Luminosity-temperature relation as a probe for modified gravity

We investigate the luminosity-temperature ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>L</a:mi> <a:mtext>−</a:mtext> <a:mi>T</a:mi> </a:mrow> </a:math> ) relation of galaxy clusters as a probe for testing modified gravity (MG) theories, focusing on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>f</c:mi> <c:mo stretchy="false">(</c:mo> <c:mi>R</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> gravity and symmetron models. Using an improved semianalytic framework that incorporates angular momentum acquisition, dynamical friction, and shock heating within the modified punctuated equilibrium model, we compare predictions against hydrodynamical simulations and observational data. While massive clusters remain largely screened and follow standard <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi mathvariant="normal">Λ</g:mi> </g:math> cold dark matter ( <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi mathvariant="normal">Λ</j:mi> <j:mi>CDM</j:mi> </j:math> ) predictions, low-mass systems ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>k</m:mi> <m:mi>T</m:mi> <m:mo>≲</m:mo> <m:mn>1</m:mn> <m:mi>–</m:mi> <m:mn>2</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>keV</m:mi> </m:math> ) exhibit systematic deviations characterized by steeper <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mi>L</o:mi> <o:mtext>−</o:mtext> <o:mi>T</o:mi> </o:mrow> </o:math> slopes in MG scenarios. Crucially, we demonstrate that these signatures cannot be mimicked by conventional astrophysical processes such as feedback or angular momentum effects, which primarily affect normalization rather than curvature. Our results establish the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>L</q:mi> <q:mo>−</q:mo> <q:mi>T</q:mi> </q:math> relation as a robust diagnostic tool for distinguishing general relativity from screened MG theories, with the strongest discriminatory power emerging at group scales accessible to current and future x-ray surveys. Moreover, a normalized reduced <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msup> <s:mi>χ</s:mi> <s:mn>2</s:mn> </s:msup> </s:math> analysis of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mrow> <u:mi>L</u:mi> <u:mtext>−</u:mtext> <u:mi>T</u:mi> </u:mrow> </u:math> relation shows that MG models provide significantly better agreement with observational data than <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi mathvariant="normal">Λ</w:mi> <w:mi>CDM</w:mi> </w:math> , with several realizations achieving excellent fits while the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi mathvariant="normal">Λ</z:mi> <z:mi>CDM</z:mi> </z:math> model consistently performs worst.