A Method for Exploring Systematics Due to Galactic Interstellar Emission Modeling: Application to the Fermi LAT SNR Catalog
aa r X i v : . [ a s t r o - ph . H E ] A p r th Fermi Symposium : Monterey, CA : 28 Oct-2 Nov 2012 A Method for Exploring Systematics Due to Galactic InterstellarEmission Modeling: Application to the
Fermi
LAT SNR Catalog
F. de Palma
INFN Sezione di Bari, 70126 Italia
T. J. Brandt
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
G. Johannesson
Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland
L. Tibaldo
Kavli Institute for Particle Astrophysics & Cosmology, SLAC National Accelerator Laboratoty, USA on behalf of the
Fermi
LAT collaboration.
Galactic interstellar emission contributes substantially to
Fermi
LAT observations in the Galactic plane, wherethe majority of Supernova Remnants (SNRs) are located. We have developed a method to explore somesystematic effects on SNRs’ properties caused by interstellar emission modeling. We created eight alternativeGalactic interstellar models by varying a few input parameters to GALPROP, namely the height of the cosmicray propagation halo, cosmic ray source distribution in the Galaxy, and atomic hydrogen spin temperature.We have analyzed eight representative candidate SNRs chosen to encompass a range of Galactic locations,extensions, and spectral properties using the eight different interstellar emission models. The models were fittedto the LAT data with free independent normalization coefficients for the various components of the model alongthe line of sight in each region of interest. We will discuss the results and compare them with those obtainedwith the official LAT interstellar emission model.
1. INTRODUCTION
Galactic interstellar γ -ray emission is producedthrough interactions of high-energy cosmic ray(CR) hadrons and leptons with interstellar gasvia nucleon-nucleon inelastic collisions and electronBremsstrahlung, and with low-energy radiation fields,via inverse Compton (IC) scattering. Such interstellaremission accounts for more than 60% of the photonsdetected by the Fermi
Large Area Telescope (LAT)and is particularly bright toward the Galactic disk.In this paper, we present our ongoing effort to ex-plore the systematic uncertainties due to the model-ing of Galactic interstellar emission in the analysis of
Fermi
LAT sources, with particular emphasis on itsapplication to the 1 st Fermi
LAT Supernova Remnant(SNR) Catalog. We compare the results of analyz-ing sources with eight alternative interstellar emissionmodels (IEMs), described in Section 2, to the sourceparameters obtained with the standard model in Sec-tion 3. In Section 4 we discuss the future applicationof this method to the SNR Catalog.
2. INTERSTELLAR EMISSION MODELS
In order to estimate the systematic uncertainty in-herent in the choice of standard interstellar emissionmodel (IEM) in analyzing a source, we have developedeight alternative IEMs. By comparing the results ofthe source analysis using these eight alternative mod-els to the standard model, we can approximate thesystematic uncertainty therefrom.
The standard IEM for
Fermi
LAT data analysiswas developed by the collaboration using the sim-ple assumption that energetic CRs uniformly pene-trate all gas phases in the interstellar medium. Un-der this assumption, the Galactic interstellar γ -rayintensities can be modeled as a linear combination ofgas column densities and an inverse Compton (IC)intensity map as a function of energy. The gas col-umn densities are determined from emission lines ofatomic hydrogen (H I ) and CO, the latter a surrogatetracer of molecular hydrogen, and from dust opticaldepth maps used to account for gas not traced bythe lines. To account for a possible large scale gra-dient of CR densities, the gas column density mapswere split into 6 Galactocentric rings using the emis-sion lines’ Doppler shift. The IC map is obtained us-ing GALPROP to reproduce the direct CR measure-ments with a realistic model of the Galactic interstel-lar radiation field (ISRF), as was done in Porter et al. [2008]. To account for some extended remaining resid-uals, notably Loop I Casandjian et al. [2009] and theso-called Fermi bubbles Su et al. [2010], the standardIEM includes them as additional templates. H I column densities are extracted from the radio data usinga uniform value for the spin temperature (200 K). The GALPROP code has been developed over severalyears, starting with, e.g. Moskalenko and Strong [1998] andStrong and Moskalenko [1998]. eConf C121028 th Fermi Symposium : Monterey, CA : 28 Oct-2 Nov 2012
This IEM, along with sources in the 2FGL Cata-log Nolan et al. [2012] and an isotropic intensity ac-counting for the extragalactic γ -ray and instrumentalbackgrounds, was fit to two years of LAT data. Thisyielded best fit values of the linear combination co-efficients which can be interpreted as gas emissivitiesin the various Galactocentric rings and a renormaliza-tion for the IC model as a function of energy, as wellas the spectrum of the isotropic component. The ra-tio of CO to twice the H I emissivities and dark gas toH I emissivities are proportional to the CO-to-H anddust-to-gas ratios, respectively, under our simple as-sumption. Another explanation of this method of de-composing the γ -ray sky to create the standard modelmay be found in, e.g. Katagiri et al. [2011]. The stan-dard IEM is distributed as a cube summed over thecomponents which predicts the intensities of Galacticinterstellar γ -ray emission in a grid of directions andenergies with its accompanying isotropic model. Fur-ther description and details are available at the Fermi
Science Support Center . To explore the uncertainties related to the modelingof interstellar emission we generated eight alternativeIEMs, in particular probing key sources of systematicuncertainties by: • adopting a different model building strategyfrom the standard IEM, resulting in differentgas emissivities, or equivalently CO-to-H anddust-to-gas ratios, and including a different ap-proach for dealing with the remaining extendedresiduals; • varying a few important input parameters forbuilding the alternative IEMs: atomic hydrogenspin temperature (150 K and optically thin), CRsource distribution (SNRs and pulsars), and CRpropagation halo heights (4 kpc and 10 kpc); • and allowing more freedom in the fit by sepa-rately scaling the inverse Compton emission andH I and CO emission in 4 Galactocentric rings.The work in Ackermann et al. [2012a], using theGALPROP CR propagation and interaction code, wasused as a starting point for our model building strat-egy. The GALPROP output intensity maps associ-ated with H I , CO, and IC are then fit simultaneouslywith an isotropic component and 2FGL sources to2 years of Fermi
LAT data in order to minimize bias inthe a priori assumptions on the CR injection spectra http://fermi.gsfc.nasa.gov/ssc/data/access/lat/Model details/Pass7 galactic.html and the proton CR source distribution. The inten-sity maps associated with gas were binned into fourGalactocentric annuli (0 − − −
10 kpcand 10 −
30 kpc). The spectra of all intensity mapswere individually fit with log parabolas to the data,to allow for possible CR spectral variations betweenthe annuli for all H I and CO maps while the IC fitaccounts for spectral variations in the electron dis-tribution. We also included in the fit an isotropictemplate and templates for Loop I Casandjian et al. [2009] and the Fermi bubbles Su et al. [2010]. Thetemplate for Loop I is based on the geometrical modelof Wolleben [2007] while bubbles are assumed to beuniform with edges defined in spherical coordinatesby R = R | sin θ | , where θ is the polar angle.Ackermann et al. [2012a] explored some systematicuncertainties by varying input parameters. The H I spin temperature, CR source distribution, and CRpropagation halo height were found to be among thoseparameters which have the largest impact on the γ -ray intensity. The values adopted in this study togenerate the eight alternative IEMs were chosen to bereasonably extreme; we note that they do not reflectthe full uncertainty in the input parameters. Sepa-rately scaling the H I and CO emission in rings andthe IC emission permits the alternative IEMs to bet-ter adapt to local structure when analyzing particularsource regions. Figure 1 shows the relative differencebetween the standard model and one of the alterna-tive models (Lorimer CR source distribution with a4 kpc halo height, and 150 K H I spin temperature).Differences are particularly large along the Galacticplane, where SNRs are located.Finally, we note that this strategy for estimat-ing systematic uncertainty from interstellar emissionmodeling does not represent the complete range of sys-tematics involved. In particular, we have tested onlyone alternative method for building the IEM, and theinput parameters do not encompass their full uncer-tainties. Further, as the alternative method differsfrom that used to create the standard IEM, the result-ing uncertainties will not bracket the results using thestandard model. The estimated uncertainty does notcontain other possibly important sources of system-atic error, including uncertainties in the ISRF model,simplifications to Galaxy’s geometry, small scale non-uniformities in the CO-to-H and dust-to-gas ratiosand H I spin temperature non-uniformities, and un-derlying uncertainties in the input gas and dust maps.While the resulting uncertainty should be considereda limited estimate of the systematic uncertainty dueto interstellar emission modeling, rather than a fulldetermination, it is critical for interpreting the data,and this work represents our most complete and sys-tematic effort to date. eConf C121028 th Fermi Symposium : Monterey, CA : 28 Oct-2 Nov 2012
Fermi are shown as circleswhile point-like are shown as crosses.
3. ESTIMATING IEM SYSTEMATICS3.1. Analysis Method
We developed this method for estimating the sys-tematics from the interstellar emission model usingeight candidate SNRs chosen to represent the range ofspectral and spatial SNR characteristics in high andlow IEM intensity regions. Figure 1 shows the can-didate SNRs’ location on the sky, illustrating theirrange of Galactic longitude. The color indicates thosecandidates with a hard or soft index and the shapethe extension (pointlike or extended). The SNR can-didates are overlaid on a map of the relative differencebetween the standard IEM and one of the alternativeIEMs described in Section 2.We use the same analysis strategy to obtain all SNRcandidates’
Fermi
LAT parameter values with boththe standard and all eight alternative IEMs on 3 yearsof P7 V6SOURCE data Ackermann et al. [2012b] inthe energy range 1 −
100 GeV. We applied the standardbinned likelihood method , treating sources as follows.For each of the eight candidate SNRs, an extendedsource initially of the radio size and with a power law The standard
Fermi
LAT analysis description and tools canbe found here: http://fermi.gsfc.nasa.gov/ssc/data/analysis/ . (PL) spectral model either replaces the closest non-pulsar 2FGL source Nolan et al. [2012] within the ra-dio size or is positioned as a new source at the locationdetermined from radio observations Green [2009]. Allother 2FGL sources within the radio size which arenot pulsars are removed from the source model. Wefit the centroid and extension of the SNR candidatedisk as well as the normalization and PL index forthe source of interest and the five closest backgroundsources within 5 ◦ with a significance of & σ . Thisprocedure balances the number of degrees of freedomwith convergence and computation time requirements.Figure 2: Schematic representation of the H I andCO rings used for the split alternative IEMs crossedby lines of sight at various Galactic longitudes. Thering boundaries lie at 0 , , , ,
30 kpc from theGalactic center while the red dot marks the sunposition at 8 . Fermi
LAT IEM, we allow the normalization to varyand fix the accompanying standard isotropic model’snormalization. For each of the eight alternative mod-els, we use the corresponding isotropic model fixed toits value resulting from the fit to the all-sky data (seeSection 2). To better understand the effect of allowingfreedom in the H I and CO rings, we fit the alternativemodels in two ways: either with the rings’ normaliza-tions free (”split” models) or with the rings summedtogether, as given by the all-sky fit (see Section 2), andonly the total normalization free (”summed” mod-els). The summed alternative IEMs are thus closerto the standard IEM. For the split alternative IEMs,as shown in Figure 2, not all rings are crossed by alllines of sight. We thus fit only the two innermost H I and CO rings crossed by the line of sight to our regionof interest. The IC template is also free to vary whilethe isotropic component remains fixed. eConf C121028 th Fermi Symposium : Monterey, CA : 28 Oct-2 Nov 2012 (a) Flux for the eight candidate SNRs’ from 1 −
100 GeV. (b) Index for the eight SNR candidates from 1 −
100 GeV.
Figure 3: Results for each candidate SNR, averaging over the eight alternative IEMs separately for split (red)and summed (green) component models compared to the standard model solution (black). The error bars forresults using the alternative IEMs show the maximal range of the values given by the 1 σ statistical errors. To compare the results obtained using the eight al-ternative IEMs with the standard model results, weaverage each parameter’s eight values from the alter-native IEMs. Figure 3 shows the values for the fluxand index from fitting the data with the alternativeIEMs with the rings either split or summed. These arethen plotted along with the standard model results forall eight SNR candidates studied. We conservativelyrepresent the allowed parameter range with error barsshowing the maximal range for the alternative IEMs1 σ statistical errors.Figure 3 shows that the variation in value of the bestfit parameters obtained with the alternative IEMs islarger than the 1 σ statistical uncertainty. The im-pact of changing the IEM on the source’s parame-ters depends strongly on the source’s properties andlocation. As expected, the parameter values for thesource of interest are generally closer to the standardmodel results for the alternative IEMs with compo-nents summed rather than split. In many cases, theallowed parameter range represented by the 1 σ statis-tical errors for each of the alternative IEMs is largerwith the components split than summed. Also asnoted earlier, the alternative IEM results do not as arule bracket the standard model solution. We observethat some of the largest differences between the stan-dard and alternative IEM results for a single sourceare frequently associated with sources coincident withtemplates accounting for remaining residual emissionin the standard IEM (Section 2).SNR G347.3-0.5 proves an interesting source for un-derstanding the impact nearby source(s) can have on this type of analysis. In particular, our automatedanalysis finds a softer index and a much larger fluxfor SNR G347.3-0.5 than that obtained in a dedicatedanalysis Abdo et al. [2011]. Since the best fit radius(0 . ◦ ) is larger than that the X-ray data indicates(0 . ◦ ), the automated analysis’s disk encompassesnearby sources that are only used in the Abdo et al. [2011] model. Including this additional emission alsoaffects the spectrum, making it softer in this case thanthat found in the dedicated analysis. Given Fermi
LAT’s both increasing point spread function and num-ber of sources with decreasing energy as well as thepredominance of diffuse emission at lower energies, wenote that nearby sources may play a greater role ifextending this method below the 1 GeV minimum en-ergy examined here.
To identify which, if any, of the three IEM in-put parameters (H I spin temperature, CR source dis-tribution, and CR propagation halo height) has thelargest impact on the fitted source parameters, wemarginalize over the other parameters and examinethe relative ratio of the averaged input parametervalues to the values’ dispersion. For a fitted sourceparameter a , such as flux and a GALPROP inputparameter set P = { i, j } , e.g. spin temperature T s = {
150 K , K } , this becomes: | < a i > − < a j > | max ( σ a,i , σ a,j ) (1) eConf C121028 th Fermi Symposium : Monterey, CA : 28 Oct-2 Nov 2012
T s = {
150 K , K } divided by the maximum RMS.where σ a is the rms of the parameter a for a given in-put parameter value P . Figure 4 shows this schemat-ically. A ratio ≥
4. FUTURE APPLICATIONS
In this work we explored the effect of using alter-native interstellar emission models on the analysis ofLAT sources. As the Galactic interstellar emissioncontributes substantially to
Fermi
LAT observationsin the Galactic plane, the choice of IEM can have asignificant impact on the parameters determined fora given source of interest, as demonstrated with eightSNR candidates. To estimate the reported error wecurrently use only the most conservative extreme vari-ation of the source of interest’s output parameters.We are finalizing our definition of the systematic er- ror using this method, including through comparisonof the present estimate with previous methods’ esti-mates, typically found by varying the standard IEM’snormalization by a fraction estimated from neighbor-ing regions. Although our current method representsthe uncertainty due to a limited range of IEMs, itplays a critical role in interpreting the data and rep-resents the most complete and systematic attempt atquantifying the systematic error due to the choice ofIEM to date.As the majority of SNRs lie in the Galactic plane,coincident with the majority of the Galactic interstel-lar emission, this method is particularly pertinent toanalyses such as that underway for the 1 st Fermi
LATSNR Catalog. Figure 3 shows that the flux and in-dex can vary greatly for our eight representative SNRcandidates, depending on the source and local back-ground’s specific characteristics. Given these differ-ences, we plan to use this method to estimate the sys-tematic uncertainty associated with the choice of IEMon the full set of SNR candidates in the catalog. Sucherror estimates will allow us to, among other things,more accurately determine underlying source charac-teristics such as the inferred composition (leptonic orhadronic) and particle spectrum.Other classes of objects such as pulsar wind nebulaeand binary star systems also lie primarily in the planeand are likely to be strongly affected by the choiceof IEM. We are thus generalizing this method in or-der to be able to apply it to the study of Galacticplane sources generally. Another possible extensionto this method is extending it to energies < Acknowledgements
The
Fermi
LAT Collaboration acknowledges gen-erous ongoing support from a number of agenciesand institutes that have supported both the develop-ment and the operation of the LAT as well as scien-tific data analysis. These include the National Aero-nautics and Space Administration and the Depart-ment of Energy in the United States, the Commis-sariat `a l’Energie Atomique and the Centre Nationalde la Recherche Scientifique / Institut National dePhysique Nucl´eaire et de Physique des Particules inFrance, the Agenzia Spaziale Italiana and the Isti-tuto Nazionale di Fisica Nucleare in Italy, the Ministryof Education, Culture, Sports, Science and Technol-ogy (MEXT), High Energy Accelerator Research Or-ganization (KEK) and Japan Aerospace Exploration eConf C121028 th Fermi Symposium : Monterey, CA : 28 Oct-2 Nov 2012
Figure 5: The impact on the candidate SNRs’ flux of each of the alternative IEM input parameters,marginalized over the other GALPROP input parameters, is shown relative to the figure of merit for the otherinput parameters (source distribution, halo height, and spin temperature). We calculate the figure of merit(Eq 1) separately for the alternate IEM components fit separately (left) and summed (right). The large opencross represents the average figure of merit over all SNR candidates. As no alternative IEM input parameterhas a figure of merit significantly larger than 1, no input parameter dominates the fitted source parametersufficiently to justify neglecting the others.Agency (JAXA) in Japan, and the K. A. WallenbergFoundation, the Swedish Research Council and theSwedish National Space Board in Sweden.Additional support for science analysis during theoperations phase is gratefully acknowledged from theIstituto Nazionale di Astrofisica in Italy and the Cen-tre National d’´Etudes Spatiales in France.
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