Initial Power Spectrum Research Articles

Evolution of two-point correlation function of galaxies with a twin-peak initial power spectrum

Evolution of two-point correlation function of galaxies with a twin-peak initial power spectrum

Dwarf galaxies as a probe of a primordially magnetized Universe

Aims. The true nature of primordial magnetic fields (PMFs) and their role in the formation of galaxies remains elusive. To shed light on these unknowns, we investigated their impact by varying two sets of properties: (i) accounting for the effect of PMFs on the initial matter power spectrum and (ii) accounting for their magneto-hydrodynamical effects on the formation of galaxies. By comparing both, we can determine the dominant agent in shaping galaxy evolution. Methods. We used the magneto-hydrodynamics code RAMSES to generate multiple new zoom-in simulations for eight different host halos of dwarf galaxies across a wide luminosity range of 103 − 106 L⊙. These halos were selected from a ΛCDM cosmological box, tracking their evolution down to redshift z = 0. We explored a variety of primordial magnetic field (comoving) strengths of Bλ ranging from 0.05 to 0.50 nG. Results. We find that magnetic fields in the interstellar medium not only modify star formation processes in dwarf spheroidal galaxies, but these fields also entirely prevent the formation of stars in less compact, ultra-faint galaxies with halo masses and stellar masses below, respectively, ∼2.5 × 109 and 3 × 106 M⊙. At high redshifts, the impact of PMFs on host halos of dwarf galaxies through the modification of the matter power spectrum is more dominant than the influence of magneto-hydrodynamics in shaping their gaseous structure. Through the amplification of small perturbations ranging in mass from 107 to 109 M⊙ in the ΛCDM+PMFs matter power spectrum, primordial fields expedite the formation of the first dark matter halos, leading to an earlier onset and a higher star formation rate at redshifts of z > 9. We investigated the evolution of various energy components and demonstrated that magnetic fields with an initial strength of Bλ ≥ 0.05 nG exhibit a strong growth of magnetic energy, accompanied by a saturation phase that begins soon after the growth phase. These trends persist consistently, regardless of the initial conditions or whether it is the classical ΛCDM model or ΛCDM modified by PMFs. Lastly, we investigated the impact of PMFs on the present-time observable properties of dwarf galaxies, namely: the half light radius, V-band luminosity, mean metallicity, and velocity dispersion profile. We find that PMFs with moderate strengths of Bλ ≤ 0.10 nG show an impressive agreement with the scaling relations of the observed Local Group dwarfs. However, stronger fields lead to larger sizes and higher velocity dispersions.

Simulations and models for the Richtmyer–Meshkov instability with broadband perturbations

The Richtmyer–Meshkov instability (RMI) is shock driven and affects many phenomena from inertial fusion to supernova explosions. The behavior of single-modes in the RMI has been studied extensively but less is known with the broadband perturbations that occur in applications. Here, we describe extensive numerical simulations and modeling of the RMI with broadband perturbations with an initial power spectrum of the form P ∝ km, where k is the wavenumber. The hydrodynamic condition is the same as in the θ-Group Collaboration [Thornber et al., “Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)] with a Mach ∼1.86 shock and gamma-law = 5/3 fluids with Atwood number A = −0.5. The bubble amplitude hB is found to grow in two stages. Initially, hB undergoes a phase-inversion and grows linearly in time (t) at a rate consistent with a linear theory. Asymptotically, hB grows as a power law ∼tθ when k|hB| > O(1), where k is the average wavenumber for the initial spectrum. The RMI behavior in simulations and modeling agree over a wide range of exponent m, spectral width, initial amplitude, and time. The agreement is quantified objectively using statistical analysis.

Halo growth and merger rates as a cosmological test

ABSTRACT Dark matter haloes grow at a rate that depends on the value of the cosmological parameters σ8 and Ωm through the initial power spectrum and the linear growth factor. While halo abundance is routinely used to constrain these parameters, through cluster abundance studies, the halo growth rate is not. In recent work, we proposed constraining the cosmological parameters using observational estimates of the overall dynamical ‘age’ of clusters, expressed, for instance, by their half-mass assembly redshift z50. Here, we explore the prospects for using the instantaneous growth rate, as estimated from the halo merger rate, from the average growth rate over the last dynamical time, or from the fraction of systems with recent episodes of major growth. We show that the merger rate is mainly sensitive to the amplitude of fluctuations σ8, while the rates of recent growth provide constraints in the Ωm–σ8 plane that are almost orthogonal to those provided by abundance studies. Data collected for forthcoming cluster abundance studies, or studies of the galaxy merger rate in current and future galaxy surveys, may thus provide additional constraints on the cosmological parameters complementary to those already derived from halo abundance.

Extending the unified subhalo model to warm dark matter

ABSTRACT Using a set of high-resolution N-body simulations, we extend the unified distribution model of cold dark matter (CDM) subhaloes to the warm dark matter (WDM) case. The same model framework combining the unevolved mass function, unevolved radial distribution, and tidal stripping can predict the mass function and spatial distribution of subhaloes in both CDM and WDM simulations. The dependence of the model on the DM particle property is universally parametrized through the half-mode mass of the initial power spectrum. Compared with the CDM model, the WDM model differs most notably in two aspects. (1) In contrast to the power-law form in CDM, the unevolved subhalo mass function for WDM is scale-dependent at the low mass end due to the cut-off in the initial power spectrum. (2) WDM subhaloes are more vulnerable to tidal stripping and disruption due to their lower concentrations at accretion time. Their survival rate is also found to depend on the infall mass. Accounting for these differences, the model predicts a final WDM subhalo mass function that is also proportional to the unevolved subhalo mass function. The radial distribution of WDM subhaloes is predicted to be mass-dependent. For low mass subhaloes, the radial distribution is flatter in the inner halo and steeper in the outer halo compared to the CDM counterpart, due to the scale-dependent unevolved mass function and the enhanced tidal stripping. The code for sampling subhaloes according to our generalized model is available at https://github.com/fhtouma/subgen2.

Towards super-resolution simulations of the fuzzy dark matter cosmological model

ABSTRACT AI super-resolution, combining deep learning and N-body simulations, has been shown to successfully reproduce the large-scale structure and halo abundances in the Lambda cold dark matter cosmological model. Here, we extend its use to models with a different dark matter content, in this case fuzzy dark matter (FDM), in the approximation that the difference is encoded in the initial power spectrum. We focus on redshift z = 2, with simulations that model smaller scales and lower masses, the latter by two orders of magnitude, than has been done in previous AI super-resolution work. We find that the super-resolution technique can reproduce the power spectrum and halo mass function to within a few per cent of full high-resolution calculations. We also find that halo artefacts, caused by spurious numerical fragmentation of filaments, are equally present in the super-resolution outputs. Although we have not trained the super-resolution algorithm using full quantum pressure FDM simulations, the fact that it performs well at the relevant length and mass scales means that it has promise as a technique that could avoid the very high computational cost of the latter, in some contexts. We conclude that AI super-resolution can become a useful tool to extend the range of dark matter models covered in mock catalogues.

The halo mass function and filaments in full cosmological simulations with fuzzy dark matter

ABSTRACT Fuzzy dark matter (FDM) is a dark matter candidate consisting of ultralight scalar particles with masses around $10^{-22}\, \mathrm{eV}/c^2$, a regime where cold bosonic matter behaves as a collective wave rather than individual particles. Although constraints on FDM are accumulating in many different contexts, very few have been verified by self-consistent numerical simulations. We present new large numerical simulations of cosmic structure formation with FDM, solving the full Schrödinger–Poisson (SP) equations using the AxiREPO code, which implements a pseudo-spectral numerical method. Combined with our previous simulations, they allow us to draw a four-way comparison of matter clustering, contrasting results (such as power spectra) for each combination of initial conditions (ICs; FDM versus cold dark matter, CDM) and dynamics (SP versus N-body). By disentangling the impact of ICs and non-linear dynamics in this manner, we can gauge the validity of approximate methods used in previous works, such as ordinary N-body simulations with an FDM initial power spectrum. Due to the comparatively large volume achieved in our FDM simulations, we are able to measure the FDM halo mass function from full wave simulations for the first time, and compare to previous results obtained using analytic or approximate approaches. We also investigate the density profiles of these filaments and compare to their ΛCDM counterparts.

Magnetic field draping around clumpy high-velocity clouds in galactic halo

ABSTRACT Throughout the passage within the Galactic halo, high-velocity clouds (HVCs) sweep up ambient magnetic fields and form stretched and draped configurations of magnetic fields around them. Many earlier numerical studies adopt spherically symmetric uniform-density clouds as initial conditions for simplicity. However, observations demonstrate that HVCs are clumpy and turbulent. In this paper, we perform 3D magnetohydrodynamic simulations to study the evolution of clouds with initial density distributions described by power-law spatial power spectra. We systematically study the role of (i) the initial density structure, (ii) halo magnetic fields, and (iii) radiative cooling efficiency upon infalling HVCs. We find that (i) the clouds’ density structure regulates mixing and mass growth. Uniform clouds grow from the onset of the simulations, while clumpy clouds initially lose gas and then grow at later times. Along the same lines, the growth curve of clumpy clouds depends on the slope of the initial density power spectra. (ii) Magnetic fields suppress hydrodynamic instabilities and the growth of small-scale structures. As a result, magnetized clouds develop long filaments extended along the streaming direction, whereas non-magnetized clouds are fragmented into many small clumps. (iii) Efficient cooling keeps the main cloud body more compact and produces decelerated dense clumps condensed from the halo gas. This work potentially helps us understand and predict the observed properties of HVCs such as the detectability of magnetized clouds, the presence of decelerated HI structures associated with HVC complexes and small-scale features, and a possible link between the origin and the fate of HVCs.

Suppressing variance in 21 cm signal simulations during reionization

Current best limits on the 21 cm signal during reionization are provided at large scales (≳100 Mpc). To model these scales, enormous simulation volumes are required, which are computationally expensive. We find that the primary source of uncertainty at these large scales is sample variance, which determines the minimum size of simulations required to analyse current and upcoming observations. In large-scale structure simulations, the method of ‘fixing’ the initial conditions (ICs) to exactly follow the initial power spectrum and ‘pairing’ two simulations with exactly out-of-phase ICs has been shown to significantly reduce sample variance. Here we apply this ‘fixing and pairing’ (F&P) approach to reionization simulations whose clustering signal originates from both density fluctuations and reionization bubbles. Using a semi-numerical code, we show that with the traditional method, simulation boxes of L ≃ 500 (300) Mpc are required to model the large-scale clustering signal at k = 0.1 Mpc−1 with a precision of 5 (10)%. Using F&P, the simulation boxes can be reduced by a factor of 2 to obtain the same precision level. We conclude that the computing costs can be reduced by at least a factor of 4 when using the F&P approach.

Inner cusps of the first dark matter haloes: formation and survival in a cosmological context

ABSTRACT We use very high resolution cosmological zoom simulations to follow the early evolution of 12 first-generation haloes formed from gaussian initial conditions with scale-free power spectra truncated on small scales by a gaussian in wavenumber. Initial collapse occurs with a diverse range of sheet- or filament-like caustic morphologies, but in almost all cases it gives rise to a numerically converged density cusp with ρ = Ar−3/2 and total mass comparable to that of the corresponding peak in the initial linear density field. The constant A can be estimated to within about 10 per cent from the properties of this peak. This outcome agrees with earlier work on the first haloes in cold and warm dark matter universes. Within central cusps, the velocity dispersion is close to isotropic, and the equidensity surfaces tend to align with those of the main body of the halo at larger radii. As haloes grow, their cusps are often (but not always) overlaid with additional material at intermediate radii to produce profiles more similar to the Einasto or Navarro–Frenk–White forms typical of more massive haloes. Nevertheless, to the extent that we can resolve them, cusps survive at the smallest radii. Major mergers can disturb them, but the effect is quite weak in the cases that we study. The cusps extend down to the resolution limits of our simulations, which are typically a factor of several larger than the cores that would be produced by phase-space conservation if the initial power spectrum cutoff arises from free streaming.

Deep Zoom-In Simulation of a Fuzzy Dark Matter Galactic Halo.

Fuzzy dark matter (FDM) made of ultralight bosonic particles is a viable alternative to cold dark matter with clearly distinguishable small-scale features in collapsed structures. On large scales, it behaves gravitationally like cold dark matter deviating only by a cutoff in the initial power spectrum and can be studied using N-body methods. In contrast, wave interference effects near the de Broglie scale result in new phenomena unique to FDM. Interfering modes in filaments and halos yield a stochastically oscillating granular structure which condenses into solitonic cores during halo formation. Investigating these highly nonlinear wave phenomena requires the spatially resolved numerical integration of the Schrödinger equation. In previous papers we introduced a hybrid zoom-in scheme that combines N-body methods to model the large-scale gravitational potential around and the mass accretion onto pre-selected halos with simulations of the Schrödinger-Poisson equation to capture wave-like effects inside these halos. In this work, we present a new, substantially improved reconstruction method for the wave function inside of previously collapsed structures. We demonstrate its capabilities with a deep zoom-in simulation of a well-studied sub-L_{*}-sized galactic halo from cosmological initial conditions. With a particle mass of m=2.5×10^{-22} eV and halo mass M_{vir}=1.7×10^{11} M_{⊙} in a (60 h^{-1} comoving Mpc)^{3} cosmological box, it reaches an effective resolution of 20 comoving pc. This pushes the values of m and M accessible to simulations significantly closer to those relevant for studying galaxy evolution in the allowed range of FDM masses.

Chaotic Dynamics in the 2D System of Nonsmooth Ordinary Differential Equations

Over the last decade, the chaotic behaviors of dynamical systems have been extensively explored. Recently, discovering or developing a 2D system of ordinary differential equations (ODEs) capable of exhibiting chaotic dynamical behaviors is an attractive research topic. In this study, a chaotic system with a 2D system of nonsmooth ODEs has been developed. This system is can exhibit chaotic dynamical behaviors. Its main dynamical behaviors, including time-series trajectories, phase portraits of attractors, and equilibria and their stability, have been investigated. The developed system has been verified by an excessive variety of fascinating chaotic behaviors, such as chaotic attractor, symmetry, sensitivity to initial conditions (ICs), fractal dimension, autocorrelation, power spectrum, Lyapunov exponent, and bifurcation diagram. Analytical and numerical simulations are used to study the dynamical behaviors of such a system. The developed system has extreme sensitivity to ICs, a fractal dimension of more than 1.8 and less than 2.05, an autocorrelation fluctuating randomly about an average of zero, a broadband power spectrum, and one positive Lyapunov exponent. The obtained numerical simulation results have proven the capability of the developed 2D system for exciting chaotic dynamical behaviors

Nonlinear equation of correlation function of galaxies in an expanding universe and the solution in linear approximation

We present an analytic study of the density fluctuation of a Newtonian self-gravity fluid in the expanding universe with ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{\ensuremath{\Lambda}}}+{\mathrm{\ensuremath{\Omega}}}_{m}=1$, which extends our previous work in the static case. By the use of field theory techniques, we obtain the nonlinear, hyperbolic equation of two-point correlation function $\ensuremath{\xi}$ of perturbation. Under the Zel'dolvich approximation the equation becomes an integro-differential equation and contains also the three-point and four-point correlation functions. By adopting the Groth-Peebles and Fry-Peebles ansatz, the equation becomes closed, and contains a pressure term and a delta source term which were neglected in Davis and Peebles' milestone work. The equation has three parameters of fluid; the particle mass $m$ in the source, the overdensity $\ensuremath{\gamma}$, and the sound speed ${c}_{s}$. We solve only the linear equation in linear approximation and apply it to the system of galaxies. We assume two models of ${c}_{s}$, and take an initial power spectrum at a redshift $z=7$, which inherits the relevant imprint from the spectrum of baryon acoustic oscillations at the decoupling. The solution $\ensuremath{\xi}(\mathbf{r},z)$ is growing during expansion, and contains 100 Mpc periodic bumps at large scales, and a main mountain (a global maximum with $\ensuremath{\xi}\ensuremath{\propto}{r}^{\ensuremath{-}1}$) at small scales $r\ensuremath{\lesssim}50\text{ }\text{ }\mathrm{Mpc}$. The profile of $\ensuremath{\xi}$ agrees with the observed ones from galaxy and quasar surveys. The bump separation is given by the Jeans length ${\ensuremath{\lambda}}_{J}$, and is also modified by $\ensuremath{\gamma}$ and ${c}_{s}$. Using a decomposition we find that the main mountain is largely generated by the inhomogeneous solution with the source, and the periodic bumps come from the homogeneous solution with the initial spectrum. ${\ensuremath{\lambda}}_{J}$ is identified as the correlation scale of the system of galaxies, distinguished from the clustering scale determined by $m$. The corresponding power spectrum has a main peak located around $k\ensuremath{\sim}\frac{2\ensuremath{\pi}}{{\ensuremath{\lambda}}_{J}}$ associated with the periodic bumps of $\ensuremath{\xi}$, and also contains multiwiggles at high $k>{k}_{J}$ which are developing during evolution even if the initial spectrum has no wiggles. Since the outcome is affected by the initial condition and the parameters as well, it is hard to infer the imprint of baryon acoustic oscillations accurately. The difficulties with the sound horizon as a distance ruler are pointed out.

Cosmological boost factor for dark matter annihilation at redshifts of z=10−100 using the power spectrum approach

We compute the cosmological boost factor at high redshifts of $z=10$-$100$ by integrating the non-linear matter power spectrum measured from high-resolution cosmological $N$-body simulations. An accurate boost factor is required to estimate the energy injection from dark matter annihilation, which may affect the cosmological re-ionization process. We combined various box-size simulations (side lengths of $1 \, {\rm kpc}$-$10 \, {\rm Mpc}$) to cover a wide range of scales, i.e. $k=1$-$10^7 \, {\rm Mpc}^{-1}$. The boost factor is consistent with the linear theory prediction at $z \gtrsim 50$ but strongly enhanced at $z \lesssim 40$ as a result of non-linear matter clustering. Although dark matter free-streaming damping was imposed at $k_{\rm fs}=10^6 \, {\rm Mpc}^{-1}$ in the initial power spectrum, the damping disappears at later times of $z\lesssim40$ as a result of the power transfer from large to small scales. Because the simulations do not explore very small-scale clustering at $k>10^7 \, {\rm Mpc}^{-1}$, our result is a lower bound on the boost factor at $z \lesssim 40$. A simple fitting function of the boost factor is also presented.

Probing small-scale baryon and dark matter isocurvature perturbations with cosmic microwave background anisotropies

The Universe's initial conditions, in particular baryon and cold dark matter (CDM) isocurvature perturbations, are poorly constrained on sub-Mpc scales. In this paper, we develop a new formalism to compute the effect of small-scale baryon perturbations on the mean free-electron abundance, thus on cosmic microwave background (CMB) anisotropies. Our framework can accommodate perturbations with arbitrary time and scale dependence. We apply this formalism to four different combinations of baryon and CDM isocurvature modes, and use Planck CMB-anisotropy data to probe their initial amplitude. We find that Planck data is consistent with no small-scale isocurvature perturbations, and that this additional ingredient does not help alleviate the Hubble tension. We set upper bounds to the dimensionless initial power spectrum $\Delta_{\mathcal{I}}^2(k)$ of these isocurvature modes at comoving wavenumbers $1~\textrm{Mpc}^{-1} \le k \le 10^3$ Mpc$^{-1}$, for several parameterizations. For a scale-invariant power spectrum, our 95% confidence-level limits on $\Delta_{\mathcal{I}}^2$ are 0.023 for pure baryon isocurvature, 0.099 for pure CDM isocurvature, 0.026 for compensated baryon-CDM perturbations, and 0.009 for joint baryon-CDM isocurvature perturbations. Using a Fisher analysis generalized to non-analytic parameter dependence, we forecast that a CMB Stage-4 experiment would be able to probe small-scale isocurvature perturbations with initial power 3 to 10 times smaller than Planck limits. The formalism introduced in this work is very general and can be used more widely to probe any physical processes or initial conditions sourcing small-scale baryon perturbations.

Baryonic imprints on DM haloes: population statistics from dwarf galaxies to galaxy clusters

ABSTRACT In a purely cold dark matter (CDM) universe, the initial matter power spectrum and its subsequent gravitational growth contain no special mass- or time-scales, and so neither do the emergent population statistics of internal dark matter (DM) halo properties. Using 1.5 million haloes from three illustristng realizations of a ΛCDM universe, we show that galaxy formation physics drives non-monotonic features (‘wiggles’) into DM property statistics across six decades in halo mass, from dwarf galaxies to galaxy clusters. We characterize these features by extracting the halo mass-dependent statistics of five DM halo properties – velocity dispersion, NFW concentration, density- and velocity-space shapes, and formation time – using kernel-localized linear regression (Kllr). Comparing precise estimates of normalizations, slopes, and covariances between realizations with and without galaxy formation, we find systematic deviations across all mass-scales, with maximum deviations of 25 per cent at the Milky Way mass of $10^{12} \, {\rm M}_\odot$. The mass-dependence of the wiggles is set by the interplay between different cooling and feedback mechanisms, and we discuss its observational implications. The property covariances depend strongly on halo mass and physics treatment, but the correlations are mostly robust. Using multivariate Kllr and interpretable machine learning, we show the halo concentration and velocity-space shape are principal contributors, at different mass, to the velocity dispersion variance. Statistics of mass accretion rate and DM surface pressure energy are provided in an appendix. We publicly release halo property catalogues and kllr parameters for the TNG runs at 20 epochs up to z = 12.

Lifting weak lensing degeneracies with a field-based likelihood

ABSTRACT We present a field-based approach to the analysis of cosmic shear data to infer jointly cosmological parameters and the dark matter distribution. This forward modelling approach samples the cosmological parameters and the initial matter fluctuations, using a physical gravity model to link the primordial fluctuations to the non-linear matter distribution. Cosmological parameters are sampled and updated consistently through the forward model, varying (1) the initial matter power spectrum, (2) the geometry through the distance-redshift relationship, and (3) the growth of structure and light-cone effects. Our approach extracts more information from the data than methods based on two-point statistics. We find that this field-based approach lifts the strong degeneracy between the cosmological matter density, Ωm, and the fluctuation amplitude, σ8, providing tight constraints on these parameters from weak lensing data alone. In the simulated four-bin tomographic experiment we consider, the field-based likelihood yields marginal uncertainties on σ8 and Ωm that are, respectively, a factor of 3 and 5 smaller than those from a two-point power spectrum analysis applied to the same underlying data.

The Epoch of Reionization in Warm Dark Matter Scenarios

In this paper we investigate how the Reionization process is affected by early galaxy formation in different cosmological scenarios. We use a semi-analytic model with suppressed initial power spectra to obtain the UV Luminosity Function in thermal Warm Dark Matter and sterile neutrino cosmologies. We retrace the ionization history of intergalactic medium with hot stellar emission only, exploiting fixed and variable photons escape fraction models (fesc). For each cosmology, we find an upper limit to fixed fesc, which guarantees the completion of the process at z<6.7. The analysis is tested with two limit hypothesis on high-z ionized hydrogen volume fraction, comparing our predictions with observational results.

A fast semidiscrete optimal transport algorithm for a unique reconstruction of the early Universe

ABSTRACT We leverage powerful mathematical tools stemming from optimal transport theory and transform them into an efficient algorithm to reconstruct the fluctuations of the primordial density field, built on solving the Monge-Ampère-Kantorovich equation. Our algorithm computes the optimal transport between an initial uniform continuous density field, partitioned into Laguerre cells, and a final input set of discrete point masses, linking the early to the late Universe. While existing early universe reconstruction algorithms based on fully discrete combinatorial methods are limited to a few hundred thousand points, our algorithm scales up well beyond this limit, since it takes the form of a well-posed smooth convex optimization problem, solved using a Newton method. We run our algorithm on cosmological N-body simulations, from the AbacusCosmos suite, and reconstruct the initial positions of $\mathcal {O}(10^7)$ particles within a few hours with an off-the-shelf personal computer. We show that our method allows a unique, fast, and precise recovery of subtle features of the initial power spectrum, such as the baryonic acoustic oscillations.

Thermal instability and multiphase gas in the simulated interstellar medium with conduction, viscosity, and magnetic fields

ABSTRACT Thermal instability plays a crucial role in the formation of multiphase structures and their dynamics in the interstellar medium, and is a leading theory for cold cloud creation in various astrophysical environments. In this paper, we use 2D simulations to investigate thermal instability under the influence of various initial conditions and physical processes. We experiment with Gaussian random field (GRF) density perturbations of different initial power spectra. We also enrol thermal conduction and physical viscosity in isotropic hydrodynamic and anisotropic magnetohydrodynamic (MHD) simulations. We find that the initial GRF spectral index α has a dramatic impact on the pure hydrodynamic development of thermal instability, influencing the size, number, and motions of clouds. Cloud fragmentation happens due to two mechanisms: tearing and contraction rebound. In the runs with isotropic conduction and viscosity, the structures and dynamics of the clouds are dominated by evaporation and condensation flows in the non-linear regime, and the flow speed is regulated by viscosity. Cloud disruptions happen as a result of the Darrieus–Landau instability. However, at very late times, all individual clouds merge into one cold structure in all hydrodynamic runs. In the MHD case, the cloud structure is determined by both the initial perturbations and the initial magnetic field strength. In high-β runs, anisotropic conduction causes dense filaments to align with the local magnetic fields and the field direction can become reoriented. Strong magnetic fields suppress cross-field contraction and cold filaments can form along or perpendicular to the initial fields.