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High resolution observations and mass modelling of the CLASS gravitational lens B1152+199

a r X i v :a s t r o -p h /0110099v 2 5 O c t 2001

Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 1February 2008

(MN L A T E X style ?le v1.4)

High resolution observations and mass modelling of the

CLASS gravitational lens B1152+199

D.Rusin 1,M.Norbury 2,A.D.Biggs 2,D.R.Marlow 2,N.J.Jackson 2,I.W.A.Browne 2,P.N.Wilkinson 2,S.T.Myers 3

1Department

of Physics &Astronomy,University of Pennsylvania,Philadelphia,PA 19104-63962Jodrell Bank Observatory,University of Manchester,Maccles?eld,Cheshire,SK119DL

3National Radio Astronomy Observatory,P.O.Box 0,Socorro,NM,87801

1February 2008

ABSTRACT

We present a series of high resolution radio and optical observations of the CLASS gravitational lens system B1152+199obtained with the Multi-Element Radio-Linked Interferometer Network (MERLIN),Very Long Baseline Array (VLBA)and Hubble Space Telescope (HST).Based on the milliarcsecond-scale substructure of the lensed radio components and precise optical astrometry for the lensing galaxy,we construct models for the system and place constraints on the galaxy mass pro?le.For a single galaxy model with surface mass density Σ(r )∝r ?β,we ?nd that 0.95≤β≤1.21at 2σcon?dence.Including a second de?ector to represent a possible satellite galaxy of the primary lens leads to slightly steeper mass pro?les.Key words:gravitational lensing –galaxies:structure

1INTRODUCTION

Multiple-image gravitational lens systems are potent tools for investigating a wide range of astrophysical and cosmolog-ical issues.One promising application of strong lensing is the determination of the Hubble parameter through the mea-surement of di?erential time delays (Refsdal 1964;Schechter et al.1997;Kundi′c et al.1997;Lovell et al.1998;Wisotzki et al.1998;Biggs et al.1999;Fassnacht et al.1999;Koop-mans et al.2000;Patnaik &Narasimha 2001).In addition,lenses can directly constrain the inner several kiloparsecs of galaxy mass distributions (e.g.,Kochanek 1991,1995;Rusin &Ma 2001;Cohn et al.2001;Mu?n oz,Kochanek &Keeton 2001).Much of the recent interest in ?nding arcsecond-scale gravitational lenses through systematic searches such as the Cosmic Lens All-Sky Survey (e.g.,Myers et al.1995,1999)and the southern survey of Winn et al.(2000)has been driven by these goals.

High resolution observations are the essential step in transforming lens systems from mere novelties into useful tools.For example,optical or near-infrared imaging with the Hubble Space Telescope (HST)is necessary to pinpoint the centre of the lensing galaxy,determine its shape and orientation,and search for nearby objects that may be per-turbing the potential.This is complemented by observations with high resolution radio arrays such as the Multi-Element Radio-Linked Interferometer Network (MERLIN)and the Very Long Baseline Array (VLBA),which o?er precision astrometry and search for milliarcsecond-scale substructure

in the lensed radio components.Taken together,these data

provide the raw material for developing models of the grav-itational potential,from which the structure of the lensing galaxy is investigated and time delays are predicted for use in Hubble constant determination.

B1152+199(Myers et al.1999)was identi?ed as a grav-itational lens candidate in the third phase of the CLASS survey observations.The source consists of two compact ra-dio components with a ?ux density ratio of ~3:1,separated by 1.′′56.Follow-up observations with the Very Large Ar-ray (VLA)demonstrated that the components have nearly identical two-point spectral indices between 8.4and 15GHz,as expected for images of a single lensed source.The lens-ing hypothesis was de?nitively con?rmed via follow-up spec-troscopy obtained with the Keck II telescope,which detected lines from a background quasar at z s =1.019and a fore-ground galaxy at z d =0.439.Imaging of the system with the Palomar 5-m telescope revealed a bright (m g =16.5,m i =16.6in Gunn magnitudes)stellar-like object at the ra-dio position.The lack of structure suggested that the fainter of the images may be attenuated by dust extinction in the lensing galaxy.Subsequent observations with the Nordic Op-tical Telescope (Toft,Hjorth &Burud 2000)detected a weak counterpart to the secondary lensed image.The large opti-cal ?ux ratio between the images (?60:1at V band)points to signi?cant di?erential extinction by the lensing galaxy,which was detected following the subtraction of scaled point-spread functions (PSFs).

This paper presents vastly improved radio and optical

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observations of B1152+199,and constructs models for the lensing mass distribution based on the high resolution data. Section2analyses the radio properties of B1152+199,in-cluding expanded VLA radio spectra and deep observations with MERLIN and the VLBA.Section3presents optical imaging obtained with HST.In section4we investigate mod-

els for the system and constrain the lensing galaxy mass pro?le.Section5summarises our?ndings and outlines ad-ditional work.

2RADIO IMAGING

B1152+199consists of two radio components with a?ux density ratio of~3:1and a separation of1.′′56(Myers et al. 1999).Each of the components is unresolved by the VLA.To investigate the spectral properties of the components over a wide range of frequencies,the system was observed at1.4, 5,8.4and15GHz using the VLA in A con?guration on 1999July15.The phase calibrator was J1150+242,and ob-servations of3C286were used to set the?ux density scale. The VLA data sets were calibrated in the Astronomical Im-age Processing System(AIPS)using the standard procedure and analysed in DIFMAP(Shepherd1997).In each case the visibility data were?tted to a pair of compact Gaussian com-ponents using several iterations of model-?tting and phase-only self-calibration,with a solution interval of0.5min.The component?ux densities are given in Table1,and the ra-dio spectra are plotted in Figure1.The spectra are nearly identical,as expected for lensed images of a single back-ground source.The overall spectral indices between1.4and 15GHz areα151.4=?0.07±0.01(A)andα151.4=?0.07±0.01 (B),respectively.The?atness of the radio spectra suggests that the source may exhibit su?cient variability to allow for the measurement of a di?erential time delay.However,trial monitoring observations using the VLA at8.4GHz have thus far failed to detect any signi?cant variability(<~2%)in the lensed components.

MERLIN5GHz observations of B1152+199were per-formed on1999January2for7hr and again on1999Jan-uary5for14hr.The?ux density scale was determined by 15min observations of3C286and the point source calibra-tor OQ208.Alternate observations of the target source(8 min)and a nearby phase reference source J1148+186(2min) were iterated.The combined data were calibrated in AIPS and imaged in DIFMAP by repeating a cycle of cleaning and phase-only self-calibration,starting with long solution intervals(40min)and gradually decreasing to a minimum interval of2min.Once the model had su?ciently converged, an amplitude self-calibration was performed using a solu-tion interval of30min.The?nal map has an rms noise of70μJy/beam and is shown in Figure2.The data were modelled by two compact Gaussian components with?ux densities of52.6±0.1mJy(A)and18.2±0.1mJy(B).No further emission was detected down to the3σlevel of the residual map.

VLBA5GHz observations of B1152+199were obtained on2001February27and March18.The observing time was three hours per epoch,which was divided among three widely spaced hour angles to maximise the uv coverage.The data were recorded in two IFs,each of which was split into 160.5-MHz channels giving a total bandwidth of16MHz.

A

B

Figure 1.B1152+199component radio spectra based on the VLA1.4,5,8.4and15GHz data of1999July

15.

A

B

Figure2.MERLIN5GHz observation of B1152+199taken1999 January2and5.The lowest contour is3×the map rms noise of 70μJy/beam,and contour levels increase by factors of two.The restoring beam is72.5×63.7mas at+38.1?.The data have been naturally weighted.

Table1.B1152+199component?ux densities(in mJy)at1.4, 5,8.4and15GHz.Data for the1999July15VLA observation. Errors in the?ux densities are taken to be equal to the rms noise of the respective maps.

Comp S1.4S5S8.4S15

A50.8±0.455.2±0.148.5±0.143.0±0.3

B17.1±0.418.6±0.115.6±0.114.5±0.3

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3

M i l l i A R C S E C

MilliARC SEC

25

20

15

10

5

-5

15

10

5

-5-10-15M i l l i A R C S E C

MilliARC SEC

15105

0-5-10-15

15

10

5

-5

-10

-15

A B

Figure 3.VLBA 5GHz observation of B1152+199taken 2001February 27and March 18.The lowest contour is 3×the map rms noise of 75μJy/beam,and contour levels increase by factors of two.The beam is 3.6×1.9mas at ?1.8?.The data have been naturally weighted.Left:Component A.Right:Component B.

Table 2.B1152+199component substructure.Data from the VLBA 5GHz observation of 2001February 27and 2001March 18.Listed are the coordinates of each model component,its ?ux density and model-?tted position angle (for the Gaussian jets).Errors on the positions are ?0.1mas.All errors are the nominal 1σuncertainties estimated by the AIPS OMFIT https://www.sodocs.net/doc/038853603.html,p x 1x 2

S 5(mJy)

P A Gauss A core ≡0≡033.4±0.2A jet +0.′′0115+0.′′000617.1±0.1+87?±1?B core +0.′′9353?1.′′245411.9±0.1B jet

+0.′′9394

?1.′′2494

5.0±0.1

+143?±2?

The data were digitized using two-bit sampling and both the Stokes L and R polarizations were recorded.The integration time per visibility was 2seconds.A ?ve minute scan of the bright source 4C39.25was included for fringe-?nding pur-poses.Alternate observations of the target source (3min)and the nearby phase reference source J1148+186(1.5min)were then iterated.

Data reduction was carried out in AIPS on the com-bined epochs.The data were ?rst ?agged and amplitude calibrated using recorded system temperatures and known telescope gain curves.Next the data were fringe-?tted,using 4C39.25to derive an initial delay correction.The phase cali-brator was then used to ?nd the residual rate,phase and de-lay solutions as a function of time.This was initially fringe-?tted assuming that it was a point source and later mapped and self-calibrated to produce a model that included the e?ects of resolved structure.The solutions so found were then applied to B1152+199.The data were mapped using the IMAGR task.As the correlation centre of the data was a position close (50mas)to component A,the data were not averaged in time or frequency so as to avoid any smear-ing in the ?nal images.Maps were made of two ?elds at the positions of the lensed radio components.Several iter-ations of mapping and phase-only self-calibration were per-formed until the CLEAN model converged.The data were then amplitude self-calibrated using a long solution interval

(80min).The resulting maps are displayed in Figure 3and

have an rms noise of 75μJy/beam.Each of the components is resolved into a compact core and extended jet structure.Finally,the data were model-?tted using the OMFIT task.For each image,two components were used to crudely de-scribe the observed structure:a delta function for the core and a Gaussian for the jet.The positions,?ux densities and orientations of these components are listed in Table 2.

Note the apparent peculiarity of the B1152+192ra-dio substructure.In component A the jet is quite straight.Speci?cally,the position angle of the Gaussian jet compo-nent (+87?)is nearly identical to that of an axis drawn between the centre of that component and the core.The jet in B,however,appears to be slightly bent.Here the position angle of the Gaussian jet (+143?)is signi?cantly larger than that of an axis passing through the centres of the core and jet model components (+134?).The bending of B could be produced by substructure in the lensing mass distribution (e.g.,Metcalf &Madau 2001).Deeper imaging at higher resolution will be essential for con?rming this discrepancy and evaluating possible solutions.

3HUBBLE SPACE TELESCOPE IMAGING

HST observations of B1152+199were obtained on 2000March 28with the Wide Field and Planetary Camera 2(WFPC2).The F555W (“V-band”)and F814W (“I-band”)?lters were used.For each ?lter,four dithered exposures of 500sec duration were obtained.A standard reduction was performed on the data sets using the Image Reduction and Analysis Facility (IRAF).The resulting I-band image is dis-played in Figure 4.The V-band image detected all the same features but at a lower signal-to-noise,and is not shown.The lensing galaxy (G)and counterparts to the lensed quasar components (A &B)are clearly detected.In addition,a faint extended emission feature (X)is seen to the west of https://www.sodocs.net/doc/038853603.html,ponent X certainly cannot be an additional lensed

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A

B G

X

Figure4.HST WFPC2I-band image obtained2000March28. The shading is logarithmic.Counterparts to the lensed quasar images(A&B),the lensing galaxy(G)and a possible satellite galaxy(X)are detected.The region displayed is3′′×3′′.

Table3.HST photometry and astrometry.Listed are the posi-tions of the components derived from the I-band image,and their integrated magnitudes m V and m I.The magnitude of X was cal-culated using only the central150×150mas.Errors are10mas on the positions and?0.3on the magnitudes.

Comp x1x2m V m I

A≡0≡0<~17.3<~16.7

B+0.′′942?1.′′25121.919.9

G+0.′′554?0.′′99122.619.6

X?0.′′037?1.′′04625.023.1

image,as it has no radio counterpart.It may therefore be a satellite galaxy of the primary lens.In addition,evidence of a di?use arc is seen to the west of image B.This may be lensed extended emission from the quasar host galaxy.Its position would require that part of the host galaxy resides in the region enclosed by the tangential caustic curve,inside of which sources are lensed into four images.

Photometry and relative astrometry were performed on the HST data.The positions and magnitudes of the com-ponents are listed in Table 3.There were di?culties in subtracting PSFs because image A is probably saturated. Consequently,the errors in the magnitudes are quite large (?0.3).The relative optical and radio positions of A and B are consistent to within the HST error bars(?10mas).The position of G di?ers from the ground-based measurement of Toft,Hjorth&Burud(2000)by more than100mas,which demonstrates the importance of HST observations for inves-tigating lens systems.Finally,elliptical isophotes were?t to G.At a distance of225mas from the galaxy centre we?nd a surface brightness axial ratio of f=0.84±0.9and a po-sition angle of?63?±17?.Closer to the galaxy centre,the isophotes tend to have smaller axial ratios and somewhat more vertical orientations.

4MASS MODELLING

We now investigate simple models for the B1152+199lens-ing potential.The models were constrained using the posi-tions(x1,x2)of the two lensed core components from the VLBA data and the?ux density ratio.The consistency of the measured?ux density ratio among the various radio data sets strongly suggests that the value has been a?ected very little by variability and is therefore close to the true magni-?cation ratio.We thus set r=|S A/S B|=3.0and assumed an uncertainty of?r=0.15(5%)to account for possible e?ects from low-level variability or model-?tting errors.We set?x1=?x2=0.1mas,and the lens and source red-shifts to their measured values of0.439and1.019,respec-tively(Myers et al.1999).A?at?Λ=0.7cosmology with H0=100h km s?1Mpc?1was assumed for all calculations.

Because the lensing mass in B1152+199is dominated by a single galaxy,we modelled the system using a singular power-law ellipsoid(SPLE)mass distribution(e.g.,Barkana 1998),with scaled surface density

κ(x1,x2)=

q

?x2

i,1

+

(x′i,2?x i,2)2

?r2

(2)

where primed quantities are model-predicted and unprimed quantities are observed.To reduce the number of free pa-rameters and ensure a constrained model,the position of the galaxy was?xed at(+0.′′544,?0.′′991)relative to A. With the pro?le slope also?xed,the model has?ve pa-rameters:the normalisation,axial ratio and position angle of the SPLE,and two coordinates for the unlensed source. The number of degrees of freedom(NDF)is zero,so the best-?tting model should be described byχ2=0,regardless of the assumed uncertainties.Monte Carlo simulations were performed to examine the stability of the models.Gaussian-distributed errors accounting for observational uncertainties were added simultaneously to the galaxy position(10mas in each coordinate)and?ux density ratio(5%).The models were optimised for each of10000trials.The uncertainties in the parameters were found from the ranges enclosing95% of the results.

The optimised model parameters and time delays for

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5

Figure 5.The critical curve (thick line)and caustics (thin lines)

of the isothermal (β=1)lens model.The ?lled circle marks the recovered source position.The open circles indicate the positions of the images.Dashed lines denote contours of constant time delay in increments of 9.0h ?1days outward from the global minimum at image A.

various values of βare listed in Table 4.The di?erential time delay for the isothermal (β=1)model is 35.9±2.0h ?1days in a ?at ?Λ=0.7cosmology.The delay varies linearly with the assumed pro?le slope,as predicted by Witt,Mao &Keeton (2001).Critical curves and caustics for the isothermal case are plotted in Figure 5.

The above models can be subjected to a pair of con-sistency checks.First,the mass distributions of ellipticals tend to be well-aligned with the light (Keeton,Kochanek &Falco 1998;Kochanek 2001),so it is useful to compare the position angles of the SPLEs with the surface brightness of the lensing galaxy.From Table 4we see that the model-predicted position angles are generally compatible with the HST value,but the agreement diminishes as the pro?le is made steeper.The discrepancies are,however,broadly con-sistent with the range found by Kochanek (2001).O?sets between the mass and light position angles are often due to external shear ?elds,but we lack a su?cient number of con-straints to unravel the distribution of internal and external shear in B1152+199at this time.

Second,we considered the relative orientations of the B1152+199radio components.An in?nitesimal vector d x A associated with image A is mapped to a vector d x B associ-ated with image B according to

d x B =A ?1B A A d

x A (3)

where A A,B =? y /? x are the magni?cation matrices (e.g.,Schneider,Ehlers &Falco 1992)at the image positions A and B,respectively,and y represents a vector in the source plane.We de?ne the position angles of the radio components using the axes passing through the centres of their respective core and jet subcomponents,as our experience indicates that

this will be the cleanest indicator of orientation.Given the values in Table 2,P A A =+87?±1?and P A B =+134?±2?.Using eq.(4)and the recovered magni?cation matrices,we projected a vector d x A with P A A =+87?to a vector d x B and calculated its position angle.The resulting values are listed in Table 4,with the uncertainties determined by the Monte Carlo.Note that steeper mass pro?les lead to larger position angles for component B.A mass pro?le with β?1.1provides the best ?t to the observed orientations.The popular isothermal model is still compatible with the VLBA data,but shallower mass pro?les fail to reproduce the substructure.

To better quantify constraints on the mass pro?le,we calculated a new ?t parameter

χ2=χ2img,pos +χ2img,f lx +χ2gal,pos +χ2

P A B ,

(4)

that includes contributions from the position angle of com-ponent B (χ2P A B )and the galaxy centre (χ2

gal,pos ),which was now allowed to vary in order to best reproduce the sub-structure.The galaxy position was constrained by the HST astrometry,with a ?t tolerance of 10mas on each coordi-nate.The model-predicted position angle of B was again computed by ?xing A at the observed value of +87?.A ?t tolerance of 2?was assumed for the orientation of B.The models have NDF =1.A plot of ?χ2as a function of βis presented in Figure 6.The value of ?χ2is dominated by the contribution from P A B .The data favour a lensing mass pro?le with 0.95≤β≤1.21at 2σcon?dence (?χ2≤4).The limits are changed only slightly when the rather arbi-trary error assigned to the ?ux density ratio is set to 1%or 10%.Finally,the absence of additional components in the 5GHz MERLIN map requires that any third lensed image have a ?ux density S C such that S A /S C ≥150(see also Rusin &Ma 2001),where S A is the ?ux density of image A,and a conservative detection limit of 5times the map rms noise level has been assumed.This condition is satis?ed for all SPLE mass models with β≥0.60.Therefore,the lack of a detectable third image leads to no improvement in the pro?le constraints in this particular system,but is consistent with the bounds derived using the observed images.

We also investigated the expected perturbation due to the possible satellite galaxy X.Relative velocity dispersions can be estimated from the galaxy luminosities L and Faber-Jackson (1976)relation σ∝L 1/4.Because q ∝σ2∝L 1/2,q G /q X ?3using the V-band data and q G /q X ?5using the I-band data.?We ?xed the position of X according to the HST astrometry and modelled it as a spherical de?ector with the same power-law slope as G.We ran trials with q G /q X =3,4and 5,and the results are listed in Table 5.The inclusion of X has a negligible e?ect on the position angle and axial ratio of G for each β,but the time delay is decreased by 15?25%relative to the single de?ector case.In addition,the predicted value of P A B is smaller for a given β,making steeper mass pro?les necessary to reproduce the data in the two de?ector model (Table 5).Fixing q G /q X =4,for example,implies that 1.04≤β≤1.26at 2σcon?dence.

?Note that these values assume spherical de?ectors.Modi?ca-tions would be required in the presence of ellipticity (e.g.,Keeton,

Kochanek &Seljak 1997).For this preliminary analysis,however,we ignore such issues.

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Table 4.Lens modelling results for power-law de?ectors with di?erent mass pro?les β.Listed are the axis ratio f ,galaxy position angle P A G (in degrees),predicted time delay ?t (in h ?1days),magni?cation matrix elements A A and A B at the image positions,and the predicted position angle (in degrees)of component B assuming that P A A =+87?.Uncertainties are determined from the range enclosing 95%of the Monte Carlo results.All values assume a ?at ?Λ=0.7cosmology,and were calculated using the ?t parameter de?ned in eq.(2).

β=0.8

β=0.9

β=1.0

β=1.1

β=1.2

f 0.787+0.024

?0.025

0.755+0.029

?0.030

0.719+0.034

?0.035

0.677+0.040

?0.041

0.627+0.046

?0.048

P A G ?73.4+3.3

?3.6?76.3+3.6

?4.0?79.4+3.9

?4.2?82.6+4.2

?4.4

?85.6+4.3

?4.4

?t 28.3±1.6

32.1±1.8

35.9±2.0

39.7+2.3

?2.2

43.4+2.5

?2.4

A A,11+0.379+0.018

?0.017

+0.430+0.021

?0.020+0.482+0.024

?0.022+0.533+0.026

?0.025+0.582+0.027

?0.026A A,12?0.273+0.011

?0.010

?0.284±0.013

?0.290±0.015?0.292±0.017

?0.292±0.018

A A,22+0.682+0.009

?0.010

+0.762+0.011

?0.012

+0.838±0.013

+0.910+0.014

?0.015+0.975+0.015

?0.016

A B,11+0.247+0.054

?0.056

+0.317+0.060

?0.062

+0.396+0.066

?0.067

+0.484±0.073

+0.580+0.078

?0.079

A B,12?0.681+0.028

?0.027

?0.792+0.033

?0.032

?0.905+0.038

?0.037

?1.021+0.042

?0.041

?1.137+0.046

?0.045

A B,22?0.356+0.097

?0.103

?0.366+0.109

?0.116

?0.357+0.119

?0.127

?0.324+0.126

?0.134

?0.265+0.131

?0.138

P A B

+123.0+4.1

?3.9

+126.1+4.3

?4.0

+129.9+4.5

?4.2

+134.5+4.8

?4.4

+140.0+5.1

?4.

7

Figure 6.Constraints on the lensing galaxy mass pro?le.Plotted is ?χ2as a function of pro?le slope βfor the single de?ector model (solid line)and two de?ector (dashed line)model with q G /q X =4.The horizontal marker indicates the 2σcon?dence limit.The vertical marker denotes an additional upper bound for the two de?ector model from the absence of a third image.

For pro?les steeper than isothermal,a third,negative-parity image can be formed near X.This image becomes brighter as βis increased over the range of pro?le slopes investigated.The absence of the image tightens the upper bound on the pro?le for more massive secondary de?ectors:β≤1.13for q G /q X =3and β≤1.24for q G /q X =4.

Finally,note that if we had used a larger position an-gle for B,steeper mass pro?les would be required to ?t the data.Assuming that P A B =+143?,as derived from the orientation of the Gaussian model component in Table 2,the pro?le constraints become 1.14≤β≤1.34(2σ)for the single de?ector case and 1.2≤β≤1.4(2σ)for the two de-

Table 5.Lens modelling results for two de?ector mass models.

Listed are the ?xed normalisation ratio q G /q X ,the 2σcon?dence limit on the pro?le slope (βbound I)from the observed images,an additional upper bound from the absence of a detectable third image (βbound II),and the time delay for the isothermal (β=1)case in h ?1days.q G /q X

βbound I βbound II ?t 31.06≤β≤1.26β≤1.1327.741.04≤β≤1.26β≤1.2429.85

1.03≤β≤1.25

β≤1.32

30.8

?ector case with q G /q X =3?5.The absence of a detectable third image is satis?ed for the same range of pro?le slopes given in Table 5.This rules out virtually all βfor q G /q X =3and 4.

5DISCUSSION

We have presented high resolution observations of the grav-itational lens CLASS B1152+199obtained with MERLIN,the VLBA and HST.Such data are vital if lens systems are to ful?ll their potential for constraining galaxy mass distri-butions or determining the Hubble parameter.While pre-vious spectroscopic (Myers et al.1999)and ground-based optical (Toft,Hjorth &Burud 2000)observations were suf-?cient to con?rm B1152+199as a gravitational lens,they o?ered little detailed knowledge about the structure of the system.The motivation for this paper was therefore to pro-vide the high resolution data necessary for more advanced astrophysical and cosmological investigations of this lens.

VLA and MERLIN observations of B1152+199show two compact radio components separated by 1.′′56,with a ?ux density ratio of ~3:1.Both components have nearly identical ?at radio spectra between 1.4and 15GHz,as expected for lensed images of a single background source.VLBA 5GHz observations resolved each of the components into a compact core and extended jet.HST observations with the WFPC2camera detected optical counterparts to each of the quasar images.The ?ux density ratio is ?70:1at V band and ?20:1at I band,con?rming the strong ex-tinction of component B as it passes through the lens.In

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Observations of B1152+1997

addition to clearly detecting the primary lensing mass(G), the images show a faint nearby emission(X)feature that may be a satellite galaxy.

We investigated mass models for B1152+199based on the new radio and optical data.The predicted time delay for an ellipsoidal mass distribution with an isothermal pro?le is 35.9±2.0h?1days,assuming a?at?Λ=0.7cosmology. The delay varies linearly with the assumed mass pro?le,as predicted by Witt,Mao&Keeton(2001).The inclusion of a second power-law de?ector to represent the possible satel-lite galaxy X decreases the time delay by15?25%.The relative orientations of the lensed radio components were shown to be powerful probes of the mass pro?le.Assuming a surface mass distributionΣ(r)∝r?β,the milliarcsecond-scale substructure requires that0.95≤β≤1.21(2σ)for a single galaxy model,and slightly steeper pro?les when X is included.The lower limit onβis particularly secure,as an alternate de?nition of the component orientations,based on the model-?tted position angles of the Gaussian jets,would lead to steeper mass pro?les.B1152+199is the simplest gravitational lens system in which both upper and lower bounds on the lensing mass pro?le have been derived.This system demonstrates the power of VLBI data for the inves-tigation of mass models.

Additional modelling insights are likely to be obtained from higher resolution VLBI observations of B1152+199. Note that the jet associated with image A appears to have a pair of hotspots(Figure3).If corresponding features can be resolved in component B,it may be possible to con-struct models based on the detailed substructure of the jets,similar to the analysis performed on QSO0957+561 (Barkana et al.1999).Such observations should also deter-mine whether the slight bend in the B jet suggested by the current VLBA5GHz data is real.Observations with the HST Near Infrared Camera and Multi-Object Spectrometer (NICMOS)will also be undertaken in an attempt to detect and map emission from the quasar host galaxy.The informa-tion provided by lensed extended emission is a vital ingre-dient for properly reconstructing the mass distributions of lenses(Kochanek,Keeton&McLeod2001).Finally,future studies will focus on measuring the di?erential time delay. The system is currently being monitored at the VLA along with several other new CLASS gravitational lens systems. ACKNOWLEDGEMENTS

We thank the MERLIN,VLBA and HST sta?s for their assistance during our observing runs.We also thank the ref-eree,Alok Patnaik,for insightful comments that helped us improve our initial draft.The National Radio Astronomy Observatory is a facility of the National Science Founda-tion operated under cooperative agreement by Associated Universities,Inc.MERLIN is operated as a National Facil-ity by the University of Manchester,on behalf of the UK Particle Physics&Astronomy Research Council.This re-search used observations with the Hubble Space Telescope, obtained at the Space Telescope Science Institute,which is operated by Associated Universities for Research in Astron-omy Inc.under NASA contract NAS5-26555.D.R.acknowl-edges funding from the Zaccheus Daniel Foundation.This work was supported in part by European Commission TMR Programme,Research Network Contract ERBFMRXCT96-0034(“CERES”).

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李阳:我热爱丢脸_名人故事

李阳:我热爱丢脸 我热爱丢脸 李阳和他的公司10年来只做一件事,仍然是10年前提出的——让3亿中国人讲一口流利的英语! 其实疯狂英语最初的动机,只是针对当时传统英语教学中聋哑英语的很多问题,反其道提出的将英语脱口“说”出的办法。其次,李阳本人是一个性格内向的人,小时候,他认为自己能够去买一瓶酱油,就是很大的成功了,因为他不敢和陌生人说话。所以至今他的父母跟同学都会感到纳闷:那是李阳吗?是什么力量使他突破自己最早禁锢的心?李阳说,他是通过喊英语喊出自信来的。为了克服自己的弱点,他找了一个同学跟他一起喊,这个人绝对认死理,一旦制定计划就一定要做到,他们两个相互鼓励坚持喊英语。一段时间后,他们到外语

角讲英语,得到了别人的夸奖,尝到甜头后他们又继续努力。就这样一步一步地,小小的成就感,渐渐地坚定了信念,获得更大的成就。 当问他进展如何时,他说当时提出3亿人觉得还是容易做到的,现在才发现,这是一个庞大的工作:“第一,中华民族是一个要面子的民族,不但自己要面子,而且要求别人要面子,自己不但不能练英语,别人也不能练,你要练他还会给你泼冷水。比如你在单位讲英语,别人会把你当作异类。在中国学习英语口语的环境非常恶劣,这是个巨大的障碍。第二,我们有三四亿人在为了考试而学习英语,每年为考试而出版的书有几十亿册,要砍掉多少林木,这太可怕了,更重要的是没有去用。语言的目的就是交流,为了交流,为了完成一个国际交流的任务,而我们却把语言当作一个游戏,喜欢出选择题,三个错误答案,一个正确答案,中国人四分之三的时间在复习错误答案,这是一个非常严肃的问题。就这样,中国人一张口就是错误的英语,因为他每天都在看错误的答案,正确的东西反而记不清楚了。”

关于张海迪的励志小故事

关于张海迪的励志小故事 每一个名人的励志故事都是很值得我们去阅读的,一起来看看关于张海迪的励志小故事吧。下面是给大家整理的关于张海迪的励志小故事,供大家参阅! 关于张海迪的励志小故事:童年童年的张海迪,天真活泼,好奇心强。她爱唱歌、爱跳舞、活泼得就象林中的小鸟。她整天唱啊、跳啊,快活极了。不想,5 岁那年一场大病使张海迪失去了行动的自由。 该上学了,同龄的小朋友背起书包,高高兴兴地去上学。张海迪也哭着让妈妈找出户口本,拉着妈妈的手央求道: “妈妈,我也要上学去!我也要上学去!” 妈妈指了指张海迪的双腿,告诉她说: “玲玲(张海迪的乳名),你还不能下地,怎么去上学?” “不,我要去!我要去!我不要一个人在家里。” 张海迪哭着嚷道。 妈妈没有作声,眼泪直在眼圈里转,只是一个劲地用手抚摸着张海迪的头,任凭小海迪脸上的泪水成对成双地滚下来。 哭了一阵,张海迪又开始央求妈妈: “妈妈,你送我去吧,早晨你把我送去,中午再把我接回来。我一定好好学习,听老师的话。” 海迪的话深深刺痛着妈妈的心,多懂事的女儿啊,妈妈多希望她

能站起来,跟别人的孩子一样去读书。妈妈别说送、接,再苦再累也愿意。 可是,不能坐着怎么上课呀? 想到这里,妈妈再也抑制不住辛酸的泪,抱住海迪哭起来,懂事的小妹也在一旁哭,母女三人哭作一团。 半响,妈妈擦擦眼泪,安慰海迪说: “好玲玲,听妈妈的话,等你治好了病,妈妈就送你上学去。” 妹妹也在一旁说: “姐姐,我以后不出去玩了,在家陪你。” 妈妈和妹妹的泪水使张海迪清醒了:上学的热望,将永远成为泡影。这是多么残酷的事实啊!海迪幼小的心灵真的难以承受。 张海迪是一个自尊心很强的孩子,她暗暗下决心,不能上学,就在家里自学,别人会的,我也要会。这个性情倔强的小姑娘,她要以不同寻常的生活方式,走出自己的人生之路。 小海迪开始学识字了。她先根据识字卡片学习汉语拼音。会了拼音,不久她又学会了查字典。识字关她是“连蹦带跳”过来的。根据上、下文,她常常能“猜”出不认识的生字来。每当她“猜”到的字被别人证实是对的时,张海迪就对自己的学习方法更有信心了。谁知,这样的日子也没有维持多久,第三次的手术后,她只能一动不动地躺着,连脖子也不能扭,张海迪多么想看书啊!妈妈看出了海迪的心思,一边护理她,一边抽空给她念书听。 有一天,小海迪忽然对妈妈说:

一个很好的励志故事-(2000字)

一楼度娘并献给所有一直默默奋斗的人们。在此说明,由于工作原因做为手机党,我不能为大家整篇的去讲述我的历程,但我会一直连续的写下去。所以我希望进来的兄弟姐妹不要插楼,让我能完整去述叙我的故事。如真想留言,请大家留在回复里,我会一一为大家回复。在此先谢过。无意中进入励志吧已经有好长一段时间了,一直想写自己的故事,但总觉的不知从何说起,今天我终于鼓起勇气在这里写下自己的故事。希望与大家共勉..... 我生在一个很贫脊的小山沟里,小时候虽然贫穷但童年还是很幸福。姐姐比我大三岁,从小就待别疼我,从记事起好像我们姐弟俩从来没有打过架,村里人都说我们真是一对听话的孩子,这点我跟姐姐都很自豪。到现在我们俩都无话不谈。从小我就不太调皮,学习一直很好,尤其是数学。成绩一直在班上第二名和第三名上徘徊,因为第一名她妈是我们的语文老师加班主任。也许,如果一直这样我这辈子也就这样过了。上学,毕业,分配,娶个农村媳妇儿,生娃,上班,种地.....一辈子也就这样平平淡淡的过了。可是命运偏偏就跟我开了个玩笑,从那以后我的生活发生了彻底性的改变。 那一年初二,那天下午上着生物课。突然间发现邻居大哥在窗户外面给我挥手,示意让我出来。不知道为什么我有一种不详的预感,当我听到你妈不行了,你赶紧回去看看。那一刻我全身骨头都软了,耳朵嗡的一声。那天,我真不知道我是怎么走回家的,只觉得脚步很沉,两条腿好像贯了铅一样。回到家之后,母亲在炕上躺着。胳膊上吊着点滴,嘴唇发青。屋子里的人都乱成了一片,我不知道我该干什么我又能做点什么?我唯一能做的就是用我的小手抓紧母亲冰一样的手。我当时想的就是把母亲的手暖热,把她抓住别让她离开自己。可是.....三天后母亲还是离我而去,她自私的走了,走的无声无息,她甚至没有给我和姐姐留下一句嘱咐的话..... 母亲的离去,对我的打击很大,对这个家庭的打击也是毁灭性的。记的当时父亲一个月瘦了十多斤,后来听父亲说,他当时也想到了死,但是,看在我和姐姐无人照顾的份上,他活了下来。从此,我知道活着比死需要更大的勇气。从此,上课我总是走神。有时候想的什么连我自己都不知道。就这样成绩一次不如一次,中考那年考的一踏糊涂。考完试后我给父亲说我不想再读书,父亲没有责骂,他只是质问我你不读书,你以后干吗?只要你读书,我砸锅卖铁都要把你供出来。那年夏天,我基本上都是一个人待着。暑假过后我进入了补习班,曾经的前三名竟然也在这补习,因此,我开始把自已自我封闭,一天除了学习就是在那儿发呆。也许是因为底子好,也许是因为这一年的默默努力。第二年中考,我以全乡第一名的成绩进入了县一中。从此,我以为我会青云直上,向

疯狂英语李阳的成长故事

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?Do your best this moment and you will be at the best place for your next moment and opportunity. 此时此刻全力以赴,你就会永远处于人生最佳的时刻 ?Sometimes unhappiness is not only the best form of therapy, it is also the only form possible for teenagers. A crash course in reality is the only way to change an adolescent's behavior. 有时候,痛苦不仅是最好的治疗手段,也是改造青少年唯一的手段。残酷的现实才能改变青少年的行为! ?Life's not about waiting for the storms to pass...It's about learning to dance in the rain.生活不是等待暴风雨过去,而且学会在雨中跳舞 ?In order to succeed, your desire for success should be greater than your fear of failure!为了获得成功,你对成功的欲望要超过你对失败的恐惧 ?Good fortune favors the brave and courageous.好运总是宠爱那些勇敢的人。 ?Our responsibility is to make our teenagers miserable. If they are happy every day, you're doing something seriously wrong. They don't need any phone, mp3, vedio games, QQ to live.我们的责任就是让青少年悲惨。如果他们天天快乐,你一定做错了事情。他们不需要电话、游戏机、QQ也能生存。 ?Education is the most important key to success. 教育是通向成功最重要的钥匙 ?Listen, follow, and imitate! You can speak standard English! 听,跟读,并模仿! 你可以讲一口标准的英语! ?Instead of thinking about doing something,do something.与其空想,不如马上行动。?The world makes way for the man who knows where he is going. - 只要你明确了自己的方向,世界也会为你让路。 ?此时此刻,我在北海机场享受飞机晚点带来的读书时光。吃了一碗无比难吃的康师傅泡面,买了三本超级好书,准备在两小时之内看完。今天再次上演飞车行动,在高速公路上开到了180公里,赶到机场却发现飞机还没有从起始地起飞。不要抱怨,要马上采取行动,让自己人生的每一分钟都充满意义!开始读书了! ?控制情绪是一生需要操练的能力、修炼的品德!与您分享:寒山子问拾得:“世间有人谤我、欺我、辱我、笑我、轻我、贱我,如何处之呼?”拾得笑曰:“只要忍他、让他、避他、由他、耐他、敬他、不要理他,再过几年,你且看他”!感悟“心净、心静、心境”! ?今天三八妇女节,我再次创造工作纪录:一天之内到访三个省,五个城市,五场演讲;一趟飞机,四趟汽车,睡着了五次。收获:迟到三分钟仍破例登上了飞机,享受了免费头等舱。真是太疯狂了,我的团队太牛了,能把我利用到这个地步!Winners are simply people who are willing to work more than losers. ?李阳对俞敏洪说: 俞老师,您永远是我的榜样!是所有从事教育事业的人的榜样。我是李阳。 ?无论我多么辛苦,还有比我更辛苦的人!要付出不亚于任何人的努力!吃苦就是吃补!越苦就越补!今年我准备每天工作18个小时,每天演讲至少三场,每个月至少直接影响60万人!今年,我要在1000所大学建立李阳疯狂英语俱乐部!英语就是大喊出来的,事业就是苦干出来的!吃苦才是人间唯一正道!一起来吃苦! ?美国人是世界上最伟大的销售员!发布一款ipad2,连中央电视台都当成新闻联播!真够弱智的!为苹果公司叫好!太牛了!没有比这更伟大的营

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