Draft of the Single Dish Spectral Analysis Section of CASA paper
2013/11/17 v.3
Kanako Sugimoto, Takahiro Tsutsumi, Takeshi Nakazato, Wataru Kawasaki, and
Shinnosuke Kawakami
A single dish radio telescope is suitable for studying large scale astronomical
source structures and for measuring a total power of radiation received from a given
direction of the sky. Although it cannot sample a range of spatial distribution of
radiation within field of view as interferometers do, it can measure the larger scale
distribution by moving telescope along the sky of interest and measuring the
intensity of radiation at each point of sky. Single dish telescopes and
interferometers are complementary to each other in terms of sensitivities to
different spatial scale, i.e., the former has sensitivity to the angular resolution from
approximately lambda/d up to size of area of sky observed, while the latter, from
lambda/D_min down to lambda/D_max, where lambda, d, D_min (> d) and D_max
denote the observing wavelength, antenna diameter, the minimum and maximum
distance between any pairs of antennas in an interferometer, respectively. For some
science objectives that require accurate measurement of the large scale structure as
well as finer structures, the best approach may be to combine both the single dish
and interferometry data as Atacama Large Millimeter/submillimeter Array (ALMA)
supports such observing modes.
In general, the electromagnetic radiation received by a ground-based single dish
telescope is not purely from astronomical sources of interest, but is affected by the
atmospheric absorption and emission, cosmic microwave background, leakage of
ambient radiation and receiver system noise.
The output power from the receiver on the single dish radio telescope is typically
expressed in terms of temperature which is related by Nyquist theorem (ref. Ch.7?
of Tools of Radio Astronomy [2]). Therefore the power measured on an astronomical
source at a certain frequency, P_{source}, is described as,
𝑃𝑠𝑜𝑢𝑟𝑐𝑒 = 𝐺𝜂𝑒 −𝜏𝑍 [𝑇𝐴∗ + 𝑇𝑠𝑦𝑠 ] ... (1),
where T_A^*, T_{sys}, G, ¥eta, ¥tau, and Z denote the effective temperatures of
astronomical source corrected for atmospheric absorption, system temperature,
gain factor of receiver, feed efficiency, atmospheric opacity, and optical path length
though the atmosphere, respectively. Z is defined as Z = sec(za), where za is the
zenith angle of telescope pointing. The system temperature, T_{sys}, is off source
temperature contributed from various noise sources,
1
𝑇𝑠𝑦𝑠 = 𝜂𝑒 −𝜏𝑍 [𝜂𝑇𝐶𝑀𝐵 𝑒 −𝜏𝑍 + 𝜂(1 − 𝑒 −𝜏𝑍 )𝑇𝑎𝑡𝑚 + (1 − 𝜂)𝑇𝑎𝑚𝑏 + 𝑇𝑅𝑋 ] …(2)
where T_{CMB}, T_{atm}, T_{amb}, and T_{RX} denote temperatures of cosmic
microwave background, atmosphere, and receiver system noise, respectively.
The
processing of single dish observation data starts with calibration in which T_A^* is
derived from observed power.
General steps to process single dish observation data and their purposes are
similar to interferometer counter part, i.e., calibration, baseline subtraction,
flagging, imaging, viewing/plotting spectra or image, and image analysis. However,
details of operations are different due to difference in calibration strategies in single
dish and interferometer observation, and also to difference in observed quantities,
i.e., amplitudes of the power (auto-correction) in former while visibility amplitudes
and phases (cross-correlation) in the latter. Since in the auto-correlation the noise is
not isolated from the measured signals as opposed to the case in cross-correlation
where the noise can be isolated from the correlated signals.
CASA provides capabilities to process all the steps described in the above. In this
section, the calibration, baseline subtraction, and flagging steps are described with
the capabilities provided by CASA. For the other steps, single dish imaging is
described in Section ??? and image analysis is common to the inteferometry case.
Calibration: In single dish observation, it is common to observe a couple of additional
sources to calibrate the observed radiation of the interest, i.e., radiation from blank sky
without astronomical sources and absorber devices with known temperatures. The
calibration equation of single dish observation can be generalized as,
𝑇𝐴∗ =
𝑃𝑠𝑜𝑢𝑟𝑐𝑒 −𝑃𝑠𝑘𝑦
𝑃𝑐𝑎𝑙
𝑇𝑐𝑎𝑙 ... (2)
where P sky and P cal are the power of radiation measured on blank sky, the power
detected for a certain calibration temperature, T cal, respectively. The details of how to
obtain P sky, P cal and T cal depend on observation strategies and telescope facilities (see,
e.g., O’Neil 2002 for details). For example, in position switching observation by ALMA,
P sky is observed by pointing the telescope toward the sky where no astronomical source
exists, i.e. the equation (1) is reduced to,
𝑃𝑠𝑘𝑦 = 𝐺𝜂𝑒 −𝜏𝑍 𝑇𝑠𝑦𝑠 ... (3)
T cal is obtained by observing the power of the absorber device. For ALMA, two loads
with different temperatures in the amplitude calibration device which is located in
the front end system of the telescope is used (ref. ALMA Handbook Appendix 5).
CASA supports calibration of various combination of telescopes and observation
strategies, e.g., position-switching and on-the-fly observations by ALMA,
position-switching, frequency-switching, and beam-switching observation by Green
Bank Telescope, etc.
Baseline subtraction: Radiation of astronomical sources often contains transition
lines of certain molecules and atoms as spectral lines. They are observed as excess
or decrement of brightness temperature in narrow frequency range. In some cases it
is desirable to extract line components from “background” continuum component,
which smoothly varies in frequency, and analyze the lines separately. This process
is called baseline subtraction. In this process continuum component is fit as a
known function and subtracted from spectra to extract spectral line emissions.
CASA provides various fit functions for baseline subtraction including, Chebyshev
polynomial, cubic spline, and sinusoidal functions. It also provides facilities to
define frequency ranges free from emission lines automatically for the fitting.
Flagging: CASA provides capabilities to discard a part of single dish observation
data from processing, if it is contaminated by non-astronomical radiation, e.g.,
strong instrumental noise or other artifacts. Similar to flagging of interferometer
data, this is realized by storing flag information to certain columns in single dish
data but not by modifying data itself. CASA supports meta-data flagging as well as
flagging by brightness temperature and frequency range of spectra. It is also
possible to back up snapshot of flag statuses and restore one of them later.
Reference:
[1] Tools of Radio Astronomy - Fifth Edition, by Wilson, T. L., Rohlfs, K., &
Hüttemeister, S. (Springer)
[2] O’Neil, K. 2002, ASP Conference Series, vol. 278, 294.
[3] AMLA Technical Handbook