Detection Of Planetary Systems

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The technology for Optical Heterodyne SETI would also be of considerable benefit to the light sciences. Even though a device like the Hubble Space Telescope has sufficient aperture to resolve the planetary systems of a nearby stars (once its present mirror problem is corrected), scattering imperfections in the telescope, its side-lobe suppression factor, and interstellar scattering, limits the ability to separate the planet from the star. Thus, even though the Rayleigh resolution is more than adequate to resolve two equally bright objects, this is not easily done here since the light from a star is far more intense than the light reflected from one of its planets.

The fundamental narrow frequency selective nature of an optical heterodyne receiver allows us to achieve much better discrimination between the light of a star and its planets, by virtue of the fact that there are differential Doppler shifts present. An optical heterodyne receiver should allow us to analyze the weak fine-line spectra found in the Fraunhofer absorption and bright-line emission bands. By looking for Doppler shifted "bright" lines produced by the planet within the "dark" Fraunhofer bands of its star, it may then be possible to filter out and discern the very weak light from the planet, and determine its orbital parameters. If these lines are further modified by a planetary atmosphere, we could then determine the constituency of that atmosphere.

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Let us now do some simple calculations to see if the light reflected from an alien planet could be detected near the Earth. The graph 9006-015 showed that the Sun's irradiance at 656 nm and 1 A.U. to be 1.5 W/m².nm. If we assume a planet like Jupiter, at a distance of 5 A.U. from the Sun, then the Sun's irradiance falls to 1.5 x (1 A.U./5 A.U.)², i.e., 0.060 W/m².nm. The spectral irradiance of Jupiter, based on an albedo (fraction of incident light reflected) of 0.4, is about 3 x 10^-10 W/m².nm at a distance of 4 A.U. from Earth. Planckian starlight radiation at 4 A.U. is 0.094 W/m².nm. By taking ratios, we see that Jupiter's irradiance is a factor of 3.1 x 10⁸ smaller than the planckian starlight radiation, i.e, -85 dB. Thus, 85 dB is the ratio between the starlight and the planetary light. The telescope's resolution and contrast ratio must be sufficient to separate out the planet's light from that of its star. This 310 million ratio appears to be a formidable number, but let us now see if there are approaches that can allow us to overcome this.

At 10 light years from us, a planet like Jupiter would produce a spectral irradiance of about 3 x 10^-10 x (4 A.U./10 L.Y.)² W/m².nm, i.e., 1.2 x 10^-20 W/m².nm. We can turn this into a spectral density number by noting that at 656 nm, 1 nm = 7 x 10¹¹ Hz. Thus, the spectral irradiance can also be written as 1.7 x 10^-32 W/m².Hz.

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Can we detect this? Certainly, not in a 1 Hz bandwidth, but what about a 1 GHz bandwidth? Remember that we should halve these numbers when considering only one plane of polarization, and double them when considering the one-sided spectral density in the I.F. bandwidth.

In a 1 GHz bandwidth, both the direct starlight and planetary light noise power within the I.F. filter will increase by a factor of 10⁹. This now means that the polarized Planck starlight noise is now 2.4 x 10^-15 W/m² and the polarized planetary reflected starlight noise is 8.6 x 10^-24 W/m².

We have already seen that a signal beacon intensity of 2.05 x 10^-17 W/m², corresponding to a detected power of 1.6 x 10^-15 W and the arrival of 2640 photons/second, produces a CNR = 34 dB in a 1 Hz bandwidth. Our "noise" signal at 2.4 x 10^-15 W/m² is about 21 dB greater than the beacon strength, resulting in a photon arrival rate of 3.1 x 10⁵ photons/second. This signal is easily detectable using a square-law post-detection integrator. With some signal integration we should also be able to detect the Planckian "noise" signal from an alien planet. The "noise" received from the planet is 6.8 x 10^-22 W. This will produce a photon detection rate of 1.1 x 10^-3 photons/second. In one hour (3600 seconds) we can detect 4 photons.

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It would appear that integration of this "noise" signal over several hours would yield a detectable signal, as long as we are not "blinded" by the direct starlight. Of course, bright emission lines in the continuum can give us a significant increase in photon detection rate.

The 1 GHz I.F. bandwidth is much smaller than the expected Doppler shifts of the Fraunhofer lines due to alien planetary motion. Hence, as long as we have sufficient SNR we can resolve in frequency this planet's motion.

Graph 9008-057 illustrates the basic concept for detecting the presence of an alien planet. Under normal circumstances, whatever the photon detection sensitivity of the receiver, it would be difficult to separate out the small number of photons from the alien planet from the much larger number of photons arriving per second from the alien star. However, there is a difference in the spectrum of the light reflected from the planet since it will have undergone a differential Doppler shift and perhaps been modified by an atmosphere, if present. The high spectral resolution of the optical heterodyne receiver allows us to not only detect the photons from the planet, but separate them in frequency from those emitted directly by the star.

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Graphs 9008-058 and 9008-059 illustrate the concept of improving our ability to "see" the alien planet in its star's background by steering the telescope off axis so that its main central lobe is pointed at the position of the would be planet, and the star is positioned to the side, preferably in one of the many nulls in the polar response.

In this way, perhaps more than 40 dB of extra discrimination can be obtained. With is 40+ dBs and the frequency discrimination provided by the Doppler shifted planetary light, it may be at last possible to detect an alien planetary body.

Graph 9008-058 shows an alien star at 10 light years, positioned in the 2nd null of its polar response. Although the Sun-type star has been drawn to scale in terms of its apparent size in relation to the telescope's angular beamwidth, for annotative reasons the planet has been shown somewhat nearer to its star than would be the case in reality. However, graph 9008-059 is for a star at 100 light years, and here its planetary orbital distance has been drawn to scale. The star is situated within the 6th response null.

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This project migh be done with the smaller Hubble Space Telescope after its mirror problem is corrected. Whether there will be enough sensitivity and dynamic range available to see a bright line from a planet in a dark line of a star remains to be seen.

For the first time we may be able to detect alien planetary systems, the atmospheres on the planets, and planetary magnetic fields (Zeeman splitting). There is a project to measure the perturbations in motions of nearby stars, and thereby indirectly infer the presence of large planetary bodies.

If the I.F. is passed through a radio frequency filter of bandwidth B_e (Hz), then passed through a second square-law detector and time-constant averaged for time (sec), the signal-to-noise ratio may be increased or the minimum detectable signal decreased. For spectral line and continuum observations, the minimum detectable signal intensity is given by:

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              hf
Imin = ----------------  W/m2
       eta.Ar(Be.Tau)½

where:

Note that hf/ k is the effective system temperature (T_eff) of the optical heterodyne receiver, where k is Boltzmann's constant (1.38 x 10^-23 J/K). See graph 9006-016 where T_eff is shown to be 44,000 K at 656 nm.

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The sensitivity is improved by using a larger I.F. bandwidth and a longer signal integration time, and that the signal-to-noise ratio will thus be proportional to the square root of the bandwidth and integration time.

Substituting the values given in parentheses for a 1 hour signal integration, the minimum detectable signal intensity is:

I_min = 3.2 x 10^-27 W/m²

We have all ready shown that a Jupiter-type planet's reflected starlight is of the order of 8.6 x 10^-24 W/m². This is a factor 34 dB greater than the planet's light. It thus seems reasonable that we could "just" detect this signal in about one second of signal integration. Notice that if B_e = Tau = 1, then the above equation may also be used to predict the CNR for an ETI laser signal. It gives the same result as the shot-noise limited relationship given in 9006-009.