stellar evolution

We have accounted for all of these crite- ria to set up the archive of stellar evolution- ary models described in this paper. In the next section we shortly discuss the physical inputs adopted in the model computation; the grid of masses and chemical compositions is dis- cussed in section 3. A presentation of the WEB database interface will close the paper. We re- fer the reader interested in assess the level of agreement between our library and obser- vational constraints to the following papers: Pietrinferni et al. (2004), Salaris et al. (2004), Cassisi et al. (2003) and references therein.

We compare our isochrones with results from a series of widely used stellar evolution databases and perform some empirical tests for the reliability of our models. Since this work is devoted to scaled solar chemical compositions, we fo- cus our attention on the Galactic disk stellar populations, employing multicolor photometry of unevolved field main sequence stars with precise Hipparcos par- allaxes, well-studied open clusters and one eclipsing binary system with precise measurements of masses, radii and [Fe/H] of both components. We find that the predicted metallicity dependence of the location of the lower, unevolved main sequence in the Color Magnitude Diagram (CMD) appears in satisfactory agree- ment with empirical data. When comparing our models with CMDs of selected, well-studied, open clusters, once again we were able to properly match the whole observed evolutionary sequences by assuming cluster distance and reddening es- timates in satisfactory agreement with empirical evaluations of these quantities. In general, models including overshooting during the H-burning phase provide a better match to the observations, at least for ages below ∼ 4 Gyr. At [Fe/H] around solar and higher ages (i.e. smaller convective cores) before the onset of radiative cores, the selected efficiency of core overshooting may be too high in our as well as in various other models in the literature. Since we provide also canonical models, the reader is strongly encouraged to always compare the results from both sets in this critical age range.

We present a large, new set of stellar evolution models and isochrones for an -enhanced metal distribution typical of Galactic halo and bulge stars; it represents a homogeneous extension of our stellar model library for a scaled-solar metal distribution already presented by Pietrinferni et al. The effect of the -element enhancement has been properly taken into account in the nuclear network, opacity, equation of state, and for the first time in the bolometric corrections and color transformations. This allows us to avoid the inconsistent use—common to all -enhanced model libraries currently available—of scaled-solar bolometric corrections and color transformations for -enhanced models and isochrones. We show how bolometric corrections to magnitudes obtained for the U, B portion of stellar spectra for T e A 6500 K are significantly affected by the metal mixture, especially at the higher metallicities. Our models cover

A crucial test for binary evolution scenarios of Han et al. [5, 6] is provided by the comparison with the empirical mass distribution for hot B subdwarfs. Standard measurements of the total mass for sdB stars are relatively rare, and only possible for sdB in binaries with favorable conditions such as eclipses or reflection effects. Fortunately, a fraction of sdB stars exhibit nonradial pulsations, offering the opportunity to use asteroseismology in order to determine the mass of sdB stars that are single or that reside in binaries. The first pulsating sdB star, discovered in 1997 [11], shows short-period (1 − 10 min) variations that are typical of sdB pulsators of the first group, the V361 Hya stars. These pulsations are low-order, low-degree acoustic p-modes. The pulsating sdBs of the second group have long-period (∼ 1 − 4 h) oscillations that correspond to mid/high order, low degree gravity waves (g-modes). The prototype of this class was discovered in 2003 [12], and a dozen is currently being observed from space with the NASA Kepler mission. The first pulsating sdB modeled by asteroseismology was PG 0014+067 in 2001 [13], and since a decade our group has published detailed analyses of 15 pulsating B subdwarfs, including estimates of the masses of these pulsators. Several mass estimates are also available in the literature for sdBs residing in binary systems, from binary light curve modeling combined with accurate spectroscopic measurements. The empirical mass distribution of sdB stars on the basis of this sample is presented in Section 2, as a summary of [14] where all details can be found. Implications for stellar evolution theory on the formation of sdB stars are discussed in Section 3, and finally early conclusions are presented in Section 4.

The theory of stellar structure and evolution is one of the most successful theories of complex astrophysical systems. It incorporates a major fraction of the accumu- lated knowledge of atomic and nuclear physics, as well as the behavior of matter in an extremely wide range of physical conditions, ranging from very diluted perfect gases to nuclear matter at extremely high densities. The outcome of evolutionary calculations consists of an impressive set of rich and detailed predictions, concern- ing the structure, evolution and outcome of stars in the whole range of masses and compositions that Nature has been able to produce. The resulting body of da- ta represents the pedestal upon which rests the theory of stellar populations, its incarnation into synthetic spectral energy distributions, and ultimately their appli- cations to galaxies all the way to the highest redshifts. Much of what we know today of such galaxies, their masses, star formation rates, ages and chemical enrichment, ultimately rests on the results of stellar evolution theory.

We know that planetary systems are just as common around white dwarfs as around main- sequence stars. However, self-consistently linking a planetary system across these two phases of stellar evolution through the violent giant branch poses computational challenges, and previous studies restricted architectures to equal-mass planets. Here, we remove this constraint and perform over 450 numerical integrations over a Hubble time (14 Gyr) of packed planetary systems with unequal-mass planets. We characterize the resulting trends as a function of planet order and mass. We find that intrusive radial incursions in the vicinity of the white dwarf become less likely as the dispersion amongst planet masses increases. The orbital meandering which may sustain a sufficiently dynamic environment around a white dwarf to explain observations is more dependent on the presence of terrestrial-mass planets than any variation in planetary mass. Triggering unpacking or instability during the white dwarf phase is comparably easy for systems of unequal-mass planets and systems of equal-mass planets; instabilities during the giant branch phase remain rare and require fine-tuning of initial conditions. We list the key dynamical features of each simulation individually as a potential guide for upcoming discoveries.

main sequence mass stated in the plot title. Dots (which are green) indicate stable simulations, whereas star symbols indicate unstable simulations. Orange and brown stars respectively represent instability on the main sequence and giant branch phases of stellar evolution. Purple and blue stars represent instability on the white dwarf phase when the white dwarf is respectively younger or older than 100 Myr. Overplotted as solid black lines is the Hill stability limit (equation 1) for the main sequence (upper curve) and white dwarf phase (lower curve). Overplotted as vertical dashed lines are, from left to right, the mean motion commensurabilities 3:2, 5:2 and 2:1. The plots illustrate that despite the stability dependencies on initial parameters, (i) late instability along the white dwarf phase occurs throughout the sampled inclination range, and (ii) the assumption of near-coplanarity would be most adequate as a representation for ensemble global stability studies when the planets are away from strong mean-motion commensurabilities or within the Hill stability semimajor axes ratio limits (but external to global chaos from resonance overlap boundary, here near the 3:2 commensurability).

instability proceeds to allow runaway oxygen and silicon burning of the star’s core in a few seconds, creating a thermonuclear explosion[1]. With more thermal energy released than the stars’ gravitational binding energy, it is completely disrupted; no black hole or other stellar remnant is left behind. A PISN is sometimes called a “hypernova”, a term that used to refer an exceptionally energetic explosion with an inferred energy over 100 SNe. But the observationally inference of such an energy is not necessarily physical, depending on the assumption of the isotropy of the radiation. In addition to the immediate energy release, a large fraction of the star’s core is transformed to 56 Ni, a radioactive isotope which decays with a half-life of 6.1 days into 56 Co, which has a half-life of 77 days, and then further decays to the stable isotope 56 Fe. Thus a PISN may be distinguished from other SNe by its very long duration

In Section (4.2 and 4.3), we have derived the basic evolution equations; Equations ((72), (73), (75), and (76)) from Equations ((51)-(54)) in Section (3.1) that for the numerical results and the corresponding analytic solu- tions for different cases, under certain restrictive approximations. These analytic solutions are a useful reference to compare our numerical results to, since in the limit that the assumptions used to derive the analytic solution are met, the numerical solutions should approach the analytic ones. However, in general, the analytic solutions cannot explain the behavior of a given system accurately and especially when the system evolves rapidly, solv- ing the evolution equations numerically leads to a different outcome than what one would expect analytically. Limitations of the Analytic Solutions

Stars lose energy from the surface (mainly) due to photon emission. The whole star is in thermal equilibrium that is the amount of energy per unit time (luminosity) which exits from a given shell direct outward is equal to the amount of energy which enters in the shell plus the energy possibly produced in the shell itself. The mechanisms of energy production active in stars are: nuclear reactions, thermodynamic transformations of the gas linked to contractions and expansions of stellar regions (the so called “gravitational energy”) and neutrino energy losses. Neutrinos have a mean free path larger than the stellar radius (except the case of very dense stellar nuclei of massive stars at the end of their life) and thus they escape from the stars without interacting with the stellar matter, that is without releasing their energy to the stellar structure.

Figure 5 shows the evolution in the HR diagram of 3 M models computed with a solar chemical composition and a solar-calibrated mixing-length parameter. The rotating model has an initial velocity on the ZAMS of 150 km s − 1 . By comparing models computed without overshooting from the convective core, we note that the inclusion of rotation results in a widening of the main sequence with a significant increase of the stellar luminosity for the rotating model compared to the non-rotating one. In particular, the core helium-burning phase is shifted to higher values of the luminosity when rotational effects are taken into account. These changes are due to rotational mixing, which brings fresh hydrogen fuel into the convective core and transports helium and other H-burning products in the radiative zone.

similar. Between models 1 and 2, however, the neutrino losses begin to have an appreciable effect. The central temperature, instead of continuing to increase as in the earlier sequence, passes through a maximum and decreases thereafter (Figure 2). Figure 3 gives the run of temperature with interior mass for selected models. By model 2 the temperature maximum in the star has shifted from the centre to q = 0.3. Interior to this point there is an inward flow of energy to balance the neutrino energy loss. This situation continues for the remainder of the evolution. The neutrino luminosity at model 2 is still small

At the moment it seems that the short-range forces (of strong as well as weak interaction) are not accidentally discarded from the consideration of the strength of gravitational and electrical interactions. It is possible that the gravitational interaction at short distances between the nucleons is modified into close interaction. However, this point is outside the scope of this paper and will need further in-depth discussion. At the moment, it is only obvious that short-range action does not only stabilize the accumulation of nucleons, but converts them into a new form of matter, transforming the cluster of the nucleons into a single undivided elementary particle, which is no longer a thermodynamic system. Perhaps, understanding the neutron star as the composite elementary particle helps us focus on some problems of fundamental physics. In turn, deepening the foundation of physics will allow us to better understand the existing problems in astronomical sciences. For example, nothing forbids the nuclei of planets, which form magnetic fields around planets, to exist in a degenerate state (the questions of proto-nucleus formation of the planets are still the most poorly worked out elements of the theory of planetary evolution). But this is a complex question, closely intertwined with the general theory of the evolution of the stellar system as a whole, which it is too early to interpret in the proposed angle.

We investigate how different stellar initial mass functions (IMFs) can affect the mass-loss and survival of star clusters. We find that IMFs with radically different low-mass cut-offs (between 0.1 and 2 M ) do not change cluster destruction time-scales as much as might be expected. Unsurprisingly, we find that clusters with more high-mass stars lose relatively more mass through stellar evolution, but the response to this mass-loss is to expand and hence significantly slow their dynamical evolution. We also argue that it is very difficult, if not impossible, to have clusters with different IMFs that are initially ‘the same’, since the mass, radius and relaxation times depend on each other and on the IMF in a complex way. We conclude that changing the IMF to be biased towards more massive stars does speed up mass-loss and dissolution, but that it is not as dramatic as might be thought.

Fig. 1.—Nitrogen abundance (12 log [N/H]) against the projected rotational velocity ( v sin i ) for (a) core hydrogen burning and (b) supergiant objects. Open symbols, radial velocity variables; downward arrows, abundance upper limits; dotted line, LMC baseline nitrogen abundance. The mean uncertainty in the nitrogen abundance is 0.25 dex while that in v sin i is 10%, and these are illustrated. These errors are largely independent of rotational velocity since the systematic uncertainties are comparable to the measurement errors. The bulk of the core hydrogen burning objects occupy a region at low v sin i and show little or modest nitrogen enrichment. The tracks are computed for an initial mass of (a) 13 M , and (b) 19 M , , corresponding to the average mass of our non-supergiant and supergiant stars, respectively, and their rotational velocity has been multiplied by p/4. Although the plot contains stars with a range of masses, comparison of the tracks shown in (a) and (b) show that any mass effect is negligible compared to the abundance uncertainties. In (a) the surface gravity has been used as an indicator of the evolutionary status and the objects (see key) and tracks have been split into red and blue to indicate younger and older stars, respectively. However, this is illustrative only, since the evolutionary status is obviously continuous and not discrete. Gray shading in (a) highlights two groups of stars which remain unexplained by the stellar evolution tracks. In (b) gray shading highlights the apparent division of the supergiants into two distinct groups. The surface gravity estimates of many of the objects in group 3, and the two apparently rapidly rotating unenriched supergiants, are consistent with being in the core hydrogen phase within their uncertainties.

(after nighttime condensation) at an altitude of a few kilome- tres above Sputnik Planitia. This would result in a larger thermal gradient that would be closer to the DO15 profile, but still too far away from it according to GCM models, as discussed previously. In this context, we have tested the REX profiles after modi- fying our ray-tracing procedure to generate new synthetic central flashes. We now account for the fact that the two stellar images that travel along the limb of Pluto probe different density pro- files. To simplify the problem as much as possible, we assume that the stellar images that follow the northern and southern limbs probe an atmosphere that, respectively, has the entry and exit REX density profiles, in conformity with the geometry described in Fig. 6. This is an oversimplified approach as the

tion an OB star can have w.r.t. other OB stars, stellar concentra- tions around an OB star may continue to increase. We find that Tr16 does not follow this trend, which is consistent with what is known about the structure of the Trumpler clusters. Unlike the Tr14 and Tr15 clusters, Tr16 does not have a strong cen- tral concentration but instead is irregularly shaped and heavily sub-structured with multiple sub-clusters (Ascenso et al. 2007, Wang et al. 2011, Wolk et al. 2011). Thus the index values of Tr16 reflect that the OB stars are not clustered together in a sin- gle concentration with a (near) constant degree of clustering, but are instead scattered across a region with local concentrations of stars and a variable degree of association.

One way to study this problem is to directly observe galaxies forming and evolving in the distant Universe. At high redshift ( z > 1), deep near-infrared observations are vital to select galaxies by rest-frame optical light. Selecting high-redshift galaxies using optical imaging will introduce strong biases against dusty galaxies or those with evolved (i.e. passive) stellar populations (e.g. Cowie et al. 1996). It is only recently that deep near-infrared surveys have been conducted with the required depth and area to produce large galaxy samples at high redshift, sufficient to allow accurate determinations of the galaxy stellar mass function while min- imising the influence of cosmic variance. In particular, the UKIDSS Ultra Deep Survey (UDS) (Lawrence et al. 2007, Almaini et al. in prep.) and UltraVISTA (McCracken et al. 2012) are now deep enough to detect typical (i.e. M ∗ ) galax- ies to z ∼ 3, over large volumes of the distant Universe (∼ 100 × 100 projected comoving Mpc at z = 3). Using these surveys, we can directly test model predictions for the build- up of the galaxy populations, rather than inferring their evo- lution by extrapolating back in time. However, each galaxy is only being seen at one point in its life and we cannot infer the full evolutionary history.

SIGMA (Simple Icy Grain Model for Aggregates) relies on effective medium theory to compute refractive indexes from laboratory measurements and Mie theory applied to a distri- bution of hollow spheres (DHS) to mimic non–spherical dust shapes. An important charac- teristic of the DHS method is to reproduce the increased absorption opacity in the Rayleigh regime with respect to pure spherical shape. This emissivity enhancement is at least a fac- tor of 2–3 compared to spherical shape (see Fig. 3, left). Also, the DHS method has been shown to be very effective in reproducing the properties of natural samples of complex parti- cle shapes, including the correct positions of features related to solid-state resonances [17–19, and Fig. 3]. Attached to SIGMA, we also computed a set of dust size distributions representa- tive of dynamical coagulation (see Fig. 3, right). Our goal is to characterize the dust evolution of the size distribution with temperature and density based on coagulation computation as a function of turbulence [20, 21]. SIGMA is able to deal with such size distributions including variable porosity as a function of size.

We wanted the targeted cloud to be nearby and have a large protostellar population so that one can statisti- cally constrain protostellar evolution, but not so large of a sample that a survey is impractical for the SMA (e.g., Orion). The Perseus molecular cloud has over 70 protostellar objects, ranging from candidate first hydro- static cores that have just formed central, hydrostatic objects, all the way to evolved Class I systems near the end of the protostellar stage. For star-forming clouds within ∼350 pc, Perseus (and possibly Aquila; distance to cloud is uncertain) is the only star-forming cloud with more than 40 protostellar objects (Dunham et al. 2015). At DEC = +31 ◦ , Perseus is ideally located in the sky for maximum SMA visibility and can be targeted by most telescopes in the world. Aquila, on the other hand, has a declination near 0 ◦ , which causes difficulty in attaining sufficient SMA uv coverage to produce high fidelity maps with the SMA. As one of the best-studied sites of nearby star formation, copious complementary data is available for Perseus to aid with analysis, including single-dish imaging at mid-IR (Spitzer), far-IR (Herschel), and (sub)mm (James Clerk Maxwell Telescope, Caltech Sub- millimeter Observatory; JCMT, CSO) wavelengths (e.g, Hatchell et al. 2005; Jørgensen et al. 2006; Kirk et al. 2006; Enoch et al. 2006; Evans et al. 2009; Sadavoy et al. 2014; Dunham et al. 2015; Chen et al. 2016; Zari et al. 2016). Finally, the VANDAM Perseus survey had al- ready observed the same targets to reveal multiplicity down to a projected separation of 15 au (Tobin et al. 2016). The synergy between connecting the physical and kinematic properties of the dense gas and dust re- vealed by the SMA and the multiplicity revealed by the VLA is one of the key strengths of this survey.