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We have tested the model using two detailed N-body xus hydrodynamical simulations of massive clusters with contrasting merger histories. | We have tested the model using two detailed N-body plus hydrodynamical simulations of massive clusters with contrasting merger histories. |
In both cases. using realistic mock data from presently available X-ray and SZ telescopes. he mocel is able to accurately fit both the integrated cluster xwameters and. their radial profiles. | In both cases, using realistic mock data from presently available X-ray and SZ telescopes, the model is able to accurately fit both the integrated cluster parameters and their radial profiles. |
LE high-quality. data with very low noise are simulated. the cluster parameters are returned with essentially no bias. | If high-quality data with very low noise are simulated, the cluster parameters are returned with essentially no bias. |
Our fitting code includes roth random. noise and systematic calibration errors in the cata and. Lully includes the elfect. of contamination [roni wimordial CMD. Hluctuations ancl radio sources in the SZ data. | Our fitting code includes both random noise and systematic calibration errors in the data and fully includes the effect of contamination from primordial CMB fluctuations and radio sources in the SZ data. |
We also use a hivper-parameter approach to scale the relative constraints [from the two data sets. | We also use a hyper-parameter approach to scale the relative constraints from the two data sets. |
C'omparison with the widelv-used isothermal 2 model confirms previous results that this mocel can result in significant biases in fitted: cluster parameters (e.g.??).. | Comparison with the widely-used isothermal $\beta$ model confirms previous results that this model can result in significant biases in fitted cluster parameters \citep[e.g.][]{Kay:2004b, Hallman:2007}. |
The quality of the available SZ data is now high enough to require a more sophisticated modelling approach. especially with data that are sensitive to the outskirts of cluster. | The quality of the available SZ data is now high enough to require a more sophisticated modelling approach, especially with data that are sensitive to the outskirts of cluster. |
This model. however remains simplistic in several potentially important wavs. | This model however remains simplistic in several potentially important ways. |
The assumption of hydrostatic equilibrium. is clearly broken badly in the central cores of clusters. anc we are forced. to ignore the data in this region. | The assumption of hydrostatic equilibrium is clearly broken badly in the central cores of clusters, and we are forced to ignore the data in this region. |
Hvdrostatie equilibrium will also be broken in the main body of the cluster due to bulk motions and. οἱher non-thermal support. although in our simulations this does not seem to be a significant impediment to measuring accurate. cluster. profiles. | Hydrostatic equilibrium will also be broken in the main body of the cluster due to bulk motions and other non-thermal support, although in our simulations this does not seem to be a significant impediment to measuring accurate cluster profiles. |
We do not. currently treat. the boundary of the cluster in a Lully consistent way at some radius the virialisecl gas. must. meet a boundary shock of in-falling material and we do not model the corresponding step in pressure. | We do not currently treat the boundary of the cluster in a fully consistent way – at some radius the virialised gas must meet a boundary shock of in-falling material and we do not model the corresponding step in pressure. |
We also do not vet. consider. additional observation constraints such as X-rav. spectral ancl optical weak lensing measurements. although these are in. principle straightforward to incorporate in to our analysis Framework. | We also do not yet consider additional observation constraints such as X-ray spectral and optical weak lensing measurements, although these are in principle straightforward to incorporate in to our analysis framework. |
In subsequent papers we will use this model to analyse SZ data from the CDI2 experiment jointly with relevant imaging cata. | In subsequent papers we will use this model to analyse SZ data from the CBI2 experiment jointly with relevant X-ray imaging data. |
al. ( | al. ( |
2009), the mass-weighted mean age is a more physical parameter, but it has a much less direct relation with the observables. | 2009), the mass-weighted mean age is a more physical parameter, but it has a much less direct relation with the observables. |
Although the mass fraction of a young stellar population might be small, it is much more luminous. | Although the mass fraction of a young stellar population might be small, it is much more luminous. |
Thus their contribution to the luminosity is much higher. | Thus their contribution to the luminosity is much higher. |
A secondary parameter to describe the stellar population is the metallicity, also defined as light- and mass- weighted mean metallicity. | A secondary parameter to describe the stellar population is the metallicity, also defined as light- and mass- weighted mean metallicity. |
Both definitions are bounded by the range of Z used in the base. | Both definitions are bounded by the range of $Z$ used in the base. |
Results for the metallicity are also presented in the bottom panel of Figure 7. | Results for the metallicity are also presented in the bottom panel of Figure 7. |
These results point out to a mean value around solar for both definitions, but the light-weighted average gives higher values for the mean metallicity than the mass-weighted. | These results point out to a mean value around solar for both definitions, but the light-weighted average gives higher values for the mean metallicity than the mass-weighted. |
Again, the light-weighted values are more sensitive to the younger components, while the mass-weighted results are more sensitive to the older components. | Again, the light-weighted values are more sensitive to the younger components, while the mass-weighted results are more sensitive to the older components. |
This result is consistent with a galaxy chemical enrichment scenario, in which the young population is enriched by the evolution of the early massive stars. | This result is consistent with a galaxy chemical enrichment scenario, in which the young population is enriched by the evolution of the early massive stars. |
The power law component is important in the nucleus, as expected, contributing with about 25% of the light. | The power law component is important in the nucleus, as expected, contributing with about $\%$ of the light. |
Cid Fernandes Terlevich (1995) predicted that a broad component in HG becomes distinguishable whenever the scattered FC contributes with > 20% to the optical | Cid Fernandes Terlevich (1995) predicted that a broad component in $\beta$ becomes distinguishable whenever the scattered FC contributes with $\geq$ $\%$ to the optical |
(Ho). Hy!. Hy Hy Ho Ho Hy 3. 4.. 5.. | $H_0$ $H_0^{-1}$ $H_0$ $H_0$ $H_0$ $H_0$ $H_0$ \ref{sec:vla} \ref{sec:atca}, \ref{sec:data}. |
6 7 z=2.78. | \ref{sec:discussion} \ref{sec:conclusions} $z=2.78$ |
observing time. 2000BUL33 and 2000BUL34 where our data cover a significant portion of the amplification. | observing time, 2000BUL33 and 2000BUL34 where our data cover a significant portion of the amplification. |
Phe good coverage and high amplifications of these events allow us to place strict constraints on the fitted. parameters and to exclude the presence of planetary conpanions in the lensing zone 0.6Saflex1.6 being the planetary orbital raclius) with high levels of confidence as discussed in section 6. | The good coverage and high amplifications of these events allow us to place strict constraints on the fitted parameters and to exclude the presence of planetary conpanions in the lensing zone ${0.6 \le a/R_{E} \le 1.6}$ being the planetary orbital radius) with high levels of confidence as discussed in section 6. |
2000BUL37 was again covered in the decline and we obtained &ood coverage of the second half of the peak. | 2000BUL37 was again covered in the decline and we obtained good coverage of the second half of the peak. |
The OGLE dataset lacks any points in the decline and it is the JIT data that help to define the shape of the lighteurve. | The OGLE dataset lacks any points in the decline and it is the JKT data that help to define the shape of the lightcurve. |
2000BUL36 and 2000DBUL39 were low amplification events selected by the priority algorithm mainly because. they were close to maximum amplification while the remaining ongoing events at the time were away from their maximum amplification values. | 2000BUL36 and 2000BUL39 were low amplification events selected by the priority algorithm mainly because they were close to maximum amplification while the remaining ongoing events at the time were away from their maximum amplification values. |
Clearly. the information extracted from these last two events is not of the highest quality as their faintness and low amplifications result in poorer data points ancl a deviation should be more pronounced to be detected. | Clearly, the information extracted from these last two events is not of the highest quality as their faintness and low amplifications result in poorer data points and a deviation should be more pronounced to be detected. |
All data is available upon request. | All data is available upon request. |
Following the S-parameter PSPL fit. we refit the data assuming a binary lens (?:?)| ancl proceed to calculate he net detection probability (for a given. mass ratio q) for each of the sampled. events. | Following the 8-parameter PSPL fit, we refit the data assuming a binary lens \cite{witt90,Schneider86} and proceed to calculate the net detection probability (for a given mass ratio $q$ ) for each of the sampled events. |
This involves two additional xwameters. d and q. where d is the projected. separation xtween the planet and the star. and q the planet to star mass ratio. | This involves two additional parameters, $d$ and $q$, where $d$ is the projected separation between the planet and the star, and $q$ the planet to star mass ratio. |
A similar analysis using a cilferent method has n recently presented in (?:7).. | A similar analysis using a different method has been recently presented in \cite{gaudi00,Albrow01}. |
Prior to calculating the detection. probability for a xanet of mass ratio d we set up a fine eric of planet positions in .r.y on the lens plane and for each of these positions we it the binary model to the data optimizing all parameters. | Prior to calculating the detection probability for a planet of mass ratio $q$ we set up a fine grid of planet positions in $x,y$ on the lens plane and for each of these positions we fit the binary model to the data optimizing all parameters. |
The density of sampling in wey has to be dense enough so hat planetary fits are not missed. | The density of sampling in $x,y$ has to be dense enough so that planetary fits are not missed. |
Our grid step size spacing was defined as J/q/4. where q is the mass ratio. | Our grid step size spacing was defined as $\sqrt{q}/4$, where $q$ is the mass ratio. |
This sets up à very fine grid. for each selected. mass ratio. | This sets up a very fine grid for each selected mass ratio. |
We then make a Ay? map versus planet position by subtracting the minimum X? of the PSPL fit from the minimum X7 of the binary fit for each wey. | We then make a $\Delta\chi^2$ map versus planet position by subtracting the minimum $\chi^2$ of the PSPL fit from the minimum $\chi^2$ of the binary fit for each $x,y$. |
Examples of such maps are shown in figure 7... | Examples of such maps are shown in figure \ref{fig:chi}. |
Albay values where the Ay? exceeds the threshold value GNATyp 760) are shown in black. | All $x,y$ values where the $\Delta\chi^2$ exceeds the threshold value ${\Delta\chi^2}_{\mbox{thr}}$ =60) are shown in black. |
These “black zones? show us where the PSPL mocdel gives a better fit to the data. | These `black zones' show us where the PSPL model gives a better fit to the data. |
For various reasous. such as camera optics. aliguimenut errors. filter irregularities. non-Ilat CCDs. and CCD manufacturing defects. the mapping of the square array of square pixels of a detector outo the tangent-plane projection of the sky requires a nou-linear trauslormation. | For various reasons, such as camera optics, alignment errors, filter irregularities, non-flat CCDs, and CCD manufacturing defects, the mapping of the square array of square pixels of a detector onto the tangent-plane projection of the sky requires a non-linear transformation. |
Positious measured within the pixel grid need to be corrected. [or geometric distortion. (CD) before they cau be accurately compared with other positious in tlie same image. or compared with positions measured iu other image. | Positions measured within the pixel grid need to be corrected for geometric distortion (GD) before they can be accurately compared with other positions in the same image, or compared with positions measured in other image. |
While almost all scientific programse nuust make use of the distortiou solution. most are relatively insensitive to it. | While almost all scientific programs must make use of the distortion solution, most are relatively insensitive to it. |
So loug as each detector pixel is mappecl to within a fraction of a pixel of its true | So long as each detector pixel is mapped to within a fraction of a pixel of its true |
The fundamental assumption here is that the galaxies seen al 2e6 are (he remnants of star-Formation responsible for reionization. | The fundamental assumption here is that the galaxies seen at $z\sim6$ are the remnants of star-formation responsible for reionization. |
It is plausible that the ο6 galaxies (hat are seen in deep surveys are actually comprised of Population I stars with a Salpeter IME which are responsible for a second late epoch of reionization. | It is plausible that the $z\sim6$ galaxies that are seen in deep surveys are actually comprised of Population II stars with a Salpeter IMF which are responsible for a second late epoch of reionization. |
In (hat scenario. the earlier epochs would be entirely due to Population I1I stars which do not contribute to the ultraviolet and visible light huminosity density al z~6. à scenario that has been considered previously (e.&2005). | In that scenario, the earlier epochs would be entirely due to Population III stars which do not contribute to the ultraviolet and visible light luminosity density at $z\sim6$, a scenario that has been considered previously \citep[e.g][]{Cen:03, Furl:05}. |
. These stars. which are more more massive (han MAL. evolve into black holes within 30 Myr. ie. bv z6. | These stars, which are more more massive than $_{\sun}$ evolve into black holes within 30 Myr, i.e. by $z\sim6$. |
The number of ionizing photons required io keep the IGM ionized between 15<z6 is 11 photons/barvon. | The number of ionizing photons required to keep the IGM ionized between $15<z<6$ is $\sim$ 11 photons/baryon. |
An IMFE. extending between 10—100 MM... with a Salpeter slope of 2.3 provides a total of 1.38 photons per barvon for a stellar mass densitv of 2.5x 10mun.. | An IMF extending between $10-100$ $_{\sun}$, with a Salpeter slope of $2.3$ provides a total of 1.38 photons per baryon for a stellar mass density of $\times$ $^{6}$. |
The stellar mass density in massive Population IHE stars must therefore be 2x 10*7. | The stellar mass density in massive Population III stars must therefore be $\times$ $^{7}$. |
Thus. if reionization was initiated by massive stars which evolve into neutron stars aud black holes by 2~6. there must be as much mass density in (hese remnants as in (he stars (hat we detect in the galaxies. | Thus, if reionization was initiated by massive stars which evolve into neutron stars and black holes by $z\sim6$, there must be as much mass density in these remnants as in the stars that we detect in the galaxies. |
If in a contrived scenario. the initial z13 epoch of reionization from Population II stars was relatively brief. lasting A:=2 (e.g.e.CCen2003).. it would require that the stellar mass densitv in the initial burst was ~ 10°mun. | If in a contrived scenario, the initial $z\sim13$ epoch of reionization from Population III stars was relatively brief, lasting $\Delta z=2$ \citep[e.g.][]{Cen:03}, it would require that the stellar mass density in the initial burst was $\sim$ $^{6}$. |
. This corresponds to of barvons that are in stars al 2ον6. | This corresponds to of baryons that are in stars at $z\sim6$. |
Since the lifetime of stars are ~30 Myr while (he interval between 13<215 spans 60 Myr. the first epoch of reionization must be relatively inhomogeneous ancl will depend on the exact epoch al which starlormation in dark matter halos was initiated. | Since the lifetime of $_{\sun}$ stars are $\sim$ 30 Myr while the interval between $13<z<15$ spans 60 Myr, the first epoch of reionization must be relatively inhomogeneous and will depend on the exact epoch at which star-formation in dark matter halos was initiated. |
Furthermore. (he iruncation of Population HI star-formation through [feedback processes argues against them being significant. contributors to reionization (Greil&Bromm|. | Furthermore, the truncation of Population III star-formation through feedback processes argues against them being significant contributors to reionization \citep{Greif_Bromm}. |
O006).. Measuring the distribution of Stromgren sphere size using hieh spatial resolution IHE observations will reveal the true nature of the reionization historv at z>10. | Measuring the distribution of Stromgren sphere size using high spatial resolution HI observations will reveal the true nature of the reionization history at $z>10$. |
It should be noted that Population HI star formation could potentially extend down to lower redshifts. depending on the effect of feedback on the metallicity of the star-lormine environments. | It should be noted that Population III star formation could potentially extend down to lower redshifts, depending on the effect of feedback on the metallicity of the star-forming environments. |
The rates of star-Dormation in such stars are however thought to be 3x10.! of the Population Ε star-formation rate and are inconsequential to the ultraviolet luminosity density or tlie co-moving star-formation rate density 2OOT).. | The rates of star-formation in such stars are however thought to be $3\times10^{-4}$ of the Population II star-formation rate and are inconsequential to the ultraviolet luminosity density or the co-moving star-formation rate density \citep{Tornatore, Brook:07}. . |
The svstems we selected can be grouped into three categories based on their broad-banud spectral energy. distribution (SED). | The systems we selected can be grouped into three categories based on their broad-band spectral energy distribution (SED). |
VW Cha. Sz τὸ, and Sz 102 have significant excess enussion relative to the photospheric [lux from near- through to far-infrared wavelengths (Gauvin&Strom1992:IIughesetal.1994:Nessler-Silacci2006). | VW Cha, Sz 73, and Sz 102 have significant excess emission relative to the photospheric flux from near- through to far-infrared wavelengths \citep{gauvin92,hughes94,kessler06}. |
. Such broad SEDs can be well reproduced bydisks. extending [rom a few stellar radii out to hundreds of AU. | Such broad SEDs can be well reproduced by, extending from a few stellar radii out to hundreds of AU. |
TW Ilva. CS Cha. and T Cha are classified asdisks in the literature. | TW Hya, CS Cha, and T Cha are classified as in the literature. |
Their SEDs present a stronglv reduced (or lack of) near-inlrared excess emission but large mid- and far-infrared emission. | Their SEDs present a strongly reduced (or lack of) near-infrared excess emission but large mid- and far-infrared emission. |
Detailed modeling of their SEDs points to relatively large inner dust cavities almost devoid of sub-micron- aud micron-sized dust grains: e 1-4AAU for TW Iva (Calvetetal.2002:Ratzka2007). e-43AAU for CS Cha (Espaillatetal.2007).. and ~15 AAU for T Cha (Brownetal.2007). | Detailed modeling of their SEDs points to relatively large inner dust cavities almost devoid of sub-micron- and micron-sized dust grains: $\sim$ AU for TW Hya \citep{calvet02,ratzka07}, $\sim$AU for CS Cha \citep{espaillat07}, and $\sim$ AU for T Cha \citep{brown07}. |
. There is no evidence of gas inner holes in these svstems: TW [va is accretingdisk gas at a rale o[ e5xLO MAL. /vr (Muzerolleetal.2000).. the spectroscopic binary CS Cha at <10 M, /vr (Espaillatetal.2007)star. while the small (< LOA)) but variable Ho. equivalent width from T Cha suggests low-level and possibly episodic accretion (Alealaetal.1993). | There is no evidence of gas inner holes in these systems: TW Hya is accretingdisk gas at a rate of $\sim 5 \times 10^{-10}$ $_{\sun}$ /yr \citep{muzerolle00}, the spectroscopic binary CS Cha at $< 10^{-8}$ $_{\sun}$ /yr \citep{espaillat07}, while the small $< 10$ ) but variable $\alpha$ equivalent width from T Cha suggests low-level and possibly episodic accretion \citep{alcala93}. |
. Finally. the SED of WD 347004 has little excess enission al all wavelengths produced by a (enuous dust disk. possibly adish (Sylvester&Skinner1996). | Finally, the SED of HD 34700A has little excess emission at all wavelengths produced by a tenuous dust disk, possibly a \citep{sylvester96}. |
. We performed long-slit high-resolution spectroscopy wilh the spectrograph VISIR mounted on the VLT telescope Melipal (Lagageetal. 2004).. | We performed long-slit high-resolution spectroscopy with the spectrograph VISIR mounted on the VLT telescope \citep{lagage04}. . |
The observations were executed | The observations were executed |
The key difference is that RISE is a frame transfer CCD whose dead time is the frame transfer time. 35 milliseconds for observations longer than | second. | The key difference is that RISE is a frame transfer CCD whose dead time is the frame transfer time, 35 milliseconds for observations longer than 1 second. |
For the brightest comparison star in our field. (Vz 9). we found the optimum exposure times with RISE are approximately 2.7. 7.8. 10.8 seconds during bright. gray and dark time. respectively. | For the brightest comparison star in our field, $V \approx 9$ ), we found the optimum exposure times with RISE are approximately 2.7, 7.8, 10.8 seconds during bright, gray and dark time, respectively. |
We iterate that the improvement in signal-to-noise for defocussed observations. reported by ? is only due to deadtime losses: hence. the defocussing needed is proportional to the CCD readout time. | We iterate that the improvement in signal-to-noise for defocussed observations, reported by \citet{Southworth2009} is only due to deadtime losses; hence, the defocussing needed is proportional to the CCD readout time. |
If the deadtime was zero the best theoretical signal-to-noise would always be for focused observations. mainly due to the increase in background noise for wider profiles. | If the deadtime was zero the best theoretical signal-to-noise would always be for focused observations, mainly due to the increase in background noise for wider profiles. |
Moreover. in our case. the improvement on signal-to-noise between | second and 10.8 seconds exposure times is quite small on the order of 10 ppm per 30 sec bin. | Moreover, in our case, the improvement on signal-to-noise between 1 second and 10.8 seconds exposure times is quite small on the order of $10\,$ ppm per $30\,$ sec bin. |
As we will see below. the strongest reason for defocussing is to minimise systematic noise which. due to its nature. is not accounted for in the ealeulation and can substantially increase the noise in a transit light curve. | As we will see below, the strongest reason for defocussing is to minimise systematic noise which, due to its nature, is not accounted for in the calculation and can substantially increase the noise in a transit light curve. |
Figure shows systematic noise variations larger than 400 ppm. | Figure \ref{complc} shows systematic noise variations larger than 400 ppm. |
Exoplanet transit observations are often dominated by systematic noise. | Exoplanet transit observations are often dominated by systematic noise. |
Therefore. to improve the precision of the light curves it is important to determine and minimise this noise source. | Therefore, to improve the precision of the light curves it is important to determine and minimise this noise source. |
For the 2009 September 09 observations. the brightest comparison star (c1) on the field was affected by systematic noise. | For the 2009 September 09 observations, the brightest comparison star (c1) on the field was affected by systematic noise. |
This can clearly be seen in Figure 2.. where we show the flux of cl relative to the ensemble of comparison stars used in the final 2009 WASP-?21 ight curve. | This can clearly be seen in Figure \ref{complc}, where we show the flux of c1 relative to the ensemble of comparison stars used in the final 2009 WASP-21 light curve. |
This shows a variation of 400 ppm. | This shows a variation of 400 ppm. |
We found that his systematic noise was correlated with the star position in the CCD. which during the transit observation varied by 10 pixels in he .r direction and 8 in the jy. | We found that this systematic noise was correlated with the star position in the CCD, which during the transit observation varied by 10 pixels in the $x$ direction and 8 in the $y$. |
Given that we used an aperture radius of 22 pixels. this implies that only half of the pixels used o perform aperture photometry were common for the duration of he observation. | Given that we used an aperture radius of 22 pixels, this implies that only half of the pixels used to perform aperture photometry were common for the duration of the observation. |
Hence. we concluded that the systematic noise was due to variations in the pixel-to-pixel sensitivity which were not corrected by flat fielding. | Hence, we concluded that the systematic noise was due to variations in the pixel-to-pixel sensitivity which were not corrected by flat fielding. |
In fact. the systematic noise is slightly uigher if we flat field the data. | In fact, the systematic noise is slightly higher if we flat field the data. |
Our master flat is a combination of 150 frames. each with a mean of 35000 counts. | Our master flat is a combination of 150 frames, each with a mean of 35000 counts. |
The uncertainty in this flat is 0.5 millimags per pixel which is smaller than the johetometrie error (~4.4 milimags per unbinned point) and the observed systematic noise. | The uncertainty in this flat is 0.5 millimags per pixel which is smaller than the photometric error $\sim 4.4$ milimags per unbinned point) and the observed systematic noise. |
After careful analysis of the data. we ound that the οἱ comparison star crossed a reflection feature in the CCD that is rotator dependent (LT is on an. alt-azimuth mount) and thus was not corrected by flat tielding. | After careful analysis of the data, we found that the c1 comparison star crossed a reflection feature in the CCD that is rotator dependent (LT is on an alt-azimuth mount) and thus was not corrected by flat fielding. |
This experience demonstriites the importance of good guiding in decreasing the sources of systematic noise. | This experience demonstrates the importance of good guiding in decreasing the sources of systematic noise. |
If the observations were performed in focus and assuming the seeing was | arcsec. the FHWM would have been —2 pixels. | If the observations were performed in focus and assuming the seeing was 1 arcsec, the FHWM would have been $\sim 2$ pixels. |
Using an aperture radius of 1.5... FWHM pixels. it would have implied that there were no common pixels during the observations. | Using an aperture radius of $1.5 \times\,$ FWHM $=3\,$ pixels, it would have implied that there were no common pixels during the observations. |
Therefore. we infer. if the observations were focused. the amount of systematic noise would have doubled. | Therefore, we infer, if the observations were focused, the amount of systematic noise would have doubled. |
Note that the defocussing does not affect the guiding since the guide camera is always kept in focus. | Note that the defocussing does not affect the guiding since the guide camera is always kept in focus. |
After this incident the RISE instrument was upgraded. | After this incident the RISE instrument was upgraded. |
The source of the reflected feature was identified and removed from the instrument field of view. | The source of the reflected feature was identified and removed from the instrument field of view. |
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