{"arxiv_id":"2108.04279","incoming":{"papers":5,"sentences":12,"groups":[{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":2,"quotes":[{"arxiv_id":"2404.04827","title":"Dark Matter-Induced Low-Mass Gap Black Hole Echoing LVK Observations","url":"/paper/2404.04827","section":"Lower Mass Black hole distribution","sentence":"The total stellar mass is related to $M_h$ through a relationship derived from the Bolshoi-Planck simulation [ref] .","intent_p":0.91,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2305.07569","title":"Probing the Origin of Primordial Black Holes through Novel Gravitational Wave Spectrum","url":"/paper/2305.07569","section":"Introduction","sentence":"The literature on probing the PBHs utilising the features in the gravitational waves is quite large [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"2311.02876","title":"Gravitational Wave Probe of Primordial Black Hole Origin via Superradiance","url":"/paper/2311.02876","section":"Introduction","sentence":"The literature on probing the PBHs utilizing the features in the gravitational waves is quite large [ref] [It is to be noted that in recent time there have been studies to probe PBH using methods other than GW as well [ref] .].","intent_p":0.97,"contests_p":null}]}],"unlabelled_sentences":8},"outgoing":{"papers":69,"sentences":80,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":6,"sentences":7,"quotes":[{"arxiv_id":"1603.00464","title":"Did LIGO detect dark matter?","url":"/paper/1603.00464","section":"ABH-PBH binary formation probability","sentence":"We assume both the ABH and the PBH velocities follow the same Maxwell-Boltzmann distribution with a cutoff at the virial velocity, $v_vir≡√(2GM_h/R_vir)$, of a halo with mass $M_h$ [ref] : P(v,v_m) = F_0[exp(-v^2/v_m^2) - exp(-v_vir^2/v_m^2) ] , v_m = v_vir/√(2)√(C/C_mg(C_m)/g(C)) , g(X) = ln(1+X)-1/1+X , where $v_m$ is the maximum circular velocity in an NFW halo which occurs at $R_m=C_m R_s$ with $C_m=2.1626$, and $F_0$ is the normalization factor so that $∫_0^v_vir dv 4πv^2 P(v,v_m)=1$.","intent_p":0.88,"contests_p":null},{"arxiv_id":"1608.06699","title":"Stochastic Gravitational-Wave Background due to Primordial Binary Black Hole Mergers","url":"/paper/1608.06699","section":"ABH-PBH binary formation probability","sentence":"We assume both the ABH and the PBH velocities follow the same Maxwell-Boltzmann distribution with a cutoff at the virial velocity, $v_vir≡√(2GM_h/R_vir)$, of a halo with mass $M_h$ [ref] : P(v,v_m) = F_0[exp(-v^2/v_m^2) - exp(-v_vir^2/v_m^2) ] , v_m = v_vir/√(2)√(C/C_mg(C_m)/g(C)) , g(X) = ln(1+X)-1/1+X , where $v_m$ is the maximum circular velocity in an NFW halo which occurs at $R_m=C_m R_s$ with $C_m=2.1626$, and $F_0$ is the normalization factor so that $∫_0^v_vir dv 4πv^2 P(v,v_m)=1$.","intent_p":0.88,"contests_p":null},{"arxiv_id":"astro-ph/9901122","title":"Large scale bias and the peak background split","url":"/paper/astro-ph/9901122","section":"Halo mass function","sentence":"For the halo mass distribution, we adopt the Sheth-Tormen halo mass function [ref] which is an extension to the Press-Schechter formalism [ref] that fits well with the results of numerical simulations.","intent_p":0.84,"contests_p":null},{"arxiv_id":"0710.2335","title":"A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries","url":"/paper/0710.2335","section":"GW radiation power spectrum","sentence":"Using the hybrid GW waveform for non-spinning binaries presented in Ref. [ref] , the GW energy spectrum can be written as [equation] in which $M_c=(m_1 m_2)^3/5/(m_1+m_2)^1/5$ is the chirp mass of the binary.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1104.5130","title":"Halo concentrations in the standard LCDM cosmology","url":"/paper/1104.5130","section":"PBH distribution","sentence":"In this study, we determine the concentration parameter using the fitting formula in Ref. [ref] and only consider $C(M_h, z)$ between $0.5$ and $1000$ in order to avoid a divergent result [ref] .","intent_p":0.84,"contests_p":null}]},{"kind":"data_used","label":"Uses data or values from","papers":9,"sentences":9,"quotes":[{"arxiv_id":"1903.02886","title":"Search for the isotropic stochastic background using data from Advanced LIGO's second observing run","url":"/paper/1903.02886","section":"Introduction","sentence":"Currently, Advanced LIGO and Advanced Virgo have placed an upper limit on the dimensionless GW energy density, $Ω_GW$, for isotropic background at approximately $𝒪(10^-9)$ [ref] at $25 Hz$.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1612.02029","title":"Upper Limits on the Stochastic Gravitational-Wave Background from Advanced LIGO's First Observing Run","url":"/paper/1612.02029","section":"Introduction","sentence":"Currently, Advanced LIGO and Advanced Virgo have placed an upper limit on the dimensionless GW energy density, $Ω_GW$, for isotropic background at approximately $𝒪(10^-9)$ [ref] at $25 Hz$.","intent_p":0.98,"contests_p":null},{"arxiv_id":"2101.12130","title":null,"url":"/paper/2101.12130","section":"Introduction","sentence":"Currently, Advanced LIGO and Advanced Virgo have placed an upper limit on the dimensionless GW energy density, $Ω_GW$, for isotropic background at approximately $𝒪(10^-9)$ [ref] at $25 Hz$.","intent_p":0.98,"contests_p":null},{"arxiv_id":"2111.03634","title":"The population of merging compact binaries inferred using gravitational waves through GWTC-3","url":"/paper/2111.03634","section":"Introduction","sentence":"Currently, Advanced LIGO and Advanced Virgo have placed an upper limit on the dimensionless GW energy density, $Ω_GW$, for isotropic background at approximately $𝒪(10^-9)$ [ref] at $25 Hz$.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1102.4340","title":"Mass models of the Milky Way","url":"/paper/1102.4340","section":"PBH-ABH binaries in the Milky Way","sentence":"For $ρ_MW$, we use the best-fitting mass model of the MW as well as its host halo provided in Ref. [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":21,"sentences":21,"quotes":[{"arxiv_id":"1602.03837","title":"Observation of Gravitational Waves from a Binary Black Hole Merger","url":"/paper/1602.03837","section":"Introduction","sentence":"The first detection of gravitational waves (GW) [ref] by the LIGO and Virgo collaborations [ref] in 2015 has opened a new window to study astrophysics and cosmology.","intent_p":0.99,"contests_p":null},{"arxiv_id":"0806.2794","title":"Astrophysical Sources of Stochastic Gravitational-Wave Background","url":"/paper/0806.2794","section":"Introduction","sentence":"and magnetars [ref] , and cosmological sources such as cosmic string [ref] , inflation [ref] and first-order phase transitions [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"0708.2279","title":"Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: implications for the early universe","url":"/paper/0708.2279","section":"Introduction","sentence":"and magnetars [ref] , and cosmological sources such as cosmic string [ref] , inflation [ref] and first-order phase transitions [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1009.1240","title":"Stochastic background of gravitational waves emitted by magnetars","url":"/paper/1009.1240","section":"Introduction","sentence":"and magnetars [ref] , and cosmological sources such as cosmic string [ref] , inflation [ref] and first-order phase transitions [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1410.6211","title":"Searching for stochastic gravitational waves using data from the two co-located LIGO Hanford detectors","url":"/paper/1410.6211","section":"Introduction","sentence":"and magnetars [ref] , and cosmological sources such as cosmic string [ref] , inflation [ref] and first-order phase transitions [ref] .","intent_p":0.95,"contests_p":null}]}],"unlabelled_sentences":43},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2108.04279"}}