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As a result. the generalized. pressure W is the sum of a static term Vi, given by and a dynamical term given hy In the single fluid case. the static pressure Win. reduces to the ordinary. pressure usually denoted by P. | As a result, the generalized pressure $\Psi$ is the sum of a static term $\Psi_{\rm ins}$ given by and a dynamical term given by In the single fluid case, the static pressure $\Psi_{\rm ins}$ reduces to the ordinary pressure usually denoted by $P$ . |
Note that in multi-Duid svstems. if the static internal energv density is of the form the static pressure can then be written asthe sum of the partial pressures 2. with | Note that in multi-fluid systems, if the static internal energy density is of the form the static pressure can then be written asthe sum of the partial pressures $P_{_{\rm X}}$ with |
little as 3.«10 & 1 accreting onto tle NS surface is sufficient to account for the observed luminosity. | little as $3 \times 10^{13}$ g $^{-1}$ accreting onto the NS surface is sufficient to account for the observed luminosity. |
This model was proposed by Alpar(2001) for CCOs in eoncral. with the additional requirement that their weak. or undetected pulsations nüght be washed out bv au electron scattering corona accunulated from the much larger a at the propeller radius. | This model was proposed by \cite{alp01} for CCOs in general, with the additional requirement that their weak or undetected pulsations might be washed out by an electron scattering corona accumulated from the much larger $\dot m$ at the propeller radius. |
Now. of course. this caveat no longer applies iu the case of10. | Now, of course, this caveat no longer applies in the case of. |
. Iudeed. the nearlv modulation of its pulsed liebt curve in the fist observation requires that the propeller uechanisui create no siguificaut N-ray cussion or X-ray scattering screen at the maguetospherie boundary. | Indeed, the nearly modulation of its pulsed light curve in the first observation requires that the propeller mechanism create no significant X-ray emission or X-ray scattering screen at the magnetospheric boundary. |
As Ong as an accretion scenario is beius considered. there τομάτας the associated possibility that the X-rays are surface thermal cnussion. but a broad cyclotron feature hat corresponds to a range of magnetic field streneths B<lot? G just above the surface. | As long as an accretion scenario is being considered, there remains the associated possibility that the X-rays are surface thermal emission, but a broad cyclotron feature that corresponds to a range of magnetic field strengths $B < 10^{12}$ G just above the surface. |
Because of the large distance aud interstellar extinction o0010... our optical observation docs not vet rule out the presence of a fossil accretion disk. | Because of the large distance and interstellar extinction to, our optical observation does not yet rule out the presence of a fossil accretion disk. |
We computed the optical emission of a standard. blackbody disk that is termumated at immer radius ry,My, and having values of i allowed in the propeller scenario forJ1552,|0010. | We computed the optical emission of a standard blackbody disk that is terminated at inner radius $r_{\rm in} = r_{\rm m}$ and having values of $\dot m$ allowed in the propeller scenario for. |
. These important paramcters mist satisfy the criterion dir2,«3.0«107 gs 1 o? derived in the previous paragraph. | These important parameters must satisfy the criterion $\dot m\,r_{\rm in}^2 < 3.7 \times 10^{32}$ g s $^{-1}$ $^2$ derived in the previous paragraph. |
We include au extinction of 6S mas in the αι. correspoucding to Ng1.5«1072 cin7. | We include an extinction of 6.8 mag in the $R$ -band, corresponding to $N_{\rm H} =
1.5 \times 10^{22}$ $^{-2}$. |
We find that face-on disks with rg,>5«106 cm. an order of magnitude simaller than the heht cylinder radius. have Ros25 mae. which is fainter than our optical limit. | We find that face-on disks with $r_{\rm in} > 5 \times 10^7$ cm, an order of magnitude smaller than the light cylinder radius, have $R > 25$ mag, which is fainter than our optical limit. |
As lone as there are sienificant difficulties in understanding the temperature and(possibly variable) modulation of the pulsed emissiou in the context of an isolated) NS. accretion from a fallback disk remains a viable option for(0. | As long as there are significant difficulties in understanding the temperature and(possibly variable) modulation of the pulsed emission in the context of an isolated NS, accretion from a fall-back disk remains a viable option for. |
. Appareuth. the Criffirlike properties of aare typical ouly of the CCOs. aud are not easily accounted for in anv one theoretical framework. | Apparently, the Griffin-like properties of are typical only of the CCOs, and are not easily accounted for in any one theoretical framework. |
Detailed colmparison is possible oulv with PSR J12105226. the 121 imus pulsar in PINS 120951/52 that has similar huninosity but is modulated with a pulsed fraction of only z10: (Zavlimctal.2000). | Detailed comparison is possible only with PSR J1210–5226, the 424 ms pulsar in PKS 1209–51/52 that has similar luminosity but is modulated with a pulsed fraction of only $\approx
10\%$ \citep{zav00}. |
. Althoueh still classified as a CCO. the complex spin-down behavior and spectrum of PSR J12105226 set it apart from any other isolated NS. | Although still classified as a CCO, the complex spin-down behavior and spectrum of PSR J1210–5226 set it apart from any other isolated NS. |
Whether it is unique or a typical CCO is not vet clear. | Whether it is unique or a typical CCO is not yet clear. |
Its flux is found to bo steady. but large variations of its period derivative may imply a wide binary svstem (4,~026 vr). frequent larec elitches. or accretion from fall-back imaterial (Zavlinetal. 2001). | Its flux is found to be steady, but large variations of its period derivative may imply a wide binary system $P_{\rm orb} \sim
0.2-6$ yr), frequent large glitches, or accretion from fall-back material \citep{zav04}. |
. Tn any case. its wildly varvius spiu-dowu age is inconsistent with the remnant age of ~10 kyr. | In any case, its wildly varying spin-down age is inconsistent with the remnant age of $\sim 10$ kyr. |
The Nav spectrum shows broad absorption features at 0.7 and 1.1 keV (αναetal.2002). and possibly at 2.] aud 2.8 keV when fitted with a thermal blackbody continu model of AZppz0.21 keV and hard tail of kTypzz0.10 keV (Bienamictal.2003). | The X-ray spectrum shows broad absorption features at $0.7$ and $1.4$ keV \citep{san02} and possibly at $2.1$ and $2.8$ keV when fitted with a thermal blackbody continuum model of $kT_{\rm BB} \approx 0.21$ keV and hard tail of $kT_{\rm BB}
\approx 0.40$ keV \citep{big03}. |
. Tf lis like PSR J12105226. we would expect to see similar spectral features and timing behavior: the linited data in haud are not strouely coustrainiug. | If is like PSR J1210–5226, we would expect to see similar spectral features and timing behavior; the limited data in hand are not strongly constraining. |
ls clearly a voung NS associated with Ies 79. aud apparently not a close binary. | is clearly a young NS associated with Kes 79, and apparently not a close binary. |
As a rotation-powered pulsar. the interred upper ΠΕ on its spin-down power Is consistent with the absence of a bright pulsar wiud uchula. | As a rotation-powered pulsar, the inferred upper limit on its spin-down power is consistent with the absence of a bright pulsar wind nebula. |
From the age discrepancy between the pulsar aud SNR. itf is possible that the initial spin-down power of lis sub-critical|0010 (Ly«E):. this may prove to be a defining property of the CCOs. | From the age discrepancy between the pulsar and SNR, it is possible that the initial spin-down power of is sub-critical $\dot E_0 < \dot E_c$ ); this may prove to be a defining property of the CCOs. |
What is clearly distinctive about lis its hot thermal euission aud relatively ΠΠ. (for its age and E). | What is clearly distinctive about is its hot thermal emission and relatively high luminosity (for its age and $\dot E$ ). |
These factors. along with the large pulse imiodulatiou. suggest a rotating hot spot. but the area and Iuninositv of this spot are ercater by an order-ofanagnitude than cau be explained by existing theories of isolated neutron stars. | These factors, along with the large pulse modulation, suggest a rotating hot spot, but the area and luminosity of this spot are greater by an order-of-magnitude than can be explained by existing theories of isolated neutron stars. |
Accretion of fall-back material fromi a fossil disk iu the propeller regime reais au option. | Accretion of fall-back material from a fossil disk in the propeller regime remains an option. |
Au alternative interpretation is a low-luninosity ANP. but the inferred magnetic field aud rotation period are sinaller than expected iu this scenario. | An alternative interpretation is a low-luminosity AXP, but the inferred magnetic field and rotation period are smaller than expected in this scenario. |
The X-ravs from the pulsar are not casily produced iu the contest of the magnetar theory as the interred D field is iusufficicut to power the observed enmüssiou over the implied age of the NS. | The X-rays from the pulsar are not easily produced in the context of the magnetar theory as the inferred $B$ field is insufficient to power the observed emission over the implied age of the NS. |
These unexplained Xaav properties of nunav be sviuptoniatic of the entire class of CCOs. and may require intensive observational and theoretica efforts to understand. | These unexplained X-ray properties of may be symptomatic of the entire class of CCOs, and may require intensive observational and theoretical efforts to understand. |
A radio detection woul demonstrate cleanly that lis a rotation-powered pulsar. but the absence of radio pulsations would be incouchlusive. | A radio detection would demonstrate cleanly that is a rotation-powered pulsar, but the absence of radio pulsations would be inconclusive. |
Frequent N-rav monitoring will test for evidence of accretion torques and/or elitches. aud establish whether the A-rayv flux au pulse profile are variable. | Frequent X-ray monitoring will test for evidence of accretion torques and/or glitches, and establish whether the X-ray flux and pulse profile are variable. |
By analogy with other isolate neutron stars that have broad X-ray absorption features. a deeper spectral study of nuuav prove to be revealing. | By analogy with other isolated neutron stars that have broad X-ray absorption features, a deeper spectral study of may prove to be revealing. |
This investigation is based onu observations obtained withNewton. an ESA science ΣΣ with iustruiients and contributions directly funded by. ESA Member States aud NASA. | This investigation is based on observations obtained with, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. |
We thank Don Terudrup for obtaining the optical unage used in Figure L. | We thank Don Terndrup for obtaining the optical image used in Figure \ref{optical_image}. . |
This work is supported by NASA NMM eraut. NNCO5SCDL6G. | This work is supported by NASA XMM grant NNG05GD46G. |
lanit of 2.81019 cu above the photosphere (see Sect. | limit of $2.8 \times 10^{10}$ cm above the photosphere (see Sect. |
5.3). | 3.3). |
For YZ CAG (see Table 1)) we obtain a mean brightucss temperature 754=7.3«10* K. while for AD Leo we set oan upper lanit of Tj=L93«Loo K. These mean Z5, values are sinaller than previously reported for YZ OAG bv Deuz&Alef (1991) and AD Leo at 15 απ (Jacksonetal. 19893). | For YZ CMi (see Table \ref{tab:sum}) ) we obtain a mean brightness temperature $T_{b}=7.3 \times 10^{7}$ K, while for AD Leo we set an upper limit of $T_{b}=4.93 \times 10^{7}$ K. These mean $T_{b}$ values are smaller than previously reported for YZ CMi by \cite{B1} (1991) and AD Leo at 18 cm \cite{Jack}) ). |
The lower values at 3.6 cin ave still consistent with a ion-theriual spectrum frou evrosvuchnrotron but do not formally exclude thermal oocesses, | The lower values at 3.6 cm are still consistent with a non-thermal spectrum from gyrosynchrotron but do not formally exclude thermal processes. |
However the significant circular polarisation ound durius the observations stronglv argues for a evrosvcelirotron emission mechlanisu. | However the significant circular polarisation found during the observations strongly argues for a gyrosychrotron emission mechanism. |
The derived extent of the coronae above the xiotosphere of the dle stars is compared to the Sun in Table 3. | The derived extent of the coronae above the photosphere of the dMe stars is compared to the Sun in Table \ref{tab:size}. |
The solar value refers to stereoscopic neasurements of the thermal gvroresonance enmiüsson of active regions. | The solar value refers to stereoscopic measurements of the thermal gyroresonance emission of active regions. |
The average value at 10-11 GITz reported w Asclavandenetal. (1995) has been used. | The average value at 10-14 GHz reported by \cite{Aschw} (1995) has been used. |
The experience frou the solar radio enission makes it clear that the observed radio size is only a lower limit of he size of the stellar corona. | The experience from the solar radio emission makes it clear that the observed radio size is only a lower limit of the size of the stellar corona. |
Nevertheless. these results indicate that the observed active dAle stars have much arecr active coronae than the Sun. | Nevertheless, these results indicate that the observed active dMe stars have much larger active coronae than the Sun. |
It wieght be that such dAle stars posess systems of closed loops reaching heights in excess of a stellar diameter. | It might be that such dMe stars posess systems of closed loops reaching heights in excess of a stellar diameter. |
One wav to realize such extended coronae is bv large distances between footpoiuts as possibly seen iu the case of UW Cet B (Deuzctal. 1998). | One way to realize such extended coronae is by large distances between footpoints as possibly seen in the case of UV Cet B \cite{B4} 1998). |
This indicates either that active regions are very large. or that active loops prefercutially connect different active regions. | This indicates either that active regions are very large, or that active loops preferentially connect different active regions. |
RILESSI ΗΝΗ fluxes are shown with respect to the right ordinate axis. | RHESSI HXR fluxes are shown with respect to the right ordinate axis. |
The shaded. area shows the (me range of the transients. | The shaded area shows the time range of the transients. |
It is evident Irom panel (b) that the change i1 line profile al Ps is temporally associated with the transients. | It is evident from panel (b) that the change in line profile at $_2$ is temporally associated with the transients. |
This is also the period of the peak phase of the flare as seen [rom panel (c). | This is also the period of the peak phase of the flare as seen from panel (c). |
The spectral line intensitv near the core (i.e. al wavelength 34.4 )) increased towards the continuun. | The spectral line intensity near the core (i.e. at wavelength $\pm$ ) increased towards the continuum. |
The intensity enhancement was found to be stronger al the blue wing as compared to that in the red wing. | The intensity enhancement was found to be stronger at the blue wing as compared to that in the red wing. |
This asvinnelrv resulted in t1e enhancement of Doppler velocity in the same sign (Figure ΕΙ} as explained earlier. | This asymmetry resulted in the enhancement of Doppler velocity in the same sign (Figure \ref{MDProf}d d) as explained earlier. |
From the spectral data. available during this flare. it is (hus evident that line prolile changes occurred during the impulsive phase of the flare. | From the spectral data available during this flare, it is thus evident that line profile changes occurred during the impulsive phase of the flare. |
The estimated magnetic Πας ancl Doppler velocity values as obtained by LAID algorithms were affected by (hese changes during (he impulsive phase of the flare. resulting in (he observed transient features in maeneto(Doppler)grams. | The estimated magnetic flux and Doppler velocity values as obtained by HMI algorithms were affected by these changes during the impulsive phase of the flare, resulting in the observed transient features in magneto(Doppler)grams. |
It is to note that a purely line-obsieht magnetic field would result in à spectral line with a missing pi-component. | It is to note that a purely line-of-sight magnetic field would result in a spectral line with a missing pi-component. |
Also. the horizontal ancl vertical gradie1(s in magnetic field can cause asymmetric line profiles. | Also, the horizontal and vertical gradients in magnetic field can cause asymmetric line profiles. |
The wav (to resolve these ambiguitles would be to not just look at the LCP and RCP profiles. but all the stokes profiles. i.e... FEC and EQ. | The way to resolve these ambiguities would be to not just look at the LCP and RCP profiles, but all the stokes profiles, i.e., $\pm$ and $\pm$. |
Such profiles are now available [rom the 5DO/IIMI. | Such profiles are now available from the SDO/HMI. |
We obtained the required data corresponding to this flare and aligned the Stokes vectors in a similar mniumer as was done for other data sets of this study. | We obtained the required data corresponding to this flare and aligned the Stokes vectors in a similar manner as was done for other data sets of this study. |
Figure 12 shows the consecutive difference maps ol the Stokes parameters(Z.Q.U ancl V) constructed for the AR NOAA 11153 at the six wavelengths during the peak phase of the [Iare. | Figure \ref{StkDiffMap} shows the consecutive difference maps of the Stokes parameters, and ) constructed for the AR NOAA 11158 at the six wavelengths during the peak phase of the flare. |
Strong (transient signals are seen in all these SLokes maps. which are particularly more prominent around the Fe line center (1.0... al -34.4 and )). | Strong transient signals are seen in all these Stokes maps, which are particularly more prominent around the Fe line center (i.e., at -34.4 and ). |
We have further analvzed the line profiles at several flare and equiet locations of the AR NOAA 11158 [οι examining the (transient changes in the Stokes profiles. | We have further analyzed the line profiles at several flare and quiet locations of the AR NOAA 11158 for examining the transient changes in the Stokes profiles. |
These profiles [EU and FEQ al the transient location P2 are plotted in Figure 13.. | These profiles $\pm$ and $\pm$ at the transient location P2 are plotted in Figure \ref{StkProf}. |
Solid (dotted) curves correspond to the profiles during pre(peak) phase of the flare. | Solid (dotted) curves correspond to the profiles during pre(peak) phase of the flare. |
There is a strong reversal al the wavelength away from the line center. similar to the profile derived from tje continuum as shown in Figure T((d). | There is a strong reversal at the wavelength away from the line center, similar to the profile derived from the continuum as shown in Figure \ref{LineProf}( (d). |
Here it is to note that the magnitude of Stokes{ ls much larger al all wavelengths compared to the magnitude of StokesQ and C. | Here it is to note that the magnitude of Stokes is much larger at all wavelengths compared to the magnitude of Stokes and . |
Hence. ἰle differences seen in the computed Stokes profiles EQ and LEU are small. | Hence, the differences seen in the computed Stokes profiles $\pm$ Q and $\pm$ U are small. |
The observed line prolile changes could be related to the (hermocdvuaniuc change occurring during the flare peak time as the height of line formation can drastically change due to |le moderate perturbation of temperature and density. | The observed line profile changes could be related to the thermodynamic change occurring during the flare peak time as the height of line formation can drastically change due to the moderate perturbation of temperature and density. |
This can be attributed to a large increase ol electron density as shown by the non-LTE caleulations of Dingetal.(2002) [or the Ni 6768 Aline. | This can be attributed to a large increase of electron density as shown by the non-LTE calculations of \citet{Ding2002} for the Ni 6768 line. |
Thev suggested that the non-thermalexcitation and ionization bv the penetrating | They suggested that the non-thermalexcitation and ionization by the penetrating |
at ο=lY defined by several sets of multiple. images identified in the ACS/C'EFO images. | at $z=1.7$ defined by several sets of multiple images identified in the ACS/GTO images. |
This agrees in particular with the mean radius of the famous 5-image system of. 787 ares ab a spectroscopically measured. redshift of +=1.685 (Broachurstetal.2000). | This agrees in particular with the mean radius of the famous 5-image system of $\theta$ ” arcs at a spectroscopically measured redshift of $z=1.685$ \citep{Br00}. |
. “Phis set of multiple images and the distortion. measurements of background. galaxies with photometric redshifts has been used. hy Jeeetal.(2007) to constrain the inner mass profile. | This set of multiple images and the distortion measurements of background galaxies with photometric redshifts has been used by \citet{Jee} to constrain the inner mass profile. |
Their result is in general consistent in form with the earlier analysis of the inner profile by Broachurstctal.(2000)... but with the addition of a narrow low-contrast ring that. it is claimed. can be reproduced in simulations where merging of two massive clusters occurs along the line of sight. | Their result is in general consistent in form with the earlier analysis of the inner profile by \citet{Br00}, but with the addition of a narrow low-contrast ring that, it is claimed, can be reproduced in simulations where merging of two massive clusters occurs along the line of sight. |
X line-of-sight merger is also blamed for the relatively small central velocity. dispersion. (όρκοetal.2002). | A line-of-sight merger is also blamed for the relatively small central velocity dispersion \citep{Czoske}. |
However. in the extensive weak lensing analysis of Ixneibetal.(2003). only one small subgroup is visible. olfset by 3° in projection from. the center of mass and accounting for only 15% ofthe tota mass of the cluster. | However, in the extensive weak lensing analysis of \citet{Kneib} only one small subgroup is visible, offset by $3\arcmin$ in projection from the center of mass and accounting for only $\sim 15\%$ of the total mass of the cluster. |
Ixneibetal.(2003). find that the main cluster is well fitted by an NEW profile with a virial mass of M65107AL.fh and with a high concentration. co~20. | \citet{Kneib} find that the main cluster is well fitted by an NFW profile with a virial mass of $\sim
6\times10^{14}M_{\odot}/h$ and with a high concentration, $\cv \sim
20$. |
In a more recent analysis of deep multicolour B.It.Z Subaru images. Medezinski et ((2007. in preparation) find &oo agreement with Ixneibetal.(2003) (Table 1). | In a more recent analysis of deep multicolour B,R,Z Subaru images, Medezinski et (2007, in preparation) find good agreement with \citet{Kneib} (Table 1). |
In addition. we use the very deep ACS/CGTO images of the massive cluster [1703 for which many sets of multiple images are visible. so that the tangential critical line is easily ⋠⋠identified⋠⋅ with. a mean EinsteinM. radius. of Zu"32" a 2=AN. in good agreement with the radius of the main eint arc at a similar recshift (Table 1). | In addition, we use the very deep ACS/GTO images of the massive cluster A1703 for which many sets of multiple images are visible, so that the tangential critical line is easily identified with a mean Einstein radius of $32\arcsec$ at $z=2.8$, in good agreement with the radius of the main giant arc at a similar redshift (Table 1). |
In the weak lensing analvsis of \lecdezinski et ((2007. in preparation) à very good [it to an NEW profile is found. with a virial mass May=7107AL.fh. | In the weak lensing analysis of Medezinski et (2007, in preparation) a very good fit to an NFW profile is found with a virial mass $\Mv=
7\times10^{14} M_{\odot}/h$. |
This cluster appears relaxed. and centrally concentrated. with little obvious substructure. | This cluster appears relaxed and centrally concentrated, with little obvious substructure. |
To date. deep N-ray imaging is unfortunately missing. | To date, deep X-ray imaging is unfortunately missing. |
Finally. a weak lensing analysis o£ 1N.1347 (Alecezinski et 22007. in preparation) shows this cluster to have a very circular shear pattern. with an estimated. virial mass May95101AL.fh based on an NEW fit to the radial distortion profile. | Finally, a weak lensing analysis of RXJ1347 (Medezinski et 2007, in preparation) shows this cluster to have a very circular shear pattern, with an estimated virial mass $\Mv= 9\times10^{14}
M_{\odot}/h$ based on an NFW fit to the radial distortion profile. |
This cluster has the highest observed. X-rav temperature of 13 keV and a symmetric X-ray emission map that indicates that it is relaxed (Vikhlininetal. | This cluster has the highest observed X-ray temperature of 13 keV and a symmetric X-ray emission map that indicates that it is relaxed \citep{vik}. |
2002).. AX very svinmetric clistribution of ares is visible around the cluster center. implying a well-determined. Einsteinracius at zoLS of 35" from the full model. a value which is also in agreement with a svstem of 5 multiply-Iensed images at this recdshift (Lalkolaetal.2008). | A very symmetric distribution of arcs is visible around the cluster center, implying a well-determined Einsteinradius at $z=1.8$ of $35\arcsec$ from the full model, a value which is also in agreement with a system of 5 multiply-lensed images at this redshift \citep{halkola08}. |
. These four clusters are particularly useful. for our purpose. by virtue of their well-defined. Einstein radii and precise measurements of thevirial masses. which allows a comparison with the theoreticalpredictions as a function of halo mass. | These four clusters are particularly useful for our purpose, by virtue of their well-defined Einstein radii and precise measurements of thevirial masses, which allows a comparison with the theoreticalpredictions as a function of halo mass. |
We convert Mo to Ago Lor cach cluster using the measured: value of e. ancl adopt error. bars of X15'A on Moog and 410% on 6p for all four clusters (but see the next subsection for an alternative measurement. of the virial mass of AI1689). | We convert $\Mv$ to $\M2$ for each cluster using the measured value of $\cv$, and adopt error bars of $\pm 15\%$ on $\M2$ and $\pm 10\%$ on $\tE$ for all four clusters (but see the next subsection for an alternative measurement of the virial mass of A1689). |
Lt is also interesting to note the many examples of strong lensing by other galaxy clusters for which the total mass is not so well constrained. | It is also interesting to note the many examples of strong lensing by other galaxy clusters for which the total mass is not so well constrained. |
Samples of clusters defined by some reasonable criteria (Smithetal.2005:Sandctal.Comerloreet2006). show that invariably the observed Einstein radius (hen detected) forintermediate redshift clusters does not fall short of 10". with a meanof ~15". | Samples of clusters defined by some reasonable criteria \citep{Smith,Sand,Comerford} show that invariably the observed Einstein radius (when detected) forintermediate redshift clusters does not fall short of $10\arcsec$, with a meanof $\sim 15\arcsec$. |
Ες may be compared with the predicted typical Einstein radius of only ~5" from the simulations of Netoetal.(2007). and LHennawietal.(2007). for a cluster of Mao= several 10A4. (Figure 2)). | This may be compared with the predicted typical Einstein radius of only $\sim 5\arcsec$ from the simulations of \citet{Neto} and \citet{Hennawi} for a cluster of $\M2=$ several $\times 10^{14} M_\odot$ (Figure \ref{fig:NetoMean}) ). |
Of the two observational quantities we use to characterize each cluster. 8g. is more directly estimated. from. the positions of multiple images. | Of the two observational quantities we use to characterize each cluster, $\tE$ is more directly estimated, from the positions of multiple images. |
The mass Alou requires a nmieasured mass profile out to large angles. which can be used to estimate the angular position corresponding to ου. i.c. to an enclosed relative densitv of 200 times the critical density. | The mass $\M2$ requires a measured mass profile out to large angles, which can be used to estimate the angular position corresponding to $\r2$, i.e., to an enclosed relative density of 200 times the critical density. |
Deep images provide a large density. of weakly-lensecl background sources. but weak lensing distortions measure only the reduced shear and. suller from the well-known mass-sheet degeneracy. | Deep images provide a large density of weakly-lensed background sources, but weak lensing distortions measure only the reduced shear and suffer from the well-known mass-sheet degeneracy. |
This means that the mass profile can be measured without degeneracies only by fitting a particular parametrized density profile model to the data. | This means that the mass profile can be measured without degeneracies only by fitting a particular parametrized density profile model to the data. |
Llowever. combining lensing distortions with observations of the variation in the number density of background. sources due to weak magnilication breaks the degeneracy ancl vields a direct. measurement of the projected. surface density in each radial bin (Broadhurstetal.2005b). | However, combining lensing distortions with observations of the variation in the number density of background sources due to weak magnification breaks the degeneracy and yields a direct measurement of the projected surface density in each radial bin \citep{Br05b}. |
. Given such independent measurements out to large radius. we can derive the corresponding value of Λου directly. from. the data. without the intermediary of an assumed mocdoel profile. the use of which inevitably introduces a non-trivial systematic error. | Given such independent measurements out to large radius, we can derive the corresponding value of $\M2$ directly from the data, without the intermediary of an assumed model profile, the use of which inevitably introduces a non-trivial systematic error. |
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