Brightness-Temperature Threshold

Murphy (1998) has found a detection threshold of K for ARISE on a 40,000-km baseline to a VLBA telescope, or K on a 50,000-km baseline, given an 8-Gbit sec data rate and telescope sensitivities similar to those quoted in this document. For a 100,000-km baseline, the observed threshold rises to K, corresponding to K. If a large telescope such as the GBT were used to anchor the ground array, the observed limits would be reduced to K for a 40,000-km baseline, or K for a 100,000-km baseline.

Given these brightness temperatures, the assumptions made in Section 3 can be summarized in a useful way. The estimate of detectable sources for ARISE above a threshold of 120 mJy (Table 2) assumed that those sources have cores with observed 86-GHz brightness temperatures above the threshold. Since blazars are beamed toward the observer, the brightness temperatures are expected to be near or above the inverse Compton limit in most cases. Thus, in general, we can expect K, as found in the TDRSS experiments (Linfield et al. 1989). Most of the 210 sources above 600 mJy in total 86-GHz flux will then be detectable by ARISE on baselines up to km (cf. Murphy 1998 for the brightness temperature calculations). However, on baselines near 100,000 km, the detection requirement of K would be higher than the highest brightness temperature observed with centimeter-wavelength Space VLBI, with either TDRSS (Linfield et al. 1989) or VSOP (Preston et al. 1999). Therefore, the evidence is that very few sources would be detectable at 86 GHz on a 100,000-km ARISE baseline, but that a maximum ARISE orbit altitude of 40,000 km (and corresponding maximum baseline length of 50,000 km) is fairly well-matched to the properties of blazars.

Table 6. Required Aperture Efficiency for
Threshold of K
Baseline Length (km)	Aperture Efficiency
50,000	0.08
60,000	0.12
70,000	0.16
80,000	0.20
90,000	0.26
100,000	0.32

If it is desired to fly ARISE at an apogee altitude of 100,000 km, observations of a large number of blazars would require a sensitivity increase of a factor of 4 to achieve a detection threshold of K at 86 GHz. This would mean that a 25-meter ARISE antenna must have a total aperture efficiency greater than 30% at 86 GHz, rather than the low efficiency of 8% that is currently assumed. Table 6 gives the aperture efficiency that would be required (assuming 8 Gbit sec and K) in order to achieve a brightness temperature detection threshold of K on baselines ranging from 50,000 to 100,000 km.