In article <4093CA55.3746A4FE@nospam.com>,
Andrew Nowicki "<andrew@nospam.com>" <> wrote:

If we treat the Sun as a black body, intensity of its
microwave radiation at 100 GHz is about 10 million times
smaller than intensity of its visible radiation. The total
visible output of the Sun is on the order of 10^17W, so the
total microwave output of the Sun is on the order of 10^10W.

This is getting power densities and integrated powers confused.
In particular, the power density issue means that it is using a figure
for the power integrated over the whole of the microwave band when what
matters for SETI is typically the power integrated over a band of about
1Hz, and down to about 0.05 Hz.

The quiet sun component of the microwave noise at the earth, at about
1.4Ghz, is about 5E-21 watts / square metre / Hz (5E5 Janskies).  The Sun
is about 1.5E11 metres away, so the illuminated surface is 4 pi times
the square of this (2.83E23 square metres) giving a total isotropic
power output of about 1,400 watts per Hz.  Over the 0.1Hz of a stable
carrier subject to the Drake-Helou limit, that is 140 watts.  (Note
this is a lot more than 10E10 watts integrated over any reasonable
definition of the whole microwave band.)

If the ET lives near a sun-like star and beams to us 1 watt

                                           ^^^^^

of microwave signals, his star makes so much microwave noise

But as already pointed out, they are beaming.  Current interstellar
capable transmitters have antenna gains of over 80dB, so that 1 watt
represents an effective isotropic radiated power of 100,000,000 watts,
meaning that the signal outshines the sun by a factor of almost 
700,000.

Quite a lot of TV transmitters in the USA transmit more than 1MW EIRP,
so even if only 1% of the power leaks to space, their carriers will
outshine the sun in achievable bandwidths by a factor of more than 70
(actually more like 700, because the solar output is about 10 times less
at UHF TV frequencies).

(Note that, even wideband signals can be detected well below the noise if
you know how they are structured, although this doesn't help for initial
detection.)

that we cannot read the signal unless one beep lasts at least
10^10 seconds (about 300 years).

The only way I can interpret this figure is to assume that there are two
mistakes here, which have opposite effects on the result.  Firstly, it
seems to be assuming a bandwidth of 1Hz rather than the whole microwave
band, that has been assumed in getting the 1E10 watts.  Secondly it fails
to account for the fact that non-coherent integration only gives a signal
to noise ratio gain in proportion to the square root of the integration
time.  If the source star were the dominant noise source (it isn't),
a 1 watt isotropic, 0.1Hz signal would reach 1:1 SNR in about 2.3 days.

Note that an effective 1:1 signal to noise ratio is too poor for initial
detection, as the false positive rate is worse than 1 in 10.

The signal-to-noise ratio improves 3 orders of magnitude
when the ET's microwave transmitter is moved away from
their star. 

Even the cosmic microwave background will dominate it for any reasonably
achievable antenna antenna gain, at interstellar distances.

            If the ET replaces his microwave transmitter
with a laser and moves it away from his star, the

But then you have suddenly allowed antenna gain!  Incidentally, the limit
on laser systems is set by quantum shot noise, not by Planckian noise.
Realistically achievable optical bandwidths are of the range of 10s of
kHz.  On the other hand, because of absorption lines in the star's 
spectrum there are lots of quiet places for a close in transmitter
to use.

Solar output figures are taken from the 1982 edition of Handbook of
Space Astronomy and Astrophysics, by Martin V Zombeck, and are taken
from a graph, so only read approximately. Disturbed sun figures are 
about 200 times higher than the quiet sun figures at that frequency.