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Appendix B Appendix B: An Accreting Black Hole Model The accretion-driven luminosity of a black hole is derived from Einstein’s well-known mass-energy equivalence formula E = M c2, where E is the energy, M is the mass and c is the speed of light. If a quantity of mass M falls into a black hole in timet, liberating energy E, then the accretion luminosity Lacc = E / t will be Lacc = f M t c2 (B.1) where f is an efficiency factor accounting for the conversion of accreted material into energy, and where M / t is the amount of material accreted into the black hole per unit time (i.e., the accretion rate). Now, the maximum accretion rate is typically taken to be that which produces a luminosity Lacc = LEdd, where LEdd is the so-called Eddington luminosity. The Eddington luminosity for an accreting black hole corresponds to the situation in which the radiation pressure on the infalling gas exactly balances the gravitational attraction of the black hole. For a black hole of mass Mbh, accret...

Appendix A The mass-luminosity relationship for a fully mixed, chemically homogeneous Sun-like star was described in Chapter 3. Indeed, Equation (3.12) indicates that the luminosity L is related to the mass M and the chemical composition via the relationship L = L0 75 (1 + X) −1 M5, where L0 = L(X = X0) is a constant, is the mean molecular weight and 0 ≤ X ≤ X0 is the hydrogen mass fraction of the stellar gas. When the mass fraction of the chemical elements other than hydrogen (X) and helium (Y) within a star are small (which corresponds to the condition Z ≈ 0), the expression for the mean molecular weight simplifies1 to (X) ≈ 2(1 + X) −2. With this approximation for the mean molecular weight, the mass-luminosity relationship becomes L X = L0 1+X −16 M5 (A.1) Equation (A.1) determines the luminosity of a fully mixed star of mass M and hydrogen mass fraction X. In order to determine the effect of mass loss upon our model star, we assume that the mass loss rate is proportional to ...

9. Glossary of Terms Astronomical Unit (AU) The semi-major axis of Earth’s orbit around the Sun, corresponding to a distance of about 150 million km. Blackbody radiator An idealized object that radiates electromagnetic energy into space in accordance with Wien’s law and the Stefan-Boltzmann law. Black dwarf A near fully cooled-off white dwarf. Brown dwarf An object with a mass of between ∼0.01 and ∼0.1 M Such objects are not massive enough to initiate hydrogen fusion reactions within their interiors. Chandrsekhar limit The limiting mass for a stable white dwarf star – MWD ≤ 1.4 M The limit is set according to the degenerate electrons acquiring relativistic speeds. CNO cycle The catalytic fusion reaction that enables the conversion of four protons into a helium nucleus with the liberation of energy. The process begins with the reaction 12C+P ⇒ 13C. Croll-Milankovitch cycle Climate changes that are driven in response to small variations in the size, eccentricity, and orientation of...

8 Epilogue Los Alamos Laboratories, New Mexico, 2145. It is lunchtime. Our gaze is directed towards a quiet corner of the otherwise busy refectory hall. “The Time Traveler” (for so it will be convenient to speak of him) was expounding a recondite matter to us.1 “I have seen the desolation that will be wrought upon Earth by the aging Sun.” The response at the table was immediate. A multitude of crop-haired heads turned in unison. Conversations stopped in mid-sentence. The Time Traveler had our attention. “As you all no doubt know,” he continued, “The Osgiliath2 Project unlocked the fundamental secrets of time travel two years back. But just four days ago, by Earth time, I took the very first human journey down a deep-future timeline.” We sat in stunned silence. This was news indeed. Certainly we all knew of the Osgiliath Project, and two Nobel Prizes had come to the laboratory as a result of it. But to actually send a human into the future—that was incredible. The official line was t...

iBook The Future of the Universe - 7. Between Now and Then Predictions concerning the future development of technology have, throughout recorded history, been notoriously poor, and this will probably always be the case. The future cannot be read, but it can be dictated to, and this is humanity’s best hope for longterm survival. Indeed, our actions in the here and now will both influence and shape future events. The distant future of our descendants is not disconnected from our present. The scale of engineering capabilities in the far future is entirely unknown to us. Certainly we can try to guess what might be, and without doubt we can try to steer research directions. But history tells us that it is more often the unexpected discovery that enables truly revolutionary advances. There is no obvious reason why such serendipitous advances should not continue to come about in the future, which begs the question, do we (that is, all humanity) actually have a long-term future? Lord Sir M...

6. Stars Transformed  In the preceding chapter we examined the ways in which an aging Sun might be rejuvenated and how the timescale over which life might be supported within the Solar System can be prolonged. In this chapter the focus will shift toward the broader question, which asks whether any galactic civilizations might have managed to alter their parent stars into a long-lived state. Revisiting Carter Physicist Brandon Carter has argued (recall Chapter 1) that the most likely time for an intelligent species to emerge is that corresponding to TMS, the main-sequence lifetime of the planetary system’s parent star. In this sense most intelligent species are likely to appear, if indeed they appear at all, at a time close to that in which the habitability zone is about to dramatically shift outward in response to the parent star becoming a red-giant. Stars with planets that have ages close to their main-sequence lifetime limits, therefore, are perhaps the most likely candida...

5. Rejuvenating the Sun  In Chapter 3 the physical processes underlying the workings of a Sun-like star were described. In this chapter we will examine the ways in which the properties of a star might, at least in principle, be manipulated by our distant descendants. Specifically, our task is to see how the Sun might be ‘engineered’ or ‘rejuvenated’ to enable the continued survival of life on the innermost planets, on timescales greater than the canonical main-sequence lifetime [T > TMS (canonical)]. In the case of Venus and Mars, of course, this clearly means future human life on terraformed worlds. As already stated, the task of the would-be asteroengineer is to find ways to stop the Sun from becoming over-luminous, and from becoming a bloated red-giant – the dire consequences of these effects for the Solar System having been discussed in the last chapter. It turns out, fortuitously for humankind, that these goals are compatible; by stopping the red-giant Sun from coming...