Comparing simulated $^{26}$Al maps to gamma-ray measurements

Context. The diffuse gamma-ray emission of $^{26}{\rm Al}$ at 1.8 MeV reflects ongoing nucleosynthesis in the Milky Way, and traces massive-star feedback in the interstellar medium due to its 1 Myr radioactive lifetime. Interstellar-medium morphology and dynamics are investigated in astrophysics through 3D hydrodynamic simulations in fine detail, as only few suitable astronomical probes are available. Aims. We compare a galactic-scale hydrodynamic simulation of the Galaxy's interstellar medium, including feedback and nucleosynthesis, with gamma-ray data on $^{26}{\rm Al}$ emission in the Milky Way extracting constraints that are only weakly dependent on the particular realisation of the simulation or Galaxy structure. Methods. Due to constraints and biases in both the simulations and the gamma-ray observations, such comparisons are not straightforward. For a direct comparison, we perform maximum likelihood fits of simulated sky maps as well as observation-based maximum entropy maps to measurements with INTEGRAL/SPI. To study general morphological properties, we compare the scale heights of $^{26}{\rm Al}$ emission produced by the simulation to INTEGRAL/SPI measurements.} Results. The direct comparison shows that the simulation describes the observed inner Galaxy well, but differs significantly from the observed full-sky emission morphology. Comparing the scale height distribution, we see similarities for small scale height features and a mismatch at larger scale heights. We attribute this to the prominent foreground emission sites that are not captured by the simulation.


Introduction
Al is an ideal tracer of ongoing nucleosynthesis in the Galaxy. It is produced in massive stars and ejected to their surroundings via stellar winds and supernovae (SNe). It decays with a half life time of ∼ 0.7 Myr to 26 Mg and emits a photon at 1809 keV, which can be measured by gamma-ray telescopes. The spatial distribution of 26 Al provides information about active sites of nucleosynthesis and galactic chemical enrichment, as well as dynamics and feedback processes in the interstellar medium (ISM) throughout the Milky Way (e. g. Diehl et al. 2006;Wang et al. 2009;Diehl et al. 2010;Kretschmer et al. 2013;Bouchet et al. 2015;Siegert & Diehl 2017). Hydrodynamic simulations are a crucial tool for understanding the dynamics and chemical enrichment of galaxies, and for interpreting observations. Empirical models that may describe diffuse radioactivity in the interstellar medium of the Galaxy have a long history (cf. Prantzos 1993;Prantzos & Diehl 1995;Knödlseder et al. 1996;Lentz et al. 1999;Sturner 2001;Drimmel 2002;Alexis et al. 2014). Yet, it is only recent that Fujimoto et al. (2018) reported the first galactic-scale hydrodynamic simulation that starts from basic physical processes and aims to track the synthesis and transport of radioactive isotopes, such as 26 Al and 60 Fe in a Milky Way-like galaxy.
Previous, heuristic model comparisons identify morphological similarities between 26 Al emission and multi-wavelength tracers or geometric emission models (e.g. Hartmann 1994;Prantzos & Diehl 1995;Diehl et al. 1997;Knödlseder et al. 1999;Diehl et al. 2004;Kretschmer et al. 2013), leaving astrophysical implications to their interpretations. It is important to cross-check simulations that are based on astrophysical assumptions with observations. A fundamentally informative comparison of hydrodynamical simulations to actual measurements is challenging because the Milky Way is one particular realisation of a galaxy, and any given hydrodynamic simulation will, even if intended to be similar, not perfectly match it. It is further complicated by the observational limitations of gamma-ray data due to the necessity of image reconstruction methods, compared to direct imaging. In this paper we investigate a range of methodological approaches for a generalised comparison of 26 Al full-sky emission maps from the simulation performed by Fujimoto et al. (2018) to gamma-ray data measured with the spectrometer SPI  aboard the INTEGRAL satellite (Winkler et al. 2003). In Sect. 2 the data analysis procedure for INTE-GRAL/SPI observations as well as the properties of the simulation by Fujimoto et al. (2018)

Gamma-ray measurements
Imaging with gamma-ray telescopes, either coded-mask based such as SPI or Compton telescopes, such as COMPTEL aboard the CGRO satellite, suffers from the large instrumental background due to cosmic-ray bombardment. Typically, background amounts to 90-99 % of measured events in SPI, so that direct imaging is only possible for strong sources. On the other hand, maximum likelihood and maximum entropy approaches are well-tested and can be directly applied to the raw data including an elaborate background model. The first full-sky image of the 1.8 MeV emission was obtained by Oberlack et al. (1996) using a maximum entropy deconvolution applied to data from 3.5 yr of observations with COMPTEL. In this work, we use the map from the entire nine-year CGRO mission obtained with the same method ( Fig. 1, Plüschke et al. 2001). The COMPTEL telescope has an angular resolution of 3.8 • . The map shows a large latitude extent on top of a clumpy structure, concentrated to the inner galactic disk region, and associated with spiral arm tangents as well as nearby massive star regions. For our analysis, we use observations of this 26 Al gamma-ray emission as was subsequently obtained with INTEGRAL, with a SPI data set comprising ∼ 200 Ms exposure time from 13.5 yr of data in the energy range from 1.795 to 1.820 MeV. We excluded observations with high rates of saturated detector events as well as 20 % of the orbital phase around the perigee in order to avoid background from solar flares and passages through the Van Allen radiation belt. The observational sky coverage of the data set in time and space is shown in Fig. 2. The patchy structure comes from the observation strategy of INTEGRAL, observing regions of interest separately, rather than performing a uniform full-sky survey. In order to spatially resolve this emission, SPI uses a codedmask technique. It measures gamma-ray energies between 20 and 8000 keV with an angular resolution of 2.7 • . According to the morphology of a source or extended emission feature and the orientation of the telescope, a characteristic shadow pattern is projected onto an array of 19 high purity Ge-detectors. The celestial signal is overlaid by an instrumental background, originating from nuclear excitations of the instrument and spacecraft material itself. To determine the celestial gamma-ray signal from the shadow pattern, simple background subtraction would lead  (Attie et al. 2003). to erroneous results, as we expect only a small number of counts per energy bin per detector per second and 90 % background. Instead, a simultaneous fit for celestial and background signals has to be applied (Strong et al. 2005;Diehl et al. 2018;Siegert et al. 2019). We use the model description for the measured instrument counts in each particular energy bin k for N I sky and N B background model components (Siegert et al. 2019). For each image element j, the celestial source model intensities M i j are convolved with the image response function R jk , i.e. the mask pattern. The parameters θ i scale the intensities for all model components i. The background contributions B ik are independent of the mask and the spacecraft orientation but vary on different time scales and over the entire mission due to the solar cycle, nuclear build-up processes, solar flares, and radiation belt transits. A detailed background model has been obtained from spectral fitting of the entire mission data , which is then adapted to the particular data set subjected to a specific analysis (Siegert et al. 2019). In this adaption, the background component has to be rescaled on an adequate time scale to properly represent such temporal variations. For the 26 Al analysis, we choose half-year intervals for the background normalisation, in addition to detector failure times (cf. Siegert et al. 2019, Sect. 5.1.2). Short-term variations are taken into account and modelled according to the saturated detector events tracking these at high statistical precision (e.g. Jean et al. 2003). The thickness of the SPI anticoincidene shield, made of 91 individual BGO crystals, is 5 cm. The attenuation cross section for photon energies around 1.8 MeV in BGO is 4.7 × 10 −2 cm 2 g −1 (Berger et al. 2010). With a density of the crystals of 7.13 g cm −3 , we estimate that the transmission probability for perpendicularly-incident photons is about 18%. This leads to an additional signal mainly when the Galactic disk emission is coming from the side. The transmission probability drops below 1% for incidence angles larger than 69 • ; only 32% of all pointings are oriented towards these higher latitudes of |b| > 21 • . Thus, the additional signal due to shield transparency can be considered as small. Additionally, this component imprints more signal in outer detectors compared to inner ones. As the orientation of the spacecraft usually remains rather constant during one orbit, this would lead to a characteristic and quasi-constant background detector pattern on that timescale. Such celestial detector count contributions are generally included in our modelled background, because we determine the background and its detector pattern per orbit. In contrast, the pattern for counts from a sky signal captured within the coded mask varies according to the spacecraft orientation due to the coded mask pattern. This enables us to distinguish background and source contributions. As the measured detector counts are Poisson-distributed, the likelihood of a set of model parameters θ, given a data set D with n data points is calculated by the full Poisson likelihood where d k is the measured number of instrument counts and m k is the model predicted value as described in Eq. (1). To determine the parameter set θ that maximises the likelihood, we use the negative logarithm of the Poisson likelihood dropping the datadependent term, which is commonly referred to as Cash statistic (Cash 1979) log In our case, full-sky maps are taken as emission models, which are fitted to the data in detector space for each energy bin separately. In order to compare non-nested models, we employ a likelihood-ratio test, which will be described in Sect. 3.1. We perform a spectral analysis of each fitted model to determine the 1.809 MeV line flux accurately above Galactic continuum emission which contributes about 5 % of the flux in the line band between 1805 and 1813 keV. We treat the spectral shape as a degraded Gaussian function which includes the effect of charge collection efficiency due to detector worsening over time (e. g. Kretschmer et al. 2013;Siegert 2017;Siegert et al. 2019). The average instrumental resolution at 1.8 MeV is 3.17 keV ).

Simulated maps
Fujimoto et al. (2018) performed a high resolution hydrodynamic simulation of a Milky Way-like spiral galaxy. They included self-gravity of gas, a fixed axisymmetric logarithmic potential to represent the gravity of old stars and dark matter, radiative cooling, photoelectric heating, as well as stellar feedback in the form of photoionisation, stellar winds, and SNe. The chemical enrichment of the galaxy was traced by following the dynamics of stellar 26 Al and 60 Fe ejecta, calculated via the Stochastically Lighting Up Galaxies (SLUG) population synthesis code (da Silva et al. 2012;Krumholz et al. 2015). Star-by-star yields of 26 Al are taken from Sukhbold et al. (2016). For their simulation, they assumed an isolated gas disk orbiting in an otherwise static background potential representing dark matter and a stellar disk component. The system evolved for t = 750 Myr with a maximum spatial resolution of 8 pc. After that running time, the physical and chemical structure of the ISM had reached a statistical equilibrium characterized by a steady large scale structure of superbubbles filled with the freshly ejected nucleosynthesis products 26 Al and 60 Fe. These bubbles around massive star forming regions were mainly following the spiral arm 150 120 90 60 30 0 330 300 270 240 210 0°7 5°1 0 4 10 3 Intensity [cm 2 sr 1 s 1 ] pattern that developed spontaneously in the simulations, spatially exceeding the size of their host giant molecular clouds (GMCs). This is consistent with measurements from SPI determining the large scale gas dynamics of 26 Al (Kretschmer et al. 2013). They derived full-sky flux maps for an hypothetical observer at the Solar Circle at r = 8 kpc by line-of-sight integration of the 1.8 MeV emission weighted with the distance squared. This was done for 36 different observer positions with 10 • step size in the plane of the simulated galaxy. These maps cover the whole sky with a pixel size of 1 • × 1 • . An example of such an integrated map, for an observer at position 0 • , is shown in Fig. 3.

Direct likelihood comparison
The most straightforward approach to compare a simulation with observations is a direct evaluation of how well the simulation describes the data. We expect, however, clear deviations due to the specific morphological features of the Milky Way, which are largely random results of the particular distribution of SN bubbles around the Sun, which we should not expect a simulation to match in detail. In this approach to comparison, we adopt the 36 flux maps obtained from the simulation by Fujimoto et al. (2018) as emission models for the 26 Al sky. We then perform maximum likelihood fits to the observational datasets using proper instrument response and backgrounds (cf. Sect. 2.1) to determine the likelihood of the fitted simulation map. Since our statistical method does not provide an absolute goodness of fit, we cannot directly evaluate resulting likelihoods. As a criterion to rate the relative fit quality of different sky models, we apply the test statistic which characterises a likelihood-ratio test of a sky model M 1 describing celestial emission on top of the background versus the null-model M 0 including only the background model. Thus, T S gives the likelihood of M 1 relative to the null-hypothesis of observing background only given the data D. With a sample of 1000 synthetic Monte Carlo datasets we verify that T S is χ 2 /2-distributed and we can associate it with the probability of M 1 occurring by chance in D (cf. Appendix A). We chose two different realms of this comparison: In the first case, we restrict our analysis to the inner galactic region with −10 • < b < 10 • and −30 • < l < 30 • (black box in Fig. 2), to treat the regions with highest intensity and longest exposure time separately. For the second case, we analyse the full sky emission. For each of the spatial realms, we determine the 26 Al signal in one energy band from 1805 keV to 1813 keV. The model comparison is shown in Fig. 4. As observation-based reference points we include model comparisons with the full-sky maximum entropy map obtained from COMPTEL (Plüschke et al. 2001) and a map obtained from SPI measurements (Bouchet et al. 2015) as sky models. This gives test statistic values for maps representing observations of the actual Milky Way emission. For the inner Galaxy, the simulated maps show values of T S mostly below the observation-based maps which are consistent with each other. Nevertheless, there are maps from sight-lines in the simulation which are as unlikely to occur by chance in the data as the observation-based maximum entropy reconstructions. This indicates that the observed structure in this region is by and large dominated by the overall Galactic morphology and therefore well described by the generic hydrodynamic simulation. There are surprising variations among the different simulation samples, however. It is particularly striking that there are some observer positions where the simulations are actually less likely to be found by chance in the SPI data than the maximum entropy reconstruction. It is difficult to identify distinct morphological features, to which the striking improvement for some of the observer positions may be attributed.
There is indication that this may be mainly due to the geometric configuration of superbubbles in the direction of the Galactic centre. We return to this issue in Sect. 3.2.1. Taking the full sky into account, the observation-based maps show overall larger and also consistent values of the test statistic T S , while values for the simulated maps fall below, with a larger scatter than for the inner galaxy case. This indicates less-matching models (through a higher probability of chance coincidence for the simulated maps, compared to the observation-based maps). Thus the simulations diverge significantly from the maximum entropy reconstruction over the full sky, particularly when we include higher latitudes. Because the simulation primarily gives relative intensity variations on the sky, we fit the line flux to estimate the absolute changes. The obtained fluxes are given in Table 1  state, prominent 1.8 MeV emission regions such as Cygnus, Carina, or Sco-Cen, as well as the characteristic spiral arm structure of the Miky Way have been omitted in their simulation. Thus, it is reasonable that especially the characteristic foreground emission in the Milky Way, which originates from regions relatively close to the Earth and extends to higher latitudes, is missing. The COMPTEL map as well as the SPI map include such regions and features, thus providing a better fit to INTEGRAL/SPI data. Nevertheless, the good fitting results for the inner Galaxy indicate that this region is less influenced by characteristic foreground features but by the galaxy-wide emission.

Scale height analysis
Given our finding that numerical simulations fail to mimic the particular structure of the sky as seen from Earth, we now seek a more general method of comparing simulations and observations. Thus, we analyse their morphological features in a generalized way which can be applied to SPI measurements as well. Common morphological analyses like expansion in spherical harmonics or wavelets are very sensitive to the assumptions made for image reconstructions, for example starting points of maximum entropy deconvolution. Thus, we stick to maximum likelihood estimations of chosen models, and evaluate characteristic distributions that can be inferred from those models. A representation of the sky in spherical harmonics has basically an infinite number of realisations for each combination of degree and mode already by simple rotation on the sky. As we can only test each realisation of such an analytic model individually, this is not a basis for a viable approach. Thus, we have to choose a simpler model which contains basic morphological information and for which we can fit individual realisations to the data.

Galaxy-wide scale height and scale radius
Extragalactic studies show an exponential decrease of young massive stars with radius. As the 1.8 MeV emission from 26 Al traces such massive star groups, we expect it to follow a similar trend. Therefore, we assume a doubly exponential disk model with the galactocentric radius r 2 = x 2 + y 2 , the height above the disk z, scale radius r 0 , scale height z 0 , and amplitude of the disk A 0 , as a first-order model for the galactic 3D distribution of the 26 Al emissivity in units of ph cm −3 s −1 . The 2D flux projection of this emission model onto the celestial sphere in galactic longitude l and latitude b is obtained by line-of-sight integration from the relative position of the Sun with respect to the Galactic centre p s = (x s , y s , z s ) = (8.5, 0, 0) kpc along the line-of-sight vector u = (u x , u y , u z ) = (cos(l) cos(b), sin(l) cos(b), sin(b)). The integration boundaries s min and s max confine the emission model to the volume of the Milky Way. Earlier studies of the inner Galaxy with SPI find a 26 Al scale height between 60 and 250 pc (Diehl et al. 2006;Wang et al. 2009) for a fixed scale radius of 4 kpc. COMPTEL all-sky datasets also suggested a scale height of 150-170 pc Diehl et al. 1997). In order to obtain a galaxy-wide evaluation of the 26 Al emission with SPI, we fit a grid of 32 × 64 combinations of different r 0 and z 0 to our set of 13.5 yr of SPI data. The scale radius r 0 ranges from 0.50 to 8.25 kpc in 250 pc steps. The scale height z 0 ranges from 10 to 475 pc in 15 pc steps and from 500 to 2050 pc in 50 pc steps (Siegert 2017). From the resulting Poisson likelihood values we calculate the probability density distribution for combinations of scale height and scale radius of the galaxy-wide 26 Al emission. The results are shown in Fig. 5. From the likelihood profiles of both parameters, we find a best fitting exponential disk model with r 0 = 5.81 ± 0.64 kpc and z 0 = 0.77 ± 0.17 kpc for the Milky Way emission. The smaller scale height of 180 pc found with SPI by Wang et al. (2009) is due to a spatial restriction to the inner Galaxy. We fit the same grid of exponential disk emission models to the 36 simulated 26 Al flux maps. This enables a comparison of the galaxy-wide morphology of simulations and gamma-ray measurements. We evaluate the best fitting amplitude for each exponential disk model and calculate the difference between each simulated map and all exponential disk maps. In order to capture the same dynamical range as in SPI observations, we multiply the simulated sky maps with the SPI exposure map. This transfers the sky maps into count space projected onto the sky with effective area and sky coverage of SPI taken into account. We perform a Pearson's χ 2 fit to estimate the best fitting amplitudes of all exponential disk models for each simulated map, treating the maps from the simulation as synthetic data and the exponential disk maps as model prediction. From the minimum χ 2 values we find the mean values of r 0 = 3.02 kpc and z 0 = 0.07 kpc for all synthetic sky maps. While the overall scale radius in the simulation is close to what we observe in the Milky Way, the scale height appears to be one order of magnitude smaller. However, we find one outlier at an observer position of 100 • in the simulated galaxy, which shows the maximum overall scale height of z 0 = 0.7 kpc in agreement with observations. In the simulation, this is a unique spot where the observer is placed directly inside a superbubble of ∼ 1 kpc in size around two high star formation clumps, located in the direction of the galactic centre. This could indicate that, from a nucleosynthesis point of view, the Sun inside the Local Bubble is located at such a rather exceptional location in the Galaxy.

Scale height frequency spectrum
In order to spatially resolve how the overall scale height is composed of certain features with different latitude extent, we investigate separate rectangular regions of interest (ROIs) of 12 • in longitude and 180 • in latitude each. The width in longitude was chosen to achieve a compromise between spatial resolution and intensity of the 26 Al signal per bin (Kretschmer et al. 2013). We also apply synthetic noise reflecting the dynamical range of the observations by a weighting with the SPI exposure as it was done in Sect. 3.2.1. For simplicity, we assume a fixed scale radius of r 0 = 5.5 kpc for the exponential disk models and retain only z 0 as free parameter. We determine the fit quality for a set of 123 fullsky exponential disk models with different scale heights between 10 pc and 5 kpc for each ROI separately. The step size is 15 pc from 10 to 475 pc and 50 pc from 0.5 to 5 kpc. The scale height of the best fitting model in each longitude bin gives a measure of the extent of 26 Al emission in latitude. Since SPI has a field of view of 16 × 16 deg 2 , two adjacent ROIs are overlapping. To account for the variability arising from the arbitrary placement of bins and their overlap, the evaluation was done for 12 different sets of bins shifted in 1 • longitude steps. This allows for a generalized comparison of the variances present in synthetic and observed maps of the galactic 26 Al emission that is particularly independent of the specific morphology

Scale height vs. longitude
To see how the different scale height components are linked to the galactic morphology, we break down the results according to galactic longitude. This is depicted in Fig. 7. The uncertainties in scale height represent the average width of the log(L )-profile in each longitude bin. Due to overlapping ROIs neighbouring data points are not strictly independent and grouped together alternately. The error bars in longitude account for the overlap.
In regions looking away from the Galactic centre at −60 • > l > 60 • , SPI observations are dominated by emission with small scale heights of ∼ 10 pc with a few contributions at intermediate large scale heights. On average, this general structure is also seen in the simulation, indicating that these regions in the Milky Way are shaped according to the stochastic galaxy-wide star formation processes. On the other hand, around the Galactic centre at −60 • < l < 60 • , the measurements show intermediate to very  Fujimoto et al. (2018) individually. Their median is given by the green line with the 68th percentile as shaded green region. The purple crosses represent the maximum likelihood scale heights obtained from SPI data with errors in y-direction depicting the average width of the log(L )-profile in each longitude bin. Since adjacent ROIs are overlapping, data points are shown alternately with bold and thin markers to group mostly-independent data points together. The shaded region follows only the bold data points to guide the eye for a possible trend. The fits are restricted to 5 kpc scale heights.
large scale heights of the order of kpc. The flux maps from the simulation show overall smaller scale heights between 10 pc and 100 pc in this region. In contrast to the previously considered outer regions, this implies a strong contribution of characteristic nearby foreground emission in the direction around l = 0 • , e.g. from the Sco-Cen region at l = 350 • (Krause et al. 2018). The structural difference could indicate that the run of star formation rate density with galactocentric radius differs in the simulation from the true conditions in the Milky Way, i.e. there may be more star formation locally than the simulation assumes. Another possible reason could be that the clustering of star formation in the simulation could differ from the one in the observation. The clustering of superbubbles affects the vertical flow of nucleosynthesis material, with bigger superbubbles causing stronger vertical flows (von Glasow et al. 2013). Additionally, the spiral arms in the Milky Way could be more classical density waves than the spontaneously formed structures in the simulation, perhaps related to external perturbations or the bar. This may concentrate star formation in fewer, more prominent spiral arms in reality.

Conclusions
In this paper we present methodological routes for comparison between observed maps of 26 Al decay in the gamma-ray sky and hydrodynamic simulations of a galactic 26 Al distribution. A direct comparison of a generic simulation with observations necessarily yields relatively poor fits because the simulation does not match particular prominent foreground features of the sky as seen from Earth. Nevertheless, we find that the portion of the sky around the Milky Way centre seems to be dominated by the overall galactic emission rather than characteristic foreground structures, and that the simulation provides a reasonably good match to the observed γ-ray sky in this region. This provides information about the 3D distribution of the 26 Al emission.
For a morphologically more generalised approach, we investigated the latitude extent of the 1.8 MeV emission as parametrized by the exponential scale height. The rather broad emission with z 0 = 0.77 ± 0.17 kpc from SPI observations is only seen in one configuration in the simulation. In this case, the observer is placed inside a large superbubble structure filled with freshly produced 26 Al. This may imply that the Sun is placed in a similarly exceptional location in the Milky Way. In order to spatially resolve certain emission features, we evaluated the scale height extent in 12 • longitude bins. Analysis of the SPI maps reveals an almost bi-modal distribution, with most longitudes showing a small scale height 50 pc, but a small number showing extremely large scale heights of a few kpc. These large scale height bins are mainly seen around the direction towards the Galactic centre. The simulation lacks such features on average. Such large latitude extent of 26 Al has to be associated with nearby regions. Thus, we confirm that the 1.8 MeV emission contains a significant contribution from nearby superbubbles, e.g. from Sco-Cen or regions along the spiral arm tangents (e.g. del Rio et al. 1996;Diehl et al. 2010;Krause et al. 2018). We find indications that one of the most-nearby Sco-Cen 26 Al-filled superbubbles may have overrun the Solar System already and thus contribute an omnidirectional emission component (cf. Krause et al. 2018). This characteristic seen in the observations, and its relative infrequency in simulated sky maps, suggests that the Milky Way may have a more coarse-grained superbubble structure than modelled in the simulation. Indeed, Fujimoto et al. (2019) found that the pre-supernovae stage feedback implemented in Fujimoto et al. (2018) is inefficiently strong to disperse the surrounding gas completely, leaving star formation tracer emission too strongly associated with molecular gas tracer emission, inconsistent with observations of nearby galaxies. Thus, the 1.8 MeV map contains important information about the detailed geometry of massive star feedback in the Milky Way. The bimodal distribution of scale heights apparent in SPI measurements along different longitudes indicates that Galactic 1.8 MeV emission deviates significantly from a simple exponential disk model. This implies that previously determined scale heights to describe the 1.8 MeV emission of the entire Galaxy do not correspond to a physical scale height of 26 Al, and instead are probably significantly biased by local foregrounds. Thus, an exponential disk model is insufficient to fit the local scale heights and a purely phenomenological model should be used for this kind of analysis in further studies. This adds systematic uncertainties to the current total 26 Al mass estimate in the Milky Way, because it is based on the assumption of a consistent Galactic scale height (Diehl et al. 2006).