6 Discussion and examples of capabilities

We now consider the capabilities of telescopes using the proposed techniques to tackle some of the astrophysical objectives which gave rise to the studies described here. In assessing the feasibility of directly imaging the emission from an object, two considerations arise - if the angular scale is too small it will not be resolved and only a total flux measurement will be obtained. If it is too large then the surface brightness will be insufficient for a useful detection.

Ignoring the small losses in the lens, the surface brightness of the image of a resolved object will be ${\sim} (d/f)^2$ of that of the object. This ratio is $2\times 10^{-17}$ for the example systems considered here. For an observation of at least a few days, significant detection will be obtained if the surface density of the detected photons at the detector is comparable with with the background event density (because of the small detector and narrow bandwidth the telescope would be signal limited and not background limited for shorter observations). Again using the expected Integral SPI background, this requirement corresponds to an object with a brightness temperature at 500 keV exceeding kT=8.1 keV (or 3.2 keV, 13.7 keV at 200, 847 keV). Athough one is far from the Rayleigh-Jeans regime, this is in some circumstances still a useful yard-stick. A black body with these temperatures and large enough to be resolved would be have a luminosity orders of magnitude greater than any conceivable astrophysical object, whatever distance scale is considered. Thus observable resolved sources will be in practice be optically thin and/or non-thermal.

6.1 Imaging Black Hole systems in AGNs

The origin of the gamma-ray emission from Active Galactic Nucleii (AGNs) is poorly understood. Indeed the possibility of direct visualisation of this process to understand what is going on was one of the incentives for the studies presented here.

For Seyferts, it is generally accepted that the emission at a few hundred keV arises from Comptonisation of soft photons, but whether the Comptonising electrons are thermal or non-thermal, and to some extent the size of the region in which the Comptonisation occurs, is less certain. Several characteristic scales can be recognised:

• The event horizon $R_{\rm H} =0.5-1 \,R_{\rm S}$, depending on the spin, where $R_{\rm S}$ is the Schwarzschild radius of the black hole.
• The inner radius of the accretion disk, which can be supposed to be equal to the radius of the innermost stable orbit - between 3 $R_{\rm S}$ for a non-rotating (Schwarzschild) Black Hole and 0.62$R_{\rm S}$ for a maximally rotating Kerr Black Hole.
• The size of the shadow of the black hole defined by the apparent size of the boundary between the regions of a source behind the black hole which can reach the observer and those that cannot. For a Schwarzschild Black Hole this is 5.2$R_{\rm S}$ (Falcke et al. 2000).
• The outer radius of the accretion disk, which is probably an order of magnitude greater than its inner radius.

Where jets are involved, the gamma-ray emitting region could be on the same size scale as the accretion disk or could be much larger.

Thus the resolution needed to study such systems is likely to be from one to a fews tens of Schwarzschild radii.

There have now been estimates made of the central mass in numerous galaxies, by reverbration mapping and other techniques. Figure 5 shows how these estimates are distributed as a function of redshift z or, in the case of nearby objects, of distance expressed as an equivalent redshift z=d H₀/c. The plot also shows the locus of points for which 1 micro arcsecond angular resolution would correspond to one Schwarzschild radius and to 100 Schwarzschild radii. Clearly the objects for which estimates of the central mass are available are in no way an unbiased sample, but Fig. 5 gives an indication of the region of parameter space which is most likely to be most interesting.

Figure 5: Estimates from the literature of masses of the central object in AGN and other galaxies. The estimates are plotted as a function of a distance measure (see text). Solid lines show the locii of points for which the Schwarzschild radius has a particular angular scale and dashed lines show the locii of objects which would be detectable if emitting at a specific fraction of their Eddington limit. The 5$\sigma$ in 1 day point source sensitivity of the 200 keV telescope in Table 1 is taken and $\nu F_\nu$ at 200 keV in the rest frame of the object is assumed to be $f L_{\rm Eddington}$, where f= 10-9, 10-6, 10-3 and 1. Redshift corrections assume a photon index of -2. H0 is taken to be 70 km s-1 Mpc-1 and q0=1/2. Mass estimates are from various sources and compilations (Ferrarese & Merritt 2000; Franceschini et al. 1998; Fromerth & Melia 2000; Gebhardt & Bender 2000; Gebhardt et al. 2000; Kaspi et al. 2000; Magorrian et al. 1998; Marconi et al. 2000; Merritt & Ferrarese 2001; Nelson 2000; Nishiura & Taniguchi 1998; Peterson & Wandel 2000; Wandel 1999); where multiple estimates exist the geometrical mean is plotted.

Few of the objects for which central mass estimates are available have been detected in the gamma-ray band. This probably results from a combination of selection effects and the limited sensitivity of current gamma-ray instruments. Present measurements provide little indication of how many AGN might be detectable with a factor of 1000 improvement in sensitivity. To help in addressing this question, Fig. 5 shows (as dashed lines) the locii of objects which would be just detectable if emitting gamma-rays at particular fractions f of their Eddington limits.

6.2 The special case of Sgr A*

The mass of the black hole in Sgr A* is now thought to be $(2.6-3.3)\times 10^6$ $M_\odot$ and the angular equivalent of $R_{\rm S}$ is thus 6 $\mu''$. There has been continued interest in trying to take advantage of the poximity of Sgr A* to enable sensitive probing of massive black hole systems. Falcke et al. (2000), for example, have discussed the feasibility of viewing the shadow of the black hole using sub-millimeter VLBI observations, with 16 $\mu''$ resolution, which should be possible if VLBI measurements can be made at $\lambda = 0.6$ mm. At first site Sgr A* appears to be an obvious target for a PFL gamma-ray telescope.

Gamma-ray emission from Sgr A* is known to be weak, except possibly in the Egret (GeV) band. The best models for the emission from Sgr A* over wide range of energy are probably those based on Advection Dominated Accretion Flows (ADAFs) (Lasota 1999). The currently available ADAF models (Narayan et al. 1998) are based on estimates of the X-ray flux from Rosat. Of the range of parameters considered by Narayan et al. recently available results from Chandra (Baganoff et al. 2001) suggest that the lowest luminosity combinations should be taken. However the sensitivity at 200 keV shown in Table 2 is such that even on this assumption a ${\sim} 100\sigma$ detection should be obtained in 1 day.

The most serious problem is that the source is likely to be be over-resolved. If emission is from a disk of 10 $R_{\rm S}$, the signal will be spread over 2000-3000 pixels and even sophisticated modelling techniques would barely offer a simple detection. In these circumstances there is some advantage in collecting data from a wider bandwidth and accepting the resulting degradation in resolution, but the factor gained is not large. It is probably better to consider lower energies and a shorter focal length for objects so weak and so "large''. Variations on the PFL technique which may help with this problem will be discussed in Paper II but MAXIM will be well suited to such observations.

Even at X-ray wavelengths there may be surface brightness problems if there is outflow. Ozel & Di Matteo (2001) have shown that in low luminosity models, particularly those with high outflow parameters, the low energy X-ray emission can extend to large radii, even to $10^6 \,R_{\rm S}$ at 1 keV.

6.3 Studies of gamma-ray emission from around hot stars

Inverse Compton gamma-rays are expected to be produced as the particles accelerated in the instabilities in winds around OB supergiants interact with the stellar uv photons (Chen & White 1991a,b). Such a star at 5 kpc would have an apparent radius of more than 10 $\mu''$ and the emission around it could be directly imaged with a PFL telescope, allowing detailed study of the instabilities and the acceleration processes.

When massive hot stars are in close binary systems, the colliding winds are likely to produce strong gamma-ray sources (Eichler & Usov 1993; Pittard & Stevens 1997). For binary periods of a few days, and source distances of a few kpc, the angular scale of the system will be of the order of 10 $\mu''$, well matched to the capabilities of a PFL telescope.

There is also the possibility of directly imaging the particle acceleration in the instabilities in the winds in, for example, OB supergiants.

6.4 Stellar coronal activity and flares

With micro arcsecond resolution, stellar disks will be resolvable even at large distances (a 1 $M_\odot$ main sequence star will submit 1 $\mu''$ at 4.6 kpc). High energy activity in stellar coronae could be directly imaged.

6.5 Line emission from supernovae

The extremely good sensitivity resulting from the large collecting area and flux concentrating capabilities of systemns using the principles proposed here mean that they are of interest even where the target may be unresolved. An example of this is in studying gamma-ray emission from supernovae. The analysis of (Timms & Woosley 1997) shows that a broad line sensitivity of $2\times 10^{-6}~\gamma$ s^-1 cm^-2 would be needed to detect the 847 keV ⁵⁶Co line from at least one Type Ia supernova per year. This is at the limit of the capabilities of the projected ATHENA mission and an order of magnitude more sensitive than INTEGRAL. An instrument with parameters of the 847 keV example in Table 2 would have a broad line sensitivity of $1.5\times 10^{-8}~\gamma$ s^-1 cm^-2 (5$\sigma$ in 10⁶ s) so it would be able to detect gamma-ray emission out to z=0.1.

The line emission from Type II will be much narrower but much weaker; SN1987a was only detected in gamma-rays because of its extreme proximity. Nevertheless, the narrow line sensitivity of the instruments discussed here ( $2\times 10^{-9}$ $\gamma$ s^-1 cm^-2) would, on the basis of the calculations of Timms and Woosely, allow the detection of most Type II supernovae within 70 Mpc.

Even the use of the imaging properties of the telescope to study the spread of the ejecta from a Type Ia supernova is conceivable for events within about 50 Mpc (${\sim}1$ per year), which attain diameters of several micro arcseconds in a few months and for which the ${>}100\sigma$ signal would allow the imaging properties to be used to good advantage.