Metrics:
• Precision P
• Accuracy A
• Fraction f
• Goodness of fit TDC0 qualifying:
• ~50 datasets
• 7 teams, 27 entries
• 3 teams have beaten 15% P, A so far
• Goal: A=0.2%
● Shaded area = success
Liao (UCSB)
Lens measurement
• Time delay estimation. Needs:
good photocal, long seasons, regular sampling, optimal
lightcurve extraction, multi-filter AGN/SN+microlensing model.
Lens measurement
8 Suyu et al.
G1 D C
A
B G2
1"
Fig. 1.— HST ACS image of B1608+656 from 11 orbits in F814W and 9 orbits in F606W. North is up and east is left. The lensed images of the source galaxy are labeled by A, B, C, and D, and the two lens galaxies are G1 and G2. 1 arcsec corresponds to approximately 7 kpc at the redshift of the lens.
are, respectively, zs= 1.394 (Fassnacht et al. 1996) and zd= 0.6304 (Myers et al. 1995).11We note that the lens galaxies are in a group with all galaxy members in the group lie within ±300 km s−1of the mean redshift (Fass-nacht et al. 2006a). Thus, even a conservative limit of 300 km s−1for the peculiar velocity of B1608+656 rela-tive to the Hubble flow would only change D∆tby 0.5%.
As we will see, this is not significant compared to the sys-tematic error associated with κext. This system is special in that the three relative time delays between the four im-ages were measured accurately with errors of only a few percent: ∆tAB= 31.5+2.0−1.0days, ∆tCB= 36.0+1.5−1.5days, and ∆tDB= 77.0+2.0−1.0days (Fassnacht et al. 1999, 2002).
The additional constraints on the lens potential from the extended source analysis and the accurately mea-sured time delays between the images make B1608+656 a good candidate to measure H0with few-percent pre-cision. However, the presence of dust and interacting galaxy lenses (visible in Figure 1) complicate this system.
In Paper I, we presented a comprehensive analysis that took into account the extended source surface brightness distribution, interacting galaxy lenses, and the presence of dust for reconstructing the lens potential. In the fol-lowing subsections, we summarize the data analysis and lens modeling from Paper I, and present the resulting Bayesian evidence values (needed in Equation (30)) from the lens modeling.
4.1. Summary of observations, data analysis, and lens modeling in Paper I
Deep HST ACS observations on B1608+656 in F606W and F814W filters were taken specifically to obtain high signal-to-noise ratio images of the lensed source emission.
In Paper I, we investigated a representative sample of PSF, dust, and lens galaxy light models in order to ex-tract the Einstein ring for the lens modeling. Table 1
11We assume that the redshift of G2 is the same as G1.
lists the various PSF and dust models, and we refer the readers to Paper I for details of each model.
The resulting dust-corrected, galaxy-subtracted F814W image allowed us to model both the lens poten-tial and source surface brightness on grids of pixels based on an iterative and perturbative potential reconstruction scheme. This method requires an initial guess potential model that would ideally be close to the true model. In Paper I, we adopt the SPLE1+D (isotropic) model from Koopmans et al. (2003) as the initial model, which is the most up-to-date, simply-parametrized model combining both lensing and stellar dynamics. In the current paper, we additionally investigate the dependence on the initial model by describing the lens galaxies as SPLE models for a range of slopes (γ"= 1.5, 1.6, . . . , 2.5). Contrary to the SPLE1+D (isotropic) model, the parameters for the SPLE models with variable slopes are constrained by lensing data only, without the velocity dispersion measurement.
The source reconstruction provides a value for the Bayesian evidence, P (d|γ", η, δψ, MD), which can be used for model comparison (where model refers to the PSF, dust, lens galaxy light, and lens potential model).
The reconstructed lens potential (after the pixelated cor-rections δψ) for each data model (PSF, dust, lens galaxy light) leads to three estimates of the Fermat potential differences between the image positions. These are pre-sented in the next subsection for the representative set of PSF, dust, lens galaxy light, and pixelated potential model.
4.2. Lens modeling results
In Paper I, we successfully used a pixelated reconstruc-tion method to model small deviareconstruc-tions from a smooth lens potential model of B1608+656. The resulting source surface brightness distribution is well-localized, and the most probable potential correction δψMP has angular structure approximately following a cos φ mode with am-plitude ∼ 2%. The cos 2φ mode, which could mimic an additional external shear or lens mass distribution ellip-ticity, has a lower amplitude still, indicating that the smooth model of Koopmans et al. (2003) — which in-cludes an external shear of " 0.08 — is giving an ade-quate account of the extended image light distribution.
This was the main result of Paper I. The key ingredient in the ACS prior for the lens density profile slope pa-rameter γ"(Equation (30)) coming from this analysis is the likelihood P (d|γ", MD). For a particular choice of slope γ"and data model MD, this is just the evidence value resulting from the Paper I reconstruction. In this section, our objective is to use the results of this analysis to obtain P (γ"|d) and ∆φ(γ", κext), marginalizing over a representative sample of data models.
4.2.1. Marginalization of the data model Table 1 shows the results of the pixelated poten-tial reconstruction at fixed density slope in the inipoten-tial smooth lens potential model, for various data models MD. Specifically, we used the SPLE1+D (isotropic) model in Koopmans et al. (2003) with γ"= 2.05. The un-certainties in the log evidence in Table 1 were estimated as ∼ 0.03 × 104 for the log evidence values before po-tential correction, and ∼ 0.05 × 104for the log evidence values after potential correction.
HS
Lens measurement
• Time delay estimation. Needs:
good photocal, long seasons, regular sampling, optimal
lightcurve extraction, multi-filter AGN/SN+microlensing model.
8 Suyu et al.
G1 D C
A
B G2
1"
Fig. 1.— HST ACS image of B1608+656 from 11 orbits in F814W and 9 orbits in F606W. North is up and east is left. The lensed images of the source galaxy are labeled by A, B, C, and D, and the two lens galaxies are G1 and G2. 1 arcsec corresponds to approximately 7 kpc at the redshift of the lens.
are, respectively, zs= 1.394 (Fassnacht et al. 1996) and zd= 0.6304 (Myers et al. 1995).11We note that the lens galaxies are in a group with all galaxy members in the group lie within ±300 km s−1of the mean redshift (Fass-nacht et al. 2006a). Thus, even a conservative limit of 300 km s−1for the peculiar velocity of B1608+656 rela-tive to the Hubble flow would only change D∆tby 0.5%.
As we will see, this is not significant compared to the sys-tematic error associated with κext. This system is special in that the three relative time delays between the four im-ages were measured accurately with errors of only a few percent: ∆tAB= 31.5+2.0−1.0days, ∆tCB= 36.0+1.5−1.5days, and ∆tDB= 77.0+2.0−1.0days (Fassnacht et al. 1999, 2002).
The additional constraints on the lens potential from the extended source analysis and the accurately mea-sured time delays between the images make B1608+656 a good candidate to measure H0with few-percent pre-cision. However, the presence of dust and interacting galaxy lenses (visible in Figure 1) complicate this system.
In Paper I, we presented a comprehensive analysis that took into account the extended source surface brightness distribution, interacting galaxy lenses, and the presence of dust for reconstructing the lens potential. In the fol-lowing subsections, we summarize the data analysis and lens modeling from Paper I, and present the resulting Bayesian evidence values (needed in Equation (30)) from the lens modeling.
4.1. Summary of observations, data analysis, and lens modeling in Paper I
Deep HST ACS observations on B1608+656 in F606W and F814W filters were taken specifically to obtain high signal-to-noise ratio images of the lensed source emission.
In Paper I, we investigated a representative sample of PSF, dust, and lens galaxy light models in order to ex-tract the Einstein ring for the lens modeling. Table 1
11We assume that the redshift of G2 is the same as G1.
lists the various PSF and dust models, and we refer the readers to Paper I for details of each model.
The resulting dust-corrected, galaxy-subtracted F814W image allowed us to model both the lens poten-tial and source surface brightness on grids of pixels based on an iterative and perturbative potential reconstruction scheme. This method requires an initial guess potential model that would ideally be close to the true model. In Paper I, we adopt the SPLE1+D (isotropic) model from Koopmans et al. (2003) as the initial model, which is the most up-to-date, simply-parametrized model combining both lensing and stellar dynamics. In the current paper, we additionally investigate the dependence on the initial model by describing the lens galaxies as SPLE models for a range of slopes (γ"= 1.5, 1.6, . . . , 2.5). Contrary to the SPLE1+D (isotropic) model, the parameters for the SPLE models with variable slopes are constrained by lensing data only, without the velocity dispersion measurement.
The source reconstruction provides a value for the Bayesian evidence, P (d|γ", η, δψ, MD), which can be used for model comparison (where model refers to the PSF, dust, lens galaxy light, and lens potential model).
The reconstructed lens potential (after the pixelated cor-rections δψ) for each data model (PSF, dust, lens galaxy light) leads to three estimates of the Fermat potential differences between the image positions. These are pre-sented in the next subsection for the representative set of PSF, dust, lens galaxy light, and pixelated potential model.
4.2. Lens modeling results
In Paper I, we successfully used a pixelated reconstruc-tion method to model small deviareconstruc-tions from a smooth lens potential model of B1608+656. The resulting source surface brightness distribution is well-localized, and the most probable potential correction δψMP has angular structure approximately following a cos φ mode with am-plitude ∼ 2%. The cos 2φ mode, which could mimic an additional external shear or lens mass distribution ellip-ticity, has a lower amplitude still, indicating that the smooth model of Koopmans et al. (2003) — which in-cludes an external shear of " 0.08 — is giving an ade-quate account of the extended image light distribution.
This was the main result of Paper I. The key ingredient in the ACS prior for the lens density profile slope pa-rameter γ"(Equation (30)) coming from this analysis is the likelihood P (d|γ", MD). For a particular choice of slope γ"and data model MD, this is just the evidence value resulting from the Paper I reconstruction. In this section, our objective is to use the results of this analysis to obtain P (γ"|d) and ∆φ(γ", κext), marginalizing over a representative sample of data models.
4.2.1. Marginalization of the data model Table 1 shows the results of the pixelated poten-tial reconstruction at fixed density slope in the inipoten-tial smooth lens potential model, for various data models MD. Specifically, we used the SPLE1+D (isotropic) model in Koopmans et al. (2003) with γ"= 2.05. The un-certainties in the log evidence in Table 1 were estimated as ∼ 0.03 × 104 for the log evidence values before po-tential correction, and ∼ 0.05 × 104for the log evidence values after potential correction.
HS
Lens measurement
• Time delay estimation. Needs:
good photocal, long seasons, regular sampling, optimal
lightcurve extraction, multi-filter AGN/SN+microlensing model.
• Detailed pixel modeling. Needs:
high res follow-up: JWST, ELTs
8 Suyu et al.
G1 D C
A
B G2
1"
Fig. 1.— HST ACS image of B1608+656 from 11 orbits in F814W and 9 orbits in F606W. North is up and east is left. The lensed images of the source galaxy are labeled by A, B, C, and D, and the two lens galaxies are G1 and G2. 1 arcsec corresponds to approximately 7 kpc at the redshift of the lens.
are, respectively, zs= 1.394 (Fassnacht et al. 1996) and zd= 0.6304 (Myers et al. 1995).11We note that the lens galaxies are in a group with all galaxy members in the group lie within ±300 km s−1of the mean redshift (Fass-nacht et al. 2006a). Thus, even a conservative limit of 300 km s−1for the peculiar velocity of B1608+656 rela-tive to the Hubble flow would only change D∆tby 0.5%.
As we will see, this is not significant compared to the sys-tematic error associated with κext. This system is special in that the three relative time delays between the four im-ages were measured accurately with errors of only a few percent: ∆tAB= 31.5+2.0−1.0days, ∆tCB= 36.0+1.5−1.5days, and ∆tDB= 77.0+2.0−1.0days (Fassnacht et al. 1999, 2002).
The additional constraints on the lens potential from the extended source analysis and the accurately mea-sured time delays between the images make B1608+656 a good candidate to measure H0with few-percent pre-cision. However, the presence of dust and interacting galaxy lenses (visible in Figure 1) complicate this system.
In Paper I, we presented a comprehensive analysis that took into account the extended source surface brightness distribution, interacting galaxy lenses, and the presence of dust for reconstructing the lens potential. In the fol-lowing subsections, we summarize the data analysis and lens modeling from Paper I, and present the resulting Bayesian evidence values (needed in Equation (30)) from the lens modeling.
4.1. Summary of observations, data analysis, and lens modeling in Paper I
Deep HST ACS observations on B1608+656 in F606W and F814W filters were taken specifically to obtain high signal-to-noise ratio images of the lensed source emission.
In Paper I, we investigated a representative sample of PSF, dust, and lens galaxy light models in order to ex-tract the Einstein ring for the lens modeling. Table 1
11We assume that the redshift of G2 is the same as G1.
lists the various PSF and dust models, and we refer the readers to Paper I for details of each model.
The resulting dust-corrected, galaxy-subtracted F814W image allowed us to model both the lens poten-tial and source surface brightness on grids of pixels based on an iterative and perturbative potential reconstruction scheme. This method requires an initial guess potential model that would ideally be close to the true model. In Paper I, we adopt the SPLE1+D (isotropic) model from Koopmans et al. (2003) as the initial model, which is the most up-to-date, simply-parametrized model combining both lensing and stellar dynamics. In the current paper, we additionally investigate the dependence on the initial model by describing the lens galaxies as SPLE models for a range of slopes (γ"= 1.5, 1.6, . . . , 2.5). Contrary to the SPLE1+D (isotropic) model, the parameters for the SPLE models with variable slopes are constrained by lensing data only, without the velocity dispersion measurement.
The source reconstruction provides a value for the Bayesian evidence, P (d|γ", η, δψ, MD), which can be used for model comparison (where model refers to the PSF, dust, lens galaxy light, and lens potential model).
The reconstructed lens potential (after the pixelated cor-rections δψ) for each data model (PSF, dust, lens galaxy light) leads to three estimates of the Fermat potential differences between the image positions. These are pre-sented in the next subsection for the representative set of PSF, dust, lens galaxy light, and pixelated potential model.
4.2. Lens modeling results
In Paper I, we successfully used a pixelated reconstruc-tion method to model small deviareconstruc-tions from a smooth lens potential model of B1608+656. The resulting source surface brightness distribution is well-localized, and the most probable potential correction δψMP has angular structure approximately following a cos φ mode with am-plitude ∼ 2%. The cos 2φ mode, which could mimic an additional external shear or lens mass distribution ellip-ticity, has a lower amplitude still, indicating that the smooth model of Koopmans et al. (2003) — which in-cludes an external shear of " 0.08 — is giving an ade-quate account of the extended image light distribution.
This was the main result of Paper I. The key ingredient in the ACS prior for the lens density profile slope pa-rameter γ"(Equation (30)) coming from this analysis is the likelihood P (d|γ", MD). For a particular choice of slope γ"and data model MD, this is just the evidence value resulting from the Paper I reconstruction. In this section, our objective is to use the results of this analysis to obtain P (γ"|d) and ∆φ(γ", κext), marginalizing over a representative sample of data models.
4.2.1. Marginalization of the data model Table 1 shows the results of the pixelated poten-tial reconstruction at fixed density slope in the inipoten-tial smooth lens potential model, for various data models MD. Specifically, we used the SPLE1+D (isotropic) model in Koopmans et al. (2003) with γ"= 2.05. The un-certainties in the log evidence in Table 1 were estimated as ∼ 0.03 × 104 for the log evidence values before po-tential correction, and ∼ 0.05 × 104for the log evidence values after potential correction.
HS
Lens measurement
• Time delay estimation. Needs:
good photocal, long seasons, regular sampling, optimal
lightcurve extraction, multi-filter AGN/SN+microlensing model.
• Detailed pixel modeling. Needs:
high res follow-up: JWST, ELTs
• Redshifts. Needs: deep spectra
8 Suyu et al.
G1 D C
A
B G2
1"
Fig. 1.— HST ACS image of B1608+656 from 11 orbits in F814W and 9 orbits in F606W. North is up and east is left. The lensed images of the source galaxy are labeled by A, B, C, and D, and the two lens galaxies are G1 and G2. 1 arcsec corresponds to approximately 7 kpc at the redshift of the lens.
are, respectively, zs= 1.394 (Fassnacht et al. 1996) and zd= 0.6304 (Myers et al. 1995).11We note that the lens galaxies are in a group with all galaxy members in the group lie within ±300 km s−1of the mean redshift (Fass-nacht et al. 2006a). Thus, even a conservative limit of 300 km s−1for the peculiar velocity of B1608+656 rela-tive to the Hubble flow would only change D∆tby 0.5%.
As we will see, this is not significant compared to the sys-tematic error associated with κext. This system is special in that the three relative time delays between the four im-ages were measured accurately with errors of only a few percent: ∆tAB= 31.5+2.0−1.0days, ∆tCB= 36.0+1.5−1.5days, and ∆tDB= 77.0+2.0−1.0days (Fassnacht et al. 1999, 2002).
The additional constraints on the lens potential from the extended source analysis and the accurately mea-sured time delays between the images make B1608+656 a good candidate to measure H0with few-percent pre-cision. However, the presence of dust and interacting galaxy lenses (visible in Figure 1) complicate this system.
In Paper I, we presented a comprehensive analysis that took into account the extended source surface brightness distribution, interacting galaxy lenses, and the presence of dust for reconstructing the lens potential. In the fol-lowing subsections, we summarize the data analysis and lens modeling from Paper I, and present the resulting Bayesian evidence values (needed in Equation (30)) from the lens modeling.
4.1. Summary of observations, data analysis, and lens modeling in Paper I
Deep HST ACS observations on B1608+656 in F606W and F814W filters were taken specifically to obtain high signal-to-noise ratio images of the lensed source emission.
In Paper I, we investigated a representative sample of PSF, dust, and lens galaxy light models in order to ex-tract the Einstein ring for the lens modeling. Table 1
11We assume that the redshift of G2 is the same as G1.
lists the various PSF and dust models, and we refer the readers to Paper I for details of each model.
The resulting dust-corrected, galaxy-subtracted F814W image allowed us to model both the lens poten-tial and source surface brightness on grids of pixels based on an iterative and perturbative potential reconstruction scheme. This method requires an initial guess potential model that would ideally be close to the true model. In Paper I, we adopt the SPLE1+D (isotropic) model from Koopmans et al. (2003) as the initial model, which is the most up-to-date, simply-parametrized model combining both lensing and stellar dynamics. In the current paper, we additionally investigate the dependence on the initial model by describing the lens galaxies as SPLE models for a range of slopes (γ"= 1.5, 1.6, . . . , 2.5). Contrary to the SPLE1+D (isotropic) model, the parameters for the SPLE models with variable slopes are constrained by lensing data only, without the velocity dispersion measurement.
The source reconstruction provides a value for the Bayesian evidence, P (d|γ", η, δψ, MD), which can be used for model comparison (where model refers to the PSF, dust, lens galaxy light, and lens potential model).
The reconstructed lens potential (after the pixelated cor-rections δψ) for each data model (PSF, dust, lens galaxy light) leads to three estimates of the Fermat potential differences between the image positions. These are pre-sented in the next subsection for the representative set of PSF, dust, lens galaxy light, and pixelated potential model.
4.2. Lens modeling results
In Paper I, we successfully used a pixelated reconstruc-tion method to model small deviareconstruc-tions from a smooth lens potential model of B1608+656. The resulting source surface brightness distribution is well-localized, and the most probable potential correction δψMP has angular structure approximately following a cos φ mode with am-plitude ∼ 2%. The cos 2φ mode, which could mimic an additional external shear or lens mass distribution ellip-ticity, has a lower amplitude still, indicating that the smooth model of Koopmans et al. (2003) — which in-cludes an external shear of " 0.08 — is giving an ade-quate account of the extended image light distribution.
This was the main result of Paper I. The key ingredient in the ACS prior for the lens density profile slope pa-rameter γ"(Equation (30)) coming from this analysis is the likelihood P (d|γ", MD). For a particular choice of slope γ"and data model MD, this is just the evidence value resulting from the Paper I reconstruction. In this section, our objective is to use the results of this analysis to obtain P (γ"|d) and ∆φ(γ", κext), marginalizing over a representative sample of data models.
4.2.1. Marginalization of the data model Table 1 shows the results of the pixelated poten-tial reconstruction at fixed density slope in the inipoten-tial smooth lens potential model, for various data models MD. Specifically, we used the SPLE1+D (isotropic) model in Koopmans et al. (2003) with γ"= 2.05. The un-certainties in the log evidence in Table 1 were estimated as ∼ 0.03 × 104 for the log evidence values before po-tential correction, and ∼ 0.05 × 104for the log evidence values after potential correction.
HS
Lens measurement
• Time delay estimation. Needs:
good photocal, long seasons, regular sampling, optimal
lightcurve extraction, multi-filter AGN/SN+microlensing model.
• Detailed pixel modeling. Needs:
high res follow-up: JWST, ELTs
• Redshifts. Needs: deep spectra
• Environment density
characterisation. Needs: M* and z (photo-z?) for all galaxies within
~5 arcmin radius
8 Suyu et al.G1 D C
A
B G2
1"
Fig. 1.— HST ACS image of B1608+656 from 11 orbits in F814W and 9 orbits in F606W. North is up and east is left. The lensed images of the source galaxy are labeled by A, B, C, and D, and the two lens galaxies are G1 and G2. 1 arcsec corresponds to approximately 7 kpc at the redshift of the lens.
are, respectively, zs= 1.394 (Fassnacht et al. 1996) and zd= 0.6304 (Myers et al. 1995).11We note that the lens galaxies are in a group with all galaxy members in the group lie within ±300 km s−1of the mean redshift (Fass-nacht et al. 2006a). Thus, even a conservative limit of 300 km s−1for the peculiar velocity of B1608+656 rela-tive to the Hubble flow would only change D∆tby 0.5%.
As we will see, this is not significant compared to the sys-tematic error associated with κext. This system is special in that the three relative time delays between the four im-ages were measured accurately with errors of only a few percent: ∆tAB= 31.5+2.0−1.0days, ∆tCB= 36.0+1.5−1.5days, and ∆tDB= 77.0+2.0−1.0days (Fassnacht et al. 1999, 2002).
The additional constraints on the lens potential from the extended source analysis and the accurately mea-sured time delays between the images make B1608+656 a good candidate to measure H0with few-percent pre-cision. However, the presence of dust and interacting galaxy lenses (visible in Figure 1) complicate this system.
In Paper I, we presented a comprehensive analysis that took into account the extended source surface brightness distribution, interacting galaxy lenses, and the presence of dust for reconstructing the lens potential. In the fol-lowing subsections, we summarize the data analysis and lens modeling from Paper I, and present the resulting Bayesian evidence values (needed in Equation (30)) from the lens modeling.
4.1. Summary of observations, data analysis, and lens modeling in Paper I
Deep HST ACS observations on B1608+656 in F606W and F814W filters were taken specifically to obtain high signal-to-noise ratio images of the lensed source emission.
In Paper I, we investigated a representative sample of PSF, dust, and lens galaxy light models in order to ex-tract the Einstein ring for the lens modeling. Table 1
11We assume that the redshift of G2 is the same as G1.
lists the various PSF and dust models, and we refer the readers to Paper I for details of each model.
The resulting dust-corrected, galaxy-subtracted F814W image allowed us to model both the lens poten-tial and source surface brightness on grids of pixels based on an iterative and perturbative potential reconstruction scheme. This method requires an initial guess potential model that would ideally be close to the true model. In Paper I, we adopt the SPLE1+D (isotropic) model from Koopmans et al. (2003) as the initial model, which is the most up-to-date, simply-parametrized model combining both lensing and stellar dynamics. In the current paper, we additionally investigate the dependence on the initial model by describing the lens galaxies as SPLE models for a range of slopes (γ"= 1.5, 1.6, . . . , 2.5). Contrary to the SPLE1+D (isotropic) model, the parameters for the SPLE models with variable slopes are constrained by lensing data only, without the velocity dispersion measurement.
The source reconstruction provides a value for the Bayesian evidence, P (d|γ", η, δψ, MD), which can be used for model comparison (where model refers to the PSF, dust, lens galaxy light, and lens potential model).
The reconstructed lens potential (after the pixelated cor-rections δψ) for each data model (PSF, dust, lens galaxy light) leads to three estimates of the Fermat potential differences between the image positions. These are pre-sented in the next subsection for the representative set of PSF, dust, lens galaxy light, and pixelated potential model.
4.2. Lens modeling results
In Paper I, we successfully used a pixelated reconstruc-tion method to model small deviareconstruc-tions from a smooth lens potential model of B1608+656. The resulting source surface brightness distribution is well-localized, and the most probable potential correction δψMP has angular structure approximately following a cos φ mode with am-plitude ∼ 2%. The cos 2φ mode, which could mimic an additional external shear or lens mass distribution ellip-ticity, has a lower amplitude still, indicating that the smooth model of Koopmans et al. (2003) — which in-cludes an external shear of " 0.08 — is giving an ade-quate account of the extended image light distribution.
This was the main result of Paper I. The key ingredient in the ACS prior for the lens density profile slope pa-rameter γ"(Equation (30)) coming from this analysis is the likelihood P (d|γ", MD). For a particular choice of slope γ"and data model MD, this is just the evidence value resulting from the Paper I reconstruction. In this section, our objective is to use the results of this analysis to obtain P (γ"|d) and ∆φ(γ", κext), marginalizing over a representative sample of data models.
4.2.1. Marginalization of the data model Table 1 shows the results of the pixelated poten-tial reconstruction at fixed density slope in the inipoten-tial smooth lens potential model, for various data models MD. Specifically, we used the SPLE1+D (isotropic) model in Koopmans et al. (2003) with γ"= 2.05. The un-certainties in the log evidence in Table 1 were estimated as ∼ 0.03 × 104 for the log evidence values before po-tential correction, and ∼ 0.05 × 104for the log evidence values after potential correction.