Stars Lecture3(1)

7/30/2019 Stars Lecture3(1)

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Professor David AlexanderRochester 335 (top floor)Chapter 7 of Carroll and Ostlie

Lecture 3:Observed properties Binaries, orbits, masses


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Saha equation:

ionisation states

Boltzmann equation:

excitation states

Review of previous lecture

The tight relationship between mass and luminosity further constraint the physical

power source and structure of starsOBAFGKM (RNS): Oh Be A Fine Girl/Guy Kiss Me (Right Now Sweetie)!

Definition of line

equivalent width2


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Aims of lecture


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Binary stars: basic properties

Binary stars provide important insight intothe formation and evolution of stars. As we will see, binary stars provide a

direct method for determining masses.

About 70% of stars in

our galaxy are membersof binary systems.Planets have even been

found around binary (ormultiple) star systems!


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Binary stars: basic properties

In any binary/multiple star system the stars orbit about the centre of mass inelliptical orbits (semi-major axes of a1 and a2 for a binary system)

a2a1

Equation 7

a1 a2


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Binary stars: classification

Binary stars are classified depending on how they are identified:(1) Visual binaries(2) Astrometric binary(3) Eclipsing binary(4) Spectroscopic binaryThese classes are not mutually exclusive (a system can be in more than one

class). We focus mostly on visual, spectroscopic, and eclipsing

spectroscopic binaries (combination of eclipsing and spectroscopic).

Visual binary

In a visual binary both stars can be spatially resolved.Assuming that the orbits of both stars are not long then

it is possible to monitor the duration of the orbit and the

orbital parameters directly.

This image here shows the Castor star system, takenwith a small telescope. The Castor star system was the

first multiple-star system to be identified (in 1678).

Castor is actually a sextuple star system! Both of these

stars have a faint companion (spectroscopic binary) andanother faint binary pair orbits at a greater distance

(which is an eclipsing binary!).

Castor through a small telescope

We wont cover optical doublesand spectrum binaries


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Eclipsing binary:For binaries with orbital planes orientatedapproximately along the line of sight to the observer,

one star may periodically pass in front of the other,

blocking the light of the eclipsed component. Such a

system is recognised by regular variations in the

amount of observed light.

This technique is also used to search for exo-planets

from the small dip in brightness due to the eclipse of a

planet in front of a star.

Astrometric binary:If one member of the binary is much brighter than theother then it may not be possible to directly see the

fainter star. However, the existence of the unseen star

can be inferred from the motion of the brighter star.

A famous example is Sirius B, the white dwarfdiscovered from the motion of Sirius A in 1844

(explored in a later lecture).


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Spectroscopic binary:If the period of a binary system is not

prohibitively long, and if the orbital

motion has a component along the line of

sight, a periodic shift in the spectral lines

will be observable.

If the luminosities of the two stars arecomparable, both spectra will be

observable (double lined). If one is much

fainter than the other is, only one set of

lines is seen (single lined).

Orbital

configuration Wavelength(velocity) line shiftObserver

Stars must be quite close together for changes in velocity to be seen


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Visual binary stars: mass determination

a2a1

Equation 8

a1 a2


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This picture is a bit idealised because most binary systems will beinclined away from our line of sight and therefore the effect of the

inclination angle on our calculations need to be considered.


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Focus of observed

ellipse



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Spectroscopic binary stars

Recall from earlier slide:


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Spectroscopic binary stars: eccentricity

Orbital eccentricity has a marked effect on the shape of the velocity curves. Theinclination angle has no effect on the shape but it does effect the amplitude.

Circular orbit (no eccentricity)

Eccentric orbit: skewed velocity curves


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Spectroscopic binary stars: masses

Equation 9


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Spectroscopic binary stars: masses

So we can also express both the mass and the mass ratio in terms of velocity and period.But, again, knowledge of i is required to determine the most accurate masses.


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The inclination angle must be close to 90 degrees for aneclipse to occur, particularly if the secondary star is not in

close orbit. If the secondary star is in close orbit than i will

still be quite close to 90 degrees.

Eclipsing spectroscopic binaries

Eclipsing spectroscopic binaries are a special case of binary star. As the stars areeclipsing the inclination of the system must be close to 90 degrees. Therefore, there are

small inclination angle corrections and so we will have reliable velocity measurements.

We can use also eclipses to estimate stellar radii (as weexplored in lecture 1). The relative drop in light curve also

indicates the effective-temperature ratio of the two stars,

which we will explore in more detail here.

Primary

eclipse

Secondary

eclipse

Therefore, in eclipsing spectroscopic binarieswe get reliable velocity (and therefore mass)

measurements (little angle dependence)


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Eclipsing spectroscopic binaries

The shape of the light profile during the eclipse can further refine estimates of theinclination angle; compare these two plots. Note the overall width of the light-curve

dips are the same irregardless of whether it is a primary or secondary eclipse.

The inclination angle is almostexactly 90 degrees and the dip

in the light curve is flat.

The inclination angle is lessthan 90 degrees (but still highly

inclined) and the dip in the light

curve is peaked.


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Eclipsing spectroscopic binaries: temperature

The relative depths of the light-curve dips indicate the ratio of effective temperaturesPrimary

minimum

Secondary

minimumB0

BP

BS

(see Ch 7 of CO book for

more details)


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Stellar mass-luminosity relationship

Using the best mass constraints, astronomers have found a tight relationship between

mass and luminosity this provides constraints on the energy source (and lifetimes)

Equation 10

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Stars Lecture3(1)