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Why Single Dish?

Darrel Emerson NRAO Tucson

NAIC-N RAO School on Single-Dish Radio Astr onomy. Arecibo, June 2005

Why Single Dish?
· What's the Alternative? · Comparisons between Single-Dish, Phased Array & Interferometers · Advantages and Disadvantages of Correlation Interferometer · Scale-sizes, Spatial Frequencies, Spatial Filtering: Examples · Practical Details · Future Telescopes · Conclusions
NAIC-N RAO School on Single-Dish Radio Astr onomy. Arecibo, June 2005

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Single Dish.
Free space propagation & reflection to bring all signals together in phase

Phased Array.
Cables of just the right length, to bring all signals together in phase

Adding Interferometer or Phased Array
A single dish with missing metal.

Correlation or Mult iplying interfero meter
All aperture synthesis radio telescopes are made up of multiple correlation interferometers

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Phased Array (Adding Interferometer) vs. Correlation Interferometer
2· · · Element Phased array: Signal into each antenna element: a, b Noise of each antenna amplifier: A, B Before detector: (A + a) + (B + b) · After detector: [(A+a) + (B+b)]2 or A2 + B2 + a2 + b2 + 2.(A.a + A.b + B.a + B.b + A.B + a.b) Time-averaged products of uncorrelated quantities tend to zero, so this averages to just: A2 + B2 + a2 + b2 + 2.a.b

Multiplying or Correlation Interferometer: ·After multiplier: (A + a).(B + b) or A.B + A.b + a.B + a.b
NB: multiplication + averaging = correlation

·After averaging, uncorrelated products tend to zero, so this becomes just a.b The averaged output no longer depends on A or B, the internally generated amplifier noise voltages (ignoring statistical fluctua tio ns)

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Adding Interferometer or Phased Array
·A2 + B2 + a2 + b2 + 2.a.b

Correlation or Mult iplying interfero meter
·a.b

Phased Array (Adding Interferometer) vs. Correlation Interferometer · Phased Array (Adding Interferometer) is the same as the Single-dish telescope (just missing some metal & using more
cable instead).

· Single Dish very suscept ible to changes in receiver gain, and to changes in receiver no ise temperature · Correlation Interferometer nearly immune to receiver gain and noise changes · Some source distributions, or combinat ion of sources may be invisible to the correlat ion interferometer.

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Diameter D

d1 d2 d3

A single dish of diameter D includes all baselines from 0 to D

Dish Diameter D

Interferometer separation d

Dish diameters D d-D d1 d2 d3 d+D

A single dish of diameter D includes all baselines from 0 to D

A correlation interferometer of separation d, using dishes of diameter D, includes all baselines from d ­ D to d + D

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Angle on sky = ( /Baseline) radians Spatial Frequency is proportional to Baseline

Angle on sky = ( /Baseline) radians Spatial Frequency is proportional to Baseline

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Angle on sky = ( /Baseline) radians Spatial Frequency is proportional to Baseline

Angle on sky = ( /Baseline) radians Spatial Frequency is proportional to Baseline

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Spatial frequency distribution of the all-sky 408 MHz distribution

Spatial frequency (1/degrees)

A cut through NGC 1068.

Complete data

2.7K cosmic background and other large scale emissio n features removed

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Spatial frequency distribution of several degrees of sky around NGC1068

Baseline removed

Spatial frequency (1/degrees)

Spatial Frequencies: Single Dish vs. Interferometer
· Single Dish has a high spatial frequency cut-off in resolution set by its diameter · Interferometer has a low spatial frequency cut-off set by its minimum antenna separation · Sometimes, the interferometer low frequency cut-off is advantageous · Usually, Single Dish maps are analysed in a way that removes the lowest spatial frequencies too. We don't normally want the 3 K cosmic background in our data · The relative flux in low spatial frequencies is typically far greater than that at higher spatial frequencies · For cases where we DO want large scale structure, we may HAVE TO use a Single Dish.

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Sensit ivit y
· Even after allowing for the insensitivity to large scale structure, the BRIGHTNESS TEMPERATURE sensitivity of an aperture synthesis telescope is usually FAR poorer than a single dish, even for the same collecting area. ­ For equal total collecting area and rx performance, the sensitivity to point sources S (in Jy) is identical for a SD and a synthesis array. (Ignoring factors of order sqrt(2)) ­ For a SD, the observed antenna temperature on an extended source approximately equals the source brightness temperature. ­ Converting from flux density S, in Jy per beam, into temperature Tb of an extended source, one expression is: Tb=(S/(2.k)).( / )2 where is the beam solid angle ­ Note that is inversely proportional to diameter D for a Single Dish, and to maximum baseline d for an aperture synthesis array.
¡ ¡

Tb=(S/(2.k)).( / )2


where

is the beam solid angle, approximately ( /D)2 for a dish of Diameter D or approximately ( /d)2 for an interferometer with maximum baseline d


So, for a given sensitivity to point sources S, the sensitivity in brightness temperature Tb Tb = S.D2/(2.k) Tb = S.d2/(2.k) for dish of diameter D for interferometer of maximum baseline d

The interferometer of equal collecting area has worse sky brightness temperature sensitivity by a factor (d/D)2 . This is the filling factor of the array of antennas. This poorer brightness temperature sensitivity is in addition to potentially poor spatial frequency coverage for large-scale structure

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If your science requires the large scale structure, there's probably NO ALTERNATIVE to including Single Dish data

Practical Details
· The fundamental characteristics of a Single Dish are its good potential sensitivity to large scale structure, and its lack of sensitivity to fine structure, or high spatial frequencies. · Practical details are just as important.

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Practical Advantages of Single Dish observing:
· · Spatial frequency response Sensitivity:
­ Sensitivity in Jy (point source) depends just on collecting are a, SD or Inter fer ometer . ­ Sensitivity in brightness temperatur e K (extended emission) gets WORSE a s (Max.Ba seline) squar ed, for the same collecting ar ea ­ i.e. r oughly as (d/D)2
· 100-mete r single dish: ~ 2 K/ Jy · 1-mile max baseli ne apert ure synthe sis telescope: ~1600 K/ Jy

· · · · · · · · · ·

Ability to map very extended areas quickly May provide large collecting area with manageable electronic complexity Simplicity: one receiver, not N receivers, nor N.(N-1)/2 correlations BUT relatively easy to implement large imaging arrays, including bolometers, which can increase mapping speed by orders of magnitude. Multi-frequency receivers relatively easy investment Flexibility: Relative ease of upgrading, customizing hardware to an experiment Relative ease of implementing radar tx systems A single large dish can add significant sensitivity to (e.g.) VLBI arrays Software possibly simpler: "Conceptually" easier to understand for novice astronomers. (But this is inexcusable!)

Practical Disadvantages of Single Dish observing: · Spatial frequency response · Mechanical co mplexit y replaces electronic complexit y · Susceptibilit y to instrumental drifts in gain and noise don't have the correlat ion advantage of interfero meters · Interfero meters can in principle give high sensit ivity and high total collect ing area. · Aperture synthesis imaging is a form of mult i-beaming arguably obtaining more informat ion fro m the radiation falling on a telescope than is possible with a single dish. The overall key parameters are 1. Spatial frequency response and sensit ivit y 2. Relat ive co mplexit y.

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SUMMARY
· Don't think in terms of a "Single Dish Observer" or an "Interferometrist." · Both technologies have their advantages and disadvantages. Choose the right tools for the job. · Often, a combination of both tools may be required in order to do a good job · Future telescopes (e.g. ALMA) may be built to allow both Single Dish and Interferometer observing, in order to provide the astronomer with the complete range of spatial frequencies needed for the science. In future the distinction between "Single Dish" and "Interferometer" observing may become blurred.
NAIC-N RAO S chool on Si ngle -Di sh Radio Ast ronomy. Are ci bo, June 2005

The ALMA array is designed to operate as 64 "independent" single dish telescopes, as well as a 2016-baseline interfero meter

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The ALMA array is to now be augmented by the compact array, the ACA. The purpose is to add 4 large single dishes plus 12 small interferometer dishes to give the short baselines, which will give full, optimum coverage of the low spatial frequencies.

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