We present a search for the hyperfine transition of the 57Fe+23 ion at 3.071 mm in clusters of galaxies with the ATNF Mopra telescope. The results are compared with a realistic estimate of the peak brightness temperature of the line in a cooling flow cluster A85, using the available X-ray data

Dickey, JM

Ekers, RD

Liang, H

Moorey, G

English

Nottingham Trent Institutional Repository (IRep)

Astron. Astrophys. 326, 108–112 (1997) ASTRONOMYANDASTROPHYSICSObservations of the 57Fe+23 hyperfine transitionin clusters of galaxiesH. Liang1,2,3, J.M. Dickey2,4, G. Moorey2, and R.D. Ekers21 H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK2 Australia Telescope National Facilities, CSIRO, Epping, NSW 2112, Australia3 Institut d’Astrophysique Spatiale, Universite´ Paris XI, F-91405 Orsay Cedex, France4 University of Minnesota, 116 Church St. SE, Minneapolis, MN 55455 USAReceived 3 March 1997 / Accepted 24 April 1997Abstract. Wepresent a search for the hyperfine transition of the57Fe+23 ion at 3.071 mm in clusters of galaxies with the ATNFMopra telescope. The results are compared with a realistic esti-mate of the peak brightness temperature of the line in a coolingflow cluster A85, using the available X-ray data.Key words: galaxies: clusters – clusters of galaxies: individualAbell 85 – X-rays: galaxies – H ii regions: 30 Dor1. IntroductionIt has been suggested by Sunyaev and Churazov (1984) that itmight be possible to detect the hyperfine transition of a Li-like57Fe+23 ion line in clusters of galaxies. Hyperfine transitionshave been very important in astronomy. The first such tran-sitions was predicted for neutral hydrogen atoms (the famous21cm line) by van deHulst in 1945 and detected in 1951.Atomichyperfine splitting is the result of the interaction between themagnetic moment of the nucleus and the magnetic moment ofthe electron plus the magnetic field generated by the circulat-ing electrons. In the case of the H i 21cm hyperfine transition at1420MHz, the ground state 12S1/2 is split into 2 sublevels. Deu-terium has a similar line predicted at 327 MHz but there havebeennodetections to date despitemanyefforts. The spontaneoustransition probability (or Einstein coefficient) of the H i hyper-fine transition is very low,W = 2.85× 10−15 sec−1. However,external excitation mechanisms such as collisions with other Hatoms and electrons orLyα radiation increase the transition ratesenormously. Hyperfine splitting is not present for all atoms orions, since the interactionbetween thenuclearmagneticmomentand the electronic magnetic moment does not occur if either ofthem is zero. We know from quantum mechanics that the totalnuclear angular momentum (or nuclear spin) is zero for nucleiwith an even number of protons and neutrons, and that the totalSend offprint requests to: H. Liang, h.liang@bristol.ac.ukelectronic angular momentum of an ion with completely filledelectron shells is zero. Thus the commonly available isotopeof iron 56Fe has no hyperfine structure. However, Sunyaev andChurazov (1984; SC) pointed out that the Li-like 57Fe+23 ionexhibits hyperfine structure with a higher spontaneous transi-tion rate (W = 9.4×10−10 sec−1) than that of the H i hyperfinetransition (W = 2.85 × 10−15sec−1), which compensates thelow abundance of the 57Fe isotope (57Fe/56Fe=2.3%; Vo¨kening1989). The wavelength of the 57Fe+23 hyperfine transition hasbeen calculated theoretically to be 0.3071(3)cm (Shabaeva &Shabaev 1992). The FWHM of the line is 40 MHz (or 130km s−1), assuming a cluster gas temperature of 2 × 107K andthat the line width is due to thermal Doppler broadening alone.Clusters of galaxies are known to possess hot gas of tem-perature 107 − 108K. This intracluster medium is found to bemetal rich with typically half solar abundance (Sarazin 1988).The early X-ray observations detected the prominent “7 Kev Feline” which is a blend of Fe+24 and Fe+25 Kα and Kβ lines.The detection of this line not only provided the concrete proofthat the primary X-ray emission mechanism for clusters is ther-mal bremstralung, but also showed that the intracluster gas hasnearly solar abundances and that at least some of the gas musthave been ejected from galaxies. Other Fe lines at lower energysuch as Fe+23 L lines have been detected at∼ 1 keV in clusters.Thus we know that Fe+23 is abundant in cluster environments.SC had estimated the 57Fe+23 line strength in the centre of thePerseus cluster to be∼ 1.5 mK, assuming a central temperatureof 1.4 keV inside a 10-20 kpc radius with an X-ray emissionintegral of ∼ 4.8× 1066 cm−3.The detection of the 57Fe+23 line will have significant as-trophysical implications on our understanding of the propertiesof the galaxy clusters. Firstly, it will provide us with a directmeasure of the dynamics of the ICM, such as turbulence andaccretion flows. There have been great debates on the forma-tion of tailed radio sources in clusters of galaxies (e.g. Burnset al. 1986; O’Donoghue et al. 1993; Roettiger et al. 1993),with some suggesting that the sources are bent by their motionsthrough the ICM and others suggesting that the bending is theH. Liang et al.: Observations of the 57Fe+23 hyperfine transition in clusters of galaxies 109result of an intracluster wind. This debate would benefit greatlyfrom a direct measure of the intracluster turbulence. Secondly,mm observations of the 57Fe+23 line will complement the X-raymeasurements of the distribution of iron in clusters andmeasurethe 57Fe/56Fe ratio which would determine the nucleosynthesishistory of the intracluster gas. Finally, the mm line would pro-vide a direct and high precision measure of the cluster redshiftsince the spectral resolution at mm-wavelength is much higherthan in X-rays.2. ObservationsOur search for the λ 3.1-mm 57Fe+23 line was carried out in1996 September using the Mopra telescope of the AustraliaTelescope National Facility. The antenna is 22m in diameter ofwhich the inner 15m is illuminated by the 3-mm feed, givinga beam width (FWHM) of 45” and gain of 40 Jy K−1. Thereceiver is a cooled SiS mixer with receiver temperature of 80K which was checked with hot-cold load measurements twiceduring the seven day observation period. Pointing was testedby using SiO masers, the largest pointing error measured was10”. Atmospheric opacity was checked by skydips, the zenithopacity varied between 0.06 and 0.12 for all but a few hoursduring the run.The spectrometer is an autocorrelator with two sections,each covering 256 MHz with 256 channels (1 MHz per chan-nel). We overlapped these two by 125MHz so as to cover a totalbandwidth of 384MHz. Roughly 50MHz on each side are com-promised by the IF filter shape, leaving a total bandwidth withconsistent sensitivity of about 285MHz which translates to 920km s−1 at a wavelength of 3.2 mm (the redshifted wavelength).Since the line width is not well known, we do not remove base-lines from the spectra, but simply edit the records on the basisof their raw rms noise.Each record consists of a pair of two minute on and offsource spectra from which we take the difference normalizedby the bandpass shape. The reference position is offset by sixminutes of right ascension. The expected spectral rms per recordis about 20mK, which is what we find in almost all cases. A fewrecords (∼ 10%) show significantly higher noise due to baselineinstabilities in the IF system. They are removed from the aver-age. With this editing, the rms noise in the average decreasesas integration time√tint up to our maximum integration timeof 10.5 hours. Because the spectra have not been baseline fit-ted, there remains some structure in the average spectra, but itis quite broad band (typically 100 MHz wide or greater). Thisbaseline structure limits our ability to detect broad lines.The clusters which we are searching for the 57Fe line are atredshifts of ' 0.06. Assuming rest frequency of 97.611± 0.03GHz (λ = 3.0713mm) the cluster center frequencies come out inthe range 92 - 92.5 GHz.More nearby clusters would not neces-sarily give stronger signals, since the beam size of 45” translatesto only 35 h−1 kpc for a cluster at a redshift of 16,000 km s−1.Thus the emission region is probably considerably larger thanthe beam. This is the reason for taking the reference position sofar from the source.-200 0 200 400 600 800-40-200204060Fig. 1. Spectrum of the H41α line from 30 Dor. The antenna tempera-ture is plotted against the helio-centric velocity for the data from bothspectrometer channels separately and combined. The vertical separa-tions of 30 mK are for clarity in display and arbitary.As tests of the sensitivity and stability of our system andobserving strategy, we have observed several calibration lines.The first test is simply to check the pointing using SiOmasers at86 GHz. We did these pointing checks every few hours for thefirst several days of the run observing five positions offset by ahalf beamwidth from the tabulated source position. We alwaysdetected the masers within 10” of their nominal positions andwith their nominal line strengths. Since both the beam size andthe cluster sizes aremuch larger than thiswe have not introducedany pointing offsets. This test is limited in that the 86 GHz SiOfrequency requires a different receiver tuning than the 92 GHz57Fe line, so we checked the receiver performance by observingtest lines at 92 GHz. The best candidates are 13CS line fromOrion (SiO position) and M17SW, whose frequency is 92.494GHz and the H41α recombination line at 91.955 GHzwhich weobserved in the 30 Dor region of the Large Magellanic Cloud.The 13CS line is so strong that it shows up in a single on-offpair, but the H41α line is weak enough to provide a good test ofa moderately long integration. Our spectrum of this test line isshown in Fig. 1; the position chosen was the 20-cm continuumpeak at 05:38:46.675, -69:04:58.6 (J2000). The total integrationtime is 112 minutes and the noise level is 2.5 mK, 2.0 mKwould be predicted by the radiometer equation, so the systemis evidently performing well for integration times of an hour orso.Table 1 lists the clusters which we have searched for 57Feemission. Columns 1-3 give the cluster name and position, col-umn 4 gives the integration time on-source, column 5 givesthe detection threshold, and column 6 gives the useful velocityrange. The detection threshold is a strong function of the width110 H. Liang et al.: Observations of the 57Fe+23 hyperfine transition in clusters of galaxies16 16.5 17-5051015Fig. 2. Spectrum for the cluster A85. Antenna temperature is plottedagainst the helio-centric velocity for the 2 spectrometer channels sepa-rately. The vertical separation of 6 mK is arbitary, for clarity in display.Table 1. Summary of observationsName α (2000.0) δ (2000.0) tint Tb cz rangeh m s ◦ ′ ′′ min. mK 102 km s−1A85 00 41 50.9 −09 18 10.7 630 5 160-168A3266 04 30 33.4 −61 33 34.3 108 21 174-180A3391 06 25 16.0 −53 39 39.0 124 20 160-168A3667 20 12 27.4 −56 49 35.7 282 18 160-168of the line because we have subtracted no baselines from ourspectra. The threshold given on Table 1 applies to lines nar-rower than about 150 km s−1 in full-width. For broader linesthe residual baselines in the receiver system begin to degradeour detection threshold. This effect is illustrated in Fig. 2, whichis the pair of spectra for the cluster A85 for the two spectrom-eter channels. The vertical offset between the two is arbitrary,here it has been set at 6 mK for convenience. One channel isdominated by a linear baseline, while the other shows primar-ily a quadratic baseline shape. If we were to remove first andsecond order baselines and align the two channels we wouldobtain a spectrum with no features above 2 mK or less (depend-ing on the smoothing). On the other hand, if cluster lines areas broad as several hundred km s−1 then this baseline removalcould remove a real feature, and so our threshold would haveto be raised; we cannot rule out the lump between 16200 and16500 km/s being part of a real feature of strength 3 mK andlinewidth '300 km s−1. For linewidths of 200 km/s or greaterwe must set the threshold at 5 mK in this case. For the otherclusters on table 1 there are similar baseline irregularities thatset the maximum linewidth corresponding to the threshold atabout 150 km/s.3. Discussions and conclusionFollowing the formalism given in Sunyaev and Churazov(SC;1984), we can calculate the expected line intensity for acluster given the cluster gas parameters derived from X-ray ob-servations.The peak brightness temperature of the 57Fe+23 hyperfinetransition should be∆Tb =c28pi3/2νhk1∆νDαguglΦ (1)where gu,gl are the statistical weights of the hyperfine sublevels,∆νD is the Doppler line width (i.e. the half-width at e−1 ofthe maximum), α is the cluster isotope abundance relative tohydrogen and the function Φ is given byΦ =∫Wδ(T ) 12n2e〈σv〉W (1 +N ) + 12ne〈σv〉 + gugl WN +gugl12ne〈σv〉dl (2)where W is the spontaneous transition probability, δ(T ) is thefraction of ions of a given species at temperature T, N is theoccupation number of the microwave background at the wave-length of transition, 〈σv〉 is the excitation coefficient by reso-nance scattering which is the dominant excitation process (SC).Note that Eq. (2) differs slightly from equation (2) in SC (seeAppendix).In the case of clusters of galaxies where WN  12n2e〈σv〉(or ne  1 cm−3), Eq. (2) is reduced toΦ =∫δ(T ) 12〈σv〉1 +N + gugl Nn2edl (3)Assuming a constant temperature, we have from Eq. (1) andEq. (3)∆Tb ∝∫n2edl ∝ Sx (4)where Sx is the X-ray surface brightness. If we assume solarabundance for clusters, where solar 57Fe abundance was takento be 8.8 × 10−7 (SC), and isothermal cluster gas temperaturewithin the Mopra beam to be at its optimum value of 2× 107Kwhere δ(T ) has its peak value of ∼ 0.3 (Jacobs et al. 1977),we can deduce a simple relation between the peak brightnesstemperature of the 57Fe line and the X-ray surface brightness:∆Tb ∼ 100Sx (5)where ∆Tb is the peak brightness temperature of the line inunits of mK before convolution with the beam of the radiotelescope, and Sx is the X-ray surface brightness in units ofergs s−1 cm−2 ster−1in the ROSAT band of [0.1,2.4] keV af-ter corrections for the telescope response and Galactic ab-sorption. In the case of an average cluster of galaxies, wherene ∼ 10−3−10−2 cm−3, the peakbrightness temperaturewouldbe ∼ 0.001 mK. However in the centre of cooling flow clus-ters of galaxies where the central density could be as high asH. Liang et al.: Observations of the 57Fe+23 hyperfine transition in clusters of galaxies 111ne ∼ 0.1 − 0.2 cm−3, the peak brightness temperature couldonly reach∼ 0.1 mK in the most extreme cases, contrary to theestimate of ∼ 1.5 mK given by SC for the Perseus cluster.The cluster A85 is considered a classic example of a coolingflow cluster with high X-ray luminosity and thus one of the bestcandidates for this experiment. To obtain a realistic predictionfor the 57Fe line brightness for A85, we examine the X-raydata available for the cluster. The ROSAT PSPC data for A85has been analysed by Pislar et al. (1996), who found an X-rayluminosity of 9.3 ± 0.2 × 1044 ergs s−1 within a radius of 1.4Mpc in the ROSAT band of [0.1-2.4]keV. The X-ray surfacebrightness was fitted with a β model given by,Sx ∝ [1 + (r/rc)2]−3β+1/2 (6)which corresponds tone(r) = n0[1 + (r/rc)2]−3β/2 (7)for the electron density distribution, where n0 = 0.01cm−3,β = 0.438 and rc = 32kpc (25′′). However, the surface bright-ness profile obtained with the ROSAT HRI (Prestwich et al.1995) which has a resolution of 5′′ (c.f. 20′′ the PSPC) clearlyshows that there is an excess above the β model within the cen-tral 20′′ radius. Taking the X-ray surface brightness from HRI,we obtain from the above relation a peak brightness temperatureof 0.003mK for the 57Fe line. This predicted line brightness canbe increased, if the abundance of 57Fe is significantly differentfrom the terrestrial abundance and/or the distribution of Fe in-creases towards the centre. However, such effects are unlikelyto increase the detectability of the line by more than a factor of10.This analysis shows that the expected brightness tempera-ture of the 57Fe line to be 1 mK in cluster cores, even for anarchetype cooling flow cluster such as Abell 85.We have shownthat the MOPRA telescope can reach a sensitivity level compa-rable to the original prediction given by SC of the line intensitybut is certainly inadequate given the more realistic estimatesshown above.Acknowledgements. We would like to thank Malcom Gray, MikeMasheder and Rashid Sunyaev for useful discussions, Graeme Car-rad for helping with the instrument set up. HL would like to thank theATNF and INSU (Franco-Australian collaboration fund) for support.Appendix A: derivation of Eqs. (1) and (2)The number of transitions upwards equals to the number oftransitions downwards:nuW + nuBulBν + nucul = nlBluBν + nlclu (A1)wherenu,nl are the number in the upper and lower states respec-tively, W and B are the Einstein A and B coefficients relatingto spontaneous and stimulated emission/absorption, Bν is theintensity of the microwave background and c is the collisionalexcitation/de-excitation rate. The W ,B and c coefficients arerelated as follows (Rybiki and Lightman 1979):Blu =guglBul, BulBν = WN, clu =guglcul exp(−hν/kT )(A2)whereN = (exp(hν/kT )−1)−1 is the occupation number of themicrowave background. As was discussed in SC, the dominantexcitation mechanism in this case is resonance scattering ofan electron by the ion and the rate of excitation is given bycul =12ne〈σv〉, where 〈σv〉 is the average of the product ofthe resonance scattering cross section and the relative velocitybetween the electron and the ion.The peak intensity of the line is given byI0 = (NuW +NuBulBν −NlBluBν)hν04piφ(ν0) (A3)whereNu,Nl are the total number of ions in the upper and lowerlevels per unit area along the line of sight respectively,W is thespontaneous emission coefficient or Einstein A-coefficient, ν0is the central frequency of the line and φ is the line profile.Assuming thermal doppler broadening alone, we haveφ(ν) =1√pi∆νDe−(ν−ν0)2/∆ν2D (A4)where ∆νD =√2kTMc2 ν0 is the doppler width which is related tothe FWHM ∆νL = 2√ln 2∆νD. In our case where hν  kT ,we have the peak brightness temperature of the line given by∆Tb =c22kν2 I0(ν0). By substituting Eq. (A1) into the expressionfor I0 in Eq. (A3), we have∆Tb =c28pi3/2ν1∆νDhk(Nlgugl12ne〈σv〉 −Nu 12ne〈σv〉) (A5)whereNu =∫αδ(T )nunl + nunHnenedl (A6)with nHne ∼ 1 and αδ(T ) giving the abundance of 57Fe+23 inthe cluster, and Nl = (nl/nu)Nu. From Eq. (A1) and (A2), wehavenunl=guglWN + 12ne〈σv〉W (N + 1) + 12ne〈σv〉(A7)Thus the peak brightness temperature is given by∆Tb =c28pi3/2νhk1∆νDαguglΦ (A8)whereΦ =∫Wδ(T ) 12n2e〈σv〉W (1 +N ) + 12ne〈σv〉 + gugl WN +gugl12ne〈σv〉dl (A9)The term gugl12ne〈σv〉 in the denominator is absent in equation 2of SC, however in cases where WN  12n2e〈σv〉 this term isinsignificant.112 H. 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Observations of the 57Fe+23 hyperfine transition in clusters of galaxies

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Observations of the 57Fe+23 hyperfine transition in clusters of galaxies

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