Bayesian inference for radio observations

New telescopes like the Square Kilometre Array (SKA) will push into a new sensitivity regime and expose systematics, such as direction-dependent effects, that could previously be ignored. Current methods for handling such systematics rely on alternating best estimates of instrumental calibration and models of the underlying sky, which can lead to inadequate uncertainty estimates and biased results because any correlations between parameters are ignored. These deconvolution algorithms produce a single image that is assumed to be a true representation of the sky, when in fact it is just one realization of an infinite ensemble of images compatible with the noise in the data. In contrast, here we report a Bayesian formalism that simultaneously infers both systematics and science. Our technique, Bayesian Inference for Radio Observations (BIRO), determines all parameters directly from the raw data, bypassing image-making entirely, by sampling from the joint posterior probability distribution. This enables it to derive both correlations and accurate uncertainties, making use of the flexible software meqtrees to model the sky and telescope simultaneously. We demonstrate BIRO with two simulated sets of Westerbork Synthesis Radio Telescope data sets. In the first, we perform joint estimates of 103 scientific (flux densities of sources) and instrumental (pointing errors, beamwidth and noise) parameters. In the second example, we perform source separation with BIRO. Using the Bayesian evidence, we can accurately select between a single point source, two point sources and an extended Gaussian source, allowing for ‘super-resolution' on scales much smaller than the synthesized bea

Astronomy below the survey threshold in the SKA era

Astronomy at or below the 'survey threshold' has expanded significantly since the publication of the original 'Science with the Square Kilometer Array' in 1999 and its update in 2004. The techniques in this regime may be broadly (but far from exclusively) defined as 'confusion' or 'P(D)' analyses (analyses of one-point statistics), and 'stacking', accounting for the flux-density distribution of noise-limited images co-added at the positions of objects detected/isolated in a different waveband. Here we discuss the relevant issues, present some examples of recent analyses, and consider some of the consequences for the design and use of surveys with the SKA and its pathfinders

The optically selected 1.4-GHz quasar luminosity function below 1 mJy

We present the radio luminosity function (RLF) of optically selected quasars below 1 mJy, constructed by applying a Bayesian-fitting stacking technique to objects well below the nominal radio flux density limit. We test the technique using simulated data, confirming that we can reconstruct the RLF over three orders of magnitude below the typical 5σ detection threshold. We apply our method to 1.4-GHz flux densities from the Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) survey, extracted at the positions of optical quasars from the Sloan Digital Sky Survey over seven redshift bins up to z = 2.15, and measure the RLF down to two orders of magnitude below the FIRST detection threshold. In the lowest redshift bin (0.2 < z < 0.45), we find that our measured RLF agrees well with deeper data from the literature. The RLF for the radio-loud quasars flattens below log10[L1.4/WHz−1]≈25.5 and becomes steeper again below log10[L1.4/WHz−1]≈24.8⁠, where radio-quiet quasars start to emerge. The radio luminosity where radio-quiet quasars emerge coincides with the luminosity where star-forming galaxies are expected to start dominating the radio source counts. This implies that there could be a significant contribution from star formation in the host galaxies, but additional data are required to investigate this further. The higher redshift bins show a similar behaviour to the lowest z bin, implying that the same physical process may be responsible

High resolution AMI Large Array imaging of spinning dust sources: spatially correlated 8 micron emission and evidence of a stellar wind in L675

We present 25 arcsecond resolution radio images of five Lynds Dark Nebulae (L675, L944, L1103, L1111 & L1246) at 16 GHz made with the Arcminute Microkelvin Imager (AMI) Large Array. These objects were previously observed with the AMI Small Array to have an excess of emission at microwave frequencies relative to lower frequency radio data. In L675 we find a flat spectrum compact radio counterpart to the 850 micron emission seen with SCUBA and suggest that it is cm-wave emission from a previously unknown deeply embedded young protostar. In the case of L1246 the cm-wave emission is spatially correlated with 8 micron emission seen with Spitzer. Since the MIR emission is present only in Spitzer band 4 we suggest that it arises from a population of PAH molecules, which also give rise to the cm-wave emission through spinning dust emission.Comment: accepted MNRA

Microwave observations of spinning dust emission in NGC6946

We report new cm-wave measurements at five frequencies between 15 and 18GHz of the continuum emission from the reportedly anomalous "region 4" of the nearby galaxy NGC6946. We find that the emission in this frequency range is significantly in excess of that measured at 8.5GHz, but has a spectrum from 15-18GHz consistent with optically thin free-free emission from a compact HII region. In combination with previously published data we fit four emission models containing different continuum components using the Bayesian spectrum analysis package radiospec. These fits show that, in combination with data at other frequencies, a model with a spinning dust component is slightly preferred to those that possess better-established emission mechanisms.Comment: submitted MNRA

Bayesian modelling of clusters of galaxies from multi-frequency pointed Sunyaev--Zel'dovich observations

We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev--Zel'dovich effect. We use the recently developed MultiNest technique (Feroz, Hobson & Bridges, 2008) to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the presence of primary CMB signal, radio point sources (detected as well as an unresolved background) and receiver noise, show that our algorithm is able to analyse jointly the data from six frequency channels, sample the posterior space of the model and calculate the Bayesian evidence very efficiently on a single processor. We also illustrate the robustness of our detection process by applying it to a field with radio sources and primordial CMB but no cluster, and show that indeed no cluster is identified. The extension of our methodology to the detection and modelling of multiple clusters in multi-frequency SZ survey data will be described in a future work.Comment: 12 pages, 7 figures, submitted to MNRA

AMI observations of Lynds Dark Nebulae: further evidence for anomalous cm-wave emission

Observations at 14.2 to 17.9 GHz made with the AMI Small Array towards fourteen Lynds Dark Nebulae with a resolution of 2' are reported. These sources are selected from the SCUBA observations of Visser et al. (2001) as small angular diameter clouds well matched to the synthesized beam of the AMI Small Array. Comparison of the AMI observations with radio observations at lower frequencies with matched uv-plane coverage is made, in order to search for any anomalous excess emission which can be attributed to spinning dust. Possible emission from spinning dust is identified as a source within a 2' radius of the Scuba position of the Lynds dark nebula, exhibiting an excess with respect to lower frequency radio emission. We find five sources which show a possible spinning dust component in their spectra. These sources have rising spectral indices in the frequency range 14.2--17.9 GHz. Of these five one has already been reported, L1111, we report one new definite detection, L675, and three new probable detections (L944, L1103 and L1246). The relative certainty of these detections is assessed on the basis of three criteria: the extent of the emission, the coincidence of the emission with the Scuba position and the likelihood of alternative explanations for the excess. Extended microwave emission makes the likelihood of the anomalous emission arising as a consequence of a radio counterpart to a protostar or a proto-planetary disk unlikely. We use a 2' radius in order to be consistent with the IRAS identifications of dark nebulae (Parker 1988), and our third criterion is used in the case of L1103 where a high flux density at 850 microns relative to the FIR data suggests a more complicated emission spectrum.Comment: submitted MNRA