The Sun and the Stars - PowerPoint Presentation

Slide1

The Sun and the Stars

The Sun and the StarsSlide2

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 typesApparent – chance alignment – not true binariesVisual – resolved binaries (individual components can be separated visually) >1” ,generally long orbital periodsAstrometric – unresolved, companion identified by stellar wobbleSpectroscopic – unresolved, other component revealed by period shift in spectral linesSpectrum – unresolved – spectral decomposition reveals two stellar componentsEclipsing- 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 binariesWhy 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).Slide3

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 BThe angular separations and orbital paths are only apparentbecause 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”Slide4

The Sun and the Stars

e.g. consider the following:

From Kepler’s III law we have

In the case of the Earth-Sun system, m

Sun

>>m

Earth,

and the common centre of mass is located

within the stellar radius, i.e. a

1

>>a

2

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

where m

1

and m

2

are the masses of the 2 components,

and a

1

,a

2

are the semi-major axes of their orbitsSlide5

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)

Proper motion of the visual binary Sirius A and B

relative to background stars

where r

1

+r

2

=aSlide6

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 

v

r

~ km/s

for a planet/star vr ~ m/sSlide7

Spectroscopic BinariesSlide8

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 curve for a hot Jupiter**

Radial velocity curves for nearby binary starsSlide9

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

and

The system is completely determined!!

The relative semi-major axis isSlide10

The Sun and the Stars

This rarely ever happens because

The system may be single lined (can only determine P and r

1

)

Unless the system is also eclipsing we don’t know the inclination

If (i) is true then we can only quote the

mass function

NB if the primary mass m

1

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

V

r

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

Why?

Recall

and

then

So

i

is the inclinationSlide11

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 59683Slide12

Eclipsing BinariesSlide13

The Sun and the Stars

Conditions for eclipse:

Note that the type of eclipse observed, depends upon

the orbital eccentricity and inclination and the stellar

radii and surface temperatures.

R

c

R

p





R

p

+R

c

(i)

(ii)

(iii)

no eclipse

partial eclipse

total and annular eclipse

NB

=90-i

From timing the points of contact we can estimate the relative stellar radii

R

p

/a,

and

R

c

/a

From the relative depths of the eclipses we can estimate the relative effective surface temperatures

T

p

/T

cSlide14

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 dwarfOccasionally the disc suffers a thermonuclear detonation when too much material has accumulatedObserved as novaeSee also Xray Binaries (accretion onto a neutron star or a black hole, eg Sco X-1)Slide15

Accretion in BinariesSlide16

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