Spectral ageing in the era of big data : Integrated versus resolved models

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society. © 2017 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.Continuous injection models of spectral ageing have long been used to determine the age of radio galaxies from their integrated spectrum; however, many questions about their reliability remain unanswered. With various large area surveys imminent (e.g. LOw Frequency ARray, MeerKAT, MurchisonWidefield Array) and planning for the next generation of radio interferometers are well underway (e.g. next generationVLA, SquareKilometreArray), investigations of radio galaxy physics are set to shift away from studies of individual sources to the population as a whole. Determining if and how integrated models of spectral ageing can be applied in the era of big data is therefore crucial. In this paper, I compare classical integrated models of spectral ageing to recent well-resolved studies that use modern analysis techniques on small spatial scales to determine their robustness and validity as a source selection method. I find that integrated models are unable to recover key parameters and, even when known a priori, provide a poor, frequency-dependent description of a source's spectrum. I show a disparity of up to a factor of 6 in age between the integrated and resolved methods but suggest, even with these inconsistencies, such models still provide a potential method of candidate selection in the search for remnant radio galaxies and in providing a cleaner selection of high redshift radio galaxies in z - α selected samples.Peer reviewe

Ergodic theory and Diophantine approximation for translation surfaces and linear forms

This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this record.We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to Schmidt (1960 Can. J. Math. 12 619–31, 1964 Trans. Am. Math. Soc. 110 493–518). The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattices from the Birkhoff genericity of almost all lattices in the whole space and similarly for the space of affine unimodular lattices.JSA partially supported by NSF grant DMS 1069153, and NSF grants DMS 1107452, 1107263, 1107367 ‘RNMS: GEometric structures And Representation varieties’ (the GEAR Network), and NSF CAREER grant DMS 1351853. JT acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 291147 and acknowledges support by the Heilbronn Institute for Mathematical Research

Spiraling of approximations and spherical averages of Siegel transforms

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We consider the question of how approximations satisfying Dirichlet’s theorem spiral around vectors in Rd. We give pointwise almost everywhere results (using only the Birkhoff ergodic theorem on the space of lattices). In addition, we show that for every unimodular lattice, on average, the directions of approximates spiral in a uniformly distributed fashion on the d − 1 dimensional unit sphere. For this second result, we adapt a very recent proof of Marklof and Strombergsson [19] to show a spherical average result for Siegel transforms on SLd+1(R)/ SLd+1(Z). Our techniques are elementary. Results like this date back to the work of Eskin-Margulis-Mozes [9] and KleinbockMargulis [14] and have wide-ranging applications. We also explicitly construct examples in which the directions are not uniformly distributedJ.S.A. partially supported by NSF grant DMS 1069153, and NSF grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). A.G. partially supported by the Royal Society. J.T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 291147

AGN Feedback in groups and clusters of galaxies

The lack of very cool gas at the cores of groups and clusters of galaxies, even where the cooling time is significantly shorter than the Hubble time, has been interpreted as evidence of sources that re-heat the intergalactic medium. Most studies of rich clusters adopt AGN feedback to be this source of heating. From ongoing GMRT projects involving clusters and groups, we demonstrate how low-frequency GMRT radio observations, together with Chandra/XMM-Newton X-ray data, present a unique insight into the nature of feedback, and of the energy transfer between the AGN and the IGM.Comment: 5 pages, 3 figures, To appear in ASP Conference Series, Vol. 407, The Low-Frequency Radio Universe, Eds: D. J. Saikia, D. A. Green, Y. Gupta and T. Venturi (Invited talk, conference held at NCRA-TIFR, Pune, INDIA, 8-12 December, 2008

Localised HI 21-cm absorption towards a double-lobed z=0.24 radio galaxy

We present the results of a mini-survey for associated HI 21-cm absorption at z < 0.42 with the Giant Metrewave Radio Telescope. Our targets are radio galaxies, selected on the basis that the 1216 Angstrom luminosities are below 10^23 W/Hz, above which there has never been a detection of 21-cm absorption. Of the three sources for which we obtained good data, two are unclassified active galactic nuclei (AGN) and one is type-2. Being a non-detection, the type-2 object is consistent with our previous result that 21-cm absorption in radio sources is not dictated by unified schemes of AGN. In the case of the detection, the absorption only occurs towards one of the two resolved radio lobes in PKS 1649-062. If the absorption is due to an another intervening galaxy, or cool HI gas in the intergalactic medium, covering only the south-west lobe, then, being at the same redshift, this is likely to be gravitationally bound to the optical object identified as PKS 1649-062. If the absorption is due to an inclined disk centred between the lobes, intervening the SW lobe while being located behind the NE lobe, by assuming that it covers the emission peak at 150 kpc from the nucleus, we estimate a dynamical mass of ~3 x 10^12 solar masses for the disk.Comment: 5 pages accepted by MNRAS Letter

Weighted distances in scale-free preferential attachment models

We study three preferential attachment models where the parameters are such that the asymptotic degree distribution has infinite variance. Every edge is equipped with a non-negative i.i.d. weight. We study the weighted distance between two vertices chosen uniformly at random, the typical weighted distance, and the number of edges on this path, the typical hopcount. We prove that there are precisely two universality classes of weight distributions, called the explosive and conservative class. In the explosive class, we show that the typical weighted distance converges in distribution to the sum of two i.i.d. finite random variables. In the conservative class, we prove that the typical weighted distance tends to infinity, and we give an explicit expression for the main growth term, as well as for the hopcount. Under a mild assumption on the weight distribution the fluctuations around the main term are tight.Comment: Revised version, results are unchanged. 30 pages, 1 figure. To appear in Random Structures and Algorithm