to the critical size for?nite source size effect(r?/r crit).

12

F IG.4.—The same as Fig.3,by10times repetition of consecutive monitoring during a night(6hrs)with observing mode(1),but in the limit of the caustic-crossing approximation,which is valid only when sμ 1.

13

F IG.5.—The same as Fig.3,but by the observing mode(2)with T obs=10days and N sample=10.This?gure is assuming the single lens limit,which is valid only when sμ 1.

14

F IG.6.—The same as Fig.3,but by the observing mode(2)with T obs=10days and N sample=10,and in the limit of the caustic-crossing approximation,which is valid only when sμ 1.

旅游与文化 翻译

旅游与文化I Part I 1.charming autumn scenery in a most fresh air and clear weather 秋高气爽,秋色宜人 2.the 15th General Assembly Session of the World Tourism Organization 世界旅游组织第15届全体大会3.to travel ten thousand li and read ten thousand books 读万卷书,行万里路 4.enriching themselves mentally and physically 承天地之灵气,接山水之精华 5.tourist arrival 旅游人数 6.foreign currency receipts 外汇收入 7.outbound tourists 出境旅游人数 8.unique, rich and varied tourism resources 得天独厚的旅游资源 9.World Cultural and Natural Heritages sites 世界文化遗产地和世界自然遗产地 10.t o add radiance and charm to each other 交相辉映 11.a thriving modern metropolis 繁华的现代化大都市 12.a patchwork of cottages 村舍星罗棋布 13.t o exist side by side 鳞次栉比 14.I nternational Architecture Exhibition 万国建筑博览会 15.c lock towers and turrets , marble pillars 钟塔、角楼和大理石柱 16.e ach representing a distinctively individual appearance 风格迥异,各领风骚 17.t he rainy season 梅雨季节 18.t o linger longer 留连忘返 19.e xcellence, elegance and the best quality 卓越超群,富丽堂皇,一流质量 20.e mbroidery, inlaid lacquer 刺绣,金漆镶嵌 21.g old and silver jewelleries, water-color woodblock prints 金银首饰,木刻水印 22.c arvings in jade, ivory, bamboo and woven bamboo baskets 玉雕、牙雕,竹雕,竹编筐篮 23.b ird cages, lanterns 鸟笼灯笼 24.d ouble-sided embroidery and sandal wood fans from Suzhou 双面绣和苏州的檀香扇 25.t erracotta teapots from Yixing, and clay figures from Wuxi 宜兴的陶制茶壶和无锡的泥人 26.t he Peach Blossom Fair 桃花节 27.t he Daci Temple Fair 大慈寺庙会 28.t he Chengdu Tourism Festival 成都旅游节 29.a place blessed with favorite climate, fertile land, rich resources and outstanding talents 物华天宝,人杰地灵30.s uperb artistic style of aiming at catching the sprit of the landscape 写意山水 31.a rtistic gems 艺术瑰宝 32.U NESCO Heritage Committee 联合国教科文组织遗产委员会 33.t he list of World cultural heritage 世界文化遗产名录 34.b ronzeware 青铜器 35.b amboo, wood and lacquer ware 竹木漆器 36.i nscribed bones and tortoise shells 甲骨 37.s eals 玺印 38.a rchaeology 39.r estoration room 文物修复馆 旅游与文化II Part II景点描述常用语 Match work: 雄伟壮丽imposing 灯火辉煌glittering

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Cast P earls before swine.牛一猪) 7)落汤鸡/落水狗:Like a drow ned mouse .鸡/狗一鼠) 8)热锅上的蚂蚁: Like a cat o n hot bricks.蚂蚁一猫) 9)宁为鸡头,毋为牛后: Better be the head of a dog than the tail of a lio n.鸡 —狗,牛一狮) 由此可见,中国成语中的动物在英语成语中已不属于同一动物了。 2. 与颜色有关的成语或谚语英汉也不尽相同 在颜色的作用上,有相同点。比如,红色(red ),无论是在英语国家,还是在 中国,往往都与庆祝活动和喜庆日子有关。如中国有 开门红”代表着好运气。 英语有“redletter days 纪念日,喜庆日)等。但更多的还是有不同点,而且两种 语言在颜色 的意义上也有区别。如 黄色”(yellow )在西方黄色表示懦弱,胆小, 不敢面对现实。而在中国,黄色是帝王的象征。只有皇帝才配着黄色。再如 蓝 色” (blue )在英语中通常表示不快活,心情不好。如: 1) He is blue today 文化与翻译 英汉成语、谚语中的语言文化差异 其语言也必然会有很大的差别。语言 来谈 由于中西方的社会文化存在着很大的差异, 离不开文化,文化也离不开语言。本文就英汉成语或谚语对译的几个实例, 谈两种语言在成语或谚语中所存在的文化差异。 1.与动物有关的成语或谚语英汉不尽相同 1)他壮得像头牛。 He is as stro ng as a horse 牛一马) 2)她胆小如 鼠。 She is as timid as a hare (鼠一兔) 3)养虎遗 患: Warm a sn ake in on e's bosom 虎—蛇) 4)瓮中之鳖: Like a rat in a hole.(鳖一鼠) 5)害群之 马: Black shee p.马一羊) 6)对牛弹琴:

短歌行赏析介绍

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