THE ASTROPHYSICAL JOURNAL, 487:L57L60, 1997 September 20
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Annihilation Fountain in the Galactic Center Region

C. D. DERMER AND J. G. SKIBO

E. O. Hulburt Center for Space Research, Code 7653, Naval Research Laboratory, Washington, DC 20375-5352

Received 1997 May 9; accepted 1997 July 7

ABSTRACT

     Two different model-independent mapping techniques have been applied to Compton Gamma Ray Observatory OSSE, SMM, TGRS, and balloon data and reveal a feature in the 0.511 MeV e⁺-e^- annihilation radiation pattern of our Galaxy centered at l -2° and b 10° with a flux of approximately 5 × 10^-4 0.511 MeV photons cm^-2 s^-1. If near the Galactic center, then positron (e⁺) sources are producing about 10⁴² e⁺ s^-1, which annihilate 12 kpc above the Galactic plane. A starburst episode within the inner few hundred parsecs of our Galaxy would drive hot pair-laden gas into the halo, with the one-sidedness pointing to the site of initial pressure release at the onset of the starburst activity. Positrons lose energy and annihilate as they are convected upward with the gas flow, and we calculate high-latitude annihilation patterns and fluxes in accord with the observations. Changes in the ionization state when the escaping gas cools could give annihilation radiation substructure. The fountain of hot (10⁶10⁷ K) gas rising into the Galactic halo would be seen through its enhanced dispersion measure, thermal emission, and recombination radiation.

Subject headings: gamma rays: theoryISM: jets and outflowsnuclear reactions, nucleosynthesis, abundancessupernova remnants

CONTENTS

• 1. INTRODUCTION
• 2. POSITRON PRODUCTION FROM SUPERNOVAE AND GALACTIC CENTER ACTIVITY
• 3. ANNIHILATION FOUNTAIN MODEL
• 4. PREDICTIONS AND SUMMARY
• ACKNOWLEDGMENTS
• REFERENCES
• FIGURES
• REFERENCES TO THIS ARTICLE

§1. INTRODUCTION

     In addition to the previously identified (e.g., Purcell et al. 1993; Ramaty, Skibo, & Lingenfelter 1994) 0.511 MeV annihilation glow from the disk and nuclear bulge of our Galaxy, recent analyses (Purcell et al. 1997a, 1997b; Cheng et al. 1997) of data obtained with the Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma Ray Observatory, the Solar Maximum Mission (SMM) (Share et al. 1990), the Transient Gamma Ray Spectrometer (TGRS) (Teegarden et al. 1996) on the Wind spacecraft, and GRIS (Gehrels et al. 1991; Leventhal et al. 1993), FIGARO (Niel et al. 1990), and HEXAGONE (Chapuis et al. 1991) balloon experiments show a very significant annihilation emission component 5°10° north of the Galactic plane in the general direction defined by the axis of the Galactic center lobe (Pohl, Reich, & Schlickeiser 1992; Mezger, Duschl, & Zylka 1996). Imaging limitations of the -ray telescopes make it impossible to resolve fine structure, but the high-latitude component appears extended rather than pointlike. If near the Galactic center at distance 8d₈ kpc, then positron sources are producing (2 - 3f2)^-14 × 10⁴²d = e⁺ s^-1, which annihilate 12 kpc above the Galactic plane. Here f is the fraction of e⁺ that annihilates via positronium (Ps) formation.

     Positron sources include radioactive emitters from supernovae (SNs) and novae, black hole jets, and low-energy (10100 MeV nucleon^-1) cosmic rays. Because of the proximity to the Galactic center and the feebleness of annihilation radiation from star-forming regions, we conclude that the region of enhanced e⁺-e^- annihilation radiation exists about 1 kpc above the Galactic center. A starburst episode within the inner few hundred parsecs of our Galaxy would drive hot pair-laden gas into the halo, with the one-sidedness pointing to the site of initial pressure release at the onset of the starburst activity. Here we investigate the production, transport, and annihilation of e⁺ convected to high Galactic latitudes in a wind produced in the Galactic center region.

§2. POSITRON PRODUCTION FROM SUPERNOVAE AND GALACTIC CENTER ACTIVITY

     The origin of positrons through the decay of radioactive nuclei is confirmed by observations of ⁵⁶Co and ⁵⁷Co nuclear decay lines from SN 1987A (Matz et al. 1988; Kurfess et al. 1992), the ²⁶Al 1.809 MeV line found in clumped structure along the Galactic plane (Diehl et al. 1995), and the ⁴⁴Ti nuclear decay line from Cas A (Iyudin et al. 1994). The mean lifetimes of the ⁵⁶Ni ⁵⁶Co and ⁵⁶Co ⁵⁶Fe decays in the ⁵⁶Ni ⁵⁶Co ⁵⁶Fe chain are 8.8 and 111.4 days, respectively, with a ⁺ emitted 19% of the time in the latter reaction. Type Ia SNs involving white dwarf detonation or deflagration produce a time-averaged e⁺ production rate 1.4 × 10⁴³_-2M_56IaC e⁺ s^-1, where M₅₆ is the average number of solar masses of synthesized ⁵⁶Fe per SN Ia, _IaC is the number of Type Ia SNs per century throughout the Milky Way, and = 10^-2_-2 is the escape fraction. Chan & Lingenfelter (1993) calculate the escape fraction to be in the range 0.1 _-2 10, and report (Woosley & Weaver 1992) that 0.6 < M₅₆ < 0.9. For core-collapse Type II SNs, only an average 0.08 M of ⁵⁶Fe is synthesized per SN, and the escape fraction could reach 0.7% for well-mixed ejecta, implying that 10⁴²_-2(M₅₆0.08)_IIC e⁺ s^-1.

     The mean lifetime of the ⁴⁴Ti ⁴⁴Sc ⁴⁴Ca chain is 78 yr, with a positron produced 95% of the time in the latter decay. Compared to the mass of ⁵⁶Fe, a ⁴⁴Ti mass fraction = 10^-4_-4 in the range 0.3 _-4 1.4 is calculated for SN Ia and _-4 < 25 is found for SN II (Chan & Lingenfelter 1993). This gives 8 × 10⁴¹_-4M_56SNC, noting that most e⁺ escape from the SN ejecta and mix with the surrounding medium. The ²⁶Al decays into ²⁶Mg with a mean lifetime of 10⁶ yr, producing a positron 82% of the time. Production of ²⁶Al is most important in Type II SNs, although only 0.3 × 10^-5 M₂₆ 20 × 10^-5 M of ²⁶Al are produced per SN II, depending on initial stellar mass and the treatment of semiconvection (Prantzos 1996). This gives 10⁴¹(M₂₆10^-5)_IIC e⁺ s^-1, a value probably insufficient to account for the 1.5 M of ²⁶Al required to explain the total observed (Diehl et al. 1995) 1.809 MeV ²⁶Al line flux of 3.1(±0.9) × 10^-4 cm^-2 s^-1 for which, at least, Wolf-Rayet stars and novae make important contributions. This mass of ²⁶Al produces 2 × 10⁴² e⁺ s^-1, which contributes to the disk annihilation emissivity.

     An episode of starburst activity in a region a few hundred parsecs across enclosing the Galactic center could account for Ginga observations (Koyama et al. 1989; Yamauchi et al. 1990) of 6.7 keV emission from He-like Fe at temperatures 10⁷ K. Heating of the gas requires 10⁵⁴ ergs of energy to be injected within the last 10⁶ yr, which could be achieved by 10³ Type II SNs over the preceding 10⁵ yr, each injecting 12 × 10⁵¹ ergs of kinetic energy into the interstellar medium (ISM) (Hartmann, Timmes, & Diehl 1997). Other indications of explosive events near the Galactic center include large-scale X-ray structures, radio structures, and indeed the 1.809 MeV line (Hartmann 1995) . The radio emission of the Galactic center lobe can be explained by the synchrotron emission of nonthermal electrons convecting and diffusing outward (see Pohl et al. 1992).

     Within the limits of uncertainty, ⁺ production from Type II SNs could account for the flux of the high-latitude annihilation glow if _SNC 1 in the central 100200 pc nuclear region of our Galaxy and, furthermore, if e⁺ are transported to the annihilation site and efficiently annihilated. Pair-laden hot gas from the Galactic center starburst would vent into the Galactic halo while expanding, radiating and cooling, and slowing in transit from the Galactic center to the lower pressure Galactic halo. While convecting outward, e⁺ would lose energy and annihilate with the plasma electrons in the hot wind, and this is our explanation for the observations (Purcell et al. 1997a, 1997b; Cheng et al. 1997). The venting would be preferentially one-sided because of the location of the initial starburst activity and the morphology of the confining gas.

§3. ANNIHILATION FOUNTAIN MODEL

     We sketch a model for the fountain of rising annihilating gas energized by a starburst episode. Suppose that gas rises with speed 10⁷v₇ cm s^-1 from a region of radius r_b = 100r₁₀₀ pc undergoing a starburst phase, implying a gas crossing time of order r₁₀₀v₇ 10⁶ yr. We approximate the shape of the volume of the gas expanding into the Galaxy's halo by an inverted cone with opening angle , cut off at both ends, so that the cross-sectional area of the fountain is r (1 + u)², where u = z tan r_b and z is the height above the Galactic plane. Our major simplification, which can be relaxed in more general treatments, is that the gas rises with constant velocity. Continuity of the mass flux for a steady state situation considered here (see Ramaty et al. 1992 for a treatment of time-dependent injection and annihilation in a uniform medium) implies that the density of the gas at the base of the fountain is n 0.13_C(v₇r) cm^-3, where _C solar masses of gas are expelled per century from the starburst region and rise into the halo. The time- and spatially averaged density distribution as a function of height z above the Galactic plane is therefore n_p(z) = n(1 + u)².

     The timescale for a positron injected with kinetic energy m_ec²( - 1) to thermalize with the background hot thermal gas is controlled primarily by Coulomb losses at mildly relativistic and nonrelativistic energies. Coulomb losses operate on a timescale of 5 × 10⁵ ( - 1)(n_-130) yr, where ₃₀ is the Coulomb logarithm divided by 30, the density is 0.1n_-1 protons cm^-3, and c is the positron's speed. The kinetic energy distributions of positrons entering the ISM after SN II explosions are given for the ⁵⁶Co ⁵⁶Fe and the ⁴⁴Sc ⁴⁴Ca decays by functions peaking near 0.6 MeV with FWHM widths of 0.9 MeV and high-energy tails reaching to 1.45 MeV (Chan & Lingenfelter 1993). The fraction of e⁺ that annihilates in flight prior to thermalizing usually amounts to less than 10%, and these positrons do not contribute to the 0.511 line emission (Murphy, Dermer & Ramaty 1987). After entering the thermal pool, the positrons annihilate in a fully ionized thermal plasma through direct annihilation and radiative combination on a thermal annihilation timescale of 3 × 10⁷(_-14n_-1) yr, where the annihilation rate coefficient = 10^-14_-14 cm³ s^-1 (Bussard, Ramaty, & Drachman 1979). When a significant fraction of neutral atoms or partially ionized ions is present, the annihilation rate can dramatically increase because _-14 10⁶ near temperatures of 10⁵ K due to the onset of charge exchange processes that have atomic-sized cross sections. A pair of 0.511 MeV line -rays comes from direct annihilation in the thermal gas and, one-fourth of the time, from annihilation via Ps formation.

     We calculate the annihilation flux at height z after tracking the energy evolution and spatial propagation of the e⁺ following injection. The e⁺ height-dependent injection function is approximated by a Gaussian function that is allowed to be, in general, offset from the Galactic plane. The FWHM of the injection function is taken to be 180 pc, comparable to twice the scale height of massive stars. Although diffusion must be important for very relativistic e⁺ (Lerche & Schlickeiser 1980), we assume that the nonthermal and thermal e⁺ are entrained in the hot gas and convect away from the Galactic midplane with constant speed v₀. The general e⁺ equation of motion involves Coulomb, bremsstrahlung, adiabatic expansion, synchrotron, and Compton energy losses, but for ⁺ injection, only Coulomb and adiabatic expansion losses are important. The e⁺ energy-loss rate from adiabatic expansion is given by -_adia = ( - ^-1)(3V), which bridges the nonrelativistic and relativistic regimes and applies to high- plasmas, which is suitable for magnetic fields weaker than about 10^-3 G. The volume expansion rate for the fountain geometry is V = 2v₀ tan [r_b(1 + u)], from which we find that Coulomb losses dominate adiabatic expansion losses when ( - ^-1) K = 36_30C[vr₁₀₀(tan 0.1)].

     After ⁺ emission, positrons convect away from the Galactic plane and, if injected with sufficiently low energies, thermalize with the background gas through Coulomb processes (excepting those few that annihilate in flight). We call the distance between injection and thermalization the Maxwell-Boltzmann length (MBL), which is a nonlinear function of the injection height z_i and the e⁺ injection kinetic energy m_ec²( - 1). When Coulomb processes dominate, the MBL is given by u_MB = [(1 + u_i)^-1 - K (_ii - arccos )]^-1 - 1, where u_MB(i) = z_MB(i) tan r_b. The constant K_c = 2.4_C30(vr₁₀₀ tan ).

     When K 1, as with standard parameter values, positrons injected through ⁺ production thermalize close to their injection site. Thus, the spatial dependence of positrons thermalizing with hot gas is, in this regime, equal to the energy-integrated ⁺-injection function. Following thermalization, a positron continues to convect upward into the Galactic halo until it either annihilates or merges with the dilute halo gas. The decay law through annihilation for the rising positrons is governed by the value of the temperature-dependent reaction rate coefficient (T), the ionization state, composition, and density of the medium. For hot gases with T 10⁶ K, the two-photon direct annihilation channel is most important with _-14 1. The decay law for thermal positrons annihilating in a thermal gas is -₊(t) N₊(t)n_p(t). From this equation, we derive the height-dependent differential production rate of 0.511 MeV annihilation line photons, given by



Here (z) is the MB injection function differential in height z, which is obtained by convolving the ⁺ injection function with its MBL and integrating over the initial energies of the ⁺ positrons. The constant K_a = 0.039_-14C(vr₁₀₀ tan ), n is the electron density at the base of the fountain, and u⁽⁾ = z⁽⁾ tan r_b.

     In the approximation where e⁺ thermalize close to their injection site, equation (1) is easily solved to give the results shown in Figure 1. The total e⁺ injection rate is 10⁴²₊₄₂ e⁺ s^-1, with ₊₄₂ = 1. The solid curves give the integral 0.511 MeV photon production rate between the Galactic midplane and height z, and the dashed curves give the differential 0.511 MeV production rate in units of 0.511 MeV photons s^-1 z(pc)^-1. The dotted curves represent the spatial e⁺ distribution function, which are centered at and 50 pc above the Galactic midplane in Figures 1a and 1b, respectively.

Fig. 1

     Before interpreting Figure 1, note that _{0.511 MeV}(<) 2 × 10⁴² 0.511 MeV photons s^-1 if all e⁺ annihilate. This limiting value is reached only if most ⁺ injection occurs high above the Galactic plane, so that few e⁺ are convected to negative values of z. Standard parameter assignment with no source offset and tan = 0.1 (Fig. 1a), corresponding to a 6° fountain opening angle, yields an integral annihilation flux of 3 × 10⁴¹ 0.511 MeV photons s^-1, implying a one-sided annihilation efficiency of about 15%. In contrast, when the fountain opens to 45° (tan = 1), the annihilation efficiency plummets because of the severe thinning of gas density with height. In Figure 1b, the wind speed parameter for the hot gas is increased by an order of magnitude from the standard value, and the injection Gaussian is offset by 50 pc. This also reduces the annihilation efficiency because flux continuity demands a reduced density in a steady state approximation.

     The rate at which 0.511 MeV annihilation photons are emitted between 0.1 and 2 kpc is 2 × 10⁴¹₊₄₂ and 3 × 10⁴¹₊₄₂ 0.511 MeV photons s^-1 for the top curves in Figures 1a and 1b, respectively. Matching the OSSESMMTGRSballoon data analyses (Purcell et al. 1997a, 1997b; Cheng et al. 1997) implies that annihilation occurs at the rate of 4 × 10⁴²d 0.511 MeV photons s^-1. Thus, injection rates of ₊₄₂ 20 and ₊₄₂ 13 are required to match the observations for these two cases. Such rates could be supplied by ⁺ production from freshly synthesized ⁴⁴Ti in Type II SNs given the uncertainty of the ⁴⁴Ti mass fraction, the SN rate, and the parameters of the outflowing wind. This rate could perhaps also derive from ⁺ production in the ⁵⁶Ni ⁵⁶Co ⁵⁶Fe chain if either the calculated escape fraction or amount of synthesized ⁵⁶Ni per Type II SN were underestimated. Black hole e⁺ production could provide an additional source of the positrons.

     Figure 2 shows a contour map of the annihilation flux produced by the Galactic center fountain, added to a disk and Galactic bulge distribution fitted to the measured (Purcell et al. 1997a) annihilation emissivity. The axis of the fountain is directed away from the center of our Galaxy along the direction of the Galactic center lobe, which is inclined in projection by about 20° from the axis of the north Galactic pole. (Note that the location of the centroid of the spheroidal bulge flux is offset from the location of the Galactic center.) The agreement of this idealized model with the data is satisfactory and predicts that peak enhancement of the fountain's annihilation flux occurs 100 pc above the Galactic plane.

Fig. 2

§4. PREDICTIONS AND SUMMARY

     Owing to, in large part, -ray observations with the OSSE instrument on CGRO, a new component of the ISM has been discovered: hot plasma pushing into the Galactic halo from a region of starburst activity surrounding the Galactic center a few hundred parsecs in extent. The existence of hot gas and an outflowing wind is suggested by radio and X-ray observations (Pohl et al. 1992; Koyama et al. 1989; Yamauchi et al. 1990; Morris & Serabyn 1996) and represents a low-power analog of nuclear starburst outflows detected in M82 and NGC 253 (Shopbell & Bland-Hawthorn 1997). Hot ionized plasma can be detected through pulsar dispersion measurements, and we predict a dispersion measure jump of about 30 pc cm^-3 when scanning across the fountain several degrees above the Galactic plane. The difficulty is to have independent distance measurements of pulsars located more than 8 kpc away. Continuum free-free and recombination Ly lines of H, He, and Ps are predicted from the fountain, but obscuring foreground gas makes it difficult to view the Galactic center region at optical and UV wavelengths. As ²⁶Al is convected upward with the flow, a characteristic decay law for the diffuse 1.809 MeV emission (Chen, Gehrels, & Diehl 1995) should be observed, although at a flux level requiring at least INTEGRAL telescope sensitivities. Turbulent hot gas in the central region might also explain the broadened 1.809 MeV lines observed (Naya et al. 1996) with the GRIS instrument. The width of the 2 0.511 MeV line from annihilation in hot gas will be broader than the Galactic disk 0.511 MeV line emission because of the larger temperature of the plasma (depending in detail on the dust content of the fountain), and the 3 Ps continuum fraction f will be spatially varying (R. Ramaty 1997, private communication).

     If the annihilation fountain is our first clear view of a conduit of hot gas venting the starburst activity near the Galactic center into the Galactic halo, then it is likely that cosmic rays are efficiently transported into and diffuse throughout the halo along this route. The greater than 100 MeV EGRET (Hunter et al. 1997) and 408 MHz Effelsberg (Haslam et al. 1982) all-sky maps show enhanced emission north of the Galactic plane that could be ascribed to this effect. Positrons that fail to annihilate in the fountain will diffuse throughout the halo and annihilate if they encounter the gaseous disk. This could explain the large-scale height of the disk component of the diffuse annihilation radiation 10°20° away from the Galactic center (Ramaty et al. 1994). Long-lived radioactivity produced by SNs would also trace this channel. Small-scale variations of the 0.511 MeV map would indicate localized OB associations, changes in the ionization state of the gas, and sites of black hole e⁺ injection. More observations and analyses are required to understand better the activity occurring near the center of the Milky Way.

ACKNOWLEDGMENTS

     We thank members of the OSSE team, especially W. Purcell and J. Kurfess, for conversations about the annihilation radiation observations. We also acknowledge useful discussions with R. Ramaty, R. Schlickeiser, J. Lazio, and A. Harding. In addition, we acknowledge support from the Office of Naval Research.

REFERENCES

• Bussard, R. W., Ramaty, R., & Drachman, R. J. 1979, ApJ, 228, 928 First citation in article | NASA ADS
• Chan, K. W., & Lingenfelter, R. E. 1993, ApJ, 405, 614 First citation in article | NASA ADS
• Chapuis, C. G. L., et al. 1991, Gamma-Ray Line Astrophysics, ed. P. Durouchoux & N. Prantzos (New York: AIP), 54 First citation in article
• Chen, W., Gehrels, N., & Diehl, R. 1995, ApJ, 440, L57 First citation in article | NASA ADS
• Cheng, L. X., et al. 1997, ApJ, 481, L43 First citation in article | Full Text | NASA ADS
• Diehl, R., et al. 1995, A&A, 298, 445 First citation in article | NASA ADS
• Gehrels, N., Barthelmy, S. D., Teegarden, B. J., Tueller, J., Leventhal, M., & MacCallum, C. J. 1991, ApJ, 375, L13 First citation in article | NASA ADS
• Hartmann, D. H. 1995, ApJ, 447, 646 First citation in article | NASA ADS
• Hartmann, D. H., Timmes, F. X., & Diehl, R. 1997, in ASP Conf. Proc. 112, The History of the Milky Way and Its Satellite Systems, ed. A. Burkert, D. H. Hartmann, & S. R. Majewski (San Francisco: ASP), 197 First citation in article
• Haslam, C. G. T., Salter, C. J., Stoffel, H., & Wilson, W. E. 1982, A&AS, 47, 1 First citation in article | NASA ADS
• Hunter, S. D., et al. 1997, ApJ, 481, 205 First citation in article | Full Text | NASA ADS
• Iyudin, A. F., et al. 1994, A&A, 284, L1 First citation in article | NASA ADS
• Koyama, K., et al. 1989, Nature, 339, 603 First citation in article | NASA ADS
• Kurfess, J. D., et al. 1992, ApJ, 399, L17 First citation in article
• Lerche, I., & Schlickeiser, R. 1980, ApJ, 238, 1089 First citation in article
• Leventhal, M., Barthelmy, S. D., Gehrels, N., Teegarden, B. J., & Tueller, J. 1993, ApJ, 405, L25 First citation in article | NASA ADS
• Matz, S., et al. 1988, Nature, 331, 416 First citation in article | NASA ADS
• Mezger, P. G., Duschl, W. J., & Zylka, R. 1996, A&A, 7, 289 First citation in article
• Morris, M., & Serabyn, E. 1996, ARA&A, 34, 645 First citation in article | NASA ADS
• Murphy, R. J., Dermer, C. D., & Ramaty, R. 1987, ApJS, 63, 721 First citation in article | NASA ADS
• Naya, J., et al. 1996, Nature, 384, 44 First citation in article | NASA ADS
• Niel, M., et al. 1990, ApJ, 356, L21 First citation in article | NASA ADS
• Pohl, M., Reich, W., & Schlickeiser, R. 1992, A&A, 262, 441 First citation in article | NASA ADS
• Prantzos, N. 1996, A&AS, 120, 303 First citation in article
• Purcell, W. R., et al. 1993, ApJ, 413, L85 First citation in article | NASA ADS
• . 1997a, ApJ, in press First citation in article
• . 1997b, in Proc. 2d INTEGRAL Workshop, The Transparent Universe, ed. C. Winkler, T. J.-L. Courvoisier, & P. Durouchoux (ESA SP-382), 67 First citation in article
• Ramaty, R., Leventhal, M., Chan, K. W., & Lingenfelter, R. E. 1992, ApJ, 392, L63 First citation in article | NASA ADS
• Ramaty, R., Skibo, J. G., & Lingenfelter, R. E. 1994, ApJ, 92, 393 First citation in article
• Share, G. H., Leising, M. D., Messina, D. C., & Purcell, W. R. 1990, ApJ, 358, L45 First citation in article | NASA ADS
• Shopbell, P., & Bland-Hawthorn, J. 1997, ApJ, in press First citation in article
• Teegarden, B. J., et al. 1996, ApJ, 463, L75 First citation in article | Full Text | NASA ADS
• Woosley, S. E., & Weaver, T. A. 1992, in Supernovae, ed. J. Audouze et al. (New York: Elsevier) First citation in article
• Yamauchi, S., et al. 1990, ApJ, 365, 532 First citation in article | NASA ADS

FIGURES

Full image (52kb)

Full image (27kb)

-(2 + n)5