{"arxiv_id":"astro-ph/9901122","incoming":{"papers":304,"sentences":446,"groups":[{"kind":"contests","label":"Contests it","papers":3,"sentences":3,"quotes":[{"arxiv_id":"2412.03485","title":"Accelerating HI density predictions during the Epoch of Reionization using a GPR-based emulator on N-body simulations","url":"/paper/2412.03485","section":"Variation","sentence":"The conditional PS [ref] and ST [ref] mass functions can only be used to get the field at a resolution of $Δx ≥1$, and any finer resolution causes the values to turn out negative.","intent_p":0.31,"contests_p":0.71},{"arxiv_id":"1009.5085","title":"Nonlinear clustering in models with primordial non-Gaussianity: the halo model approach","url":"/paper/1009.5085","section":"Conclusions","sentence":"We found that the Gaussian mass function of [ref] was a poor description of the simulation data.","intent_p":0.67,"contests_p":0.84},{"arxiv_id":"2509.13690","title":"Conditioning halos on the tidal environment for fast and accurate HI power spectra during reionization","url":"/paper/2509.13690","section":"Introduction","sentence":"While semi-analytical prescriptions, such as the conditional Press-Schechter [ref] and Sheth-Tormen [ref] mass functions, can be used to generate the field, they are known to be approximations of the more complex physics of halo formation and are quite inaccurate compared to N-body simulations at the redshifts relevant to reionization [ref] .","intent_p":0.39,"contests_p":0.81}]},{"kind":"extends","label":"Builds on it","papers":1,"sentences":2,"quotes":[{"arxiv_id":"2505.07697","title":"Cosmology with Galaxy Clusters","url":"/paper/2505.07697","section":"Theoretical Background","sentence":"[ref] further refined the mass function by calibrating the function $f(σ)$ motivated by [ref] against N-body simulation suites with a box size spanning from $∼100 ()^3$ to $∼1000 ()^3$ populated with $512^3$ to $1024^3$ particles, resulting in a fitting function with an accuracy of $∼5 %$.","intent_p":0.8,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":134,"sentences":152,"quotes":[{"arxiv_id":"1110.2310","title":"Galaxy cluster number count data constraints on cosmological parameters","url":"/paper/1110.2310","section":"IIa. Theory","sentence":"Mass function.– To compute the mass function, we use the Press-Schechter (PS) approach [ref] , as modified by Sheth and Tormen (ST) [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2402.16849","title":"The dark timbre of gravitational waves","url":"/paper/2402.16849","section":"Total lens effect","sentence":"The total number of halos within that radius is N = ∫M_v ∫_0^z_s z_l ∫_0^ r_max r_l 2π(1+z_l)^2 r_l/H(z_l) n(z_l)/M_v , where $n(z_l)/M_v$ is the HMF which we compute using the Sheth-Tormen approximation [ref] with the CDM power spectrum [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"2604.19726","title":"Breaking the UV Luminosity Function Degeneracy:Self-Interacting Dark Matter Constraints from Reionization Topology","url":"/paper/2604.19726","section":"Model and Data","sentence":"The UVLF is computed by convolving the Sheth–Tormen halo mass function [ref] with the UV magnitude mapping using the Kennicutt relation [ref] and Gaussian scatter $$ [ref] (Supplemental Material B).","intent_p":0.99,"contests_p":null},{"arxiv_id":"2103.01964","title":"Multi-tracer intensity mapping: Cross-correlations, Line noise & Decorrelation","url":"/paper/2103.01964","section":"Introduction","sentence":"In all the halo model calculations, we make use of the Sheth & Tormen halo mass distribution function and linear bias [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2601.13312","title":"Multi-Tracer Cross-Correlations of the Unresolved $\\gamma$-Ray Sky","url":"/paper/2601.13312","section":"Physical model for the galaxy--ray correlation","sentence":"Their 3D power spectrum of cross-correlation with galaxies can be thus written as [ref] : P_g_r,γ_S^1h(k,z) = ∫_L_γ^min^L_γ^max L_γ Φ_S(L_γ,z)/⟨f_S ⟩ F/E (L_γ,z) ⟨N_g_r(L_γ) ⟩/n̅_g_rṽ_g(k|M(L_γ)) , P_g_r,γ_S^2h(k,z) = [∫_L_γ^min^L_γ^max L_γ b_h(M(L_γ)) Φ_S(L_γ,z)/⟨f_S ⟩ F/E (L_γ,z)] × [∫_M_min^M_max M dn/dM b_h(M) ⟨N_g_r ⟩/n̅_g_r ṽ_g(k|M) ] P^lin(k) , where $b_h$ is the halo bias [ref] , $F$ is the BLZ -ray flux, and $⟨f_S ⟩=∫L_γ Φ_S F/E$.","intent_p":0.81,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":11,"sentences":12,"quotes":[{"arxiv_id":"1103.0694","title":"Coupled Quintessence and the Halo Mass Function","url":"/paper/1103.0694","section":"Mass functions","sentence":"We use $A=0.322$, $a=0.707$ and $p=0.3$ [ref] , for all the quintessence models considered.","intent_p":0.89,"contests_p":null},{"arxiv_id":"1109.4934","title":"Cross-correlating the Thermal Sunyaev-Zel'dovich Effect and the Distribution of Galaxy Clusters","url":"/paper/1109.4934","section":"The SZ Effect and the SZ Power Spectrum","sentence":"Below in our calculation, we would use the halo mass function from [ref] , specifically their Eq. (B3), and the halo bias from [ref] .","intent_p":0.89,"contests_p":null},{"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":"Next we calculate the relative probability distribution of LMBHs as a function of logarithmic halo mass , [equation] Here the halo mass distribution $n/log[M_h]$ is taken as the Sheth-Tormen distribution at $z=0$ [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"1112.4517","title":"Cosmological Radio Emission induced by WIMP Dark Matter","url":"/paper/1112.4517","section":"Constraints on WIMP parameter space","sentence":"In both models, we adopt the halo mass function from Ref. [ref] , the concentration of halos from Ref. 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following, we assume a parametrisation of the halo mass function as given by the Sheth-Tormen formula [ref] : [equation] where $ρ_m$ is the mean matter density, $δ_c$ is the linearly extrapolated spherical collapse threshold which we compute using the formula by [ref] , and [equation] is the variance of the linear density field smoothed on a spherical volume of radius $R$ enclosing the mass $M=4/3πρ_m R^3$ with [equation] and $P(k,z)$ being the linear matter power spectrum at a given redshift $z$, which we compute assuming the linear transfer function from [ref] .","citing":"2103.03283","section":"Halo Sparsity"},"citing":[{"self":false,"year":2021,"title":"Cosmological Constraints from Galaxy Cluster Sparsity, Cluster Gas Mass Fraction and Baryon Acoustic Oscillations Data","arxiv_id":"2103.03283"}],"verified":true,"paraphrase":"Assumed a parametrisation of the halo mass function as given by this paper's Sheth-Tormen formula."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2021,"title":"A general framework to test gravity using galaxy clusters V: A self-consistent pipeline for unbiased constraints of $f(R)$ gravity","arxiv_id":"2107.14224"}],"verified":true,"paraphrase":"Adopted this paper's prescription of the halo mass function for its constraint pipeline."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2023,"title":"Reconstruction of Cosmological Initial Density Field with Observations from the Epoch of Reionization","arxiv_id":"2311.14940"}],"verified":true,"paraphrase":"Used the Press-Schechter halo mass function to calculate the collapse fraction and its derivative, normalizing them with this paper's Sheth-Tormen correction."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2019,"title":"The Void Size Function in Dynamical Dark Energy Cosmologies","arxiv_id":"1906.00409"}],"verified":true,"paraphrase":"Computed the effective bias of the FoF halos using this paper's Sheth 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.","citing":"2112.06943","section":"The 21-cm hydrogen line"},"citing":[{"self":false,"year":2021,"title":"Probing ultra-light axions with the 21-cm Signal during Cosmic Dawn","arxiv_id":"2112.06943"}],"verified":true,"paraphrase":"Evolved initial conditions with the Zel'dovich approximation to match the mean collapse fraction for this paper's conditional Sheth-Tormen halo mass function."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2022,"title":"Galaxy luminosity functions at redshifts 0.6 to 1.2 in the Chandra Deep Field South","arxiv_id":"2203.03563"}],"verified":true,"paraphrase":"Used this paper's bias formalism in a web tool to obtain fractional errors on its normalisation."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2023,"title":"Warm dark matter constraints from the JWST","arxiv_id":"2303.14239"}],"verified":true,"paraphrase":"Used this paper's Sheth-Tormen form for the first-crossing distribution."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2026,"title":"Probing power spectrum enhancement at small scales with the SKA","arxiv_id":"2602.24117"}],"verified":true,"paraphrase":"Calculated the halo mass function from this paper's Sheth and Tormen formalism."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2021,"title":"Explaining the LIGO black hole mass function with field binaries: Revisiting Stellar Evolution at low Metallicity or Invoking Growth via gas accretion?","arxiv_id":"2105.08746"}],"verified":true,"paraphrase":"Constructed a halo mass function following this paper."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2021,"title":"Ultra-light axions and the kinetic Sunyaev-Zel'dovich Effect","arxiv_id":"2109.13268"}],"verified":true,"paraphrase":"Obtained the halo mass function and bias using the semi-analytic excursion set formalism of this paper."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2020,"title":"Joint constraints on thermal relic dark matter from strong gravitational lensing, the Lyman-$\\alpha$ forest, and Milky Way satellites","arxiv_id":"2010.13802"}],"verified":true,"paraphrase":"Assumed this paper's formulation to describe the CDM field halo mass function."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2011,"title":"Galaxy cluster number count data constraints on cosmological parameters","arxiv_id":"1110.2310"}],"verified":true,"paraphrase":"Used the Press-Schechter approach as modified by this paper's Sheth and Tormen prescription to compute the mass function."},{"p":0.91,"quote":{"text":"In what follows, I use the [ref] dark matter halo mass function $dn(M,z)/dM$ — the number of dark matter halos of mass $M$ per unit mass per unit comoving volume at redshift $z$ — to compute the comoving number density of halos above a given halo mass threshold, [equation] and the comoving mass density in halos more massive than $$, [equation] These translate directly to upper limits on the statistics of galaxies through the straightforward assumption that the largest stellar content a halo can have given its cosmic allotment of baryons is $=$.","citing":"2208.01611","section":"Assumptions"},"citing":[{"self":false,"year":2022,"title":"Stress Testing $\\Lambda$CDM with High-redshift Galaxy Candidates","arxiv_id":"2208.01611"}],"verified":true,"paraphrase":"Used this paper's dark matter halo mass function to compute the comoving number density of halos above a mass threshold and the comoving mass density in halos above a mass."},{"p":0.99,"quote":null,"citing":[{"self":false,"year":2021,"title":"Multi-tracer intensity mapping: Cross-correlations, Line noise & Decorrelation","arxiv_id":"2103.01964"}],"verified":true,"paraphrase":"Made use of this paper's Sheth and Tormen halo mass distribution function and linear bias in all its halo model calculations."},{"p":0.98,"quote":{"text":"Following [ref] , we can express the LF as [equation] where $d n / d M_h$ is the halo mass function [ref] and the observable $𝒪$ is taken to be either the 1500Å UV continuum magnitude, $M_UV$, or the H$α$ luminosity, $L_Hα$, in this paper.","citing":"2410.21409","section":"Luminosity function"},"citing":[{"self":false,"year":2024,"title":"Constraining bursty star formation histories with galaxy UV and H$\\alpha$ luminosity functions and clustering","arxiv_id":"2410.21409"}],"verified":true,"paraphrase":"Expressed the luminosity function using this paper's halo mass function."},{"p":0.97,"quote":null,"citing":[{"self":false,"year":2011,"title":"Coupled Quintessence and the Halo Mass Function","arxiv_id":"1103.0694"}],"verified":true,"paraphrase":"Presented results for three analytic forms of the CDM halo mass function, including this paper's Sheth-Tormen form."}],"papers_all":259,"self_papers":0,"self_entries":[]},{"kind":"data_used","label":"Uses its data or values","papers":1,"entries":[{"p":0.84,"quote":null,"citing":[{"self":false,"year":2023,"title":"Subaru High-$z$ 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