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One of the main assumptions used in Chapter 1 is that the dynamical model is deterministic. This assumption can be too optimistic for celestial bodies small enough to be significantly affected by complex non-gravitational interactions. Both drag and radiation pressure can be so poorly known that the errors in the dynamical model can affect the predictions by amounts exceeding, by orders of magnitude, the measurement accuracy.
When this is the case, there are three possible ways out, including the multi-arc strategy presented in this chapter. The others are the use of on-board accelerometers, see Chapters 16, 17, and the empirical parameterization of the unknown effects, see Section 14.5.
The multi-arc approach gives up the attempt to model the orbit of the spacecraft, over the entire time span of the observations, in a deterministic way with a single set of initial conditions. The time span of the observations is decomposed into shorter intervals and the set of observations belonging to each interval is called an observed arc, or just an arc. Each arc has its own set of initial conditions, as if there were a new spacecraft for each one of them. This results in over-parameterization, with the additional initial conditions absorbing the dynamical model uncertainties. Other parameters, e.g., in the dynamic model, can also be local to a single arc.
The identification problem is the attempt to find, among independent detections of celestial bodies, those belonging to the same physical object. The problem becomes more difficult as the population of observed objects increases (see Chapter 11). This chapter is based on (Milani 1999, Milani et al. 2000a, Milani et al. 2001a) and ongoing research. The main example is the population of small Solar System bodies. Most of the observable ones are asteroids, although the observed population contains a smaller fraction of comets and others. We will use the word asteroid in the following discussion, although it applies also to the other populations.
An asteroid is typically observed only over a time span of a few hours to a few weeks, and is bright enough to be visible only over the apparition, a time interval spanning at most a few months. If this time span is not exploited in full, the single apparition orbit determination either is impossible or results in a rapidly growing prediction uncertainty: by the time of the next apparition the asteroid could be in a portion of the sky larger than the field of view of the telescopes available for the recovery. Thus we have a lost asteroid, that is, it is more likely to be rediscovered by chance than by looking at the predicted position. The databases of detected Solar System objects contain many single apparition arcs: the goal is to join together those of the same object, allowing for an accurate orbit determination.
This book is a tool for our own teaching and an opportunity to rethink and reorganize the results of our own research. However, I think such a book can be useful to others, for two main reasons. First, spaceflight is no longer the privilege of the few superpowers, but is becoming available to many nations and agencies. Orbit determination is an essential knowhow, both in the planning phase of mission analysis and in the operations of space missions. Thus its mathematical tools need to become widely available.
Second, the knowledge and skill used in orbit determination, for both natural and artificial celestial bodies, was available only among a restricted group of specialists. The prevailing attitude was a proprietary one: the knowledge and the software were protected by formal copyright and/or by secrecy, although protecting in this way the pure mathematical theory is, in the long run, impossible. This attitude might have been justified under the conditions of the world of 30–40 years ago, in the critical phases of the competition to achieve space firsts. Now it is time to teach and disseminate this knowledge, allowing the formation of a wider group of specialists.
I know that many of the rules of thumb and practical advice contained in this book will be rated as well known, even obvious, by the few experts, but this is not the point. Even well-known results may need to be presented in a rational, rigorous, and didactically effective new way, together with the outcome of recent innovative research.
Nonrotating stars that end their lives with masses 140 M⊙ ≤ M* ≤ 260 M⊙ should explode as pair-production supernovae (PPSNe). Here I review the physical properties of these objects, as well as the prospects for them to be observationally constrained.
In very massive stars, much of the pressure support comes from the radiation field, meaning that they are loosely bound, and that (d lgp/d lg Ρ)adiabatic near the center is close to the minimum value necessary for stability. Near the end of C/O burning, the central temperature increases to the point that photons begin to be converted into electron–positron pairs, softening the equation of state below this critical value. The result is a runaway collapse, followed by explosive burning that completely obliterates the loosely bound star. While these explosions can be up to 100 times more energetic than core collapse and Type Ia supernovae, their peak luminosities are only slightly greater. However, due both to copious Ni56 production and hydrogen recombination, they are brighter much longer, and remain observable for ≈1 year.
Since metal enrichment is a local process, PPSNe should occur in pockets of metal-free gas over a broad range of redshifts, greatly enhancing their detectability, and distributing their nucleosynthetic products about the Milky Way. This means that measurements of the abundances of metal-free stars should be thought of as directly constraining these objects.
By
Rolf. P. Kudritzki, Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA,
Miguel. A. Urbaneja, Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
Edited by
Mario Livio, Space Telescope Science Institute, Baltimore,Eva Villaver, Space Telescope Science Institute, Baltimore
In recent years a new generation of model atmosphere codes, which include the effects of metal line blanketing of millions of spectral lines in NLTE, has been used to re-determine the properties of massive stars through quantitative spectral analysis methods applied to optical, IR and UV spectra. This has resulted in a significant change of the effective temperature scale of early-type stars and a revision of mass-loss rates. Observed mass-loss rates and effective temperatures depend strongly on metallicity, both in agreement with theoretical predictions. The new model atmospheres, in conjunction with the new generation of 10-m-class telescopes equipped with efficient multi-object spectrographs, have made it possible to study blue supergiants in galaxies far beyond the Local Group in spectroscopic detail to determine accurate chemical composition, extinction and distances. A new distance determination method, the flux-weighted gravity–luminosity relationship, is discussed as a very promising complement to existing stellar distance indicators.
Observationally, there are still fundamental uncertainties in the determination of stellar mass-loss rates, which are caused by evidence that the winds are inhomogeneous and clumped. This may lead to major revisions of the observed rates of mass loss.
Introduction
Hot massive stars are cosmic engines of fundamental importance, not only in the local, but also in the early universe. A first generation of very massive stars has very likely influenced the formation and evolution of the first building blocks of galaxies.
The Galactic center is a hotbed of star-formation activity, containing the most massive-star-formation site and three of the most massive young star clusters in the Galaxy. Given such a rich environment, it contains more stars with initial masses above 100 M⊙ than anywhere else in the Galaxy. This review concerns the young stellar population in the Galactic center as it relates to massive-star formation in the region. The sample includes stars in the three massive stellar clusters, the population of younger stars in the present sites of star formation, the stars surrounding the central black hole, and the bulk of the stars in the field population. The fossil record in the Galactic center suggests that the recently formed massive stars there are present-day examples of similar populations that must have been formed through star-formation episodes stretching back to the time period when the Galaxy was forming.
Introduction
The Galactic center (GC) is an exceptional region for testing massive-star formation and evolution models. It contains 10% of the present star-formation activity in the Galaxy, yet fills only a tiny fraction of a percent of the volume in the Galactic disk. The initial conditions for star formation in the GC are unique in the Galaxy. The molecular clouds in the region are extraordinarily-dense, are under high thermal pressure, and are subject to a strong gravitational tidal field.
High-mass stars form in deeply embedded cores with very high visual extinction. Such star-forming regions are typically located at distances > 1 kpc from the Sun. Radio interferometric observations are hence vital for studying such regions at spatial resolutions of < 1000 AU. I will review radio observations of high-mass young stellar objects in our Galaxy, with emphasis on recent results from the Submillimeter Array. There now exists a large sample of sources which represent the earliest stages of high-mass star formation. Radio observations of these sources in dust continuum and molecular line emission have shown that they share many characteristics with low-mass star formation. Stars with masses up to ∼20 M⊙ may form via the disk-accretion mechanism instead of merging of lower-mass stars. Several questions regarding masses and stability of such disks still remain outstanding, such as driving mechanisms of the outflows, and multiplicity of sources. Detailed observations of higher-mass stars, which are at > 2 kpc, will be possible with the next generation of radio interferometers, such as the Atacama Large Millimeter Array, which will help address these questions.
Introduction
Massive stars are important due to their role in the creation of heavy nuclei and the chemical enrichment of our Galaxy, and their dynamical effects on the surrounding interstellar medium via stellar winds, photoionization and supernovae shocks, which could even trigger further star formation (Patel et al. 1998).
The sequence of massive-star supernova types IIP (plateau light curve), IIL (linear light curve), IIb, IIn (narrow line), Ib, and Ic roughly represents a sequence of increasing mass loss during the stellar evolution. The mass loss affects the velocity distribution of the ejecta composition; in particular, only the IIP's typically end up with H moving at low velocity. Radio and x-ray observations of extragalactic supernovae show varying mass-loss properties that are in line with expectations for the progenitor stars. For young supernova remnants, pulsar wind nebulae and circumstellar interaction provide probes of the inner ejecta and higher velocity ejecta, respectively. Among the young remnants, there is evidence for supernovae over a range of types, including those that exploded with much of the H envelope present (Crab Nebula, 3C 58, 0540–69) and those that exploded after having lost most of their H envelope (Cas A, G292.0+1.8).
Introduction: Core-collapse supernovae
Core-collapse supernovae show considerable diversity among their properties. A basic observational division is into the SNe II (Type II supernovae), which have hydrogen in their spectra, and SNe Ib/c, which do not (or have weak hydrogen lines). The reason for the difference is that the progenitors of the SN Ib/c have lost their H envelopes, and perhaps more, during their evolution leading up to the supernova.
The non-gravitational perturbations arise because outer space is not empty. First, planetary atmospheres extend to large altitudes, where they can be thin enough to allow for a satellite orbit but still generate a significant aerodynamic drag, given the high relative velocity of the spacecraft. As will be discussed in Chapter 16, there is interest in satellites orbiting as low as possible to determine high-order harmonics of the planetary gravity field. This may require propulsion to compensate for orbital decay and/or the use of on-board accelerometers to measure the amount of drag; that is, non-gravitational perturbations are critical in the design phase of the mission.
Second, outer space is pervaded by electromagnetic radiation: the light arriving directly from the Sun, reflected by the Earth, and by the other planets. The photons exchange momentum with spacecraft when they are absorbed and reflected; spacecraft themselves emit infrared radiation and electromagnetic waves carrying away some momentum. The resulting accelerations are small, but at the level of accuracy of current tracking systems they are not negligible, hence the need to model and/or measure them. Even small natural bodies, such as asteroids with diameters in the km range, have orbits affected by non-gravitational perturbations in a measurable way.
This chapter cannot be a full revision of the textbook by Milani et al. (1987), which should take into account all the new results accumulated in more than 20 years since its publication.
By
M. S. Oey, Department of Astronomy, 830 Dennison Building, University of Michigan, Ann Arbor, MI 48109-1042, USA,
C. J. Clarke, Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Edited by
Mario Livio, Space Telescope Science Institute, Baltimore,Eva Villaver, Space Telescope Science Institute, Baltimore
Massive stars as a population are the source of various feedback effects that critically impact the evolution of their host galaxies. We examine parameterizations of the high-mass stellar population and self-consistent parameterizations of the resulting feedback effects, including mechanical feedback, radiative feedback, and chemical feedback, as we understand them in the local universe. To date, it appears that the massive-star population follows a simple power-law clustering law that extends down to individual field massive stars, and the robust stellar IMF appears to have a constant upper-mass limit. These properties result in specific patterns in the H II-region luminosity function, and the ionization of the diffuse, warm, ionized medium. The resulting supernovae generate a population of superbubbles whose distributions in size and expansion velocity are also described by simple power laws, and from which a galaxy's porosity parameter is easily derived. A critical star-formation threshold can then be estimated, above which the escape of Lyman-continuum photons, hot gas, and nucleosynthetic products is predicted. A first comparison with a large sample of Hα observations of galaxies is broadly consistent with this prediction, and suggests that ionizing photons are likely to escape from starburst galaxies. The superbubble size distribution also offers a basis for a Simple Inhomogeneous Model for galactic chemical evolution, which is especially applicable to metal-poor systems and instantaneous metallicity distributions. This model offers an alternative interpretation of the Galactic halo metallicity distribution and emphasizes the relative importance of star-formation intensity, in addition to age, in a system's evolution. The fraction of zero-metallicity, Population III stars is easily predicted for any such model. We emphasize that all these phenomena can be modeled in a simple, analytic framework over an extreme range in scale, offering powerful tools for understanding the role of massive stars in the cosmos.