1 - Max-Planck-Institut für extraterrestrische Physik, Postfach 1312, 85741 Garching, Germany
2 - Department of Physics & Astronomy, Clemson University, Clemson, SC 29634-0978, USA

Abstract
The shape of the gamma-ray line from radioactive ²⁶Al, at 1808.7 keV energy in the frame of the decaying isotope, is determined by its kinematics when it decays, typically 10⁶ y after its ejection into the interstellar medium from its nucleosynthesis source. Three measurements of the line width exist: HEAO-C's 1982 value of (0+3) keV FWHM, the GRIS 1996 value of $(5.4\pm 1.3)$ keV FWHM, and the recent RHESSI value of $(2.0\pm 0.8)$ keV FWHM, suggesting either "cold'', "hot'', or "warm'' ²⁶Al in the ISM. We model the line width as expected from Galactic rotation, expanding supernova ejecta, and/or Wolf-Rayet winds, and predict a value below 1 keV (FWHM) with plausible assumptions about ²⁶Al initial velocities and expansion history. Even though the recent RHESSI measurement reduces the need to explain a broad line corresponding to 540 km s^-1 mean ²⁶Al velocity through extreme assumptions about grain transport of ²⁶Al or huge interstellar cavities, our results suggest that standard ²⁶Al ejection models produce a line on the narrow side of what is observed by RHESSI and INTEGRAL. Improved INTEGRAL and RHESSI spatially-resolved line width measurements should help to disentangle the effects of Galactic rotation from the ISM trajectories of ²⁶Al.

Key words: nuclear reactions, nucleosynthesis, abundances - gamma rays: observations - supernovae: general - ISM: supernova remnants - stars: formation

Current Galactic nucleosynthesis reveals itself through the decay of ²⁶Al, one of its radioactive by-products with a mean lifetime of $1.04\times 10^6$ y. ²⁶Al undergoes $\beta^+$ -decay into an excited state of ²⁶Mg, which de-excites through emission of a gamma-ray photon at 1808.7 keV. This gamma-ray line has been observed and imaged throughout the Galaxy (Mahoney et al. 1982; Plüschke et al. 2001; Diehl et al. 1995; Oberlack 1997; Knödlseder et al. 1999). Sources of ²⁶Al may be AGB stars and novae, but massive stars (via core-collapse supernovae and winds from Wolf-Rayet stars) have been found the most plausible and probably dominating sources (Prantzos & Diehl 1996). The rather irregular ²⁶Al emission along the plane of the Galaxy, and its consistency with the patterns of tracers of massive-star activity, is the main argument for favouring massive stars as the sources (Plüschke et al. 2001; Diehl et al. 1996; Knödlseder et al. 1999). Flux measurements have been employed to study the nature of the sources, comparing with predicted ²⁶Al yields from models of the source types. The amount of ²⁶Al present in the ISM of the Galaxy has been estimated at $\approx$ 2 ${M}_\odot$ , and used to argue for the roles of different source types. But the uncertainties about the spatial distribution and total number of nucleosynthesis events add to source yield uncertainties, providing only qualitative arguments for the nature of ²⁶Al sources (Prantzos & Diehl 1996). Therefore, locally constrained candidate source populations have been studied, such as in the Cygnus region (Plüschke et al. 2001; Knödlseder et al. 2000). In such a case, the distance to the sources is constrained to a smaller interval, along with the radial velocity due to Galactic rotation.

Measurements of Galactic ²⁶Al with high-resolution spectrometers have produced somewhat controversial results: The initial discovery with the space-borne HEAO-C Ge spectrometer had reported a narrow line (intrinsic width (FWHM) (0+3) keV; Mahoney et al. 1984). But the GRIS balloon-borne Ge spectrometer found the line to be significantly broadened (intrinsic FWHM $(5.4\pm1.4)$ keV; Naya et al. 1996). Such a broad line, however, cannot be explained easily (see Chen et al. 1997). If the origin of the line broadening was thermal, the ²⁶Al decay region would need to be at a temperature of ${\approx} 4.5\times 10^8$ K. Alternatively, ²⁶Al isotopes would have to maintain a mean velocity around 540 km s^-1 over their 1 My decay time, travelling kpc distances at those speeds. One may either assume that a substantial fraction of ²⁶Al is injected into such rather large interstellar cavities, or that a substantial fraction of ²⁶Al condenses onto dust grains before deceleration, so it maintains its momentum throughout passages of supernova remnant shells or other obstacles. The velocity could also be a result of re-acceleration of dust grains by interstellar shocks in the neighbourhood of the source, allowing them to maintain a high velocity over the ²⁶Al decay time scale (Sturner & Naya 1999). None of these explanations is straightforward or without problems. A firm measurement of the ²⁶Al gamma-ray line width is desirable, before questioning our understanding of ²⁶Al fate from its production sites until decay in interstellar space.

New measurements have been obtained recently with Ge spectrometers aboard the high energy solar spectroscopy imager RHESSI (Smith 2003) and the INTEGRAL observatory. The RHESSI result was derived through Earth occultation analysis of data while pointing at the sun. They obtain an intermediate intrinsic line width of about $(2.0\pm 0.8)$ keV FWHM. The preliminary INTEGRAL measurement also suggests a narrow line, but systematic uncertainties are still large (Diehl et al. 2003). Within the given uncertainties, the current set of measurements is mildly inconsistent. But more measurements have been recorded with INTEGRAL's SPI Ge spectrometer already, so that longitude-resolved line width results are at the horizon.

We explore the potential of ²⁶Al decay line shape measurements for diagnostics on the sources of ²⁶Al and their interstellar environment. We follow up on earlier analysis by Gehrels & Chen (1996), who showed that the structure of the Galaxy should be reflected in the position of the line due to Doppler shift from Galactic rotation. In this paper we employ an updated spatial distribution model for the plausible sources of ²⁶Al in the Galaxy. We also account for the fate of ejected ²⁶Al in interstellar space through different model variants which reflect ejections by winds and/or supernovae into cavities of plausible sizes for the massive-star environment of the ²⁶Al sources. Our aim is to illustrate the diagnostic power of measuring the ²⁶Al gamma-ray line's position and width; this should be feasible with current instrumentation through imaging spectroscopy, even if a detailed decomposition of the line shape may still be beyond reach.

2 ²⁶Al sources in the Galaxy

Our model for the distribution of ²⁶Al in the Galaxy is based on two separate aspects: the distribution of nucleosynthesis events in the Galaxy, and the distribution of ²⁶Al in interstellar space following an individual nucleosynthesis event. For each of these, spatial as well as velocity-space densities have to be considered.

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{Fg071_f1.eps} \end{figure}$	Figure 1: Model of the free electron density in the galactic plane (Taylor & Cordes 1993), used as ²⁶Al source density distribution. Dotted lines represent $-60\hbox {$^\circ $ }$ , $-30\hbox {$^\circ $ }$ , $-4\hbox {$^\circ $ }$ , 0 $^\circ$ , 4 $^\circ$ , 30 $^\circ$ and 60 $^\circ$ galactic longitude. Hatched areas illustrate the eastern/western parts of the inner galactic region.
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The angular distribution of ²⁶Al 1809 keV emission on the sky correlates well with tracers of ionisation, such as H $_\alpha$ or free-free emission. Therefore we adopt a three-dimensional model for the space density of free electrons as our parent distribution for ²⁶Al sources in the Galaxy. Such a model has been derived by Taylor & Cordes (1993) from pulsar dispersion measure observations (a cut through this model along the Galactic plane can be seen in Fig. 1); it was updated in Cordes & Lazio (2002). Alternative spatial models, such as the smooth, axisymmetric one by Gómez et al. (2001) will probably yield similar line shape results.

The Doppler shifts due to Galactic rotation can then be determined from the Galactic rotation curve. For our model we used the results obtained by Olling & Merrifield (2000) from fitting radial velocity measurements with a five-component mass model of the Galaxy, consisting of a stellar bulge, a stellar disc, two gas discs (H I, H₂) and a dark-matter halo. Because their determination of the rotation curve depends on the values of the distance to the galactic centre R₀ and the local circular speed $\Theta_0$ , which are not known to a high degree of precision, they allowed these parameters to vary over a broad range of values. In view of these uncertainties and because we are interested mainly in the inner Galaxy, we approximated the rotation curve given by Olling & Merrifield for the IAU standard values $R_0=8.5\ {\rm kpc}$ and $\Theta_0=220\ {\rm km~s}^{-1}$ with the radial dependence:

$\begin{displaymath}\vert\vec v\vert(R) = 220\ {\rm km~s}^{-1} \cdot \left[1 - \exp(-R / 1\ {\rm kpc})\right] \end{displaymath}$

Superimposed on Galactic rotation is the motion of freshly synthesised radioactive material due to the parental supernova explosion or the ejecting Wolf-Rayet star wind and its slowed-down motion in the ISM before decay, i.e. within ${\approx} 10^6$ yr. Concentrating first on supernovae, we adopt a particular expansion behaviour: Recent hydrodynamic simulations of type II supernovae by Kifonidis et al. (2003) find that the expansion of the bulk of nucleosynthetic SN products such as ²⁶Al may be at velocities less than 1200 km s^-1. To reflect their results, we allow ²⁶Al to expand freely with a velocity of 1500 km s^-1until it reaches the radius of the SN reverse shock formed by circumstellar interaction. After this point, we expand ²⁶Al at the velocity of the blast wave shock; this gives us a conservative estimate because ²⁶Al is likely to move slower than the forward shock. For our model of SNR dynamics from circumstellar interaction, we adopt the values for Kepler's supernova remnant shock positions and velocities given by McKee & Truelove (1995).

At present, our model does not include other ²⁶Al sources; type Ib/Ic supernovae and Wolf-Rayet stars (Prantzos & Diehl 1996), which eject matter at similar or even higher speeds than Type II SNe (Mellema & Lundqvist 2002; Prinja et al. 1990; Garcia-Segura et al. 1996). Also, the interaction of ejected matter with the surrounding medium depends on the star formation history of the source region, where bubbles forming around groups of young massive stars play a potentially large role. Cavities extending over several hundred pc have been observed in galaxies (Oey & Clarke 1996), and the Eridanus cavity (Burrows et al. 1993) presents us with a nearby example of such a cavity, extending from the Orion star forming region to very near the Sun. Matter ejected into such a low-density bubble could expand almost freely until reaching the boundary whereas typically assumed ISM densities $(n_{\rm H}\simeq 1~{\rm cm}^{-3})$ would slow it down quite rapidly. To keep the model simple at first, we adopt above SNR model as typical for ²⁶Al sources; refinements will be discussed in our subsequent studies.

With these assumptions, the ejected ²⁶Al moves freely for $\approx$ 2 kyr, then decelerates with the SNR's shell. The shell reaches a radius where it dissolves in the ISM at an age comparable to the lifetime of ²⁶Al , when a significant fraction has therefore already decayed. We note that the expansion velocity drops below the characteristic rotational velocity of 220 km s^-1 at $\approx$ 40 kyr, when 96% of the ²⁶Al is still left. Therefore the contribution from expansion to the overall line width will be rather small in our model.

3 Line shape diagnostics

We obtain simulated sky maps and spectra from a Monte Carlo scheme: ²⁶Al source locations are chosen randomly from a spatial distribution proportional to the free electron density, distributing candidate source positions within a volume centered on the Galaxy and extending 25 kpc in the plane and 7.5 kpc perpendicular to the plane. The free-electron density within this volume is taken from Taylor & Cordes (1993). For each nucleosynthesis event, a random age is chosen within the interval $[0, 10^7\ {\rm yr}]$ . From this we evaluate the intrinsic velocity distribution and size of the ²⁶Al source, following the above expansion model. The age of the nucleosynthesis event thus determines extent and intrinsic velocity of its ejecta, as well as their 1.809 MeV luminosity. We represent each event by 2¹⁰ mass elements to reflect its spatial extent.

With the observer at $R_0=8.5\ {\rm kpc}$ and $\Theta_0=220\ {\rm km\ s^{-1}}$ , we obtain viewing direction and radial velocity of ²⁶Al sources. Direction and radial velocity give us the coordinates of the ²⁶Al source mass element in a data space of ²⁶Al decay luminosity as a function of longitude, latitude and photon energy.

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{Fg071_f2.eps} \end{figure}$	Figure 2: ²⁶Al line intensity as a function of Galactic longitude and gamma-ray photon energy, with the source longitude profile superimposed.
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Projecting this data volume onto the longitude-energy plane, we obtain a map of ²⁶Al line intensities as a function of Galactic longitude and observed photon energy (See Fig. 2). The intrinsic velocity spreads and spatial source distributions lead to a line blurring of $\approx$ 0.3-0.5 keV along the plane of the Galaxy. Galactic rotation leads to the symmetric line shifts east and west of the Galactic centre. Deviating from the trend of decreasing surface brightness with increasing separation from the Galactic centre, we notice a prominent flux enhancement around $-70\hbox{$^\circ$ }$ , which corresponds to the direction tangential to the Carina-Sagittarius spiral arm, which is also clearly visible in the longitude profile of our source distribution model, superimposed as a histogram in the upper half of the figure; see also Fig. 1.

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{Fg071_f3.eps} \end{figure}$	Figure 3: Spectrum of the inner galaxy ( $l \in [-30\hbox {$^\circ $ }, 30\hbox {$^\circ $ }]$ . The full line is the source spectrum, the dotted line the best-fitting Gaussian, and the dashed line results from a convolution with a 2.8 keV FWHM Gaussian adopted for instrumental resolution of the measuring detector. $b \in [-5\hbox {$^\circ $ }, 5\hbox {$^\circ $ }]$ ).
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In order to compare with a measured line profile, we integrate our simulated skymap of line energies and intensities over a region of interest of and obtain a resulting spectrum corresponding to an observation of this region without spatial, but with perfect spectral resolution. The spectrum shown in Fig. 3 represents a region-of-interest chosen to reflect the RHESSI analysis of the inner Galaxy (Smith 2003). Fitting a Gaussian to this spectrum yields an equivalent line width of 1.0 keV (FWHM). The deviation from a Gaussian shape, which appears clear in our model spectrum (Fig. 3, continuous line versus dotted line) is probably too small to be detectable with a realistic Ge detector of instrumental resolution 2.8 keV FWHM (approximate for SPI on INTEGRAL, determined by in-orbit measurements of detector background lines; Attié et al. 2003), convolution with the instrument response suppresses the difference between the measured flux and a Gaussian by a factor of $\approx$ 2000 (see dashed line in Fig. 3).

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{Fg071_f4.eps} \end{figure}$

Figure 4: Illustrations of lines from different Galactic regions: The histograms (dotted/dashed lines) show the spectra of the eastern/western part of the inner galactic region (i.e. $\pm 5\hbox {$^\circ $ }$ in latitude, $\pm [4\hbox {$^\circ $ }{-}30\hbox {$^\circ $ }]$ in longitude) Energy-resolution limited spectra (obtained by convolving with 2.8 keV FWHM Gaussians) are shown as dash-dotted/long-dashed lines.

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We used data analysis parameters from the first inner-Galaxy observations of INTEGRAL's core programme to estimate the possible precision of gamma-ray line centroid measurements. By using Gaussian fits to simulated spectra with varying levels of statistical noise, we tested the relation of the achievable line position determination accuracy and the signal-to-noise ratio. We confirm the centroid uncertainty to be proportional to the noise-to-signal ratio, therefore scaling with the inverse square root of exposure time. At present, noise is dominated by systematic uncertainties, resulting in a position uncertainty of $\pm 0.19$ keV. If we extrapolate to the full exposure of 3 Ms scheduled for the first year of INTEGRAL operations, we estimate a statistical uncertainty for the ²⁶Al line centroid of $\pm 0.06$ keV. We expect that systematic uncertainties in INTEGRAL results can be reduced in the near future through studies of SPI's spectral resolution, energy calibration stability, and background in-flight behaviour. When systematic uncertainties are reduced below the level of statistical uncertainty, we expect a $3\sigma$ detection of the Doppler shift relative to an equally long observation at the Galactic longitude of maximum Doppler shift at $l=330\hbox{$^\circ$ }$ .

4 Conclusions

We model ²⁶Al sources in the Galaxy, adopting massive stars as the dominating sources. Using Galactic rotation and plausible assumptions for the fate of ²⁶Al from ejection by the supernova or Wolf Rayet star into until decay in interstellar space, we derive an expected profile for the 1809 keV gamma-ray line from the decay of Galactic ²⁶Al. For this, we integrate along the lines of sight over the Doppler-shifted source regions of ²⁶Al emission with their intrinsic state of dynamical evolution.

Measurements of the 1809 keV emission from galactic ²⁶Al play in principle a role similar to the H I 21 cm radiation, with the benefit that the Galaxy is always optically thin to MeV gamma radiation. Current instruments are unable to improve the knowledge of galactic rotation over H I results, the basis for the inner galaxy rotation curve by Olling & Merrifield (2000), but the knowledge of rotation can be used to test the position of ²⁶Al sources.

Our result demonstrates that the gamma-ray line profile reflects the kinematics of decaying ²⁶Al in the ISM. However, current Ge detectors will probably be unable to detect line shape departures from a simple Gaussian shape for spectra such as predicted by our model. Nevertheless, centroid and width of the line will provide a diagnostic for the ²⁶Al sources in the Galaxy.

Detection of the expected amount of line shift would put a limit on the contribution of local emission to the ²⁶Al flux in the direction of the inner galaxy. By their massive star origin, ²⁶Al and H II-regions are connected; the latter having also been used to measure galactic rotation (Brand & Blitz 1993). H II regions are created by the ionising radiation from O stars, therefore probe the first 2 My of star formation. The peak of ²⁶Al emission from a coeval group of massive stars only begins at 2 My, continuing for another 10 My (Plüschke et al. 2001). This demonstrates that ²⁶Al and the other analyses of galactic rotation may complement each other.

Our model parameters, chosen to represent supernova-produced ²⁶Al with ejection into an typical ISM environment, predict a line width of $\approx$ 1 keV for the inner Galaxy. This value is on the low side of the recent RHESSI measurement (Smith 2003), and significantly below the "broad'' line reported from the GRIS balloon measurement (Naya et al. 1996). We suggest, therefore, that ²⁶Al decay in the interstellar medium is likely to teach us more about the ejection and expansion characteristics of nucleosynthesis ejecta, and thus about the morphology of the interstellar medium in the vicinity of massive stars, our assumed sources of ²⁶Al in the Galaxy. For example, if ²⁶Al sources typically are surrounded by cavities from earlier massive-star action, this could lead to some additional broadening of the observed ²⁶Al gamma-ray line. Further imaging spectroscopy analysis of RHESSI data and of measurements with the SPI Ge spectrometer on INTEGRAL (launched in October 2002; Winkler et al. 2003) promise to provide the data for such studies.

Line shape diagnostics of Galactic ²⁶Al

1 Introduction

2 ²⁶Al sources in the Galaxy

3 Line shape diagnostics

4 Conclusions

References

Line shape diagnostics of Galactic 26Al

1 Introduction

2 26Al sources in the Galaxy

3 Line shape diagnostics

4 Conclusions

References

Line shape diagnostics of Galactic ²⁶Al

2 ²⁶Al sources in the Galaxy