global distance duality relation and the temperature profile of galaxy clusters

21
GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS Speaker: Shuo Cao Department of Astronomy, BNU

Upload: dusan

Post on 05-Feb-2016

35 views

Category:

Documents


0 download

DESCRIPTION

GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS. Speaker: Shuo Cao Department 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. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: 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

Page 2: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS
Page 3: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

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

Page 4: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

- 4. CONCLUSIONS

- 1. Introduction

- 2. GALAXY CLUSTER SAMPLES

- 3. ANALYSIS AND RESULTS

Contents

Page 5: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

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

Page 6: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

• 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)

Page 7: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

• 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.

Page 8: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

• 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

Page 9: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

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):

Page 10: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS
Page 11: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

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

Page 12: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS
Page 13: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

3. ANALYSIS AND RESULTS

Page 14: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS
Page 15: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS
Page 16: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

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)

Page 17: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

• 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.

Page 18: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS
Page 19: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

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.,

Page 20: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

• 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.

Page 21: GLOBAL DISTANCE DUALITY RELATION AND THE TEMPERATURE PROFILE OF GALAXY CLUSTERS

• 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.