Sirius

1. Sirius • Sirius is the brightest star in the night sky.

2. Sirius • Bessel made the first parallax measurement of a star, 61 Cygni. • Suspecting that Sirius is close, Bessel then measured a parallax to Sirius of 0˶.379, corresponding to a distance of 2.64 pc.

3. Sirius • Bessel found that the apparent motion of Sirius across the sky exhibited a “wobble,” leading him to suggest the presence (and predict the position) of a companion star with an orbital period of ~50 years.

4. Sirius • In 1862, 26 years after the death of Bessel, the companion star was discovered at its predicted location.

5. Sirius • In 1915, Walter Adams showed that Sirius B has virtually the same spectral type (and therefore comparable surface temperature) as Sirius A, both early-A.

6. Sirius • In 1915, Walter Adams showed that Sirius B has virtually the same spectral type (and therefore comparable surface temperature) as Sirius A, both early-A. • This implies that Sirius B must be much smaller than Sirius A, somewhat smaller than the Earth! • From the orbits of the two stars about their center of mass, the masses of the two stars were deduced to be ~2.3 M for Sirius A and ~1 M for Sirius B.

7. Sirius • In 1915, Walter Adams showed that Sirius B has virtually the same spectral type (and therefore comparable surface temperature) as Sirius A, both early-A. • This implies that Sirius B must be much smaller than Sirius A, somewhat smaller than the Earth! • From the orbits of the two stars about their center of mass, the masses of the two stars were deduced to be ~2.3 M for Sirius A and ~1 M for Sirius B. • Today, we know Sirius B to be a white dwarf, a star with an original mass of ~5 M and which expelled most of its mass during its post-main-sequence evolution.

8. Sirius • The pressure (~107 times the pressure at the center of the Sun) and temperature (similar to the temperature at the center of the Sun) at the center of Sirius B is so high that that, if Sirius B shines by thermonuclear fusion, it would be several orders of magnitudes more luminous than observed. • In fact, hydrogen cannot be present at any appreciable amounts even just below the stellar surface, otherwise thermonuclear fusion of hydrogen would produce luminosities much higher than are observed for white dwarfs. Instead, white dwarfs shine solely by radiating away their thermal energy. • The interiors of white dwarfs comprise (full ionized) atomic nuclei and free electrons. • In normal stars, the outward pressure resisting gravity is provided mainly by thermal gas pressure. If the same is true in white dwarfs, then they should shrink to become black holes as they cool!

9. Quantum States of Fermion Gas • Imagine fermions, in this case electrons, confined in a box. Thinking of electrons as being standing waves in a box, their wavelengths in each dimension are given by • where Nx, Ny, and Nz are integer quantum numbers associated with each direction.

10. Quantum States of Fermion Gas • Imagine fermions, in this case electrons, confined in a box. Thinking of electrons as being standing waves in a box, their wavelengths in each dimension are given by • where Nx, Ny, and Nz are integer quantum numbers associated with each direction. • Recall that the de Broglie wavelength is related to momentum by • The kinetic energy of a particle is therefore (non-relativistic limit) (relativistic) (non-relativistic limit)

11. Quantum States of Fermion Gas • Recall that Pauli’s exclusion principle states that no two electrons can have the same set of quantum numbers. Thus, at most, only two electrons (opposite spins) can occupy each state with the same quantum number Nx, Ny, and Nz. • At T = 0 K, electrons will fill all the lowest energy states, and the gas is completely degenerate. Even at T = 0 K, most of the particles in a degenerate fermion gas has kinetic energy. • The interior of a white dwarf is close to being a degenerate fermion gas. • The kinetic energy of this fermion gas provides pressure against gravity.