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We assume that the disc is replenishecl due to continuous infall. and in this section we analyze a steady-state ACN disc which is heated ow the energy released due to the the accretion onto mass black holes embedded in the disc. | We assume that the disc is replenished due to continuous infall, and in this section we analyze a steady-state AGN disc which is heated by the energy released due to the the accretion onto stellar-mass black holes embedded in the disc. |
We make an anzatz that the heated. dise is optically hick and is supported by the radiation pressure. | We make an anzatz that the heated disc is optically thick and is supported by the radiation pressure. |
Once we obtain the solution for the structure of the disc. we will derive the regime of validity for our anzats. | Once we obtain the solution for the structure of the disc, we will derive the regime of validity for our anzats. |
We thus have or the sound speed in the cise midplane: and hence llere we have used the expression for the flux through the dise face. οea/{(2n). | We thus have for the sound speed in the disc midplane: and hence Here we have used the expression for the flux through the disc face, $F\sim caT^4/(2\Sigma \kappa)$. |
For simplicity. we assume that there are Iq, black holes of mass Adi, embectelecl in a cise within radius ¢ from the central hole of mass AZ. | For simplicity, we assume that there are $N_{\rm bh}$ black holes of mass $M_{\rm bh}$ embedded in a disc within radius $r$ from the central hole of mass $M$ . |
For this “planetary” system to be stable. Min cannot be much bigger than CUAia)7 Le. the embedded. holes cannot be within cach other's Hill spheres. | For this “planetary” system to be stable, $N_{\rm bh}$ cannot be much bigger than $(M/M_{\rm bh})^{1/3}$, i.e. the embedded holes cannot be within each other's Hill spheres. |
To make further progress. we need to know the rate of accretion onto the black holes embedded in the disc. | To make further progress, we need to know the rate of accretion onto the black holes embedded in the disc. |
Because the density of the disc material is high. the well-known 3oncli-Llovle formula gives à super-Edcington accretion rate: it is not clear at this moment how feasible this is (but see c.g. Degelman 2002). | Because the density of the disc material is high, the well-known Bondi-Hoyle formula gives a super-Eddington accretion rate; it is not clear at this moment how feasible this is (but see e.g. Begelman 2002). |
We therefore consider below two separate mocels: the ~Bondi-Llovle” model. in which the embedded black holes accrete at the Boncli-llovle rate. and the “Eddington” mocdel. in which the accretion onto the embedded: holes occurs at the I5ddington limit. | We therefore consider below two separate models: the “Bondi-Hoyle” model, in which the embedded black holes accrete at the Bondi-Hoyle rate, and the “Eddington” model, in which the accretion onto the embedded holes occurs at the Eddington limit. |
.. In this moclel. the accretion rate for the embedded: black home of mass Mig is given by the Bondi-Hovle formula. For the latter expression to be true. the Bondi radius UVhendi=CALf0; must be less than the scaleheight of the disc: this condition will be checked once the structure of the disce is worked out. | In this model, the accretion rate for the embedded black home of mass $M_{\rm bh}$ is given by the Bondi-Hoyle formula, For the latter expression to be true, the Bondi radius $r_{\rm bondi}=GM_{\rm bh}/c_s^2$ must be less than the scaleheight of the disc; this condition will be checked once the structure of the disc is worked out. |
We assume that the fraction ο of the rest-mass energy of. the accreted material+ &oes into. heating. of thedisce... is. thermalized. ancl is eventually racdiated as lux f° from the disc surface: together with the Equations (29)). (30)). and (31)) allow us to find the structure of the disc once the quantities Ada. Nun. M. Al=malu. FS OO. HB. and c are fixed. | We assume that the fraction $\epsilon$ of the rest-mass energy of the accreted material goes into heating of the, is thermalized, and is eventually radiated as flux $F$ from the disc surface: Finally, the equation for the central hole's accretion rate together with the Equations \ref{csmid1}) ), \ref{dotMbh}) ), and \ref{fluxbh}) ) allow us to find the structure of the disc once the quantities $M_{\rm bh}$, $N_{\rm bh}$, $M$, $\dot{M}=\dot{m}\dot{M}_{\rm edd}$, $r$, $\alpha$, $\kappa$, and $\epsilon$ are fixed. |
After some algebra. we find the expression for the Toomre parameter of the disc We see that a typical AGN cise can be stabilized. by feedback [rom embedded black holes out to a radius of about a parsec. | After some algebra, we find the expression for the Toomre parameter of the disc We see that a typical AGN disc can be stabilized by feedback from embedded black holes out to a radius of about a parsec. |
Here αυ is the opacity for Thompson scattering. and Nin was set to its upper limit. (ALAla). | Here $\kappa_0$ is the opacity for Thompson scattering, and $N_{\rm bh}$ was set to its upper limit, $(M/M_{\rm bh})^{1/3}$. |
Recenth. Sirko and. Goodman (2002) analyzed SEDs from AGN cises in which Q=1 is enforced by the unspecified heating sources. | Recently, Sirko and Goodman (2002) analyzed SEDs from AGN discs in which $Q=1$ is enforced by the unspecified heating sources. |
“Phey have shown that current observations limit such selt-gravitating cdises to be no larger than ~107 Selwartzchild. raclii. about O.1pe for 10AZ, black hole. | They have shown that current observations limit such self-gravitating discs to be no larger than $\sim 10^5$ Schwartzchild radii, about $0.1$ pc for $10^7M_{\rm odot}$ black hole. |
This motivates our normalization for the radius used in Eq. (33)). | This motivates our normalization for the radius used in Eq. \ref{Qbh}) ). |
We now check the assumptions which were used in calculating the disc structure: so the disce is radiation-pressure dominated: hence the cise is optically thick: and which gives some credibility to. the Bondi-LHovle estimate of the aecretion rate onto the cise-born black hole. | We now check the assumptions which were used in calculating the disc structure: so the disc is radiation-pressure dominated; hence the disc is optically thick; and which gives some credibility to the Bondi-Hoyle estimate of the accretion rate onto the disc-born black hole. |
The expressions for otheruseful quantities characterizing the disc are given below: The last quantity is the characteristic fraction. of the disc mass which gets converted into embedded black holes. | The expressions for otheruseful quantities characterizing the disc are given below: The last quantity is the characteristic fraction of the disc mass which gets converted into embedded black holes. |
candidate scanning webpage. | candidate scanning webpage. |
At the time of discovery, the scanner is also asked to suggest a crude classification choice, between variable star (VarStar), transient (Transient), and asteroid (rock). | At the time of discovery, the scanner is also asked to suggest a crude classification choice, between variable star ), transient ), and asteroid ). |
To mimic this interaction, removing the need for human scanning, one of the main roles of the automation is to provide the same set of initial classifications based on available data. | To mimic this interaction, removing the need for human scanning, one of the main roles of the automation is to provide the same set of initial classifications based on available data. |
As we now describe, the classification routines also try to provide more refined statements about the nature of the variability. | As we now describe, the classification routines also try to provide more refined statements about the nature of the variability. |
At a given place in the sky, there are broadly two categories of information available (in principle): the changes of brightness in time as a function of wavelength and the context of where 8 source is located in relation to known objects (e.g., stars and galaxies) and coordinates plane, ecliptic, etc.). | At a given place in the sky, there are broadly two categories of information available (in principle): the changes of brightness in time as a function of wavelength and the context of where a source is located in relation to known objects (e.g., stars and galaxies) and coordinates (super-galactic plane, ecliptic, etc.). |
Context information also includes the metrics on those nearby objects, such as color, apparent size, redshift, and spectroscopic type. | Context information also includes the metrics on those nearby objects, such as color, apparent size, redshift, and spectroscopic type. |
To condense and homogenize all of the available information on a given transient or variable, like with image classification, we compute both context and time-domain features which may be used in decision rules or in a machine-learned classifier. | To condense and homogenize all of the available information on a given transient or variable, like with image classification, we compute both context and time-domain features which may be used in decision rules or in a machine-learned classifier. |
Since one the primary goals of the PTF collaboration is to rapidly identify new transient sources or extreme variable stars (e.g., Gal-Yametal. 2011)), we wanted to build a classification engine that was capable of making decisions with only a few epochs of imaging. | Since one the primary goals of the PTF collaboration is to rapidly identify new transient sources or extreme variable stars (e.g., \citealt{ptf10vdl}) ), we wanted to build a classification engine that was capable of making decisions with only a few epochs of imaging. |
To this end, we generated time-domain features that could have meaning in the limit of even a small number ofepochs!”. | To this end, we generated time-domain features that could have meaning in the limit of even a small number of. |
. Those features are described in Table 2.. | Those features are described in Table \ref{tab:tdfeatures}. |
With limited time-domain data available, it is clear that strong classification statements can be made based on context alone. | With limited time-domain data available, it is clear that strong classification statements can be made based on context alone. |
A variable point source with quiescent colors in the SDSS bands of 0.7«u—g1.35 mag and —0.15«g—r0.4 mag is very likely an RR Lyrae star 2010).. | A variable point source with quiescent colors in the SDSS bands of $0.7 < u - g < 1.35$ mag and $-0.15 < g - r < 0.4$ mag is very likely an RR Lyrae star \citep{2010ApJ...708..717S}. |
A transient source near the outskirts of an intrinsically red galaxy is very likely a type Ia supernova. | A transient source near the outskirts of an intrinsically red galaxy is very likely a type Ia supernova. |
When a new discovery is made, in addition to computing the time-domain features, we make separate HTTP/GET external database queries to SDSS (DR7), USNO-B1.0, and SIMBAD. | When a new discovery is made, in addition to computing the time-domain features, we make separate HTTP/GET external database queries to SDSS (DR7), USNO-B1.0, and SIMBAD. |
We also search a database of galaxies within 200 Mpc and record the projected offset of the source to the nearest galaxy. | We also search a database of galaxies within 200 Mpc and record the projected offset of the source to the nearest galaxy. |
For all queries, information about nearby sources (and the distances to them) is saved in a database and associated with the newly discovered source. | For all queries, information about nearby sources (and the distances to them) is saved in a database and associated with the newly discovered source. |
A subset of that information is converted into features for that source and becomes available to the | A subset of that information is converted into features for that source and becomes available to the |
mean that (he emergent spectrin will be eenerically harder compared to an atmosphere where magnetic support is neelectecd. | mean that the emergent spectrum will be generically harder compared to an atmosphere where magnetic support is neglected. |
We empliasize that these spectral implications will apply (o all accretion disks in which the MRI is thought to act. including active galactic nuclei. cataclysmic variables. ancl binaries. | We emphasize that these spectral implications will apply to all accretion disks in which the MRI is thought to act, including active galactic nuclei, cataclysmic variables, and X-ray binaries. |
In (he one whole disk model we constructed. around a stellar mass black hole. we found that the magnitude of this hardening was equivalent to choosing a color correction factor in a relativistic. multitemperature blackbody of 1.74. as opposed to 1.48 in (he nonmaenelized case. | In the one whole disk model we constructed, around a stellar mass black hole, we found that the magnitude of this hardening was equivalent to choosing a color correction factor in a relativistic, multitemperature blackbody of 1.74, as opposed to 1.48 in the nonmagnetized case. |
This has important implications for recent attempts (o measure black hole spins in N-rav. binaries by continuum spectral fitting (e.g. Shaleeοἱal.2005)). | This has important implications for recent attempts to measure black hole spins in X-ray binaries by continuum spectral fitting (e.g. \citealt{sha05}) ). |
Because magnetic pressure support hardens the spectrum. the fitted black hole spin to the observed continuum will have to compensate by being smaller. | Because magnetic pressure support hardens the spectrum, the fitted black hole spin to the observed continuum will have to compensate by being smaller. |
It is conceivable (hat magnetic pressure support may be exaggerated in the local shearing box simulations. | It is conceivable that magnetic pressure support may be exaggerated in the local shearing box simulations. |
Long wavelength Parker instability modes might be suppressed because thev cannot fit inside the box. | Long wavelength Parker instability modes might be suppressed because they cannot fit inside the box. |
This is an issue which will need further investigation. but we did a preliminary check by comparing with. elobal. non-radiative. general relativistic MBI simulations (DeVilliers.Hawley.&τομ]2003). | This is an issue which will need further investigation, but we did a preliminary check by comparing with global, non-radiative, general relativistic MRI simulations \citep{dev03}. |
. In the shearing box simulations. magnetic pressure becomes dominant when the density falls below 0.03 (times the midplane density. | In the shearing box simulations, magnetic pressure becomes dominant when the density falls below 0.03 times the midplane density. |
In contrast. in a elobal simulation in Schwarzschild geometry. (he magnetic pressure becomes dominant below 0.1 (times the local midplane density. | In contrast, in a global simulation in Schwarzschild geometry, the magnetic pressure becomes dominant below 0.1 times the local midplane density. |
Magnetic support therelore appears {ο be even more important in (he elobal simulation which. however. was non-radiative. | Magnetic support therefore appears to be even more important in the global simulation which, however, was non-radiative. |
The shearing box simulations show significant time-dependence. horizontal structure. and asvimmetries above and below the disk midplane. effects. which we have ignored by ruthless averaging. | The shearing box simulations show significant time-dependence, horizontal structure, and asymmetries above and below the disk midplane, effects which we have ignored by ruthless averaging. |
More sophisticated radiative Gausler techniques will have to be emploved io investigate their ellect on the emergent spectrum. | More sophisticated radiative transfer techniques will have to be employed to investigate their effect on the emergent spectrum. |
Density inregularities in particular are expected to be even more prominent in the radiation pressure dominated inner regions of black hole accretion disks (Turnerοἱal.2003:Turner2004:et2005). | Density irregularities in particular are expected to be even more prominent in the radiation pressure dominated inner regions of black hole accretion disks \citep{tur03, tur04,tur05}. |
. Monte Carlo simulations of the photon transfer through such inhomogeneous structures sugeest that the enhanced ratio of absorption to scattering opacity in the denser regions helps to thermalize (and therefore soften) the emergent spectrum (Davisetal.2004)... at least when (he inhomogeneities are treated as static structures. | Monte Carlo simulations of the photon transfer through such inhomogeneous structures suggest that the enhanced ratio of absorption to scattering opacity in the denser regions helps to thermalize (and therefore soften) the emergent spectrum \citep{dav04}, at least when the inhomogeneities are treated as static structures. |
Whether or not this persists in a calculation. or whether or not the hardening due to magnetic pressure support (urns out (to be (he more important effect. remains to be seen. | Whether or not this persists in a time-dependent calculation, or whether or not the hardening due to magnetic pressure support turns out to be the more important effect, remains to be seen. |
This research was supported bv the National Science Foundation under grant nos. | This research was supported by the National Science Foundation under grant nos. |
PIIY99-07949 and AST 03-07657. and bv NASA under grant no. | PHY99-07949 and AST 03-07657, and by NASA under grant no. |
NAG5-13228. | NAG5-13228. |
nass and mass profile and in the values they vield for he clusters limiting radius. | mass and mass profile and in the values they yield for the cluster's limiting radius. |
The various wavs of defining a limiting radius for Α1050 are cousistent with cach other. | The various ways of defining a limiting radius for A1689 are consistent with each other. |
This suggests hat there is uo major iufall of DAL auc galaxies. | This suggests that there is no major infall of DM and galaxies. |
Significant ongoing infall would add to the projected xofiles of mmass aud galaxy nuuber aud also affect the dvuamical measurements. likely making the cluster edge ess apparent. | Significant ongoing infall would add to the projected profiles of mass and galaxy number and also affect the dynamical measurements, likely making the cluster edge less apparent. |
Iu this paper we have continued our exploratiou of Ál689 making use of niu high quality datasets available for this cluster. | In this paper we have continued our exploration of A1689 making use of many high quality datasets available for this cluster. |
This work builds upou our earlier work on this cluster (LOS). where we developed a colprehensive joint analysis of high quality strong lensing (IIST/AC'S). weak leusiug (Subaru). and N-rav (Chandra) measurements. from which we tested the consistency of N-vav and lensing data in a model incdepeudent wav aud derived an imuproved mass profile for Ál689. | This work builds upon our earlier work on this cluster (L08), where we developed a comprehensive joint analysis of high quality strong lensing (HST/ACS), weak lensing (Subaru), and X-ray (Chandra) measurements, from which we tested the consistency of X-ray and lensing data in a model independent way and derived an improved mass profile for A1689. |
In this paper we have incorporated two other biel quality data sets. the galaxw surface munber density measured from deep. wide-field imagine with Subaru/Suprime-Cam aud a large spectroscopic study of the internal ealaxy dywuanues measured usimg VLT/VIMOS. | In this paper we have incorporated two other high quality data sets, the galaxy surface number density measured from deep, wide-field imaging with Subaru/Suprime-Cam and a large spectroscopic study of the internal galaxy dynamics measured using VLT/VIMOS. |
While the lensing and X-ray data eave us the information on the DAL aud gas content of the cluster. the two new data sets added here provide direct information on the galaxy distribution and motions. leading to new deteriuunatious of the DAL distribution of the cluster. | While the lensing and X-ray data gave us the information on the DM and gas content of the cluster, the two new data sets added here provide direct information on the galaxy distribution and motions, leading to new determinations of the DM distribution of the cluster. |
The 3D ealaxy nuuuber deusitv profile derived from. our combined analysis of the above datasets is more consistent with a cored profile. rather than a cuspy profile such as the NEW profile. which seems to fit well the DAL density distribution. | The 3D galaxy number density profile derived from our combined analysis of the above datasets is more consistent with a cored profile, rather than a cuspy profile such as the NFW profile, which seems to fit well the DM density distribution. |
This is in agreement with Adami et (1998) who examined a sample of 62 clusters aud found that the majority are better fit with a core than a cuspy profile. though for idividual clusters the preference for a cored profile is rarely siguificaut at the confidence level. | This is in agreement with Adami et (1998) who examined a sample of 62 clusters and found that the majority are better fit with a core than a cuspy profile, though for individual clusters the preference for a cored profile is rarely significant at the confidence level. |
The galaxy distribution also resembles a ine (1962) profile aud falls off as pBISFUL2S oxeoedine the slope of ¢21792? sneeested by Balcall Lubin (1991) iun order to explain the 7.7discrepancy. | The galaxy distribution also resembles a King (1962) profile and falls off as $r^{-3.18\pm 0.42}$, exceeding the slope of $r^{-2.4\pm0.2}$ suggested by Bahcall Lubin (1994) in order to explain the $\beta$ -discrepancy". |
This asvinptotic behavior of the cluster ealaxy profile at large ris in fact very similar to our total matter profile (clominated by DM). which we have shown Ci be well fit by an NEW profile where the asvauptotic behavior is rk | This asymptotic behavior of the cluster galaxy profile at large $r$ is in fact very similar to our total matter profile (dominated by DM), which we have shown can be well fit by an NFW profile where the asymptotic behavior is $r^{-3}$. |
A principal finding of our work is the fist direct determination of the velocity anisotropy profile for a ealaxy cluster. | A principal finding of our work is the first direct determination of the velocity anisotropy profile for a galaxy cluster. |
This followed frou: an application of the Jeans equation. using as input the observed projected velocity dispersion profile. the observed projected galaxy distribution. and our independently deteriuned lass profile. allowing us to solve for the 3D velocity anisotropy as a function of radius. | This followed from an application of the Jeans equation, using as input the observed projected velocity dispersion profile, the observed projected galaxy distribution, and our independently determined mass profile, allowing us to solve for the 3D velocity anisotropy as a function of radius. |
The resulting anisotropy profile is well fit by the expression iu equation (7)) proposed by Carlbere et ((1997) on the basis of N-hbocky siuulatious. | The resulting anisotropy profile is well fit by the expression in equation \ref{beta analytic expression}) ) proposed by Carlberg et (1997) on the basis of N-body simulations. |
The simulations covered a wide range of cosmiolosies and showed that the radial dependence of the velocity anisotropy 2 has a nearly universal form (Cole Lacey 1996: Crlberg et 11997). with a characteristic radial dependence. | The simulations covered a wide range of cosmologies and showed that the radial dependence of the velocity anisotropy $\beta$ has a nearly universal form (Cole Lacey 1996; Carlberg et 1997), with a characteristic radial dependence. |
This depeucdence is also observed in ALGS9 - maiulv radial motion is deduced at laree radius. teudius towards isotropic (or possibly tangential) motion within the central region r£5001. + kpc. | This dependence is also observed in A1689 - mainly radial motion is deduced at large radius, tending towards isotropic (or possibly tangential) motion within the central region $r \la 500$ $^{-1}$ kpc. |
This prestunably is a manifestation of the overall formation and erowth of clusters. with initial collapse and virialization of the ceutral region. and continued erowtli of the cluster mass through accretion. a two-staee process for which there seeumis to be some evidence also from the DM cutropy distribution (c.g.. Lapi Cavaliere 2008). | This presumably is a manifestation of the overall formation and growth of clusters, with initial collapse and virialization of the central region, and continued growth of the cluster mass through accretion, a two-stage process for which there seems to be some evidence also from the DM entropy distribution (e.g., Lapi Cavaliere 2008). |
Additionally. we used new extensive iuieasureiments of ealaxy positions aud velocities to determine the cluster ass profile. | Additionally, we used new extensive measurements of galaxy positions and velocities to determine the cluster mass profile. |
This was doue in two independent wavs: first. usine the velocity data alone. we ideutified clearly apparent velocity caustics using the method of D99. | This was done in two independent ways; first, using the velocity data alone, we identified clearly apparent velocity caustics using the method of D99. |
The derived amplitude of the velocity caustics was interpreted as the local escape velocity. from which the mass profile was determined using eq. (8)). | The derived amplitude of the velocity caustics was interpreted as the local escape velocity, from which the mass profile was determined using eq. \ref{M_from_A}) ). |
Secondly. we followed the traditional approach of usine the Jeans equation (eq. 2)). | Secondly, we followed the traditional approach of using the Jeans equation (eq. \ref{Jeans equation}) ), |
lucorporating both the galaxy surface umber density and the projected velocity data. and adopting the above velocity anisotropy profile. | incorporating both the galaxy surface number density and the projected velocity data, and adopting the above velocity anisotropy profile. |
These two different lass estinates are in good agreement with the profile derived from our earlier leusiug aud X-ray analysis (LOS). as shown in figure 8.. | These two different mass estimates are in good agreement with the profile derived from our earlier lensing and X-ray analysis (L08), as shown in figure \ref{mass profile comparison}. |
Iun estimating the caustic-based lass profile we adopted the previously suggested value £j;=0.5. | In estimating the caustic-based mass profile we adopted the previously suggested value $F_{\beta}=0.5$. |
We were able to separately check this assumption using the velocity anisotropy profile obtained as described above. | We were able to separately check this assumption using the velocity anisotropy profile obtained as described above. |
Our previously determined mass profile mace it possible to deduce 3: the coniparison of the resulting mass profile with that from our previous leusiug/X-rav snalvsis is then essentially a consistency check ou the general validity of the caustic method. | Our previously determined mass profile made it possible to deduce $\beta$; the comparison of the resulting mass profile with that from our previous lensing/X-ray analysis is then essentially a consistency check on the general validity of the caustic method. |
We found that at lavee radi s2100 3 kpce the factor Fy varies slowly with radius aud stavs within ~50% of the value of 0.5 (see figure 9)). so that the relatively simple caustic method vields the mass profile accurately except at the center. | We found that at large radii, $r \gtrsim 100$ $^{-1}$ kpc, the factor $F_{\beta}$ varies slowly with radius and stays within $\sim 50\%$ of the value of 0.5 (see figure \ref
{F_B profile}) ), so that the relatively simple caustic method yields the mass profile accurately except at the center. |
Note that D99 derived the mean value of Fs=05 from simulated CDM. halos. which typically have concentration paramucter =7. well below that of AlG659 (e=12,207 LOS). | Note that D99 derived the mean value of $F_{\beta}=0.5$ from simulated CDM halos, which typically have concentration parameter $\la 7$, well below that of A1689 $c_{\rm vir}=12.2^{+0.9}_{-1}$; L08). |
Thus. our results sugeest that the caustic-based mass estimation is applicable also for high concentration clusters. | Thus, our results suggest that the caustic-based mass estimation is applicable also for high concentration clusters. |
This shows that dynamical analysis may be iiproved upon by combining the traditional method based on the Jeans equation witli the additional insight gained fromthe caustics Gn relaxed clusters). | This shows that dynamical analysis may be improved upon by combining the traditional method based on the Jeans equation with the additional insight gained from the caustics (in relaxed clusters). |
The virial mass derived from the caustic imnoethod. Ae,=(1.23£0.12).to AL... aud from the Jeans equation. Ma,=1.6is.tot ht AL... | The virial mass derived from the caustic method, $M_{\rm vir} =
(1.23\pm 0.42)\times 10^{15}$ $^{-1}$ $_{\odot}$, and from the Jeans equation, $M_{\rm vir}=1.6^{+1.1}_{-0.8} \times 10^{15}$ $^{-1}$ $_{\odot}$. |
The two colmbined dynamical methods gave AM,=(1.3250.1)«101 ALL. as compared with the value obtained in our joint leusiug/N-rav analysis (105). Ma,(1.58+ 3 AL. | The two combined dynamical methods gave $M_{\rm vir}=(1.3\pm 0.4) \times 10^{15}$ $^{-1}$ $_{\odot}$, as compared with the value obtained in our joint lensing/X-ray analysis (L08), $M_{\rm vir}=(1.58\pm 0.15) \times 10^{15}$ $^{-1}$ $_{\odot}$. |
These mass estimates are consistent. and in agreement also with the result of πισίνα Broadhurst (2008). who combined strong leusing. weal chsingdistortion aud maguification data ina 2D analysis (without assunmiug axial svuuuetiv). and derived AM,= 1M (Gchere this 10 crror inchides οι statistical aud svstematic uncertainties). | These mass estimates are consistent, and in agreement also with the result of Umetsu Broadhurst (2008), who combined strong lensing, weak lensing distortion and magnification data in a 2D analysis (without assuming axial symmetry), and derived $M_{\rm vir} =1.5^{+0.6}_{-0.3} \times 10^{15}$ $^{-1}$ $_{\odot}$ (where this $1-\sigma$ error includes both statistical and systematic uncertainties). |
A novel aspect of our work is au estimation of the initiue radius of AT689 in several different wavs. | A novel aspect of our work is an estimation of the limiting radius of A1689 in several different ways. |
All our | All our |
We have determined for NGC2506 a confidence interval for distance. age. reddening and metallicity (see Table 5). | We have determined for NGC2506 a confidence interval for distance, age, reddening and metallicity (see Table 5). |
a) Distance: in all our trials with the six sets of moclels we have a best fit for (m-M)o in the range 12.5. 12.7. | a) Distance: in all our trials with the six sets of models we have a best fit for $_0$ in the range 12.5 – 12.7. |
This is to be compared with the 12.2 value found by MC'TE using the Ciardullo Demarque (1977). isochrones. | This is to be compared with the 12.2 value found by MCTF using the Ciardullo Demarque (1977) isochrones. |
We must emphasize that with none of our models are we able to provide a stellar distribution in the CALD compatible with the data with such a low distance modulus. | We must emphasize that with none of our models are we able to provide a stellar distribution in the CMD compatible with the data with such a low distance modulus. |
CC94 have derived (m-M)o4212.5. which is in agreement with our derivation. | CC94 have derived $_0$ =12.5, which is in agreement with our derivation. |
b) Age: it varies from 1.5 to 2.2 Gar depending on the adopted set of stellar evolutionary models. with better fits for ages 1.5-1.7 ανν, | b) Age: it varies from 1.5 to 2.2 Gyr depending on the adopted set of stellar evolutionary models, with better fits for ages 1.5-1.7 Gyr. |
This value is much smaller than the 3.4 Gyr derived by AICTE and the 6 €ivr found by Barbaro Pigatto (1984). | This value is much smaller than the 3.4 Gyr derived by MCTF and the 6 Gyr found by Barbaro Pigatto (1984). |
Only part. of. the age overestimates of those studies is attributable to their adopted: shorter distance. which naturally implies lower intrinsic brightness uid. therefore. older age. | Only part of the age overestimates of those studies is attributable to their adopted shorter distance, which naturally implies lower intrinsic brightness and, therefore, older age. |
Most. of the problem. resides in re use of the isochrone fitting. method with older. less ccurate. stellar models combined. with the uncertainty in 1e definition of the AIS turn-olf. (fig.6 in AICTE clearly garows that what we have considered as the turn-oll is closer o their 2 Civr than to the 3 CGvr isochrone). | Most of the problem resides in the use of the isochrone fitting method with older, less accurate, stellar models combined with the uncertainty in the definition of the MS turn-off (fig.6 in MCTF clearly shows that what we have considered as the turn-off is closer to their 2 Gyr than to the 3 Gyr isochrone). |
Our age is also Lgmaller than the 2.5 Gye cited in Friel (1995). and based on 1 MAT defined by JP94: this point will be shortly discussed ater. | Our age is also smaller than the 2.5 Gyr cited in Friel (1995), and based on the MAI defined by JP94: this point will be shortly discussed later. |
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