REVIEW
Fluid Dark Matter
Astrophysics · Submitted 26 Feb 2000 · 26 references
Pith's verdict: A clean derivation of an ideal-fluid scalar dark matter with a fitted exponent; the real open question is whether the fluid survives at late times, and the paper says so itself.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
Dark matter made of a self-interacting scalar field could behave as an ideal fluid whose pressure depends only on density, tying together galaxy halo cores and the small-scale end of the primordial fluctuation spectrum.
The reading
What carries the argument
The load-bearing device is the time-averaging of the field wave equation in a static or slowly varying gravitational potential. Multiplying the wave equation by $y$ and averaging gives a virial relation; multiplying by the field gradient and averaging gives a momentum-balance equation whose pressure term is $p_y = (q-2)Klangle|y|^qrangle/(2q)$, which reduces to the stated power law when $y propto sin mt$. The same averaging applied to the mass flux $langle f_yrangle = -langle dot{y}nabla yrangle = rho_y v$ turns the dynamical equation into the Euler equation $partial_t(rho_y v_alpha) + partial_beta(rho_y v_alpha v_beta) = -rho_y varphi_{,alpha} - partial_alpha p_y$. A Lorentz-boosted oscillation $y = eta(gamma(t - vcdot r))$ is what makes the gradient and the flux line up with a moving proper density, and it is this identity that lets a field be described as a fluid at all. The second piece of machinery is the transfer-function relation $k_c c_s t_{eq} z_{eq} sim pi$, which converts a lower bound on $k_c$ into an upper bound on the sound speed at recombination and hence, through $r_c propto rho^{q/4-1}$, into a relation between $q$ and the halo parameters.
Extended reading notes
Core claim
The paper's claim is that a scalar field with potential $V = m^2y^2/2 + K|y|^q/q$ for $q>2$, oscillating at frequency $m$ and averaged over intervals long compared with $1/m$ but short compared with the Hubble time, satisfies the continuity and Euler equations of an ideal fluid with no viscosity. The mass density is $rho_y = m^2langle y^2rangle$ and the pressure is $p_y = Frho_y^{q/2}$ with a coefficient $F$ given explicitly in terms of $q$, $K$ and $m$. Because the equation of state is a pure power law, the Jeans length scales with density as $r_c propto rho_y^{q/4-1}$, so the same exponent that fixes the sound speed also fixes how core radius varies from halo to halo and how strongly the smallest scales in the dark matter distribution are erased. Peebles then imposes two constraints: halo cores must be large enough to produce the observed solid-body rotation, with $r_c geq Rrho_c^{q/4-1}$, and the first zero of the transfer function must lie at $k_c gtrsim 10h$ Mpc$^{-1}$ so that structure formation is not damaged. For $Omega_y = 0.25$, $h = 0.7$, and a halo with $v_c = 50$ km s$^{-1}$ at $r_c = 1h^{-1}$ kpc, the two constraints meet at $q = 3.7$; enlarging the core to $3$ kpc gives $q = 3.4$. With $q = 3.6$ the Jeans length varies only as $rho_y^{-0.1}$, nearly a universal core size, while $q = 4$ forces $hr_c lesssim 0.5$ kpc.
Load-bearing premise
The whole late-time picture rests on the averaged field continuing to behave as a fluid, and the paper itself says this cannot be complete because pressure waves steepen into shock-like features and the field energy must eventually cascade to short enough wavelengths that a gas of particles is the better description, with the time for that to happen left to be investigated.
Editorial extensions
If this is right
- Dark halo core radii should not be arbitrary: they should follow a power law in central density, $r_c propto rho_c^{q/4-1}$, with $q$ between roughly 3.4 and 3.7 if the model is to satisfy both halo and structure-formation constraints.
- Inner rotation curves of halos supported by this fluid should approach solid-body form, $v(r) = v_c r/r_c$ with $v_c = 2^{1/2}c_s$, inside the core radius, with velocity dispersion only able to increase $r_c$ at fixed central density.
- The primeval dark matter power spectrum should be cut off below a comoving scale of order $10h$ Mpc$^{-1}$, a suppression similar in effect to warm dark matter but arising from pressure in a field rather than from particle free-streaming.
- For $q = 4$ the Jeans length becomes a universal constant, with $hr_c lesssim 0.5$ kpc at the required cutoff scale, so the quartic model can only produce small cores unless Reynolds stress does the supporting.
- Because the fluid has no viscosity in the averaged equations, density lumps in it should behave like solitons, which is offered as a possible route by which dwarf-galaxy dark matter survives passage through a larger halo.
Reading between the lines
- The model makes a sharp, checkable prediction that couples two very different observations: the exponent measured from the core-radius versus central-density relation in nearby halos should match the exponent inferred from the shape of the small-scale cutoff, since a single $q$ controls both.
- If the cascade to particle-like behaviour turns out to be fast compared with a Hubble time, the fluid picture would still leave a signature in the transfer function at high redshift while failing in present-day halos, which would show up as a mismatch between the two inferred values of $q$.
- The reversible shock behaviour is imported from earlier numerical work on the pure quartic case, so a simulation of the $q approx 3.5$ potential would be the natural next test of whether the averaged fluid equations remain valid once density contrasts grow large.
- The near-universal core size at $q = 3.6$ is close to what is sometimes reported for low surface brightness galaxies, which makes the scaling relation, rather than any single object, the more informative target for observation.
Original abstract
Dark matter modeled as a classical scalar field that interacts only with gravity and with itself by a potential that is close to quartic at large field values and approaches a quadratic form when the field is small would be gravitationally produced by inflation and at the present epoch could act like an ideal fluid with pressure that is a function only of the mass density. This could have observationally interesting effects on the core radii and solid body rotation of dark matter halos and on the low mass end of the primeval mass fluctuation power spectrum.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Dark matter modeled as a classical scalar field that interacts only with gravity and with itself by a potential that is close to quartic at large field values and approaches a quadratic form when the field is small would be gravitationally produced by inflation and at the present epoch could act like an ideal fluid with pressure that is a function only of the mass density. This could have observationally interesting effects on the core radii and solid body rotation of dark matter halos and on the low mass end of the primeval mass fluctuation power spectrum.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Dark matter modeled as a classical scalar field that interacts only with gravity and with itself by a potential that is close to quartic at large field values and approaches a quadratic form when the field is small would be gravitationally produced by inflation and at the present epoch could act like an ideal fluid with pressure that is a function only of the mass density. | contribution 0.58 | 0.24 | 0.75 | hedged possibility 0.80 |
| s1 | This could have observationally interesting effects on the core radii and solid body rotation of dark matter halos and on the low mass end of the primeval mass fluctuation power spectrum. | interpretation 0.98 | 0.10 | 0.17 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
References
How later papers used it
128 later papers cite it
1 later paper by other authors is listed below: 1 used its data or values.
Uses its data or values 1 of 2 papers with this label
-
Used electron densities from this paper to find that the plasma frequency can fall below 10^-11 eV during the reduction in free electron density leading to the dark era.
Quantum break in models of axion dark matter (2019) · 1.00 · paraphrased: the licence does not allow quoting
How the literature uses it
82 arXiv papers cite this in 94 sentences
Papers citing it · 38 sentences without a confident label
Uses its data or values 2 papers
-
During the reduction in free electron density that leads to the “dark era", the plasma frequency can fall below 10$^-11$eV (using electron densities from [ref] ).
Quantum break in models of axion dark matter · 6.Discussion · 1.00
-
For instance, QCD axions have masses in the range $10^-11-10^-2$ eV [ref] , while the ultralight boson particles have masses as low as $10^-22-10^-19$ eV [ref] .
New insights into the formation and growth of boson stars in dark matter halos · Introduction · 0.80
Cites it as support 1 paper
-
This model suppresses low mass galaxies and provide cored profiles in CDM-dominated galaxies [ref] .
Boson Stars and Oscillatons: A Review · Boson stars and dark matter · 0.99
Cites it as background 52 papers
-
This gravitational clustering is typically studied using a perturbative framework, known commonly as standard perturbation theory (SPT), and its extensions [ref] - however, these results are valid only in the quasilinear regime and tend to break down at smaller length scales.
Consistency Relations in Effective Field Theory · Introduction · 0.94
-
This type of ALP dark matter, also including ultra-light or “fuzzy dark matter,” is usually described by a classical scalar field rather than particles [ref] .
Nonclassicality of axion-like dark matter through gravitational self-interactions · Introduction · 0.81
-
Several alternative models to CDM have been proposed, such as warm dark matter [ref] , self-interacting dark matter [ref] , and fuzzy dark matter (FDM) [ref] .
A theoretical perspective on the almost dark galaxy Nube: exploring the fuzzy dark matter model · Introduction · 0.96
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.