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

Overview of AlzPathway 3 overlaid with sphingolipid-related canonical pathway annotations.

<p>AlzPathway 3 consists of 1,384 molecules, 1,127 reactions, and 138 phenotypes. Purple lines are newly added relations involving sphingolipids.</p

Binary-relation notation AlzPathway 3 and the key molecules.

<p>(a) The top 50 high-centrality relations as the highlighted primary pathway of AlzPathway. Circles are nodes in AlzPathway 3. Lines are edges between nodes. As represented, red lines have high edge betweeness centrality and blue lines have low. (b) The top 10 high-betweenness centrality nodes and their centrality.</p

Knockdown of VASH2 inhibited the forskolin-induced fusion of BeWo cells.

<p>A: BeWo cells with or without siRNA treatment were stimulated with FK, and cell fusion was observed as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104728#s2" target="_blank">Materials and Methods</a>. Bar = 100 µm. Arrows indicate fused cells with multiple nuclei. B: Expression of human VASH2 was quantified (N = 3). *P<0.01, NS; not significant. C: Cell fusion was quantified as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104728#s2" target="_blank">Materials and Methods</a> (N = 2, 10 fields each). *P<0.01. D–F: Expression of Gcm-1, Syn-2, and Syn-1 in BeWo cells with each treatment (N = 3) was determined by qRT-PCR. NS; not significant.</p

Localization of VASH1 and VASH2 in human placenta.

<p>Immunohistochemical analysis for the localization VASH1 (A) and VASH2 (B) in the human placenta was performed. Arrowheads indicate VASH1 vessels (A). Bar = 100 µm.</p

Serum levels of VEGF, sVEGFR1, and PlGF in WT, <i>Vash1^(−/−)</i>, and <i>Vash2^(−/−)</i> dams.

<p>A: Serum levels of VEGF-A at 12.5, 16.5, and 18.5 dpc. The respective numbers of WT dams at these time points were 6, 3 and 4; of <i>Vash1^(−/−)</i> ones, 7, 10 and 22; and of <i>Vash2^(−/−)</i> dams, 4, 4 and 8. ^#P<0.05, *P<0.01. B: Serum levels of sVEGFR1 at 12.5, 16.5, and 18.5 dpc. The respective numbers of WT dams at these time points were 5, 4, and 5; of <i>Vash1^(−/−)</i> ones, 6, 8 and 17; and of <i>Vash2^(−/−)</i> dams, 4, 4, and 5. C: Serum levels of PlGF at 12.5, 16.5, and 18.5 dpc. Respective numbers of WT dams at these stages were 4, 2 and 2; of <i>Vash1^(−/−)</i> ones, 5, 5, and 5; and of <i>Vash2^(−/−)</i> dams, 3, 3, and 4.</p

Course of pregnancy in WT, <i>Vash1^(−/−)</i> and <i>Vash2^(−/−)</i> mice.

<p>A: Comparison of maternal weights of WT (N = 30), <i>Vash1^(−/−)</i> (N = 45), and <i>Vash2^(−/−)</i> (N = 20) mice. *P<0.01. B: Comparison of number of neonates per WT (N = 32), <i>Vash1^(−/−)</i> (N = 45), and <i>Vash2^(−/−)</i> (N = 20) dams. C: Blood pressure of WT (N = 16), <i>Vash1^(−/−)</i> (N = 15), and <i>Vash2^(−/−)</i> (N = 7) dams measured at 0, 4.5, 8.5,10.5, 12.5, 14.5, 16.5, and 18.5 dpc. #P<0.05. D: Wet weight of WT (N = 37), <i>Vash1^(−/−)</i> (N = 37), and <i>Vash2^(−/−)</i> (N = 19) placentas. *P<0.01.</p

Vascularization of placenta in WT, <i>Vash1^(−/−)</i>, and <i>Vash2^(−/−)</i> mice.

<p>Upper panels show vascular morphogenesis. The triple staining with tomato lectin (green), anti-CD31 (blue), and anti-type IV collagen (red) was performed as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104728#s2" target="_blank">Materials and Methods</a>. Tomato lectin identified the maternal blood vessels; and CD31-positive structures, the fetal blood vessels. The presence of type IV collagen indicated the basement membrane. Bar = 50 µm. Lower graph on the left show the fetal vascular area, and that on the right shows the maternal vascular area determined for WT (N = 5), <i>Vash1^(−/−)</i> (N = 3), and <i>Vash2^(−/−)</i> (N = 3) placentas. Ten 400× fields per placenta were used for quantification. *P<0.01.</p

Hierarchy of terminology in PEO.

<p>(A) Hierarchy of terminological super classes about objects. (B) Hierarchy of terminological super classes about processes. (C) Examples of PE-specific terminology. Terms in blue box are gynecology-specific such as “Ultrasonography”. Terms in green box are PE-specific such as “Pregnancy test urine” and “Finding of brain”.</p

The overexpression of VASH2 augmented the fusion of BeWo cells.

<p>A: BeWo cells were infected with adenovirus vectors. Expression of human VASH2 was quantified by qRT-PCR (N = 3). B: Cell fusion was observed as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104728#s2" target="_blank">Materials and Methods</a>. Bar = 100 µm. Arrowheads indicate a fused cell with multiple nuclei. Cell fusion was quantified as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104728#s2" target="_blank">Materials and Methods</a> (N = 3, 5 fields each). #</p