The drift technique adopted by ALFALFA is designed to allow for adequate bandpass
subtraction using the drift scans themselves with no manipulation of the
data taking stream or electronics during a drift, e.g. with
"minimum intrusion". We make use of the fact that most of the time, nearly all of
the bandpass contains no signal.
In ALFALFA, the bandpass subtraction is performed in the LOVEDATA
routine called BPD. A linear fit is calculated along the time dimension for
each frequency channel. The rms noise for each channel is calculated, and a record
is kept of what fraction of the time sequence deviates less that 2 times the rms. Outliers
are then excluded, and a final bandpass value for each frequency channel is taken
as equal to the zeroth order coefficient of the linear fit. The adopted "OFF" bandpass
then is the normalized bandpass times the system temperature Tsys. Removing the
noise contribution in this way
works very effectively for sources that are not very large; it does not
work for very extended features such as galactic hydrogen. But, for nearly all
ALFALFA galaxies, this is quick and easy and quite acceptable.
The purpose of the LBW observations is to increase the integration time ON-source,
so, rather than letting the sky drift across the beam, we actually track the
target. Therefore, in order to perform the bandpass/sky subtraction, we need an
equivalent OFF-source observation, i.e. one in which we expect the instrument+sky
noise at each channel to be identical to that contained in the ON-source spectrum.
Thus, we need to acquire an appropriate OFF-source bandpass that can be
subtracted for each ON-source observation; we end up then with matched
ON-OFF "pairs". This method is very common in radio
astronomy and is called "total power" or "ON-OFF" observing.
Let's define a few terms:
- Trx(f): The receiver noise temperature at each frequency f
- Tsource(f): The source noise temperature at each frequency f (during the ON observation only)
- Tconf(f): The contribution to the noise from "confusion" (caused by lots of
weak unresolved sources) within the main beam during the OFF observation;
this will normally be negligible and negligibly different from the general contribution
during the ON-source observation
- Tsky(f): The sky noise temperature at each frequency f, which includes
the CMB contribution and the galactic background
- Tspill(f): The contribution to the noise temperature from other sources
such as ground pickup ("spillover", atmospheric noise, etc.)
- Grx(f): The receiver gain (from the all elements, including the backend, mixers, etc)
- Gmainbeam(f): The telescope gain, i.e. the response to cosmic radiation
in the main telescope beam (from the aperture plane until the receiver)
|
Click on image to see larger version. (Thanks, BK!) |