The operation and sensitivity, and the present situation and
future wishes of mm-VLBI are easily explained from a discussion
of the relation expressing the signal-to-noise ratio of an
observation with a two-telescope VLBI interferometer. An
unresolved source with a size comparable or smaller than the
synthesized beamwidth (), measured with both telescopes
(1,2), is considered to be detected if the signal-to-noise ratio
(SNR) of the observation is
7 or higher, i.e. 7
SNR. The relation of the SNR is ([Rogers et al. 1984])
with A the geometrical area = (D/2)
and
the diameter of the telescope (Tables 3.2 &
3.3);
the aperture efficiency
(Table 3.2);
A the effective collecting area;
T
the system temperature (Table 3.2);
the bandwidth (112MHz for MkIII);
the
integration time; F the correlated flux density; k the Boltzmann
constant; and L the correlator efficiency (
2/
for a
2-level quantization). cm From this relation
we note that: cm
the incorporation
of a large-diameter high-precision telescope significantly
improves the performance of a mm-VLBI array. If an array of two
telescopes of diameter
= 15m and
efficiency
performs at the
signal-to-noise ratio SNR(2
15m), the replacement of one
telescope by, for instance, the IRAM 30-m telescope with
= 30m and
improves the signal-to-noise ratio by SNR(15m & 30m) =
2
SNR(2
15m): the array has a 2 times higher
sensitivity. It is evident that the future incorporation of the
PdB interferometer, the LMT, and ALMA (Table 3.2) will
greatly improve the sensitivity of mm-VLBI. cm
for observations at mm-wavelengths the
location of a telescope at 2000-3000m altitude generally
reduces T
because of the lower amount of atmospheric water
vapour, i.e. T
(high site)
(1/3)
T
(low site)
(1/3)
(300-500)K
150K. The lower value
of T
increases the SNR by a factor of 2, or more. Such a
decrease of the line-of-sight T
is especially important
for intercontinental/transatlantic baselines where the sources are
usually observed at low local elevations (Figure 3.3).
Table 3.2 shows that several telescopes of the CMVA array
unfortunately are located at low altitudes. Again, the
incorporation of PdB Interferometer (2500m), the LMT (4600m),
and ALMA (5000m) will greatly improve the sensitivity of
mm-VLBI. cm
for continuum
observations, the foreseen increase in bandwidth of presently
= 112MHz by a factor of two, or more (MkIV), will
increase the sensitivity of mm-VLBI by a factor of 1.5, or more.
cm
the integration time
is
usually limited by the stability of the Hydrogen-maser to values
(100GHz)
1000s and
(230GHz)
100s (Sect.3.6). Often however, the integration time is
shorter,
(100GHz)
100-200s and
(230GHz)
10-20s, because of phase
disturbances introduced by atmospheric water vapour fluctuations.
Segmented correlations and atmospheric phase corrections increase
the sensitivity of mm-VLBI. cm
the SNR is proportional to the correlated (unresolved) flux
density (F) of the source. At mm-wavelengths it is found that the
correlated flux density is often significantly smaller than the
total flux density (S) measured with a single dish telescope. It
is found, globally, that F
(1/3-1/5)
S. As example, for 3C273 it is
observed that S(86GHz)
20Jy while F(86GHz)
4Jy, and S(230GHz)
10Jy while
F(230GHz)
2Jy. The presently available CMVA array
has sufficient sensitivity to detect sources of total flux density
S
2-3 Jy. cm To illustrate the
present situation and possibilities of mm-VLBI,
Table 3.6 summarizes the SNR of detections at 86GHz
measured on the baseline Pico Veleta (Spain) - Haystack (USA)
([Krichbaum et al. 1994]; [Beasley et al. 1995]).
Source | S(86GHz) [Jy] | SNR |
(single dish) | (VLBI) | |
3C273 | 25 | 182-203 |
3C279 | 20 | 163 |
3C345 | 5.5 | 6-13 |
NRAO530 | 6.5 | 21-81 |
1749+096 | 3.0 | 21-43 |
1823+568 | 2.8 | 35-43 |
2145+067 | 4.5 | 5-19 |
3C454.3 | 10 | 78-66 |
Source | z | S(215GHz) [Jy] | SNR | F(215GHz) [Jy] |
(single dish) | (VLBI) | (VLBI) | ||
4C39.25 | 0.69 | 3.5![]() |
![]() |
![]() |
3C273 | 0.16 | 9.2![]() |
7 | 0.4-0.7 |
3C279 | 0.54 | 11.0![]() |
35 | 3-3.8 |
1334-127 | 0.54 | 3.1![]() |
12 | 0.5-1.1 |
3C345 | 0.59 | 3.0![]() |
6 | ![]() |
NRAO530 | 6.2![]() |
11 | 0.5-0.8 | |
SgrA![]() |
4.1![]() |
6 | 0.5-0.9 |