Moved appendix location to D

Added in github links to repos
removed purple text
Added in shear catalogue webpage

Appendices.tex

@@ -46,25 +46,6 @@ \section{Galaxy properties and the \tttp covariance}
 	\end{center}
 \end{figure}
 
-\ch{
-\section{Modelling Intrinsic Galaxy Alignment}
-\label{app:IAmodel}
-In this analysis we adopt the \citet{bridle/king:2007} NLA model in order to marginalise over our uncertainty in the contribution to the observed two-point shear correlation function from the intrinsic alignment (IA) of galaxies within their surrounding density field.   More sophisticated models exist, however, and in this appendix we briefly discuss these alternatives.   We then provide justification for our choice by summarising the analysis of \citet{fortuna/etal:2020} which demonstrates that for the statistical power of KiDS-1000, the use of the somewhat adhoc NLA model is sufficiently flexible so as not to introduce any biases in the cosmological parameter constraints.
-
-There are two advanced methods to determine a non-linear IA model.    The first uses a perturbative approach to model the non-linear behaviour of the tidal alignment (where the galaxy is preferentially aligned with the `stretching axis' of the tidal quadrupole) and tidal torquing (where the galaxy disc forms perpendicular to the angular momentum axis which is dependent on the tidal field) \citep{blazek/etal:2019, vlah/etal:2020}.  The second uses a halo model approach, which introduces a model for the small-scale alignment of satellite galaxies within central haloes \citep{schneider/bridle:2010}, and allows for different alignment strengths to be included for the evolving red and blue galaxy population \citep{fortuna/etal:2020}.  On large physical scales both techniques, along with the NLA model, recover the linear alignment model of \citet{hirata/seljak:2004}.  On small physical scales the accuracy of the perturbative approach is limited by the order of the corrections adopted \citep{blas/etal:2013}.  The accuracy of the halo model approach is limited by the challenge of modelling the transition between the properties of galaxies within single halos and across the full density field, commonly referred to as the one-to-two halo transition \citep[see for example the discussion in][]{mead/etal:2020b}.   Both models are nevertheless a significant improvement on the NLA model, which developed an adhoc solution to a small-scale mismatch of the \citet{hirata/seljak:2004} model with IA numerical simulations \citep{heymans/etal:2004}, by replacing the linear matter power spectrum in the \citet{hirata/seljak:2004} formalism with the non-linear matter power spectrum.
-
-IA observations of red and blue galaxies have been both direct \citep{joachimi/etal:2011,mandelbaum/etal:2011,singh/etal:2015,tonegawa/etal:2018,johnston/etal:2019} and indirect \citep{heymans/etal:2013, samuroff/etal:2019}, recovering a common conclusion of significant alignment for red galaxies, and, as yet, no detection of alignment for blue galaxies.   Direct observations are limited by the depth of the spectroscopic, or high-accuracy photometric redshift, galaxy samples that can be studied.  Indirect observations, where an IA model is constrained simultaneously with a cosmological model, are limited by degeneracies with nuisance parameters.   As the IA and cosmological signal scale differently with redshift, a flexible IA model can absorb any systematic errors in the shape of the source redshift distributions, such that the resulting IA parameter constraints are not a true reflection of the underlying IA  model.    This point is nicely illustrated in figure 5 of \citet{efstathiou/lemos:2018} where indirect constraints on the amplitude of the NLA model for the full galaxy sample are shown to vary from $ -6 < A_{\rm IA} < 6$ across a wide range of published cosmic shear surveys.  \citet{wright/etal:2020b} present another example, analysing mock galaxy catalogues to improve the accuracy of the priors on the redshift uncertainty for the previous KiDS data release.  In this case the fiducial IA constraint $A_{\rm IA} = 0.95 \pm 0.67$ reduces to $A_{\rm IA} = 0.28 \pm 0.59$ with the inclusion of a more accurate redshift uncertainty model.   As the intrinsic alignment model depends on the cosmology, any tendency for the model to incorrectly absorb redshift errors would inadvertently lead to unexpected biases in the cosmological parameter constraints.   The more freedom afforded to the IA model, the more opportunity there is for such biases to occur.    Given this concern, we choose to adopt the minimal IA model freedom afforded by current direct observational IA constraints.  In this way any unaccounted errors in our redshift distributions can be detected through a poor goodness-of-fit of the combined cosmological and IA model, as seen, for our second tomographic redshift bin, in the KiDS-1000 internal consistency analysis of \citet[][appendix B.2]{asgari/etal:2020}.   
-
-Our choice of the one-parameter NLA model is motivated by the IA halo model analysis of \citet{fortuna/etal:2020}.   In this analysis central red galaxies are modelled using the  \citet{hirata/seljak:2004} model, with an amplitude $A_{\rm red}$ and a luminosity dependent scaling $\propto L^\beta$.   Combining the observed constraints from \citet{joachimi/etal:2011, singh/etal:2015} they model a simple power-law scaling model with $A_{\rm red} = 5.3 \pm 0.6$ and $\beta=1.2 \pm 0.4$.   The additional constraints from \citet{johnston/etal:2019} motivate a broken power-law model with $A_{\rm red} = 5.1 \pm 1.0$ and $\beta_{L \geq L_0}=1.2 \pm 0.4$, which they also consider.    Central blue galaxies follow the \citet{hirata/seljak:2004} model, with a \citet{johnston/etal:2019} constrained amplitude of $A_{\rm blue} = 0.2 \pm 0.4$ and no luminosity dependence, as there is no observational evidence to support this.    The small-scale satellite galaxy alignments are modelled following \citet{schneider/bridle:2010}.  The amplitude, radial and luminosity dependence of the alignment of red and blue satellite galaxies within their host halo is independently constrained following \citet{georgiou/etal:2019}.     The large-scale galaxy alignment signal is considered to be sourced solely by central galaxies, as there is currently no observational evidence to support large-scale (two-halo) alignments between the different satellite populations.
-
-The direct IA observational constraints adopted by \citet{fortuna/etal:2020} are determined from low redshift galaxy samples, where the properties of the full galaxy population differ significantly from the high redshift galaxy population analysed in KiDS-1000.  Given that the fundamental physical processes that underpin the intrinsic alignment mechanisms are unlikely to significantly evolve out to $z \sim 1$, however, these galaxy-type-specific constraints are relevant at the redshifts sampled by KiDS, provided the evolution in the relative fractions, luminosities and distribution of the red and blue, central and satellite, galaxy populations are accurately modelled.   
-
-\citet{fortuna/etal:2020} determine a sample of plausible IA models for a KiDS-like survey.  They combine the different galaxy-type IA contributions using a halo occupation distribution model taken from the MICE mock galaxy catalogues \citep{fosalba/etal:2015}, with a magnitude limit corresponding to KiDS-depth.   The range of full-population models encompasses the observational uncertainty on the IA model parameters for each galaxy type.    Analysing these IA halo-models with the NLA model, they find the highest NLA model amplitude of $A_{\rm IA}=0.54 \pm 0.13$ when adopting a broken power-law for the red-central luminosity scaling.    This is fully consistent with the \citet{asgari/etal:2020} KiDS-1000 COSEBIs cosmic shear constraints with $A_{\rm IA}=0.26 ^{+0.42}_{-0.34}$, the KiDS-1000 band power cosmic shear constraints with $A_{\rm IA}=0.97 ^{+0.29}_{-0.38}$ and the KiDS-1000 \tttp band power constraints with $A_{\rm IA}=1.07^{+0.27}_{-0.31}$, with the largest difference found for the \tttp results which are in 1.6$\sigma$ agreement.    
-
-Adopting the NLA model in a cosmological parameter inference of a mock KiDS-like data vector of the cosmic shear signal contaminated by the range of different IA halo models allowed by observations, \citet{fortuna/etal:2020} conclude that the redshift dependence of the true IA halo model is not large enough to bias the cosmological parameters in a KiDS-like cosmic shear analysis with the NLA model.   \citet{asgari/etal:2020} nevertheless explore one extension of the NLA model, with the inclusion of a redshift-dependent scaling term, which does not change the recovered KiDS-1000 cosmic shear MAP $S_8$ value.  It only serves to increase the marginal credible region of $S_8$ by $\sim 10\%$.   Given these analyses, we choose to adopt a minimal one-parameter NLA model in our \tttp analysis, but recognise that in future surveys such as LSST and {\it Euclid}, this adhoc model will no longer be sufficient given the expected statistical power of these next-generation surveys \citep{blazek/etal:2019, fortuna/etal:2020}.
-
-}
-
 \section{Parameter priors}
 \label{app:priors}
 This Appendix tabulates the adopted KiDS-1000 priors and sampling parameters in Table~\ref{tab:priors}.   
@@ -128,6 +109,23 @@ \section{Parameter constraints}
 This Appendix tabulates the maximum posterior (MAP) and marginalised constraints on the flat $\Lambda$CDM cosmological parameters, in Table~\ref{tab:fullparams}, for the different combinations of the three large-scale structure probes considered in this work.   For constraints from KiDS-1000 cosmic shear alone, we refer the reader to \citet{asgari/etal:inprep}.
 \input{Table_param_constraints_C.tex}
 
+\section{Modelling Intrinsic Galaxy Alignment}
+\label{app:IAmodel}
+In this analysis we adopt the \citet{bridle/king:2007} NLA model in order to marginalise over our uncertainty in the contribution to the observed two-point shear correlation function from the intrinsic alignment (IA) of galaxies within their surrounding density field.   More sophisticated models exist, however, and in this appendix we briefly discuss these alternatives.   We then provide justification for our choice by summarising the analysis of \citet{fortuna/etal:2020} which demonstrates that for the statistical power of KiDS-1000, the use of the somewhat adhoc NLA model is sufficiently flexible so as not to introduce any biases in the cosmological parameter constraints.
+
+There are two advanced methods to determine a non-linear IA model.    The first uses a perturbative approach to model the non-linear behaviour of the tidal alignment (where the galaxy is preferentially aligned with the `stretching axis' of the tidal quadrupole) and tidal torquing (where the galaxy disc forms perpendicular to the angular momentum axis which is dependent on the tidal field) \citep{blazek/etal:2019, vlah/etal:2020}.  The second uses a halo model approach, which introduces a model for the small-scale alignment of satellite galaxies within central haloes \citep{schneider/bridle:2010}, and allows for different alignment strengths to be included for the evolving red and blue galaxy population \citep{fortuna/etal:2020}.  On large physical scales both techniques, along with the NLA model, recover the linear alignment model of \citet{hirata/seljak:2004}.  On small physical scales the accuracy of the perturbative approach is limited by the order of the corrections adopted \citep{blas/etal:2013}.  The accuracy of the halo model approach is limited by the challenge of modelling the transition between the properties of galaxies within single halos and across the full density field, commonly referred to as the one-to-two halo transition \citep[see for example the discussion in][]{mead/etal:2020b}.   Both models are nevertheless a significant improvement on the NLA model, which developed an adhoc solution to a small-scale mismatch of the \citet{hirata/seljak:2004} model with IA numerical simulations \citep{heymans/etal:2004}, by replacing the linear matter power spectrum in the \citet{hirata/seljak:2004} formalism with the non-linear matter power spectrum.
+
+IA observations of red and blue galaxies have been both direct \citep{joachimi/etal:2011,mandelbaum/etal:2011,singh/etal:2015,tonegawa/etal:2018,johnston/etal:2019} and indirect \citep{heymans/etal:2013, samuroff/etal:2019}, recovering a common conclusion of significant alignment for red galaxies, and, as yet, no detection of alignment for blue galaxies.   Direct observations are limited by the depth of the spectroscopic, or high-accuracy photometric redshift, galaxy samples that can be studied.  Indirect observations, where an IA model is constrained simultaneously with a cosmological model, are limited by degeneracies with nuisance parameters.   As the IA and cosmological signal scale differently with redshift, a flexible IA model can absorb any systematic errors in the shape of the source redshift distributions, such that the resulting IA parameter constraints are not a true reflection of the underlying IA  model.    This point is nicely illustrated in figure 5 of \citet{efstathiou/lemos:2018} where indirect constraints on the amplitude of the NLA model for the full galaxy sample are shown to vary from $ -6 < A_{\rm IA} < 6$ across a wide range of published cosmic shear surveys.  \citet{wright/etal:2020b} present another example, analysing mock galaxy catalogues to improve the accuracy of the priors on the redshift uncertainty for the previous KiDS data release.  In this case the fiducial IA constraint $A_{\rm IA} = 0.95 \pm 0.67$ reduces to $A_{\rm IA} = 0.28 \pm 0.59$ with the inclusion of a more accurate redshift uncertainty model.   As the intrinsic alignment model depends on the cosmology, any tendency for the model to incorrectly absorb redshift errors would inadvertently lead to unexpected biases in the cosmological parameter constraints.   The more freedom afforded to the IA model, the more opportunity there is for such biases to occur.    Given this concern, we choose to adopt the minimal IA model freedom afforded by current direct observational IA constraints.  In this way any unaccounted errors in our redshift distributions can be detected through a poor goodness-of-fit of the combined cosmological and IA model, as seen, for our second tomographic redshift bin, in the KiDS-1000 internal consistency analysis of \citet[][appendix B.2]{asgari/etal:2020}.   
+
+Our choice of the one-parameter NLA model is motivated by the IA halo model analysis of \citet{fortuna/etal:2020}.   In this analysis central red galaxies are modelled using the  \citet{hirata/seljak:2004} model, with an amplitude $A_{\rm red}$ and a luminosity dependent scaling $\propto L^\beta$.   Combining the observed constraints from \citet{joachimi/etal:2011, singh/etal:2015} they model a simple power-law scaling model with $A_{\rm red} = 5.3 \pm 0.6$ and $\beta=1.2 \pm 0.4$.   The additional constraints from \citet{johnston/etal:2019} motivate a broken power-law model with $A_{\rm red} = 5.1 \pm 1.0$ and $\beta_{L \geq L_0}=1.2 \pm 0.4$, which they also consider.    Central blue galaxies follow the \citet{hirata/seljak:2004} model, with a \citet{johnston/etal:2019} constrained amplitude of $A_{\rm blue} = 0.2 \pm 0.4$ and no luminosity dependence, as there is no observational evidence to support this.    The small-scale satellite galaxy alignments are modelled following \citet{schneider/bridle:2010}.  The amplitude, radial and luminosity dependence of the alignment of red and blue satellite galaxies within their host halo is independently constrained following \citet{georgiou/etal:2019}.     The large-scale galaxy alignment signal is considered to be sourced solely by central galaxies, as there is currently no observational evidence to support large-scale (two-halo) alignments between the different satellite populations.
+
+The direct IA observational constraints adopted by \citet{fortuna/etal:2020} are determined from low redshift galaxy samples, where the properties of the full galaxy population differ significantly from the high redshift galaxy population analysed in KiDS-1000.  Given that the fundamental physical processes that underpin the intrinsic alignment mechanisms are unlikely to significantly evolve out to $z \sim 1$, however, these galaxy-type-specific constraints are relevant at the redshifts sampled by KiDS, provided the evolution in the relative fractions, luminosities and distribution of the red and blue, central and satellite, galaxy populations are accurately modelled.   
+
+\citet{fortuna/etal:2020} determine a sample of plausible IA models for a KiDS-like survey.  They combine the different galaxy-type IA contributions using a halo occupation distribution model taken from the MICE mock galaxy catalogues \citep{fosalba/etal:2015}, with a magnitude limit corresponding to KiDS-depth.   The range of full-population models encompasses the observational uncertainty on the IA model parameters for each galaxy type.    Analysing these IA halo-models with the NLA model, they find the highest NLA model amplitude of $A_{\rm IA}=0.54 \pm 0.13$ when adopting a broken power-law for the red-central luminosity scaling.    This is fully consistent with the \citet{asgari/etal:2020} KiDS-1000 COSEBIs cosmic shear constraints with $A_{\rm IA}=0.26 ^{+0.42}_{-0.34}$, the KiDS-1000 band power cosmic shear constraints with $A_{\rm IA}=0.97 ^{+0.29}_{-0.38}$ and the KiDS-1000 \tttp band power constraints with $A_{\rm IA}=1.07^{+0.27}_{-0.31}$, with the largest difference found for the \tttp results which are in 1.6$\sigma$ agreement.    
+
+Adopting the NLA model in a cosmological parameter inference of a mock KiDS-like data vector of the cosmic shear signal contaminated by the range of different IA halo models allowed by observations, \citet{fortuna/etal:2020} conclude that the redshift dependence of the true IA halo model is not large enough to bias the cosmological parameters in a KiDS-like cosmic shear analysis with the NLA model.   \citet{asgari/etal:2020} nevertheless explore one extension of the NLA model, with the inclusion of a redshift-dependent scaling term, which does not change the recovered KiDS-1000 cosmic shear MAP $S_8$ value.  It only serves to increase the marginal credible region of $S_8$ by $\sim 10\%$.   Given these analyses, we choose to adopt a minimal one-parameter NLA model in our \tttp analysis, but recognise that in future surveys such as LSST and {\it Euclid}, this adhoc model will no longer be sufficient given the expected statistical power of these next-generation surveys \citep{blazek/etal:2019, fortuna/etal:2020}.
+
+
 \section{Sensitivity tests}
 \label{app:sensitivity}