Search for Intrasupercluster Gas in the Shapley Supercluster

THE ASTROPHYSICAL JOURNAL, 497 : 1È9, 1998 April 10 ( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

SEARCH FOR INTRASUPERCLUSTER GAS IN THE SHAPLEY SUPERCLUSTER S. M. MOLNAR AND M. BIRKINSHAW1 Department of Physics, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, England, UK Received 1996 September 4 ; accepted 1997 November 14

ABSTRACT We set limits to the amount of intrasupercluster gas in the Shapley supercluster, using COBE DMR data to search for the Sunyaev-Zeldovich e†ect and HEAO 1 A-2 data to search for di†use X-ray emission. Chance alignments of the Shapley supercluster with primordial Ñuctuations were taken into account in the analysis of the COBE DMR data using the two-point correlation function. We modeled the X-ray emission allowing for known point sources and a gradient in galactic emission. We found no evidence for intrasupercluster gas following a truncated isothermal beta model distribution. The Shapley supercluster does not hold much more hot (º10 keV) large-scale di†use intrasupercluster gas than the average baryon density derived from standard nucleosynthesis theories. Subject headings : cosmic microwave background È galaxies : clusters : general È intergalactic medium È X-rays : galaxies 1.

INTRODUCTION

Missing mass is being sought in both nonbaryonic (““ exotic ÏÏ) and baryonic forms. Superclusters of galaxies, the largest known luminous structures in the universe, should hold correspondingly large masses of dark matter. Their study may lead us to the structure (Bahcall, Lubin, & Dorman 1995) and perhaps the constituents of dark matter (David et al. 1995 ; Turner 1991), and their mass and kinematics probe ) (Gramann et al. 1995 ; Bahcall, Gramann, & Cen 1994 ; Cen 1994 ; Zabludo† & 0 predict that superclusters contain residual intrasupercluster (ISC) matter in Geller 1994). Most models of structure formation the form of di†use, hot gas at the present epoch. This ISC gas could be either primordial (Cen & Ostriker 1993), processed by an early generation of stars and subsequently ejected in winds from early massive star formation or active galactic nuclei (Elbaz, Arnaud, & Vangioni-Flam 1995 ; Matteucci & Gibson 1995 ; Metzler & Evrard 1994), or stripped from merging clusters and protoclusters. Governato et al. (1996), using N-body simulations, found this tidal stripping very e†ective. Eskridge, Fabbiano, & Kim (1995) used Einstein data to show that the deep potential wells in clusters of galaxies can retain the enriched ejecta of early starbursts. The expected temperature of the ISC gas is about 107È108 K (Metzler & Evrard 1994 ; Anninos & Norman 1996) and will remain hot, since the cooling time for gas at the expected low density (\10~3 cm~3) is longer than the Hubble time (Rephaeli & Persic 1992). Several X-ray searches for di†use emission from ISC gas have been carried out. It was claimed that the UHURU data show evidence for ISC gas emission in some superclusters (Murray et al. 1978), but this was not supported by HEAO 1 A-2 data (Pravdo et al. 1979). Recently Persic, Rephaeli, & Boldt (1988) searched for X-ray emission in the HEAO 1 A-2 database using superclusters from the Bahcall & Soneira (1984) list. They excluded areas within 6¡ of known bright X-ray sources. Ten Ðelds were included in the Ðnal analysis. The average mean Ñux in the 2È10 keV band of these superclusters, corrected for di†use background, and assuming a thermal bremsstrahlung spectrum characterized by kT B 10 keV, was f \ 3.8 ^ 2.1 ] 10~12 ergs cm~2 s~1. Persic et al. concluded that di†use emission is not present in the A-2 data at a statistically signiÐcant level and set a 3 p upper limit on the X-ray Ñux from the ISC gas of f \ 10~11 ergs cm~2 s~1. More recently the search on the A-2 database was extended to the Batuski & Burns (1985) sample of superclusters using similar methods (Persic et al. 1990). No signiÐcant emission at the 3 p level was found, and an upper limit f ¹ 5 ] 10~12 ergs cm~2 s~1 was set in 3¡ ] 1¡.5 Ðelds of view. They repeated their search using collimators with 3¡ ] 3¡ Ðelds of view to check for lower surface brightness extended emission, with the same result. These searches could not rule out the existence of extended, lower surface brightness features. Some recent observational results seem to indicate that superclusters do contain detectable baryonic matter. Boughn (1996) found evidence in the HEAO data for gas in the local supercluster with X-ray emissivity 5 ] 1039 ergs~1 Mpc~3. Using pointed ROSAT PSPC observations, Bardelli et al. (1996) found evidence for some enhanced di†use X-ray emission in the Shapley supercluster (SSC) between the two clusters A3558 and SC1327[312, possibly as a result of their gravitational interaction. Although this work has used X-ray data, the ISC gas may also be sought using its signature on the cosmic background radiation (CBR). The hot electron gas interacts with the CBR via inverse Compton scattering and shifts the incoming photons to higher energies. Since photon number is conserved, this means that the CBR intensity decreases in the Rayleigh-Jeans region and increases in the Wien part of the spectrum. This is the Sunyaev-Zeldovich (SZ) e†ect (Sunyaev & Zeldovich 1980 ; for a recent review see Rephaeli 1995). This e†ect has been used successfully to determine physical properties of the intracluster gas in clusters of galaxies (for a review see Birkinshaw 1998). Using the Persic et al. (1988, 1990) limits for di†use X-ray emission, Rephaeli (1993) sets limits for the Comptonization parameter y \ / (kT /m c2)n p dl (where T , m , n , and p are the electron temperature, mass, density, and Thomson e erespectively, e T e e of distance T scattering cross section, dl is theeincrement along the line of sight, k is the Boltzmann constant, and c 1 Also : Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138.

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is the speed of light) in superclusters. This limit on y is y ¹ 4 ] 10~7

A

BA

R 20 Mpc

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T , 4 ] 107 K

(1)

where R and T are the characteristic radius and temperature of the ISC gas, and is a few hundred times less than the values of y that are typical of a gas-rich cluster. Rephaeli (1993) used this to estimate that the supercluster-generated anisotropy in the spatial distribution of the CBR, *T /T ¹ 10~7, signiÐcantly below the anisotropy detected by the COBE DMR experiment (Bennett et al. 1996a). Banday et al. (1996)Ïs cross-correlation analysis of the four year COBE DMR sky maps with rich clusters of galaxies, extragalactic IRAS sources, HEAO 1 A-2 X-ray emission, and 5 GHz radio sources found no noncosmological signals at an rms level greater than 8 kK (95% CL at 7¡ resolution). They also found no evidence for the SZ e†ect in several nearby clusters. This tends to support the idea that superclusters are not detectable SZ e†ect sources. Although cross-correlation population studies have not found evidence for ISC matter (see, e.g., Persic et al. 1990 ; Kogut et al. 1996b), it is still important to examine individual rich superclusters. The most prominent supercluster near us (at z ¹ 0.1) is the Shapley Supercluster (SSC), which consists of many Abell and other clusters centered on A3558 (Shapley 8), at mean recession velocity 14,000 km s~1 (at a distance d \ 280 h~1 Mpc, where H \ 50 h km s~1 Mpc~1), and with an extended SSC 50 0 50 core radius of about 37 h~1 Mpc. The estimated baryon overdensity, o/o6 \ 2.4, is the largest known on such a scale : the SSC 50 may be the largest gravitationally bound structure in the observable universe (Raychaudhury et al. 1991 ; Fabian 1991). These features make the SSC a good candidate for searches for ISC gas. If the SSC contains hot gas with the emissivity suggested by Boughn for the local supercluster, then the surface brightness is expected to be 5 ] 10~13 ergs~1 cm~2 deg~2 in the 2È10 keV energy band. Day et al. (1991) carried out a search for large-scale ISC gas in the SSC with Ginga by using three scans, each 12¡È14¡ long. After removing point sources, a Ðt was made to a smooth background with a slope to account for Galactic di†use emission. Good Ðts were obtained for two scans, but the shortest Ðt badly. It was concluded that there was no evidence for excess di†use emission associated with the SSC and a strong limit on the 2È10 keV Ñux, f ¹ 2 ] 10~13 ergs cm~2 s~1 deg~2 was obtained (at 1 p). This is less than the emission expected from BoughnÏs (1996) result, and about 1 order of magnitude more sensitive than Persic et al.Ïs (1990) result. The Ginga measurements are limited by Ñuctuations in the X-ray background, unresolved point sources, and the model used to remove the underlying background. Although the surface brightness of the SZ e†ect for the SSC must be low, the SZ e†ect will be more extended than the X-ray emission by a factor of roughly 2. That means that with a suitable CBR database it should be possible to integrate over the angular structure of the supercluster to obtain a better signal-to-noise ratio than would be possible for a point source, and hence perhaps to Ðnd the di†use ISC gas through the SZ e†ect. Based on these ideas, we selected the SSC as a Ðrst candidate for a search for the SZ e†ect on a large angular scale database. Because of the way ground-based observations are carried out (neither beam switching nor position switching gives enough angular coverage ; Birkinshaw 1990), we have to use satellite data. The best large angular scale satellite data were collected by the COBE satellite, so we used the COBE DMR four year data in the SZ e†ect search. Although the ROSAT all-sky survey has now been released and covers the entire SSC, the identiÐcation and subtraction of any galactic foregrounds are more complicated for its soft X-ray passband than the hard X-ray passband of the HEAO 1 A-2 experiment (Snowden et al. 1995). We therefore used the HEAO 1 A-2 data, repeating the analysis of Persic et al. (1988) to search for di†use ISC X-ray emission from the SSC. In this paper we describe Ðts of template maps to the HEAO 1 A-2 and COBE DMR data. The template maps are generated based on the thermal bremsstrahlung X-ray emission and SZ decrement of truncated isothermal beta models for the assumed ISC gas, although the assumptions on which these models are based, such as constant temperature and hydrostatic equilibrium, are questionable. 2.

SEARCH FOR SZ EFFECT IN SSC USING THE COBE DMR DATA

2.1. T he COBE Data We worked with the four year COBE DMR maps (Bennett et al. 1996a ; Kogut et al. 1996a). The DMR experiment measured power di†erences at frequencies 31.5, 53, and 90 GHz (wavelengths 9.5, 5.7, and 3.3 mm) between regions in the sky separated by 60¡. The six microwave radiometers provided measurements of the three frequencies on two nearly independent channels (A and B). The data, the measured antenna temperatures in mK, are supplied as quadrilateralized sky cubes, with 2¡.59 pixelization in ecliptical coordinates, which gives 6144 pixels in the sky. Residual systematic e†ects in the DMR maps are small compared to either the noise or the celestial signal. The 95% upper limit for the pixel-to-pixel rms from all identiÐed systematic e†ects is less than 5.5 kK in the worst channel (Kogut et al. 1996a), and the mean instrumental noise level is 0.249, 0.318, 0.087, 0.102, 0.147, and 0.115 mK in the 31A, 31B, 53A, 53B 90A, and 90B channels, respectively (Bennett et al. 1996b). DMR maps above the Galactic plane are dominated by cosmic microwave background and the synchrotron, dust, and free-free emissions of the Galaxy. The synchrotron emission arises from relativistic electrons accelerated in the Galactic magnetic Ðeld and dominates at low radio frequencies. Unfortunately its spectral index steepens with frequency and has poorly determined spatial variation, so it is not possible to extrapolate low-frequency survey data to correct the COBE maps accurately, but this component of the contamination should be small. Dust emission, which dominates far infrared surveys, has di†erent spectra depending on the shape, composition, and size distribution of the dust grains, which are poorly known. Here again a precise extrapolation to the DMR image is not possible, but the dust contribution should be small. The most important Galactic contaminant in our case is free-free emission, which occurs when free electrons are accelerated by

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interactions with ions. It has a well-determined spectrum, but unfortunately we do not have a good template map for it. We checked the e†ects of the Galactic emissions on the DMR maps at the SSC region using maps of synchrotron, dust and free-free emissions (Bennett et al. 1996b) The synchrotron and dust emissions contribute about 20 and 3 kK at 53 GHz, slowly varying in the SSC region. Comparing the 31, 53, and 90 GHz DMR maps of the SSC region, we see a spectrum of di†use radiation characteristic of Galactic contamination. It seems to be important to deal with corrections for Galactic emission at the SSC. Bennett et al. (1992) used three methods to estimate and remove the Galactic contamination. The subtraction technique extrapolates synchrotron and dust emission maps made at frequencies where these dominate to DMR frequencies assuming constant spectral indices. It removes this emission from the DMR maps, which then are combined with coefficients which cancel out any remaining free-free emission. The Ðtting technique Ðts models of free-free and cosmic emissions to the DMR maps after models of synchrotron and dust emissions have been subtracted. The main problem with these methods is in the uncertainty of the extrapolation. The combination method uses only a linear combination of the DMR maps. The coefficients are determined to cancel out free-free emission. The Ðnal maps still need correction for synchrotron and dust emission, which cause a signiÐcant increase in the noise level. Kogut et al. (1996b) used cross-correlation and linear combination methods to separate high latitude ( o b o [ 20¡) Galactic and cosmic emissions. Their estimated upper limit on rms Ñuctuations from synchrotron emission at 31 GHz is *T \ 11 kK at 95% CL. Their estimates on the contributions from free-free and dust emissions at the DMR resolution aresynch *T \ 21.7 ^ 5.2 kK and *T \ 2.7 ^ 1.3 kK. We used maps generated by the free dust cross-correlation method of Kogut et al. (1996b) and a linear combination method. The cross-correlation method produces a map of *T , where corr 6 *T \ ; Ci *T @ , (2) corr corr i i/1 and the *T @ values are thermodynamic temperature di†erences after removal of models of free-free, synchrotron, and dust emission ati frequency/channel i. The six channelsÈ31A, 31B, 53A, 53B, 90A, or 90BÈhave combination coefficients Ci \ 0.049, 0.032, 0.378, 0.275, 0.102, or 0.164. corr The combination method produces a map of *T , comb 6 *T \ ; Ci *T , (3) comb comb i i/1 where the *T values are the DMR thermodynamic temperature di†erences, and Ci \ [0.185, [0.117, 0.367, 0.266, 0.256, i six channels. comb or 0.413 for the The values of the coefficients Ci and Ci were determined by minimizing noise, and in the case of the combination corr emission comb with assumed spectral index of [2.15 (in antenna temperature) as well technique by eliminating the free-free (Hinshaw et al. 1996a). Although the correlation technique is insensitive to emission which is uncorrelated with the Galactic template maps (Kogut et al. 1996b), and the combination method leaves less than 1% of the free-free emission but does not remove synchrotron or dust emission, the remaining Galactic contamination is negligible for our purposes. The cross-correlation map is less noisy than the combination map. The cross-correlation and linear combination methods retain about 62% and 90% of the SZ e†ect at 53 GHz. 2.2. Fitting Models to COBE Data The electron density in spherically symmetric isothermal beta models (Cavaliere & Fusco-Femiano 1976) with the inclusion of a truncation radius, R, may be expressed as n \ e

7A n

0 0,

1]

B

r2 ~3@2b , r2 c

r\R ,

(4)

rºR ,

where km p2 p z . (5) kT e n is the electron density at the center, r is the core radius, m is the proton mass, T is the electron temperature, k is the 0 c dispersion in the linep of sight, and b [ 1 if the e gas mass is not to be inÐnite or the average molecular weight, p is the velocity z model (eq. [4]) is not truncated. For nonrelativistic electrons with small Comptonization parameter, and at low frequencies, we can use the Kompaneets (1957) approximation with sufficient accuracy (see Rephaeli 1995 for the relativistic formulation). The thermodynamic temperature change due to the SZ e†ect is b\

*T \ *T gC(rü Æ rü ) , 0 0

(6)

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where *T (x) is the central e†ect for a truncated beta model 0 kT e *T \ 4 ] 10~5T f 0 CBR x 5 keV

A BA BA r c Mpc

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n 0 N h~1 , 10~3 cm~3 C 50

(7)

where T \ 2.728 ^ 0.004 K (95%) is the temperature of the CBR (Fixsen et al. 1996), and f is the frequency-dependent part CBR x of the e†ect f (x) \ x coth

AB

x [4 , 2

(8)

where the dimensionless frequency x(l) \ The normalization, coming from the spatial part, N , is C

P

hl . kT CBR

(9)

tR

(1 ] y2)~3@2b dy , (10) 0 where, assuming Euclidean geometry, t \ R/r \ sin h /sin h , where h and h are the projected angular sizes of the cuto† R is c and core radii (R \ d sin h and r \ Rd sinch ). The Rspatialcfunction, gC, SSC R c SSC c t 1 [ (rü Æ rü )2 1@2~3@2b 0 (1 ] y2)~3@2b dy , rü Æ rü º cos h , N~1 1] 0 R C (11) sin2 h gC(rü É rü ) \ 0 c 0 0, rü Æ rü \ cos h , 0 R where rü Æ rü [ 0 is the cosine of the projected angular separation between unit vectors rü and rü pointing to the direction of the 0 and the center of the supercluster, respectively, and the cuto† for the integral, t, is 0 observation N \ C

7C

D

t\

C

P

D

sin2 h [ 1 ] (rü Æ rü )2 1@2 R 0 . sin2 h ] 1 [ (rü Æ rü )2 c 0

(12)

Note that rü Æ rü º cos h for the cuto†, t, is real. 0 R The thermodynamic temperature change measured by the COBE DMR at pixel i may be expressed as / d) gC(rü Æ rü )PDMR(rü Æ rü ) “ 0 i ] b \ *T S ] b , (13) 0 i / d) PDMR(rü Æ rü ) “ i where *T is the frequency-averaged (over the DMR band passes), central, thermodynamic temperature, SZ e†ect in mK, rü and rü are0unit vectors pointing to the assumed center of the SSC, and the position of the measurement in the sky respectivelyk; j convolution variable ; PDMR is the beam pattern normalized to 1 at the peak ; S is the SZ model projected on the sky rü is the cube at pixel i, and b is a baseline o†set in mK due to other e†ects, such as residual largei angular scale primordial Ñuctuations, or emission from the Galaxy. We Ðtted the two key parameters of this model, *T and b, the central peak SZ e†ect and baseline, using the s2 statistics 0 deÐned deÐned by *T \ *T i 0

s2 \ (T [ *T S [ b)TM~1(T [ *T S [ b) , (14) C 0 0 where T and S are the COBE data and the SZ model projected on the sky cube (cf. eq. [13]). M includes the e†ect of primordial Ñuctuations that add noise to the measurement of the central SZ e†ect and the baseline and the measurement errors, p . We may use a Legendre series expansion of the two-point correlation function derived by Bond & Efstathiou (1987) i 1 (15) M \ ST T T \ ; (2l ] 1)W 2 C P (nü Æ nü ) ] d p p , ij i j ij i j l l l i j 4n lz2 where T and T are the COBE DMR temperatures at pixels i and j, and d is the Kronecker delta function. If we assume a i jHarrison-Zeldovich primordial Ñuctuation spectrum with nij\ 1, which is a reasonable assumption (Hinshaw scale-invariant et al. 1996b ; Gorski et al. 1996), then 24n Q2 rms~PS . C\ l 5 l(l ] 1)

(16)

The W values are the Legendre coefficients of the smeared COBE DMR beam, and P (x) is the Legendre polynomial of order l. l l not present in the DMR maps). The The series in equation (15) is over l (l º 2 since the monopole and dipole terms are argument of P is the cosine of the angle between unit vectors nü and nü for pixels i and j. We used quadrupole amplitude j power spectrum for the primordial Ñuctuations Q \ (18.0l ^ 1.4) kK, which was derived assuming a scale iinvariant rms~PS (Hinshaw et al. 1996b). Our results are not sensitive to the value of Q . rms~PS

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The parameters of the model were derived from s2 deÐned by equation (12), and the errors were estimated from the diagonal elements of the inverse covariance matrix assuming the noise is uncorrelated from pixel to pixel (Lineweaver et al. 1994). We discarded pixels closer to the galactic plane than 20¡. 3.

MODELING AND FITTING OF THE X-RAY EMISSION FROM THE SSC AREA

3.1. T he HEAO 1 A-2 X-Ray Data We used a HEAO 1 A-2 map provided by K. Jahoda (Jahoda & Mushotzky 1989) to set limits to the X-ray emission of the SSC. This map is an instrumental background subtracted combination of measured Ñuxes of the large and small Ðeld of view (3¡ ] 3¡ and 3¡ ] 1¡.5) maps from the MED and HED detectors (Shafer 1983). It is pixelized in Cartesian ecliptic coordinates, with a pixel size of 0¡.5 ] 0¡.25. The Ñuxes (in units of ““ total ÏÏ counts s~1) were converted into physical units using clusters of galaxies as standard sources (Jahoda & Mushotzky 1989). The conversion factor (2.2 ] 10~11 ergs cm~2 s~1 (counts s~1)~1 in the 2È10 keV band) is appropriate for sources with thermal bremsstrahlung spectra at temperatures between about 1 and 10 keV, with an error of about 15%. The subtracted instrumental background was about 2 counts s~1, the sky background is about 3 counts s~1. 3.2. Fitting Procedure We modeled the X-ray emission from the SSC region using point sources, a galactic model, and a truncated isothermal beta model for the di†use emission of ISC gas. Assuming thin thermal bremsstrahlung emission, the X-ray surface brightness in the 2È10 keV band becomes

P

`zR e(T , r) dz , (17) 4n ~zR where ^z are the line-of-sight coordinates of the cuto† radius, R. The integrated volume emissivity is R lb e(T , r) 4.9 ] 10~38n2(r)T ~1@2g (l, T )e~hl@(kT) dl , (18) \ e ff ergs s~1 cm~3 la where hl \ 2 keV, and hl \ 10 keV are the limits of integration, and we assume solar abundance to relate n to the baryon b averaged Gaunt factor, may be approximated in the hard X-ray band for a hot gas e with density. ga (l, T ), the velocity ff e 3 kT 1@2 (19) , g (l, T ) \ ff n hl b \ X

P

SA B

which is between 0.4 and 2.6 in the 2È10 keV band for temperatures between 1È15 keV (Novikov & Thorne 1973). Thus the integrated volume emissivity becomes

A B

kT 1@2 e(T , r) e *c(T ) , \ 7.6 ] 10~24n2(r) e e 5 keV ergs s~1 cm~3

(20)

where *c(T ) \ c(1 , 10 keV/kT ) [ c(1 , 2 keV/kT ) and c(a, x) is the incomplete gamma function. This approximation breaks e 2 temperatures e 2 e down for lower gas because line radiation becomes more important. At higher gas temperatures relativistic corrections should be taken into account. These corrections do not exceed 10% for T \ 10 keV. e Using a truncated beta model, from equations (17) and (20) we get b \ b gH(rü Æ rü ) , X 0 0 where b is the central surface brightness 0 T 1@2 r b e c 0 \ 5.2 ] 10~6*c(T ) e 5 keV Mpc ergs s~1 cm~2 sr~1

A B A BA

(21)

B

n 2 0 N h~1 , H 50 10~3 cm~3

where the normalization coming from the spatial part, N , is H tR (1 ] y2)~3b dy . N \ H 0 The spatial dependence, gH, is given by

P

gH(rü Æ rü ) \ 0

7C

1]

0,

D

(23)

P

1 [ (rü Æ rü )2 1@2~3b t 0 N~1 (1 ] y2)~3bdy , H sin2 h c 0

and it is deÐned after equation (12). This model leads to an X-ray luminosity

A

b L 0 X \ 7.52 ] 106 ergs s~1 cm~2 sr~1 1044 ergs s~1

BA B

r 2 c h~2 N~1 50 H Mpc

(22)

rü Æ rü º cos 0 rü Æ rü \ cos 0

P

h , R h , R

tR y2(1 ] y2)~3b dy . 0

(24)

(25)

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The Ñux measured by the HEAO 1 A-2 experiment at pixel i is the convolution of the HEAO PSF (PH) with the X-ray surface brightness distribution of the beta model FH \ i

P

d) b gH(rü Æ rü )PH(rü , rü ) \ F X , “ 0 0 i 0 i

(26)

where F is the central Ñux that the HEAO A-2 instrument would measure, 0 F \ 0

P

d) b gH(rü )PH(rü ) , “ 0

(27)

and / d) gH(rü Æ rü )PH(rü , rü ) “ 0 i (28) / d) gH(rü )PH(rü ) “ is the projection of the convolution on pixel i normalized to 1. The HEAO A-2 PSF is not radially symmetric. Although it is a simple triangular-shaped function (Shafer 1983), it is smeared by the movements of the satellite (scanning motion along ecliptic latitude, movements along ecliptic longitude, wobbling, etc.). Additional smearing occurs owing to pixelization. As a result the simplest and most e†ective way of determining the PSF for our map is modeling a region dominated by point sources, convolving the model with the PSF, and Ðtting for the parameters of the known functional form of the smeared PSF (equal weighting between detectors proved to be satisfactory). As a Ðrst approximation (which proved to be good) we did the Ðtting on point sources in the SSC Ðeld. We used this PSF in an iterative process to determine the parameters of our model and then redetermine the parameters of the PSF. Our sky model consisted of point sources (with positions from Breen et al. 1994 and Raychaudhury et al. 1991), Galactic and sky backgrounds with linear gradients in Galactic longitude and latitude, and a constant component in addition to the truncated isothermal beta model discussed above. After convolution with the PSF, the model was projected to each image pixel, and the peak Ñuxes of the components were determined using a linear s2 test, with s2 deÐned as X\ i

A

B

nsrc npxls 1 D [ ;F X , (29) s2 \ ; i 0j ij H p2 j/1 i/1 i where n is the number of pixels of the map of the SSC region, n is the number of sources (point sources, the two ““ sources ÏÏ pxls emission, the constant ““ source ÏÏ and the di†use emission). src of galactic The Ðtting procedure was done by minimizing s2 with respect to the parameters F . The errors were estimated by the components of the inverse of the covariance matrix assuming that the errors of each pixel 0j are independent from those of the neighboring pixels. The extensive data processing leading to the map that we used means that we can assume Gaussian statistics for the errors, and we assumed that the errors do not change from pixel to pixel. This is a good approximation in the small region of the sky near the SSC. The iteration process was the following : (1) we determined the Ñuxes of the sources ; (2) we adjusted the positions of the point sources (although accurate positions are available, errors in the absolute pointing, as well as movements of the satellite and the pixelization process introduce errors ; therefore, to get the best Ðt, we have to ““ Ðnetune ÏÏ the positions) ; (3) we Ðtted for the parameters of smearing of the PSF ; (4) we determined the errors per pixel p (assumed to be the same for each pixel) from the data minus best model i This process converged very fast. We used p \ 0.34 counts s~1. This map, assuming only noise left on the modeled region. i estimate includes the instrument error and Ñuctuations caused by the cosmic background. 4.

RESULTS AND DISCUSSION

In the Ðts discussed in °° 2 and 3, we searched for parameters of our model of the SSC gas which would minimize s2 but found that the value of s2 is largely insensitive to these model parameters since no signiÐcant SZ or X-ray signals of the modelled form are present. We used a cuto† of h \ 40¡ (several core radii for all models in Table 1), which corresponds to R \ h~1 180 Mpc at the distance of the SSC, andRcalculated s2 values for our models within windows with 40¡ and 30¡ radii for Ðts50on the COBE and the HEAO data respectively, centered at A3558. Our results are not sensitive the cuto† and window parameters as long as they are large. Table 1 shows the 95% conÐdence upper limits on the peak SZ e†ect and on the peak X-ray emission for Ðts of representative beta models to the COBE and the HEAO data. Varying the parameters of the model leads to only insigniÐcant changes in the s2 values, but the values s2 for Ðts to the HEAO 1 A-2 data decrease toward a Ñat H model (small b, large h ), and s2 and s2 for Ðts to the DMR data decrease toward a point source, implying an unphysically c cr cb deep SZ e†ect. If we assume (based on optical results), a core radius of 7¡ and beta of 0.6 or 1.2, a cuto† at h \ 40¡, which corresponds to R \ h~1 180 Mpc at the distance of the SSC, the resulting limits are o *T (b \ 0.6) o ¹ 122 kK,Rand o *T (b \ 1.2) o ¹ 96 kK, 50 COBE DMR data corrected by the cross-correlation method, or ocr*T (b \ 0.6) o ¹ 183 kK, and o cr using the *T (b \ 1.2) o ¹ 251 cb 18) kK, ([24 ^ 15) kK, ([5 cb ^ 20) kK, and kK, from the combination method. The baseline e†ects are small : ([21 ^ ([10 ^ 17) kK, respectively, and are never more than about 1.5 p di†erent from zero for plausible model parameters. From the HEAO 1 A-2 data the limits on the peak Ñux are F (b \ 0.6) ¹ 0.21 counts s~1 [b (b \ 0.6) ¹ 1.9 ] 10~9 ergs cm~2 s~1 0 1.8 ] 10~9 ergs cm~2 s~1 sr~1] 0 at 95 % conÐdence. These limits are sr~1], and F (b \ 1.2) ¹ 0.18 counts s~1 [b (b \ 1.2) ¹ 0 0 about 3 times less stringent than Day et al. (1991)Ïs Ginga limit for the peak surface brightness, b ¹ 7.25 ] 10~10 ergs cm~2 0 s~1 sr~1. Assuming solar abundance and using equation (25), we get upper limits on the X-ray luminosities of L (b \ 0.6) \ X 17 ] 1044 h~2 ergs~1 and L (b \ 1.2) \ 4 ] 1044 h~2 ergs~1. 50 X 50

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7

TABLE 1 95% CONFIDENCE UPPER LIMITS ON THE PEAK SZ EFFECT AND ON THE PEAK X-RAY EMISSION b

h c (deg)

0.6 . . . . . . 0.6 . . . . . . 0.6 . . . . . . 0.6 . . . . . . 0.9 . . . . . . 0.9 . . . . . . 0.9 . . . . . . 0.9 . . . . . . 1.2 . . . . . . 1.2 . . . . . . 1.2 . . . . . . 1.2 . . . . . .

5.0 7.0 9.0 11.0 5.0 7.0 9.0 11.0 5.0 7.0 9.0 11.0

o *T (kK) o cr 124 122 123 123 110 106 108 112 107 96 96 100

s2 cr 429.1 429.1 429.0 428.9 428.9 429.0 429.1 429.1 428.6 428.8 429.0 429.1

o *T

s2 cb 440.5 440.6 440.8 440.8 440.2 440.4 440.5 440.6 440.0 440.2 440.3 440.5

(kK) o

cb 212 183 165 154 271 217 189 172 335 251 211 188

F 0 (counts s~1) 0.198 0.206 0.219 0.234 0.185 0.183 0.189 0.199 0.185 0.178 0.178 0.183

s2 H 3639.6 3638.3 3636.4 3634.5 3639.9 3639.8 3639.0 3637.7 3639.4 3639.9 3639.8 3639.1

NOTE.È95% conÐdence upper limits on the absolute values of the central SZ e†ect in kK from Galactic emissionÈsubtracted COBE DMR maps using cross-correlation (*T ) and combination cr (*T ) techniques (see text for details), and on the central peak of the X-ray emission (F ) from the cb 1 A-2 map in counts s~1. s2 , s2 , and s2 are the corresponding s2 values, with 450, 0 450, and HEAO cr cb H 3707 degrees of freedom for the two COBE and the HEAO data sets, respectively.

Although we used truncated isothermal beta models to describe the the structure of the SSC gas, the assumptions on which these models are based, such as constant temperature and hydrostatic equilibrium, and an arbitrary cuto† radius, are questionable. The isothermal beta model could be a good approximation at moderate distances from the center (as some numerical simulations suggest ; see Metzler & Evrard 1994 ; Anninos & Norman 1996) but is likely to be severely in error farther out. Searches for large-scale distribution of intra(super)cluster gas would provide information on the distribution of baryonic matter on large scales and may provide some clues to solve the beta problem (Gerbal, Durret, & Lachieze-Rey1994 ; Fusco-Femiano & Menci 1995). In order to discuss the cosmological consequences of our results, we need to convert our results into limits on intrinsic physical properties of the SSC. For the COBE data, we used the Ðts for the DMR map generated by the subtraction technique, since this map has the least noise. Using equation (8) and taking into account the weighting of the cross-correlation method (eq. [2]), f becomes x f 6 \ 0.081f (31.5 GHz) ] 0.307f (53 GHz) ] 0.266f (90 GHz) \ [1.154 . (30) x x x x In equation (7), as a good approximation we may use the frequency-averaged *T that we determined from observations, 0 as a function of gas temperature : instead of the frequency-dependent *T , and obtain the central electron number density 0 nSZ r ~1 kT ~1 *T [5.2 ] 10~4 , if b \ 0.6 ; 0 c e 0 h ] \ (31) cm~3 Mpc 5 keV 100 kK 50 [9.3 ] 10~4 , if b \ 1.2 .

A B A B A B A

B

G

Similarly, from the Ðts to the HEAO A-2 data and using equations (22) and (27), we obtain the X-ray derived value for the central electron density :

A B A B A B A

B

G

nX r ~1@2 kT ~1@4 F 1@2 5.4 ] 10~5 , 0 \ c e 0 h1@2 ] 50 cm~3 Mpc 5 keV counts s~1 7.2 ] 10~5 ,

if b \ 0.6 ; if b \ 1.2 .

(32)

In Figure 1 we plot 95% upper limits on the central electron number density as a function of electron temperature for truncated beta models with b \ 0.6 (Fig. 1a) and b \ 1.2 (Fig. 1b), which bracket the likely range of this parameter, and a core radius of 7¡ from our Ðts to COBE DMR and HEAO data, from using the Ginga limits (Day et al. 1991) and estimates of the limits that could be reached using moderate-duration XTE scans across the SSC (Jahoda et al. 1996). Galactic emission had been removed from the COBE data using the cross-correlation method (see above). The HEAO 1 A-2 limits are slightly less sensitive than the Ginga limits of Day et al. (1991) and more sensitive than those obtained using the COBE DMR data, unless the gas temperature is unexpectedly high. The central electron density in the SSC is constrained to be less than about 5 ] 10~6 cm~3 for most values of T . XTE scans should achieve about a factor of 3 improvement on the Ginga limits. Two proposed missions to study the CBR,e MAP and COBRAS/SAMBA, have (2 p) sensitivities of 40 kK at 90 GHz (the highest MAP frequency, where Galactic contamination has the minimum antenna temperature) and 2.4 kK at 143 GHz (a COBRAS/ SAMBA frequency, where the SZ e†ect has its maximum in intensity units), with an angular resolution of 20@ and 10@, respectively (Bennett et al. 1995 ; Tauber et al. 1996). MAP and COBRAS/SAMBA should be able to detect gas in the SSC with central electron densities of about 10~8 and 10~9 cm~3, based on their sensitivity alone, but the practical detection limit is likely to be set by primordial Ñuctuations. White & Fabian (1995) have shown that the average baryonic densities in a sample of 13 clusters are considerably higher (0.10 h~1.5 \ ) \ 0.22 h~1.5) than the limit on the average baryon density of the universe derived from standard nucleo50 theories, B ) ¹ (0.05 50 ^ 0.01) h~2 (assuming ) \ 1 ; Walker et al. 1991 ; Smith, Kawano, & Malaney 1993). It is synthesis B 50 exists at a supercluster 0 important to Ðnd out if this baryon problem scale. Fabian (1991) estimated the baryon fraction in the SSC by extrapolating the gas mass and luminosity relation for clusters of galaxies (Jones & Forman 1984) and concluded that

8

MOLNAR & BIRKINSHAW

FIG. 1a

Vol. 497

FIG. 1b

FIG. 1.È95% upper limits on the central electron number density of assumed intrasupercluster gas as a function of electron temperature from the COBE DMR (Galactic emission removed) and HEAO 1 A-2 data. The solid line represents the limits that can be set based on the sensitivity of Ginga (see Day et al. 1991). The 95% estimated sensitivity limits that could be achieved by a long XTE scan (Jahoda et al. 1996) are also shown. The two panels correspond to truncated isothermal beta models with a core radius of 7¡ ; (a) b \ 0.6 ; (b) b \ 1.2.

) º 0.18 h~1.3. We derived limits on the average gas density over a 7¡ core radius in the SSC from the same two truncated B models50we used for Figure 1 (b \ 0.6 and 1.2), using Ginga sensitivity limits, the estimated sensitivity of proposed XTE beta scan, and the expected sensitivities of the MAP and COBRAS/SAMBA missions. We plot the 95% upper limits on the ISC gas density in units of the critical density () ) in Figure 2. We also plot average densities derived from the same isothermal avr estimated primordial Ñuctuation on a 7¡ scale at two frequencies, 90 and 143 models with a central peak (4 kK) equal to the GHz. These models represent limits below which single-frequency observations are limited by primordial Ñuctuations. The lower lines represent limits using b \ 0.6, and the upper lines belong to b \ 1.2. The area enclosed by these lines represent the upper limits over the full likely range of beta. The prediction for the average baryon density derived from standard nucleosynthesis theories is also shown with 2 p error bars (two horizontal lines). The limits on ) based on Ginga sensitivities range avr does not contain much more hot from 0.19 to 0.08 h1@2 with increasing temperature. Thus, we can conclude that the SSC 50 (T º 10 keV) large-scale di†use ISC gas than it is predicted by standard nucleosynthesis theories. Any reasonable value for h e would not change our conclusion. 50The temperature and distribution of the intra(super)cluster di†use gas strongly depend on the dynamics of the clustering (Governato, Tozzi, & Cavaliere 1996). The lack of such di†use gas could tell us about the efficiency of clustering (Frisch et al. 1995 ; West, Jones, & Forman 1995). Therefore, it is important to continue to search for ISC gas in superclusters with instruments with higher sensitivity. Assuming hot ISC gas (T º 10 keV), we can conclude from Figure 2 that XTE would be e able to detect gas in the SSC with ) º 0.05 h~2. The proposed XTE scan could decide if the SSC contains more or less gas avr 50 than the predicted baryon density by nucleosynthesis theories. Single-frequency observations with sensitivities ) ¹ 0.01 are avr limited by primordial Ñuctuations.

FIG. 2.È95% upper limits on the average intracluster gas density )(avr) as a function of electron temperature in the core (7¡) of the SSC in units of the critical density, which can be derived based on nondetections with Ginga (see Day et al. 1991) and a long XTE scan (Jahoda et al. 1996), and limits derived from models with a central peak (4 kK) equal to the estimated primordial Ñuctuation on a 7¡ scale (PRIM) using truncated isothermal models with a core radius of 7¡, and b \ 0.6 (lower line) or b \ 1.2 (upper line). The two horizontal lines (NS limit) bound at ^2 p the average baryon density required by standard nucleosynthesis theories.

No. 1, 1998

SHAPLEY SUPERCLUSTER GAS

9

The estimated 95% detection limits of MAP and the COBRAS/SAMBA for extended objects at 90 and 143 GHz are about 6 ] 10~2 and 2 ] 10~3 kK, which make it possible to detect ISC gas in the SSC at density ) º 10~4 h~2 and ) º 10~5 avr 50 single-frequency avr h~2. These limits are much lower than the limits derived from standard nucleosynthesis theories and the 50 primordial limits. These observations are limited by primordial Ñuctuations on the angular scale of the observed extended object and on the accuracy of spectral separation of the SZ e†ect from primordial Ñuctuations and Galactic contamination. We thank Keith Jahoda and Al Kogut for providing us with the HEAO A-2 map and the COBE DMR Galactic emissionÈsubtracted map based on the cross-correlation method, and assistance in using them, and Al Kogut for useful comments on a draft of the paper. S. M. M. is grateful for the hospitality of the CfA and the GSFC CGIS. 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