source
stringlengths 1
2.05k
⌀ | target
stringlengths 1
11.7k
|
|---|---|
Dynamical processes which destrov (and equally may create) cluster binaries are density dependent. | Dynamical processes which destroy (and equally may create) cluster binaries are density dependent. |
In. aclelition. the central stellar clensity of a cluster is a funetion of the number. AV. of cluster members. | In addition, the central stellar density of a cluster is a function of the number, $N$, of cluster members. |
Thus. itis not clear (hat (hese prior results apply to globular cluster conditions. | Thus, it is not clear that these prior results apply to globular cluster conditions. |
More recently Ivanova et al. ( | More recently Ivanova et al. ( |
2005) have conducted Monte Carlo simulations of clusters with up to 5xLO? | 2005) have conducted Monte Carlo simulations of clusters with up to $5 \times 10^5$ |
obviously represents a numerical challenge. | obviously represents a numerical challenge. |
An example of accuracy issue is shown in Fig. 4.. | An example of accuracy issue is shown in Fig. \ref{spectraA}. |
Cancelation errors appear when the relative difference of two terms is smaller than the machine precision. | Cancelation errors appear when the relative difference of two terms is smaller than the machine precision. |
Here we focus on computations in double precision, i.e. when reals are coded in 8 octets (64 bits) and their mantissa is coded in 52 bits. | Here we focus on computations in double precision, i.e. when reals are coded in 8 octets (64 bits) and their mantissa is coded in 52 bits. |
The relative error due to machine precision is then of the order of e=2-9?zz107). | The relative error due to machine precision is then of the order of $\epsilon = 2^{-52} \approx 10^{-15}$. |
We have checked the accuracy of the scattered distribution for a large range of photon and lepton energies and identify the domain of the (wo,po) plane where Eq. | We have checked the accuracy of the scattered distribution for a large range of photon and lepton energies and identify the domain of the $(\omega_0,p_0)$ plane where Eq. |
12 gives accurate results. | \ref{Eq1} gives accurate results. |
Results are shown in Fig. 2.. | Results are shown in Fig. \ref{domain}. |
We find that Compton scattering of mildphotons (wo~ 1) by mid-relativistic particles (po~ 1) is well described by this formula but problems arise for lower or higher energies. | We find that Compton scattering of mildphotons $\omega_0\sim1$ ) by mid-relativistic particles $p_0\sim 1$ ) is well described by this formula but problems arise for lower or higher energies. |
In particular, the scattered distribution cannot be evaluated in the most typical astrophysical case, namely the up-scattering of soft photons by high energy particles. | In particular, the scattered distribution cannot be evaluated in the most typical astrophysical case, namely the up-scattering of soft photons by high energy particles. |
In the latter case, Jones(1968) derived asymptotic expansions in wo/o<<1. | In the latter case, \citet{Jones68} derived asymptotic expansions in $\omega_0/\gamma_0<<1$. |
However, a large number of orders must be kept when wo/*oS1 and the numerical evaluation often becomes time consuming. | However, a large number of orders must be kept when $\omega_0/\gamma_0\la1$ and the numerical evaluation often becomes time consuming. |
Moreover, other situations are also affected by numerical issues, for which such an expansion is not relevant. | Moreover, other situations are also affected by numerical issues, for which such an expansion is not relevant. |
Here, we rather concentrate on analytical manipulation of the original formula to get an exact expression free of cancelation issues. | Here, we rather concentrate on analytical manipulation of the original formula to get an exact expression free of cancelation issues. |
Numerical accuracy issues result from two kinds of cancelations: when the relative difference of function F evaluated at the two integration boundaries is very small and when some terms constituting P should cancel out. | Numerical accuracy issues result from two kinds of cancelations: when the relative difference of function $F$ evaluated at the two integration boundaries is very small and when some terms constituting $F$ should cancel out. |
Here we deal with both successively. | Here we deal with both successively. |
This happens typically when z$azzi,b as for example, at thedistribution upper and lower photon energies Win and Wmax where the distribution vanishes, but where P and F? can remain large. | This happens typically when $x_\pm^a\approx x_\pm^b$ , as for example, at thedistribution upper and lower photon energies $\omega_{\rm min}$ and $\omega_{\rm max}$ where the distribution vanishes, but where $F^a$ and $F^b$ can remain large. |
Differences of hyperbolic functions between the upper and lower boundaries can be computed analytically by using the following trigonometric relations: The difference of the two hyperbolic functions between the two integration boundaries a and b simply reads: asinh(AV/A.) if Az>0, or asin(A/—A4) if Ax<0, where Although[p, the last term of Eq. | Differences of hyperbolic functions between the upper and lower boundaries can be computed analytically by using the following trigonometric relations: The difference of the two hyperbolic functions between the two integration boundaries $a$ and $b$ simply reads: ${\rm asinh}(\Delta \sqrt{\lambda_\pm})$ if $\lambda_\pm >0$, or ${\rm asin}(\Delta\sqrt{-\lambda_\pm} )$ if $\lambda_\pm<0$, where Although the last term of Eq. |
12 is not -divergent it is numerically ill-behaved when A_<<1 and it is best to use the following auxiliary function: which is evaluated\” as a series expansion for small argument: Differences of all other terms in Eq. | \ref{Eq1} is not divergent it is numerically ill-behaved when $\lambda_- << 1$ and it is best to use the following auxiliary function: which is evaluated as a series expansion for small argument: Differences of all other terms in Eq. |
12 between the two integration boundaries can also be computed analytically to factorize A and get the following quite simple expression for the scattered distribution: withBudyopo where A4=(1/1+λιΔ2)2 and ze= aha. | \ref{Eq1} between the two integration boundaries can also be computed analytically to factorize $\Delta$ and get the following quite simple expression for the scattered distribution: with where $ A_\pm = (1/z_\pm+\lambda_\pm \Delta^2)^{-1/2} $ and $z_\pm=x_\pm^ax_\pm^b$ . |
The scattered distribution is proportional to A. | The scattered distribution is proportional to $\Delta$. |
This factor holds as the difference between the two integration boundaries a and b and vanishes at the minimal and | This factor holds as the difference between the two integration boundaries $a$ and $b$ and vanishes at the minimal and |
Our chemical models predict the evolution of the He and O enrichment. both by mass. known as AY and AO. as a funetior of time. | Our chemical models predict the evolution of the He and O enrichment, both by mass, known as $\Delta$ and $\Delta$, as a function of time. |
For convenience. and to compare with observations the AY /AO ratio is often used. where AO is equal to and AY is equal to Y—Y,. | For convenience, and to compare with observations the $\Delta$ $\Delta$ ratio is often used, where $\Delta$ is equal to and $\Delta$ is equal to ${\it Y- Y_p}$. |
Here Y, is the primordial He abundance anc amounts to 0.248. the value derived from metal poor irregular galaxies and WMAP (Peimbert et al. | Here ${\it Y_p}$ is the primordial He abundance and amounts to 0.248, the value derived from metal poor irregular galaxies and WMAP (Peimbert et al. |
2007a; Dunkley et al. | 2007a; Dunkley et al. |
2009). | 2009). |
It is well known that AY versus AO mainly depends οἱ the adopted yields and the IMF. | It is well known that $\Delta$ versus $\Delta$ mainly depends on the adopted yields and the IMF. |
Fig. | Fig. |
8 shows the AY vs. AO behavior for our models MAC (solid line. this model reproduces the O/H abundances given by CELs) and MIR (dashed line. reproducing the O/H abundances given by RLs ). | \ref{YvsO} shows the $\Delta$ vs. $\Delta$ behavior for our models M4C (solid line, this model reproduces the O/H abundances given by CELs) and M1R (dashed line, reproducing the O/H abundances given by RLs ). |
Both lines show a similar behavior (same form. different slope) which depends mainly on the history of the mass accretion. the variation of the SFR with time. and on the time delays assigned to the LIMS for their contribution to the chemical enrichment of He. | Both lines show a similar behavior (same form, different slope) which depends mainly on the history of the mass accretion, the variation of the SFR with time, and on the time delays assigned to the LIMS for their contribution to the chemical enrichment of He. |
In Fig. | In Fig. |
8. the initial slope corresponds to the first epochs of the galaxy. where only infall and IRA from MS are the processes controlling the He and O abundances. | \ref{YvsO} the initial slope corresponds to the first epochs of the galaxy, where only infall and IRA from MS are the processes controlling the He and O abundances. |
The sudden discontinuity with a large increase in He. occurs when LIMS start their contribution to the He enrichment of the ISM; these stars mainly produce He but not O. From this point onwards both curves evolve in a continuous increase of He and O. with an almost constant slope. perturbed only by a small loop which occurs when the SFR changes suddenly. in the epoch from 6.3 to 10.5 Gyr (see Fig. | The sudden discontinuity with a large increase in He, occurs when LIMS start their contribution to the He enrichment of the ISM; these stars mainly produce He but not O. From this point onwards both curves evolve in a continuous increase of He and O, with an almost constant slope, perturbed only by a small loop which occurs when the SFR changes suddenly, in the epoch from 6.3 to 10.5 Gyr (see Fig. |
| bottom). | \ref{varfis} bottom). |
At even later times both curves increase with an apparently constant slope. | At even later times both curves increase with an apparently constant slope. |
Interestingly. although the behavior ts similar. both curves showing the same perturbations due to the behavior of the SFR. the slopes are very different. | Interestingly, although the behavior is similar, both curves showing the same perturbations due to the behavior of the SFR, the slopes are very different. |
As expected. the slope is larger for MAC. which has ©, of 40 M... and thus in this model less oxygen is produced. | As expected, the slope is larger for M4C, which has $M_{up}$ of 40 $_\odot$, and thus in this model less oxygen is produced. |
The slope derived for model MAC. considering only the zone from AO>0.5x107. is about 7.2. while for model MIR it is about 3.7. | The slope derived for model M4C, considering only the zone from $\Delta {\it O}
> 0.5 \times 10^{-3}$, is about 7.2, while for model M1R it is about 3.7. |
In Fig. | In Fig. |
8. we also include two observational points. | \ref{YvsO} we also include two observational points. |
The filled square represents the (AY. AO) values derived. from the RLs by Peimbert et al. ( | The filled square represents the $\Delta$, $\Delta$ ) values derived from the RLs by Peimbert et al. ( |
2005) and the CEL (HPCGO09) under the assumption of a constant temperature given by the [Om] CELs. | 2005) and the ] CEL (HPCG09) under the assumption of a constant temperature given by the ] CELs. |
The open square represents the values derived from abundances obtained through and RLs. considering the presence of spatial temperature variations. | The open square represents the values derived from abundances obtained through and RLs, considering the presence of spatial temperature variations. |
It is observed that. in both cases. AO is well fitted because the models were tailored to fit O/H. On the other hand. the observed AY shows huge uncertainties. because it is very difficult to derive à precise value for He abundances due to: 1) the large statistical errors due to the faintness of the lines (represented in the Fig. | It is observed that, in both cases, $\Delta$ is well fitted because the models were tailored to fit O/H. On the other hand, the observed $\Delta$ shows huge uncertainties, because it is very difficult to derive a precise value for He abundances due to: i) the large statistical errors due to the faintness of the lines (represented in the Fig. |
8 by the error bars). and ii) the possible presence of neutral He in the observed regions. that would increase the derived AY value for both determinations. | \ref{YvsO} by the error bars), and ii) the possible presence of neutral He in the observed regions, that would increase the derived $\Delta$ value for both determinations. |
BothY values are derived from RLs. one under the assumption of constant temperature and the other under the assumption of the presence of temperature variations. the second one gives aY value smaller than the primordial value probably indicating the presence of neutral helium inside the observed region. | Both values are derived from RLs, one under the assumption of constant temperature and the other under the assumption of the presence of temperature variations, the second one gives a value smaller than the primordial value probably indicating the presence of neutral helium inside the observed region. |
We can compare also the slopes predicted by our models with observational data in the literature. | We can compare also the slopes predicted by our models with observational data in the literature. |
For instance. Izotov et al. ( | For instance, Izotov et al. ( |
2007) have derived chemical abundances for a large number of galaxies of different metallicities. | 2007) have derived chemical abundances for a large number of galaxies of different metallicities. |
From these data they derived a slope AY/AO = 3.640.7 or 3.3 40.6. depending on the emissivities used. these numbers have not been corrected by the fraction of O atoms trapped in dust grains. | From these data they derived a slope $\Delta$ $\Delta$ = $\pm$ 0.7 or 3.3 $\pm$ 0.6, depending on the emissivities used, these numbers have not been corrected by the fraction of O atoms trapped in dust grains. |
By considering that such dust fraction amounts to 0.08 dex (Peimbert et al. | By considering that such dust fraction amounts to 0.08 dex (Peimbert et al. |
2005) we obtain from Izotov et al. ( | 2005) we obtain from Izotov et al. ( |
2007) | 2007) |
and d quarks of two color are paired in single condensates. while (he ones of the third color and s quarks of all three colors are unpaired. | and $d$ quarks of two color are paired in single condensates, while the ones of the third color and $s$ quarks of all three colors are unpaired. |
In this phase. electrons are present. | In this phase, electrons are present. |
La other words. electrons may be absent in (lie core of strange stars bul present. at least. near the surface where the density is lowest. | In other words, electrons may be absent in the core of strange stars but present, at least, near the surface where the density is lowest. |
Nevertheless. (he presence of CFL effect can reduce the electron density at the surface and hence increases the bremsstrahlung emissivity. | Nevertheless, the presence of CFL effect can reduce the electron density at the surface and hence increases the bremsstrahlung emissivity. |
In conclusion. in (he present paper we have pointed out (vo effects (hat could significantly reduce or even fully suppress the bremsstrahlung radiation [rom the surface of quark stars: (he significant decrease of the intensity due to the multiple collisions in a dense medium aud the absorption bv the outer electron laver of the stars. | In conclusion, in the present paper we have pointed out two effects that could significantly reduce or even fully suppress the bremsstrahlung radiation from the surface of quark stars: the significant decrease of the intensity due to the multiple collisions in a dense medium and the absorption by the outer electron layer of the stars. |
The possible observational significance for the detection of quark stars of these effects will be considered in a future publication. | The possible observational significance for the detection of quark stars of these effects will be considered in a future publication. |
The authors would like to thank to the anonymous referee. whose comments helped (o improve (he manuscript. | The authors would like to thank to the anonymous referee, whose comments helped to improve the manuscript. |
We are grateful for the useful comments of Prof. V. V. Usov. | We are grateful for the useful comments of Prof. V. V. Usov. |
This work is supported by a RGC erant of ILong Ixong Government. | This work is supported by a RGC grant of Hong Kong Government. |
Table 1 lists the differences between LG galaxy model and measured redshifts. Clea. aud distances. AD=Da—Da. | Table 1 lists the differences between LG galaxy model and measured redshifts, $\Delta cz = cz_{\rm mod}-cz_{\rm cat}$ , and distances, $\Delta D = D_{\rm mod}-D_{\rm cat}$. |
Figure 2. shows the distributions of these differences. | Figure \ref{Fig:2} shows the distributions of these differences. |
The model reclshifts of 23 of the 27 galaxies are within the goal of 10 km ! differences from (he catalog redshifts. | The model redshifts of 23 of the 27 galaxies are within the goal of $10$ km $^{-1}$ differences from the catalog redshifts. |
The four exceptions — Cetus. Tucana. DDO 210. and the Sagittarius dwarl irregular have modelredshilts that are too small bv ~30 kms }: they make up the left-hand. tail of the redshift error distribution in Figure 2.. | The four exceptions — Cetus, Tucana, DDO 210, and the Sagittarius dwarf irregular — have modelredshifts that are too small by $\sim 30$ km $^{-1}$; they make up the left-hand tail of the redshift error distribution in Figure \ref{Fig:2}. |
The moclel distances of these four misfit galaxies all are too large. bv να—Peat)/op~© lo 9 (where ap is the catalog distance uncertainty. not the larger allowance in our 47 measure of fit). | The model distances of these four misfit galaxies all are too large, by $(D_{\rm mod}-D_{\rm cat})/\sigma_D\sim 6$ to 9 (where $\sigma_D$ is the catalog distance uncertainty, not the larger allowance in our $\chi^2$ measure of fit). |
These are (he four largest distance discrepancies: (hey dominate the right-hand (ail in the distance error distribution in Figure 2.. | These are the four largest distance discrepancies; they dominate the right-hand tail in the distance error distribution in Figure \ref{Fig:2}. |
The next two greatest discrepancies relative to the catalog errors αλα—Deal/op25 for ICIO and. M33. | The next two greatest discrepancies relative to the catalog errors are $|D_{\rm mod}-D_{\rm cat}|/\sigma_D\simeq 5$ for IC10 and M33. |
The next largest are —4.5 for NGC 185. 3.8 for NGC 3109. and 3.6 for Sextans D. The rest are within three times the catalog uncertainty. | The next largest are $-4.5$ for NGC 185, 3.8 for NGC 3109, and 3.6 for Sextans B. The rest are within three times the catalog uncertainty. |
The offsets D... of the particles [rom the catalog positions (transverse to the line of sight are listed in Table 1. | The offsets $D_\perp$ of the particles from the catalog positions transverse to the line of sight are listed in Table 1. |
The offset of LMC is D.=3 kpc. which seems acceptable. and the rest are well within what seemed to be optimistic goals when the computation was planned. | The offset of LMC is $D_\perp=3$ kpc, which seems acceptable, and the rest are well within what seemed to be optimistic goals when the computation was planned. |
The last column in Table 1 is the velocities of the LG galaxies al 1+2;= 10. | The last column in Table 1 is the velocities of the LG galaxies at $1+z_i=10$ . |
Thev are comparable to reasonable-looking escape velocities [rom small galaxies. and arguably in line | They are comparable to reasonable-looking escape velocities from small galaxies, and arguably in line |
asviuuuetries of significantly higher mode than /=1 or 9 | asymmetries of significantly higher mode than $l=1$ or 2. |
The code (7?) was used to follow shock xopagation and mining iu the models in two cinensious. | The code \citep{Fryxell:2000} was used to follow shock propagation and mixing in the models in two dimensions. |
This code has been extensively verified aud tested (27).. | This code has been extensively verified and tested \citep{Calder:2002,Weirs:2005}. |
is an adaptive mesh refinement code based on an Eulerian unplemeutation of the Piecewise Parabolic Method (PPM) of ?.. | is an adaptive mesh refinement code based on an Eulerian implementation of the Piecewise Parabolic Method (PPM) of \citet{Colella&Woodward:1984}. |
The code can be configured in a imiuber of differcut wavs. | The code can be configured in a number of different ways. |
We used the TLLE Bieiuaun solver to resolve shocks. | We used the HLLE Riemann solver to resolve shocks. |
uses 19 differcut isotopes o evolve stellar models through stable stages of nuclear nurnnug. | uses 19 different isotopes to evolve stellar models through stable stages of nuclear burning. |
We use the "aprox19" composition nodule iucluded. with the FLASH22.5 distribution to map these isotopes directly toFLASH. | We use the “aprox19” composition module included with the 2.5 distribution to map these isotopes directly to. |
. The abundances of 19 different isotopes. from ΤΠ to 79Ni. are stored for each grid cell. | The abundances of 19 different isotopes, from $^1$ H to $^{56}$ Ni, are stored for each grid cell. |
Explosive nuclear burning could have oen followed in using this network. but the ring was over bv the time the models were mapped iutoFLASH. | Explosive nuclear burning could have been followed in using this network, but the burning was over by the time the models were mapped into. |
. Mappiug the star in at earlier times to ollow the explosive burning in two dimensions would jiwe had little effect. as no departure from spherical sviunietry is expected until the formation of the reverse shock. which occurs much later im the calculation. | Mapping the star in at earlier times to follow the explosive burning in two dimensions would have had little effect, as no departure from spherical symmetry is expected until the formation of the reverse shock, which occurs much later in the calculation. |
was configured to use axisviunietrie coordinates. | was configured to use axisymmetric coordinates. |
The gravitational potential was computed using a nultipole method. to solve Poissou's equation. | The gravitational potential was computed using a multipole method to solve Poisson's equation. |
The mass distribution iu this simulation had only sheht deviations roni spherical svuuuetry. so the additional eravitational orce frou overdensitics in the sinulatious was παπα. | The mass distribution in this simulation had only slight deviations from spherical symmetry, so the additional gravitational force from overdensities in the simulations was small. |
The eravitational potential from the poiut mass at the origin of the exid was added to the potential computed by the uultipole solver at cach time step. | The gravitational potential from the point mass at the origin of the grid was added to the potential computed by the multipole solver at each time step. |
The bydrodvuamiic equations were solved using an explicit. dimensioually-split approach: the lvdrodvuamic equations were solved first alone one coordinate ericd direction. then the other at cach time step. | The hydrodynamic equations were solved using an explicit, dimensionally-split approach: the hydrodynamic equations were solved first along one coordinate grid direction, then the other at each time step. |
Au equation of state was eiiploved. that assiuned full ionization and included contributions from radiation aud ideal σας pressure: where P is the pressure. o is the radiatiouconstant. Ap is Doltziuaun's coustaut. T is the temperature. pis the deusity. a, is the proto dass. jf is tle mean molecular weight. aud E is the energy. | An equation of state was employed that assumed full ionization and included contributions from radiation and ideal gas pressure: where $P$ is the pressure, $a$ is the radiationconstant, $k_{B}$ is Boltzmann's constant, $T$ is the temperature, $\rho$is the density, $m_p$ is the proton mass, $\mu$ is the mean molecular weight, and $E$ is the energy. |
Although the outer regions of the reiiunanut may not alwavs be fully ionized. the reeious where BRavleigh-Taxlor mixing takes place are. | Although the outer regions of the remnant may not always be fully ionized, the regions where Rayleigh-Taylor mixing takes place are. |
Exploratory simulations performed ia one diuceusiou witi using a Παuholtz equatio1 of state were ideitical to one-dimeusioial sinulatious performed with the perfect gas and raclation equatiolji of state used iu he simulations preseited in this payer. | Exploratory simulations performed in one dimension with using a Helmholtz equation of state were identical to one-dimensional simulations performed with the perfect gas and radiation equation of state used in the simulations presented in this paper. |
These one-diuiensional simmlations were ouly run to 2.104 seconds. | These one-dimensional simulations were only run to $2 \times
10^4$ seconds. |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.