Supplementary Material to:

An Introduction to Radio Astronomy

4^th edition Cambridge University Press 2019

Last updated 20/06/2019

Chapter 2: Emission and General Properties of Radio Waves

Radiation from sources with continuum spectra

Thermal black body: the Moon

The Moon at mm-wavelengths (103 GHz); images made with raster scans with the prototype dishes for ALMA - see https://www.nrao.edu/news/newsletters/enews/enews_1_5/images/alma8_lg.jpg.

Even though the Moon radiates effectively as a black body, whose emission is unpolarised, a radio image of the Moon will exhibit linear polarisation around the edge of disk with the E-vector pointing radially. For a discussion of the physical basis of the effect and results at 90 GHz see Bischoff (2003) http://oberon.roma1.infn.it/lezioni/Moon_polar.pdf

In the calculation in Sections 2.3 and 5.2 we refer to brightness temperatures averaged over the whole disk. However, as is apparent from the ALMA mm-wave images above, the brightness temperatures across the resolved disk are both time and position dependent (since the lunar phase varies and the properties of the sub-surface layers vary); they are also frequency dependent since longer wavelengths penetrate down into cooler layers.

Further reading

Gu-Ping Hu et al. (2016) “Microwave Brightness Temperature of the Moon: The Possibility of Setting a Calibration Source of the Lunar Surface” IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 13, 182

Xi-Zhen Zhang et al. (2012) “New radio observations of the Moon at L band” Research in Astron. Astrophys., 12 1297–1312 http://www.raa-journal.org/raa/index.php/raa/article/view/842

Free-free (bremsstrahlung): a planetary nebula

The continuum radio emission from ionised gas in HII regions (main text Section 13.10) is thermal free-free radiation which is unpolarised. Free-free emission throughout the Galaxy is strongly correlated with the optical emission from the hydrogen Balmer line H-alpha (e.g. Dickinson et al. 2003, MNRAS, 341,369).

Continuum emission from planetary nebulae (PNe) is also free-free emission. Above is a radio image of NGC7027 at 5 GHz made with a combination of VLA and eMERLIN data (image credit Abeer Almutairi and Albert Zijlstra). NGC 7027 is the brightest known planetary nebula at radio frequencies. The nebula was ejected by the central star at the end of its evolution, and is now ionized by the remaining core of the star whose temperature is >150,000 K. The ionized plasma shell has a density of ~10⁵ cm^-3 and has a physical temperature of ~10,000K. The ionized shell is surrounded by neutral and molecular envelope which does not show in the radio continuum.

Synchrotron: the Crab Nebula

Synchrotron radiation: a VLA radio image of the Crab Nebula. Most high-intensity radiation from cosmic sources is from energetic (relativistic) electrons spiralling around magnetic fields. Synchrotron emission can be distinguished from free-free emission, which can have a similar spectrum (see Supp Mat Chapter 14), by means of its linear polarisation and/or brightness temperatures exceeding 10⁵ K. In a radio polarisation image the direction of the electric vector (conventionally drawn) is perpendicular to the component of the magnetic field in the plane of the sky. (Image courtesy of NRAO/AUI and M. Bietenholz)

Anomalous Microwave Emission (AME): Perseus nebula (not in main text)

Image credit : Planck Collaboration – see references in Dickinson et al. (2017)

One recently recognised radiation phenomenon, not discussed in the text, is the so-called anomalous microwave emission (AME) which is thought to be due to spinning ultra-small dust grains. AME forms a component of diffuse radiation from the galaxy and is most prominent in the range 10-60 GHz. The broad-band radio spectrum of the Perseus molecular cloud shown above reveals a diagnostic “bump” peaking around 30 GHz. An update on the latest thinking and results on AME can be found in the review by Dickinson et al (2017).

Coherent Emission (not in main text)

In contrast to all the processes above, in which the electrons radiate independently, if the electrons move together (e.g. in bunches smaller than a radio wavelength) their radiation will be approximately in phase and the combined intensity from a compact region can be much higher than from an incoherent process in a region of similar size; the inferred brightness temperature from coherent emission can therefore greatly exceed the limits (~10¹² K) imposed on incoherent emission (see sections 2.8 and sections 16.3.10). The rapid intensity variations in the radiation from pulsars and Fast Radio Burst sources (FRBs) require such extreme brightness temperatures (10²⁵ to >10³⁵ K ) that they can only be understood in terms of coherent radiation processes (see e.g. Mitra 2017; Ghisellini and Locatelli 2018). Solar radio bursts, while not exhibiting such extreme brightness temperatures, also involve coherent mechanisms. For a review on the general topic of coherent emission the interested reader should consult Melrose (2017 and references therein).

References

Dickinson et al 2017 https://arxiv.org/pdf/1802.08073

Mitra, D 2017 https://arxiv.org/abs/1709.07179

Ghisellini G. and Locatelli, N., 2018 A&A, 613, A61

Melrose, D.B. https://arxiv.org/pdf/1707.02009