The Sun and the Stars

1. The Sun and the Stars The Sun and the Stars

2. The Sun and the Stars • Binary stars: • Most stars are found in binary or multiple systems. • Binary star systems consist of 2 stars which are gravitationally bound with each star • orbiting a common centre of mass. We can distinguish between several different types • Apparent – chance alignment – not true binaries • Visual – resolved binaries (individual components can be separated visually) >1” ,generally long orbital periods • Astrometric – unresolved, companion identified by stellar wobble • Spectroscopic – unresolved, other component revealed by period shift in spectral lines • Spectrum – unresolved – spectral decomposition reveals two stellar components • Eclipsing- systems which show periodic dips in their apparent brightness • (systems may also be visual, astrometric or spectroscopic) • [check out eclipsing binary simulator at http://astro.unl.edu/naap/ebs/animations/ebs.html] • The most important of these are visual, spectroscopic and eclipsing binaries • Why are binaries important? • because analysis of their orbits allow us to determine the masses of the individual stars, their radii and shape (particularly in eclipsing systems), and the physical characteristics of the systems (separations, periods) • .

3. The Sun and the Stars Visual binaries– in the optical, require separations of > 1” from the ground, otherwise components are unresolved. Examples – alpha-Cen A and B, Sirius A and B The angular separations and orbital paths are only apparent because in general the orbit is inclined to the plane of the sky, so we see the orbit in projection Measuring the displacement of the primary relative to the apparent focus, yields the orbital inclination, i, the true ellipticity e, and the true semi-major axis a”

4. The Sun and the Stars e.g. consider the following: From Kepler’s III law we have where m1 and m2 are the masses of the 2 components, and a1 ,a2 are the semi-major axes of their orbits In the case of the Earth-Sun system, mSun>>mEarth, and the common centre of mass is located within the stellar radius, i.e. a1>>a2 Expressing the masses in solar masses and orbital radii in AU, then P has units of years, and thus the general form of Kepler’s third law can be written: If we express the separation between the binary components in seconds of arc, ”, then

5. The Sun and the Stars Since , to determine the individual masses, we must find the relative distance of each star from the centre of mass of the system. NB In proper motion, the centre of mass travels along a straight line relative to background stars (see e.g. Sirius A and B) where r1+r2=a Proper motion of the visual binary Sirius A and B relative to background stars

6. The Sun and the Stars Spectroscopic binaries • Two unresolved stars, separation 1AU, Period ~ hours to months, inclination i>0. • Binaries exhibit lines (in absorption or emission) that show periodic variations. • Systems may be: • single-lined(only one component displays lines) or • double-lined(both components display lines) • Lines are shifted in wavelength by an amount  • relative to the rest-wavelength 0, ,blueward (star • approaching), and redward (star receding) • [doppler effect], such that Detection of shifts limited by spectral resolution for two stars  vr ~ km/s for a planet/star vr ~ m/s

7. Spectroscopic Binaries

8. The Sun and the Stars Radial Velocity curves Constructed by converting wavelength shifts to velocity shifts as a function of time, folded on the orbital period e.g. Radial velocity curves for nearby binary stars **Radial velocity curve for a hot Jupiter**

9. The Sun and the Stars The simplest radial velocity curves are from those systems viewed edge-on (i=90 degrees). They appear sinusoidal with opposite phases e.g. In this case, each star orbits around the centre of mass with orbital period P, so and The ratio of the stellar masses is given by The relative semi-major axis is and The system is completely determined!!

10. The Sun and the Stars • This rarely ever happens because • The system may be single lined (can only determine P and r1) • Unless the system is also eclipsing we don’t know the inclination • If (i) is true then we can only quote the mass function Why? Recall and then i is the inclination So NB if the primary mass m1 can be obtained from the spectral type, the system can be solved. More generally the system will be inclined. If the radial velocity curve is sinusoidal, we know we are dealing with circular orbits in which case we measure the projected velocity Vr sini for each component. In the case of elliptical orbits, the velocity curves are no longer sinusoidal. Although radial velocity curves are mirror images, they may have differing amplitudes

11. The Sun and the Stars Eclipsing binaries Close binary systems (small separations and short periods) in which one star passes in front of the other periodically blocking some of the light. For each orbit there will be two eclipses, a primary eclipse (when the primary star is eclipsed by the secondary and a secondary eclipse wherein the primary passes in front of the secondary (by convention, the hotter star is designated the primary, the cooler star the secondary). Eclipses can be either total or partial e.g. SV Cam HIP 59683

12. Eclipsing Binaries

13. The Sun and the Stars Note that the type of eclipse observed, depends upon the orbital eccentricity and inclination and the stellar radii and surface temperatures. Rc Rp Conditions for eclipse: (i) no eclipse  partial eclipse (ii) Rp+Rc  total and annular eclipse (iii) NB =90-i From timing the points of contact we can estimate the relative stellar radii Rp /a, and Rc /a From the relative depths of the eclipses we can estimate the relative effective surface temperatures Tp /Tc

14. Accreting binaries • Cataclysmic variables consist of a white dwarf and a cool secondary (usually an M dwarf) • Periods of 1.5 to a few hours • Material is accreted via Roche Lobe Overflow into a disc surrounding the white dwarf • Occasionally the disc suffers a thermonuclear detonation when too much material has accumulated • Observed as novae • See also Xray Binaries (accretion onto a neutron star or a black hole, eg Sco X-1)

15. Accretion in Binaries

16. The Sun and the Stars Additional notes – derivation of Keplers III law Balance between gravity and centripetal force Relocate to frame of one of the masses and replace mass with reduced mass Since ,then The period of the orbit T, is So, and therefore