There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Table Of Integrals Series And Products

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

Many aspects of the large-scale structure of the Universe can be described successfully using cosmological models in which $27\ifmmode\pm\else\textpm\fi{}1%$ of the critical mass-energy density consists of cold dark matter (CDM). However, few---if any---of the predictions of CDM models have been successful on scales of $\ensuremath{\sim}10\text{ }\text{ }\mathrm{kpc}$ or less. This lack of success is usually explained by the difficulty of modeling baryonic physics (star formation, supernova and black-hole feedback, etc.). An intriguing alternative to CDM is that the dark matter is an extremely light ($m\ensuremath{\sim}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$) boson having a de Broglie wavelength $\ensuremath{\lambda}\ensuremath{\sim}1\text{ }\text{ }\mathrm{kpc}$, often called fuzzy dark matter (FDM). We describe the arguments from particle physics that motivate FDM, review previous work on its astrophysical signatures, and analyze several unexplored aspects of its behavior. In particular, (i) FDM halos or subhalos smaller than about $1{0}^{7}(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}3/2}$ ${M}_{\ensuremath{\bigodot}}$ do not form, and the abundance of halos smaller than a few times $1{0}^{10}(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}4/3}$ ${M}_{\ensuremath{\bigodot}}$ is substantially smaller in FDM than in CDM. (ii) FDM halos are comprised of a central core that is a stationary, minimum-energy solution of the Schr\"odinger-Poisson equation, sometimes called a ``soliton,'' surrounded by an envelope that resembles a CDM halo. The soliton can produce a distinct signature in the rotation curves of FDM-dominated systems. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating N-body systems, which proceeds as if the halo were composed of particles with mass $\ensuremath{\sim}\ensuremath{\rho}{\ensuremath{\lambda}}^{3}$ where $\ensuremath{\rho}$ is the halo density. (iv) Relaxation may have substantial effects on the stellar disk and bulge in the inner parts of disk galaxies, but has negligible effect on disk thickening or globular cluster disruption near the solar radius. (v) Relaxation can produce FDM disks but a FDM disk in the solar neighborhood must have a half-thickness of at least $\ensuremath{\sim}300(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}2/3}\text{ }\text{ }\mathrm{pc}$ and a midplane density less than $0.2(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{2/3}$ times the baryonic disk density. (vi) Solitonic FDM subhalos evaporate by tunneling through the tidal radius and this limits the minimum subhalo mass inside $\ensuremath{\sim}30\text{ }\text{ }\mathrm{kpc}$ of the Milky Way to a few times $1{0}^{8}(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}3/2}$ ${M}_{\ensuremath{\bigodot}}$. (vii) If the dark matter in the Fornax dwarf galaxy is composed of CDM, most of the globular clusters observed in that galaxy should have long ago spiraled to its center, and this problem is resolved if the dark matter is FDM. (viii) FDM delays galaxy formation relative to CDM but its galaxy-formation history is consistent with current observations of high-redshift galaxies and the late reionization observed by Planck. If the dark matter is composed of FDM, most observations favor a particle mass $\ensuremath{\gtrsim}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$ and the most significant observational consequences occur if the mass is in the range $1--10\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$. There is tension with observations of the Lyman-$\ensuremath{\alpha}$ forest, which favor $m\ensuremath{\gtrsim}10--20\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$ and we discuss whether more sophisticated models of reionization may resolve this tension.

Ultralight scalars as cosmological dark matter

Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

Search for New Physics with Atoms and Molecules

The cosmological relaxion can address the hierarchy problem, while its coherent oscillations can constitute dark matter in the present universe. We consider the possibility that the relaxion forms gravitationally bound objects that we denote as relaxion stars. The density of these stars would be higher than that of the local dark matter density, resulting in enhanced signals in table-top detectors, among others. Furthermore, we raise the possibility that these objects may be trapped by an external gravitational potential, such as that of the Earth or the Sun. This leads to formation of relaxion halos of even greater density. We discuss several interesting implications of relaxion halos, as well as detection strategies to probe them. Here, we show that current and near-future atomic physics experiments can probe physical models of relaxion dark matter in scenarios of bound relaxion halos around the Earth or Sun. The origin of Dark Matter (DM) in the Universe remains one of the main unresolved questions in Cosmology. The authors propose to probe a scenario where DM forms a compact object known as boson star, or a small DM halo bound to the Earth or sun, with a density higher than the local DM density making them detectable via atomic physics table top experiments.

/pdf/relaxion-stars-and-their-detection-via-atomic-physics-s6iabl91nm.pdf

Relaxion stars and their detection via atomic physics

We study the possibility that self-interacting bosonic dark matter forms star-like objects. We study both the case of attractive and repulsive self-interactions, and we focus particularly in the parameter phase space where self-interactions can solve well standing problems of the collisionless dark matter paradigm. We find the mass radius relations for these dark matter bosonic stars, their density profile as well as the maximum mass they can support.

/pdf/boson-stars-from-self-interacting-dark-matter-1uukhl101w.pdf

Boson stars from self-interacting dark matter

Axion stars, gravitationally bound states of low-energy axion particles, have a maximum mass allowed by gravitational stability. Weakly bound states obtaining this maximum mass have sufficiently large radii such that they are dilute, and as a result, they are well described by a leading-order expansion of the axion potential. Heavier states are susceptible to gravitational collapse. Inclusion of higher-order interactions, present in the full potential, can give qualitatively different results in the analysis of collapsing heavy states, as compared to the leading-order expansion. In this work, we find that collapsing axion stars are stabilized by repulsive interactions present in the full potential, providing evidence that such objects do not form black holes. In the last moments of collapse, the binding energy of the axion star grows rapidly, and we provide evidence that a large amount of its energy is lost through rapid emission of relativistic axions.

/pdf/collapse-of-axion-stars-ymnt1psabv.pdf

Collapse of axion stars

We investigate the decay of condensates of scalars in a field theory defined by V (&#x1d49c;) = m2f2[1 −cos(&#x1d49c;/f)], where m and f are the mass and decay constant of the scalar field. An example of such a theory is that of the axion, in which case the condensates are called axion stars. The axion field, &#x1d49c;, is self-adjoint. As a result, the axion number is not an absolutely conserved quantity. Therefore, axion stars are not stable and have finite lifetimes. Bound axions, localized on the volume of the star, have a coordinate uncertainty δx ∼ R ∼ 1/(maΔ), where R is the radius of the star and Δ = 1 − E0 2/ma 2. Here ma and E0 are the mass, and the ground state energy of the bound axion. Then the momentum distribution of axions has a width of δp ∼ maΔ. At strong binding, Δ = &#x1d4aa;(1), bound axions can easily transfer a sufficient amount of momentum to create and emit a free axion, leading to fast decay of the star with a transition rate Γ ∼ ma. However, when Δ ≪ 1, the momentum distribution is more restricted, and as show...

The Lifetime of Axion Stars

Analytic arguments and numerical simulations show that bosonic ultra-light dark matter (ULDM) would form cored density distributions (`solitons') at the center of galaxies. ULDM solitons offer a promising way to exclude or detect ULDM by looking for a distinctive feature in the central region of galactic rotation curves. Baryonic contributions to the gravitational potential pose an obstacle to such analyses, being (i) dynamically important in the inner galaxy and (ii) highly non-spherical in rotation-supported galaxies, resulting in non-spherical solitons. We present an algorithm for finding the ground state soliton solution in the presence of stationary non-spherical background baryonic mass distribution. We quantify the impact of baryons on the predicted ULDM soliton in the Milky Way and in low surface-brightness galaxies from the SPARC database.

Joshua Eby

Papers

Relaxion stars and their detection via atomic physics

Boson stars from self-interacting dark matter

Collapse of axion stars

The Lifetime of Axion Stars

Ultralight dark matter in disk galaxies