The Fermi Haze: A Gamma-Ray Counterpart to the Microwave Haze
Gregory Dobler, Douglas P. Finkbeiner, Ilias Cholis, Tracy R. Slatyer, Neal Weiner
aa r X i v : . [ a s t r o - ph . H E ] M a y Draft version August 21, 2018
Preprint typeset using L A TEX style emulateapj v. 03/07/07
THE
FERMI
HAZE:A GAMMA-RAY COUNTERPART TO THE MICROWAVE HAZE
Gregory Dobler,
Douglas P. Finkbeiner,
Ilias Cholis, Tracy Slatyer, & Neal Weiner Draft version August 21, 2018
ABSTRACTThe
Fermi Gamma-Ray Space Telescope reveals a diffuse inverse Compton signal in the inner Galaxywith a similar spatial morphology to the microwave haze observed by WMAP, supporting the syn-chrotron interpretation of the microwave signal. Using spatial templates, we regress out π gammas,as well as IC and bremsstrahlung components associated with known soft-synchrotron counterparts.We find a significant gamma-ray excess towards the Galactic center with a spectrum that is signif-icantly harder than other sky components and is most consistent with IC from a hard populationof electrons. The morphology and spectrum are consistent with it being the IC counterpart to theelectrons which generate the microwave haze seen at WMAP frequencies. In addition, the impliedelectron spectrum is hard; electrons accelerated in supernova shocks in the disk which then diffuse afew kpc to the haze region would have a softer spectrum. We describe the full sky Fermi maps usedin this analysis and make them available for download.
Subject headings: diffuse radiation — microwaves — gamma-rays INTRODUCTION
The most detailed and sensitive maps of diffuse mi-crowave emission in our Galaxy have been produced bythe
Wilkinson Microwave Anisotropy Probe (WMAP).An analysis of the different emission mechanisms in thesemaps uncovered a microwave “haze” towards the Galac-tic center (GC) that has roughly spherical morphologyand radius ∼ softer at higher frequencies sincethe electrons lose energy preferentially at high energies asthey diffuse from their source. While there are significantuncertainties in the spectrum of the haze (see the discus-sion in Dobler & Finkbeiner 2008), the data require thatthe diffused spectrum be roughly as hard as the expected injection spectrum from first-order Fermi acceleration atsupernova shock fronts (number density dN/dE ∝ E − ).That is, if the electrons were produced in shocks in thedisk, then they would have to have undergone no diffu-sive energy losses over a ∼ π/ volume, which Institute for Theory and Computation, Harvard-SmithsonianCenter for Astrophysics, 60 Garden Street, MS-51, Cambridge, MA02138 USA Kavli Institute for Theoretical Physics, University of Califor-nia, Santa Barbara Kohn Hall, Santa Barbara, CA 93106 USA Physics Department, Harvard University, Cambridge, MA02138 USA Center for Cosmology and Particle Physics, Department ofPhysics, New York University, New York, NY 10003 USA [email protected] seems unlikely. Furthermore, there is significant emissionin WMAP 23, 33, and 41 GHz bands from electrons that were generated in SN shocks; this emission has a verydisk-like morphology (and softer spectral index which isconsistent with shock acceleration), while the haze has amore spherical morphology. Together, the haze spectrum and morphology imply ei-ther (1) a new class of objects distributed in the Galacticbulge and largely missing from the disk; (2) significantacceleration from shocks several kpc off the plane towardsthe Galactic center; or, perhaps most intriguingly, (3) anew electron component from a new physical mechanism.The claim that novel physics or astrophysics is requiredto explain the WMAP data is called the haze hypothe-sis to distinguish it from the two null hypotheses: (1)that the microwave haze is not synchrotron, but rathersome combination of free-free and spinning dust; and (2)that the haze is synchrotron, but the electron spectrumrequired is not unusual. In this work we do not addressthe origin of the electrons, but instead consider what thedata from the
Fermi Gamma-ray Space Telescope implyfor their existence.Electron cosmic rays at 10 −
100 GeV primarilylose energy in the diffuse interstellar medium by pro-ducing synchrotron microwaves and inverse-Compton(IC) scattered gammas. Synchrotron losses are pro-portional to magnetic field energy density, U B = B / π , while IC losses are proportional to the inter-stellar radiation field energy density, U ISRF , in theThomson limit, and less in the Klein-Nishina limit.Bremsstrahlung off the ambient gas also occurs, but isexpected to be sub-dominant in the regions of inter-est. Therefore, the best test of the haze hypothesisis to search for IC gammas in the
Fermi data, whichwas studied in the context of dark matter signals by Hereafter “spherical” is taken to mean “not disk-like” – if any-thing, the haze is non-spherical in the direction perpendicular tothe disk (see § See http://fermi.gsfc.nasa.gov/ssc/data/ [ k e V c m - s - s r - ]
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Fig. 1.—
Top and bottom left:
Full sky
Fermi γ -ray maps in various energy bins. The mask includes the 3-month Fermi point sourcecatalog as well as the LMC, SMC, Orion-Barnard’s Loop, and Cen A.
Bottom right:
Exposure time map with our mask overlaid andstretched to 0 − Cholis et al. (2009a); Zhang et al. (2009); Borriello et al.(2009); Cirelli & Panci (2009); Regis & Ullio (2009);Belikov & Hooper (2009); Meade et al. (2009).Previous studies of high latitude gamma-ray emis-sion have reported measurements of an excess of emis-sion above the Galactic plane, most notably SAS-2 (Fichtel et al. 1975; Kniffen & Fichtel 1981), COS-B(Strong 1984), and EGRET (Smialkowski et al. 1997;Dixon et al. 1998). However, in each case the experi-ments either covered an insufficient energy range (SAS-2and COS-B) or did not have sufficient sensitivity andangular resolution (EGRET) to permit a spatial corre-lation with the WMAP haze.
Fermi overcomes both ofthese obstacles and allows us to search for the gamma-raycounterpart to the microwave haze for the first time.The presence of an IC signal at the expected level canconfirm that the microwave haze is indeed synchrotron,ruling out the first null hypothesis. From the spectrumof the IC, we can estimate the electron spectrum requiredto make the signal, addressing the second null hypoth-esis. For example, the presence of ∼
50 GeV IC pho-tons requires electrons of
E >
50 GeV, perhaps muchgreater. Furthermore, IC photons provide valuable in-formation about the spatial distribution (disk vs. bulge)of the source of these particles, which in turn can con- strain hypotheses about their origin. In § Fermi data, describe ourmap-making procedure, and display full-sky maps at var-ious energy ranges. In § § DATA
The LAT (Large Area Telescope) on
Fermi (seeGehrels & Michelson 1999 as well as the
Fermi home-page ) is a pair-conversion telescope consisting of 16 lay-ers of tungsten on top of a calorimeter with a thicknessof 7 radiation lengths. The entire instrument is wrapped The synchrotron haze depends on the Galactic magnetic fieldwhile the IC haze depends on the Galactic ISRF, and so the twomorphologies should not be identical, and could be quite different. http://fermi.gsfc.nasa.gov/ in a scintillating anti-coincidence detector to provide aparticle veto. The spacecraft occupies a low Earth orbitwith an inclination of 25 . ◦ . The field of view is so widethat the entire sky may be covered in two orbits by rock-ing the spacecraft north of zenith on one orbit and southof zenith on the other. Several times per month, Fermi interrupts this pattern to point the LAT at a gamma-ray burst, though this has little impact on the integratedexposure map. When the spacecraft passes through theSouth Atlantic Anomaly (SAA), CR contamination in-creases and significant data must be discarded, reducingthe mean exposure at southern declinations. Beyond azenith angle of 105 ◦ the data are significantly contami-nated by atmospheric gammas. We excise such data, andselect only events designated “Class 3” (diffuse class) bythe LAT pipeline. The LAT collaboration plans to re-lease a cleaner class of events in the future, however, atthe time of this writing, the Class 3 events are the mostlikely to be real diffuse gamma-ray events.The events are then binned into a full sky map us-ing HEALPix, a convenient iso-latitude equal-area full-sky pixelization widely used in the CMB community. Spherical harmonic smoothing is straightforward in thispixelization, and we smooth the maps to a Gaussian PSF,usually of 2 ◦ FWHM. The full-sky
Fermi maps are dis-played in Figure 1 along with an exposure map. See Ap-pendix B for more details on map construction, smooth-ing, masking, and for instructions on how to downloadthe maps. ANALYSIS
In this work our goal is to test our general preconcep-tions about what gamma-ray signals should be present,and identify any unexpected features in the
Fermi data;we avoid detailed comparisons between the data and spe-cific theoretical models for the Galactic gamma-ray emis-sion. Our approach is to compute linear combinations of
Fermi maps at several energies and perform templateanalyses with maps of the ISM, radio maps, etc. to seewhat emerges. This sort of open-minded analysis is flex-ible enough to find the unexpected.An alternate approach would be to attempt to fit thedata with a sophisticated physical model, in the contextof some simulation code (e.g. GALPROP). Such a phys-ical model can be quite detailed, including the 3D dis-tributions of gas and dust, the 3D distribution of opticaland FIR photons density and direction, the 3D magneticfield, and a 3D model of p, e − injections. By propagatingthese primary particles with GALPROP, the resulting π , bremsstrahlung and IC signals may be predicted andcompared with Fermi . However, while a detailed physi-cal model will certainly be crucial to a full understandingof the
Fermi data (and such modeling is currently un-derway within the
Fermi collaboration), this approachmay lack the flexibility to identify new emission compo-nents that cannot be absorbed by modifying parametersin the model. On the other hand, such a model may alsohave too much freedom, so that meaningful patterns areabsorbed into the fit and left unnoticed. In future work,we will take the signals revealed by our initial analysis HEALPix software and documentation can be found at http://healpix.jpl.nasa.gov , and the IDL routines used inthis analysis are available as part of the IDLUTILS product at http://sdss3data.lbl.gov/software/idlutils . -6 -5 -4 E x i n t en s i t y [ G e V c m - s - s r - ] π decayICSbremsstotal Fig. 2.—
GALPROP model illustrating the three primarygamma-ray emission mechanisms (see §
3) and their relative am-plitudes in the Galactic plane ( | ℓ | ≤ | b | ≤ and fold them back into a full physical model. Diffuse Gamma Templates
There are three well-known mechanisms for generatinggamma-rays at the energies observed by
Fermi . First,at low ( ∼ π particlesgenerated in the collisions of cosmic ray protons (whichhave been accelerated by SNe) with gas and dust in theISM. Second, relativistic electrons colliding with nuclei(mostly protons) in the ISM produce bremsstrahlungradiation. Finally, those same electrons interact withthe interstellar radiation field (ISRF) and inverse Comp-ton scatter CMB, infrared, and optical photons up togamma-ray energies. A schematic of the relative impor-tance of these emission mechanisms in the Galactic plane( | ℓ | ≤ | b | ≤
5) generated by the GALPROP code,version 50p (Strong et al. 2000; Porter & Strong 2005;Strong et al. 2007) is shown in Figure 2.Since π gammas and bremsstrahlung are producedby interactions of protons and electrons (respectively)with the ISM, these emission mechanisms should be mor-phologically correlated with other tracers of the ISM,such as the SFD dust map based on 100 µ far IR data(Schlegel et al. 1998). The π gamma-ray intensity scaleswith the ISM volume density times the proton CR den-sity, integrated along the line of sight. In the limit wherethe proton cosmic ray spectrum and density is spatiallyuniform, the ISM column density is a good tracer of π emission. Likewise, for a uniform electron spectrum, it isa good tracer of bremsstrahlung. Because our analysis islimited to | b | > ◦ , much of the emission we see is withina few kpc, so the assumption of uniform CR density ismore valid than it would be for the entire Galaxy, partic-ularly for protons, which have much larger propagationlengths than electrons. Residual Maps [ k e V c m - s - s r - ]
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180 90 0 -90 -180 -90-4504590 -0.3580.894 [ k e V c m - s - s r - ] Fig. 3.—
Residual maps after subtracting the SFD dust template from
Fermi maps at various energies. The mask is described inAppendix B. Cross-correlations are done over unmasked pixels and for 75 ≤ ℓ ≤ Since our goal is to search for an IC emission compo-nent with a morphology which roughly matches the mi-crowave haze (i.e., centered on the GC, roughly spherical,and about 20-40 ◦ in radius), we now attempt to removethe π emission from the maps shown in Figure 1, usingthe same template fitting technique used in Finkbeiner(2004a) and Dobler & Finkbeiner (2008). We performmultiple types of template fits. Type 1 uses only the Fermi map itself at 1-2 GeV which roughly traces π emission because the gamma ray sky at those energies isdominated by π gammas (with subdominant contribu-tions from bremsstrahlung and IC). Type 2 uses only theSFD dust map which is a direct tracer of ISM density andso should roughly map where the π gammas and muchof the bremsstrahlung are produced – again, up to someuncertainty involving the line of sight distribution. Ineach case, a uniform background is included in the fit,making our results insensitive to zero point offsets in the maps.We model the Fermi map at energy E , F ( E ), as a lin-ear combination of template maps, F model = T c T , where F model is a column vector of N pix unmasked pixel values, T is the N template × N pix template matrix, and the cor-relation coefficients c T are chosen to minimize the meansquared residual, h ( F − F model ) i = h ( F − T c T ) i , (1)averaging over pixels. The least-squares solution, c T ( E ) = (cid:0) T T T (cid:1) − × (cid:0) T T F ( E ) (cid:1) , (2)yields the template correlation coefficients at each energy.In this fit, we mask out the Fermi | b | < ◦ . Cross-correlationsare done over unmasked pixels and for several different -0.030.15 T e m pe r a t u r e [ m K ]
41 GHz synchrotron
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41 GHz haze
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Fig. 4.—
Top: the WMAP Q-band (41 GHz) total synchrotron (left) and haze (right).
Bottom: the residual map obtained with theType 1 template fit using the SFD map (left) and the 1-2 GeV
Fermi map (right) as a template for π decay emission. These residualmaps are the same as the right column second row panel of Figure 3 and Figure 5 respectively though with a different stretch. Both mapsare shown with the mask used in the Dobler & Finkbeiner (2008) microwave analysis for comparison. The upper panel represents cosmicray electrons interacting with the Galactic magnetic field to produce synchrotron while the lower panel represents cosmic ray electronsinteracting with the ISRF to produce IC emission, and colliding with the ISM to produce bremsstrahlung. The morphological similaritiesbetween the microwave haze and gamma-ray haze (right) are striking, indicating a correspondence between the two electron populations. ranges in ℓ : eight longitudinal slices that have | ℓ | ≥ ◦ (to avoid the GC) and width 30 ◦ (Regions 1-7) as wellas one region with 75 ◦ < ℓ < ◦ (Region 8). Note thatRegion 8 is the union of Regions 1-7; Regions 1-7 are fitindividually to show the variation in the fit spectrum,and Region 8 is fit to obtain the mean outer Galaxysignal. With these correlation coefficients, we define theresidual map to be, R T ( E ) = F ( E ) − c T ( E ) × T. (3)To the extent that the templates in T match the morphol-ogy of the π and bremsstrahlung gammas, the residualmap will include only IC emission.Figure 3 shows the resultant residual maps using theSFD map as a morphological tracer of π emission forthe Region 8 fits. The most striking feature of the dif-ference maps is the extended emission centered aroundthe Galactic center and extending roughly 40 ◦ in b .The morphological correlation between the WMAP syn-chrotron and the R SFD (5 −
10 GeV) is striking as isshown in Figure 4. Here the 41 GHz synchrotron (hazeplus Haslam-correlated emission, see Haslam et al. 1982;Dobler & Finkbeiner 2008) is shown side by side with the5-10 GeV
Fermi residual map with the mask used in theDobler & Finkbeiner (2008) microwave analysis overlaidfor visualization.Figure 5 shows residual maps using the 1-2 GeV
Fermi maps as a template for the π emission. This sort of“internal linear combination” has the advantage that π emission cancels out as long as the shape of the protonCR spectrum is the same everywhere – it does not rely onthe proton CR density to be uniform. The residual mapslook largely similar to the case with the SFD templateregressed out, but there are some notable differences. Inparticular, using this 1-2 GeV template, the IC haze has a slightly “taller” appearance. This seems to be due to adisk-like component that is present in the 1-2 GeV mapsbut not in the dust map. This is probably because the1-2 GeV Fermi map is not entirely π emission, but alsocontains bremsstrahlung and IC components generatedby electrons accelerated by SNe in the disk. The re-sult is that when this lower energy map is regressed out(i.e., cross-correlated and subtracted) from higher energymaps, this emission component is subtracted along withthe dust-correlated emission. Conversely, the SFD mapcontains only emission from dust grains and not rela-tivistic electrons; while the bremsstrahlung from thoseelectrons largely traces the gas distribution, the IC doesnot, and so is not regressed out when using the SFDtemplate.Despite the significant shot noise in the Fermi map,Figure 4 shows that there is a clear morphological corre-lation between the microwave haze and the gamma-rayhaze. Of course, we do not expect the morphologies toagree perfectly since the microwave haze is generated byinteractions of electrons with the magnetic field while this
IC haze is due to interactions of the electrons with theISRF. Nevertheless, this is evidence that the microwavehaze seen in the WMAP data is indeed synchrotron andis not some other component such as free-free emissionor spinning dust.
Four-Component Template Fits
Because the solution to Equation 2 minimizes the vari-ance of the (zero mean) residual map R ( E ), the pres-ence of the IC haze affects the coefficients c T ( E ), sincethere is non-zero spatial correlation between the tem-plates and the IC haze. To relax the stress on the fit, weexpand our template analysis with a third Type. Type [ k e V c m - s - s r - ]
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10 GeV < E < 20 GeV
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The same as Figure 3 but using the
Fermi π (and subdominant bremsstrahlung) emission only, the low energy Fermi map includes the soft IC associated with lower energyelectrons. In fact comparing the residuals in this figure with those in Figure 3, it is clear that the disk-like component has been subtractedleaving only the IC haze. Furthermore, the IC haze is more prominent in the high energy maps indicating a harder spectrum than π emission which is the dominant emission mechanism at ∼ T : the SFD map to trace π and bremsstrahlung emission, the 408 MHz Haslam et al.(1982) map which is dominated by radio wavelength syn-chrotron and thus roughly traces soft spectrum electronswhich produce soft IC and bremsstrahlung, and a bi-variate Gaussian of width σ ℓ = 15 ◦ and σ b = 25 ◦ . Wenote that this template is chosen to roughly match themorphology in Figure 5 and has no other physical mo-tivation. We also use a uniform template to fit out theisotropic background signal in the maps, again, makingour results insensitive to zero points. Lastly, for this fitwe use all values in ℓ (Region 9).Note that since the bremsstrahlung originates from in-teractions of the electrons with the ISM, its spatial dis-tribution depends on both the gas density and the cos-mic ray electron density; consequently, some contributionfrom bremsstrahlung will be present in both the SFD-correlated and Haslam-correlated emission. The previous fits were done with uniform weightingand assuming Gaussian errors, minimizing χ . For theType 3 fit we do a more careful regression, maximizingthe Poisson likelihood of the 4-template model in order toweight the Fermi data properly. In other words, for eachset of model parameters, we compute the log likelihoodln L = X i k i ln µ i − µ i − ln( k i !) , (4)where µ i is the synthetic map (i.e., linear combinationof templates) at pixel i , and k is the map of observedcounts. Note that the last term does not depend on themodel parameters. It may appear strange at first to com-pute a Poisson likelihood on smoothed maps, however,the smoothing is necessary to match PSFs at differentenergies and with various templates (some of which havelower resolution than Fermi in the energy range of inter-est). The smoothing itself does not pose any problems [ k e V c m - s - s r - ] SFD Dust
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Fig. 6.—
The templates and fit solutions used in the Type 3 (see § Upper left: the SFD dust map, upper right: the Haslam 408 MHz map, middle left: the bivariate Gaussian haze template, middle right: the
Fermi map at 10-20 GeV (same as thefirst column, third row of Figure 5 but with a different stretch to show the detailed morphological structure), lower left: the best fittemplate solution for the observed emission, lower right: the residual map. Note the very small residuals indicating that the template fitis a remarkably good representation of the data over large areas of the sky. for relative likelihoods, as we show in Appendix C.However, we must keep in mind that the uncertaintiesderived in this way are the formal errors correspondingto ∆ ln L = 1 /
2, which would be 1 σ in the case of Gaus-sian errors. The error bars plotted are simply the squareroot of the diagonals of the covariance matrix. This es-timate of the uncertainty should be accurate at high en-ergies, where photon Poisson noise dominates. At lowenergies, although the formal errors properly reflect theuncertainty in the fit coefficients for this simple model,the true uncertainty is dominated by the fact that the4-template model is not an adequate representation ofthe data.Figure 6 shows the skymaps and best fit solution in-cluding the residual map at 10-20 GeV while Figure 7shows residual maps at other energies. It is clear fromthese residuals that the template fitting produces a rel-atively good approximation of the gamma-ray data overlarge areas of sky. Furthermore, Figure 7 shows that not including the bivariate Gaussian template for the IChaze yields a statistically significant residual towards thecenter indicating that a model including an IC haze is abetter match to the data then one without. The promi-nent North Polar spur feature in the Haslam map, which is thought to originate from synchrotron emission fromelectrons in Loop I (Large et al. 1962), is over-subtractedin each case, because the North Polar spur is brighter inthe Haslam map than in the gamma-ray maps (i.e. theratio of synchrotron microwaves to IC gamma rays in theNorth Polar spur is larger than in the rest of the Haslammap). This may be due to different ISRF, B-field andISM density values in Loop I relative to the inner Galaxy(since Loop I is thought to be quite nearby), or may bedue to a softer-than-usual electron spectrum in Loop I,since the electrons producing the synchrotron measuredin the Haslam map are much lower energy than those pro-ducing IC gamma-rays at energies measured by
Fermi .Figure 8 shows these same residual maps, but with asmoothing of 10 ◦ which is on the order of the scale of thehaze emission. With this large smoothing, smaller scalevariations (due to individual photons at high energies)are smoothed over and the residual maps clearly showthat the haze is a robust feature at all energies.In Figure 9 we show the results of a four template fitusing the 1-2 GeV map instead of SFD to trace the π See Casandjian et al. (2009) for a discussion of gamma-raysfrom Loop I seen by
Fermi . emission. This figure shows that the haze is not due tothe SFD template being an imperfect tracer of π emis-sion. If the proton cosmic ray density is higher towardsthe GC, then SFD may systematically underestimate the π emission there and perhaps the gamma-ray haze is theresult. However, Figure 9 shows that this is clearly notthe case. The 1-2 GeV template includes the effects ofproton cosmic ray density variations (as well as line ofsight gas density effects) and the haze remains as a ro-bust residual. That is, the haze is not due to imperfecttemplates as suggested by Linden & Profumo (2010).In Figure 10 we show the haze amplitude (residualmaps from the Type 3 fit plus the correlation-coefficient-weighted bivariate Gaussian template) as a function ofGalactic latitude and for the longitudinal bin: − ◦ <ℓ < ◦ . Although the data are noisy, the figure showsthat the Fermi haze dies off by roughly b ∼ ◦ in allenergy bands. For comparison, we show the same plotfor just the residual map. The figure also shows the am-plitude as a function of longitude for the latitudinal bin − ◦ < b < − ◦ . The more rapid fall off of the hazeemission with ℓ compared to b indicates a haze morphol-ogy elongated in the b direction.There are two important features to note about Figures3 through 7. First, the IC haze has a spectrum which is harder than the other IC in the Galaxy. This is evidencedby the fact that using the 1-2 GeV Fermi map as a tem-plate removes the IC emission from disk electrons but thehaze IC fades more slowly with energy. Second, the IChaze is morphologically distinct from either the π emis-sion or IC and bremsstrahlung from the disk electrons.These two facts taken together strongly suggested thatthe electrons responsible for the microwave and gamma-ray haze are from a separate component with a harderspectrum than SN shock-accelerated electrons. Fermi
Galactic Diffuse Emission Model
So far, we have only done template fits of maps ofdata to other maps of data. Using the SFD dust map asa tracer of π emission is equivalent to assuming that theproton CR spectrum and density are spatially uniform,and the dust/gas ratio is constant. Using the Haslammap to estimate IC emission is equivalent to assumingthat the B-field and ISRF have similar spatial varia-tion, and neglecting the anisotropies in both IC and syn-chrotron emission. Consequently, there have been con-cerns (Linden & Profumo 2010) that this template-basedanalysis might introduce spurious large-scale residuals.To address these concerns, we investigate whether the Fermi diffuse model contains a structure similar to thehaze emission.The
Fermi team provides a model of diffuse gamma-ray emission consisting of maps sampled at 30 energybins from 50 MeV to 100 GeV. These maps are basedon template fits to the gamma-ray data and also includean IC component generated by the GALPROP cosmicray propagation code.The difference between the model and data is shownin Figure 11. We have interpolated the model to theenergy ranges of interest and performed the simple one-template fit to the data (analogous to our Type 1 and 2 The background models can be downloaded from http://fermi.gsfc.nasa.gov/ssc/data/access/lat . fits described above). This fit allows for any error in thenormalization of the diffuse model; the fit coefficients arewithin a few percent of unity in every case.At each energy range, the haze is clearly visible in theresidual maps. GALPROP uses the standard inhomo-geneous ISRF model (Porter & Strong 2005), making itunlikely that the observed residual is due to the expectedspatial variation of the ISRF. Furthermore, the diffusemodel includes a disk-like injection of primary electronsand estimates for the line of sight density variations ofthe interstellar medium. The fact that the haze residualremains suggests that, given the propagation model in-cluded in GALPROP, disk-like sources will not producethe observed IC emission, nor will expected variations inthe gas density and proton CR density along the line ofsight. Spectra
While the morphology of the gamma-ray haze is indica-tive of IC emission from the microwave haze electrons, wenow attempt to estimate the spectrum of this emission.This is difficult for several reasons. First, π emissionis dominant (or nearly so) at most energies in Fermi ’senergy range. Thus, in a given region, we must estimatethe spectral shape and amplitude of the π emission inorder to subtract it from the total. Second, the totalnumber of photons measured by Fermi decreases rapidlywith increasing energy. For example, in the inner Galaxy( | ℓ | ≤ | b | ≤ ∼ c T ( E )and total fluxes dN/dE . Isotropic Background
The
Fermi data contain gamma-rays from an un-resolved extragalactic signal with dN/dE ∼ E − . (Ackermann 2009) as well as particle contamination. Wemake no attempt to separate the extragalactic gamma-ray signal from the particle contamination. Instead wemeasure the spectrum of this (nearly) isotropic back-ground in 8 regions at high latitude and test the assump-tion of isotropy. Specifically, we take combinations oflongitude ranges of − ◦ < ℓ < − ◦ , − ◦ < ℓ < ◦ ,0 ◦ < ℓ < ◦ and 90 ◦ < ℓ < ◦ together with latituderanges of − ◦ < b < − ◦ and 60 ◦ < b < ◦ for the4 × not the standard deviation of the mean. To be conserva-tive, we use this standard deviation as the uncertainty inthe background in the remaining stages of the analysis.Future work by the Fermi team to understand both theparticle contamination and the gamma-ray sky will likelyreduce this error in the background substantially. -1.1312.828 [ k e V c m - s - s r - ]
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180 90 0 -90 -180 -90-4504590 -0.3580.894 [ k e V c m - s - s r - ] Fig. 7.—
Residual maps using the Type 3 template fit. The right column is the same as the lower right map in Figure 6 but for mapsat different energy bands. The left column performs the same fit without including a bivariate Gaussian template for the IC haze. It isclear that not including the haze template results in a significant residual towards the GC in each energy band, but particularly at highenergies. Including the haze template improves ln L by 504, 215, 78, and 54, respectively, for the 4 energy bins shown. Template-Correlated Spectra
Figure 13 shows c T ( E ) × h T i for the two templates andregions 1-7 used in the Type 1 and Type 2 fits along withthe model π spectrum from GALPROP, which uses theBlattnig et al. (2000) parameterizations for pion produc-tion. It is clear from the figure that the cross-correlationtechnique produces π spectra that are remarkably simi-lar to the model spectrum at low energies, while at highenergies the cross-correlation spectrum is slightly higherthan the model spectrum. This could be due to a numberof reasons such as non-zero spatial correlation betweenthe templates and the harder spectrum haze IC, contam-ination from background events like heavy nuclei, or un-certainties in the π emission model. Of these, the first ismost likely since the cross-correlation between the tem-plates and a nearly isotropic background is likely smalland since the spectrum of π gammas is quite well known.Template-correlated spectra for the Type 3 template fit are shown in Figure 14. Here the correlation coeffi-cients are weighted by the mean of each template in the“haze” region (see Table 2). As shown in the figure, thespectra for the SFD and Haslam maps reasonably matchthe model expectations in that region . That is, theSFD-correlated emission roughly follows the model π spectrum while the Haslam-correlated spectrum resem-bles a combination of IC and bremsstrahlung emission.However, the haze -correlated emission is clearly signif-icantly harder than either of these components. Thisfact coupled with the distinct spatial morphology of thehaze indicates that the IC haze is generated by a separate electron component. Total Intensity Spectra The GALPROP model here was tuned to match locally mea-sured protons and anti-protons as well as locally measured electronsat ∼ -1.1312.828 [ k e V c m - s - s r - ]
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20 < E < 50 GeV residual (four templates)
180 90 0 -90 -180 -90-4504590 -0.3580.894 [ k e V c m - s - s r - ] Fig. 8.—
The same as Figure 7 but for a FWHM smoothing of 10 ◦ . Smoothing the residuals at this scale demonstrates that the hazeis a robust feature and, in particular, is not the consequence of single photon fluctuations at high energies. While the template-correlated spectra and residualmaps are useful for identifying separate components, forthe purposes of comparing the map intensities to a modelfor the physical mechanisms, we now generate total in-tensity spectra in several regions of interest. We definethree key regions: a “haze region” south of the GC ,the “four corners” region from Cholis et al. (2009b), anda Galactic plane region used by Porter (2009).The spectrum of each region is shown (Figure 15),with the background spectrum from Figure 12 subtractedfrom the other spectra to remove any isotropic compo-nent. The inner Galaxy region clearly shows the low en- The region south of the GC is greatest interest for studying themicrowave and gamma-ray haze. This is because, north of the GC,the microwave maps from WMAP include bright free-free emissionfrom ζ Oph, and spinning dust emission from ρ Oph, both of whichare bright enough to leave substantial residuals, even though theyare relatively well subtracted by the template fitting described inDobler & Finkbeiner (2008). South of the Galactic center there aresome small dust and gas features that should provide some signalin the gamma-ray map, but the situation is much simpler. ergy behavior characteristic of π emission (though it isimportant to note that there may be significant emissionfrom unresolved point sources such as pulsars in this re-gion which have a similar spectral shape; see AppendixA and Abdo et al. 2009c). At high energies however,there is a significant excess which is not expected for π emission (cf., Figure 2). The spectrum of this excess issimilar to the spectrum derived for the haze templatefrom Figure 14 and is consistent with an IC signal froma hard electron population with energies >
10 GeV. Theevidence for this excess is more pronounced in the hazeand four corners region. Lastly, we take the template es-timate of π emission in the haze region from the Type 3fits and subtract it from the total emission. This revealstwo clear features: a bump centered on roughly 1-2 GeVthat is likely due to either bremsstrahlung from a lowenergy electron component or emission from unresolvedpulsars, and a hard tail above ∼
10 GeV that is the ICsignal from the haze electrons.1 -1.1312.828 [ k e V c m - s - s r - ]
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180 90 0 -90 -180 -90-4504590 -0.3580.894 [ k e V c m - s - s r - ] Fig. 9.—
The same as Figure 7 but using the 1-2 GeV map instead of the SFD dust map to trace π emission. The clear haze residualseen, particularly at high energies, indicates that the gamma-ray haze is not due to shortcomings of the SFD template resulting fromvariations in the proton cosmic ray density. These variations, as well as line of sight gas density effects, are automatically included in the1-2 GeV template. Comparison to the Microwave Haze
Both the morphology and the relatively hard spectrumof the gamma-ray haze motivate a common physical ori-gin with the WMAP haze. We now provide a simpleestimate of the microwave and gamma-ray signals froma population of hard electrons in the inner Galaxy, todemonstrate that the magnitudes and spectral indices ofthe two signals are consistent for reasonable parametervalues.We consider a steady-state electron spectrum describedby a power law, dN/dE ∝ E − α , with a high-energy cutoffat 1 TeV (here the cutoff is implemented as a step func-tion, not an exponential fall-off; of course this is onlyan approximation to the true spectrum). This choiceis motivated by the local measurement of the cosmic rayelectron spectrum by Fermi (Abdo et al. 2009b). We con-sider a region ∼ ∼ ◦ below the Galactic plane,and compute the corresponding synchrotron and IC spec-tra. The WMAP Haze was estimated to have a spec-trum I ν ∝ ν − β , β = 0 . − .
67 (Dobler & Finkbeiner2008), corresponding approximately to an electron spec-tral index of α ≈ . − .
4; Figure 16 shows our re-sults for a magnetic field of 10 µ G, and electron spectralindices α = 2 −
3. This field strength is appropriatefor an exponential model for the Galactic B -field inten-sity, | B | = | B | e − z/z s , with B ≈ − µ G (whichseems reasonable; see e.g. Ferriere (2009) and referencestherein) and scale height z s ≈ α ≈ − .
5, consistent with the spectrum of the WMAP2 residual + haze template -50 0 50b [deg]-0.50.00.51.01.52.0 E d N / d E x [ G e V / c m / s / s r ] -15.0 < l < 15.0 residual -50 0 50b [deg]-0.50.00.51.01.52.0 E d N / d E x [ G e V / c m / s / s r ] -15.0 < l < 15.02 < E < 5 GeV5 < E < 10 GeV10 < E < 20 GeV20 < E < 50 GeV residual + haze template -50 0 50l [deg]-0.50.00.51.01.52.0 E d N / d E x [ G e V / c m / s / s r ] -20.0 < b < -10.0 residual -50 0 50l [deg]-0.50.00.51.01.52.0 E d N / d E x [ G e V / c m / s / s r ] -20.0 < b < -10.02 < E < 5 GeV5 < E < 10 GeV10 < E < 20 GeV20 < E < 50 GeV Fig. 10.—
Top left:
The haze amplitude (Type 3 residual map plus haze template) as a function of Galactic latitude for four differentenergy ranges. The data are binned in steps of 0.055 in sin b , i.e. roughly 4 ◦ bins near the plane. The plot shows that haze amplitude hasroughly the same fall off with b ( ∼ ◦ ) in all energy ranges. Top right:
The same but for the Type 3 residual map.
Bottom left and right: the same as the top left and right, but as a function of ℓ for a fixed range of b . The haze profile clearly falls off more quickly with ℓ thanwith b indicating a profile elongated in the b direction. Haze.
Comments on Haze Morphology
Although a detailed analysis of the possible sources ofthe
Fermi haze are beyond the scope of this paper, a fewsimple comments are in order. First, the profile is notwell described by a disk source. While quantifying thisis a subtle task, the success of the template makes thispoint clear. There are many possibilities to explain theoblong shape, should that persist in future data. For in-stance, AGN jets and triaxial DM profiles could both pro-duce signals of this shape. Even approximately sphericalinjection could yield such a signal, should the diffusionbe considerably anisotropic. That said, while one mighthave attempted to invoke, e.g., rapid and significant lon-gitudinal variation of the magnetic field to explain the microwave haze with a disk-like electron injection pro-file, such approaches are no longer tenable (and moreoveralready had significant tension with an understanding ofthe Haslam synchrotron maps). The presence of this fea-ture in both gamma rays and microwaves demonstratesthat the electrons themselves do not follow a disk-likeinjection profile. Furthermore, we emphasize that theangular scale of the haze is very large, roughly 25-40 ◦ in b . This region of the sky is far from the Galactic disk orthe very GC where complications from the central blackhole, other point sources, or disk-like pulsars could com-plicate the analysis. DISCUSSION/CONCLUSIONS
We have presented full sky maps generated from pho-ton events in the first year data release of the
FermiGamma-Ray Space Telescope (see Appendix B for data3 [ k e V c m - s - s r - ]
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20 GeV < E < 50 GeV residual
180 90 0 -90 -180 -90-4504590 -0.3580.894 [ k e V c m - s - s r - ] Fig. 11.—
The same as Figure 3 but using the official
Fermi team Galactic diffuse model. The strong haze residual in the right handpanels shows that the haze is not included in the model. Since the IC emission in the model was obtained with GALPROP, this indicatesthat variation in the ISRF with position in the Galaxy cannot account for the haze emission. In addition, the haze morphology is notreproduced by disk-like injection of electrons, nor by the cosmic ray propagation model employed by GALPROP. TABLE 1
E range Energy background χ ν (GeV) (GeV) ( × − GeV/cm /s/sr)0 . − . . . ± .
187 86 . . − . . . ± .
190 76 . . − . . . ± .
181 51 . . − . . . ± .
157 27 . . − . . . ± .
119 10 . . − . . . ± .
069 2 . . − . . . ± .
098 4 . . − . . . ± .
068 1 . . − . . . ± .
078 0 . . − . . . ± .
125 1 . . − . . . ± .
199 1 . . − . . . ± .
205 1 . Note . — The background is tabulated in each energy binfor 8 polar ( | b | > ◦ ) regions after point source masking. Theuncertainty is the RMS of the 8 regions, not the uncertaintyin the mean, which is √ σ p , which for low E is much smaller. To test the significance of backgroundvariation, we compute χ ν = h σ /σ p i , averaging over the 8regions. There is no strong indication of anisotropy at highlatitude for E > -7 -6 -5 B a ck g r ound E d N / d E [ G e V c m - s - s r - ] Eight high-latitude regionsMean of eight regionsdN/dE ∝ E -2.45 Fig. 12.—
Background spectrum, including gamma-rays andparticle backgrounds. The background is tabulated in each energybin for 8 high-latitude polar ( | b | > ◦ ) regions after point sourceremoval (dotted gray lines). The mean of the 8 regions is shownwith a solid black line and the uncertainty is the RMS of the 8 re-gions, not the uncertainty in the mean, which is √ dN/dE ∝ E − . model for the unresolved back-ground is shown with a dot-dashed line. TABLE 2
Region ℓ range b rangeInner Galaxy | ℓ | < ◦ | b | < ◦ Haze | ℓ | < ◦ − < b < − ◦ < | ℓ | < ◦ < | b | < ◦ Note . — Regions for which the total gamma-ray intensity is evaluated (see also Figure 15). processing details).Using a template fitting technique, we have approx-imated both the spectrum and morphology of the wellknown gamma-ray emission components at
Fermi en-ergies. The SFD dust map was used to trace the π decay gammas generated by collisions of cosmic ray pro-tons with the ISM, while the Haslam 408 MHz map wasused to trace inverse Compton (IC) scattered photonsfrom interactions of supernova shock-accelerated elec-trons ( ∼ −
10 GeV) with the interstellar radiation field(ISRF). Bremsstrahlung radiation, generated by interac-tions of these electrons with the ISM, should be approx-imately traced by some combination of these two maps.Although our template fitting technique is subject to sig-nificant uncertainties due to uncertain line of sight gasand CR distributions, a robust positive residual has beenidentified.This excess diffuse emission is centered on the Galac-tic center, and can be parameterized by a simple two-dimensional Gaussian template ( σ ℓ = 15 ◦ , σ b = 25 ◦ ).The template-correlated spectrum of this emission is sig-nificantly harder than either π emission or IC fromsofter electrons, whose fitted spectra agree well withmodels. This harder spectrum coupled with the distinctspatial morphology of the gamma-ray and microwavehaze are evidence that these electrons originate from a separate component than the softer SN shock-acceleratedelectrons.The gamma-ray excess is almost certainly the ICcounterpart of the microwave haze excess described byFinkbeiner (2004a) and Dobler & Finkbeiner (2008). Al-though it is still possible that a significant fraction isprompt photons from WIMP annihilations (e.g. the 200GeV wino advocated by Grajek et al. 2009) such expla-nations are difficult to reconcile with the spatial simi-larity to the WMAP haze (see Figure 4). The simplesthypothesis is that the signal is mainly IC from the sameelectrons that produce the WMAP haze synchrotron.This addresses the stubborn question about the ori-gin of the WMAP haze. Until recently, it has been ar-gued that the WMAP haze had alternative explanations,such as free–free emission from hot gas or spinning dipoleemission from rapidly rotating dust grains. However, theexistence of this IC signal proves that the microwave hazeis indeed synchrotron emission from a hard electron spec-trum. Fermi
LAT photon data are contaminated by particleevents, especially at high energies. We have taken care toaccount for the isotropic background resulting from ex-tragalactic sources, cosmic ray contamination, and heavynuclei contamination and found that this background,though significant, is below the observed IC excess evenup to 100 GeV.
Particle contamination is extremely un-likely to mimic the observed signal.
The LAT collaboration continues to refine the cutsused to define “diffuse class” events, and plans to re-lease a cleaner class of events in coming months. This,along with a new public version of GALPROP, includingupdated ISRF models, will allow a more sophisticatedanalysis than that presented in this paper. We eagerlyawait the release of these software and data products.The spectrum and morphology of both the microwaveand gamma-ray haze constrain explanations for thesource of these electrons. There have been speculations5 π s pe c t r u m [ E d N / d E , a r b . un i t s ] Cross-correlation π spectrumGALPROP π model SFD template π s pe c t r u m [ E d N / d E , a r b . un i t s ] Cross-correlation π spectrumGALPROP π model Fig. 13.—
Left:
The π spectrum derived using the cross-correlation technique defined in § Fermi π template. The dotted Gray lines are the cross-correlation spectra in several different regions of the sky and the solid black line is themean of those spectra. Error bars on the cross-correlation spectrum are defined as the variance in the values for the different regions. Thedot-dashed line is the π spectrum output from a GALPROP model (shown here with arbitrary normalization). Right:
The same butusing the SFD dust map as a template. that the microwave haze could indicate new physics, suchas the decay or annihilation of dark matter, or new as-trophysics, such as a GRB explosion, an AGN jet, or aspheroidal population of pulsars emitting hard electrons.We do not speculate in this paper on the origin of thehaze electrons, other than to make the general observa-tion that the roughly spherical morphology of the hazemakes it difficult to explain with any population of diskobjects, such as pulsars. The search for new physics – oran improved understanding of conventional astrophysics– will be the topic of future work.
Acknowledgments:
We acknowledge helpful conversa-tions with Elliott Bloom, Jean-Marc Casandjian, CarlosFrenk, Isabel Grenier, Igor Moskalenko, Simona Mur-gia, Troy Porter, Andy Strong, Kent Wood. This workwas partially supported by the Director, Office of Sci-ence, of the U.S. Department of Energy under Con-tract No. DE-AC02-05CH11231. NW is supported byNSF CAREER grant PHY-0449818, and IC and NW aresupported by DOE OJI grant Available at http://idlastro.gsfc.nasa.gov SFD -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] GALPROP π decayGALPROP brem Haslam -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] GALPROP ICGALPROP brem
Haze -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Uniform -7 -6 -5 E d N / d E [ G e V / c m / s / s r ] Fig. 14.—
Correlation coefficients for the templates used in the Type 3 template fit (see § Upper left:
SFD-correlated spectrumwhich roughly traces π emission. Upper right:
Haslam-correlated emission which traces the soft IC and bremsstrahlung component.
Lower left: haze template-correlated emission. This component has a notably harder spectrum than both the SFD- and Haslam-correlatedspectra or their model shapes (dashed lines, cf., Figure 2), indicating a separate component. The dashed lines in the upper two panels area GALPROP estimate of π decay (left) and IC emission (right). The GALPROP estimate of bremsstrahlung emission is shown in bothpanels. Lower right: the uniform template-correlated spectrum which traces the isotropic background. Here the dashed line is the resultfrom Figure 12. This high latitude estimate is higher than the uniform template estimate likely because the π emission is non-zero athigh latitudes and leaks into our measured background. This is less of an issue for the uniform template which uses the morphological (i.e.,uniform) information. -7 -6 -5 -4 E d N / d E [ G e V c m - s e c - s r - ] Inner Galaxy (|l| < 30, |b| < 5)Four Corners (5 < |l| < 10, 5 < |b| < 10)Haze (-15 < l < 15, -30 < b < -10Haze - π (SFD-correlated) Fig. 15.—
Total intensity spectra in three regions of interest(solid, dashed, dot-dashed; see Table 2). All three show the charac-teristic π spectrum at low energies as well as an excess at higherenergies with roughly the same spectrum as the haze spectrumderived from the Type 3 template fits. Furthermore, subtractingthe template π spectrum in the haze region (dot-dot-dot-dashed)yields two features, one centered on ∼ ∼
50 GeV. The lower energy feature is likely either bremsstrahlungfrom a low energy electron population (like those accelerated by SNshocks) or emission from unresolved pulsars. The higher energy tailis the IC signal from the haze electrons. γ [GeV]10 -8 -7 -6 -5 E d N / d E [ G e V c m - s - s r - ] I ν [ kJy / s r ] WMAP 23 GHz
Fig. 16.—
The estimated spectrum of IC gamma rays ( upperpanel ) and synchrotron radiation ( lower panel ) originating froma hard electron spectrum along a line of sight 2 kpc above theGalactic center (i.e. b ≈ ◦ ). The steady-state electron spectrumis taken to be a power law, dN/dE ∝ E − α , with index α = 2( solid ), 2.5 ( dashed ) and 3 ( dotted ). In all cases the spectrum has acutoff at 1 TeV. The interstellar radiation field model is taken fromGALPROP, and the magnetic field is set to be 10 µ G. The datapoints in the upper panel show the magnitude of the
Fermi
Hazeaveraged over | b | = 10 −
18, for | l | <
15, as a function of energy,taken from Figure 10. The highest two bins contain 3 σ upperlimits rather than data points with 1 σ error bars, due to the largeuncertainties in the Haze amplitude at those energies. The datapoint in the lower panel shows the magnitude of the WMAP Hazeaveraged over b = −
10 to −
18, for | l | <
10, in the 23 GHz K-band(the overall normalization is chosen to fit this value), and the grayarea indicates the range of synchrotron spectral indices allowed forthe WMAP Haze by Dobler & Finkbeiner (2008). REFERENCESAbdo, A. A., et al. 2009a, Astrophys. J., 700, 597—. 2009b—. 2009cAckermann, M. 2009Belikov, A. V., & Hooper, D. 2009Blattnig, S. R., Swaminathan, S. R., Kruger, A. T., Ngom, M., &Norbury, J. W. 2000, Phys. Rev., D62, 094030Borriello, E., Cuoco, A., & Miele, G. 2009, Astrophys. J., 699, L59Casandjian, J., Grenier, I., & for the Fermi Large Area TelescopeCollaboration. 2009, ArXiv e-printsCholis, I., Dobler, G., Finkbeiner, D. P., Goodenough, L., &Weiner, N. 2009a, Phys. Rev., D80, 123518Cholis, I., et al. 2009bCirelli, M., & Panci, P. 2009, Nucl. Phys., B821, 399Dixon, D. D., Hartmann, D. H., Kolaczyk, E. D., Samimi, J., Diehl,R., Kanbach, G., Mayer-Hasselwander, H., & Strong, A. W. 1998,New Astronomy, 3, 539Dobler, G., & Finkbeiner, D. P. 2008, ApJ, 680, 1222Ferriere, K. 2009Fichtel, C. E., Hartman, R. C., Kniffen, D. A., Thompson, D. J.,Ogelman, H., Ozel, M. E., Tumer, T., & Bignami, G. F. 1975,ApJ, 198, 163Finkbeiner, D. P. 2004a, Astrophys. J., 614, 186—. 2004bGehrels, N., & Michelson, P. 1999, Astropart. Phys., 11, 277Gilfanov, M. 2004, Mon. Not. Roy. Astron. Soc., 349, 146Grajek, P., Kane, G., Phalen, D., Pierce, A., & Watson, S. 2009,Phys. Rev., D79, 043506Grimm, H. J., Gilfanov, M., & Sunyaev, R. 2003, Mon. Not. Roy.Astron. Soc., 339, 793 Haslam, C. G. T., Salter, C. J., Stoffel, H., & Wilson, W. E. 1982,A&AS, 47, 1Hooper, D., Finkbeiner, D. P., & Dobler, G. 2007, Phys. Rev., D76,083012Kim, D.-W., & Fabbiano, G. 2004, Astrophys. J., 611, 846Kniffen, D. A., & Fichtel, C. E. 1981, ApJ, 250, 389Large, M. I., Quigley, M. J. S., & Haslam, C. G. T. 1962, MNRAS,124, 405Linden, T., & Profumo, S. 2010Meade, P., Papucci, M., Strumia, A., & Volansky, T. 2009Padovani, P., Giommi, P., Landt, H., & Perlman, E. S. 2007,Astrophys. J., 662, 182Porter, T. 2009Porter, T. A., & Strong, A. W. 2005Regis, M., & Ullio, P. 2009Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, Astrophys. J.,500, 525Slatyer, T. R., & Finkbeiner, D. P. 2009Smialkowski, A., Wolfendale, A. W., & Zhang, L. 1997,Astroparticle Physics, 7, 21Strong, A. W. 1984, Advances in Space Research, 3, 87Strong, A. W., Moskalenko, I. V., & Ptuskin, V. S. 2007, Ann. Rev.Nucl. Part. Sci., 57, 285Strong, A. W., Moskalenko, I. V., & Reimer, O. 2000, Astrophys.J., 537, 763Voss, R., & Gilfanov, M. 2006, Astron. Astrophys., 447, 71Zhang, J., et al. 2009, Phys. Rev., D80, 023007APPENDIX
UNRESOLVED POINT SOURCES
In this section we explore the possibility that the diffuse excess discussed in this work (the
Fermi haze) couldoriginate from a large number of unresolved point sources. The limit where the contribution from unresolved pointsources is dominated by emission from many very faint ( ≪ ∼ S : dN/dS ∝ S − α , with S min < S < S max . Smaller values of α , and larger values of S max and S min , correspondto a larger fraction of bright point sources and thus strengthen any upper bounds on the flux fraction from pointsources. Examining known point source populations (of AGN and X-ray binaries) generally yields spectral indices α ∼ . − .
2, although at high luminosities steeper power laws with α ∼ . α ∼ . α = 2 . S max = 10, as pessimistic benchmark parameters to provide a robust upper bound.This power law must break at some low-luminosity cutoff to avoid divergences if α >
2; we will display the statisticallimits obtained for S min = 0 . . Fermi
LAT data in the haze region ( | l | < − < b < − r , and (2) the fraction of 10 randomly distributed circles of radius r whichcontain no events (“empty circles”). If r is chosen appropriately (i.e. r ∼ PSF) then the ratio of these two quantities, R ≡ “isolated”/“empty,” is related to the fraction of counts arising from unresolved point sources. If the averagenumber of events per circle of radius r , denoted λ , is greater than 1, then we redefine “isolated” events to be thosewith fewer than λ neighbors, and “empty circles” to be those containing fewer than λ events. Neighbors are foundefficiently using the publicly available IDL routine spherematch , and we take the test radius r to be equal to theestimated 1 σ value for the LAT PSF, corresponding to 39% flux containment (our results are not very sensitive tothis choice). We apply this test separately to the diffuse class data in each of the energy bins in Fig. 1, removing eventswith a large zenith angle as described previously, and calibrate our results via Monte Carlo simulations. The smallerthe PSF, the better the bounds (the PSF is an input to our Monte Carlo calibration); since the PSF size decreaseswith increasing energy, and is greater for back-converting events compared to front-converting events, for each energybin we take the PSF for back-converting events at the minimum energy of the bin, in order to set robust limits. The energy-dependent PSF for the LAT is taken from .The radius of 68% containment used by the
Fermi
Collaboration would in the case of a Gaussian PSF be r = 1 . σ .
10 100Energy (GeV)0.00.20.40.60.81.0 % c on f i den c e li m i t on po i n t s ou r c e c on t r i bu t i on Energy PSF 1 σ Fig. 17.—
Upper limits on the fraction of diffuse class events originating from unresolved point sources, in the
Fermi haze region( | l | < − < b < − α = 2 . S max = 10. The dotted and dashed lines indicate the bounds with a steeper luminosity function α = 1 .
8, for S min = 1and S min = 0 . σ for the detector point spread function used in the Monte Carlo calibration, asconservatively estimated for each energy bin. At low energies we find values of R consistent with a significant point source component (although the point sourcefraction cannot be precisely determined without knowing the luminosity function). Above 10 GeV, however, the valueof R is consistent with entirely diffuse emission. In the 50 −
100 GeV bin, low statistics nonetheless allow the haze-correlated fraction of the emission to be explained entirely by point sources with 0.1+ expected counts/year (since inthis bin the haze-correlated flux in this region corresponds to ∼
30 photons), but at ∼ −
50 GeV there is a clearexcess over the 95% confidence limits on the unresolved point source contribution, for S min = 0 . , ∼ / it seems very unlikely that the hard spectral shape of the Fermi haze could be due to point source contamination over the entire relevant energy range.
FERMI
FULL-SKY MAP PROCESSING AND DATA RELEASE
In this section we describe full-sky maps generated from photon events in the first year data release of the
FermiGamma-Ray Space Telescope . These maps are corrected for exposure, point source masked, and are smoothed to aGaussian PSF, usually of 2 ◦ FWHM. The lowest energy maps are smoothed to 3 ◦ or 4 ◦ . For convenience, we providetwo sets of energy bins: 12 logarithmically spaced bins for use in spectral analyses (“specbin”) and 8 somewhat largerbins with better signal/noise for visual inspection (“imbin”).Although the maps were generated from a public Fermi data release, the maps are not an official LAT data release,and the procedure used to make them has not been endorsed by the LAT collaboration.Event Selection and Binning
The LAT is a pair-conversion telescope, in which incoming photons strike layers of tungsten and convert to e + e − pairs, which are then tracked (to determine direction) on the way to a calorimeter (to determine energy). The firstyear P6 V3 DIFFUSE data file contains records of 15,878,650 events, providing the time, energy, arrival direction, (withrespect to the spacecraft, and in celestial coordinates), and zenith angle for each event. Events are divided into 3classes, using a number of cuts to separate photon events from particle background. “Class 3” rejects the largestfraction of background contamination, and these events are used to study diffuse emission. We also require the zenith0angle be less than 105 ◦ to exclude most atmospheric gammas. By choosing to use these cuts, we study the events mostlikely to be real gamma rays, at the expense of a smaller effective area. These cuts discard roughly 3/4 of the signal,but vastly reduce the noise.The class 3 events are then binned in energy and into spatial pixels to produce counts maps. We use the hierarchicalequal-area isolatitude pixelization (HEALPix), a convenient iso-latitude equal-area full-sky pixelization widely used inthe CMB community. Exposure maps
Because the exposure on the sky is non-uniform, we generate an exposure map using the gtexpcube tool developedby the LAT team. The exposure for each pixel is the LAT effective area at each θ (angle with respect to the LATaxis) summed over the livetime of the LAT at that θ , and has units of cm s. The exposure map spatially modulatesthe signal ±
20% from raw photon counts and is slightly energy dependent for photon energies
E > ◦ in latitude and longitude is adequate, as neighboring bins haveexposure differences of < . e + e − pair in any of the layers, and events are labeled “front” or“back” accordingly. The effective area as a function of energy is different for front and back events, so we use the“ P6 V3 DIFFUSE::FRONT ” and “
P6 V3 DIFFUSE::BACK ” instrumental response functions, respectively. Maps of countsare divided by the exposure and pixel solid angle to produce intensity maps (cts/s/cm /sr). The “combined” mapsare simply an exposure-weighted linear combination of the front and back intensity maps. The full-sky Fermi mapsare displayed in Figure 1 along with the exposure map and mask.
Smoothing
In our analysis we wish to compare
Fermi maps at different energies to each other, and to other templates. In orderto match the PSFs of all these maps, we smooth each map by an appropriate kernel. On average, the front and backconverting events have different PSFs (by a factor of ∼ ◦ ) to produce “front” and “back” smoothed maps (which can be averaged to obtain “combined” smoothedmaps as above).For the PSF, we use a simple fit to the radius of 68% flux containment (in degrees): r = (( c E β ) α + c α ) /α (B1)where E is in GeV, α = 1 . β = − .
83, and ( c , c ) = (0 . , .
04) and (0 . , .
09) for front- and back-convertingevents, respectively. This yields r = c E β at low E and r = c at high E . For simplicity, we assume the PSF isa Gaussian so that the FWHM, f = 2 r ≈ . r . The “raw” FWHM of a counts map is then taken to be Eq. B1evaluated at E mean = √ E E , where E < E < E for the events in the map. In order to smooth to the target PSF(usually f targ = 2 ◦ ), a Gaussian smoothing kernel of size f kern is used such that f kern = q f − f . (B2)For the lowest energy maps ( E < f raw is large, we take f targ = 3 or 4 ◦ . Point Source Mask
The point source mask (Figure 1) contains the 3-month 10 σ point source catalog, plus the LMC, SMC, Orion, andCen A. The mask radius for point sources is taken to be the 95% containment radius for the lowest energy event inthe energy bin. For unsmoothed maps, both the counts map and the exposure map are multiplied by the mask. Forsmoothed maps, counts and exposure are multiplied by the mask, then smoothed, then divided. Pixels where thesmoothed masked exposure drops below 25% of the mean unmasked exposure are replaced with zeros. In cases wherethe mask radius is much smaller than the smoothing radius, the mask is “smoothed away.” In other cases, maskedpixels are visible in the smoothed maps. Because of the energy dependence of the mask radius, the effective maskchanges with energy, so care must be taken in cross comparisons between energy bins, especially within a few degreesof the Galactic plane. Data Release All LAT maps described in this section are available in the HEALPix pixelization on the web. Maps of front- andback- converting events are available, as well as the combined maps. All three are available smoothed and unsmoothed,and with and without point source masking, for a total of 12 maps at each energy. Both the imbin and specbin energybinnings are available, for a total of 240 FITS files. Grayscale and color jpegs are also available to provide a quickoverview. Software used to make the maps is available on request. HEALPix software and documentation can be found at http://healpix.jpl.nasa.gov , and the IDL routines used in this analysis areavailable as part of the IDLUTILS product at http://sdss3data.lbl.gov/software/idlutils . http://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation http://fermi.skymaps.info Background -3 -2 -1 0 1 2 3 χ χ ): -0.058245Stdev( χ ): 1.001867 SFD dust -2 0 2 χ χ ): -0.042479Stdev( χ ): 0.997240 Haslam 408 MHz -3 -2 -1 0 1 2 3 χ χ ): 0.042587Stdev( χ ): 1.021746 "Haze" -3 -2 -1 0 1 2 χ χ ): 0.019846Stdev( χ ): 1.006392 bin02-fwhm120-shift000/mock-results.fits Nmock:1000 model fwhm (arcmin):120 shift (deg): 0 Background -3 -2 -1 0 1 2 3 χ χ ): 0.030324Stdev( χ ): 1.002813 SFD dust -4 -3 -2 -1 0 1 2 χ χ ): -0.514531Stdev( χ ): 0.958451 Haslam 408 MHz -2 0 2 4 χ χ ): 0.267902Stdev( χ ): 1.012980 "Haze" -3 -2 -1 0 1 2 3 χ χ ): -0.275034Stdev( χ ): 1.020841 bin02-fwhm060-shift000/mock-results.fits Nmock:1000 model fwhm (arcmin): 60 shift (deg): 0 Fig. 18.—
Left panel: a 2 ◦ FWHM mock map fit to a 2 ◦ model. Right panel: a 1 ◦ mock map is smoothed to a 2 ◦ PSF and then fitto the 2 ◦ model. In each case, 1000 realizations are computed, and the histograms of χ are shown for the four parameters. In each case,the χ histogram has a mean near zero and RMS near 1, indicating that the error analysis is correct, even in the case of a smoothed map.Biases introduced are small ( ≪ σ ) for the case shown, and are relatively even less important at higher energy. POISSON LIKELIHOOD ANALYSIS
Ideally the spatial templates (dust map, synchrotron map, etc.) going in to the Type 3 likelihood analysis ( § Fermi dataproperly. In other words, for each set of model parameters, we compute the log likelihoodln L = X i [ k i ln µ i − µ i − ln( k i !)] , (C1)where µ i is the synthetic counts map (i.e., linear combination of templates times exposure and mask) at pixel i , and k is the map of observed counts. The µ i term depends only on the model parameters, and is not affected by smoothingthe data. The ln( k i !) term does not depend on the model parameters, and so it cannot affect the best-fit model oruncertainties. Furthermore, there is no problem evaluating the likelihood for fractional k using the gamma function.So the k i ln µ i is the only potentially problematic term.In order to investigate the effects of smoothing, we generate each mock map by taking a linear combination oftemplates (including the uniform background), multiplying it by the exposure and mask to obtain a map of predictedcounts, and Poisson sampling it in HEALPix pixels. This map is then passed to our parameter estimation code toobtain the best fit values and uncertainties for the 4 parameters. Repeating this procedure for 1000 mock maps, wecompute χ = (cid:18) fit − true σ (cid:19) (C2)for each parameter and plot the histograms (Figure 18). An unbiased fit corresponds to h χ i = 0 and a correctuncertainty estimate corresponds to stdev( χ ) = 1. The uncertainties appear to be correctly estimated and the biasis small. Note that this behavior is different from an exp( − χ /
2) likelihood on a smoothed map: in that case thecorrelated noise induced by the smoothing must be taken account of carefully.The above analysis was done for a range of energy bins with similar results. The analysis was also completely redonewith a χ2