Gamma-ray Emission of 60Fe and 26Al Radioactivities in our Galaxy
W. Wang, T. Siegert, Z. G. Dai, R. Diehl, J. Greiner, A. Heger, M. Krause, M. Lang, M. M. M. Pleintinger, X.L. Zhang
aa r X i v : . [ a s t r o - ph . H E ] D ec Gamma-ray Emission of Fe and Al Radioactivities in our Galaxy
W. Wang , , T. Siegert , , Z. G. Dai , , R. Diehl , , J. Greiner , A. Heger , , M. Krause , M.Lang , M. M. M. Pleintinger , X.L. Zhang School of Physics and Technology, Wuhan University, Wuhan 430072, China;[email protected] WHU-NAOC Joint Center for Astronomy, Wuhan University, Wuhan 430072, China Center for Astrophysics and Space Sciences, UC San Diego, 92093-0424, La Jolla (CA), U.S.A.;[email protected] Max-Planck-Institut f¨ur extraterrestrische Physik, 85741 Garching, Germany; [email protected] School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China;[email protected] Munich Cluster of Excellence ‘Universe’, 85748 Garching, Germany School of Physics and Astronomy, Monash University, VIC 3800, Australia Tsung-Dao Lee Institute, Shanghai 200240, China Centre for Astrophysics, University of Hertfordshire, Hatfield, AL10 9AB, United Kingdom
ABSTRACT
The isotopes Fe and Al originate from massive stars and their supernovae, re-flecting ongoing nucleosynthesis in the Galaxy. We studied the gamma-ray emissionfrom these isotopes at characteristic energies 1173, 1332, and 1809 keV with over15 years of SPI data, finding a line flux in Fe combined lines of (0 . ± . × − ph cm − s − and the Al line flux of (16 . ± . × − ph cm − s − above thebackground and continuum emission for the whole sky. Based on the exponential-disk grid maps, we characterise the emission extent of Al to find scale parameters R = 7 . +1 . − . kpc and z = 0 . +0 . − . kpc, however the Fe lines are too weak to spa-tially constrain the emission. Based on a point source model test across the Galacticplane, the Fe emission would not be consistent with a single strong point source inthe Galactic center or somewhere else, providing a hint for a diffuse nature. We car-ried out comparisons of emission morphology maps using different candidate-sourcetracers for both Al and Fe emissions, and suggests that the Fe emission is morelikely to be concentrated towards the Galactic plane. We determine the Fe / Al γ -rayflux ratio at (18 . ± .
2) % , when using a parameterized spatial morphology model.Across the range of plausible morphologies, it appears possible that Al and Fe aredistributed differently in the Galaxy. Using the best fitting maps for each of the ele-ments, we constrain flux ratios in the range 0.2–0.4. We discuss its implications formassive star models and their nucleosynthesis. 2 –
Subject headings:
Galaxy: abundances – ISM: abundances – nucleosynthesis – gamma-rays: observations
1. Introduction
The radioactive isotope Fe is produced in suitable astrophysical environments through suc-cessive neutron captures on pre-existing Fe isotopes such as (stable) , , , Fe in a neutron-richenvironment. Candidate regions for Fe production are the He and C burning shells inside massivestars, where neutrons are likely to be released from the Ne( α ,n) reaction. Fe production mayoccur any time during late evolution of massive stars towards core collapse supernovae (Woosley& Weaver 1995; Limongi & Chieffi 2003, 2006, 2013; Pignatari et al. 2016; Sukhbold et al. 2016;and references therein). There is also an explosive contribution to the Fe yield by the supernovashock running through the carbon and helium shells (Rauscher et al. 2003). Electron-capture su-pernovae may be a most-significant producer of Fe in the Galaxy (Wanajo et al. 2013, 2018;Jones et al. 2016, 2019a). There are other possible astrophysical sources of Fe. From similarconsiderations, Fe can also be made and released in super-AGB stars (Lugaro et al. 2012). Fur-thermore, high-density type Ia supernova explosions that include a deflagration phase (Woosley1997) can produce even larger amounts per event.Due to its long lifetime (radioactive half-life T / ≃ Fe survives to be detected in γ -rays after being ejected into theinterstellar medium: Fe β -decays to Co, which decays within 5.3 yr to Ni into an excitedstate that cascades into its ground state by γ -ray emission at keV and 1332 keV. Al has asimilarly-long radioactive lifetime of ∼ years, and had been the first live radioactive isotopedetected in characteristic γ -rays at 1809 keV (Mahoney et al. 1978), thus proving currently on-going nucleosynthesis in our Galaxy. Mapping the diffuse Al γ -ray emission suggested that itfollows the overall Galactic massive star population (Diehl et al. 1995; Prantzos and Diehl 1996).If Fe and Al have similar astrophysical origins, with their similar radioactive life time, the ratioof Fe to Al γ -ray emissions in the Galaxy would be independent of the true specific distancesand locations of the sources, and thus important for testing stellar evolution models with theirnucleosynthesis and core-collapse supernova endings (Woosley and Heger 2007; Diehl 2013).The steady-state mass of these radioactive isotopes maintained in the Galaxy through suchproduction counterbalanced by radioactive decay thus converts into a ratio for the γ -ray flux ineach of the two lines through I ( F e ) I ( Al ) ∼ . · ˙ M ( F e )˙ M ( Al (1)Timmes et al. (1995) carried the massive-star yields into an estimate of chemical evolution for Fe 3 –and Al in the Galaxy, predicting a γ -ray flux ratio of 0.16. Various revisions of models presenteddifferent ratio values ( ∼ . − , see Limongi & Chieffi 2003, 2006; Rauscher et al. 2002; Prantzos2004; Woosley and Heger 2007). Different massive star regions, such as Scorpius-Centaurus orCygnus, may show a different Fe / Al ratio as the age of such associations dictates the expectedfluxes (Voss et al. 2009). The average over the whole Milky Way, on the other hand, is determinedby the number of massive stars and their explosions over the characteristic lifetimes of Al and Fe , respectively, providing an independent measure of the core-collapse supernova rate in theMilky Way, and up to which masses stars actually explode.The yields of these two isotopes depend sensitively on not only the stellar evolution detailssuch as shell burnings and convection, but also the nuclear reaction rates. Tur et al. (2010) foundthat the production of Fe and Al is sensitive to the 3 α reaction rates during He burning, i.e.the variation of the reaction rate by a factor of two will make a factor of nearly ten change in the Fe/ Al ratio. Fe may be destroyed within its source by further neutron captures Fe ( n, γ ).Since its closest parent, Fe is unstable, the Fe( n, γ ) production process competes with the Fe β decay to produce an appreciable amount of Fe . This reaction pair dominates the nuclear-reaction uncertainties in Fe production, with Fe( n, γ ) being difficult to measure in nuclear lab-oratories due to its long lifetime and E1 and M1 reaction channels (Jones et al. 2019b). Usingeffective He-burning reaction rates can account for correlated behaviour of nuclear reactions andmitigate the overall nuclear uncertainties in these shell burning environments (Austin et al, 2017).Astronomical observations of the Fe / Al ratio will help to constrain the nuclear-reaction aspectsof massive stars, given the experimental difficulties to measure all reaction channels involved atthe astrophysically-relevant energies.Such comparison and interpretation, however, relies on the assumption that Al and Feoriginate from the same sources (see, e.g., Timmes et al. 1995; Limongi & Chieffi 2006, 2013),and have the similar diffuse emission distributions, originating from nucleosynthesis in massivestars throughout the Galaxy. Therefore, the observational verification of the diffuse nature of Feemission is key to above interpretation of measurements of a Fe / Al ratio in terms of massive-star models.Several detections of Fe enriched material in various terrestrial as well as lunar samples(Knie et al. 2004; Wallner et al. 2015; Fimiani et al. 2016; Neuh¨auser et al. 2019) confirmthe evidence for a very nearby source for Fe within several Myr. A signal from interstellar Fewas first reported from the NaI spectrometer aboard the RHESSI spacecraft (2.6 σ ) which wasaimed at solar science (Smith 2004). They also presented a first upper limit of ∼ . (1 σ ) forthe flux ratio of Fe/ Al γ -ray emissions (Smith 2004). The first solid detection of Galactic Fe emission was obtained from INTEGRAL/SPI measurements, detecting Fe γ -rays with asignificance of . σ after combining the signal from both lines at 1173 and 1332 keV (Wang et al. 4 –2007), constraining the flux ratio of Fe/ Al γ -ray emissions to the range of . − . (Wang etal. 2007). Subsequent analysis of ten-year INTEGRAL/SPI data with a different analysis methodsimilarly suggested a ratio in the range ∼ . − . (Bouchet et al. 2015).In this paper, we use more than 15 years of SPI observations through the entire Galaxy, andcarry out a broad-band spectral analysis in the γ -ray range 800 keV – 2000 keV. Rather than strivingfor high spectral resolution and line shape details, this wide-band γ -ray study aims at study of both Fe and Al emission signals at 1173, 1332 and 1809 keV simultaneously, i.e., using identical dataand analysis methods, including data selection and background treatments. This paper is structuredas follows. In §
2, we will describe the SPI observations and the data analysis steps. Our emissionmodels to describe the 800–2000 keV band are introduced in §
3. We present our morphological aswell as spectral findings in §
4. Implications and conclusion are shown in Section §
2. Observations and data analysis2.1. SPI observational data
The
INTEGRAL mission (Winkler et al. 2003) began with its rocket launch on October 17,2002. The spectrometer SPI (Vedrenne et al. 2003) is one of INTEGRAL’s two main telescopes.It consists of 19 Ge detectors, which are encompassed into a BGO detector system used in anti-coincidence for background suppression. SPI has a tungsten coded mask in its aperture, whichallows imaging with a ∼ ◦ resolution within a ◦ × ◦ fully-coded field of view. The Ge detec-tors record γ -ray events from energies between 20 keV and 8 MeV. The performance of detectors,and the behaviour and variations of instrumental backgrounds, have been studied over the mission,and confirmed that scientific performance is maintained throughout the mission years (Diehl et al.2018). The INTEGRAL satellite with its co-aligned instruments is pointed at predesignated targetregions, with a fixed orientation for intervals of typically ∼ s (referred to as pointings ).The basic measurement of SPI consists of event messages per photon triggering the Ge de-tector camera. We distinguish events which trigger a single Ge detector element only (hereafter single event , SE), and events which trigger two Ge detector elements nearly simultaneously (here-after multiple event , ME). The fast Pulse Shape Discriminator electronic unit (PSD), digitizes theshape of the current pulse, and allows suppression of background events, e.g. from localized β -decays within the Ge detectors (Roques et al. 2003), or from electronic noise. In this work, weuse event data which hit only one detector (i.e., SE event data) and which carry the PSD flag foracceptable pulse shape (event type ‘PE’).We applied a selection filter to reject corrupted, invalid, or background-contaminated data. Weapply selection windows to ‘science housekeeping’ parameters such as the count rates in several 5 –background-monitoring detector rates, proper instrument status codes, and orbit phase. In particu-lar, we use the SPI plastic scintillator anti-coincidence counter (PSAC) mounted beneath the codedmask, and the rate of saturating events in SPI’s Ge detectors (i.e., events depositing > § σ above a fit ofthis background plus the expected signal contribution per pointing, thus eliminating pointings withabnormal background (note that SPI data are dominated by instrumental background counts, sothat source counts from diffuse emission such as Fe alone cannot deteriorate the fit to a pointingdataset significantly). These outliers are mainly due to missing ‘science housekeeping’ parameterswhich are interpolated later, or due to burst like events in the field of view, for example gamma-raybursts, flares from X-ray binaries, or solar activity.The resulting dataset for our Fe and Al study encompasses 99,864 instrument pointingsacross the entire sky, equivalent to a total (deadtime-corrected) exposure time of 213 Ms. Thisincludes data from INTEGRAL orbits 43 to 1950, or February 2003 to May 2018. The sensitivity(effective exposure time, effective area) of SPI observations is further reduced by the successivefailure of four of the 19 detectors (December 2003, July 2004, 19 Feb 2009 and 27 May 2010). InFig. 1 we show the resulting exposure map from our cleaned data set.We bin detector events from the range between 800 keV and 2000 keV into seven energy bins:three of these address γ -ray line bands for Fe and Al (1169 – 1176 keV; 1329 – 1336 keV; 1805– 1813 keV), and four continuum bands in between (800 – 1169 keV; 1176 – 1329 keV; 1336 –1805 keV; 1813 – 2000 keV) are added to robustly determine the line flux above the diffuse γ -raycontinuum. In the Appendix, we present an investigation of the impact of event selections usingthe PSD (see Fig. 12). PSD selections succeed to suppress an apparent electronics noise that isvisible in raw detector spectra in the energy range 1300 –1700 keV. We therefore use such PSDselections, although the impact on the resulting spectra from celestial sources is not clear exceptfor this continuum band (see Appendix). The raw data of SPI are dominated by the intense background (BG) radiation characteristicof platforms undergoing cosmic-ray (CR) bombardment. In SPI data analysis, we combine back-ground models with a spatial model for sky emission to fit our data, allowing for adjustments of fit 6 –parameters for background and sky intensities. In general, the counts per energy bin, per detector,and per pointing are fitted by the background model described in Siegert et al. (2019), with detailsoutlined shortly below, and the assumed sky map of celestial emission (e.g., the Al distributionobtained by COMPTEL or exponential disk models, see §
3) as convolved into the domain of theSPI data space for the complete pointing sequence, by the instrument coded-mask response: D e,d,p = X m,n k X j =1 A j,m,ne,d,p β js I m,nj + X t k X i =1 β ib,t B ie,d,p + δ e,d,p , (2)where e,d,p are indices for data space dimensions: energy, detector, pointing; m,n indices for thesky dimensions (galactic longitude, latitude); A is the instrument response matrix, I is the intensityper pixel on the sky, k is the number of independent sky intensity distribution maps; k is thenumber of background components, δ is the count residue after the fitting. The coefficients β s forthe sky map intensity are constant in time, while β b,t is allowed time dependent, see 2.3 below.The sky brightness amplitudes β s comprise the resultant spectra of the signal from the sky. Forthis model fitting analysis, we use a maximum-likelihood method, implementing Poisson statisticswhich applies to such detector count analysis. Our software implementation is called spimodfit (Strong et al. 2005). The fitted model components are analysed for further consistency checks onpossible systematics in residuals.We thus derive, per energy bin, best-fitted parameter values with uncertainties, and their co-variance matrices. This provides flux estimates which are independent of spectral-shape expecta-tions. Fe Background characteristics
Much of the radiation from instrumental background is promptly emitted directly from CRimpacts. Background components arise from radioactive isotopes produced by the CR impacts.Local radioactivity in the spacecraft and instruments themselves thus will generate both broadcontinuum background emission and narrow gamma-ray lines from long and short-lived radio-isotopes. Varying with energy, background components may exhibit complex time variability dueto their origins from more than one physical source (Weidenspointner et al. 2003). Backgroundmodelling by using the entire mission spectroscopy history has been established recently (Siegertet al. 2019).For the energy bands studied here, we follow this general approach, and model the back-ground by fitting two components, one for the continuum and one for instrumental lines. Fromthe mission spectral database (Diehl et al. 2018), we construct these background models at fine 7 –Fig. 1.— Exposure sky map of fully-coded FOV in Galactic coordinates (the number at the colorbar in units of sec) for the data selected from 15-year SPI observations for our Fe and Al study(INTEGRAL orbits 43 – 1950).Fig. 2.— SPI background tracer variations with time from saturated events in the Ge camera(GEDSAT). In the panel, the full SPI data base is shown in black, and the chosen data based onour selection criteria in red. 8 –spectral precision. Then, we allow for adjustment of its overall normalisation in intensity, whichaccounts for the fact that the (small) celestial signal that had been part of the mission data usedfor this database now needs to be separated out. The instrument records several detector triggerswhich have sufficiently-high count rates, such as the one of onboard radiation monitors, the SPIanti-coincidence shield count rate, and the rate of saturating Ge detector events (events depositing > γ -ray background, while the long-term trends of radioactive build-up and decays is inherent to the spectral background data base. In this analysis, we use the GeDSatrates as a short-term background tracer and first-order description of the background variationswith time scales of pointing-to-pointing, from 800 keV - 2000 keV. This tracing is sufficient inenergy bins at or below the instrumental resolution, however in broader energy bins such as usedin this work the superposition of the effects from different background lines blended together in abroader bin require re-scalings after suitable time-intervals.The coefficients β b,t for background normalisations are therefore allowed time dependent, tocater for such effects, and for different background normalisations for each camera configurationof 19/18/17/16/15 functional detector elements, as well as for possible variations on time scalesshorter than our background model was built.In Fig. 4, we show the optimal re-normalisation time scale for the Fe energy bin includingthe 1173 keV line. We find an optimum fit when re-normalising background at a time scale of oneorbit, which corresponds to 1,674 background parameters per component. As a consistency check,we performed an estimate of the Fe signal significance of the 1169–1176 keV band (continuumplus line) as could be expected from earlier measurements (Wang et al. 2007). In this estimation weconsider only the inner Galaxy, and assume the COMPTEL Al map as a tracer for the morphologyof Fe emission, and we adopt a total galaxy-wide flux of × − ph cm − s − . We then make useFig. 3.— SPI background continuum and line components relevant in the spectral regime of Felines: (left) the continuum count rate, (middle) Co activation, (right) and a Ge activation line. Ineach panel, the full SPI data base is shown in black, and the chosen data based on our selectioncriteria in red. 9 – E x pe c t ed s i gn i f i c an c e i n − k e V b i n const. det. fail. anneal. 30 20 10 5 3 2 1 1/2 1/4Background re−scaling per [revolution] × × × × A I C − m i n ( A I C ) Fig. 4.— Expected significance (in σ units, black points) above a background only description ofthe data in the 1169 to 1176 keV band, estimated from likelihood tests, BG vs. BG plus source,using different numbers of background parameters (bottom axis), i.e. varying the background ondifferent time scales (top axis: re-scaling per number of INTEGRAL revolutions; or whenever anannealing was performed, a detector failed; or assuming a constant background). The red pointsshow the Akaika Information Criterion ( AIC = 2 n par − L ) , where n par is the total number offitted parameters, right axis) which was used to find the required number of background parametersto describe the data in this bin sufficiently well. The optimum is found at one INTEGRAL orbit or1,674 background fit parameters, respectively. The black points show the expected significance inthe band with a total flux of × − ph cm − s − as a function of fitted background parameters.See text for details.of the approach by Vianello (2018), who extended the Bayesian significance estimates of Li & Ma(1983), and assume herein that our background model parameters are normally distributed. Thisobtains the black line shown in Fig. 4, estimating a significance of σ for our optimal backgroundmodel re-scaling. In case about half of the flux of × − ph cm − s − would be degenerate andabsorbed in the diffuse γ -ray continuum component, the line significance would be around σ inour estimate for a single line.The background rescaling investigations in the remaining energy bins show similar optimumtime scales, except for the lowest energy bin (800– 1169 keV), which requires four parameters per 10 –orbit. The number of degrees of freedom is thus 1,591,831 for 1,595,180 data points in the Fe, Al , and higher-energy continuum bins, taking into account all fitted parameters for the sky,detector failures and background variations.Analysing the resulting background variations in the Fe line bands, we now investigate thecandidate origins, based on our detailed spectral analysis of instrumental background with highspectral resolution. The most important background lines are the ones expected from the decay of Co in the instrument and the satellite, at the same line energies because this is the same cascadede-excitation in both cases. This Co background builds up in intensity with time, due to its5.3 yr radioactive lifetime, and thus will increasingly contribute to the total measured Co γ -rayline signal. In addition, there is a strong background line from activated Ge at 1337 keV, whichblends into the high-energy Fe line at 1332 keV. This Ge line, however, shows no radioactivebuild-up as the decay time is of the order of nano-seconds, and hence the count rate in this lineclosely follows the general activation of backgrounds. All these lines are superimposed onto aninstrumental continuum background which is dominated by bremsstrahlung inside the satellite, andalso includes Compton-scattered photons and a composite of weaker lines that escape identificationin our deep spectral background analysis (Diehl et al. 2018). In Figs. 2 to 3, we show characteristicbackground components as they vary with time, as determined from our data set.Here we focus on the total galactic emission, so that extrapolated estimates from the innerGalaxy towards the full Galaxy only may serve as a guidance, rather than a precise prediction.Nevertheless, we see that the steadily rising Co background line flux leads to a very shallowincrease in the significance of celestial Fe over time, shallower than Fe count accumulationalone would suggest. While our previous result with only three years of data (Wang et al. 2007)showed a . σ signal, in this case using both Fe lines together and both SE and ME (singleand multiple-trigger event types), which is consistent with our expectations, the increase of databy more than 200 % in our current dataset would result in only σ significance for SE and thetwo lines combined. We now also understand the additional background time variation: becausethe background line rate increases almost linearly (Fig. 3), fitting the background requires moreparameters than typical for SPI background that follows the solar cycle directly.
3. Modelling Fe in the Milky Way
The Fe signal is too weak to derive the spatial distribution or perform an imaging analysis.Therefore, we attempt to constrain the size of the Fe emission region through fitting a param-eterized geometrical model, an exponential disk profile, and we determine the scale radius andscale heights. Doing this for all energy bins between 800 and 2000 keV, we obtain information onhow this approach deals with known spatial distributions of γ -ray emission, thus helping to judge 11 –systematics limitations with the Fe interpretation. The exponential-disk models in this analysishave been adopted in the following form: ρ ( x, y, z ) = A exp ( − R/R ) exp ( −| z | /z ) , with R = p x + y (3)In Eq. 3, ρ ( x, y, z ) is the 3D-emissivity that is integrated along the line of sight ( l/b ) to pro-duce maps of sky brightness, with a pixel size of ◦ × ◦ . These maps are then folded through thecoded-mask response to create expected count ratios for all selected pointings. The normalisation A , equivalent to β js in Eq. 2, is determined (fitted) for a grid of scale radii R and scale heights z that we test. Here, we use a grid of 16 R -values, from 500 pc to 8000 pc in steps of 500 pc, times32 z -values between 10 and 460 pc in steps of 30 pc and between 500 and 2000 pc in steps of100 pc. These models are independently fitted to all seven energy bins, to obtain a likelihood chartfor all morphologies tested. From this, we can determine both the best-fitting flux as well as thebest scale dimensions of the emission, plus their uncertainties. Doing this in all our energy bands,we can directly compare the emission size characteristics of Al versus Fe , obtaining system-atics information from the continuum bands in between (i.e. possible biases for scale dimensions,influenced by the continuum below the lines).All previous searches for Fe (Wang et al. 2007; Harris et al. 2005; Bouchet et al. 2015),generally assumed that the Fe diffuse emission follows the sky distribution of the Al line. In thisstudy, we explore the morphology of Fe by comparing with Al emission as well as continuumemission. We test different tracers of potential candidate sources for Fe emission, and comparethose tracer maps to that of Al emission as measured and deconvolved from γ -ray data. Thisprovides an independent judgement of how similar Fe and Al are ( § Al . Similarto previous studies (Wang et al. 2009; Siegert 2017), we fit all-sky survey maps from a broadrange of different wavelengths to our SPI data. From this we obtain a qualitative measure whichmaps are favoured at our chosen energies, respectively. We test a comprehensive set of maps totrace different emission mechanisms which may be related to our SPI data in the different energybands. The list of tested maps (Tab. 1) includes also source tracers which may be weakly or notat all related to the candidate Al and Fe sources. We use this list of tracers for all or energybands, in order to reveal degeneracies and systematics, because differences between maps are hardto quantify through fit likelihoods in absolute terms. We also include a background-only fit forreference. In Tab. 1 we comment on each map briefly to illustrate its main features. 12 –Table 1: The inventory of candidate source tracers, for which we compare how they can representemission in the 7 energy bands of SPI measurements between 800 and 2000 keV.
Energy Tracer Type & Comments408 MHz Synchrotron emission of CR e-; mosaic Jodrell Bank/Effelsberg/Parkes (Haslam et al. 1982; Remazeilles et al. 2015)21 cm HI neutral hydrogen, Effelsberg-Bonn HI Survey (EBHIS) (Kerp et al. 2011; Winkel et al. 2016)1.25–4.9 µ m DIRBE infrared emission from star light of M, K, G stars, 4 individual maps (Hauser et al. 1998)12–240 µ m IRAS infrared emission from dust, 6 individual maps (Hauser et al. 1998) –
672 nm
Optical emission, all sky mosaic from > H α emission, partly ionised interstellar gas, star forming regions (Haffner et al. 2016)1.809 keV Al decay emission from , massive star groups, COMPTEL (Plueschke 2001), and SPI (Bouchet et al. 2015)1–30 MeV COMPTEL MeV γ rays, CR-ISM interactions (Sch¨onfelder et al. 1993; Strong et al. 1994) >
100 MeV EGRET . –
30 GeV band; CR-ISM interactions (Hartman et al. 1999)1–3 GeV Fermi/LAT, CR-ISM interactions; high-energy sources (Atwood et al. 2009)0.25–1.5 keV ROSAT all sky survey, hot ISM, X-ray binaries, 3 individual maps (Snowden et al. 1997; Voges et al. 1999)14–150 keV Swift/BAT hard X-ray sources, X-ray binaries, point-like, 7 individual maps (Krimm et al. 2013)30–857 GHz Planck radio bands, 9 individual maps, synchrotron emission; individual sources (Planck collaboration 2016)30–857 GHz: AME Anomalous Microwave Emission (Planck collaboration 2016)30–857 GHz: CMB Cosmic Microwave Background (Planck collaboration 2016)30–857 GHz: CO J (1 → emission at 150 GHz (Planck collaboration 2016)30–857 GHz: Dust - (Planck collaboration 2016)30–857 GHz: FreeFree Bremsstrahlung emission (Planck collaboration 2016)30–857 GHz: Synchrotron - (Planck collaboration 2016)30–857 GHz: SZ-effect Sunyaev-Zeldovich effect (Planck collaboration 2016)30–857 GHz: X-lines Strong non-CO lines in the centre of the Galaxy (Planck collaboration 2016)
800 1000 1200 1400 1600 1800 200010 −5 −4
800 1000 1200 1400 1600 1800 2000Energy [keV]10 −5 −4 F l u x [ ph c m − s − k e V − ] Fig. 5.— Spectral intensities (black) obtained from the fit to an exponential-disk model with R = 7 kpc and z = 0 . kpc. The fitted total model, Eq. 4, is shown in red. 13 –
4. Results
From independently fitting spatial emission models to SPI data for each of our seven energybands, we obtain intensity values for the celestial emission detected in each of these bands, for thesame adopted spatial distribution model. In Tab. 2, we presented the χ values for seven energybands in the modelling fittings. So that the present fits are reliable, and the background model isacceptable.For further discussion and analysis, we fit each extracted set of sky-intensity values with F ( E ; C , α, F , F ) = C × (cid:18) E (cid:19) α + (4) + F × ( T (1172 . , T (1332 . , F × T (1809 . , , where C is the continuum flux density nomalisation at 1000 keV, α is the power-law index, and F and F , respectively, are the integrated fluxes as derived from tophat functions, T ( E , ∆ E ) ,centred at E with bin width ∆ E . We link the parameters of the two Fe lines as they are expectedto reflect the same incident flux in intensity and width. The lines are expected to be somewhatbroadened above instrumental line widths by 0.1–0.2 keV due to large-scale galactic rotation ofsources (Wang et al. 2009, Kretschmer et al. 2013), and the instrumental line width would be ∼ . keV around the Fe lines and ∼ . keV around the Al line (Diehl et al. 2018). Withinthe 7 keV bins for the Fe lines and the 8 keV for the Al line bands thus, . σ (99.7 %) of theexpected line fluxes would be contained. Fe and Al emission
In Fig. 5, we show the 7-band spectral intensities as derived from an exponential disk withscale radius 7 kpc and scale height 0.8 kpc, as a typical example. We selected this as it reflectsTable 2: The χ values for the analysed set of 7 energy bins from 800 -2000 keV, together with thenumber of degrees of freedom and the number of fitted parameters, where χ P refers to Pearson χ , χ is modified χ , χ is Cstat χ (see Mighell 1999). Energy bin (keV) 800-1169 1169-1176 1176-1329 1329-1336 1336-1805 1805-1813 1813-2000 χ P χ χ
14 –best-fit dimensions in the Al line band. In this example, the continuum is determined as (2 . ± . × ( E/ ( − . ± . × − ph cm − s − keV − . The Fe and Al line fluxes are (2 . ± . × − ph cm − s − and (14 . ± . × − ph cm − s − , respectively, which results in a Fe/ Al ratio of (18 . ± .
4) % .Our ×
32 = 512 scale size grid covers the full range of the Galactic plane, and thereforeprovides a measure of the emission extents for Fe and Al as well as for the continuum emissionexpected from Bremsstrahlung and inverse-Compton interactions of cosmic-ray electrons. Each ofthe 512 exponential disk templates is treated individually in the first place, fitting its parameterswithout any priors or constraints. As a result, the absolute fluxes of continuum and lines vary withthe emission dimensions. We find that with larger scale dimensions, the fluxes of continuum andlines increase. We find no strong variation of the line-to-continuum ratio for either Fe or Al .This supports our assessment that the shape constraints that we derive are consistent and withoutmajor bias.The strong background line at 1337 keV (see Section 2) could affect the 1332 keV Fe lineresult, which we therefore compare to the more-isolated 1173 keV line; for our Fe spatial results,we prefer to rely on the latter line for this reason, while the Fe / Al flux ratio uses the dataconstraints from both Fe line bands combined. In our goal to determine the spatial extent of Fe emission, we show next to each other for Fe and Al in the 1173 and 1809 keV lines thelikelihood contour regions versus scale heights and scale radii (in Fig. 6). For the Al emission,we can obtain the characteristic scale radius of R = 7 . +1 . − . kpc and scale height of z = 0 . +0 . − . kpc. However, for the Fe emission lines, the constraints are very poor due to the weak signals,formally resulting in R = 3 . +2 . − . kpc, and z = 0 . +2 . − . kpc. We will use the point source modeltest to exclude one point source model in the Galactic center (see Section 4.2).In our goal to exploit maximum information for the Fe / Al flux ratio while catering for theuncertainty of the spatial extent of Fe emission, we include the quality of the fits to SPI data fromthis grid of exponential disk model fits in our assessment. We apply a weighting with the AikaikeInformation Criterion (AIC, Akaike 1974), derived from the likelihood and the number of fittedparameters in each energy bin, thus taking the individual measurement and fitting uncertainties ofeach model map into account. This yields a Fe line flux value of (3 . ± . × − ph cm − s − ,and a Al line flux of (16 . ± . × − ph cm − s − . The Fe / Al ratio resulting from thisemission-extent averaged analysis is (18 . ± .
2) % . The derived Al flux for the full Galaxyis also consistent with the previous Al map study with SPI data (Bouchet et al. 2015). Inaddition, a recent SPI analysis reported the Al flux values for both the inner Galaxy and thewhole sky (Pleintinger et al. 2019): ∼ . × − ph cm − s − for the inner region, and ∼ (1 . − . × − ph cm − s − for the whole sky. We show the Fe / Al ratio distribution fromall 512 exponential-disk configurations in Fig. 7, also indicating characteristic uncertainties. 15 –
In this section, we aim to constrain the morphology of the weak Fe in another way. Weproduced a catalogue of point source locations with ×
21 = 1911 entries between l = − ◦ − ◦ and b = − ◦ − ◦ , in 2 degree steps. Then we used this catalogue to test a point source origin forboth Al and Fe emission lines in the Galactic plane. In this way, in Fig. 8, we can check if andhow extended the Al and Fe emissions are. These morphology studies of Al and Fe emissiondistributions suggested the γ -ray emissions are not attributed to one or several point sources in thisregion. In positive longitudes, the Al emission extended to l ∼ ◦ which may be contributedby Aquila, and at l ∼ ◦ , the emission structure is Cygnus. The truncated structure in positivelongitudes will be the influence of the exposure map partially (see Figure 1). In the negativelongitudes, the Al emission extended to l ∼ − ◦ , probably Carina. However, these maps shouldnot be interpreted as the real sky distribution map, but can imply that the emission is not point-like. The use of this simplified emission model at different galactic coordinates would yield largeresiduals in the raw SPI data space. Likewise, the Fe emission morphology is unknown and couldbe particularly similar to Al .From these number of trials, we can estimate the influence of diffuse or point-like emissionby taking into account that a background-only fit would result in a test-statistics defined as:
T S = 2 (log( L BG ) − log( L P S ( l/b ))) , (5)with L BG and L P S being the likelihoods of a background-only fit and a background plus point-source fit, respectively, for finding a point source by chance at a trial position ( l/b ) , would bedistributed as . χ with 3 degrees of freedom (2 position, 1 amplitude), we can compare howmuch the measured T S -distributions deviate. A single point source would have one (or more) highpoints that at high TS at a particular, sharply defined,
T S -value. We can see that the Fe case isdeviating from the background-only case in more than a few points and consistently for
T S > .This would be a signature of a diffuse signal for the Fe emission. For comparison, the Al linecase is shown as well. Therefore, we can exclude a single strong point source in the galactic centeras well as somewhere else in this region as the origin of the detected Fe emission.
In our effort to investigate the spatial distribution of Fe emission, we fit the SPI data witha large set of maps representing different source tracers (see Tab. 1). These include the 408 MHzmap reflecting cosmic-ray electrons through their radio emission, cosmic-ray illuminated interstel-lar gas shining in GeV γ -rays, the COMPTEL and SPI maps reflecting Al radioactivity, different 16 –sets of infrared emission, and X-ray emission maps. The fit quality of these maps can be com-pared through their different likelihood ratios, where we normalize to a background-only reference(Fig. 10). For the Al line, as expected, we find again as best-fitting tracer map the SPI Al linemap that had beed derived from a different data set and different analysis method (Bouchet et al.2015), which supports consistency of our methods. For the Fe line, the best fitting tracer mapturns out to be the DIRBE 4.9 µ m map representing emission from small dust grains and star lightfrom mostly M, K, and G-type stars.From our set of candidate-source tracers, Tab. 1, we use the likelihood ratio of the combinedcontinuum bins, the two Fe lines, and the Al line, each normalized to a background only fit , asa measure for significance of a signal from the sky. We illustrate these signal significance levelsand the resulting flux values in Fig. 10.For most of the tested maps, such as 408 MHz, IRAS 25 µ m, COMPTEL Al emission, GeV γ -ray emission, and CO/dust/free-free emission maps, both the Al and Fe radioactive-line bandsshow a significant detection of a signal from the sky in our SPI dataset, with significance levelsof > σ for the Al line, and > σ for the Fe lines. In general, for the cases for which weobtain a significant Al signal, such as the 408 MHz map or the COMPTEL Al map, also Feshows a significant signal above the background. Somewhat surprisingly, however, the SPI Almap, which fits best at 1809 keV, is particularly poor in detecting sky emission in the 1173 keV lineband of Fe . This may be an indication that Al and Fe may indeed have a different emissionmorphology. In Fig. 7, we also presented the Fe / Al ratio ranges derived from these tracer mapswith the significant detections of both Al and Fe emission lines. The Al all-sky emission mapsobserved by COMPTEL and SPI gave a ratio range of . − . , and 408 MHz, IRAS 25 µ m andthe Fermi γ -ray emission maps produced a ratio range of ∼ . − . . The DIRBE . µ m emissionmap can produce a highest detection significance level for Fe lines, which gave a Fe / Al ratioof 0.22 – 0.32.For some cases, such as the hard X-ray map from SWIFT/BAT, the soft X-ray (0.25 keV)map from ROSAT, the Planck CMB map, and the SZ-effect map, in both the Al and Fe bandswe obtain no or at most marginal detections of sky emission. The hard X-ray map (100-150keV) is dominated by emission of point sources along the Galactic plane, such as X-ray binaries.Therefore, the non-detection of signals in Al and Fe bands would be in line with both the Aland Fe emission having a diffuse nature, rather than a strong contribution from such sources. ThePlanck SZ effect map follows the distribution of clusters of galaxies, which are mainly locatedat high Galactic latitudes. The ROSAT soft X-ray (0.25 keV) map is mostly bright also at highGalactic latitude regions due to the strong soft X-ray absorption by the Galactic plane. Non-detection of Al and Fe emission signals with these two tracer maps therefore is consistent withour belief in origins of Fe and Al signals in the plane of the Galaxy and its sources. 17 –To compare the acceptable fits for the lines and continuum from the set of tracer maps, weshow the sample spectra in our energy bands in Fig. 11 from six typical all-sky distribution models,including the diffuse emission maps from observations (408 MHz, Al γ -ray emission, infraredemission) and analytical formula (disk models), and point sources based on hard X-ray surveys.This provides an additional check against, or insight towards, possible systematics in our spectralfit results. γ -ray continuum The hard X-ray to soft γ -ray Galactic diffuse emissions include the continuum and γ -raylines such as positron annihilation line, Fe emission lines, and Al line. The diffuse contin-uum emission would originate from several physical processes: inverse-Compton scattering of theinterstellar radiation field, bremsstrahlung on the interstellar gas from cosmic-ray electrons andpositrons; the neutral pion decays produced in interactions of the cosmic rays with the interstellargas (see Strong et al. 2010 and references therein), and some unresolved hard X-ray/soft γ -raysources.With the 7-year INTEGRAL/SPI observations, Bouchet et al. (2011) derived the hard X-rayspectrum from 20 keV to 2.4 MeV in the Galactic ridge region,with power-law index of Γ ∼ . − . for the diffuse continuum, and a flux level of ∼ − ph cm − s − keV − . Using the 15-year SPIdata covering 800 keV to 2 MeV, we also determine the continuum spectra of the whole Galacticplane from the fittings, which have the average flux level of ∼ (2 . ± . × − ph cm − s − keV − with a power-law index of Γ ∼ (1 . ± . . The continuum flux derived in this work is fitted fromthe whole Galactic plane, rather than only from the inner Galactic ridge (Bouchet et al. 2011).The spectral indices are consistent with each other. We conclude that our broad-band analysis alsodetermines the Galactic continuum emission that underlies the targeted line emissions.
5. Summary and discussion
With more than 15 years of INTEGRAL/SPI observations, we carried out a wide range ofspatial model fits to SPI data from 800 – 2000 keV in seven energy bands, including the line bandsfor Fe at 1773 and 1332 keV and for Al at 1809 keV, as well as wider continuum energy bandsaround these. We clearly detected the signals from both Fe and Al emissions, as well as diffuseGalactic continuum emission. With only the SE data base, assuming the exponential-disk distribu-tion model, we obtained a detection significance level of Fe lines of ∼ . σ with a combined lineflux of (3 . ± . × − ph cm − s − , and the Al flux of (16 . ± . × − ph cm − s − for 18 –the whole Galaxy above the background continuum. From the consistent analysis approach, withidentical data selections, response, and background treatments, we minimise biases or systematics,and obtain a result for the Fe / Al flux ratio of (18 . ± .
2) % based on the exponential diskgrid maps. This large-scale galactic value is consistent with a local measurement from deposits ofmaterial on Earth (Feige et al. 2018). Since we do not know the real sky distribution of Fe inthe Galaxy, the derived Fe / Al flux ratio will depend on the sky distribution tracers. In Fig. 10,we compared the detection significance levels and flux values for Al and Fe using different skydistribution tracers. The best fits for Al are the the SPI Al and the IRAS 25 µ m maps, whilefor Fe , the best one are the DIRBE 4.9 µ m and IRAS 25 µ m maps. Thus, we can use these bestfit maps to constrain uncertainties of the Fe / Al flux ratio. If we use the same tracer for both Al and Fe , i.e. the IRAS 25 µ m map, the Fe / Al flux ratio is . − . ; then using thedifferent tracers, i.e., the SPI map for Al and the DIRBE map for Fe , one finds the ratio rangeof . − . .Using an astrophysically-unbiased geometrical description of a double-exponential disk, weexplore a broad range of emission extents both along Galactic longitude and latitude for Al and Fe . For Al emission we find R = 7 . +1 . − . kpc and z = 0 . +0 . − . kpc. The Fe γ -ray signalis weak and near the sensitivity limit of current γ -ray telescopes, so that imaging similar to whatis obtained for Al γ -rays cannot be obtained at present. Formally, the scale radius and heightare determined to be R = 3 . +2 . − . kpc, and z = 0 . +2 . − . kpc. We carried out a point sourcemodel scan in the Galactic plane ( | l | < ◦ ; | b | < ◦ ) for both Al and Fe emission line cases.The morphology and test-statistics results suggest that the Fe emission is not consistent with astrong single point source in the Galactic center or somewhere else in the Galactic plane. Fromour comparison with different sky maps, we provide the evidence for a diffuse nature of Feconcentrated towards the Galactic plane, which is similar to that of Al . But it is possible that the Al and Fe are distributed differently in the Galaxy.The ratio of Fe/ Al has been promoted as a useful test of stellar evolution and nucleosyn-thesis models, because the actual source number and their distances cancel out in such a ratio.A measurement therefore can help theoretical predictions and shed light on model uncertainties,which are a result of the complex massive star evolution at late phases and related nuclear reactionrate uncertainties. Timmes et al. (1995) published the first detailed theoretical prediction of this ra-tio of yields in Fe and Al , giving a gamma-ray flux ratio F ( Fe) /F ( Al) = 0 . ± . . Withdifferent stellar wind models and nuclear cross sections for the nucleosynthesis parts of the mod-els, different flux ratios F ( Fe) /F ( Al) = 0 . ± . were presented (Prantzos 2004). Limongi& Chieffi (2006) combined their yields for stellar evolution of stars of different mass, using astandard stellar-mass distribution function, to produce an estimate of the overall galactic Fe/ Algamma-ray flux ratio around . ± . . Woosley & Heger (2007) suggested that a majorsource of the large discrepancy was the uncertain nuclear cross sections around the creation and 19 –destruction reactions for the unstable isotopes Al and Fe which cannot be measured in the lab-oratory adequately. A new generation model of massive stars with the solar composition and thesame standard stellar mass distributes from 13 – 120 M ⊙ compared yields with and without effectsof rotation (Limongi & Chieffi 2013). For the models including stellar rotation, they determineda flux ratio of F ( Fe) /F ( Al) = 0 . ± . . For the non-rotation models, they obtained a fluxratio of F ( Fe) /F ( Al) = 0 . − . ; and if one only considers the production of stars from13 – 40 M ⊙ , the predicted flux ratio reduces to ∼ . ± . . For stars more massive than 40 M ⊙ , the stellar wind and its mass loss effects on stellar structure and evolution contributes ma-jor uncertainty in Fe ejecta production. But these stars may actually not explode as supernovaeand rather collapse to black holes, so that their contributions may not be effective and could beignored in a stellar-mass weighted galactic average. The measured values from gamma-rays sug-gest that the (generally) higher values from theoretical predictions may over-estimate Fe and/orunder-estimate Al production. This could be related to the explodability of massive stars for verymassive stars beyond 35 or 40 M ⊙ . Acknowledgements
We are grateful to the referee for the fruitful suggestions to improve the manuscript. W. Wangis supported by the National Program on Key Research and Development Project (Grants No.2016YFA0400803) and the NSFC (11622326 and U1838103). Thomas Siegert is supported bythe German Research Society (DFG-Forschungsstipendium SI 2502/1-1). The INTEGRAL/SPIproject has been completed under the responsibility and leadership of CNES; we are grateful toASI, CEA, CNES, DLR (No. 50OG 1101 and 1601), ESA, INTA, NASA and OSTC for supportof this ESA space science mission.
A. Appendix
In Fig. 12, we present the spectral examples from 800 keV - 2000 keV for the seven energybands for both SE and PSD datasets. In the case of SE, the strong electronic noise cannot besuppressed in the band of 1336 - 1805 keV. While, this electronic noise does not affect the spectralcounts for the PSD dataset. The reader can also refer to the supplementary information in Siegertet al. (2016), where we have done the test on the pule shape selections. Thus, in this work, weonly refer to the PSD dataset.In the present work, we have tried to constrain the sky distributions of Fe and Al lines inthe Galaxy, so we determine the gamma-ray spectra of three gamma-ray lines (1173 keV, 1332 20 –keV and 1809 keV) for the entire sky. In the previous work (Wang et al. 2007, 2009), we studiedthe spectra and fluxes of Fe and Al using the maps only covering the inner Galaxy ( − ◦ Akaike, H. 1974, IEEE Trans. Autom. 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For the Fe line, thebest fit gives ( R /z ) = (3 . +2 . − . / . +2 . − . ) kpc. 24 –Fig. 7.— Fe / Al flux ratio for the grid of exponential disk models (blue, left axis). Includingthe uncertainties of the fluxes from each spectral fit, the total estimated Fe / Al flux ratio fromexponential disks is (18 . ± . 2) % . Alternative to exponential disks, we also show the flux ratiosderived from a set of tracer maps (see section 4.2), as vertical lines according to their significance(right axis), together with their uncertainties as shaded bands. Clearly, these systematically showlarger values compared to the exponential disk models. The IRIS (25 µ m ) map shows the largestimprovement above a background only description for both lines consistently (see Fig. 11), so thata flux ratio estimate from this map serves as a measure of the systematic uncertainty. We find theratio of . ± . based on the IRAS 25 µ m map, suggesting a systematic uncertainty of the orderof . 25 –Fig. 8.— Summary of scanning the inner part of the Galactic plane for both Fe (top) and Al(bottom) line emissions ( − ◦ < l < ◦ , − ◦ < b < ◦ ) with individual point sources,separated by 2 degree each. Each pixel in these visualisations represents one complete likelihoodratio test of BG only vs. BG plus point source, i.e. it includes all fitted parameters of the completedata set with one additional sky component, here modelled as a point source at Galactic coordinates(l/b). Each point is independent from all other points, as they represent another likelihood ratiotest, and thus may not be interpreted as linked to each other. The particular choice of fittinga single point source at individual positions stems from the fact that, within 3 σ uncertainties, theexponential disk model extents (see Fig. 7) are indistinguishable from a point source at the Galacticcentre. Thus the opposite extreme of having only one or more point source containing all the fluxis tested with this procedure. 26 –Fig. 9.— The test-statistics in the Fe and Al lines, together with expectations from BG-onlyfits, which would be distributed as . χ with 3 d.o.f. A single point source would have one (ormaybe a few) value at high TS. Fe is deviating from the background-only case in more than afew points and consistently for T S > .Fig. 10.— Likelihood-ratio results for fits of different tracer maps (including the exponential diskmaps) of candidate sources to the 1173 keV (left) and 1809 keV (right) data for Fe and Alemissions, respectively. The ratio was derived relative to the background-only fit. The fitted fluxesare given in colour. For the Fe lines, the best fit sky distribution model is the DIRBE infraredemission map at . µ m . While for the Al line, the best fit one is the Al emission map derivedby INTEGRAL/SPI. 27 – 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 20000.000000.000050.000100.000150.000200.000250.00030 HomoDisk 26AlMap ExpDisk 408 MHz DIRBE 4.9 m BAT 100keV I n t en s i t y ph c m - s - E (keV) Fig. 11.— Comparison of the spectra from – keV for different candidate-source tracers inour continuum and line bands. We have included three γ -ray lines using six typical distributionmodels: a homogenous disk model (constant brightness along the Galactic plane with scale height200 pc, see Wang et al. 2009), a COMPTEL maximum entropy Al emission map (Pl¨uschke etal. 2001), an exponential disk model (scale radius . kpc, scale height pc), the 408 MHz map(Remazeilles et al. 2015), the DIRBE infrared emission map at 2.5 µ m (Hauser et al. 1998), and ahard X-ray sky map derived by SWIFT/BAT surveys from keV– keV (bright point sources,Krimm et al. 2013). 28 –Fig. 12.— A comparison between the fitted broad spectra derived by the SE dataset and PSDdataset from 800 keV - 2000 keV. In the band of 1336 - 1805 keV, the strong electronic noisecannot be suppressed in the case of SE. 29 –Fig. 13.— The fitted broad spectrum derived from the COMPTEL Al map only for the innerGalaxy − ◦ < l < ◦ , − ◦ < b < ◦ . From this fitting, we derive the combined Fe fluxof (4 . ± . × − ph cm − s − , and the Al flux of (2 . ± . × − ph cm − s −1