Detecting the auroral radio emission of an Earth-like planet
Neil Zimmerman
The aurora is the result of interaction between the solar wind and the Earth's
magnetosphere. In addition to the serene optical glow of recombining ionized
oxygen and nitrogen, intense kilometer wavelength radiation is emitted, peaking
at a frequency of about 250 kHz. This peak frequency is to first order
dependent on the classical electron gyroradius, which means that any planet
with a magnetic field around the same strength as Earth's would result in a
similar radio spectrum. Could a survey be carried out for the signature of this
phenomenon occurring on Earth-like exoplanets? In the future, for terrestrial
exoplanets already discovered, this emission could provide a means of measuring
their magnetic fields or even their rotational periods, depending on the
alignment of the magnetic field with respect to the rotation axis.
The following analysis assumes that the standard scattering formulae may be
extrapolated from the meter regime all the way up to km wavelengths. Although
such an assumption is probably invalid (based on personal correspondence with
several experts), it is a starting point that at least underscores the
importance of the role of scattering in considering this problem.
Due to scattering caused by inhomogeneities in the electron density of the
interstellar medium, a point source at a distance of 10 parsecs is spread out
over a solid angle of ~10-5 steradians at 250 kHz. After considering
the spectral power of Earth's emission, and the brightness of the galactic
synchrotron background, I find that the background exceeds the brightness of
the 10 parsec-distant Earth by a factor of ~104 instantaneously and
~106 on average.
Details of calculation:
We take a typical measurement of local electron turbulence by Phillips et al.: Cn2 = 3×10-5 m-20/3.1 The scattering measure over a path of uniform turbulence, as defined in Cordes et al., is
SM = Cn2·L
where L is distance.2 Conventionally, SM is expressed in units of kpc·m-20/3. The SM of a source at a distance of 10 pc from the Sun would therefore be 3×10-7 kpc·m-20/3.
Cordes et al. relate the angular broadening, Θ, to the SM using the following formula:
Θ = (ν/GHz)-11/5·0.071"·(SM/[kpc·m-20/3])3/5
Plugging in the above SM results in Θ = 730" = 0.20 degrees = 3.5×10-3 radians for ν = 250 kHz (the peak frequency of Earth's auroral emission). The corresponding solid angle is 2π·[1 - cos(Θ/2)] = 2π·[1 - cos(3.5×10-3/2)] = 9.8×10-6 steradians.
Zarka reports the typical flux density of auroral emission from Earth is 5×10-21 W/m2/Hz at a distance of 1 AU (= 1.5×1011 m), but the instantaneous value can reach up to 10-19 W/m2/Hz.3 This translates to a peak spectral power of 4π·(1.5×1011 m)2·10-19 W/m2/Hz = 2.8×104 W/Hz. At a distance of 10 pc, the flux density is therefore [2.8×104 W/Hz]/[4π·(10 pc·3×1016 m/pc)2] = 2.4×10-32 W/m2/Hz. Spread out over a solid angle of 9.8×10-6 ster, the maximum brightness of the 10 pc-distant Earth is therefore 2.5×10-27 W/m2/Hz/ster.
In the 1973 the lunar orbiting Radio Astronomer Explorer 2 satellite
mapped the galactic synchrotron background emission between 250 kHz and 10 MHz.
It is to date the only kilometer wavelength survey of the sky. One of the main
findings was that the λ-2 dependence of the free-free
absorption path length causes the background radiation to become increasingly
isotropic towards longer wavelengths. At 250 kHz, the brightness is uniformly
10-22 W/m2/Hz/ster.4
At 10-22 W/m2/Hz/ster, the cosmic background exceeds the instantaneous brightness of a hypothetical 10 pc-distant Earth by a factor of 4×104. The average brightness of Earth is 20 times less; in this case it is outshined by a factor of 8×105.
References
[1] J. A. Philips and A. W. Clegg. Electron density fluctuations in the local interstellar bubble. Nature, 360:137-139, Nov 1992.
[2] J. M. Cordes and T. J. Lazio. Interstellar scattering effects on the detection of narrow-band signals. Astrophysical Journal, 376:123-133, Jul 1991.
[3] P. Zarka. Auroral radio emissions at the outer planets: Observations and theories. Journal of Geophysical Research, 103:20159-20194, Sep 1998.
PDF
[4] J. C. Novaco and L. W. Brown. Nonthermal galactic emission below 10 Megahertz. Astrophysical Journal, 221:114-123, Apr 1978.
2006 Sep 10