Infrared Telescopes

Jansky Unit, Infrared Telescopes and Dyson Shells

1 Jansky is 1e-26 W/m²-Hz. Hz implies bandwidth. The bandwidth of a radio telescope is obvious - the bandwidth in Hertz, probably after a chilled reflector into a chilled low noise amplifier, then through a filter. A wider filter picks up more power, and more thermal noise. So the power in Janksy units for a source is Jy = 1e26 * Power~Received / ( Area * ( f_2 - f_1 ) with power in watts, Area of the receiving surface in square meters, and frequencies in Hertz.

Infrared telescopes have much wider bandwidth, and infrared is typically characterized with wavelength (usually micrometers) rather than Hertz. We can recast the formula as

Jy~=~1e26*(P/A)*c*(1/\lambda_2-1/\lambda_1)~=~1e26*(P/A)*c(\lambda_1-\lambda_2)/(\lambda_1\lambda_2)

where c is the speed of light. Defining \Delta\lambda~=~\lambda_1-\lambda_2 and center wavelength \lambda = \sqrt{\lambda_1\lambda_2}, this simplifies to:

Jy ~=~ 1e26*(P/A)*c~\Delta\lambda/\lambda^2

So, how much is that? A parsec is 3.26 light years or 3.0857e16 meters, like a star that appears to move one arcsecond in the sky as the earth moves 1 AU across its orbit. So, a sphere 1 AU in diameter would appear one arc-second across from 1 parsec away. From 200 parsecs away ( 6.1714e18 meters ), a sphere 100 AU in radius or 200 AU in diameter, and heated by the entire sun's output (3.86e26 W), would be about 60K, and deposit all that power on a 200 parsec diameter sphere with an area of 4.786e38 square meters, a power density of 8.07e-13W/m². We still don't know enough to compute the Jansky units, because we don't know the bandwidth. That is a function of the filtering and imager on our telescope - and if the telescope is not in orbit, the passband and emissions of the atmosphere.

Dyson Server Sky

A shell 100 AU in diameter at 60K enclosing the 3.84e26 Watt sun. Peak emissions at 48μm and a power flux of 0.1366 W/m². The in-band fraction of total black body emissions as a function of the mean wavelength λ and the wavelength concentration λ/Δλ can be computed from this C program: irin01.c. The program expects three command line arguments - temperature T , λ, and λ/Δλ, then computes various parameters, including the fraction of total power in-band. It is a bit of a kludge!

$ cc -o irin01 irin01.c -lm ; ./irin01 300.0 5.6 5.0
T    =  3.00000e+02 K 
peak =  9.65924e+00 μm
hckt =  4.79592e+01   
wl   =  5.60000e+00 μm
wr   =  5.00000e+00 μm
ws   =  1.12000e-06 μm
wl1  =  5.06793e+00 μm
wl2  =  6.18793e+00 μm
frac =  3.22066e-02   
frac =     3.22e-02   

James Webb Space Telescope

NASA's JWST Mid Infrared Instrument (MIRI), scheduled to deploy in 2018, will be the most powerful long distance infrared imager available, with a 6.5 meter mirror. The imager is a 1024x1024 pixel Raytheon Si:As sensor chip assembly (SCA) with 25 µm pixels. The pixels are 0.11 arcseconds.

• This table gives the sensitivity, recomputed below,

  • (detection limit, 10 sigma, 10,000 seconds)

• Assuming 3.84e26 Watts, The point source detection distance is sqrt( fraction * 3.84e26 / 4 π 3.0857e16 ² sensitivity ) parsecs

  • = 1.79e-4 sqrt( fraction / sensitivity ) parsecs.
• Earthlike planet, 152 PW of IR = 3.56E-9 sqrt( fraction / sensitivity ) parsecs.

Using the F2100W and F2550W filters, JWST can detect a 60K 200 AU diameter Dyson shell as a point source almost anywhere in the galaxy. But a Dyson shell probably cannot be differentiated from a gas cloud unless it is close enough to show a disk, which it would at a distance of less than 200 AU / .11 (arc seconds) = 1800 parsecs, encompassing on the order of 100 million stars, perhaps a million G stars like our own.

JWST seems to be optimized for looking for 300K objects, perhaps nearby earth-temperature planets. Dyson shells emit such vast amounts of power that, even at 60K and 1/30th of the sensitivity, they will be visible across most of the galaxy.

We can expect to see "star" clusters of similar temperature (because of similar technology) Dyson shells in "small" regions a few hundred light years across, size dependent on the future discount rate for the source civilization.

Herschel

ESA's Herschel Space Telescope, active from 2009 to 2013, has a 3.5 meter mirror and a wavelength range of 55 to 672 μm. The Photodetector Array Camera and Spectrometer (PACS) uses two low resolution arrays of bolometers:

These measure in 3 bands, either 70 alone or 100 and 160 together:

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