Scalar Field Dark Matter Model Research Articles

Could galactic magnetic fields be generated by charged ultra-light boson dark matter?

We study the possibility that large-scale magnetic fields observed in galaxies could be produced by a dark matter halo made of charged ultra-light bosons, that arise as excitations of a complex scalar field described by the Klein–Gordon equation with local U(1) symmetry which introduces electromagnetic fields that minimally couple to the complex scalar current and act as dark virtual photons. These virtual photons have an unknown coupling constant with real virtual photons. We constrain the final interaction using the observed magnetic fields in galaxies. We use classical solutions of the Klein–Gordon–Maxwell system to describe the density profile of dark matter and magnetic fields in galaxies. We consider two cases assuming spherical and dipolar spatial symmetries. For the LSB spherical galaxy F563-V2, we test the sensitivity of the predicted rotation curves in the charged Scalar Field Dark Matter (cSFDM) model to variations of the electromagnetic coupling and using the Fisher matrix error estimator, we set a constraint over that coupling by requiring that theoretical rotation curves lay inside the 1sigma confidence region of observational data. We find that cSFDM haloes generate magnetic fields of the order of mu G and reproduce the observed rotation curves of F563-V2 if the ultra-light boson has a charge sim <10^{-13}e for the monopole-like density profile and sim <10^{-14}e for the dipole-like one.

Dark matter from backreaction? Collapse models on galaxy cluster scales

In inhomogeneous cosmology, restricting attention to an irrotational dust matter model, backreaction arises in terms of the deviation of the averaged spatial scalar curvature from a constant-curvature model on some averaging domain , , and the kinematical backreaction . These backreaction variables can be modeled as an effective scalar field, called the ‘morphon field’. The general cosmological equations still need a closure condition to be solved. A simple example is the class of scaling solutions where and are assumed to follow a power law of the volume scale factor . But while they can describe models of quintessence, these and other models still assume the existence of dark matter in addition to the known sources. Going beyond scaling solutions by using a model for structure formation that we argue is reasonably generic, we investigate the correspondence between the morphon field and fundamental scalar field dark matter models, in order to describe dark matter as an effective phenomenon arising from kinematical backreaction and the averaged spatial curvature of the inhomogeneous Universe. While we find significant differences with those fundamental models, our main result is that the energy budget on typical collapsing domains is provided by curvature and matter in equal parts already around the turn-around time, leading to curvature dominance thereafter and increasing to a curvature contribution of 3/4 of the energy budget at the onset of virialization. Kinematical backreaction is subdominant at early stages, but its importance rises quickly after turn-around and dominates the curvature contribution in the final phase of the collapse. We conclude that backreaction can indeed mimic dark matter (in the energy budget) during the collapse phase of megaparsec-scale structures.

Brief Review on Scalar Field Dark Matter Models

The existence of dark matter in the Universe has been solidly established in the last decades, after the arrival of accurate cosmological and astrophysical observations, and some consider it the most challenging problem in modern physics. Given the magnitude of the problem, one cannot discard the existence of new particles with properties that may look exotic in comparison with our current understanding of ordinary matter. This is the case for the so-called scalar field dark matter model, which assumes the existence of a (probably fundamental) scalar field with a very tiny mass that can have observable consequences in the formation of cosmological structure. We present here a brief account of the main properties of an ultra-light scalar field (with masses of the order of $10^{-22} \, \mathrm{eV}/c^2$) and how different observations have been used in the last two decades to put constraints on its physical parameters. Among other topics, we review the cosmological solutions of the model, discuss the features of its self-gravitating equilibrium configurations, revisit the gravitational collapse for the formation of galaxies, and revise the possibility to find a soliton structure in the center of dark matter halos.

Scalar field dark matter with a cosh potential, revisited

Dark matter models in which the constituent particle is an ultra-light boson have become part of the mainstream discussion in cosmology and astrophysics. At the classical level, the models are represented by the dynamics of a (real or complex) scalar field endowed with a potential that contains its self-interactions, and for this reason are generically known as scalar field dark matter models. Here, we revisit the properties of such a model with a cosh potential and compare it with other known examples in the literature. Within the cosmological context, the self-interaction in the potential induces a radiation-like behavior at early times of the scalar field density, which is followed by a proper matter-like behavior at the onset of rapid field oscillations around the minimum of the potential. The solutions are found by numerical means, and from them we obtain information about the cosmological observables up to the level of linear density perturbations. We also study the general properties of self-gravitating objects in the non-relativistic limit and determine the role in them of the self-interaction obtained from the cosh potential. An overall conclusion is that, for the range of values in its parameters allowed by different constraints, a cosh potential behaves almost indistinguishable from the simpler quadratic one, which also means that the two models suffer the same tight constraints from cosmological and astrophysical observations.

Black hole shadow of Sgr A* in dark matter halo

We study, for the first time, the shadow of the supermassive black hole Sgr A* at the center of the Milky Way in dark matter halos. For the Cold Dark Matter and Scalar Field Dark Matter models considered in this work, the apparent shapes of the shadow depend upon the black hole spin a and the dark matter parameter k. We find that both dark matter models influence the shadow in a similar way. The shadow is a perfect circle in the non-rotating case (a=0) and a deformed one in the rotating case (a≠0). The size of the shadow increases with increasing k in both non-rotating and rotating cases, while the shadow gets more and more distorted with increasing a in the rotating case. We further investigate the black hole emission rate in both dark matter halos. We find that the emission rate decreases with increasing k and the peak of the emission shifts to lower frequency. Finally, by calculating the angular radius of the shadow, we estimate that the dark matter halo could influence the shadow of Sgr A* at a level of order of magnitude of 10−3 μas and 10−5 μas, for CDM and SFDM, respectively. Future astronomical instruments with high angular resolution would be able to observe this effect and shed light on the nature of Sgr A*. More interestingly, it may be possible to distinguish between CDM and SFDM models given the resolutions required differing by two orders of magnitude from each other.

Rapid cosmological simulations in Scalar Field Dark Matter models

The process of structure formation in the Universe can be explained by means of the gravitational instability of the different matter components, in particular that of the so-called dark matter field. In this work, we consider that dark matter can be described by an ultra-light scalar field minimally coupled to gravity, and its gravitational instability in an expanding universe is studied with the help of standard techniques for fluid matter components. Analytical and numerical solutions are shown, for both linear and non-linear perturbations, and compared with those of the standard cold dark matter model. We conclude that non-linear perturbations of the scalar field are indistinguishable from those of cold dark matter as long as the field mass is larger than 10−25eV.

Towards a calculation of the halo mass function of a scalar field dark matter

In this work we are going to build the halo mass function for a scalar field dark matter model. This will be done with the aim of determine the minimum size of halos that our model predicts, in contrast with the LCDM model, which predicts an overabundance of substructures. We find that, for a scalar field mass m = 10−22eV and a Sharp-k window function, is possible to reproduce the suppression in the halo formation at small scales.

Comparison between two scalar field models using rotation curves of spiral galaxies

Scalar fields have been used as candidates for dark matter in the universe, from axions with masses ∼ 10-5eV until ultra-light scalar fields with masses ∼ Axions behave as cold dark matter while the ultra-light scalar fields galaxies are Bose-Einstein condensate drops. The ultra-light scalar fields are also called scalar field dark matter model. In this work we study rotation curves for low surface brightness spiral galaxies using two scalar field models: the Gross-Pitaevskii Bose-Einstein condensate in the Thomas-Fermi approximation and a scalar field solution of the Klein-Gordon equation. We also used the zero disk approximation galaxy model where photometric data is not considered, only the scalar field dark matter model contribution to rotation curve is taken into account. From the best-fitting analysis of the galaxy catalog we use, we found the range of values of the fitting parameters: the length scale and the central density. The worst fitting results (values of much greater than 1, on the average) were for the Thomas-Fermi models, i.e., the scalar field dark matter is better than the Thomas- Fermi approximation model to fit the rotation curves of the analysed galaxies. To complete our analysis we compute from the fitting parameters the mass of the scalar field models and two astrophysical quantities of interest, the dynamical dark matter mass within 300 pc and the characteristic central surface density of the dark matter models. We found that the value of the central mass within 300 pc is in agreement with previous reported results, that this mass is ≈ 107 M⊙/pc2, independent of the dark matter model. And, on the contrary, the value of the characteristic central surface density do depend on the dark matter model.

Brief History of Ultra-light Scalar Dark Matter Models

This is a review on the brief history of the scalar field dark matter model also known as fuzzy dark matter, BEC dark matter, wave dark matter, or ultra-light axion. In this model ultra-light scalar dark matter particles with mass m = O(10-22)eV condense in a single Bose-Einstein condensate state and behave collectively like a classical wave. Galactic dark matter halos can be described as a self-gravitating coherent scalar field configuration called boson stars. At the scale larger than galaxies the dark matter acts like cold dark matter, while below the scale quantum pressure from the uncertainty principle suppresses the smaller structure formation so that it can resolve the small scale crisis of the conventional cold dark matter model.

Collapse threshold for a cosmological Klein-Gordon field

Oscillating scalar fields are useful to model a variety of matter components in the Universe. One or more scalar fields participate in the reheating process after inflation, while at much lower energies scalar fields are robust dark matter candidates. Pertaining to structure formation in these models, it is well known that inhomogeneities of the Klein-Gordon field are unstable above the characteristic de Broglie wavelength. In this paper we show that such instability implies the existence of a threshold amplitude for the collapse of primordial fluctuations. We use this threshold to correctly predict the cutoff scale of the matter power spectrum in the scalar field dark matter model. Furthermore, for a Klein-Gordon field during reheating we show that this same threshold allows for abundant production of structure (oscillons but not necessarily black holes). Looking at the production of primordial black holes (PBHs) in this scenario we note that the sphericity condition yields a much lower probability of PBH formation at the end of inflation. Remarkably, even after meeting a such stringent condition, we find that PBHs may be overproduced during reheating. We finally constrain the epochs at which an oscillating Klein-Gordon field could dominate the early universe.

Mass discrepancy-acceleration relation: A universal maximum dark matter acceleration and implications for the ultralight scalar dark matter model

Recent analysis of the rotation curves of a large sample of galaxies with very diverse stellar properties reveal a relation between the radial acceleration purely due to the baryonic matter and the one inferred directly from the observed rotation curves. Assuming the dark matter (DM) exists, this acceleration relation is tantamount to an acceleration relation between DM and baryons. This leads us to a universal maximum acceleration for all halos. Using the latter in DM profiles that predict inner cores implies that the central surface density $\mu_{DM} = \rho_s r_s$ must be a universal constant, as suggested by previous studies in selected galaxies, revealing a strong correlation between the density $\rho_s$ and scale $r_s$ parameters in each profile. We then explore the consequences of the constancy of $\mu_{DM}$ in the context of the ultra-light scalar field dark matter model (SFDM). We find that for this model $\mu_{DM} = 648 \, M_\odot {\rm pc}^{-2}$, and that the so-called WaveDM soliton profile should be an universal feature of the DM halos. Comparing with data from the Milky Way and Andromeda satellites, we find that they are consistent with a boson mass of the scalar field particle of the order of $10^{-21} \, {\rm eV}/c^2$, which puts the SFDM model in agreement with recent cosmological constraints.

Scalar field dark matter in clusters of galaxies

One alternative to the cold dark matter (CDM) paradigm is the scalar field dark matter (SFDM) model, which assumes dark matter is a spin-0 ultra-light scalar field (SF) with a typical mass $m\sim10^{-22}\mathrm{eV}/c^2$ and positive self-interactions. Due to the ultra-light boson mass, the SFDM could form Bose-Einstein condensates (BEC) in the very early Universe, which are interpreted as the dark matter haloes. Although cosmologically the model behaves as CDM, they differ at small scales: SFDM naturally predicts fewer satellite haloes, cores in dwarf galaxies and the formation of massive galaxies at high redshifts. The ground state (or BEC) solution at zero temperature suffices to describe low-mass galaxies but fails for larger systems. A possible solution is adding finite-temperature corrections to the SF potential which allows combinations of excited states. In this work, we test the finite-temperature multistate SFDM solution at galaxy cluster scales and compare our results with the Navarro-Frenk-White (NFW) and BEC profiles. We achieve this by fitting the mass distribution of 13 \textit{Chandra} X-ray clusters of galaxies, excluding the region of the brightest cluster galaxy. We show that the SFDM model accurately describes the clusters' DM mass distributions offering an equivalent or better agreement than the NFW profile. The complete disagreement of the BEC model with the data is also shown. We conclude that the theoretically motivated multistate SFDM profile is an interesting alternative to empirical profiles and ad hoc fitting-functions that attempt to couple the asymptotic NFW decline with the inner core in SFDM.

Towards accurate cosmological predictions for rapidly oscillating scalar fields as dark matter

As we are entering the era of precision cosmology, it is necessary to count on accurate cosmological predictions from any proposed model of dark matter. In this paper we present a novel approach to the cosmological evolution of scalar fields that eases their analytic and numerical analysis at the background and at the linear order of perturbations. The new method makes use of appropriate angular variables that simplify the writing of the equations of motion, and which also show that the usual field variables play a secondary role in the cosmological dynamics. We apply the method to a scalar field endowed with a quadratic potential and revisit its properties as dark matter. Some of the results known in the literature are recovered, and a better understanding of the physical properties of the model is provided. It is confirmed that there exists a Jeans wavenumber kJ, directly related to the suppression of linear perturbations at wavenumbers k > kJ, and which is verified to be kJ = a √mH. We also discuss some semi-analytical results that are well satisfied by the full numerical solutions obtained from an amended version of the CMB code CLASS. Finally we draw some of the implications that this new treatment of the equations of motion may have in the prediction of cosmological observables from scalar field dark matter models.

Characteristic size and mass of galaxies in the Bose–Einstein condensate dark matter model

We study the characteristic length scale of galactic halos in the Bose-Einstein condensate (or scalar field) dark matter model. Considering the evolution of the density perturbation we show that the average background matter density determines the quantum Jeans mass and hence the spatial size of galaxies at a given epoch. In this model the minimum size of galaxies increases while the minimum mass of the galaxies decreases as the universe expands. The observed values of the mass and the size of the dwarf galaxies are successfully reproduced with the dark matter particle mass $m\simeq 5\times 10^{-22}eV$. The minimum size is about $6\times 10^{-3}\sqrt{m/H}\lambda_c$ and the typical rotation velocity of the dwarf galaxies is $O(\sqrt{H/m}$) c, where $H$ is the Hubble parameter and $\lambda_c$ is the Compton wave length of the particle. We also suggest that ultra compact dwarf galaxies are the remnants of the dwarf galaxies formed in the early universe.

Scalar dark matter in light of LEP and proposed ILC experiments

In this work we study a scalar field dark matter model with mass of the order of 100 MeV. We assume dark matter is produced in the process $e^-+e^+\to \phi +\phi^*+\gamma$, that, in fact, could be a background for the standard process $e^-+e^+\to \nu +\bar\nu+\gamma$ extensively studied at LEP. We constrain the chiral couplings, $C_L$ and $C_R$, of the dark matter with electrons through an intermediate fermion of mass $m_F=100$ GeV and obtain $C_L=0.1(0.25)$ and $C_R=0.25(0.1)$ for the best fit point of our $\chi^2$ analysis. We also analyze the potential of ILC to detect this scalar dark matter for two configurations: (i) center of mass energy $\sqrt{s}=500$ GeV and luminosity $\mathcal{L}=250$ fb$^{-1}$, and (ii) center of mass energy $\sqrt{s}=1$ TeV and luminosity $\mathcal{L}=500$ fb$^{-1}$. The differences of polarized beams are also explored to better study the chiral couplings.

Dwarf galaxies in multistate scalar field dark matter halos

We analyse the velocity dispersion for eight of the Milky Way dwarf spheroidal satellites in the context of finite temperature scalar field dark mater. In this model the finite temperature allows the scalar field to be in configurations that possess excited states, a feature that has proved to be necessary in order to explain the asymptotic rotational velocities found in low surface brightness (LSB) galaxies. In this work we show that excited states are not only important in large galaxies but also have visible effects in dwarf spheroidals. Additionally, we stress that contrary to previous works where the scalar field dark matter haloes are consider to be purely Bose-Einstein condensates, the inclusion of excited states in these halo configurations provides a consistent framework capable of describing LSBs and dwarf galaxies of different sizes without arriving to contradictions within the scalar field dark matter model. Using this new framework we find that the addition of excited states accounts very well for the raise in the velocity dispersion in Milky Way dwarf spheroidal galaxies improving the fit compared to the one obtained assuming all the DM to be in the form of a Bose Einstein Condensate.

Scalar field dark matter mass model and evolution of rotation curves for low surface brightness galaxies

We study the evolution of gas rotation curves within the scalar field dark matter (SFDM) model. In this model the galactic haloes are astronomical Bose-Einstein Condensate drops of scalar field. These haloes are characterized by a constant-density core and are consistent with observed rotation curves of dark matter dominated galaxies, a missing feature in CDM haloes resulting from DM-only simulations. We add the baryonic component to the SFDM haloes and simulate the evolution of the dark matter tracer in a set of grid-based hydrodynamic simulations aimed to analyse the evolution of the rotation curves and the gas density distribution in the case of dark matter dominated galaxies. Previous works had found that when considering an exact analytic solution for a static SF configuration, the free parameters of the model allows for good fits to the rotation curves, we confirm that in our simulations but now taking into account the evolution of the baryonic component in a static dark matter and stellar disk potential. Including live gas is a step forward from the previous work using SFDM, as for example, the rotation velocity of the gas is not always exactly equal to the circular velocity of a test particle on a circular orbit. Contrasting with the data the cored mass model presented here is preferred instead of a cuspy one.

Nonrelativistic approach for cosmological scalar field dark matter

We derive non-relativistic equations of motion for the formation of cosmological structure in a Scalar Field Dark Matter (SFDM) model corresponding to a complex scalar field endowed with a quadratic scalar potential. Starting with the full equations of motion written in the Newtonian gauge of scalar perturbations, we separate out the fields involved into relativistic and non-relativistic parts, and find the equations of motion for the latter that can be used to build up the full solution. One important assumption will also be that the SFDM field is in the regime of fast oscillations, under which its behavior is exactly that of cold dark matter. The resultant equations are quite similar to the Schr\"odinger-Poisson system of Newtonian boson stars plus relativistic leftovers. We exploit that similarity to show how to simulate, with minimum numerical effort, the formation of cosmological structure in SFDM models and others alike, and ultimately prove their viability as complete dark matter models.

Cosmological constraints on Bose-Einstein-condensed scalar field dark matter

(Abridged) Despite the success of Cold Dark Matter (CDM) in explaining a wide range of observations, the microscopic nature of dark matter is still unknown. Attempts to detect WIMPs, the most commonly studied form, have not yet succeeded. Some predictions are even in apparent conflict with observations (e.g. cuspy-cored halos and `missing satellite problem'). Therefore, it is important to consider different forms of CDM. We focus on dark matter comprised of ultralight bosons that form a Bose-Einstein Condensate (BEC), described by a complex scalar field, and solve the Klein-Gordon and Einstein field equations to evolve the Friedmann-Robertson-Walker universe. We find, in addition to phases of radiation-, matter- and \Lambda-domination, an earlier phase of scalar-field-domination. Moreover, while WIMP CDM is non-relativistic at all times after it decouples, BEC scalar field dark matter (SFDM) is relativistic at early times, evolving from stiff to radiation-like, before it becomes non-relativistic (CDM-like) at late times. The timing of transitions between these phases yields fundamental constraints on SFDM model parameters, particle mass m and self-interaction coupling strength \lambda. We derive the range of particle parameters required to match observations of the evolving background universe, including the CMB and abundances of light elements produced by BBN, characterized by N_eff, the effective number of neutrino species, and the epoch of matter-radiation equality z_eq. This yields m >= 2.4*10^{-21} eV/c^2 and 9.5*10^{-19} eV^{-1}cm^3 <= \lambda/(mc^2)^2 <= 4*10^{-17} eV^{-1}cm^3. Our model accommodates current observations in which N_eff at BBN is higher than at z_eq, as probed by the CMB, otherwise unexplained by WIMP CDM. SFDM without self-interaction (`Fuzzy Dark Matter') cannot satisfy current BBN constraints within 68% confidence and is therefore disfavored.

Schwarzschild scalar wigs: Spectral analysis and late time behavior

Using the Green's function representation technique, the late time behavior of localized scalar field distributions on Schwarzschild spacetimes is studied. Assuming arbitrary initial data we perform a spectral analysis, computing the amplitude of each excited quasi-bound mode without the necessity of performing dynamical evolutions. The resulting superposition of modes is compared with a traditional numerical evolution with excellent agreement; therefore, we have an efficient way to determine final black hole wigs. The astrophysical relevance of the quasi-bound modes is discussed in the context of scalar field dark matter models and the axiverse.