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Register a new userDetectability of Small-Scale Dark Matter Clumps with Pulsar Timing Arrays
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We examine the capability of pulsar timing arrays (PTAs) to detect very small-scale clumps of dark matter (DM), which are a natural outcome of the standard cold dark matter (CDM) paradigm. A clump streaming near the Earth or a pulsar induces an impulsive acceleration to encode residuals on pulsar timing data. We show that, assuming the standard abundance of DM clumps predicted by the CDM model, small-scale DM clumps with masses from $sim 10^{-11} M_odot$ to $sim 10^{-8} M_odot$ can be detectable by a PTA observation for a few decades with ${cal O}(100)$ of pulsars with a timing noise of ${cal O}(10)$ ns located at $gtrsim 3$ kpc away from the Galactic center, as long as these mass scales are larger than the cutoff scale of the halo mass function that is determined by the particle nature of DM. Our result suggests that PTAs can provide a unique opportunity for testing one of the most fundamental predictions of the CDM paradigm. In addition, the detections and non-detections can constrain the cutoff mass scale inherent to the DM model.
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Models of Dark Matter (DM) can leave unique imprints on the Universes small scale structure by boosting density perturbations on small scales. We study the capability of Pulsar Timing Arrays to search for, and constrain, subhalos from such models. The models of DM we consider are ordinary adiabatic perturbations in $Lambda$CDM, QCD axion miniclusters, models with early matter domination, and vector DM produced during inflation. We show that $Lambda$CDM, largely due to tidal stripping effects in the Milky Way, is out of reach for PTAs (as well as every other probe proposed to detect DM small scale structure). Axion miniclusters may be within reach, although this depends crucially on whether the axion relic density is dominated by the misalignment or string contribution. Models where there is matter domination with a reheat temperature below 1 GeV may be observed with future PTAs. Lastly, vector DM produced during inflation can be detected if it is lighter than $10^{-16} ,{rm GeV}$. We also make publicly available a Python Monte Carlo tool for generating the PTA time delay signal from any model of DM substructure.
An ultralight scalar field is a candidate for the dark matter. The ultralight scalar dark matter with mass around $10^{-23},{rm eV}$ induces oscillations of the pulse arrival time in the sensitive frequency range of the pulsar timing arrays. We search for the ultralight scalar dark matter using the North American Nanohertz Observatory for Gravitational Waves 11-year Data Set. We give the 95% confidence upper limit for the signal induced by the ultralight scalar dark matter. In comparison with the published Bayesian upper limits on the amplitude of the ultralight scalar dark matter obtained by Bayesian analysis using the Parkes Pulsar Timing Array 12-year data set (Porayko et al. 2018), we find three times stronger upper limit in the frequency range from $10^{-8.34}$ to $10^{-8.19},{ rm Hz}$ which corresponds to the mass range from $9.45times10^{-24}$ to $1.34times10^{-23},{rm eV}$. In terms of the energy density of the dark matter, we find that the energy density near the Earth is less than $7,{rm GeV/cm^3}$ in the range from $10^{-8.55}$ to $10^{-8.01},{ rm Hz}$ (from $5.83times10^{-24}$ to $2.02times10^{-23},{rm eV}$). The strongest upper limit on the the energy density is given by $2,{rm GeV/cm^3}$ at a frequency $10^{-8.28},{ rm Hz}$ (corresponding to a mass $1.09times10^{-23},{rm eV}$). We find that the signal of the ultralight scalar dark matter can be explained by the solar system ephemeris effect. Also, we reveal that the model of the solar system ephemeris effect prefers parameters which are contrary to the expectation that noise will be reduced on all pulsars.
Light Axionic Dark Matter, motivated by string theory, is increasingly favored for the no-WIMP era. Galaxy formation is suppressed below a Jeans scale, of $simeq 10^8 M_odot$ by setting the axion mass to, $m_B sim 10^{-22}$eV, and the large dark cores of dwarf galaxies are explained as solitons on the de-Broglie scale. This is persuasive, but detection of the inherent scalar field oscillation at the Compton frequency, $omega_B= (2.5{rm , months})^{-1}(m_B/10^{-22}eV)$, would be definitive. By evolving the coupled Schrodinger-Poisson equation for a Bose-Einstein condensate, we predict the dark matter is fully modulated by de-Broglie interference, with a dense soliton core of size $simeq 150pc$, at the Galactic center. The oscillating field pressure induces General Relativistic time dilation in proportion to the local dark matter density and pulsars within this dense core have detectably large timing residuals, of $simeq 400nsec/(m_B/10^{-22}eV)$. This is encouraging as many new pulsars should be discovered near the Galactic center with planned radio surveys. More generally, over the whole Galaxy, differences in dark matter density between pairs of pulsars imprints a pairwise Galactocentric signature that can be distinguished from an isotropic gravitational wave background.
Dark matter substructure, such as primordial black holes (PBHs) and axion miniclusters, can induce phase shifts in pulsar timing arrays (PTAs) due to gravitational effects. In order to gain a more realistic forecast for the detectability of such models of dark matter with PTAs, we propose a Bayesian inference framework to search for phase shifts generated by PBHs and perform the analysis on mock PTA data with the software texttt{enterprise}. For most PBH masses the constraints on the dark matter abundance agree with previous (frequentist) analyses (without mock data) to $mathcal{O}(1)$ factors. This further motivates a dedicated search for PBHs (and dense small scale structures) in the mass range from $10^{-8},M_{odot}$ to well above $10^2,M_{odot}$ with the Square Kilometer Array. Moreover, with a more optimistic set of timing parameters, future PTAs are predicted to constrain PBHs down to $10^{-11},M_{odot}$. Lastly, we discuss the impact of backgrounds, such as Supermassive Black Hole Mergers, on detection prospects, suggesting a future program to separate a dark matter signal from other astrophysical sources.
We discuss the theory of pulsar-timing and astrometry probes of a stochastic gravitational-wave background with a recently developed total-angular-momentum (TAM) formalism for cosmological perturbations. We review the formalism, emphasizing in particular the features relevant for this work and describe the observables we consider (i.e. the pulsar redshift and stellar angular displacement). Using the TAM approach, we calculate the angular power spectra for the observables and from them derive angular auto- and cross-correlation functions. We provide the full set of power spectra and correlation functions not only for the standard transverse-traceless propagating degrees of freedom in general relativity, but also for the four additional non-Einsteinian polarizations that may arise in alternative-gravity theories. We discuss how pulsar-timing and astrometry surveys can complement and serve as cross checks to one another and comment on the importance of testing the chirality of the gravitational-wave background as a tool to understand the nature of its sources. A simple rederivation of the power spectra from the plane-wave formalism is provided in an Appendix.
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