Pointing to the minimum scatter: the generalized scaling relations for galaxy clusters

Authors

  • S. Ettori,

    1. INAF, Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127 Bologna, Italy
    2. INFN, Sezione di Bologna, viale Berti Pichat 6/2, I-40127 Bologna, Italy
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  • E. Rasia,

    1. Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109, USA
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  • D. Fabjan,

    1. Center of Excellence SPACE-SI, Aškerčeva 12, 1000 Ljubljana, Slovenia
    2. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
    3. INFN, Istituto Nazionale di Fisica Nucleare, I-34127 Trieste, Italy
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  • S. Borgani,

    1. INFN, Istituto Nazionale di Fisica Nucleare, I-34127 Trieste, Italy
    2. Dipartimento di Fisica dell’Università di Trieste, Sezione di Astronomia, via Tiepolo 11, I-34131 Trieste, Italy
    3. INAF, Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131 Trieste, Italy
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  • K. Dolag

    1. University Observatory Munich, Scheinerstr. 1, D-81679 Munich, Germany
    2. Max-Planck Institute for Astrophysics, Karl-Schwarzschild Str. 1, D-85748 Garching, Germany
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E-mail: stefano.ettori@oabo.inaf.it

ABSTRACT

We introduce a generalized scaling law, Mtot= 10K Aa Bb, to look for the minimum scatter in reconstructing the total mass of hydrodynamically simulated X-ray galaxy clusters, given gas mass Mgas, luminosity L and temperature T. We find a locus in the plane of the logarithmic slopes a and b of the scaling relations where the scatter in mass is minimized. This locus corresponds to bM=−3/2aM+ 3/2 and bL=−2aL+ 3/2 for A=Mgas and L, respectively, and B=T. Along these axes, all the known scaling relations can be identified (at different levels of scatter), plus a new one defined as Mtot∝ (LT)1/2. Simple formula to evaluate the expected evolution with redshift in the self-similar scenario is provided. In this scenario, no evolution of the scaling relations is predicted for the cases (bM= 0, aM= 1) and (bL= 7/2, aL=−1), respectively. Once the single quantities are normalized to the average values of the sample under considerations, the normalizations K corresponding to the region with minimum scatter are very close to zero. The combination of these relations allows one to reduce the number of free parameters of the fitting function that relates X-ray observables to the total mass and includes the self-similar redshift evolution.

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