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 map of the area around Soma General Hospital.

<p>Soma City is located 44 km north of Fukushima Daiichi Nuclear Power Plant. Soma General Hospital and a clinic in Minami-Soma City are the only two places that employ a full-time ENT doctor. In other hospitals, part-time doctors see patients in outpatient settings once or twice a week. Approximately one-third of the southern side of Minami-Soma City is part of the evacuation area. People in the other two-thirds of the city are suffering from a great deal of anxiety and stress. Railways were damaged by the disaster. The railway north of Soma City was washed away by the tsunami, and train service along the railway south of Minami-Soma City has been suspended for three years because of the accident at the nuclear power plant.</p

Diseases complicated with vertigo, MD, and ALHL.

<p>Depression and depressive type were the two diseases with the largest number of patients (27 cases). Other frequently seen diseases were anxiety disorder, neurosis, somatoform disorder, anxiety neurosis, adjustment disorder, and post-traumatic stress disorder (PTSD).</p

Investigation of the new ENT patients from April to the following March by living area.

<p>(a) For all new patients, the number from Soma City decreased, but that from Minami-Soma City and other evacuation areas increased. (b) Those with vertigo, MD, and ALHL increased in each area. In Soma City and Shinchi Town, the number peaked in the second year and showed a slight decrease in the third year. On the other hand, the number of new patients in Minami-Soma City and the evacuation areas remained about the same.</p

Number of outpatients from all the departments at Soma General Hospital, and the number of new patients and revisiting patients of the ENT department.

<p>Those patients who had not visited us for more than 6 months were regarded as new patients. After the disaster, the number of new patients increased 7.7% in the first year, 4.8% in the second year, but decreased 0.8% in the third year. Thus, the differences were small.</p

Additional file 1 of Association between frequency of breakfast intake before and during pregnancy and infant birth weight: the Tohoku Medical Megabank Project Birth and Three-Generation Cohort Study

Additional file 1:Supplementary Table 1. Nutrient and food group consumption by breakfast intake frequency. Supplementary Table 2. Multivariate linear regression analysis for the association between frequency of breakfast intake during pregnancy and infant birth weight (n=18,307). Supplementary Table 3. Multivariate linear regression analysis of the association between breakfast intake frequency and infant birth weight

Additional file 2 of Dietary patterns before and during pregnancy and small for gestational age in Japan: a prospective birth cohort study

Additional file 2

Additional file 1 of Dietary patterns before and during pregnancy and small for gestational age in Japan: a prospective birth cohort study

Additional file 1: Supplementary Table 1. Factor loadings and explained variation of dietary patterns identified using RRR, PLS and PCA from early to mid pregnancy. Supplementary Table 2. Associations of dietary patterns with birth weight SD score and SGA from early to mid pregnancy. Supplementary Table 3. Characteristics of participants stratified by the adoption to the RRR patterns. Supplementary Table 4. Characteristics of participants stratified by the adoption to the PLS patterns. Supplementary Table 5. Characteristics of participants stratified by the adoption to the PCA1 patterns. Supplementary Table 6. Characteristics of participants stratified by the adoption to the PCA2 patterns. Supplementary Table 7. Factor loadings and explained variation of dietary patterns identified using RRR, PLS and PCA with the excluded subjects who had available data on dietary intake and incidence of SGA (n = 18,667). Supplementary Table 8. Associations of dietary patterns with birth weight SD score and SGA with the excluded subjects who had available data on dietary intake and incidence of SGA (n = 18,667). Supplementary Table 9. The characteristics of the 17,728 mothers who were analyzed and the 4765 mothers who were excluded from the analysis. Supplementary Table 10. Factor loadings and explained variation of dietary patterns identified using RRR, PLS and PCA in subjects without gestational diabetes mellitus (n = 17,325). Supplementary Table 11. Associations of dietary patterns with birth weight SD score and SGA in subjects without gestational diabetes mellitus (n = 17,325)

Additional file 1 of Association of physiological factors with grip and leg extension strength: tohoku medical megabank community-based cohort study

Supplementary Material 1: Supplementary Table 1. Grip strength and physiological data by age groups. Supplementary Table 2. Leg extension strength and physiological data by age groups