Infrared Telescopes and Dyson Shells


Jansky Units, Microwave Telescopes, Infrared Telescopes

One 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 ~=~ 1e26*(P/A)*c~/( \lambda (\lambda / \Delta\lambda) )

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 Shell 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.

λ

λ/Δλ

sensitivity

λ0

λ1

Δλ

300K

300K

300K

60K

60K

power

384 YW

152 PW

power

384 YW

μm

μJy

W/m2

μm

μm

μm

fraction

parsec

parsec

fraction

parsec

F560W

5.6

5

0.16

1.7e-20

6.19

5.07

1.12

3.22e-02

250000

4.9

1.43e-13

0.5

F770W

7.7

3.5

0.25

2.8e-20

8.88

6.68

2.20

1.30e-01

390000

7.7

6.32e-09

85

F1000W

10

5

0.54

3.2e-20

11.05

9.05

2.00

1.35e-01

370000

7.3

6.72e-07

820

F1130W

11.3

16

1.35

2.2e-20

11.66

10.95

0.71

4.54e-02

370000

7.3

1.24e-06

1300

F1280W

12.8

5

0.84

3.9e-20

14.14

11.58

2.56

1.46e-01

350000

6.9

3.74e-05

5500

F1500W

15

5

1.39

5.6e-20

16.57

13.57

3.00

1.36e-01

280000

5.6

2.79e-04

13000

F1800W

18

6

3.46

9.6e-20

19.56

16.56

3.00

9.66e-02

180000

3.6

1.44e-03

22000

F2100W

21

4

7.09

2.5e-19

23.79

18.54

5.25

1.19e-01

120000

2.4

7.98e-03

32000

F2550W

25.5

6

26.2

5.1e-19

27.71

23.46

4.25

5.78e-02

60000

1.2

1.69e-02

33000

300K Sum

0.898

60K Sum

0.027

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.

If the JWST imager and mirror was colder, with longer wavelength Filters up to "F8000W" or so, it would be optimal for imaging 60K Dyson shells. With 3 times the wavelength, it would need 3 times larger optics to provide the same .11 arcsecond angular resolution, thus a 20 meter main mirror. In order to image a 200 AU diameter sphere at the far side of the galaxy, as a sphere, it would need to be 60 times larger, perhaps a 400 meter main mirror, or a few smaller mirrors arranged as a sparse interferometer.

JWST is beggaringly expensive with current launch technology and solid mirrors, but with well-developed thinsat and launchloop technology, far from the sun so the system is cool, we will "soon" be able to accurately characterize any Dyson shell in our galaxy - if there are any to be seen, and if they are warmer than 50K or so. A more computationally efficient Dyson shell might be colder and very much larger, resolvable only by kilometer-scale telescopes.


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:

Red

16x32

6.4as

Blue

32x64

3.2as

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

70

60 to 85 μm

5 mJy (5σ, 1h)

100

85 to 130 μm

5 mJy (5σ, 1h)

160

130 to 210 μm

10 mJy (5σ, 1h)

MoreLater


Spitzer

MoreLater


IRAS

MoreLater


IRtelescope (last edited 2015-07-26 18:40:30 by KeithLofstrom)