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ABSTRACT While the first “seeds” of supermassive black holes (BH) can range from $$\sim 10^2-10^6 \rm ~{\rm M}_{\odot }$$, the lowest mass seeds ($$\lesssim 10^3~\rm {\rm M}_{\odot }$$) are inaccessible to most cosmological simulations due to resolution limitations. We present our new BRAHMA simulations that use a novel flexible seeding approach to predict the $$z\ge 7$$ BH populations for low-mass seeds. We ran two types of boxes that model $$\sim 10^3~\rm {\rm M}_{\odot }$$ seeds using two distinct but mutually consistent seeding prescriptions at different simulation resolutions. First, we have the highest resolution $$[9~\mathrm{Mpc}]^3$$ (BRAHMA-9-D3) boxes that directly resolve $$\sim 10^3~\rm {\rm M}_{\odot }$$ seeds and place them within haloes with dense, metal-poor gas. Second, we have lower resolution, larger volume $$[18~\mathrm{Mpc}]^3$$ (BRAHMA-18-E4), and $$\sim [36~\mathrm{Mpc}]^3$$ (BRAHMA-36-E5) boxes that seed their smallest resolvable $$\sim 10^4~\&~10^5~\mathrm{{\rm M}_{\odot }}$$ BH descendants using new stochastic seeding prescriptions calibrated using BRAHMA-9-D3. The three boxes together probe key BH observables between $$\sim 10^3\,\mathrm{ and}\,10^7~\rm {\rm M}_{\odot }$$. The active galactic nuclei (AGN) luminosity function variations are small (factors of $$\sim 2-3$$) at the anticipated detection limits of potential future X-ray facilities ($$\sim 10^{43}~ \mathrm{ergs~s^{-1}}$$ at $$z\sim 7$$). Our simulations predict BHs $$\sim 10-100$$ times heavier than the local $$M_*$$ versus $$M_{\mathrm{ bh}}$$ relations, consistent with several JWST-detected AGN. For different seed models, our simulations merge binaries at $$\sim 1-15~\mathrm{kpc}$$, with rates of $$\sim 200-2000$$ yr−1 for $$\gtrsim 10^3~\rm {\rm M}_{\odot }$$ BHs, $$\sim 6-60$$ yr−1 for $$\gtrsim 10^4~\rm {\rm M}_{\odot }$$ BHs, and up to $$\sim 10$$ yr−1 amongst $$\gtrsim 10^5~\rm {\rm M}_{\odot }$$ BHs. These results suggest that Laser Interferometer Space Antenna mission has promising prospects for constraining seed models.
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A diffusion approach to Stein’s method on Riemannian manifolds
We detail an approach to developing Stein’s method for bounding integral metrics on probability measures defined on a Riemannian manifold M. Our approach exploits the relationship between the generator of a diffusion on M having a target invariant measure and its characterising Stein operator. We consider a pair of such diffusions with different starting points, and through analysis of the distance process between the pair, derive Stein factors, which bound the solution to the Stein equation and its derivatives. The Stein factors contain curvature-dependent terms and reduce to those currently available for Rm, and moreover imply that the bounds for Rm remain valid when M is a flat manifold.
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- Award ID(s):
- 2015236
- PAR ID:
- 10545845
- Publisher / Repository:
- project euclid
- Date Published:
- Journal Name:
- Bernoulli
- Volume:
- 30
- Issue:
- 2
- ISSN:
- 1350-7265
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3150/23-BEJ1625
