Using spin to understand the formation of LIGO's black holes

With the detection of four candidate binary black hole (BBH) mergers by the Advanced LIGO detectors thus far, it is becoming possible to constrain the properties of the BBH merger population in order to better understand the formation of these systems. Black hole (BH) spin orientations are one of the cleanest discriminators of formation history, with BHs in dynamically formed binaries in dense stellar environments expected to have spins distributed isotropically, in contrast to isolated populations where stellar evolution is expected to induce BH spins preferentially aligned with the orbital angular momentum. In this work we propose a simple, model-agnostic approach to characterizing the spin properties of LIGO's BBH population. Using measurements of the effective spin of the binaries, which is LIGO's best constrained spin parameter, we introduce a simple parameter to quantify the fraction of the population that is isotropically distributed, regardless of the spin magnitude distribution of the population. Once the orientation characteristics of the population have been determined, we show how measurements of effective spin can be used to directly constrain the underlying BH spin magnitude distribution. Although we find that the majority of the current effective spin measurements are too small to be informative, with LIGO's four BBH candidates we find a slight preference for an underlying population with aligned spins over one with isotropic spins (with an odds ratio of 1.1). We argue that it will be possible to distinguish symmetric and anti-symmetric populations at high confidence with tens of additional detections, although mixed populations may take significantly more detections to disentangle. We also derive preliminary spin magnitude distributions for LIGO's black holes, under the assumption of aligned or isotropic populations

A rock or a hard place? Teaching assistants supporting physically disabled pupils in mainstream secondary school physical education: the tensions of professionalising the role

As a Physical Education (PE) teacher in both special and mainstream schools over a 15 year period, I witnessed the use of the teaching assistant (or Learning Support Assistant as they were known) for purposes which might be deemed to be related to a medical/welfare/care-giver role. In addition, previous small-scale research into the experiences of secondary-age disabled pupils in mainstream as opposed to special school PE showed that their experiences in an inclusive setting were restricted and that the presence of a TA did little to rectify this situation (Farr, 2005). Recently, the professionalisation of the role of the TA may have created a ‘teacher-in-waiting’ (Neill, 2002) and thus the nature of the TA’s role in PE, and the ability of the specialist teacher to work collaboratively with them is complex. This mixed methods study, inspired by critical ethnography (Thomas, 1993, 2003) incorporated five techniques of enquiry initially based on the work of Giangreco and Broer (2005). In keeping with a constructionist paradigm and integrating what I have termed a distorical theoretical perspective, I counted the interaction between people and the social structure in which they operated as important (Crotty, 1998, Broido, 2002) and drew on dominant participant voices (Lincoln and Guba, 2003). Adopting a theoretical perspective grounded in disability studies, I explored the perceptions of the role of the TA in inclusive PE through qualitative and quantitative data and presented a role definition which combines the humanistic with the instructional (or professional) after Reiter, 2000. I argued whether responsibility for the child’s learning should be devolved through the TA. Do we use the TA to make the teacher’s life easier or to support, collaboratively, the inclusion of the disabled pupil? The impact of this study on professional practice relates to the clarity of role definition for TAs generally and for TAs specifically who work in PE; the collaborative nature (or otherwise) of the TA/teacher relationship and the implications of these findings for the future training and deployment of teaching assistants in PE with a physically disabled pupil in a mainstream secondary school. This study found that TAs in PE share many traits or characteristics with those TAs working in other subject disciplines, or across subjects. However, in PE they were inclined to rate a willingness and ability to ‘join in’ and participate in practical activities alongside pupils above pedagogical knowledge. Training either reinforces an instructional or coaching role, or it focuses on the caring or medical aspects. The reality for the TA in this study however, is that they neither define themselves as one or the other but see themselves as drawing on their own skills, empathy and initiative to facilitate a positive, inclusive environment, with or without the input of the PE teacher. They deem themselves to be both care-givers where appropriate as well as supporters of autonomous participation (as opposed to learning). That the professionalization of their role moves them towards the pedagogical places the TA between a rock and a hard place

A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves

Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this 'picture', the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binary's spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binary's gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for BNS, NS-BH, and BBH signals.Comment: 11 pages, 5 figures, submitted to Phys. Rev.

Minors for alternating dimaps

We develop a theory of minors for alternating dimaps --- orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that they are related by the triality relation of Tutte. They do not commute in general, though do in many circumstances, and we characterise the situations where they do. The relationship with triality is reminiscent of similar relationships for binary functions, due to the author, so we characterise those alternating dimaps which correspond to binary functions. We give a characterisation of alternating dimaps of at most a given genus, using a finite set of excluded minors. We also use the minor operations to define simple Tutte invariants for alternating dimaps and characterise them. We establish a connection with the Tutte polynomial, and pose the problem of characterising universal Tutte-like invariants for alternating dimaps based on these minor operations.Comment: 51 pages, 7 figure