Number Density Of Stars Research Articles

The Spectacular Tidal Tails of Globular Cluster M3 (NGC 5272)

We provide a detailed analysis of the tidal tails of the globular cluster M3 (NGC 5272). We first discover clear extratidal structures with a slight S shape near the cluster. This inspires us to examine the existence of its long tidal tails. We highlight potential stream stars using the proper motions (PMs) of a model stream combined with the cluster’s locus in a color–magnitude diagram (CMD). A 35° long leading tail and a 21° long trailing tail are successfully detected at the same time. Their corresponding overdensities can be recognized in CMD and PM space after subtracting the background. We estimate the stream width, star number density, and surface brightness for both tails, as well as the distance variation along the entire stream. We then verify the connection of M3 and the Svöl stream. Finally, we tabulate 11 member stars belonging to the M3 tidal stream with available spectroscopic observations.

An MCMC approach to the three-dimensional structure of the Milky Way bulge using OGLE-IV δ Scuti stars

ABSTRACT We present an analysis of high-latitude δ Scuti stars (|b| > 1°) in the Galactic bulge region (−8${_{.}^{\circ}}$3 < l < 9${_{.}^{\circ}}$4) using a clean sample of the photometric data of 7440 stars recently released by the OGLE-IV project. The geometrical parameters of the bulge are determined based on Maximum Likelihood (ML) analysis in five-dimensional parameter space. More refined values of these parameters as well as their uncertainties are obtained from a fully Bayesian Markov chain Monte Carlo (MCMC) analysis. Approximating the bulge as an ellipsoid, the distribution of the number density of stars as a function of Galacto-centric distance has been modelled using three distribution functions: two Exponential ($\rm E_{1},\rm E_{2}$) types and one Gaussian ($\rm G$) type. Based on the AIC and BIC values, the exponential model $\rm E_{1}$ is chosen as the best statistical model for the parameter values obtained from the MCMC analysis. The MCMC analysis yields the following results: the mean distance to the Galactic Centre (GC) is found to be R0 = 8.034 ± 0.012stat ± 0.586sys kpc; the bulge δ Scuti distribution has a triaxial shape with normalized (a ≡ 1) axes ratios (a: b: c) as 1.000 ± 0.005: 0.348 ± 0.002: 0.421 ± 0.002. Here a is the semi-major axis lying in the Galactic plane and pointing towards us; b and c are the two semi-minor axes, the former lying in the Galactic plane and the later perpendicular to it. Smaller values of b as compared to a obtained for Galacto-centric distances R ≥ 2.0 kpc indicate the presence of a bar-like structure of the bulge with a bar angle of 22${_{.}^{\circ}}$006 ± 2${_{.}^{\circ}}$078.

Recent star formation history of the dwarf irregular galaxy Leo A

Context.Leo A is a gas-rich dwarf irregular galaxy of low stellar mass and metallicity. Its star formation history extends up to ∼10 Gyr. A few prominent H II regions indicate that star formation processes are active in the galaxy to this day. In the present epoch, Leo A is a highly isolated galaxy, which allows for it to be studied in a self-propagating star formation regime. Aims. Our aim is to study the recent star formation history of the Leo A galaxy over the last ∼300 Myr. Methods. We analysed populations of main sequence (MS) and blue helium-burning (BHeB – ‘blue loop’) stars using multi-colour photometry data obtained with the Subaru/Suprime-Cam (B, V, R, I, Hα) and the Hubble Space Telescope (HST) Advanced Camera for Surveys (F475W and F814W) cameras. We made use of colour-magnitude diagrams and stellar isochrones to determine individual ages of the BHeB stars, which enabled us to study the spatial distribution of these stars in different age bins. In addition, we used Hα emission and H I column density maps to study the relationship between young stellar populations and the surrounding interstellar medium. Results. We found that significant differences are visible in the morphology of stellar distributions represented by the BHeB and MS stars of different ages. We also studied a well-known H I hole in the Leo A galaxy and found that there is a noticeable difference in the surface number density of stars in the western and eastern parts of the hole. The bright young (< 20 Myr) MS stars residing in the western part of the hole indicate the recent star-forming activity in this region after the quiescent period of ∼300 Myr. Furthermore, there is a shock front (prominent in Hα) that closely resembles the shape of the western edge of the H I hole. This shock front could have been formed by the combined stellar feedback from the young MS stars or a Type II supernova located within the H I hole. Additionally, an analysis of the Suprime-Cam photometry in Hα and R passbands enabled us to identify 17 stars with a prominent Hα emission (Hα − R ≤ −0.06) which indicate the presence of early-type (Be, B[e], or A-shell) emission-line stars in the Leo A galaxy.

Carina High-contrast Imaging Project for massive Stars (CHIPS)

Context.Most massive stars belong to multiple systems, yet the formation process leading to such high multiplicity remains insufficiently understood. To help constrain the different formation scenarios that exist, insights into the low-mass end of the companion mass function of such stars is crucial. However, this is a challenging endeavour as (sub-)solar mass companions at angular separations (ρ) below 1″ (corresponding to 1000–3000 au in nearby young open clusters and OB associations) are difficult to detect due to the large brightness contrast with the central star.Aims.With the Carina High-contrast Imaging Project of massive Stars (CHIPS), we aim to obtain statistically significant constraints on the presence and properties of low-mass companions around massive stars in a previously unreachable observing window (Δmag ≳ 10 atρ ≲ 1″). In the second paper of the series, we focus on the Trumpler 14 cluster, which harbours some of the youngest and most massive O-type stars in the Milky Way.Methods.We obtained VLT-SPHERE observations of seven O-type objects in Trumpler 14 using IRDIFS_EXT mode. These provide us with a 12″ × 12″ field of view (approximately ((3 × 3)×104au) centred on each O star and allow us to search for companions at separations larger than 0″​​.15 (approx. 360 au) and down to magnitude contrast > 10 mag in the near-infrared. We used angular and spectral differential imaging along with Point Spread Function (PSF) fitting to detect sources and measure their flux relative to that of the central object. We then used grids of ATLAS9 and PHOENIX Local Thermodynamic Equilibrium (LTE) atmosphere models combined with (pre-)main-sequence evolutionary tracks to estimate the mass of the detected candidate companions.Results.We detected 211 sources with near-infrared magnitude contrast in the range of 2–12. Given the large surface number density of stars in Trumpler 14, one cannot reliably distinguish between cluster members and genuine companions for most of the detected sources. The closest companion, at only 0″​​.26, is characterised as a 1.4M⊙star with an age of 0.6 Myr, in excellent agreement with previous age estimates for Tr 14. The mass function peaks at about 0.4M⊙and presents a dearth of stars in the 0.5–0.8M⊙mass range compared to previous estimates of the initial mass function in Tr 14. While statistically significant, part of these differences may result from contamination of theK-band fluxes by circumstellar material.Conclusions.SPHERE is clearly suitable to probe the low-mass end of the mass function in the vicinity of massive stars. Follow-up SPHERE observations to obtain the full Y to K spectral energy distribution would allow for better constraints on the masses of the detected sources, and to confirm (or invalidate) the curious mass function that we derived for low-mass stars in the vicinity of the O-type objects in Trumpler 14.

Study of the open cluster Alessi-Teutsch 9 (ASCC 10) using multiband photometry and Gaia EDR3

There is a growing interest in the automated characterization of open clusters using data from the Gaia mission. This work evidences the importance of choosing an appropriate sampling radius (the radius of the circular region around the cluster used to extract the data) and the usefulness of additional multiband photometry in order to achieve accurate results. We address this issue using as a case study the cluster Alessi-Teutsch 9. The optimal sampling is determined by counting the number of assigned members at different sampling radii. By using this strategy with data from Gaia EDR3 and with observed photometry in 12 bands spanning the optical range from 3000 to 10000 \AA, approximately, we are able to obtain reliable members and to determine the properties of the cluster. The spatial distribution of stars show a two-component structure with a central core of radius ~12-13 arcmin and an outer halo extending out to 35 arcmin. With the derived cluster distance (654 pc) we obtain that the number density of stars is ~0.06 star/pc^3, making Alessi-Teutsch 9 one of the less dense known open clusters. The short relaxation time reveals that it is a dynamically relaxed and gravitationally bound system.

Close stellar encounters kicking planets out of habitable zone in various stellar environments

Continuous habitability of a planet is a critical condition for advanced forms of life to appear, but it can be endangered by astronomical events such as stellar encounters. The purpose of this study is to analyze close stellar encounters able to change planetary orbits initially in circumstellar habitable zones and to investigate the expected encounter rates in a variety of stellar environments. Using gravitational simulations for three-body systems, this study analyzed the dependencies of encounter impact-parameters with kinematic, geometric, and habitability parameters of the system. We also used kinematic properties of various stellar regions and estimated encounter rates of the events. The expected number of threatening stellar encounters in the Solar neighborhood is [Formula: see text] in 4 billion years, while for the Galactic bulge environment, we expect approximately 5.5 times the value. The encounter rates for other stellar environments are calculated and spheroidal dwarf galaxies and globular clusters encounter rates are estimated. The results show that in contrast with the solar neighborhood, close stellar encounters can play a significant role in the expected number of planets with continuous habitability in dense stellar environments. Another notable result shows that threatening stellar encounter rate follows the number density of stars, and is not strongly dependent of the region’s velocity dispersion. Further investigations are needed to study long-term multiple planetary systems and how they can change the overall expected value of continuously habitable planets.

Testing MOdified Gravity (MOG) theory and dark matter model in Milky Way using the local observables

ABSTRACT In this paper, we have investigated one of the alternative theories to dark matter named MOdified Gravity (MOG) by testing its ability to describe the local dynamics of the Milky Way (MW) in vertical and transverse directions with the baryonic matter. MOG is designed to interpret the dynamics of galaxies and cluster of galaxies without the need for dark matter. We use local observational data such as the vertical dispersion, rotation curve, surface density, and number density of stars in the Milky Way to obtain the parameters of MOG and the baryonic component of MW by implementing a Bayesian approach to the parameter estimation based on a Markov Chain Monte Carlo method. We compare our results with the dark matter model of MW. The two models of MOG and cold dark matter are able to describe equally well the rotation curve and the vertical dynamics of stars in the local MW. The best values for the free parameters of MOG in this analysis are obtained as α = 8.99 ± 0.02 and μ = 0.054 ± 0.005 kpc−1. Also, we obtain the parameters of the generalized gNFW model in the dark matter model. Our best value of bulge mass from MOG is $(1.06 \pm 0.26)\times 10^{10}\, \rm M_{\odot }$, which is consistent with the estimations form the microlensing observations.

HD 165054: An Astrometric Calibration Field for High-contrast Imagers in Baade’s Window

Abstract We present a study of the HD 165054 astrometric calibration field that has been periodically observed with the Gemini Planet Imager (GPI). HD 165054 is a bright star within Baade’s Window, a region of the galactic plane with relatively low extinction from interstellar dust. HD 165054 was selected as a calibrator target due to the high number density of stars within this region (∼3 stars per square arcsecond with H < 22), necessary because of the small field of view of the GPI. Using nine epochs spanning over five years, we have fit a standard five-parameter astrometric model to the astrometry of seven background stars within close proximity to HD 165054 (ρ < 2″). We achieved a proper motion precision of ∼0.3 mas yr−1 and constrained the parallax of each star to be ≲1 mas. Our measured proper motions and parallax limits are consistent with the background stars being a part of the galactic bulge. Using these measurements, we find no evidence of any systematic trend of either the plate scale or the north angle offset of GPI between 2014 and 2019. We compared our model describing the motions of the seven background stars to observations of the same field in 2014 and 2018 obtained with Keck/NIRC2, an instrument with excellent astrometric calibration. We find that the predicted position of the background sources is consistent with that measured by NIRC2, within the uncertainties of the calibration of the two instruments. In the future, we will use this field as a standard astrometric calibrator for the upgrade of GPI and potentially for other high-contrast imagers.

A deep learning model to emulate simulations of cosmic reionization

ABSTRACT We present a deep learning model trained to emulate the radiative transfer during the epoch of cosmological reionization. CRADLE (Cosmological Reionization And Deep LEarning) is an auto-encoder convolutional neural network that uses 2D maps of the star number density and the gas density field at z = 6 as inputs and that predicts 3D maps of the times of reionization treion as outputs. These predicted single fields are sufficient to describe the global reionization history of the intergalactic medium in a given simulation. We trained the model on a given simulation and tested the predictions on another simulation with the same parameters but with different initial conditions. The model is successful at predicting treion maps that are in good agreement with the test simulation. We used the power spectrum of the treion field as an indicator to validate our model. We show that the network predicts large scales almost perfectly but is somewhat less accurate at smaller scales. While the current model is already well suited to get average estimates about the reionization history, we expect it can be further improved with larger samples for the training, better data pre-processing and finer tuning of hyper-parameters. Emulators of this kind could be systematically used to rapidly obtain the evolving H ii regions associated with hydro-only simulations and could be seen as precursors of fully emulated physics solvers for future generations of simulations.

Emergence of theGaiaphase space spirals from bending waves

We discuss the physical mechanism by which pure vertical bending waves in a stellar disc evolve to form phase space spirals similar to those discovered by Antoja et al. ( arXiv:1804.10196) in Gaia Data Release 2. These spirals were found by projecting Solar Neighbourhood stars onto the $z-v_z$ plane. Faint spirals appear in the number density of stars projected onto the $z-v_z$ plane, which can be explained by a simple model for phase wrapping. More prominent spirals are seen when bins across the $z-v_z$ plane are coloured by median $v_R$ or $v_\phi$. We use both toy model and fully self-consistent simulations to show that the spirals develop naturally from vertical bending oscillations of a stellar disc. The underlying physics follows from the observation that the vertical energy of a star (essentially, its "radius" in the $z-v_z$ plane) correlates with its angular momentum or, alternatively, guiding radius. Moreover, at fixed physical radius, the guiding radius determines the azimuthal velocity. Together, these properties imply the link between in-plane and vertical motion that lead directly to the Gaia spirals. We show that the cubic $R-z$ coupling term in the effective potential is crucial for understanding the morphology of the spirals. This suggests that phase space spirals might be a powerful probe of the Galactic potential. In addition, we argue that self-gravity is necessary to properly model the evolution of the bending waves and their attendant phase space spirals.

A Near-infrared RR Lyrae Census along the Southern Galactic Plane: The Milky Way’s Stellar Fossil Brought to Light

Abstract RR Lyrae stars (RRLs) are tracers of the Milky Way’s fossil record, holding valuable information on its formation and early evolution. Owing to the high interstellar extinction endemic to the Galactic plane, distant RRLs lying at low Galactic latitudes have been elusive. We attained a census of 1892 high-confidence RRLs by exploiting the near-infrared photometric database of the VVV survey’s disk footprint spanning ∼70° of Galactic longitude, using a machine-learned classifier. Novel data-driven methods were employed to accurately characterize their spatial distribution using sparsely sampled multi-band photometry. The RRL metallicity distribution function (MDF) was derived from their K s -band light-curve parameters using machine-learning methods. The MDF shows remarkable structural similarities to both the spectroscopic MDF of red clump giants and the MDF of bulge RRLs. We model the MDF with a multi-component density distribution and find that the number density of stars associated with the different model components systematically changes with both the Galactocentric radius and vertical distance from the Galactic plane, equivalent to weak metallicity gradients. Based on the consistency with results from the ARGOS survey, three MDF modes are attributed to the old disk populations, while the most metal-poor RRLs are probably halo interlopers. We propose that the dominant [Fe/H] component with a mean of −1 dex might correspond to the outskirts of an ancient Galactic spheroid or classical bulge component residing in the central Milky Way. The physical origins of the RRLs in this study need to be verified by kinematical information.

Milky Way globular cluster metallicity and low-mass X-ray binaries: the red giant influence

Galactic and extragalactic studies have shown that metal-rich globular clusters (GCs) are approximately three times more likely to host bright low-mass X-ray binaries (LMXBs) than metal-poor GCs. There is no satisfactory explanation for this metallicity effect. We tested the hypothesis that the number density of red giant branch (RGB) stars is larger in metal-rich GCs, and thus potentially the cause of the metallicity effect. Using Hubble Space Telescope photometry for 109 unique Milky Way GCs, we investigated whether RGB star density was correlated with GC metallicity. Isochrone fitting was used to calculate the number of RGB stars, which were normalized by the GC mass and fraction of observed GC luminosity, and determined density using the volume at the half-light radius $r_{h}$. The RGB star number density was weakly correlated with metallicity [Fe/H], giving Spearman and Kendall Rank test $p$-values of 0.00016 and 0.00021 and coefficients $r_{s} = 0.35$ and $\tau = 0.24$ respectively. This correlation may be biased by a possible dependence of $r_{h}$ on [Fe/H], although studies have shown that $r_{h}$ is correlated with Galactocentric distance and independent of [Fe/H]. The dynamical origin of the $r_{h}$-metallicity correlation (tidal stripping) suggests that metal-rich GCs may have had more active dynamical histories, which would promote LMXB formation. No correlation between the RGB star number density and metallicity was found when using only the GCs that hosted quiescent LMXBs. A complete census of quiescent LMXBs in our Galaxy is needed to further probe the metallicity effect, which will be possible with the upcoming launch of eROSITA.

Kernel Density Estimation in the Study of Star Clusters

Abstract The kernel estimator method is used to evaluate the surface and spatial star number density in star clusters. Both density maps and radial density profiles are plotted. These estimates are used to derive the cluster size, the number of cluster stars and the cluster mass, and to study the cluster structure. The kernel estimator is also used to plot the luminosity function, mass function, the velocity distribution, and Hess diagrams for star clusters. The advantages of the kernel estimator method and technical details of its use are illustrated by modern results for the open cluster NGC 4337.

WHERE ARE THE LOW-MASS POPULATION III STARS?

ABSTRACT We study the number and the distribution of low-mass Population III (Pop III) stars in the Milky Way. In our numerical model, hierarchical formation of dark matter minihalos and Milky-Way-sized halos are followed by a high-resolution cosmological simulation. We model the Pop III formation in H2 cooling minihalos without metal under UV radiation of the Lyman–Werner bands. Assuming a Kroupa initial mass function (IMF) from 0.15 to 1.0 M ⊙ for low-mass Pop III stars, as a working hypothesis, we try to constrain the theoretical models in reverse by current and future observations. We find that the survivors tend to concentrate on the center of halo and subhalos. We also evaluate the observability of Pop III survivors in the Milky Way and dwarf galaxies, and constraints on the number of Pop III survivors per minihalo. The higher latitude fields require lower sample sizes because of the high number density of stars in the galactic disk, the required sample sizes are comparable in the high- and middle-latitude fields by photometrically selecting low-metallicity stars with optimized narrow-band filters, and the required number of dwarf galaxies to find one Pop III survivor is less than 10 at <100 kpc for the tip of red giant stars. Provided that available observations have not detected any survivors, the formation models of low-mass Pop III stars with more than 10 stars per minihalo are already excluded. Furthermore, we discuss the way to constrain the IMF of Pop III stars at a high mass range of ≳10 M ⊙.

The Proportion of Stars with Planets

Estimates of the proportion of Sun-like stars with accompanying planets vary widely; the best present estimate is that it is about 0.34. The capture theory of planet formation involves an interaction between a condensed star and either a diffuse protostar or a high-density region in a dense embedded cluster. The protostar, or dense region, is tidally stretched into a filament that is gravitationally unstable and breaks up into a string of protoplanetary blobs, which subsequently collapse to form planets, some of which are captured by the star. A computational model, in which the passage of collapsing protostars, with initial radii 1000, 1500 and 2000 au, through a dense embedded cluster are followed, is used to estimate the proportion of protostars that would be disrupted to give planets, in environments with star number-densities in the range 5000–25,000 pc−3. It is concluded from the results that the capture theory might explain the presently-estimated proportion of stars with exoplanet companions, although other possible ways of producing exoplanets are not excluded.

A Dynamical Gravitational Wave Source in a Dense Cluster

AbstractMaking use of a new N-body model to describe the evolution of a moderate-size globular cluster, we investigate the characteristics of the population of black holes within such a cluster. This model reaches core-collapse and achieves a peak central density typical of the dense globular clusters of the Milky Way. Within this high-density environment, we see direct confirmation of the merging of two stellar remnant black holes in a dynamically formed binary, a gravitational wave source. We describe how the formation, evolution, and ultimate ejection/destruction of binary systems containing black holes impacts the evolution of the cluster core. Also, through comparison with previous models of lower density, we show that the period distribution of black hole binaries formed through dynamical interactions in this high-density model favours the production of gravitational wave sources. We confirm that the number of black holes remaining in a star cluster at late times and the characteristics of the binary black hole population depend on the nature of the star cluster, critically on the number density of stars and by extension the relaxation timescale.

Black hole binaries in galactic nuclei and gravitational wave sources

Stellar black hole (BH) binaries are one of the most promising gravitational wave (GW) sources for GW detection by the ground-based detectors. Nuclear star clusters (NCs) located at the centre of galaxies are known to harbour massive black holes (MBHs) and to be bounded by a gravitational potential by other galactic components such as the galactic bulge. Such an environment of NCs provides a favourable conditions for the BH–BH binary formation by the gravitational radiation capture due to the high BH number density and velocity dispersion. We carried out detailed numerical study of the formation of BH binaries in the NCs using a series of N-body simulations for equal-mass cases. There is no mass segregation introduced. We have derived scaling relations of the binary formation rate with the velocity dispersion of the stellar system beyond the radius of influence and made estimates of the rate of formation of BH binaries per unit comoving volume and thus expected detection rate by integrating the binary formation rate over galaxy population within the detection distance of the advanced detectors. We find that the overall formation rates for BH–BH binaries per NC is ∼10−10 yr−1 for the Milky Way-like galaxies and weakly dependent on the mass of MBH as Γ ∝ |$M_{\rm MBH}^{3/28}$|⁠. We estimate the detection rate of 0.02–14 yr−1 for advanced LIGO/Virgo considering several factors such as the dynamical evolution of NCs, the variance of the number density of stars and the mass range of MBH giving uncertainties.

THE STRUCTURAL EVOLUTION OF FORMING AND EARLY STAGE STAR CLUSTERS

We study the degree of angular substructure in the stellar position distribution of young members of Galactic star-forming regions, looking for correlations with distance from cluster center, surface number density of stars, and local dynamical age. To this end we adopt the catalog of members in 18 young ($\sim$1-3 Myr) clusters from the Massive Young Star-Forming Complex Study in Infrared and X-ray (MYStIX) Survey and the statistical analysis of the Angular Dispersion Parameter, $\delta_{\rm ADP}$. We find statistically significant correlation between $\delta_{\rm ADP}$ and physical projected distance from the center of the clusters, with the centers appearing smoother than the outskirts, consistent with more rapid dynamical processing on local dynamical, free-fall or orbital timescales. Similarly, smoother distributions are seen in regions of higher surface density, or older dynamical ages. These results indicate that dynamical processing that erases substructure is already well-advanced in young, sometimes still-forming, clusters. Such observations of the dissipation of substructure have the potential to constrain theoretical models of the dynamical evolution of young and forming clusters.

On the dark matter profile in Sculptor: breaking the β degeneracy with Virial shape parameters

We present a new method for studying tracers in gravitational systems where higher moments of the line-of-sight velocity distribution are introduced via Virial equations rather than the Jeans equations. Unlike the fourth order Jeans equations, the fourth order Virial equations can simply be added to the standard second order Jeans equation without introducing a new anisotropy parameter $\beta^{\prime}$. We introduce two new global shape parameters $\zeta_A$ and $\zeta_B$ which replace the kurtosis as a more statistically robust measure of the shape of the line of sight velocity distribution. We show that in the case of stars in dwarf spheroidal galaxies these new parameters can significantly reduce the range of density profiles that are otherwise consistent with the observed stellar kinematics (a problem sometimes known as the $\beta$ degeneracy). Specifically, we find that $\zeta_A$ focuses tightly on a subset of solutions where cusped density profiles are degenerate with more concentrated cored dark matter halos. If the number density of stars $\nu(r)$ is fixed, then introducing $\zeta_B$ can further reduce the space of solutions by constraining the outer slope of the dark matter density profile. Assuming a Plummer profile for $\nu(r)$ we recover the surprising result that the dark matter in Sculptor may be cuspy after all, in contrast to the conclusions of other approaches.

Stellar haloes in Milky Way mass galaxies: from the inner to the outer haloes

We present a comprehensive study of the chemical properties of the stellar haloes of Milky-Way mass galaxies, analysing the transition between the inner to the outer haloes. We find the transition radius between the relative dominance of the inner-halo and outer-halo stellar populations to be ~15-20 kpc for most of our haloes, similar to that inferred for the Milky Way from recent observations. While the number density of stars in the simulated inner-halo populations decreases rapidly with distance, the outer-halo populations contribute about 20-40 per cent in the fiducial solar neighborhood, in particular at the lowest metallicities. We have determined [Fe/H] profiles for our simulated haloes; they exhibit flat or mild gradients, in the range [-0.002, -0.01 ] dex/kpc. The metallicity distribution functions exhibit different features, reflecting the different assembly history of the individual stellar haloes. We find that stellar haloes formed with larger contributions from massive subgalactic systems have steeper metallicity gradients. Very metal-poor stars are mainly contributed to the halo systems by lower-mass satellites. There is a clear trend among the predicted metallicity distribution functions that a higher fraction of low-metallicity stars are found with increasing radius. These properties are consistent with the range of behaviours observed for stellar haloes of nearby galaxies.