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ELSEVIER Nuclear Physics B (Proc. Suppl.) 48 (1996) 480--482

The Gas Deficiency of the Galactic Halo

(P. Salati *, P. Chardonnet , R. Taillet) a and (X. Luo, J. Silk) b

aLaboratoire de Physique Th6orique ENSLAPP, B.P. 110, 74941 Annecy-le-Vieux Cedex, France and Universit6 de Savoie, B.P. 1104, 73011 Charnbdry Cedex, France.

bAstronomy Depar tment , Campbel l Hall, University of California at Berkeley, Berkeley, CA 94720, USA.

The "r-ray diffuse emission has been recently observed with unprecedented accuracy by the Compton Gamma Ray Observatory (CGRO) at photon energies in the range between 100 MeV and 10 GeV. A residual isotropic diffuse radiation is measured at low galactic latitude, with little variation over different portions of the sky. That measurement translates into a tight constraint on the abundance of diffuse gas in the dark matter halo surrounding our galaxy. If that halo contained significant amounts of gas, cosmic-ray protons originating from the galactic disc would interact with it, yielding a 7-ray flux which CGRO would have observed. By using a diffusion model which correctly reproduces the radial distribution of cosmic-rays along the galactic plane, we infer an upper limit of ,.~ 2 to 4% on the fraction of gas in diffuse form or in clouds. The flatter the halo, the stronger the bound.

1. I n t r o d u c t i o n .

Two years after their initial discovery [1], the EROS and MACHO collaborations should have collected by now at least twice as many gravi- tational microlensing events as actually observed [2]. The deficit towards the Large Magellanic Cloud is obvious. Conversely, the measured op- tical depth in the direction of the galactic bulge is 3 to 6 t imes larger than expected [3]. By mod- eling the various galactic components, Gates et al. [4] have tried to accomodate those microlens- ing observations with the rotat ion curve, the lo- cal projected mass density and the distribution of luminous mater ia l in the disc and the bulge. They conclude tha t a spherical halo cannot con- tain more than 40% of low-mass stars or plan- ets. The question of the presence of gas naturally arises. De Paolis et al. [5] have outlined a sce- nario in which dark clusters of compact objects pervade the halo together with clouds of molec- ular hydrogen, at distances larger than 10 to 20 kpc.

If unseen gas was present in the galactic halo, it would be impacted by cosmic-rays originating from the disc. This would lead to a strong 7- ray signal showing up as a new component in the

*Institut universitaire de France.

galactic diffuse radiation. The latter has been re- cently measured with unprecedented accuracy by the E G R E T instrument on board the Compton G a m m a Ray Observatory (CGRO). As a mat te r of fact, it contains some residuals which cannot be explained by the known distributions of gas in the galactic ridge. An isotropic emission is found in various portions of the sky. We will take here the very conservative point of view tha t this resid- ual emission provides an upper l imit on the "/-ray emission from the halo gas. We readily infer tha t the latter cannot exceed --~ 2 to 4% of the mass of the halo [6].

2. T h e 7 - r a y d i f fuse e m i s s i o n o f h a l o gas .

The spallation of cosmic-rays with the gas po- tentially concealed in the galactic halo produces an extra 7-ray diffuse emission. Its flux obtains from the convolution along the line of sight of the density n hal° of halo gas with the 7-ray emissiv- ity IH per hydrogen atom, which varies itself with the depth s

halo f % : s) (1)

Cosmic-ray production and most of the spalla- tion reactions take place in a thin (h ~ 200 pc)

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P. Salati et al./Nuclear Physics B (Proc. Suppl.) 48 (1996) 480-482 481

gaseous disc, with radius R ~ 20 kpc. The disc is sandwiched between two extended layers, with thickness L ~ 2 to 4 kpc each, where cosmic-rays diffuse as a result of magnetic fields. Following Webber et al. [7], a reliable calculation of the cosmic-ray density P as a function of galactocen- tric radius r and height z above the plane is pos- sible, in good agreement with a variety of obser- vations. Unlike the magnitude, the spectral index of the proton radiat ion is found to vary little with position. Therefore, the atomic emissivity scales with the cosmic-ray density as

[ (2)

Relation (2) is in good agreement with the emis- sivities which E G R E T has measured in Ophi- uchus [8], Orion [9] and the Perseus arm region [10].

The halo is modeled to be an oblate spheroid with flattening e, a homogeneous fraction r/ of which is made of gas in diffuse form or in cold clouds

+ } .(3) 7" c l n H ?lhalo = r / f l h a l o ( @ ) r 2 "[- r 2 -[- ( z / e ) 2

Such a distribution generates a flat rotation curve at the sun, as long as the halo core extension rc is smaller than the solar radius r o = 9 kpc. The value of rc = 3.5 kpc has been assumed. Our re- sults are fairly insensitive to that choice.As the halo flattens out, it is compressed along the disc and its local density phalo(®) increases. However, there is an upper limit set by Oort [11] and re- fined by Bahcall [12], on the total density p(@) in the solar neighbourhood. Analysis of the vertical motion of stars with respect to the galactic plane preclude p(O) from exceeding ~ 0.15 - 0.18 Mo pc -3. The flattening factor e must be larger than 0.1.

3. C o n s t r a i n t s on t h e h a l o gas .

Observations collected by the E G R E T instru- ment on board C G R O have been thoroughly anal- ysed in three very different regions of the galac- tic ridge. Ophiuchus is toward the galactic bulge

(b = 150 , 1 = 0°), Orion is in the opposite direc- tion (b = - 15 ° , 1 = 200 ° ) while the Perseus arm is at an intermediate location (b = 0 ° , 1 = 115°). The "/-ray diffuse radiat ion observed in those fields are modeled with both HI and H2 con- tributions. For the first t ime at those low galac- tic latitudes, an isotropic component is found in the residuals of the signal. I ts integral flux above t00 MeV is 1.5 to 2.5 x 10 -5 photons cm -2 s - t sr -1, with a spectral index of ~ - 2 . It does not vary much with longitude. At low latitude, the line of sight deeply probes the galactic ridge and its surrounding halo. Column densities are large. The halo gas 7-ray diffuse emission is expected to reach m a x i m u m in the direction of the galac- tic center. The most stringent constraint on the abundance of gas in the galactic halo is provided by data in the energy range between 300 and 500 MeV. The halo 7-ray signal ~halo is required not to exceed the isotropic diffuse emission measured by CGRO. The lat ter is 2.4 x 10 -6 (Ophiuchus), 3 x 10 -6 (Orion) and 3.2 x 10 -6 (Perseus region) in units of photons cm -~ s -1 sr -1. In the up- per pannel of the figure, the bound r/max on the fraction of gas hidden in the halo, is displayed as a function of the flattening factor e. The thick- ness L of the diffusion layers has been set equal to 3 kpc. The strongest bound is derived from the Ophiuchus measurements for which the line of sight crosses entirely the galactic halo. Typi- cal column densities of the disc are on the order of 0.1 - 0.3 g cm -2 in the direction of the bulge, to be compared with a photon optical depth of 80 g cm -2 above 100 MeV. The galactic ridge is com- pletely transparent . Because high-energy 7-rays are a very penetrat ing form of radiation, the re- gion beyond the galactic center becomes entirely visible even at low galactic latitude. For Perseus and Orion, the column density of halo gas is smaller and the limit relaxes. When e decreases, the halo flattens out. Its ma t t e r is compressed along the galactic plane and the limit strengthens. The Ophiuchus region alone has been selected in the lower pannel where r/max is also plotted ver- sus flattening e, for three different values of L. The bound ranges from 2 to 9%. When L is in- creased, the halo is more deeply probed and the bound tightens. With the favoured value of L =

482 P Salati et al./Nuclear Physics B (Proc. Suppl.) 48 (1996) 480~482

~5 , , i , , , , i , , , , i , , , , i , , , , i , , ,~ i ~ , , , l ~ , , , l ~ _ -

30_ Energy bin [300-5001 MeV S

. ~ L = a kpc ~ O~io~ i

2D

10

5 / Ophiuchus 2

.1 .2 .3 .4 .& .8 .7 .S .9 10

- " " l ' " ' t ' ' " i " " l " " l " " I ' " ' l ' " ' l " " - 0 - --= . ~ Zne,gy bin [3oo-soo] ~ev

s ~ L = 2 kpc

3

Z ----- L = 4 k p c - -

0 , , , I , , , , I , , , , I . . . . I .... I,,,,I,,,,l .... I , , , .i .2 .3 .4 .5 .6 .7 .8 .0

F l a t t e n i n g e = b / a

3 kpc, we conclude that gas cannot account for more than 4% of a spherical halo.

4. I n t r o d u c t i o n .

The residuals which CGRO has measured in the "),-ray diffuse radiation of the galaxy trans- late into a t ight constraint on the abundance of gas potentially concealed in the halo. By using a diffusion model which correctly reproduces the radial distribution of cosmic-rays in the galactic disc, an upper limit of ~ 2 to 4% is inferred on the fraction of gas in diffuse form or in cold clouds. The flatter the halo, the stronger the bound.

Note that beyond the region where cosmic-rays

diffuse, for R > 20 kpc and [z] > 4 kpc, no limit may be inferred from the CGRO observations. The 7-ray hydrogen emissivity actually vanishes. This naturally leads to the possibility that gas might only be in the outer parts of the halo, turning into massive compact objects in the in- ner galaxy. Alternatively, the galactic dark mat- ter could be made of weakly interacting massive particles, such as heavy neutrinos.

R E F E R E N C E S

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