a) What is a binary star system? (b) describe briefly two methods for showing that a system is a binary.
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- a) What is a binary star system? (b) describe briefly two methods for showing that a system is a binary.
(a) A binary star system is a system of two stars orbiting each other around a common center. Binary stars are further classified based on the method by which they are detected. Binaries which can be resolved through a telescope are called visual binaries. Binaries which are detected using indirect methods are spectroscopic binaries, eclipsing binaries, Astrometric binaries.
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- A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.Problem Set on Binary Systems: 1.Consider two stars in orbit about a mutual center of mass. If a1 is the semimajor axis of the orbit of star of mass m, and a, is the semimajor axis of the orbit of star of mass m2, prove that the semimajor axis of the orbit of the reduced mass is given by a = a, + a2. points)(a) Estimate the Eddington luminosity of a 0.072 M, star and compare your answer to the main-sequence luminosity given in Problem 21. Assume k = 0.001 m² kg¯'. Is radia- tion pressure likely to be significant in the stability of a low-mass main-sequence star? (b) If a 120 Mo star forms with log1o T. = 4.727 and log1o(L/Lo) = 6.252, estimate its Eddington luminosity. Compare your answer with the actual luminosity of the star.
- Match each characteristic below to the appropriate stellar end state. (Select W-White dwarf, N-Neutron star, B-Black hole. If the first is W and the rest N, enter WNNNNNNN). A) Has a mass no greater than 1.4 solar-masses. B) Sometimes appears as a pulsar. C) Size defined by its Schwarzschild radius. D) In a binary system it can explode as a supernova. E) Supported by electron degeneracy pressure. F) Typically about the size of Earth. G) Usually has a very strong magnetic field. H) Viewed from afar, time stops at its event horizon. Answer: Submit All AnswersSuppose a protostar has a luminosity of 39,473 L⊙ and a surface temperature of 4,130 K (Kelvins). What is the radius of this protostar? [Enter your answer as a multiple of the Sun's radius. I.e., if you find R = 20 R⊙ , enter 20. This problem is easier if you start with the relevant equation and create a ratio using the Sun's values. Recall that the Sun has a surface temperature of 5778 K. ]Identify the location in the H-R diagram of the phases of stellar evolution. (For each statement select the proper symbol in the picture.) 1) red giant, helium flash2) white dwarf3) red giant with helium burning shell4) hydrogen fusion in shell around core5) helium fusion in core6) envelope ejected, planetary nebula7) main-sequence star8) helium used up, core collapses9) hydrogen used up, core collapses
- 8) A neutron star is found with a radius of 10 km and has a surface temperature of 1,000,000 K. Calculate its luminosity with respect to that of the Sun. nts)Which of the following most correctly explains why we have not yet observed any white dwarfs derived from M stars: Group of answer choices Most M stars end up as neutron stars or black holes. The lifetime of M stars is longer than the age of the universe. Most M stars are located near the edge of the universe, beyond the visible horizon. Most M stars are members of a binary system, and the white dwarf would be obscured by the glare of the more massive companion. White dwarfs are too dim to be observed with currently available techniques.(Answer don't copy with hand written please)As a star runs out of hydrogen to fuel nuclear fusion in its core, changes within the star usually cause it to leave the main sequence, expanding and cooling as it does so. Would a star with a radius 12 times that of the Sun, but a surface temperature 0.5 times that of the Sun, be more, or less luminous than the Sun? Show and explain your reasoning. You may assume the surface area of a sphere is A = 4πr2.