C H E M I C A L C O M P O S I T I O N O F T H E I N T E R S T E L L A R G A S :

X - R A Y D E T E R M I N A T I O N S

ROBERT L. BROWN National Radio Astronomy Observatory*, Green Bank, W. Va., U.S.A.

(Received 6 March; in revised form 8 June, 1972)

Abstract. Noting that observations of X-ray attenuation at the K-shell ionization edge for many elements provide, prospectively, the least ambiguous means for establishing the chemical com- position of the interstellar gas, we have evaluated the expected spectral discontinuities for all atoms from carbon to sodium and have tabulated the results. It is shown that with X-ray detectors of reasonable energy resolution and sensitivity the K-shell edges of C, N, 0, Ne, Si, S, A and Mg are potentially observable if the 'cosmic' abundances are representative of the general interstellar environment.

1. Introduction

Since an understanding of the precise chemical composition of the interstellar gas is central to several important astrophysical problems, for example the rate of radiation

transfer in protostars, the formation of dust grains and molecules, and the thermo- dynamic structure of the interstellar medium, it is unfortunate that our knowledge of this composition has, by necessity, been derived from observations of objects which may not be representative of the ambient interstellar environment. One must assume that the relative abundances derived from observations of planetary nebulae, circumstellar shells, stellar atmospheres, H II regions, terrestrial samples, metorites, cosmic rays or some weighted mean of these determinations is also applicable to the interstellar gas. Only observations of optical interstellar absorption lines have hereto- fore provided a direct means for inferring interstellar atomic abundances (for atoms other than hydrogen) and in at least one well-studied case, the Ca H/Na I ratio, have indicated the presence of a severe discrepancy between the observationally derived abundances and the putative 'cosmic' means (Munch, 1968; Habing, 1969).

Several other techniques have been proposed to obtain abundances in the interstel- lar medium. Following the earlier suggestion of Spitzer and Zabriskie (1959), Silk and Brown (1971) noted that strong ultraviolet resonance lines are to be expected from ions of carbon, nitrogen, silicon, sulfur, argon and aluminum which are ionized once beyond their most abundant state in interstellar H I clouds. Many of these lines may have equivalent widths in excess of 100 m/~ and should be easily detectable by instruments of sufficient resolution above the Earth's atmosphere. Similarly, far infrared (2 > 10 #) observations of collisionally excited fine-structure levels in ions of C, N , O, S, Fe, Ne may provide a means for evaluating the relative abundance of these particular species in interstellar H I regions (Petrosian, et al., 1969). However,

* Operated by Associated Universities, Inc., under contract with the National Science Foundation.

Astrophysics and Space Science 18 (1972) 329-333. All Rights Reserved Copyright �9 1972 by D. Reidel Publishing Company, Dordrecht-Holland

330 ROBERT L .BROWN

for either the ultraviolet or the infrared observations one can establish only the abun- dance of one or two ions of some atom and the total abundance of the element must be inferred from this data alone. To do this requires a knowledge of the appropriate spectrum of ionizing photons or particles (i.e., the ionization rate) and the physical conditions, density and temperature, in the absorbing gas (to evaluate the recombi- nation term). Since these essential parameters are likely to vary widely along the line-of-sight, abundances obtained from ultraviolet and infrared lines are also inherent- ly uncertain. We are consequently motivated to search for additional observational ways to establish the composition of the interstellar gas.

2. Attenuation of CosmieX-Rays and the ChemicalComposition of the IntersteUarGas

The only procedure capable of yielding unambiguous column densities of interstellar elements which is not affected by the state of ionization or the physical conditions within the medium is that which uses observations of the K-shell absorption edges. This result, noted earlier by Strom and Strom (1961) and by Felten and Gould (1966) with particular emphasis on the problem of determining the neon abundance through observations of the Ne K-edge in the spectrum of Sco X-l, may presently be appli- cable to several atoms whose K-shell absorption edges have energies less than a few keV: Indeed, recent observations of the soft X-ray background show suggestive depressions at energies corresponding to the K-edge of some of the more abundant elements (Hayakawa et aL, 1971; Bunner et al., 1971; Palmieri et al., 1971). While these particular features are probably statistical noise, it is to be expected that with the long integration times afforded by satellite observations together with develop- ments in instrumentation such as the Bragg crystal spectrometer which provide very narrow energy resolution (Kestenbaum et al., 1970), measurements of many K-shell edges soon may be feasible. With this in mind, in this section we propose to calculate the relative magnitude of the K-shell absorption edges for several elements and evaluate the expected spectral discontinuities as a function of hydrogen column density.

Attenuation of X-rays in the interstellar gas is principally due to photoionization of the more abundant elements for photon energies ~< 5 keV; above this energy Comp- tone scattering becomes the dominant effect. The total effective absorption coefficient per hydrogen atom has been tabulated by several authors (Brown and Gould, 1970; Bell and Kingston, 1967; Felten and Gould, 1966) and consists of a sum over the relevant atomic species A ~, of the form

where

(re (E) -- (1/NH) E N,ai (E) ~ (E i - E), (1) i

0 if E < El (2) ( E ~ - E ) = I if E>E~

CHEMICAL COMPOSITION OF THE INTERSTELLAR GAS: X-RAY DETERMINATIONS 3 31

and Ei is the K-shell ionization energy of A t. I f an initial flux of X-rays q~0 (E) of arbitrary spectral shape is incident on a uniform absorbing layer of thickness l, the resultant flux after pasage through the medium is

q~ (E) = q~o (E) exp [ - WHO" e (E)] , (3)

where Nn=nHlcm -2 is the hydrogen column density; it has been assumed that all the elements of interest are well mixed over the entire path.

Now consider what happens to the attenuation when E is near one of the K-shell ionization energies, say energy E* of species A*. Let AE be an increment of energy such that AE/E*~I and let qS<-(a(E*-AE) , 4'>-dp(E*+AE) then

log (~b </q~>) = N n , 0 (A*) IN (A*)/NH] , (4)

where o- o (A*) is the K-shell photoionization cross section of A* at threshold E*. Again assuming complete mixing the abundance of A* relative to hydrogen is

A*/H = [NHa o (A*)]- I log ~b</q~>. (5)

Once the cross sections ao(A*) are determined the interstellar abundance of the elements A* can, in principle, be obtained from observations of the spectral disconti- nuity at E* in the X-ray spectrum of sources whose hydrogen column density N H is known (from 21 cm measurements for instance).

The K-shell photoionization cross section for only one atom, hydrogen, can be evaluated precisely; for the heavier elements one must rely either on an interpolation of the available experimental data or on an appropriate theoretical expression in order to obtain the threshold photoionization cross sections. Rather than depend on the power law extrapolations that have been employed previously, we note that the shape of the K-shell photoionization cross section near threshold for most species A* is very similar to the hydrogen cross section (Samson, 1969). Consequently, by approximating both the K-shell bound-state wavefunctions and the continuum state of the photoelectron by hydrogen expressions having the same effective nuclear charge (Z-s), a generalized form for the K-shell photoionization cross section may be obtained in the form

% (A*) = 4.1 x 10Sa~ (Z - s ) re-4(1 + 4/3n 2) (Ry/hv) 4, (6)

where n 2 = vl/(v - vl); v, = (Z - s)2Ry (7)

and for IGshell electrons the Slater inner screening constant s = 0.3 (Bethe and Salpeter, 1957). Following this procedure the photoionization cross section at the K-shell thresholds for the atoms of interest have been evaluated and are given in Table I.

With these parameters the expected X-ray spectral discontinuity at an energy E* corresponding to the A* K-shell ionization edge may be expressed as

A~b = 1 - q~>/~b< (8)

and for an assumed relative abundance [A*/H] may be tabulated as a function of

332 ROBERT L. BROWN

TABLE I

K-edge spectral discontinuities

Atom Abundance K-Edge a0 logN~ Ar (%) (Nri = 1) (KeV) (10 19 cm 2) (~= 1)

log N~ (cm -2) 22.5 22.0 21.5 21.0

C 3 • 10 .4 0.284 10.4 20.17 100 95.6 62.7 26.8 N 1 • 10 -4 0.400 16.8 20.76 99,5 81.4 41.2 15.4 O 7 • 10 4 0.532 6.30 21.12 100 98.8 75.2 35.7 E 2.5 • 10 -7 0.686 4.16 0.033 0.010 0.003 0.001 Ne 1 • 10 .4 0.867 3.20 21.51 63.6 27.4 9.62 3.14 Na 1.7 • 10 .6 1.072 2.55 1.39 0.44 0.140 0.040 Mg 3 • 10 -5 1.303 1.88 21.96 16.3 5.48 1.77 0.560 A1 2 • 10 -6 1.560 1.57 0.98 0.31 0.096 0.032 Si 3 • 10 ~ 1.840 1.38 22.38 12.3 4.05 1.30 0.413 P 3.5 • 10 7 2.143 1.16 0.13 0.041 0.013 0.004 S 1.7 • 10 .5 2.470 0.984 22.69 5.14 1.66 0.527 0.167 C1 2.5 • 10 .7 2.820 0.862 0.065 0.020 0.006 0.003 A 4.2 • 10 -6 3.203 0.741 22.91 0.98 0.310 0.098 0.031 K 7.5 • 10 -8 3.608 0.651 0.015 0.005 0,002 0.001 Ca 1.7 • 10 6 4.038 0.571 0.306 0.100 0.030 0.010

hydrogen co lumn densi ty; the results are also shown in Table I for 1OgNH ( c m - 2 ) =

=22.5 , 22.0, 21.5, 21.0. These values o f N n co r re spond app rox ima te ly to dis tances

to the galact ic center, Cas A, the Crab N e b u l a and Sco X-1 respectively. Here i t can

be seen tha t the magn i tude o f some of the j u m p s can be quite large, par t i cu la r ly for

C, N, O, and Ne.

3. Discussion

Using Table I as a guide the p r o b l e m of the relat ive abundances in the inters te l lar

gas can be a p p r o a c h e d t h rough precise X- ray observat ions . To ob ta in abundances for

as many e lements as poss ible several sources of vary ing dis tance must be employed

(more precisely, those separa ted by a range in NH) because one requires s imul taneous ly

tha t Aq5 be as large as poss ible while a t the app rop r i a t e energies N H ( z = 1) is no t

NH to the source. Tha t is, the opt ica l dep th should be larger enough for subs tant ia l

a t t enua t ion to occur (so tha t a r easonab le d i scont inu i ty can be expected) bu t no t so

large tha t the abso lu te flux is rendered undetectable . Here the values of N H (z = 1)

t aken f rom Brown and G o u l d (1970) at several energies are ind ica ted in Table I.

I f the ' cosmic ' abundances adop t ed in Table I are in fact representa t ive of the general

in ters te l lar gas then one m a y conclude tha t a n a r r o w - b a n d X- ray de tec tor having a

sensit ivity A a ~ 5-10% would be sufficient to de te rmine the abundances of C, N, O,

Ne, S, Si, A and Mg. Unfor tuna te ly , one of the mos t in t r iguing observat ions , tha t of

es tabl ishing the ca lc ium and sod ium abundances by X- ray a t t enua t ion methods

seems prohib i t ive since it requires ins t ruments capab le of dis t inguishing A~b<1%

even for sources at the galact ic center.

M e n t i o n should be made of effects resul t ing f rom the finite beam of X- ray detectors .

CHEMICAL COMPOSITION OF THE INTERSTELLAR GAS: X-RAY DETERMINATIONS 333

Boywer and Field (1969) and Gould (1971) have demonstrated that when observations

of an extended source are made with a finite beam the attenuation is determined by the distribution of optical depths ~ within the beam as well as by the mean value of

z, that is it depends on the 'clumpiness' of the gas along the line of sight. For example, if the distribution of v's in the beam has a gaussian form with dispersion d then (for d ~ z) the attenuated X-ray flux (Equation 3) is properly expressed as

q~ (E) = q~o (E) exp [ - NHa e (E) + d2/2] (9)

(Gould, 1971). For large optical depths the resultant attenuation may be reduced in this manner by a significant factor. However, even using (9) in place of (3) the relative abundances inferred from Equation (5) will not be charged unless the relative disper- sion d / ( z ) changes abruptly at the K-shell edge: Such a discontinuity would occur if the chemical composition of the interstellar gas changed radically along the line

of sight and this seems rather unlikely. Moreover, this whole discussion refers only to observations of extended sources; for discrete sources attenuation only along a single path is involved (i.e., there is but a single relevant z).

Finally, we wish to emphasize that a reliable determination of the chemical compo- sition of the interstellar gas is a problem of considerable importance which, in prin- ciple, can be approached with several techniques. Of the many possibilities obser- vations of the K-shell absorption edges by soft X-ray detectors of sufficient energy resolution and sensitivity offer the greatest prospect for supplying reasonably unam- biguous results.

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