UNIVERSE (LOOSELEAF):STARS+GALAXIES
6th Edition
ISBN: 9781319115043
Author: Freedman
Publisher: MAC HIGHER
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Chapter 18, Problem 49Q
To determine
To explain:
The reason, a shock wave from a supernova seems to produce relatively few high mass O and B stars compared to the lower mass A, F, G, and K stars.
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Betelgeuse is a nearby supergiant that will eventually explode into a supernova. Let's see
how awesome it would look. At peak brightness, the supernova will have a luminosity of
about 10 billion times the Sun. It is 600 light-years away. All stellar brightnesses are
compared with Vega, which has an intrinsic luminosity of about 60 times the Sun, a distance
of 25 light-years, an absolute magnitude of 0.6 and an apparent magnitude of 0 (by
definition).
a) At peak brightness, how many times brighter will Betelgeuse be than Vega?
b) Approximately what apparent magnitude does this correspond to?
c) The Sun is about -26.5 apparent magnitude. What fraction of the Sun's brightness will
Betelgeuse be?
A supernova’s energy is often compared to the total energy output of the Sun over its lifetime. Using the Sun’s current luminosity, calculate the total solar energy output, assuming a 1010 year main-sequence lifetime. Using Einstein’s formula E=mc2 calculate the equivalent amount of mass, expressed in Earth masses. [Hint: The total energy output of the Sun over its lifetime is given by its current luminosity times the number of seconds in a year times its ten billion-year lifetime; ; mass of earth = 6×1024kg; c = 3×108m/s. Your answer should be 200-300 Earth masses.]
A supernova's energy is often compared to the total energy output of the Sun over its lifetime.
Using the Sun's current luminosity, calculate the total solar energy output, assuming a 1010
year main-sequence lifetime.
Using Einstein's formula E = mc? calculate the equivalent amount of mass, expressed in
Earth masses. [Hint: The total energy output of the Sun over its lifetime is given by its current
luminosity times the number of seconds in a year times its ten billion-year lifetime; Week 5
slide 4; mass of earth = 6x1024kg; c = 3x10®m/s. Your answer should be 200-300 Earth
masses.]
Chapter 18 Solutions
UNIVERSE (LOOSELEAF):STARS+GALAXIES
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- What observations from SN 1987A helped confirm theories about supernovae?arrow_forwardHow is a nova different from a type Ia supernova? How does it differ from a type II supernova?arrow_forwardHow do the two types of supernovae discussed in this chapter differ? What kind of star gives rise to each type?arrow_forward
- A supernova can eject material at a velocity of 10,000 km/s. How long would it take a supernova remnant to expand to a radius of 1 AU? How long would it take to expand to a radius of 1 light-years? Assume that the expansion velocity remains constant and use the relationship: expansiontime=distanceexpansionvelocity .arrow_forwardAs we have discussed, Sirius B in the Sirius binary system is a white dwarf with MB ∼ 1M , LB ∼ 0.024L ,and rB ∼ 0.0084r . For such a white dwarf, the temperature at the center is estimated to be ∼ 107 K.If Sirius B’s luminosity were due to hydrogen fusion, what is the upper limit of the mass fraction of thehydrogen in such a white dwarf?Step 1: Calculate the observed energy production rate per unit mass (remember luminosity is energy outputper unit time).Step 2: Use the per unit mass energy generation rate of hydrogen fusion (via PP chain) to estimate thepossible hydrogen mass fraction given the condition at the center of the white dwarf.arrow_forwardIf a neutron Star has a radius of 12 km and a temperature of 8.0 x 10^6 K, how luminous is it? Express your answer in watts and also in solar luminosity units. (Hint: Use the relation L/L= (R/R)^2(T/T)^4 . Use 5,800 K for the surface temperature of the Sun. The luminosity of the sun is 3.83 x 10^26W) luminosity in watts ________ W luminosity in solar luminosity units ______ Larrow_forward
- For the PP chain 0.7% of the mass participating in nuclear fusion is liberated as energy which produces a star's luminosity. Assume that the core of a main sequence star consists of 10% of its total mass. Hence, estimate the lifetime of a star on the main sequence in terms of its luminosity L/L. Give your answer in years. You may use the observed mass-luminosity relation L x M³.5, where M is the star's total mass. Using typical values, calculate estimates for the main sequence lifetime of a KO star and a 05 star. Describe briefly why your estimate might be more accurate for K stars compared to O stars.arrow_forwardConsider a star with more brightness at 280 pc from the Sun. Suppose this star gets exploded as a supernova at a temperature of 18000 K. The absolute bolometric magnitude of this supernova is-12.24. Calculate its diameter by assuming a sphere at maximum light. (Assume the luminosity of Sun as 3.8×1026 W, the mass of thesun as 1.9 ×1030 kg, and surface temperature of Sun as 5778 K).(a) 1.7×108 km(6) 3.5x108 km(c) 5.2x108 km(d) 6.9 x108 kmarrow_forwardBetelgeuse is a red giant at a distance of 428 light years. In the future it will become a supernova similar to Tycho's supernova which was observed in 1572 and lies at a distance of 9800 light years. At its peak, its brightness was similar to that of Venus (which has a peak apparent magnitude of -4). What might we expect the peak apparent magnitude of the Betelgeuse supernova explosion to be?arrow_forward
- Why does a type Ia supernova explode? in two sentences.arrow_forwardOne way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?arrow_forwardIf an X-ray binary consists of a 16 solar mass star and a neutron Star orbiting each other every 15.4 days, what is their average separation? (Hint: Use the version of Keller's third law for binary stars, Ma + Mb = a^3 /p^2 ; make sure you express quantities in unites of AU, solar masses, and years. Assume the mass of a neutron Star is 1.6 solar masses.) ___________ AUarrow_forward
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