Basics of Interferometry Satoki Matsushita (松下 聡樹) Academia Sinica, Institute of Astronomy & Astrophyscis (ASIAA)

High-Resolution vs Low-Resolution Mitton & Ryle 1969, MNRAS, 146, 221 12” x 19” Perley et al. 1984, ApJL, 285, L35 0.5” x 0.5”

Single-Dish Telescopes

Single-Dish vs Interferometer Resolution goes high with higher frequency and bigger telescope: Resolution ~ l/D l: Wavelength D: Diameter of telescope If you need <1” resolution, you need to make 1 km diameter telescope It is IMPOSSIBLE ! ⇒ Interferometer !! Telescope Diameter 115　GHz (2.6mm) 230 GHz (1.3mm) 345 GHz (0.8mm) 6m 108” 54” 36” 10m 65” 32” 22” 30m 11” 7” 100m 3” 2” 1000m 0.6” 0.3” 0.2”

Single-Dish ⇒ Interferometer

Single-Dish ⇒ Interferometer It is impossible to make huge single-dish antennas. ⇒ Divide into small pieces. Advantage: If you move antennas far away, you can obtain high spatial resolution image. Disadvantage: Light collecting area will be smaller than single-dish antennas.

Interferometers

Young’s Experiment

Young’s Experiment

Young’s Experiment

Basics of Interferometry E1 = E exp{2pin(t-t)} E2 = E exp{2pin(t)} Phase information tells us position information. Visibility (You can obtain this information from interferometer): b・s = b・(s0+s)

Basics of Interferometry Define coordinates: For the observing source: s = (l,m) E2 = E(l,m)2 = I(l,m) : Intensity distribution of observing source. We want to obtain this information. For the antenna baselines: b = (u,v) : Fourier transformation relation between V(u,v) and I(l,m) !!

Basics of Interferometry So, the intensity distribution of the observing source is : This equation tells us that if you obtain as many uv data points as possible toward the source, i.e., observe the source with many baselines, observe the source for long time, you can obtain the source intensity distribution.

Basics of Interferometry Fourier transformation relation between V(u,v) and I(l,m). l,m indicate the spatial distribution. u,v are therefore indicate the spatial frequency distribution. For example, if you FT a time sequence plot, you can obtain a frequency distribution plot. Longer the u,v distance, smaller the l,m distribution, i.e., higher the spatial resolution.

uv data ⇔ image data image data uv data ⇔ FT ⇔ FT

Further Readings “Interferometry and Synthesis in Radio Astronomy” Second Edition Thompson, Moran, & Swenson (New York: Wiley-Interscience) “Synthesis Imaging in Radio Astronomy II” ed. G.B. Taylor, C.L. Carilli, & R.A. Perley A.S.P. Conf. Ser. Vol. 180 (NRAO Summer School Textbook)