Galactic photoionization model

The emission measure from the surface of a cloud embedded in a bath of ionizing radiation gives a direct gauge, independent of distance, of the ambient radiation field beyond the Lyman continuum (Lyc) edge (e.g., Hogan & Weymann 1979). This assumes that the covering fraction () seen by the ionizing photons is known and that there are sufficient gas atoms to soak up the incident ionizing photons. We assume an electron temperature TK, as expected for gas photoionized by stellar sources, for which the Case B hydrogen recombination coefficient is cm s. At these temperatures, collisional ionization processes are negligible. In this case, the column recombination rate in equilibrium must equal the normally incident ionizing photon flux, , where is the rate at which Lyc photons arrive at the cloud surface (photons cm s), is the electron density and is the column density of ionized hydrogen. The emission measure is just where L is the thickness of the ionized region. The resulting emission measure for an ionizing flux is then where . For an optically thin cloud in an isotropic radiation field, the solid angle from which radiation is received is , while for one-sided illumination, . For the models we will be considering, however, is anisotropic and can be considerably less than .

 


Figure 1: An illustration of the LMC and the dominant clouds in the Magellanic Stream (Mathewson & Ford 1984). The LMC and the Stream have been projected onto the Galactic X-Z plane. We have ignored small projection errors resulting from our vantage point at the Solar Circle. The angle is measured from the negative X axis towards the negative Z axis where and . In reality, the orbit of the Stream lies closer to the Great Circle whose longitude is .

In order to estimate , we develop an idealized model for predicting the emission measure at the distance of the Magellanic Stream. The ionizing stars are assumed to be isotropic emitters confined to a thin disk in the x-y plane (or the X-Y plane in Galactic Coordinates, e.g. Fig. 1). For a cloud C at position a distance R from an arbitrary patch of the disk dA, the received flux (in units of erg cm s Hz) from ionizing disk sources with specific intensity through a solid angle is

where and

The angle is the polar angle measured from the positive z axis through dA to the line extending from dA to C. Thus, at an arbitrary point in the galaxy halo, the ionizing photon flux from the disk (in units of photons cm s) is

for which and d are the surface photon density and brightness, respectively, within each disk element dA.

For the opaque disk model, the patch dA is observed through the intervening disk interstellar medium (ISM) such that . For a disk population of OB stars, we consider an axisymmetric exponential disk with scale length , . We adopt a radial scale length of 3.5 kpc (Kent, Dame & Fazio 1991) and all integrations are performed out to 25 kpc in radius since there is some evidence for faint HII regions at these large radii (de Geus et al. 1993). Vacca et al. (1996) have compiled a list of 429 O stars within 2.5 kpc of the Sun from which they determine an ionizing surface density of phot cm s where is the radius of the Solar Circle. After an exhaustive study of the literature, Reid (1993) finds kpc. Thus, from equation (1), we derive phot cm s.

© Copyright Astronomical Society of Australia 1997