Statistics of thermal gas pressure as a probe of cosmology and galaxy formation

The statistics of thermal gas pressure are a new and promising probe of cosmology and astrophysics. The large-scale cross-correlation between galaxies and the thermal Sunyaev-Zeldovich effect gives the bias-weighted mean electron pressure, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">⟨</a:mo><a:msub><a:mi>b</a:mi><a:mi mathvariant="normal">h</a:mi></a:msub><a:msub><a:mi>P</a:mi><a:mi>e</a:mi></a:msub><a:mo stretchy="false">⟩</a:mo></a:math>. In this paper, we show that <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mo stretchy="false">⟨</f:mo><f:msub><f:mi>b</f:mi><f:mi mathvariant="normal">h</f:mi></f:msub><f:msub><f:mi>P</f:mi><f:mi>e</f:mi></f:msub><f:mo stretchy="false">⟩</f:mo></f:math> is sensitive to the amplitude of fluctuations in matter density, for example <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mo stretchy="false">⟨</k:mo><k:msub><k:mrow><k:mi>b</k:mi></k:mrow><k:mrow><k:mi mathvariant="normal">h</k:mi></k:mrow></k:msub><k:msub><k:mrow><k:mi>P</k:mi></k:mrow><k:mrow><k:mi>e</k:mi></k:mrow></k:msub><k:mo stretchy="false">⟩</k:mo><k:mo>∝</k:mo><k:msup><k:mrow><k:mo stretchy="false">(</k:mo><k:msub><k:mrow><k:mi>σ</k:mi></k:mrow><k:mrow><k:mn>8</k:mn></k:mrow></k:msub><k:msubsup><k:mrow><k:mi mathvariant="normal">Ω</k:mi></k:mrow><k:mrow><k:mi mathvariant="normal">m</k:mi></k:mrow><k:mrow><k:mn>0.81</k:mn></k:mrow></k:msubsup><k:msup><k:mrow><k:mi>h</k:mi></k:mrow><k:mrow><k:mn>0.67</k:mn></k:mrow></k:msup><k:mo stretchy="false">)</k:mo></k:mrow><k:mrow><k:mn>3.14</k:mn></k:mrow></k:msup></k:mrow></k:math> at redshift <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>z</t:mi><t:mo>=</t:mo><t:mn>0</t:mn></t:math>. We find that at <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>z</v:mi><v:mo><</v:mo><v:mn>0.5</v:mn></v:math> the observed <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mo stretchy="false">⟨</x:mo><x:msub><x:mi>b</x:mi><x:mi mathvariant="normal">h</x:mi></x:msub><x:msub><x:mi>P</x:mi><x:mi>e</x:mi></x:msub><x:mo stretchy="false">⟩</x:mo></x:math> is smaller than that predicted by the state-of-the-art hydrodynamical simulations of galaxy formation, MillenniumTNG, by a factor of 0.93. This can be explained by a lower value of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>σ</cb:mi><cb:mn>8</cb:mn></cb:msub></cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi mathvariant="normal">Ω</eb:mi><eb:mi mathvariant="normal">m</eb:mi></eb:msub></eb:math>, similar to the so-called “<ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>S</ib:mi><ib:mn>8</ib:mn></ib:msub></ib:math> tension” seen in the gravitational lensing effect, although the influence of astrophysics cannot be completely excluded. The difference between and MillenniumTNG at <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>z</kb:mi><kb:mo><</kb:mo><kb:mn>2</kb:mn></kb:math> is small, indicating that the difference in the galaxy formation models used by these simulations has little impact on <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mo stretchy="false">⟨</mb:mo><mb:msub><mb:mi>b</mb:mi><mb:mi mathvariant="normal">h</mb:mi></mb:msub><mb:msub><mb:mi>P</mb:mi><mb:mi>e</mb:mi></mb:msub><mb:mo stretchy="false">⟩</mb:mo></mb:math> at this redshift range. At higher <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>z</rb:mi></rb:math>, we find that both simulations are in a modest tension with the existing upper bounds on <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mo stretchy="false">⟨</tb:mo><tb:msub><tb:mi>b</tb:mi><tb:mi mathvariant="normal">h</tb:mi></tb:msub><tb:msub><tb:mi>P</tb:mi><tb:mi>e</tb:mi></tb:msub><tb:mo stretchy="false">⟩</tb:mo></tb:math>. We also find a significant difference between these simulations there, which we attribute to a larger sensitivity to the galaxy formation models in the high redshift regime. Therefore, more precise measurements of <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mo stretchy="false">⟨</yb:mo><yb:msub><yb:mi>b</yb:mi><yb:mi mathvariant="normal">h</yb:mi></yb:msub><yb:msub><yb:mi>P</yb:mi><yb:mi>e</yb:mi></yb:msub><yb:mo stretchy="false">⟩</yb:mo></yb:math> at all redshifts will provide a new test of our understanding of cosmology and galaxy formation.