Astronomy & Astrophysics manuscript no. src January 18, 2012 (DOI: will be inserted by hand later) INTEGRAL constraints on the Galactic hard X-ray background ⋆ from the Milky Way anticenter R. Krivonos1,2, S. Tsygankov1,2,3,4, M. Revnivtsev2, S. Sazonov2, E. Churazov1,2, R. Sunyaev1,2 1 Max-Planck-Institut fu¨r Astrophysik,Karl-Schwarzschild-Str. 1, D-85740 Garching beiMu¨nchen, Germany 2 Space Research Institute,Russian Academy of Sciences, Profsoyuznaya 84/32, 117997 Moscow, Russia 3 Finnish Centre for Astronomy with ESO (FINCA), University of Turku, V¨ais¨al¨antie 20, FI-21500 Piikkio¨, 2 Finland 1 4 Astronomy Division, Department of Physics, FI-90014 Universityof Oulu,Finland 0 2 thedate of receipt and acceptance should beinserted later n a J Abstract. We present results of a study of the Galactic ridge X-ray emission (GRXE) in hard X-rays with the IBIS telescope on board INTEGRAL in the region near the Galactic Anticenter (GA) at l =155◦. We assumed 7 1 a conservative 2σ upper limit on the flux from the GA in the 25−60 keV energy band of 1.25×10−10 erg s−1 cm−2(12.8 mCrab) per IBIS field of view, or 6.6×10−12 erg s−1 cm−2(0.7 mCrab) per degree longitude in the ] 135◦ <l<175◦ region. This upper limit exceeds the expected GRXE intensity in the GA direction by an order A of magnitude,given thenear-infrared (NIR)surface brightnessof theMilky Wayin thisregion andthestandard G hard X-ray-to-NIR intensity ratio for the GRXE, assuming stellar origin. Based on the CGRO/EGRET surface brightnessoftheGalaxy above100 MeVasatracerofthecosmic-ray (CR)inducedgamma-ray background,the . h expected GRXE flux in GA exceeds the measured 2σ upper limit by a factor of 4. Therefore, the non-detection p ofhardX-rayemission from theGAdoesnotcontradictthestellarnatureoftheGRXE,butisinconsistentwith - o CR origin. r t s Key words.galaxy: structure– X-rays:diffuse background a [ 2 1. Introduction face brightness over the Milky Way, which is a known v tracer of stellar mass. 1 The stellar origin of the Galactic hard X-ray back- 7 ground, better known as the Galactic ridge X-ray 4 emission (GRXE), has recently been strongly sup- Galacticdiffuse emissioninaregionfarawayfromthe 2 . portedby morphological/spectralstudies with the RXTE GalacticCenter(GC)wasstudiedbyWorrall et al.(1982) 9 and INTEGRAL observatories (Revnivtsev et al. 2006; with the A2 experiment on board the HEAO1 satellite. 0 Krivonos et al. 2007a; Tu¨rler et al. 2010), spectral stud- The observed2 10 keV emission was consistent with an 1 − 1 ies with Suzaku (Ebisawa et al. 2008; Yamauchi et al. radial exponential disk with a half-thickness of 240 pc. ∼ : 2008) and direct X-ray source counts with Chandra It was pointed out that unresolved emission likely comes v i (Revnivtsev et al. 2009, 2011). The GRXE does not arise from discrete point sources and does not have a diffuse X from the interaction of cosmic rays with the interstellar origin. In the hard X-ray domain GRXE was studied by r medium, as was believed before, but is associated with Skibo et al. (1997) using OSSE observations at longitude a the (predominantly old) stellar population of the Galaxy, l = 95 . The observed emission between 50 and 600 keV ◦ namely with hard X-ray emission from accreting white was suspected to contain a significant contribution from dwarfs and coronaly active stars. It was demonstrated brightdiscretesourcesbecauseofthewidecollimatedfield (Revnivtsev et al. 2006; Krivonos et al. 2007a) that the of view ( 11 .4 3 .8), but a major part of the de- ◦ ◦ ∼ × GRXE intensity closely follows near-infrared (NIR) sur- tected flux was interpreted as interstellar emission from non-thermal electrons (see also e.g. Valinia et al. 2000; ⋆ Valinia & Tatischeff 2001). Today, thanks to the unique Based on observations with INTEGRAL, an ESA project possibilitiesofINTEGRALgamma–raytelescopes,wecan with instruments and science data centre funded by ESA member states (especially thePI countries: Denmark, France, directlystudytheGalacticdiffusebackgroundinanyparts Germany, Italy, Switzerland, Spain), Czech Republic and oftheGalaxywithoutdealingwithsignificantsourcecon- Poland, and with theparticipation of Russia and theUSA tamination. 2 Krivonos et al.: Constraints on theridge emission from theMilky Way anticenter Giventhedistributionof4.9µmNIRintensityoverthe Table 1. INTEGRAL observations used for the GRXE Galaxy as measured by the COBE/DIRBE experiment, study. theGRXEisnotexpectedtobedetectableintheGalactic Anticenter(GA)becauseofthelowNIRsurfacebrightness Latitudescan at l=155◦, 2010 inthisregion.Nevertheless,anexplicitdemonstrationthat Observation field Orbits ScWs the GRXE is not observed from a Galactic region of low ... 960,961 2–94,11–97 stellar density, such as the GA, would substantiate the ... 962,963 12–112,1–97 ... 964,965 13–110,2–67 stellar paradigm of the GRXE even more. Placing tight ... 966 23–56 constraints on the hard X-ray flux from the GA region is 569 ScWs, total nominal exposure: 1 Ms. alsoimportantforcalibratingfuture studiesofthe GRXE Background model calibration, 2008–2009 in the central parts of the Galaxy. Observation field Orbits North Ecliptic Pole 686–689, 759–761, 824–829 2. Observations XMM-LSS 695, 696, 701 Virgo Cluster 747–754, 758, 819–820 We used data from the ISGRI detector, the first Coma Cluster 821–823 layer of the IBIS coded-mask telescope (Ubertini et al. M82 X-1 869–872 2003), on board the INTEGRAL gamma-ray observa- 3C273, 3C279 and M87 878–880 tory (Winkler et al. 2003). ISGRI operates at energies Total nominal exposure: 6 Ms. above 20 keV, with the sensitivity rapidly decreasing ∼ Crab calibration, 2010 above 100 keV. IBIS has a relatively wide field of view Observation field Orbits ( 28 28 at zero response), which allows one to mea- ∼ ◦× ◦ Crab Nebula 902, 903, 966-968, 970 sureweakdiffuseemissionfluxesbyusingthetelescopeas Total nominal exposure: 890 ks. a collimated instrument. To study the GRXE in the GA region, we used spe- cialINTEGRAL observations,partof a seriesofso-called Galactic latitude scans (GLS). This program is based on known pattern of the IBIS mask. The remaining shad- consecutiveobservationsmadealongtheGalacticlatitude owgram contains the following components: (i) variable in the range 30 with a step of 2 . This strategy al- ◦ ◦ ± instrumental background, (ii) the isotropic cosmic X-ray lows one to make independent snapshot measurements of background(CXB), and (iii) the GRXE. Throughout the the instrumental background at mid latitudes, where the analysis we assumed the CXB flux as a constant part of GRXE is expected to be negligible, along with an actual theinstrumentalbackground.Thepossibleinfluenceofthe GRXE observation near the Galactic plane. It is crucial CXBvarianceontheGRXEmeasurementisconsideredin that the instrumental background, which is usually high AppendixB.BecausetheGRXEisextendedoverthesky, in hard X-ray observations, does not exhibit strong vari- it cannot be directly resolved with the IBIS mask. The ability during an individual GLS lasting 8 hours. ∼ only way to estimate the GRXE flux is to determine the TherearetwopositionsintheGAregionobservedwith differencebetweenthe observedcollimateddetectorcount GLSs: ongoing observations at l = 215 (PI: Tsygankov) ◦ rate that is cleaned from sources and the assumedinstru- and a completed program at l = 155 with a total ex- ◦ mental background. To this end, we define a background posure of 1 Ms (PI: Krivonos). In the present study we modelin Appendix Athatpredicts the backgroundcount only used the completed GLS observations at l = 155 ◦ rate during a given GRXE observation. The background performedin August–September 2010,see Table 1 for de- model is adjusted very precisely using mid-latitude snap- tails.Afterscreeningthewholedatasetfollowingthepro- shots of the background performed shortly before and af- ceduredescribedinKrivonos et al.(2007a),hereafterK07, ter a givenGRXE observation,whichis the mainconcept we were left with 525 out of 569 short ( 2 ks) individ- ∼ of the GLS. ual INTEGRAL observations, called scientific windows (ScWs), for the subsequent scientific analysis. To model backgroundvariationsweusedpublicdataofhigh-latitude 3.1. Detector shadowgram observations (Table 1). Because IBIS is a coded aperture imaging telescope, the skyisprojectedontothedetectorplanethroughthetrans- 3. Analysis parent and opaque elements of the mask mounted above We mainly followed the approach described in K07. Our thedetectorplane.WeproducedtheISGRIdetectorshad- study of the GRXE is basedon the capability ofthe IBIS owgramfor every ScW as described in K07. We used the telescope to separate the contributions of point sources 25 60 keV working energy band because of the known − from the background count rate. evolutionof the low-energythreshold ofthe ISGRI detec- The ISGRI detector shadowgram that was accumu- tor and because the GRXE is expected to be weak above latedduringindividualINTEGRALobservationinagiven 50 keV owing to the high-energy cut-off in the GRXE ∼ energy range was cleaned from source fluxes using the spectrum (Krivonos et al. 2007a; Revnivtsev et al. 2006). Krivonos et al.: Constraints on theridge emission from theMilky Way anticenter 3 3.2. Sky map 5 4 The sky reconstruction is based on deconvolution of the detector shadowgram with a known mask pattern. We implemented the IBIS/ISGRI sky reconstruction method described in our previous publications (Revnivtsev et al. IGR J08135+5655 2004; Krivonos et al. 2005, 2007a,b). For the basic idea we referthe readerto the papers byFenimore & Cannon 0 3 (1981)andSkinner et al.(1987).Everyskyimagewasad- ditionally cleaned from systematic noise as described in MRK 3 Krivonos et al. (2010a). The resulting sky image mosaic is shown in Fig. 1. The survey area as a function of flux for sources with 5 1 S/N > 5 is shown in Fig. 2. The minimum detectable flux in the central part of the field is 2.4 10 11 erg MCG 8-11-11 − × s 1 cm 2(or 2.5 mCrab). The survey area reaches its ge- − − ometric limit of 3650 deg2 for f > 4.9 10 9erg s 1 × − − LEDA 168563 cm 2(500 mCrab), 50% of this area has a sensitivity bet- − ter than 8.1 10 11erg s 1 cm 2(8.3 mCrab). × − − − 0 RX J0440.9+4431 We performed a search for sources as excesses in the sky mosaic (Fig. 1) convolved with a Gaussian represent- 3C111 ing the effective instrumental PSF. The detection thresh- GK Per old was estimated assuming Gaussian noise of the pixel Perseus CL valuesasfollows.Thetotalareaoftheskyimage(Fig.1)is 5 3650squareddegrees,andtakingtheIBIStelescopeangu- -1 4U 0352+30 larresolutionof12 intoaccount,wegathered 9.12 104 ′ ∼ × independent pixels. With this consideration, we set the 4C 32.14 source detection threshold to 5σ, allowing at most one false detection for pure Gaussian noise. The signal-to-noise ratio distribution of pixels shown 0 3 - in Fig. 3 has the expected Gaussian shape. However, IGR J01532+2612 one notices some systematic excess at the negative side. Nevertheless, the source detection threshold of 5σ, esti- mated above, separates the noise and source dominated pixel domains. 45 165 150 135 The list of point sources is presented in Table 2. We - attribute two marginally detected, previously unknown 0 0.25 0.99 2.3 4 6.3 9 12 16 20 25 sources to the systematic noise. IGR J08135+5655 is not detected in the sky mosaic of the slightly broader energy band 20 60 keV, and the region around Fig.1. IBIS/ISGRI sky image of the 1 Ms observation of IGR J01532+2612−is affected by systematic noise at the the GA region at l = 155◦ produced in the 25 60 keV − edge of the sky mosaic. energyrange.Thecolortableoftheimagerepresentspixel values in the range 0-25 calculated as the square root of The list of sources in Table 2, except for two IGR’s thesignificance.Thecatalogedandnewlydetectedsources mentioned above, was used in the iterative source re- are labeled in yellow and green, respectively. moval (IROS) procedure that we applied to every ISGRI detector shadowgram (e.g. Krivonos et al. 2010a). This procedure introduces additional uncertainty to the back- 4. Results ground model (Appendix C), but allows one to trace source variability. For example, the known Be/X-ray bi- Using the background model (Appendix A) we obtained nary RX J0440.9+4431 (LS V +44 17) was in a strong foreachScW the predicteddetectorcountrate,asshown outburst during the observations (Krivonos et al. 2010c; inFig.5.Thedetailedviewoftheobservedandpredicted Tsygankov et al. 2011). Fig. 4 shows 25 60 keV detec- detector light curves and their residuals during a space- − tor light curve,cleaned from the source contribution, and craft orbit 964 is shown in Fig. 6. We denoted regions of ready for further analysis. backgroundmeasurement(b >=20 )inblue,andactual ◦ | | 4 Krivonos et al.: Constraints on theridge emission from theMilky Way anticenter Fig.4. Detector count rate of the individual ScWs after subtracting flux contribution from point sources during the GLS program at l = 155 . The data points contain pure statistical errors. The labeled horizontal intervals denote ◦ different spacecraft orbits. Fig.2.Coveredareaofthesurveyasafunctionoffluxfor sources with S/N >5 Fig.3. Signal-to-noise ratio distribution of pixels in the 1MsGLS observationatl=155 .Thedashedlinerepre- ◦ sents the normal distribution with unit variance and zero GRXE observations (b < 20◦) in red. Fig. 6 shows that mean. The accepted threshold of source detection (5σ) is | | thebackgroundbehaviorinanindividualorbitcanbecap- shown by the dotted line. The plot is truncated at σ = 9 tured only with fast scanning observations such as GLSs. for convenience. Thebackgroundmodel,withlowintrinsicscatter,exactly followstheobserveddetectorrate,andthescatterofresid- limit on the GRXE flux at l = 155 per unit Galactic uals(lowerpanelofFig.6)iscomparabletothestatistical ◦ longitude is 0.7 mCrab deg 1. uncertainty of the IROS procedure (Appendix C). − One can test the GRXE non-detection in the GA for UsingtheentireGLS datasetatl =155 ,weaveraged ◦ consistency with stellar and truly diffuse GRXE origins. residualsoverGalactic latitude, asshownin Fig.7 by red To this end, we compared the observed drop of the hard points. The latitude profile does not show any significant X-rayfluxfromtheGC totheGAregion(perIBISFOV) excessintheGalacticplaneregionatb=0 .Asexpected, ◦ with the corresponding change of the intensity of a given the GRXE associated with the old stellar population is tracer. We used the COBE/DIRBE 4.9µm data1 as a notdetectedintheGA.The1σ upperlimitontheGRXE tracer of stellar mass, and the EGRET gamma-ray back- flux in the b < 5 latitude range, which roughly corre- | | ◦ ground map above 100 MeV as a tracer of the cosmic- sponds to the IBIS fully coded FOV, is 2.8 mCrab, or ∼ ray induced gamma-ray background. The EGRET back- 6.4mCrabtakingsystematicuncertaintiesintoaccount. ∼ ground intensity drops from the GC to the GA by a fac- We later refer to a 2σ upper limit of 12.8 mCrab. One ∼ tor of 3. Therefore, using the conservative estimate of can convert the achieved upper limit to more convenient ∼ the GRXE flux in the GC from K07 of 150 15 mCrab, units using the effective solid angle of the IBIS telescope ± 286 deg2 and taking into account that the GRXE is 1 COBE/DIRBE4.9µm intensitymap was corrected for the ∼ muchlessextendedintheGalacticlatitudethantheaver- interstellarreddeningandmeanbackgroundlevelmeasuredin agecross-sectionofIBISFOV.Forinstance,the 2σ upper high-latitude regions, as described in K07. Krivonos et al.: Constraints on theridge emission from theMilky Way anticenter 5 Fig.5. Detector count rate (black) of the individual ScWs as shown in Fig. 4. The systematic uncertainty of the sourceremovalprocedure(Appendix C)wasaddedtothe statisticalerrorsofeachpoint.The redpoints representthe count rate predicted by the background model. Table 2. The list of sources significantly ( 5σ) detected ≥ 2350 on the sky mosaic (Fig. 1). The newly detected sources are highlighted in bold. The 68% confidence interval for estimatedsky coordinatesdepends onsourcesignificance: 2300 2.1, 1.5, and < 0.8for 5 6,10, and >20σ, respectively ′ ′ ′ − (Krivonos et al. 2007b) 2250 Name lon. lat. F25−60 keV deg. deg. mCrab 2200 4U 0352+30a 163.08 -17.14 39.42 ± 0.69 RX J0440.9+4431a 159.82 -1.26 26.12 ± 0.53 3C111b 161.68 -8.83 5.32 ± 0.60 2150 MCG 8-11-11b 165.74 10.41 7.27 ± 0.86 0.2 0.4 0.6 0.8 1 4C 32.14c 158.99 -18.77 3.15 ± 0.56 INTEGRAL orbital phase LEDA 168563b 157.26 3.43 2.76 ± 0.49 MRK 3b 143.29 22.72 7.23 ± 1.33 Perseus CLd 150.58 -13.25 3.06 ± 0.58 4 IGR J01532+2612 139.82 -34.64 20.31 ± 3.91 IGR J08135+5655 160.75 33.53 7.09 ± 1.38 2 GK Pere 150.96 -10.12 2.82 ± 0.56 a HMXB, b AGN,c QSO,d Cluster of Galaxies, e CV 0 -2 -4 0.2 0.4 0.6 0.8 1 we expect the corresponding flux from the GA to be INTEGRAL orbital phase 50 mCrab. This is definitely not observed according ∼ Fig.6. Upper panel: Detailed view of detector count rate to Fig. 7. In contrast, there is a factor of 270 drop in the (black)duringorbit964fromFig.5.Theblue andredar- NIR4.9µmintensityfrom2.7 10 5ergs 1cm 2to10 7 − − − − × easdenoteobservationsmadeat b >=20 and b <20 , erg s−1 cm−2. This implies a GRXE flux from the GA of respectively.Bottompanel:Resid|ua|lsafter◦subtra|c|tingth◦e 0.4 mCrab at 25 60 keV, which is consistent with the − model-predicted count rate from the observedcount rate. derived upper limit of 12.8 mCrab. This is illustrated in The black dashed lines represent a 1σ deviation (1.02%) Fig. 8, where the COBE/DIRBE and EGRET longitude from zero. profiles are renormalized to the hard X-ray flux observed from the GC. We conclude that the non-detection of the GRXE from the GA is consistent with the stellar mass 5. Conclusions distribution of the Galaxy traced by NIR maps, rather thanwiththecosmic-rayinducedgamma-raybackground 1) Using the 1 Ms observations of the GA at l = 155 ◦ seen by EGRET. with the INTEGRAL observatory, performed in the spe- 6 Krivonos et al.: Constraints on theridge emission from theMilky Way anticenter 3)Thedevelopedbackgroundmodelpotentiallyallows 40 one to reach the statistically limited accuracy. However, thefinaluncertaintyoftheapproachisassociatedwiththe 30 source removal procedure, the systematic uncertainty of themethoditself,andtheCXBvariance.Nevertheless,the implementedmethodalongwiththe specialGLS modeof 20 observationisanoptimalapproachofmodelingtheISGRI background and can be efficiently used for studying the 10 Galactic hard X-ray background. 0 Acknowledgements. This research was made possible thanks to the unique capabilities of the INTEGRAL observatory. The data used were obtained from the European and Russian -10 -20 0 20 40 INTEGRAL Science Data Centers. The work was supported Galactic latitude, deg. by the President of the Russian Federation (through the pro- gram of support of leading scientific schools, project NSH- Fig.7. Source flux contribution (blue) and ISGRI detec- 5069.2010.2, and grant MD-1832.2011.2), by the Presidium of tor background count rate residuals (red) averaged over theRussian Academy of Sciences/RAS (theprogram “Origin, theGalacticlatitude.Errorbarsofthebluehistogramrep- Structure, and Evolution of Objects of the Universe”), by resent rms-deviations of the summed point source fluxes the Division of Physical Sciences of the RAS (the program from average in bin. “Extendedobjectsin theUniverse”,OFN-16),bytheRussian Basic Research Foundation (grant 10-02-00492-A), State con- tract 14.740.11.0611, and the Academy of Finland grant 127512. 100 References Churazov, E., et al. 2007, A&A, 467, 529 10 Ebisawa, K., et al. 2008, PASJ, 60, 223 Fabian, A. 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Vikhlinin, A., & Sunyaev, R. 2009, Nature, 458, 1142 Krivonos et al.: Constraints on theridge emission from theMilky Way anticenter 7 Revnivtsev, M., Sazonov, S., Forman, W., Churazov, E., the 25 60 keV energy band corresponds to 9.7 10 12 − − × & Sunyaev, R. 2011,MNRAS, 414, 495 erg s 1 cm 2 for a source with a Crab-like spectrum, − − Skibo, J. G., et al. 1997, ApJ, 483, L95 10.0×Ek−e2V.1 phot cm−2 s−1 keV−1. Tsygankov, S., Krivonos, R., Lutovinov, A., 2011, MNRAS, submitted Appendix B: CXB cosmic variance Tu¨rler, M., Chernyakova, M., Courvoisier, T. J.-L., Lubin´ski, P., Neronov, A., Produit, N., & Walter, R. The CXB emission coming from the population of unre- 2010, A&A, 512, A49 solvedextragalacticsources(activegalacticnuclei,AGNs) Ubertini P., et al., 2003, A&A, 411, L131 is subject to Poissonian variations in the number of Valinia, A., Kinzer, R. L., & Marshall, F. E. 2000, ApJ, sources,intrinsicsourcevariability,andnearbylarge-scale 534, 277 structure (see e.g. Fabian & Barcons 1992). Here, we es- Valinia,A.,&Tatischeff,V.2001,Exploringthe Gamma- timate the systematic limitations to the measuredGRXE Ray Universe, 459, 153 flux caused by CXB variations. Winkler C., et al., 2003, A&A, 411, L1 Using the extragalactic logN–logS relation from Worrall, D. M., Marshall, F. E., Boldt, E. A., & Swank, Krivonos et al. (2010b) and following Revnivtsev et al. J. H. 1982, ApJ, 255, 111 (2008), we estimated the relative uncertainty of the CXB Yamauchi, S., Ebisawa, K., Tanaka, Y., Koyama, K., flux in the 25 60 keV band as − Matsumoto, H., Yamasaki, N. Y., Takahashi, H., & Ezoe, Y. 2008, arXiv:0810.0317 δI (cid:18) ICXB(cid:19) ∼5.5×10−2Sm1/a4x,11Ωd−e1g/2, (B.1) CXB Ω Appendix A: Background model where Smax,11 is the maximum flux of undetected sources in units of 10 11 erg s 1 cm 2, and Ω 286 is the − − − deg The background model used in K07 was slightly changed ≈ effectivesolidangleoftheIBIStelescope.Weadoptedthe inthis study.Since the GLS observationswereperformed CXB intensity to be equal to 1.89 10 11 erg s 1 cm 2 − − − over a relatively short time period, we removed the long- deg 2,basedontheCXBspectrum×modelofGruber et al. − term time part from the equation. Instead of using the (1999) and the 10% higher normalization measured gain parameter to trace orbital modulations of the back- ∼ by INTEGRAL (Churazov et al. 2007). Using the limit- ground rate, we used the spacecraft orbital phase P in ing flux of the survey Eq. B.1 yields a CXB variance at a quadratic polynomial form. Hereafter, we consider only the level of 0.4%. The absolute value is 2.3 mCrab as- the detector count rates after removal of the contribution ∼ suming a 550 mCrab CXB flux per IBIS FOV. In the of point sources. The model of the detector background ∼ current work, we consider the CXB variance for an area 25 60 keV count rate, D , is made of a linear combi- bgd of three IBIS FOVs, which approximately corresponds to − nation of the 600 1000 keV detector count rate, H, and the effective area of the GA survey. − phase D =const+aH +b P +b P2. (A.1) Appendix C: Uncertainty in GRXE measurements bgd 1 2 The coefficient a was calculated using observations The uncertainty of the background model, i.e. the accu- pointed away from the Galactic plane (b > 20 ) where racyoftheISGRIbackgroundrateprediction,issubjectto ◦ the GRXE is not expected to be observ|ed| (see Table 1). statisticalandsystematicalerrors.Theformercanbeeas- The constant term and b coefficients were determined in- ily estimated fromthe totalnumber ofcounts ( 3 105) ∼ × dividually for each spacecraft orbit from the observations inthe25 60keVenergybandpertypicalScW ( 2ks). − ∼ at b > 20 , thus adjusting the model to the current The additional statisticaleffect is related to the IROS ◦ | | background level. In fact, the constant term in Eq. A.1 procedure, when the count rate attributed to a given contains contribution from CXB and unknown intrinsic sourceisremovedfromthedetectorusingtheknownaper- detector background. The last is also variable, which is ture function of the mask. To a first approximation, the traced by variability of this constant with time. In the total number of counts, S, associatedwith a given source currentobservations,itsabsolutevaluevariesintherange is determined as the difference between the number of of 800 900 mCrab from orbit to orbit, while permanent counts,D1,inthedetectorpixelsilluminatedbythesource − CXBcontributionisexpectedtobeatlevelof550mCrab through the mask and the number of counts, D0, in the (Appendix B). Finding the difference between the ob- detectorpixelsblockedbythemask:S =D1 D0.Theto- − servedandpredictedbyEq.A.1detectorcountrateshould talfluxonthedetectorisD =D0+D1.Thus,subtracting yield the GRXE excess in the Galactic plane. the contributionof the source yields the residualdetector The detector count rate was converted to the conve- flux D′ = D S = 2D0. For a weak source in the center − nientunitsofCrabflux,with1mCrab=7.25×10−6cts/s ofthe field ofview, D0 ≈D1 ≈1/2×D andthereforethe in the 25 60 keV band per IBIS FOV. The conver- relative statistical uncertainty of measuring the detector sion coeffic−ient was determined from observations of the count rate D′ =√2 D increases by a factor of √2. In √2D0 √D Crab Nebula in 2010 (Table 1). A flux of 1 mCrab in practice,a morecomplicated model ofa point source(see 8 Krivonos et al.: Constraints on theridge emission from theMilky Way anticenter 10 5 1 0 -5 -10 0 2 4 6 8 10 0.2 0.4 0.6 0.8 1 Number of sources INTEGRAL orbital phase Fig.C.1. Relative root-mean-squaredvalue of the detec- Fig.C.2.Residualsaftersubtractingthemodel-predicted tor rate as a function of number of sources in the FOV. count rate from the observed count rate for the 5.3Ms high-latitudeobservationsaveragedoverspacecraftorbital phase. The black dashed lines represent a 1σ deviation K07), implemented in the source subtraction algorithm, (4.0 mCrab) of the averaged values from zero. Blue and causes an even larger increase of statistical uncertainties. redregionsdenote different phase intervals usedfor back- To estimate the IROS induced uncertainty as a func- ground model calibration and actual measurements, re- tion of number of sources in the FOV, we studied a set spectively. of 22 consecutive observations without cataloged and de- tected sources (orbit 973, ScWs 58 80). The relative standarddeviationofdetectorcountr−ate,asafunctionof – 0.30% (7.5 mCrab) – count statistics, observed in a thenumberofsimulatedsources,N ,isshowninFigC.1. typical ScW without any sources in the FOV. Since src this value differs from the expected, it cannot be ThefirstpointatN =0,RMS =0.3%,reflectstherel- src ative statisticalscatter of the data.As seenfrom Fig C.1, fullystatistical.Someunexploredsystematicsorback- the scatter rapidly increases with inclusion of sources in ground variability can contribute to the scatter of the the FOV. A typical scatter of 1.0% on the ScW time observed detector count rate. scale is observed in real data, a∼s demonstrated in Sect. 4. – 1.00% (25 mCrab) – observed in a typical ScW with several sources in the FOV, related to the IROS pro- Toestimatethesystematicuncertaintyofthemethod, cedure. wedefinedcoefficientsofthebackgroundmodelinEq.A.1 using the high-latitude observations (see Table 1) in the These uncertainties constitute the error of measurement South Galactic hemisphere (700 ks) and applied it to the and, naturally,decreasewith increasingexposure.For ex- North (5.3 Ms). The non-existent GRXE flux was aver- ample,thelargesterrorof25mCrabdecreasesto1mCrab agedoveragivenINTEGRALorbitdividedintothethree for a total exposure of 1 Ms. Systematic uncertainties: equal intervals having three parts: one in the middle and two adjacent, see Fig. C.2 for reference. The middle part – 0.16% (4.0 mCrab) – root-mean-squared residuals af- ofeachinterval(inred)wassupposedtohaveGRXEflux, ter background model subtraction from the observed and the neighboring parts (in blue) were used to correct count rate (Fig. C.2), the constant term (Eq.A.1). This set-up mimics the GLS – 0.09% (2.3 mCrab) – CXB variance per IBIS FOV, pattern of observations. – 0.16% (4.0 mCrab) – CXB variance per GA survey The standard deviation of residuals from zero repre- area. sentsthesystematicuncertaintyofourbackgroundmodel, Thesystematicsquadraticallyaddtotheerrorofthemea- which is found to be 4.0 mCrab. The 25 60 keV de- ∼ − surement. The total systematic error owing to the back- tector countrate increasedfrom 2.2to 2.5 Crabover ∼ ∼ ground model and CXB variance (per GA survey area)is the consideredtime period,hence the relativeaccuracyof 5.7 mCrab. the model is 0.17% of the observed backgroundrate. ∼ We summarize all the discussed uncertainties related to the GRXE measurements in the 25 60 keV energy − band. The values below are presented with respect to the background rate, which is assumed to be 2.5 Crab. Statistical uncertainties: – 0.18% (4.5 mCrab) – count statistics, expected for 3 × 105 counts per typical ScW ( 2 ks), ∼