Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.naic.edu/~astro/School/Talks/stanimirovic_shspac.pdf Дата изменения: Fri Jul 15 01:00:17 2005 Дата индексирования: Sat Dec 22 20:37:15 2007 Кодировка:

Short-Spacings Correction From the Single-Dish Perspective
Snez ana Stanimirovic (UC Berk eley)

Ingredients: 1. an

A R ecipe for Observing Extended Objects: extended objec t (e .g . S mall Ma gella nic C loud )

2. a n in te rferome te r (e .g . VLA, AT CA, BI MA, AT A) 3. a single -dish (e .g . A recibo , GBT, P arkes, 12 m)

VLA: FWH M>1''

Areci bo: FWHM~3'

Procedure:
1. ob serve w ith a n in te rferome te r 2. obser ve with a s in gle -dis h 3. take ad van tage of bo th wor lds: c ombine !

+
`Black magic' f or bringing the best of both worlds: short -spacings c orrection, or combination of single -dish a nd i nterferometer data
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This recipe makes:
1. p re tty pic tures: l o ts of res olu tio n elemen ts, n o image ar tifac ts 2. high reso lu tion ima ges w ith the T OTAL P OW ER inf orma tion (acc ura te fluxes, masse s e tc .) 3. ima ges sen sitive to a w ide range of s pa tia l sca les .

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Outline:
Breath and depth of combining interferometer and single-dish data ... A recipe for observing extended objects (with detours): 1. the briefest possible intro to interferometry 2. demonstration of the short-spacings problem 3. what can we do about the short-spacings problem ? 4. different methods for data combination Some recent examples Future directions....

Step 1: `Mosaic' with an interferometer

Australia Telescope Compact Array (ATCA) mosaic of the Small Magellanic Cloud at 1.4 GHz. Mosaic of 320 different pointings.

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34' = A TCA primary beam

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Single-dish and interferometer data frequently need to be combined ...
when observing EXTENDED objects (larger than /bmin or interferometer's primary beam) [you'll see why exactly] when MOSAICING: if you need to mosaic, you'll need to add single-dish data. especially at mm wavelengths where TOTAL POWER info is almost always needed.


T hompson (1994)

How does an interferometer actually w or k ?
Image domain
Fourier transform

Spatial frequency domai n

Sk y brightness d istribution

Spatial coherenc e function A ntenna primary beam

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van Cittert-Zernike theorem:

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More baselines, more u-v tracks!
V(u,v)
Very short spacings

How severe the problem is ?
1

Australia Telescope Compact Array (ATCA), an E- W linear array. 5 antennas, 5(5-1)/2 diff. baselines Lowest spatial frequency: ~31m/0.21m Highest spatial frequency: ~495m/0.21m Can not see structure > 24'. Angular resolution=1.6'

BIMA SONG CO map

Flux r ecovery ratio map

Farther away from the nucleus, the less flux is recovered!
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And what is the result ?

How much flux is missing ?
Simul ations
Helfer et al. (2002) BIMA A LMA

BIMA SONG Data, > 30 ga laxies
Helfer et al. (2003)

Small Ma ge lla nic Cloud at 1.4 GHz, interferometric (ATCA) obser vations only.

IRA M
Source size (")

Large-scal e flux recovery for a mosaic observation : S/N (BIMA ) ­ depends on the minimum distance between the dishes, bm in-D ­ is a function of the S/N ­ varies from source to source, and spatially

Large-scale distribution can not be modeled, needs to be measured!
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And what is the result ? WHY ?
Spatial frequency domai n Image domain

What can we do about the short-spacings problem ?
How to provide missing short-spacings ? 1. Homogeneous scheme = all antennas of the same size 2. Heterogeneous scheme = different-sized antennas How to combine short-spacing data with that from an interferometer ?

Bra un & W a lter bos ( 1985)

As few gaps in the u-v plane as possible ! Single-dish diameter > min. interferometer baseline. Must match flux scales of both data sets.

Missing sh ort sp. frequencies

Negative bowls
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IB
0

IMA55

/I1

2m

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Step 2: `Mosaic' with a single dish
4.5 deg = 4.7 kp c

64 m

Step 3: Cross-calibration of two data sets
Interferometer and single -dish data should have the same f lux density scale.

· Point to many directions

& gri d a ll spectra. · 1540 differ ent poi ntings with the Parkes (64 m) telescope ! · Go multi-beams!
Parkes primary beam=15'

Calibration scaling factor: fcal=Sint/S
sd

Do it your self or use Miria d's immerge
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Compare surfa ce brightne ss of your object in the ovar lap region in the u-v pla ne.
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Single-dish as an interferometer!
Can be retrieve d by scanni ng across your object, base d on Ekers & Rots (1979 ).

Step 4: Combination of single-dish and interferometer data
Data combination in the Fou rier domain:
Miriad's IMMERGE, Aips' IMERG, aips++'s IMAGER
Bajaja & Albada (19 79 ); V ogel e t a l . (19 84 ); Sau l t & K il len (20 03 )

Data combination in th e image domain:
1. `Li near Combination' `Phase d arra y' continuous ra nge of baseli nes avai lable from 0 to D.
Sta nimir ov ic e t al . (1999 )

a combination of tasks,

Ye & Tu r tle (199 1); S tewar t e t a l. (199 3);

2. ` Non-li near c ombination' or `Mergi ng during dec onvolution'
Miriad's MOSMEM through either `default image' capability or `joint deconvolution'

Similar mathematical represe ntation for both interfer ometers and single dishes!
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And what is the result ?
Small Ma ge lla nic C loud at 1.4 GHz, single -dish (Parkes) observations only. ... and its Fourier transf orm

Fourier domain combination

interferometer

FT

-1

single-d ish + interferometer single-d ish

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Linear combination

Small Cloud short corre

Ma ge lla nic AFTER -spacings ction.

Final Results:

Method
1.
2. 3. Parkes on ly ATCA onl y
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Total Flux (Jy):
560 0 650 0 630 0 6 10 0 3 200
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I

D int

I

D sd

Non-Linear combination
B
sd

Remarks on different methods:
· In recent years, all methods are commonly used from small 7point to huge > 1000-point mosaics. · All methods produce comparable results in the case of high S/N data (e.g. SMC).

B

int

· `Feathering' method is the fastest and the least computer intensive, great results, very robust. · For low S/N data, as is often case at mm wavelengths, `linear' method seems advantageous: no need for deconvolution by the single-dish beam nor deconvolution of int. dirty maps, it is easy to implement and automate.

MEM DECONVOLVER

W right (2004): CARMA Memo27 Simulations show this as the best method, but it depends on quality of SD data.
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· `MEM' method is theoretically the best way but heavily dependant on the quality of the SD image.

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Small Cloud short corre

Ma ge lla nic B E FO R E -spacings ction.

Final Results:

Data combination is routinely performed with a great success: examples
A TCA A TCA OVRO BIMA BIMA BIMA VLA D VLA D 25 25 15 8 8 8 35 35 Park es Park es IRA M FCRA O 12m 12m GBT AO 64 64 30 14 12 12 100 305 1.4 1.4 8 .8 115 113 115 8.4 1.4


Array Bm

in(m)

SD

D

(m)

(

GHz)

Method
linear imm erge im merg e linear mosm em linear immerge

Ref.
Stanimirovic et al. 1999 McClure-Griffiths 2005 Lang et al . 2002 Pound et al. 2003 Welch et al. 2000 H elfer et al . 2003 Lee et al.; Robis haw et al .

feat hering, aips++ Shep herd et al . 2003

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Recent Examples: IC443 Lee et al. (2005)
FW HM=3.9'

Future Telescopes (cont):
Future trend: het erogeneous arr ays with small dishes. Smaller dishes ha ve lower systematic error s and larger field of vie w so are faster than lar ge single di shes (Holda way & He lfer 1999 ). Data c ombination has bee n the key driver for r ecent antenna desi gns and array configurations (C ARMA, ALMA, ATA).

FW HM=9'

Sha dowi ng effects f or c losely packe d antennas
(Subrahmanyan & Deshpande 2004)

Data combination (joi nt dec onvolution) depends greatly on the qua lity of S D data (poi nting errors, ther mal noise, ground pick up, atmosph eric fluctuations).
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Recent Examples: SGPS = ATCA+PKS
Parkes

Particular (practical) single-dish needs:
· A large e nough ar ea must be covere d with single -dish obser vations (e dge -effect issue ). · Nyquist samp ling is i mportant to a voi d aliasi ng duri ng deconvolution (Voge l et a l. 1984 ). · S/N ratio of interfer ometer a nd single -dish data sh ould be c omparable.

ATCA+P arkes

· In genera l, and espe cially f or the cr oss-cali bration a very good k nowle dge of the single -dish bea m is r equire d (can start with a Ga ussian first ). · At mm wave le ngths main issues are: p ointing and calibration acc uracy.

McC lure-Griffiths et a l. (2005) : >300 deg2

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Future Telescopes (arrays of small antennas):
CA RMA A LMA A TA 4 15 ~8 OVRO A CA A TA 10 .4 7-12 6 .1 115, 230, 345 30- 950 1.4-11.12


Summary:
· Single-dish es have a h uge r ole in pr oviding infor mation that comp lements interferometric observations. · Short-spacings corre ction is a MUST in most of observations at mm wavele ngths and ma y soon become a part of a general obser ving sche me (e.g. ALMA). · Easy c ombination of single-dish and interf erometer data avai lable and fr equent ly done for differe nt telescopes a nd for sources of greatly var ying sizes. · 3 discusse d methods work fi ne a nd with comparable results. · Overlap of spatial fre que ncies is crucia l for crosscalibration.

Array Bm

in(m)

SD

D

(m)

(

GHz)

Method

Ref.

provid e OTF capability for OVRO s hort spacings hig h priority! homog eneous array!

ALMA =64 x 12 m

AT A=42(350) x 6 mSD

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Bibliography:
·

Stanimirovic 2002, ASP Conf. Ser. 278 + REFERENCES THERE

· Holdaway 1999, ASP Conf. Ser. 180 · Holdaway & Helfer 1999, ASP Conf. Ser. 180 · Helfer et al. 2002, PASP, 114, 350 · `Interferometry and Synthesis in Radio Astronomy' Thompson, Moran & Swenson (2001) · `Synthesis Imaging in Radio Astronomy' Taylor, Carilli & Perley (1999) · Sault & Killeen 2003, Miriad Users Manual

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