Radio Galaxies & Active Galactic Nuclei
The formation and evolution of galaxies is one of the major topics of research in the astrophysics community (Shapley & Curtis 1921). Many outstanding questions remain about the vast array of galaxy morphologies and processes that exist in the known universe. These include the way galaxies first formed in the universe, how galaxies evolve and interact with their local environment, and what the eventual fate of galaxies are.
An active galactic nucleus (AGN) occurs when the super-massive black hole (SMBH) at the centre of a galaxy accretion of matter. This creates two jets filled with relativistic particles that travel through the galaxy and out into intergalactic space, where they form radio lobes that can fill a volume more than 100 times the volume of a galaxy the size of the Milky Way. Hercules A in Figure 1 is a great example to visualize the scale of the objects. The energy of the radio lobes have a wide range of power, which the energy equivalent can be on the order of a billion supernova explosions.
Eventually, the energy and momentum from the outflows and radiation is re-deposited into the interstellar/intergalactic medium of a galaxy, a phenomenon known as AGN Feedback. Wise et al. (2007) examined AGN feedback in the Hydra cluster and found that AGN feedback can occur in several bursts creating several cavities over several hundreds of millions of years, which can be observed as depressions in the X-ray emission of intracluster gas. The energy deposited in the Hydra cluster gas is roughly equivalent to the energy produced by 10 billion supernova explosions (McNamara et al. 2005).
The radio lobes have high pressure, which results from the relativistic particles and magnetic fields, both of which contributes to the pressure (roughly) equally. As the radio lobes expand, they displace plasma with temperatures averaging around 50 million Kelvin that fills the intergalactic medium. The displacement of this hot plasma can prevent the gas from settling into a steady state in the gravitational potential of the cluster. If a steady state occurred, the gas density in the centre of the cluster would be high enough for the gas to cool and drop back onto the nearby galaxies. This is known as a cooling flow. Observations show very little evidence that such cooling flows are occurring, and it is widely suspected that AGN feedback is the cause of the lack of cooling flows (Balogh et al. 2001; Vernaleo & Reynolds 2006; Peterson & Fabian 2006;McNamara & Nulsen 2007). Therefore, it is also thought that AGN feedback is one of the mechanisms that can quench star formation within galaxies (Schawinski et al. 2007;Smethurst et al. 2016).
The SMBH Sagittarius A* that resides at the centre of our Milky Way galaxy, has giant gamma ray emitting structures that extend up to 55 degrees above and below the Galactic plane. These structures were discovered by Su et al. (2010), and are known as Fermi bubbles which are theorized to have formed during a short period of activity from Sagittarius A*, between 6 and 9 million years ago according to Bordoloi et al. (2017). The energy associated with the Fermi bubbles is approximately equivalent of 60 thousand supernova explosions. The event that created the Fermi bubbles can be considered at the lower end of the energy scale of lobes coming from a galactic nucleus, and the Hydra cluster at the higher end.
Magnetism in the Universe
Understanding the universe is impossible without understanding magnetism. However, the evolution, structure and origin of magnetic fields are all still open problems in astrophysics. Many astrophysical objects are known to be magnetized, from small compact objects such as neutron stars to the large scale structure of galaxies. Magnetic fields are important because in many cases the force exerted on charged particles are comparable to other forces such a gravity. Magnetism is involved in many particle accelerations processes and this helps tie things together.
One of the ways we know about magnetic fields in space because of radiation emitted in the form of synchrotron emission. A high energy (relativistic) electron moving perpendicular to a magnetic field feels a magnetic force and is accelerated around the field. The electrons gyrating around the magnetic fields present in AGN radio lobes radiate away energy in a process known as synchrotron emission. The spectrum of synchrotron radiation is a power law such that \(\rm S(\nu) \propto \nu^{\alpha}\), where the exponent \(\rm\alpha \) is denoted as the spectral index of the source. The spectral index is related to the amount of higher energy electrons relative to the amount of lower energy electrons in a radio source. Synchrotron emission produced can become linearly polarized due to the presence of magnetic fields. The degree of polarization from synchrotron emission in astrophysical sources is of significant interest because it measures the regularity of magnetic fields structure on a large scale (Stil et al. 2014). Allowing us to further understand the role of magnetism in AGN feedback on it's consequences on galactic evolution.
One of the ways that we can study magnetic fields is by observing the effect it has on radiation passing through it. If polarized radiation passes through a magnetized plasma, the direction of the polarization rotates, known as Faraday rotation. The overall strength of the effect is characterized by the rotation measure (RM), which is simply how much plane of polarization rotates. RM can be positive or negative, indicating whether a magnetic field is oriented toward or away from observer.
An example of the applications of faraday rotation to study extragalactic sources can be found in Gaensler et al. (2005). The authors used Faraday Rotation to determine the magnetic field structure of the Large Magellanic Cloud (LMC). The close proximity of the LMC provides a large enough area to take a large number of rotation measures corresponding to polarized radio sources behind the LMC. Fig. 1 shows a map of \(\rm H\alpha\) emission of the LMC with green circles indicating the rotation measures. The RM gradient from East to West indicates a large-scale magnetic field going around the galaxy (axis-symmetric spiral). Tracy Clarke (2004) did faraday mapping of the radio galaxy Hydra A (Figure 2), and found a contrast between the magnetic fields in the two lobes, with mainly positive RMs in the northern lobe (top) and negative RMs across the southern lobe. (bottom). This indicates organized structures of magnetic fields in the lobes on galactic scale (50 kpc or approx. 160,000 ly).
This brings us to concept of the rotation measure grid (RM Grid), which is to make a dense sampling of polarized extragalactic point sources across the whole sky. These sources are spread over a wide redshift range representing galaxies during various ages of the universe and this can help us understand the origin and evolution of cosmic magnetism in the universe. Currently, there are approximately 37,000 RMs currently known (Taylor et al. 2009), which is around 1 RM per square degree using data from the NRAO VLA Sky Survey (NVSS, Condon et al. 1998).
Rudnick & Owen (2014)
Rudnick & Owen (2014) did an ultra-deep field survey of a very small section of the sky, and found that linearly polarized radio emission from extragalactic sources is associated with very extended emission. All sources with detected polarized emission were resolved after convolving the images to a resolution of 10''. The authors predict fewer faint sources detected in new surveys of the SKA (diminishing returns). Moreover, Windhorst (2003) derived an angular size—flux density relation of \({\rm{\Psi }}(^{\prime\prime} )=2.0{\left({S}_{1.4}\right)}^{0.3}\). For a source with \(S_{1.4} \sim 20 \) mJy, the median angular size is \(\sim 5.0^{\prime\prime}\), half the size of what Rudnick & Owen (2014) reported. This immediatley raises the question of what subpopulation of radio sources is represented in the faint mJy polarized source population. Furthermore, which plasma is responsible for wavelength-dependent depolarization?
Stacking
Median Stacking or Stacking is a statistical technique that uses the median value of a large sample of sources that are too faint for individual analysis. Stacking is useful because it avoids detection thresholds of current surveys (use total intensity to select sources). We can investigate subsamples of sources selected by additional observable parameters (angular size, redshift, etc). Stacking also allows for investigation of a larger sample with a sensitivity that approaches that of Rudnick & Owen (2014) and future sky surverys. Without stacking, analyzing percent polarization becomes a significant problem for fainter sources because the typical median source will not formally be detected.
Polarization of Faint Radio Sources
In Johnston et al. (2021), our main focus was to further investigate the results of Rudnick & Owen (2014), but for a much larger sample size. We started with a list of unconfused sources from the unified catalog of radio sources compiled by Kimball & Ivezić (2008). We select samples using catelog data from the NRAO VLA Sky Survey (NVSS) and Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) surveys, both at 1.4 GHz. We use five samples with deconvolved mean angular size between \(1.8''\) and \(8.2''\) and two samples of symmetric double sources are analyzed across 7 flux bins with 1.4 GHz flux density of \(6.6 < S_{1.4} < 70\) mJy. For details in sample selection see Setion 2.3 of Johnston et al. (2021).
These samples represent most sources smaller than or near the median angular size of the mJy radio source population. Below are four \(5 \times 6\) mosaics example images of the appearence of our sources in each sample for flux bin 5 (\(13.0–18.2\) mJy). Each image is \(54''\) cutout of the sky on a uniform intensity scale. The first mosaic shown below consists of sources that are just resolved in FIRST. We do not show the compact sources because they would just appear as a point source.
The second mosaic consists of 30 randomly selected sources that are well-resolved in FIRST. You can see that the sources are now becoming more extended.
The third mosaic shows randomly selected double sources from flus bin 5, note that each image also shows that the lobes are randomly oriented. Each of the lobes are relativley symmetric with some variation.
The final mosaic contains sources that are rejected by our sample selection methods, many of the rejected sources are more extended than any in our samples. Smaller subsets of rejected sources consist of asymmetric doubles and compact sources whose FIRST flux density differs from the NVSS flux density, presumably because of variability.
Most sources in our samples have no host galaxy detected in the Sloan Digital Sky Survery (SDSS), sometimes there is a galaxy near the dection limit. There is a higher detection rate in the Wide-field Infrared Survey Explorer (WISE) all-sky survey, but are often lost in confusion noise in WISE images. If the host galaxies are giant elliptical or cD galaxies, then the redshift is likley \( z > 0.5\) for the samples, considering the sensitivity of SDSS and WISE all-sky (Jarret et al. 2017).
Fractional Polarization of Compact Radio Sources
We derive the median fractional polarization, \(\left(\Pi_{0,med}\right)\), of large samples of radio sources with 1.4 GHz flux density \(6.6 < S_{1.4} < 70\) mJy, by stacking 1.4 GHz NVSS polarized intensity as a function of angular size derived from the FIRST survey. The true median fractional polarization are derived from Monte-Carlo simulations, with errors derived from the variance in the Monte Carlo simulations. The Monte-Carlo analysis was conducted to correct for a strong noise bias. We find that the most compact sources (unresolved in FIRST) are only \(~1\%\) polarized, which accounts for \(\sim 85\%\) of ''single'' sources. Sources that are even slightly resolved in FIRST have a huge jump in polarization to \(\sim 2\%\), and the polarization of sources increases as a source become more extended to \(\sim 3\%\). The double sources are the most polarized \(\sim 3-4\%\). These findings are consistent across all flux bins.
By the method used for sample selection there should be no visible difference in total intensity, and there is not. We see very subtle measurable differences which may be due to systematics or different source counts. However, the stacked polarized intensity images display a significant increase in the median polarized signal with angular size of the source, most notably for the more compact sources. Note the much fainter stacked polarized signal for the sources that are unresolved in FIRST at \(5''\). We see more subtle increase for more extended sources also visible in the raw stacked images. All of the sources in each of the selected samples are distributed randomly throughout the survey. So, the differences in the raw median stacked images are not simply the result of an artifact of noise or other data bias, but instead are the result of real astrophysical differences. Therefore, the percent polarization is strongly related to their physical size, with the extended sources on a scale of \(\gtrsim 5''\) having a higher median percent polarization than more compact sources.
We find that the most compact sources (unresolved in FIRST) are only \(~1\%\) polarized, which accounts for \(\sim 85\%\) of ''single'' sources. Sources that are even slightly resolved in FIRST have a huge jump in polarization to \(\sim 2\%\), and the polarization of sources increases as a source become more extended to \(\sim 3 - 4\%\). The double sources are the most polarized \(\sim 3.5-4.5\%\). These findings are consistent across all flux bins.
We find that the median fractional polarization \(\Pi_{0,med}\) at 1.4 GHz is a strong function of source angular size \(\lesssim 5''\) and a weak function of angular size for larger sources up to \(\sim 8''\). We interpret our results as depolarization inside the AGN host galaxy and its circumgalactic medium. The curvature of the low-frequency radio spectrum is found to anticorrelate with \(\Pi_{0,med}\), a further sign that depolarization is related to the source.
Median Polarization and Physical Size
If polarization detections are associated with more extended sources they can’t be the same object just farther away. In standard \(\Lambda CDM\) cosmology, angular size distance of a source varies by only \(\sim 10\%\) in the red-shift range \(1 < z < 3\) (applicable to most radio bright AGN) and changes by less than 40% in the redshift range \(0.5 < z < 3.5\). We also see no evidence of faraday effects between us and source to depolarize. Therefore, these are likely not the same objects just farther away.
Deconvolved angular sizes were derived from the meanstacked VLASS quick-look images, and is then converted to our adopted \(\Lambda CDM\) cosmology. These correspond to projected physical sizes of 15, 24, 41, 54, and 68 kpcs, respectively, for an angular size distance of 1.72 Gpc at redshift \(z = 1\). We can see a dramatic increase on smaller scales and a more gradual increase on larger scales. An angular scale of \(5''\), such as the beam of FIRST, is a physical size of approximately 40 kpc. This is approximately the optical diameter of a large elliptical galaxy such as M87, which has an optical diameter of 42 kpc.
Physical Meaning
The most compact radio sources are depolarized by the intersellar medium (ISM) of the host galaxy (Cotton et al., 2003, Fanti et al. 2004). A break occurs around the size of \(\sim 40 \) kpc, the size of a large galaxy. The slower increase in polarization with size for larger radio sources suggests depolarization by the circumgalactic medium (CGM). The CGM is likely concentrated on the host galaxy but is dynamic, as it can be affected by AGN-driven multi-phase outflows and accretion. For example, the intergalactic medium (IGM) around quasars (Hennawi et al. 2015; Landoni et al, (2016)). Our interpretation can be tested with futures surveys.
Low Frequency Spectral Index from Median Stacking
We also stack low-frequency surveys in Stokes I. Those are:
- NVSS (1400 MHz).
- WENSS (325 MHz).
- TGSS (150 MHz) convolved to \(60''\) beam.
- VLSS (74 MHz).
Below is the results of spectral analysis for the single sources, it shows the spectral index and spectral curvature from stacking in relation to their median fractional polarization for the three brightest flux bins. We assume that \(S_{v} \sim v^{\alpha}\) for spectral index. We find a consistent and significant difference in the spectral index \((\alpha_{1400}^{325})\) between the compact and extended sources, and that the lower polarization is associated with a flatter low frequency spectrum. The Pearson correlation coefficient is found to be \(−0.76\). This is similar to the result in Webster et al. (2020) for galaxy scale jets in LOFAR, which showed a similar diagram for sources that they resolved. The authors probed similar size scales to what we investigate in Johnston et al. (2021) and found similar spectral indices.
Conclusions and Future Work
We find that the polarization of compact radio sources depends strongly on size for diameters less than 40 kpc, and depends weakly on size for larger sources. This is suggestive of a transition from depolarization by the interstellar medium (ISM) to depolarization by the low-density magentized circumgalactic medium (CGM). This is statistically significant information about the polarization of sources compared to the 14 samples of Rudnick & Owen (2014). We also predicts fewer compact sources contributing to the rotation measure grid in future surveys. So, we confirm that sources with structure on scales of \(10''\) are more strongly polarized than more compact sources. We also find that most radio sources are in unresolved in FIRST. Our findings can be tested in current Square Kilometer Array (SKA) Pathfinder surveys and SKA proper.
This still leaves us with interesting questions for future exploration, as we can only infer why the correlation exists, why the extended sources more polarized, and what it means physically. What does this mean for AGN feedback? What does this mean for the magnetic pressure of the lobes? New avenues of research include investigating the structure of these sources with high resolution images from VLASS, investigating the polarization with VLASS and POSSUM as well as Faraday rotation, and finally investigating polarization angle in relation to source structure. The latter is interesting because it shows magnetic field direction on plan of the sky, indicating the angle between the plane of polarization and a reference plane.
To learn more read the full paper with all of the details, or the preprint version on ArXiv.