Probing dark energy with Constellation­X David A. Rapetti, Steven W. Allen, Con-X Facility Science Team

KIPAC (Kavli Institute for Particle Astrophysics and Cosmology) at SLAC/Stanford

Concluding remarksOur fgas projected constraints assume a modest 10-12Ms investment of Con-X observing time (appro-ximately 10 per cent of the available observing time over the first 5 years of the mission). Using an existing Xray-SZ cluster sample and having identified the 200 -500 most dynamically relaxed systems from short Con-X snapshot observations (budget 2Ms), we will then re-observe those clusters for a further 10Ms total. This implies a typical exposure time of 20ks for a 500 cluster sample leading to individual statistical error bars in fgas of 5% (we also include a conservative 4% systematic scatter from cluster to cluster).

fgas in clusters

The matter content of rich clusters of galaxies is expected to provide an almost fair sample of the matter content of the Universe, Ωm (White & Frenk 1991, White et al. 1993, Eke et al. 1998). The ratio of baryonic to total mass in these clusters should closely match the ratio of the cosmological parameters Ωb/Ωm (where Ωb is the baryonic matter density). Measurements of the X-ray emitting gas mass in clusters as a function of redshift can also be used to measure the cosmic acceleration directly.

Here b is the 'bias' factor by which the baryon frac-tion is depleted with respect to the universal mean (a small amount of gas is expelled by shocks), d(z)'s are the angular diameter distances to the clusters. Current constraints from 41 hot (kT > 5 keV), X-ray luminous (LX > 1045h-2

70 erg s-1 ), dynamically relaxed clusters spanning the redshift range 0.06 < z < 1.07 are shown in Fig. 3 (red contours). Fig. 1 shows the complementary nature of the fgas, supernovae and CMB experiments and its crucial degeneracy breaking power (see Rapetti et al 2005).

Abstract

Con-X will carry out two powerful and inde-pendent sets of tests of dark energy based on X-ray observations of galaxy clusters: The first group of tests will measure the absolute distances to clusters, primarily using measurements of the X-ray gas mass fractionin the largest, dynamically relaxed clusters, but with additional constraining power provided by follow-up observations of the Sunyaev-Zel'do-vich (SZ) effect. As with supernovae studies, such data determine the transformation between redshift and true distance, d(z), allowing cosmic acceleration to be measured directly.

• The second, independent group of tests will use the spectroscopic capabilities of Con-X to determine scaling relations between X-ray observables and mass. Together with theoretical models for the mass function and X-ray and SZ cluster surveys, these data will help to constrain the growth of structure, which is also a strong function of cosmological parameters.

Con-X data will constrain dark energy with comparable accuracy and in a beautifully com-plementary manner to the best other techniques available circa 2018. For example, with a mo-dest ~10-15% (10-15Ms) investment of the available observing time over the first 5 years of the Con-X mission, we will be able to measure the X-ray gas mass fraction (or predict the Compton y-parameter) to 5% or 3.5% accuracy for 500 or 250 clusters, respectively, with a me-dian redshift z~1. When combined with CMB data, the predicted dark energy constraints from Con-X X-ray gas mass fraction data are comparable to those projected by future supernovae and baryon oscillations experi-ments. Only by combining such independent and complementary methods can a precise understanding of the nature of dark energy be achieved.

The observed fgas values for a chosen reference cosmology are fitted with a model that accounts for the expected apparent variation in fgas(z) as the true, underlying cosmology is varied:

Dark energy constraints from Con-X fgas(z)+CMB data

Measuring fgas(z), the ratio of X-ray gas mass to total mass, in current Chandra X-ray Observatory data of the largest, dynamically relaxed clusters in the Universe, Allen et al. (2002; 2004; 2006 in preparation) provide us with one of the most accurate measurements of Ωm and a >99.99% significant detection of the effects of dark energy (cosmic acceleration) on distances to the clusters at different redshifts.

ReferencesAllen S. W., Schimdt R. W., Fabian A. C., 2002, MNRAS, 334, L11Allen S. W., Schmidt R. W., Ebeling H., Fabian A. C., van Speybroeck L., 2004, MNRAS, 353, 457Allen et al., 2006, in preparationLinder E. (for the SNAP collaboration) 2004, astro-ph/0406186Linder E. 2005, astro-ph/0507308Molnar S. M., Birkinshaw M., Mushotzky R.F., 2002, ApJ, 570, 1Molnar S. M., Haiman Z., Birkinshaw M., Mushotzky R. F., 2004, ApJ, 601, 22Eke V. R., Navarro J. F., Frenk C. S., 1998. ApJ, 503, 569Rapetti D., Allen S. W., Weller J., 2005, MNRAS, 360, 555Rapetti et al., 2006, in preparationRiess A. G. et al., 2004, ApJ, 607, 665Schmidt R., Allen S. W., Fabian A., 2004, MNRAS, 352, 1413Upadhye A., Ishak M., Steinhardt P. J., 2005, Phys. Rev. D 72White S. D. M., Frenk C. S., 1991, ApJ, 379, 52White S., Efstathiou G., Frenk C., 1993, MNRAS, 262, 1023Vikhlinin A., Con-X Science Working Group Team, displayed at this same poster session 16.

Dark energy constraints from Con­X

f gasreferencez=

bb

10.19hm[ d referencez

d model z ]1.5

Fig1: The 68.3 and 95.4 per cent confidence limits in the (w0 , Ωm ) plane from the analysis of fgas (Allen et al 2004), SNIa (Riess et al 2004) and CMB data assuming a constant dark energy equation of state (w0) model. [Figure from Rapetti et al. (2005).]

Predicted Con­X fgas data set

Fig 2: (left panel) The predicted number density of clusters with bolometric X-ray luminosities LX>1045h-2

70 erg/s for a cluster survey flux limit of 5 × 10-14 erg/cm2 /s in the 0.1 - 2.4keV band (red curve). The blue curve shows the same results but a flux limit of 10-12 erg/cm2 /s, appro-priate for the ROSAT All-Sky Survey (right panel) The predicted fgas (z ) values for the proposed Con-X survey of 500 clusters. The median z is ~1.

• In terms of direct distance measurements the X-ray method provides similar accuracy to SNIa studies and has several advantages:

i)The physics of galaxy clusters is relatively simple and can be accurately modeled by simulations.

ii)Clusters can be revisited with X-ray observa-tories to improve signal-to-noise.

iii)The fgas technique includes an additional cons-traint on Ωm from the normalization of the curve.

iv)The combination of fgas and CMB data breaks a number of important parameter degeneracies (Rapetti et al 2005, 2006 in preparation) in an exceptionally effective manner (e.g. ns, Ωbh

2 , τ).

v)The systematic scatter in the fgas(z) is small (undetected and <10% in current Chandra data)

vi)Direct checks on the key assumptions in the fgas

method are possible using the spectral/spatial capabi-lities of Con-X and by combination with other data and techniques (e.g. X-ray+SZ; see Fig. 5 and Molnar et al. 2002, 2004; Schmidt, Allen & Fabian 2004).

• Additional powerful and independent cons-traints on dark energy will be provided by Con-X's contribution to growth of structure studies (see Vikhlinin poster).

Fig 4: Results from the analysis of simulated Con-X fgas +CMB data. The CMB data are WMAP TT data appropriate for 8 years of that mission (Upadhye et al 2005). The 68.3 and 95.4 per cent uncertainties in the (w0, w') plane for the w(a) = w0 + wa (1 - a) = w0 + 2w' (1 - a) model are shown. No priors on Ωb h

2 , h or ΩK assumed in the analysis.

Fig 3: The joint 1 and 2 contours on Ωm and ΩΛ from the current Chandra fgas (z) data (red; Allen et. al 2006, in preparation). Also shown are the constraints from SNIa (green; Riess et al. 2004) and CMB studies (blue; WMAP+CBI+ACBAR). The same contours from the analysis of the simulated Con-X fgas data set of Fig. 2 are shown in orange.

Fig 5: The projected 1, 2 and 3 constraints for the Con-X X-ray+SZ experiment for the 500 cluster sample of Fig. 2 with 5% statistical errors in the predicted Compton y-values. The blue curve shows the result from the fgas experiment, as in Fig 3 (orange). The dotted red curve shows the results assuming a combined overall 2% systematic uncertainty in the normalization of the X-ray and SZ y-values and the solid red curve when the systematic uncertainty in this and h (combined) is reduced to 0.1%.

Clusters Chandra

SNIa

CMBClusters Con-X

We analyse this Con-X fgas data set either alone, imposing 2% priors on Ωbh

2 and h (Fig. 3, orange contours) or combined with a simulated CMB data set as shown in Fig. 4. We use 2% priors on b in both cases. For the evolving dark energy case of Fig. 4 we obtain comparable results to those projected by supernovae (Linder 2004) and baryon oscillations experiments (Linder 2005).

Current Results from fgas