Annihilation line from the galactic bulge due to action of low-mass flare stars

1. Annihilation line from the galactic bulge due to action of low-mass flare stars G.S.Bisnovatyi-Kogan and A.S. Pozanenko Space Research Institute of RAS, Moscow, Russia, and National Research Nuclear University “MEPhI”, Moscow, Russia . HEPRO-6 MOSCOW, IKI, 12 September 2017

2. We consider the low-mass flare stars which form the bulk of the population in the galactic bulge as a source of the positrons needed to form the observed narrow annihilation line from the galactic bulge. Estimates based on the observed flares in low-mass stars, together with observations of the annihilation line in solar flares, show that the rate of production of positrons in flares in the stars in the bulge may be sufficient to explain the formation of the narrow stationary annihilation line observed from the region of the galactic bulge.

3. The electron-positron annihilation line from the bulge of the galaxy was discovered in aerostat experiment in 1978, with a germanium gamma-telescope, and confirmed by the OSSE experiment on the Compton gamma observatory in 1993. Prolonged observations by the INTEGRAL space observatory have yielded the detailed properties of the annihilation line from the galactic bulge. These observations led to estimate for the positron (e+) formation rate in the bulge at a level of 2 10^{43}/s Possible sources of positrons have been examined in the literature. 1. Supernova outbursts 2. Microquasars , 3. Cosmic gamma-ray-bursts, 4. Tidal destruction of stars , 5. Active processesin the vicinity of the black hole at the center of the galaxy Sgr A* 6. e+ generation by sub-relativistic cosmic rays 7. Processes associated with the decay of particles of dark matter The absence of spatially resolved sources is an important feature of the observed diffuse annihilation line. Any model for the formation of this line must take this property into account, but this has not been done in most of the above models.

4. Here we consider the low-mass flare stars which form the bulk of the population in the galactic bulge as a source of the positrons needed to form the observed narrow annihilation line from the galactic bulge. Estimates based on the observed flares in low-mass stars, together with observations of the annihilation line in solar flares, show that the rate of production of positrons during flares of stars in the galactic bulge may be sufficient to explain the formation of the observed annihilation line. Astrofizika, Vol. 60, No. 2, pp. 243-248 (May, 2017). Positrons in solar flares The intensity of the annihilation line E=511 keV observed in powerful solar flares can be used to estimate the number of positrons born in these flares. During the flare observed in July 2002, F_{511,sun} = 83 ± 14 cm-2 gamma photons were emitted over 960 s in the annihilation line. The flare was detected with a germanium detector by the orbital observatory RHESSI. Assuming that the emitted line is isotropic estimate the number of positrons ejected during the flare. Given the distance from the earth to the sun, D = 1.5 10^{13} cm, the total number of photons emitted in the 511 keV line in the flare is

5. Exact estimate of the number created during a solar flare is difficult for several reasons. * Annihilation of a positron can take place in two main channels. One of these is through the formation of orthopositronium followed by annihilation and the emission of three photons with different energies. This leads to formation of a continuum spectrum, rather than to line emission with an energy of 511 keV. The annihilation channel involving formation of parapositronium leads to the birth of two photons with equal energies of 511 keV, i.e., to formation of the annihilation line. The relative efficiency of annihilation via these two channels is given by the ratio Q3/ Q2 . If this ratio is close to unity, then the number of annihilated positrons is roughly equal to the number of gamma photons in the line, since two photons with energies of 511 keV are produced by annihilation of parapositronium. *The emission in the 511 keV line can be anisotropic, since emission takes place within a small region of the sun’s atmosphere. *Only a small fraction of the positrons can be annihilated during the time of the flare; the remaining unannihilated positrons enter the interplanetary medium.

6. Suppose the positrons annihilated along the path from the sun to the earth represent a fraction of all the positrons formed in the solar flare. Then the total number of positrons generated during the flare can be written in the form The positrons produced in flares owing to beta decay of radioactive isotopes are almost relativistic; one of the signs of this is the observed polarization of the microwave emission from solar flares . In this case, the annihilation cross section is where is the classical electron radius. The electron density in the solar corona can be approximated by a power-law function , with a density in the base of the corona of cm . The number of electrons along the line of sight from the sun to the earth can be estimated roughly to be cm . This yields a probability of annihilation of the positrons as they move from the sun to the Earth . For this value of , the estimated number of positrons born in this solar flare is .

7. Now we can calculate the ratio of the number of positrons born in the solar flare to the bolometric energy of the flare. For the class X4.8 flare discussed above, the bolometric energy is approximately erg . We then have Birth of positrons in flare stars of the galactic bulge An estimate of the rate of production of positrons in flare stars of the galactic bulge requires knowledge of the number of flare stars in the bulge, of the properties of the flares in them, and of the quantity for the flare stars. The rate of flaring in the flare stars can be estimated using data obtained from the Kepler space telescope. Observations of 4494 powerful flares in 77 class G stars yielded the following power-law distribution for the flare rate as a function of their bolometric luminosity E:

8. For individual stars, the exponent γ can range from 0.65 to 2.45. We estimate the normalization coefficient A using observations of frequently flaring stars by the Kepler space telescope to be erg year The average total energy E released by a single flare star over a year is tot As a upper bound we take the bolometric energy of the most intense of the flares observed by the Kepler telescope,erg. It is not possible to determine a minimum energy limit for the flares, since the sensitivity of the telescope is too low. Instead, we take the minimum energy of the observed solar flares, erg . Usingthese values for the limits, we obtain

9. Taking the mass of the galactic bulge to be and the average mass of the class G, K, and Mflare stars in the bulge to be roughly, we obtain a total number of stars of The total rate of production of positrons in the bulge, is given by From observations of the annihilation line in the bulge the rate of positron formation is known to be, which is sufficient to explain the line intensity. Comparing this rate with estimations from flaring stars, we find that the flare stars can provide the necessary positron production rate for =340 , which is slightly greater than the value obtained for the sun, =240 .

10. This discrepancy in the value of is not significant, given the uncertainties in the parameters used for the estimates. These parameters include the maximum and minimum energies of the stellar flares, the conversion coefficient , the exponent in the distribution of the flare rate with respect to energy, the fraction of flare stars in the bulge, and the distribution of the annihilation processes over the different channels into ortho- and para-positronium. For the solar flare considered above, only ~ of the bolometric luminosity of the flare is spended in positron production. This value may be higher for more powerful flares. Our rather crude estimates, therefore, indicate that the positron production by flare stars in the bulge is an important, perhaps the main, source of the positrons responsible for the formation of the annihilation line observed from the central part of the galaxy. This model for positron production is applicable to all objects containing many flare stars. In our galaxy, these kinds of objects are globular clusters in which red dwarfs are the main star population. For observations of the annihilation line from the nearest massive globular clusters, the most appropriate object is the globular cluster NGC 5139 with a mass of , at a distance of 4.8 kpc. Given the mass and distance of this cluster, the flux of annihilation line photons from it should be roughly 1000 times smaller than the flux from the galactic bulge.

11. Future gamma-ray telescopes may be sensitive enough for observations of this sort.