White dwarfs and neutron stars. A spectral type B7 star like Alcyone in the open cluster...

  

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White dwarfs and neutron stars. A spectral type B7 star like Alcyone in the open cluster Pleiades will end its stellar life by ejecting most of its mass into a planetary nebula. The remaining mass (the stellar core or corpse) will collapse into a white dwarf. A white dwarf is a member of a class of objects called compact objects that also includes neutron stars and black holes. Compact objects are incredibly dense. For white dwarfs, the outer electrons of the atoms that make up the star's matter are packed closely as a result of electron degeneracy. For neutron stars, under the immense pressure of gravity, the electrons have combined with the protons to form neutrons, leaving the neutrons in a state known as neutron degeneracy. Given that the density of a white dwarf is 10° kg/m³ and that the density of a neutron star is 10¹ kg/m³, determine the weights, in tons, of: (a) 1 cubic centimeter (1 cm³) of white dwarf matter = (b) 1 cubic centimeter (1 cm³) of neutron star matter (c) Write your answer to b in words: tons [Round to 1 decimal.] tons [Use scientific notation; round to 1 decimal.] tons [Write just as a whole number.] There are 100 (10²) cm in 1 m. (Hint: How many cubic centimeters are there in 1 cubic meter?) Also, 1 ton (US) = 907 kg. Show your work in the box. [Parts a, b, c each worth 10 pts; work = 10 pts] [40 pts total] 2. Black holes. Stars that are brighter than type B0 end their lives in huge explosions known as supernovae. A neutron star or a black hole is the remnant that is left after this event. Neutron stars are typically 1.4 to 2.5 solar masses. The line between neutron stars and black holes is not well known and is usually stated as greater than 2.5 solar masses. Some astronomers put the dividing line at 3 solar masses or greater. The Schwarzchild radius, R, of a black hole (the radius of its "event horizon") is related to its mass, M, by the formula: R=2GMI 2 where G = 6.674 × 10-11 m³/kg-s² and c = 2.998 x 108 m/s. Let's look at the units: R=(m³/kg-s²) x (kg) + (m/s). The units of G can be rewritten as m³ kg-¹ s². The mass of the object is kg. The units for the speed of light c can be rewritten as m-s-¹; the units for the speed of light squared (²) will then be m²-s-2. Looking at the full equation, kilograms will cancel. Seconds squared (s) in the denominator of G will cancel with the seconds squared (s²) in the denominator of ² because we are dividing: s2 s² s2 x s². Meters cubed (m³) from G divided by meters squared (m²) from ² will leave meters (m), which makes sense as the radius of an object will be in meters. Given that the mass of the Earth is 5.973 x 1024 kg, determine its Schwarzchild radius if it somehow collapses into a black hole. Do the same for the Sun (the mass of the Sun is 1.989 x 1030 kg). Show your work in the box. [60 pts total] Schwarzchild radius of Earth: (a) (b) (c) Schwarzchild radius of Sun: (d) _m [Write in scientific notation; round to 2 decimals.] cm [Convert to cm; write in scientific notation; 2 decimals.] cm [Write as a regular number; round to 1 decimal.] [Parts a, b, c, d, e each worth 10 pts; work = 10 pts] m [Write in scientific notation round to 2 decimals.] km [Convert to km; write as a regular number; round to 1 decimal.] White dwarfs and neutron stars. A spectral type B7 star like Alcyone in the open cluster Pleiades will end its stellar life by ejecting most of its mass into a planetary nebula. The remaining mass (the stellar core or corpse) will collapse into a white dwarf. A white dwarf is a member of a class of objects called compact objects that also includes neutron stars and black holes. Compact objects are incredibly dense. For white dwarfs, the outer electrons of the atoms that make up the star's matter are packed closely as a result of electron degeneracy. For neutron stars, under the immense pressure of gravity, the electrons have combined with the protons to form neutrons, leaving the neutrons in a state known as neutron degeneracy. Given that the density of a white dwarf is 10° kg/m³ and that the density of a neutron star is 10¹ kg/m³, determine the weights, in tons, of: (a) 1 cubic centimeter (1 cm³) of white dwarf matter = (b) 1 cubic centimeter (1 cm³) of neutron star matter (c) Write your answer to b in words: tons [Round to 1 decimal.] tons [Use scientific notation; round to 1 decimal.] tons [Write just as a whole number.] There are 100 (10²) cm in 1 m. (Hint: How many cubic centimeters are there in 1 cubic meter?) Also, 1 ton (US) = 907 kg. Show your work in the box. [Parts a, b, c each worth 10 pts; work = 10 pts] [40 pts total] 2. Black holes. Stars that are brighter than type B0 end their lives in huge explosions known as supernovae. A neutron star or a black hole is the remnant that is left after this event. Neutron stars are typically 1.4 to 2.5 solar masses. The line between neutron stars and black holes is not well known and is usually stated as greater than 2.5 solar masses. Some astronomers put the dividing line at 3 solar masses or greater. The Schwarzchild radius, R, of a black hole (the radius of its "event horizon") is related to its mass, M, by the formula: R=2GMI 2 where G = 6.674 × 10-11 m³/kg-s² and c = 2.998 x 108 m/s. Let's look at the units: R=(m³/kg-s²) x (kg) + (m/s). The units of G can be rewritten as m³ kg-¹ s². The mass of the object is kg. The units for the speed of light c can be rewritten as m-s-¹; the units for the speed of light squared (²) will then be m²-s-2. Looking at the full equation, kilograms will cancel. Seconds squared (s) in the denominator of G will cancel with the seconds squared (s²) in the denominator of ² because we are dividing: s2 s² s2 x s². Meters cubed (m³) from G divided by meters squared (m²) from ² will leave meters (m), which makes sense as the radius of an object will be in meters. Given that the mass of the Earth is 5.973 x 1024 kg, determine its Schwarzchild radius if it somehow collapses into a black hole. Do the same for the Sun (the mass of the Sun is 1.989 x 1030 kg). Show your work in the box. [60 pts total] Schwarzchild radius of Earth: (a) (b) (c) Schwarzchild radius of Sun: (d) _m [Write in scientific notation; round to 2 decimals.] cm [Convert to cm; write in scientific notation; 2 decimals.] cm [Write as a regular number; round to 1 decimal.] [Parts a, b, c, d, e each worth 10 pts; work = 10 pts] m [Write in scientific notation round to 2 decimals.] km [Convert to km; write as a regular number; round to 1 decimal.]

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