Source Counts

A compilation of 86-GHz flux densities for sources at declinations north of can be found in the home page of the Owens Valley Radio Observatory Millimeter Array (OVRO 1999), while measured 86-GHz flux densities south of are given by Beasley et al. (1997). The source counts for these areas, covering 92.8% of the sky, are given in Table 1, as are extrapolations over the entire sky. These source counts are conservative, since they certainly are incomplete. For instance, if the estimate of 67 sources down to 1.5 Jy is assumed to be complete, the standard relation can be used to predict the numbers of sources throughout the sky that are above lower limiting flux densities. The prediction is that there should be 123 sources stronger than 1.0 Jy, and 356 sources stronger than 0.5 Jy. Table 1 indicates that the counts may be complete to 1.0 Jy, but that more than 130 sources are missing between 0.5 and 1.0 Jy. Most of the known (and missing) sources are blazars, and 83% of the gamma-ray-detected EGRET blazars (Mattox et al. 1997) are included in the lists cited above.

Table 1. Incomplete 86-GHz Source Counts
Flux (Jy)			Total	All-Sky	All-Sky Cumulative
> 10	4	0	4	4	4
5-10	5	0	5	5	10
4-5	4	2	6	7	16
3-4	6	2	8	9	25
2-3	10	1	11	12	37
1.9	3	0	3	3	40
1.8	4	0	4	4	44
1.7	2	1	3	3	47
1.6	6	2	8	9	56
1.5	8	2	10	11	67
1.4	2	2	4	4	71
1.3	2	1	3	3	74
1.2	11	2	13	14	88
1.1	9	4	13	14	102
1.0	19	3	22	24	126
0.9	6	1	7	8	134
0.8	21	4	25	27	161
0.7	18	2	20	22	182
0.6	22	5	27	29	211
0.5	4	5	9	10	221

Lister, Marscher, & Gear (1998) have imaged eight blazars at 43 GHz using the VLBA. They find peak flux densities ranging from 51% to 85% of the total flux densities for these objects, which were not selected to be more compact than ``typical'' blazars (Marscher, private communication). Since the radio cores are expected to be more prominent relative to the resolved flux at 86 GHz, we conservatively assume that most of the strong 86-GHz sources will have correlated flux densities on long Earth baselines of at least 50% of their total flux densities.

There is no well-determined method of extrapolating to the correlated flux densities that will be seen on baselines to ARISE, so some assumption must be made about the distribution of brightness temperatures. Here, we make the simple (but arbitrary) assumption that the 86-GHz correlated flux densities on 50,000-km ARISE baselines will be % of the total flux densities (i.e., ). This actually corresponds to an assumption that the typical observed core brightness temperature is K (Murphy 1998). Table 2 contains the resulting estimate of the cumulative source counts as a function of 86-GHz correlated flux density on 50,000-km ARISE baselines, and also includes a similar estimate for the case in which ; the latter case corresponds to a typical observed source brightness temperature of K. No correction for incompleteness has been made in this table.

Table 2. Cumulative All-Sky Counts of
ARISE Correlated Fluxes at 86 GHz
Minimum Correlated Flux
(mJy)	K	K
2000	4	1
1000	10	4
800	16	5
600	25	7
400	37	16
380	40	17
360	44	18
340	47	20
320	56	21
300	67	25
280	71	26
260	74	26
240	88	29
220	102	32
200	126	37
180	134	44
160	161	56
140	182	71
120	211	88
100	221	126