Cosmology and source redshift constraints from galaxy clustering and tomographic weak lensing with HSC Y3 and SDSS using the point-mass correction model

The combination of galaxy clustering and weak lensing is a powerful probe of the cosmology model. We present a joint analysis of galaxy clustering and weak lensing cosmology using Sloan Digital Sky Survey (SDSS) data as the tracer of dark matter (lens sample) and the Hyper Suprime-Cam year-3 (HSC Y3) dataset as source galaxies. The analysis divides HSC Y3 galaxies into four tomographic bins for both galaxy-galaxy lensing and cosmic shear measurements and employs a point-mass correction model to utilize galaxy-galaxy lensing signals down to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>2</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:msup> <a:mrow> <a:mi>h</a:mi> </a:mrow> <a:mrow> <a:mo>−</a:mo> <a:mn>1</a:mn> </a:mrow> </a:msup> <a:mtext> </a:mtext> <a:mi>Mpc</a:mi> </a:mrow> </a:math> , extending up to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>70</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:msup> <c:mrow> <c:mi>h</c:mi> </c:mrow> <c:mrow> <c:mo>−</c:mo> <c:mn>1</c:mn> </c:mrow> </c:msup> <c:mtext> </c:mtext> <c:mi>Mpc</c:mi> </c:mrow> </c:math> . These strategies enhance the signal-to-noise ratio of the galaxy-galaxy lensing data vector. Using a flat <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi mathvariant="normal">Λ</e:mi> <e:mi>CDM</e:mi> </e:math> model, we find <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>S</h:mi> <h:mn>8</h:mn> </h:msub> <h:mo>=</h:mo> <h:mn>0.78</h:mn> <h:msubsup> <h:mn>0</h:mn> <h:mrow> <h:mo>−</h:mo> <h:mn>0.030</h:mn> </h:mrow> <h:mrow> <h:mo>+</h:mo> <h:mn>0.029</h:mn> </h:mrow> </h:msubsup> </h:math> , and using a <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>w</j:mi> <j:mi>CDM</j:mi> </j:math> model, we obtain <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>S</l:mi> <l:mn>8</l:mn> </l:msub> <l:mo>=</l:mo> <l:mn>0.75</l:mn> <l:msubsup> <l:mn>6</l:mn> <l:mrow> <l:mo>−</l:mo> <l:mn>0.036</l:mn> </l:mrow> <l:mrow> <l:mo>+</l:mo> <l:mn>0.038</l:mn> </l:mrow> </l:msubsup> </l:math> with <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>w</n:mi> <n:mo>=</n:mo> <n:mo>−</n:mo> <n:mn>1.17</n:mn> <n:msubsup> <n:mn>6</n:mn> <n:mrow> <n:mo>−</n:mo> <n:mn>0.346</n:mn> </n:mrow> <n:mrow> <n:mo>+</n:mo> <n:mn>0.310</n:mn> </n:mrow> </n:msubsup> </n:math> . We apply uninformative priors on the redshift mean-shift parameters for the third and fourth tomographic bins. Leveraging the self-calibration power of tomographic weak lensing, we measure <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi mathvariant="normal">Δ</p:mi> <p:msub> <p:mi>z</p:mi> <p:mn>3</p:mn> </p:msub> <p:mo>=</p:mo> <p:mo>−</p:mo> <p:mn>0.11</p:mn> <p:msubsup> <p:mn>2</p:mn> <p:mrow> <p:mo>−</p:mo> <p:mn>0.049</p:mn> </p:mrow> <p:mrow> <p:mo>+</p:mo> <p:mn>0.046</p:mn> </p:mrow> </p:msubsup> </p:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi mathvariant="normal">Δ</s:mi> <s:msub> <s:mi>z</s:mi> <s:mn>4</s:mn> </s:msub> <s:mo>=</s:mo> <s:mo>−</s:mo> <s:mn>0.18</s:mn> <s:msubsup> <s:mn>5</s:mn> <s:mrow> <s:mo>−</s:mo> <s:mn>0.081</s:mn> </s:mrow> <s:mrow> <s:mo>+</s:mo> <s:mn>0.071</s:mn> </s:mrow> </s:msubsup> </s:math> , in agreement with previous HSC Y3 results. This demonstrates that weak lensing self-calibration can achieve redshift constraints comparable to other methods such as photometric and clustering redshift calibration.