Rm Cl Research Articles

The formation of globular clusters with top-heavy initial mass functions

ABSTRACT We study the formation of globular clusters (GCs) in massive compact clouds with the low metallicity of Z = 10−3 Z⊙ by performing three-dimensional radiative-hydrodynamic simulations. Considering the uncertainty of the initial mass function (IMF) of stars formed in low-metallicity and high-density clouds, we investigate the impacts of the IMF on the cloud condition for the GC formation with the range of the power-law index of IMF as γ = 1−2.35. We find that the threshold surface density (Σthr) for the GC formation increases from 800 M⊙ pc−2 at γ = 2.35 to 1600 M⊙ pc−2 at γ = 1.5 in the cases of clouds with Mcl = 106 M⊙ because the emissivity of ionizing photons per stellar mass increases as γ decreases. For γ < 1.5, Σthr saturates with ∼2000 M⊙ pc−2 that is quite rare and observed only in local starburst galaxies due to e.g. merger processes. Thus, we suggest that formation sites of low-metallicity GCs could be limited only in the very high-surface density regions. We also find that Σthr can be modelled by a power-law function with the cloud mass (Mcl) and the emissivity of ionizing photons (s*) as $\propto M_{\rm cl}^{-1/5} s_{*}^{2/5}$. Based on the relation between the power-law slope of IMF and Σthr, future observations with e.g. the JWST can allow us to constrain the IMF of GCs.

The common division topology on $\mathbb{N}$

A topological space $X$ is totally Brown if for each $n \in \mathbb{N} \setminus \{1\}$ and every nonempty open subsets $U_1,U_2,\ldots,U_n$ of $X$ we have ${\rm cl}_X(U_1) \cap {\rm cl}_X(U_2) \cap \cdots \cap{\rm cl}_X(U_n) \ne \emptyset$. Totally Brown spaces are connected. In this paper we consider a topology $\tau_S$ on the set $\mathbb{N}$ of natural numbers. We then present properties of the topological space $(\mathbb{N},\tau_S)$, some of them involve the closure of a set with respect to this topology, while others describe subsets which are either totally Brown or totally separated. Our theorems generalize results proved by P. Szczuka in 2013, 2014, 2016 and by P. Szyszkowska and M. Szyszkowski in 2018.

APPROXIMATION SPACES VIA IDEALS AND GRILLS

In this paper, we use the notions of lower set $L_{R}(A)$ and the upper set $U_{R}(A)$ to define the interior operator ${\rm int}_{R}^{A}$ and the closure operator ${\rm cl}_{R}^{A}$ associated with a set $A$ in an approximation space $(X,R)$. These operators generate an approximation topological space different from the generated Nano topological space in $(X,R)$. Ideal approximation spaces $(X,R, \ell)$ based on an ideal $\ell$ joined to the approximation space $(X,R)$ are introduced as well. The approximation continuity and the ideal approximation continuity are defined. The lower separation axioms $T_{i}, i= 0,1,2$ are introduced in the approximation spaces and also in the ideal approximation spaces. Examples are given to explain the definitions. Connectedness in approximation spaces and ideal connectedness are introduced and the differences between them are explained. The interior and the closure operators are deduced using a grill ${\cal G}$ defined on $(X,R)$, yielding the same results.

Origin of ferromagnetic interactions in NaMnCl3 : How the response theory reconciles with Goodenough-Kanamori-Anderson rules

The on-site Coulomb repulsion $U$ is the key ingredient for describing the magnetic properties of Mott insulators, leading to a popular believe that many limitations of the density-functional theory based methods can be cured by artificially incorporating such on-site interactions for localized electrons in the model form. The layered antiferromagnet NaMnCl$_3$ reveals quite a different story: while the Coulomb $U$ on the Mn sites controls the strength of antiferromagnetic superexchange interactions, an equally important parameter is the Stoner coupling ${\cal I}_{\rm Cl}$ on the ligand sites. The latter is responsible for large ferromagnetic contributions to the interatomic exchange interactions, which in NaMnCl$_3$ nearly cancel the effect of the superexchange interactions. Although such behavior is anticipated from the phenomenological Goodenough-Kamanori-Anderson rules, the quantitative description of the ligand-related contributions remains disputable. Considering NaMnCl$_3$ as an example, we discuss how they can be generally taken into account in the linear response theory to regain the dependence of the exchange interactions on ${\cal I}_{\rm Cl}$. The problem is complicated by the fact that, for the nearly filled Cl $3p$ shell, the parameters ${\cal I}_{\rm Cl}$ are sensitive to the model assumptions.

Asymmetrical tidal tails of open star clusters: stars crossing their cluster’s práh† challenge Newtonian gravitation

ABSTRACT After their birth a significant fraction of all stars pass through the tidal threshold (práh) of their cluster of origin into the classical tidal tails. The asymmetry between the number of stars in the leading and trailing tails tests gravitational theory. All five open clusters with tail data (Hyades, Praesepe, Coma Berenices, COIN-Gaia 13, NGC 752) have visibly more stars within $d_{\rm cl}\approx 50\,{\rm pc}$ of their centre in their leading than their trailing tail. Using the Jerabkova-compact-convergent-point (CCP) method, the extended tails have been mapped out for four nearby 600–2000 Myr old open clusters to $d_{\rm cl} > 50\,{\rm pc}$. These are on near-circular Galactocentric orbits, a formula for estimating the orbital eccentricity of an open cluster being derived. Applying the Phantom of Ramses code to this problem in Newtonian gravitation the tails are near-symmetrical. In Milgromian dynamics (MOND), the asymmetry reaches the observed values for 50 < dcl/pc < 200 being maximal near peri-galacticon, and can slightly invert near apo-galacticon, and the Küpper epicyclic overdensities are asymmetrically spaced. Clusters on circular orbits develop orbital eccentricity due to the asymmetrical spill-out, therewith spinning up opposite to their orbital angular momentum. This positive dynamical feedback suggests Milgromian open clusters to demise rapidly as their orbital eccentricity keeps increasing. Future work is necessary to better delineate the tidal tails around open clusters of different ages and to develop a Milgromian direct n-body code.

Far and extreme UV radiation feedback in molecular clouds and its influence on the mass and size of star clusters

ABSTRACT We study the formation of star clusters in molecular clouds by performing three-dimensional radiation hydrodynamics simulations with far-ultraviolet (FUV; 6 eV≦hν≦13.6 eV) and extreme ultraviolet (EUV; hν≧13.6 eV) radiative feedback. We find that the FUV feedback significantly suppresses the star formation in diffuse clouds with the initial surface densities of $\Sigma _{\rm cl} \lesssim \rm 50~M_{\odot } \,\, pc^{-2}$. In the cases of clouds with $\Sigma _{\rm cl} \sim \rm 100-200~M_{\odot } \,\, pc^{-2}$, the EUV feedback plays a main role and decrease the star formation efficiencies less than 0.3. We show that thermal pressure from photodissociation regions or H ii regions disrupts the clouds and makes the size of the star clusters larger. Consequently, the clouds with the mass $M_{\rm cl} \lesssim 10^{5}~\rm M_{\odot }$ and the surface density $\Sigma _{\rm cl} \lesssim 200~\rm M_{\odot }\,\, pc^{-2}$ remain the star clusters with the stellar densities of $\sim 100~\rm M_{\odot }\,\, pc^{-3}$ that nicely match the observed open clusters in the Milky Way. If the molecular clouds are massive ($M_{\rm cl} \gtrsim 10^{5}~\rm M_{\odot }$) and compact ($\Sigma \gtrsim 400~\rm M_{\odot }\,\, pc^{-2}$), the radiative feedback is not effective and they form massive dense cluster with the stellar densities of $\sim 10^{4}~\rm M_{\odot }\,\, pc^{-3}$ like observed globular clusters or young massive star clusters. Thus, we suggest that the radiative feedback and the initial conditions of molecular clouds are key factors inducing the variety of the observed star clusters.

Radiation hydrodynamics simulations of massive star cluster formation in giant molecular clouds

ABSTRACT By performing 3D radiation hydrodynamics simulations, we study the formation of young massive star clusters (YMCs; M* > 104 M⊙) in clouds with the surface density ranging from Σcl = 80 to 3200 M⊙ pc−2. We find that photoionization feedback suppresses star formation significantly in clouds with low-surface density. Once the initial surface density exceeds ∼100 M⊙ pc−2 for clouds with Mcl = 106 M⊙ and Z = Z⊙, most of the gas is converted into stars because the photoionization feedback is inefficient in deep gravitational potential. In this case, the star clusters are massive and gravitationally bounded as YMCs. The transition surface density increases as metallicity decreases, and it is ∼350 M⊙ pc−2 for Z = 10−2 Z⊙. We show that more than 10 per cent of star formation efficiency (SFE) is needed to keep a star cluster gravitationally bounded even after the disruption of a cloud. Also, we develop a semi-analytical model reproducing the SFEs obtained in our simulations. We find that the SFEs are fit with a power-law function with the dependence ${\propto}\Sigma _{\rm cl}^{1/2}$ for low-surface density and rapidly increases at the transition surface densities. The conditions of the surface density and the metallicity match recent observations of giant molecular clouds forming YMCs in nearby galaxies.

The mass budget for intermediate-mass black holes in dense star clusters

ABSTRACT Intermediate-mass black holes (IMBHs) could form via runaway merging of massive stars in a young massive star cluster (YMC). We combine a suite of numerical simulations of YMC formation with a semi-analytic model for dynamical friction and merging of massive stars and evolution of a central quasi-star, to predict how final quasi-star and relic IMBH masses scale with cluster properties (and compare with observations). The simulations argue that inner YMC density profiles at formation are steep (approaching isothermal), producing some efficient merging even in clusters with relatively low effective densities, unlike models that assume flat central profiles resembling those of globular clusters after central relaxation. Our results can be approximated by simple analytic scalings, with $M_{\rm IMBH} \propto v_{\rm cl}^{3/2}$ where $v_{\rm cl}^{2} = G\, M_{\rm cl}/r_{\rm h}$ is the circular velocity in terms of initial cluster mass Mcl and half-mass radius rh. While this suggests IMBH formation is possible even in typical clusters, we show that predicted IMBH masses for these systems are small, $\sim \! 100-1000\, {\rm M}_{\odot }$ or $\sim \! 0.0003\, M_{\rm cl}$, below even the most conservative observational upper limits in all known cases. The IMBH mass could reach $\gtrsim 10^{4}\, {\rm M}_{\odot }$ in the centres nuclear star clusters, ultra-compact dwarfs, or compact ellipticals, but in all these cases the prediction remains far below the present observed supermassive BH masses in these systems.

A complete census of circumgalactic Mg ii at redshift z ≲ 0.5

ABSTRACT This paper presents a survey of Mg ii absorbing gas in the vicinity of 380 random galaxies, using 156 background quasi-stellar objects (QSOs) as absorption-line probes. The sample comprises 211 isolated (73 quiescent and 138 star-forming galaxies) and 43 non-isolated galaxies with sensitive constraints for both Mg ii absorption and H α emission. The projected distances span a range from d = 9 to 497 kpc, redshifts of the galaxies range from z = 0.10 to 0.48, and rest-frame absolute B-band magnitudes range from MB = −16.7 to −22.8. Our analysis shows that the rest-frame equivalent width of Mg ii, Wr(2796), depends on halo radius (Rh), B-band luminosity(LB), and stellar mass (Mstar) of the host galaxies, and declines steeply with increasing d for isolated, star-forming galaxies. At the same time, Wr(2796) exhibits no clear trend for either isolated, quiescent galaxies or non-isolated galaxies. In addition, the covering fraction of Mg ii absorbing gas 〈κ〉 is high with 〈κ〉 ≳ 60 per cent at <40 kpc for isolated galaxies and declines rapidly to 〈κ〉 ≈ 0 at d ≳ 100 kpc. Within the gaseous radius, the incidence of Mg ii gas depends sensitively on both Mstar and the specific star formation rate inferred from H α. Different from what is known for massive quiescent haloes, the observed velocity dispersion of Mg ii absorbing gas around star-forming galaxies is consistent with expectations from virial motion, which constrains individual clump mass to $m_{\rm cl} \gtrsim 10^5 \, \rm M_\odot$ and cool gas accretion rate of $\sim 0.7\!-\!2 \, \mathrm{ M}_\odot \, \rm yr^{-1}$. Finally, we find no strong azimuthal dependence of Mg ii absorption for either star-forming or quiescent galaxies. Our results demonstrate that multiple parameters affect the properties of gaseous haloes around galaxies and highlight the need of a homogeneous, absorption-blind sample for establishing a holistic description of chemically enriched gas in the circumgalactic space.

Failed and delayed protostellar outflows with high-mass accretion rates

ABSTRACT The evolution of protostellar outflows is investigated under different mass accretion rates in the range ∼10−5–$10^{-2}\, {\rm M}_\odot$ yr−1 with 3D magnetohydrodynamic simulations. A powerful outflow always appears in strongly magnetized clouds with $B_0 \gtrsim B_{\rm 0, cr}\, =10^{-4} (M_{\rm cl}/100\, {\rm M}_\odot)$ G, where Mcl is the cloud mass. When a cloud has a weaker magnetic field, the outflow does not evolve promptly with a high-mass accretion rate. In some cases with moderate magnetic fields B0 slightly smaller than B0, cr, the outflow growth is suppressed or delayed until the infalling envelope dissipates and the ram pressure around the protostellar system is significantly reduced. In such an environment, the outflow begins to grow and reaches a large distance only during the late accretion phase. On the other hand, the protostellar outflow fails to evolve and is finally collapsed by the strong ram pressure when a massive (≳ 100 M⊙) initial cloud is weakly magnetized with B0 ≲ 100 μG. The failed outflow creates a toroidal structure that is supported by magnetic pressure and encloses the protostar and disc system. Our results indicate that high-mass stars form only in strongly magnetized clouds, if all high-mass protostars possess a clear outflow. If we would observe either very weak or no outflow around evolved protostars, it means that strong magnetic fields are not necessarily required for high-mass star formation. In any case, we can constrain the high-mass star formation process from observations of outflows.

Factories of CO-dark gas: molecular clouds with limited star formation efficiencies by far-ultraviolet feedback

ABSTRACT The star formation in molecular clouds is inefficient. The ionizing extreme-ultraviolet radiation (hν ≥ 13.6 eV) from young clusters has been considered as a primary feedback effect to limit the star formation efficiency (SFE). Here, we focus on the effects of stellar far-ultraviolet (FUV) radiation (6 eV ≤ hν ≤ 13.6 eV) during the cloud disruption stage. The FUV radiation may further reduce the SFE via photoelectric heating, and it also affects the chemical states of the gas that is not converted to stars (‘cloud remnants’) via photodissociation of molecules. We have developed a one-dimensional semi-analytical model that follows the evolution of both the thermal and chemical structure of a photodissociation region (PDR) during the dynamical expansion of an H ii region. We investigate how the FUV feedback limits the SFE, supposing that the star formation is quenched in the PDR where the temperature is above a threshold value (e.g. 100 K). Our model predicts that the FUV feedback contributes to reduce the SFEs for massive (Mcl ≳ 105 M⊙) clouds with low surface densities ($\Sigma _{\rm cl}\lesssim 100~{\rm M}_\odot \, {\rm pc}^{-2}$). Moreover, we show that a large part of the H2 molecular gas contained in the cloud remnants should be ‘CO-dark’ under the FUV feedback for a wide range of cloud properties. Therefore, the dispersed molecular clouds are potential factories of CO-dark gas, which returns into the cycle of the interstellar medium.

Interband cascade laser absorption of hydrogen chloride for high-temperature thermochemical analysis of fire-resistant polymer reactivity.

A mid-infrared absorption spectroscopy technique has been developed to quantitatively and spatially resolve gas temperature and molecular abundance of $ ^1{{\rm H}^{35}}{\rm Cl} $1H35Cl in the high-temperature pyrolysis and oxidation layers of chlorinated polymers. Two transitions in the R-branch of the fundamental vibrational band of HCl near 3.34 µm are selected due to their relative strength and spectral isolation from other combustion products at elevated temperatures, and they are probed using a distributed feedback interband cascade laser. A scanned-wavelength direct absorption method is employed with a Voigt line-fitting routine to recover projected absorbance areas across the exit plane of a cylindrical polymeric slab, wherein the gaseous core comprises the axisymmetric reaction layer. Tikhonov-regularized Abel inversion of the projected absorbance areas yields line-integrated radial absorption coefficients, from which a two-line ratio is used to infer a radially resolved temperature between the gas core and solid polymer surface. The method is demonstrated to provide insights into the gas-phase combustion physics that lead to the formation of toxicants when a fire-resistant polymer, polyvinyl chloride (PVC), is burned in the presence of oxygen. Two-dimensional images were generated by assembling multiple tomographic reconstructions for several cylinder lengths. The quantitative images highlight the technique's ability to characterize the thermochemical evolution and toxicant formation during the burning of a halogenated polymer fuel.

Star cluster formation from turbulent clumps. II. Gradual star cluster formation

We investigate the dynamical evolution of star clusters during their formation, assuming that they are born from a turbulent starless clump of a given mass that is embedded within a parent self-gravitating molecular cloud characterized by a particular mass surface density. In contrast to the standard practice of most $N$-body studies, we do not assume that all stars are formed at once. Rather, we explore the effects of different star formation rates on the global structure and evolution of young embedded star clusters, also considering various primordial binary fractions and mass segregation levels. Our fiducial clumps studied in this paper have initial masses of $M_{\rm cl} = 3000\,M_\odot$, are embedded in ambient cloud environments of $\Sigma_{\rm cloud} = 0.1$ and 1 g cm$^{-2}$, and gradually form stars with an overall efficiency of 50% until the gas is exhausted. We investigate star formation efficiencies per free-fall time in the range $\epsilon_{\rm ff}=0.01$ to 1, and also compare to the instantaneous case ($\epsilon_{\rm ff}=\infty$) of Paper I. We show that most of the interesting dynamical processes that determine the future of the cluster, happen during the early formation phase. In particular, the ejected stellar population is sensitive to the duration of star cluster formation: for example, clusters with longer formation times produce more runaway stars, since these clusters remain in a dense state for longer, thus favouring occurrence of dynamical ejections. We also show that the presence of radial age gradients in star clusters depends sensitively on the star formation efficiency per free fall time, with observed values being matched best by our slowest forming clusters with $\epsilon_{\rm ff}\lesssim0.03$.

FITspec: A New Algorithm for the Automated Fit of Synthetic Stellar Spectra for OB Stars

Abstract In this paper we describe the FITspec code, a data mining tool for the automatic fitting of synthetic stellar spectra. The program uses a database of 27,000 cmfgen models of stellar atmospheres arranged in a six-dimensional (6D) space, where each dimension corresponds to one model parameter. From these models a library of 2,835,000 synthetic spectra were generated covering the ultraviolet, optical, and infrared regions of the electromagnetic spectrum. Using FITspec we adjust the effective temperature and the surface gravity. From the 6D array we also get the luminosity, the metallicity, and three parameters for the stellar wind: the terminal velocity ( ), the β exponent of the velocity law, and the clumping filling factor (F cl). Finally, the projected rotational velocity ( ) can be obtained from the library of stellar spectra. Validation of the algorithm was performed by analyzing the spectra of a sample of eight O-type stars taken from the iacob spectroscopic survey of Northern Galactic OB stars. The spectral lines used for the adjustment of the analyzed stars are reproduced with good accuracy. In particular, the effective temperatures calculated with the FITspec are in good agreement with those derived from spectral type and other calibrations for the same stars. The stellar luminosities and projected rotational velocities are also in good agreement with previous quantitative spectroscopic analyses in the literature. An important advantage of FITspec over traditional codes is that the time required for spectral analyses is reduced from months to a few hours.

Spatially associated clump populations in Rosette from CO and dust maps

Spatial association of clumps from different tracers turns out to be a valuable tool to determine the physical properties of molecular clouds. It provides a reliable estimate for the $X$-factors, serves to trace the density of clumps seen in column densities only and allows to measure the velocity dispersion of clumps identified in dust emission. We study the spatial association between clump populations, extracted by use of the GAUSSCLUMPS technique from $^{12}$CO (1-0), $^{13}$CO (1-0) line maps and Herschel dust-emission maps of the star-forming region Rosette, and analyse their physical properties. All CO clumps that overlap with another CO or dust counterpart are found to be gravitationally bound and located in the massive star-forming filaments of the molecular cloud. They obey a single mass-size relation $M_{\rm cl}\propto R_{\rm cl}^\gamma$ with $\gamma\simeq3$ (implying constant mean density) and display virtually no velocity-size relation. We interpret their population as low-density structures formed through compression by converging flows and still not evolved under the influence of self-gravity. The high-mass parts of their clump mass functions are fitted by a power law ${\rm d}N_{\rm cl}/{\rm d}\,\log M_{\rm cl}\propto M_{\rm cl}^{\Gamma}$ and display a nearly Salpeter slope $\Gamma\sim-1.3$. On the other hand, clumps extracted from the dust-emission map exhibit a shallower mass-size relation with $\gamma=2.5$ and mass functions with very steep slopes $\Gamma\sim-2.3$ even if associated with CO clumps. They trace density peaks of the associated CO clumps at scales of a few tenths of pc where no single density scaling law should be expected.

Characterizing the turbulent porosity of stellar wind structure generated by the line-deshadowing instability

We analyze recent 2D simulations of the nonlinear evolution of the line-deshadowing instability (LDI) in hot-star winds, to quantify how the associated highly clumped density structure can lead to a "turbulent porosity" reduction in continuum absorption and/or scattering. The basic method is to examine the statistical variations of mass column as a function of path length, and fit these to analytic forms that lead to simple statistical scalings for the associated mean extinction. A key result is that one can characterize porosity effects on continuum transport in terms of a single "turbulent porosity length", found here to scale as $H \approx (f_{\rm cl} - 1) a$, where $f_{\rm cl} \equiv \left < \rho^2 \right >/\left < \rho \right >^2$ is the clumping factor in density $\rho$, and $a$ is the density autocorrelation length. For continuum absorption or scattering in an optically thick layer, we find the associated effective reduction in opacity scales as $\sim 1/\sqrt{1+\tau_{\rm H}}$, where $\tau_{\rm H} \equiv \kappa \rho H$ is the local optical thickness of this porosity length. For these LDI simulations, the inferred porosity lengths are small, only about a couple percent of the stellar radius, $H \approx 0.02 R_\ast$. For continuum processes like bound-free absorption of X-rays that are only marginally optically thick throughout the full stellar wind, this implies $\tau_{\rm H} \ll 1$, and thus that LDI-generated porosity should have little effect on X-ray transport in such winds. The formalism developed here could however be important for understanding the porous regulation of continuum-driven, super-Eddington outflows from luminous blue variables.

Optimization and mechanism in preparing active magnesium oxide from magnesite

Active magnesium oxide is an important magnesium product due to its unique properties. Magnesium oxide with high activity was obtained by optimizing the technological parameters including calcination temperature and residence time. Thermal decomposition process, morphology, specific surface area and crystal structure were determined by TG-DSC thermal analyzer, optical and scanning electron microscope, specific area analyzer and X-ray diffractometer, respectively. Results indicate that magnesium oxide products prepared during the early stage are characterized by small particle size, imperfect crystal structure, large specific area and high activity, and as residence time increases, particle size grows up gradually and crystal structure becomes perfect, so activity goes poor. Under conditions of higher calcination temperature, two processes involving decomposition of magnesite and crystallization of magnesium oxide proceed simultaneously, resulting in magnesium oxide with lower activity. Therefore, highly active product with \({\Delta n}_{\rm Cl^-}\)of 40.5 mol kg−1 is prepared at a relatively low temperature of 600 °C for 9 h.

Apples to applesA2– II. Cluster selection functions for next-generation surveys

We present the cluster selection function for three of the largest next-generation stage-IV surveys in the optical and infrared: Euclid-Optimistic, Euclid-Pessimistic and the Large Synoptic Survey Telescope (LSST). To simulate these surveys, we use the realistic mock catalogues introduced in the first paper of this series. We detected galaxy clusters using the Bayesian Cluster Finder (BCF) in the mock catalogues. We then modeled and calibrated the total cluster stellar mass observable-theoretical mass ($M^*_{\rm CL}-M_{\rm h}$) relation using a power law model, including a possible redshift evolution term. We find a moderate scatter of $\sigma_{M^*_{\rm CL} | M_{\rm h}}$ of 0.124, 0.135 and 0.136 $\rm dex$ for Euclid-Optimistic, Euclid-Pessimistic and LSST, respectively, comparable to other work over more limited ranges of redshift. Moreover, the three datasets are consistent with negligible evolution with redshift, in agreement with observational and simulation results in the literature. We find that Euclid-Optimistic will be able to detect clusters with $>80\%$ completeness and purity down to $8\times10^{13} h^{-1} M_{\odot}$ up to $z<1$. At higher redshifts, the same completeness and purity are obtained with the larger mass threshold of $2\times10^{14} h^{-1} M_{\odot}$ up to $z=2$. The Euclid-Pessimistic selection function has a similar shape with $\sim10\%$ higher mass limit. LSST shows $\sim 5\%$ higher mass limit than Euclid-Optimistic up to $z<0.7$ and increases afterwards, reaching values of $2\times10^{14} h^{-1} M_{\odot}$ at $z=1.4$. Similar selection functions with only $80\%$ completeness threshold have been also computed. The complementarity of these results with selection functions for surveys in other bands is discussed.

NUMERICAL SIMULATIONS OF TURBULENT MOLECULAR CLOUDS REGULATED BY RADIATION FEEDBACK FORCES. I. STAR FORMATION RATE AND EFFICIENCY

ABSTRACT Radiation feedback from stellar clusters is expected to play a key role in setting the rate and efficiency of star formation in giant molecular clouds. To investigate how radiation forces influence realistic turbulent systems, we have conducted a series of numerical simulations employing the Hyperion radiation hydrodynamics solver, considering the regime that is optically thick to ultraviolet and optically thin to infrared radiation. Our model clouds cover initial surface densities between , with varying initial turbulence. We follow them through turbulent, self-gravitating collapse, star cluster formation, and cloud dispersal by stellar radiation. All our models display a log-normal distribution of gas surface density Σ; for an initial virial parameter , the log-normal standard deviation is and the star formation rate coefficient , both of which are sensitive to turbulence but not radiation feedback. The net star formation efficiency (SFE) increases with and decreases with . We interpret these results via a simple conceptual framework, whereby steady star formation increases the radiation force, such that local gas patches at successively higher Σ become unbound. Based on this formalism (with fixed ), we provide an analytic upper bound on , which is in good agreement with our numerical results. The final SFE depends on the distribution of Eddington ratios in the cloud and is strongly increased by the turbulent compression of gas.

Gigahertz nanomechanical oscillators based on ions inside cyclic peptide nanotubes: a continuum study

The present work aims to investigate the mechanical oscillatory behavior of ions, and in particular \({{\rm Li}^{+}, {\rm Na}^{+}, {\rm Rb}^{+}}\) and \({{\rm Cl}^{-}}\) ions, inside a cyclo[(–d-Ala–l-Ala)4–] peptide nanotube using the continuum approximation along with the 6–12 Lennard–Jones (LJ) potential function. Assuming that each peptide unit is comprised of an inner and an outer tube, the van der Waals (vdW) potential energy and interaction force between an ion and a cyclic peptide nanotube (CPN) are determined analytically. With respect to the present formulations, a detailed parametric study is conducted on the vdW potential energy and interaction force distributions by varying the number of peptide units. Employing the conservation of mechanical energy principle, a novel expression for precise evaluation of oscillation frequency is introduced. To verify the accuracy of the proposed frequency expression, the results obtained from energy equation are compared with the ones predicted through solving the equation of motion numerically. The effects of number of peptide units and initial conditions including initial separation distance and velocity on the oscillatory behavior of various ions inside CPNs are explored. Among the considered ions, \({{\rm Cl}^{-}}\) ion is found to generate the highest frequency. According to the potential energy profile, one oscillatory zone for one peptide unit and different oscillatory zones for more than one peptide unit are observed. Numerical results indicate that optimal frequency decreases with increasing the number of peptide units and almost remains unchanged when the number of peptide units exceeds four.