global distance duality relation and the temperature profile of galaxy clusters

GLOBAL DISTANCE DUALITY RELATION AND THE

TEMPERATURE PROFILE OF GALAXY CLUSTERS

Speaker: Shuo CaoDepartment of Astronomy, BNU

I. The validity of distance duality relation

II. Two groups of cluster gas mass fraction data including 52 X-ray luminous

galaxy clusters observed by Chandra

- 4. CONCLUSIONS

- 1. Introduction

- 2. GALAXY CLUSTER SAMPLES

- 3. ANALYSIS AND RESULTS

Contents

1. Introduction

• The reciprocity relation (e.g., Linder 1988; Schneider et al. 1992)

• DL/DA(1+z) ^2 = 1,• A fundamental result for astronomical

observations in cosmology.• gravitational lensing• cosmic microwave black body radiation • galaxy and galaxy cluster observations

• Diverse astrophysical mechanisms such as gravitational lensing and dust extinction are capable to cause obvious deviation from the distance Duality.

• Model parameterizations of η ( Uzan et al. 2004; Holanda, Lima & Ribeiro 2010).

• SZE and X-ray surface brightness DA 18 clusters (Reese et al. 2002) η = 0.91 (+0.04 −0.04) ; 38 clusters (Bonamente et al. 2006) η = 0.97 (+0.03 −0.03)

• The goal of this work is

• Instead of testing the reciprocity relation, we take it for granted in order to show how we may assess the cluster temperature profiles by using the constraint provided by the reciprocity relation

fgas = Mgas/Mtot,.

• The presence of temperature profiles plays an essential part in the determination of measured total mass, the fraction of mass in stars and, hence, the gas fraction.

• In this context, with two groups of cluster gas mass fraction data from the Chandra satellite (Ettori et al. 2009).

I the constant temperature ; II the Vikhlinin et al. model

• Model parameterizations of η I. η = ηc; II. η = 1+ ηa Z Inspired by similar expressions for wx

2. GALAXY CLUSTER SAMPLES

• Two samples of cluster gas mass fraction data from 52 X-ray luminous galaxy clusters obtained by Chandra in the redshift range 0.3 ∼ 1.273 and temperature range Tgas > 4 keV;

• I the constant temperature ; • II the Vikhlinin et al. model (Vikhlinin et al.

2006):

Extracting η from the gas mass fraction: Allen et al. (2008):

3. ANALYSIS AND RESULTS

The Vikhlinin et al. temperature profile sample

𝜂 ηc = 0.955 (+0.015, −0.015) (X 2dof= 47.25/52) ηa =-0.082(+0.029,−0.029) (X2dof= 49.50/52)

The constant temperature profile sample

ηc = 0.981 (+0.015, −0.015) (X 2dof= 63.44/52) ηa =-0.034(+0.034,−0.034) (X2dof= 64.28/52)

• Furthermore, considering that many parameters listed in Table 1 are fixed to their best-fit values, we perform a MCMC analysis and marginalize over these nuisance parameters by multiplying the probability distribution function and then integrating (e.g.Ganga et al. (1997)).

• The constraint results shown in Fig. 4 further confirm our conclusions.

• In spite of this, the Vikhlinin et al. model still seems to be a good fit to the cluster gas mass fraction data (judging from the reduced X2) even if it is less compatible with the distance duality relation.

4. Conclusions

• 1) By comparing the constant and Vikhlinin et al. temperature profile samples, we show that the constant temperature profile is more consistent with no violation of the distance duality relation in the context of two groups of cluster gas mass fraction data;

• 2) In the case of constant temperature sample (see Fig. 2 and 3) we find ηc = 0.981 (+0.015, −0.015) and ηa =-0.034(+0.034,−0.034) for constant and linear parametrizations, respectively.,

• 3) The Vikhlinin et al. temperature profile model (see Fig. 2 and 3) seems to be marginally incompatible with ηc = 0.981 (+0.015, −0.015) and ηa =-0.034(+0.034,−0.034) for constant and linear parameterizations, respectively.

• 4) Our analysis indicates that the constant temperature assumption tends to be more compatible with the Etherington theorem at 68.3% CL (between 68.3% and 95.4% CL for the first parametrization) compared with the Vikhlinin et al. temperature profile hypothesis, while the latter is incompatible even at 99% CL. The results with marginalized fgas parameters (Fig. 4) further confirm these conclusions.

• 5) However, we find that the Vikhlinin et al. model still seems to be a good fit to the cluster gas mass fraction data even if it is less compatible with the distance duality relation.

• 6) This reinforces the interest in the observational search for such kind of data from clusters at high redshifts. With better data, the method proposed here based on the validity of the distance duality relation should lead to improved limits on the temperature profiles of gas in galaxy clusters.