As 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 the hydrogen in such a white dwarf? Step 1: Calculate the observed energy production rate per unit mass (remember luminosity is energy output per unit time). Step 2: Use the per unit mass energy generation rate of hydrogen fusion (via PP chain) to estimate the possible hydrogen mass fraction given the condition at the center of the white dwarf.
As 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 the hydrogen in such a white dwarf? Step 1: Calculate the observed energy production rate per unit mass (remember luminosity is energy output per unit time). Step 2: Use the per unit mass energy generation rate of hydrogen fusion (via PP chain) to estimate the possible hydrogen mass fraction given the condition at the center of the white dwarf.
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As 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 the
hydrogen in such a white dwarf?
Step 1: Calculate the observed energy production rate per unit mass (remember luminosity is energy output
per unit time).
Step 2: Use the per unit mass energy generation rate of hydrogen fusion (via PP chain) to estimate the
possible hydrogen mass fraction given the condition at the center of the white dwarf.
Transcribed Image Text:As we have discussed, Sirius B in the Sirius binary system is a white dwarf with MB 1Mo, LB ~0.024Lo,
and TB 0.0084ro. 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 the
hydrogen in such a white dwarf?
Step 1: Calculate the observed energy production rate per unit mass (remember luminosity is energy output
per unit time).
Step 2: Use the per unit mass energy generation rate of hydrogen fusion (via PP chain) to estimate the
possible hydrogen mass fraction given the condition at the center of the white dwarf.
Epp 1.07 x 10-7 (10³kg/m³) X² (10K)¹ W/kg
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