HSC Physics Astrophysics Notes

HSC Physics Summary

©_{Ben 2010-present}

UNIT #4: Astrophysics

NOTE: Elements, graphics and diagrams used in this summary have been gathered from websites such as Google to produce a better quality summary for purely personal educational purposes. All copyright rights and responsibilities of phrases/graphics/diagrams belong to their respective owners.

Definitions

Annual Parallax

A change in apparent position of a nearby star (angle) with

respect to distant stars as the observer’s position changes.

The diameter of Earth’s elliptical orbit is used as the base

line for determining the annual parallax of a star. The

annual parallax of a nearby star (<300ly) is charted against

the position of distant stars, which appear ‘fixed’ in the

night sky. Positions are charted at 6-month intervals, when

the earth is at opposite sides of its orbit. Annual parallax is

expressed in arc seconds (“) – when the annual parallax is

measured to be 2”, the star is 1 parsec away.

http://www.astro.ubc.ca/~scharein/applets/Sim/new-parallax/Parallax.html

Trigonometric

Parallax

Trigonometric parallax is HALF the annual parallax

Trigonometric parallax is used to determine the distance

between earth and stars by constructing a diagram using

half the annual parallax angle in a right-angled triangle:

The perpendicular distance (d) between the star and the

radius of earth’s orbit (1AU base-line) is given by:

d =

d is distance in parsecs

p is parallax of star in arc-seconds (“)

Trigonometric parallax cannot be used to determine the

distance to distant stars (parallax angle is too minute.)

Parallax Angle (p)

HALF

the

corresponding

angle

subtending at a star when the star is

viewed on two different paths from

earth (6 months apart.) The angle is

measured from the perpendicular to

the sight path:

*logically, the smaller the parallax

angle, the further away the star (pc)

Nearby Star

A star less than 300 light years away.

Parsec (pc)

The distance that a star would have to be placed away from

earth in order subtend a parallax angle of 1”when lines are

drawn from either side of a 1AU base line (e.g. avg. radius

of earth’s orbit around the sun)

1pc = 3.26 ly

Light-Year (ly)

The DISTANCE travelled by light in one year

1 ly = 9.5x10

15

m

Astronomical Unit

(AU)

Average distance between the sun & earth (orbital radius)

1 AU = 1.496x10

8

km

1AU = 1.496x10

11

m

63 000 AU = 1 ly

Limitations of

Trigonometric

Parallax



Distant stars have an angle too small to be measured

(smallest measurable angle is approx. p=0.01”)



The Atmosphere blurs images, making angle harder to

measure (only stars <100pc away can be measured)



Earth’s orbit is not completely circular (elliptical)

1. Telescopes

Electromagnetic

Spectrum

All forms of EMR make up the Electromagnetic Spectrum –

All EMR travels at the same speed, c (speed of light), while

different forms of EMR possess different amounts of energy

due to their different frequencies.

Visible Light

EMR with a wavelength between 350-700nm (x10

-9

m)

Blue Light (400nm) high freq. / Red Light (700nm) is low

Resolution

The ability of a telescope to distinguish between two

objects that are close together (e.g. sharpness.) Resolution

is described in terms of the smallest angle between two

points at which the telescope still represents the stars as

two distinct figures. For most large astronomical telescopes

have a limit of resolution of 1 arc minute, meaning that if

two stars subtended an angle of 1’ with the telescope, the

telescope will represent the stars are two distinct, separate

stars. (Any angle smaller than the limit of resolution and

the two stars will appear as one blurred mass.)

Resolution depends upon the diameter of the lens/mirror

and the wavelength of the incident light.

Telescopes with poor resolution blur the apparent

boundaries between two close stars – making them appear

as one. High-resolution telescopes produce sharp images in

which the two close stars appear distinct and separate.

Diffraction and resolution problems are worse with radio

waves, as they have longer wavelengths than light waves

– they are also worse for small apertures (e.g. cameras)

Smaller apertures have less resolving power (blurrier)

Two factors limit a telescope’s resolution: aberrations

(imperfections in the mirror/lenses) and diffraction (the

bending of light around objects and through gaps.

Sensitivity

The photon-gathering power of a telescope. The sensitivity

is dependent upon the area of the telescope’s aperture.

Sensitivity is enhanced by increasing the aperture’s area

(thereby maximising the number of photons entering the

lens from a source) or exposing the film for a long time

(allows a sustained stream of photons to enter.) To avoid

‘star trails’, the telescope needs to ‘track’ the star being

observed over a period. Astronomers do not observe any

more, they take pictures, which they then observe.)

Doubling the diameter of a telescope’s aperture results in

an increase of sensitivity by a factor of 4.

Diffraction

The ability of a wave to bend its path around corners and narrow openings. Light passing through telescope apertures diffract,

resulting in an interference pattern where the stars are surrounded by rings. These interference patterns are the cause of ‘blurriness’ and the cause of resolution limits.

Twinkle

‘Twinkling’ of stars is caused by changing refractive indexes of the light’s path as gusts gasses, water vapour and dust come between the observer and the star.

Galileo and the Moon

The first telescopes were thin refracting telescopes which used lenses. Using a telescope, Galileo made the following astronomical discoveries:

1) The moon’s surface is not smooth – it was punctuated with craters and mountains. Galileo sketched numerous drawings of the moon’s surface as seen through a telescope – he also estimated the height of the ‘moon mountains’ by looking at the length of the shadows they cast.

2) Sun Spots – the sun wasn’t perfect but had dark ‘blemishes’ or ‘spots’ 3) The phases of Venus – Venus had phases, just like the moon

4) Jupiter has 4 moons –

5) The planets, sun and moon were not perfect spheres – this revelation and that of ‘sun spots’ debunked Ptolemy’s theory that heavenly bodies were flawless

EMR Reaching Earth

While there are many different types of EMR approaching Earth, Earth’s atmosphere – particularly the ionosphere and stratospheres – block much of this harmful radiation. There are only 3 types of EMR that reach earth’s surface without being blocked.

 Visible Light

 Radio Waves

 “Milimetre Radiation” (Between Radio & Infrared)

Atmospheric molecules (e.g. O3 ) are selective in the EMR frequencies that they absorb – this is due to the fact that electrons can only absorb photons of a particular frequency that energise them sufficiently to jump to a different energy level. Most high-energy / potentially harmful forms of EMR are blocked by atmospheric molecules. These rays

ionise molecules (transfer their energy to electrons) before they hit the ground. Even in the visible light spectrum, however, CO2 and water vapour cause absorption lines.

There are, however, many different types of telescopes that are designed to observe the different types of EMR:

 Radio telescopes (e.g. Australian Parkes)

 Microwave Telescopes (e.g. COBE – Cosmic Background Explorer)

 Infra-red Telescope (e.g. ISO – Infrared Space Observer)

 Visible Telescope

 UV Telescope

 X-ray Telescope (e.g. Chandra X-ray)

 Gamma-ray Telescope (e.g. EGRET)

Note: Only Radio and Visual Telescopes are ground based, all other types are satellites, above the atmosphere where the EMR is not blocked

Optical Telescopes

There are 2 different types of telescopes:

1)

Refracting Telescopes – Utilise an objective lens to bend incident parallel

light rays towards a focal point to magnify the image. After passing through a

single lens, however, the image is upside-down.

A Galilean Refracting Telescope has an additional eyepiece lens that inverts the image (right-way up) and enlarges it.

The advantage of using refracting telescopes is that there is nothing inside the barrel to obstruct the light. The disadvantages of using refracting lenses are that badly ground lenses can cause aberrations and reduce precision,

while refraction bends the different colours of light at different angles – resulting in a discoloured image.

2) Reflecting telescopes – Have a parabolic mirror at the bottom of the barrel

that focuses the light onto a plane mirror, into which the observer looks from

a side-mounted eyepiece lens.

*Note: Larger, fatter lenses will have a smaller focal length and will produce the greatest magnification.

Problems with Ground-based Astronomy

1) Atmospheric Absorption – Certain types of EMR are absorbed by molecules

(ionisation) as they pass through earth’s atmosphere. (e.g. UV rays) Only

radio and optical telescopes are used, as Visual Light and Radio waves are the

only EMR that reach Earth’s surface. Optical telescopes are placed on

highest mountains to minimise the amount of light absorbed on its journey

through the atmosphere.

2) Atmospheric Distortion – ‘Twinkling’ of stars is caused by atmospheric

turbulence as the light passes through migrating atmospheric cells (layers of

gases and water vapour) with different refractive indexes. Light from the star

is refracted and scattered while passing through these different mediums. To

overcome atmospheric distortion, optical telescopes are built on mountain

tops, where there is less weather fluctuation. Adaptive Optics are also

utilised

to

minimise

atmospheric

distortion.

Unlike optical telescopes, radio telescopes are largely unaffected by

atmospheric cells – they can see through clouds. However, optical

telescopes are better at resolving images than Radio telescopes because

light has a shorter wavelength (similar to use of x-rays to determine lattice.)

3) Gravity – While building bigger telescopes with wider apertures allow us to

achieve higher resolution images, big heavy telescopes bend and flex under

gravity, reducing the precision and accuracy of astronomical measurements.

Adaptive Optics

A highly sensitive computerised system that is used to

minimise atmospheric distortion caused by atmospheric

cells. High speed cameras continuously sample light from a

nearby reference star, recognising any distortions. It then

compensates for these detected distortions by making tiny

(x10

-8

m) adjustments to hexagonal mirror plates. This

measuring/adjusting occurs rapidly up to 1000times/sec.

Active Optics

Active optics are utilised to counter the issue of a large,

thick mirror flexing or distorting under gravity. Instead a

series of tesselating hexagonal mirror plates, each

possessing mechanical manoeuvrability, are utilised. This

allows the concavity of the mirror to be altered – it is more

lightweight and greater aperture areas can be reached.

Interferometry

Technique that involves linking two distinct telescopes

together so that they act as a single aperture. Does not

increase sensitivity, but improves resolution dramatically,

as there are two or multiple vantage points from which the

star is viewed from – all calibrated and synchronised using

computers to attain a greater ‘depth’ with the images.

Hawaii’s Kek 1 and 2 telescopes are linked to achieve a

higher resolution. Mexico’s Very Large Array (VLR) is a field

of satellites.

2. Parallax

See definitions for Parallax, Parsec, Light-Year

3. Spectroscopy

Emission

Spectrum

May be either ‘continuous’ or ‘line/band’ spectra. Line Emission Spectra is obtained when an element is excited by heating it to incandescence. The electrons in the atoms jump to higher energy levels, and re-radiate the energy they posses as they fall to the ground state at particular discrete frequencies, according to how far they fall through the shells. Viewing this emission through a spectroscope reveals the a pattern of coloured lines on a black background, revealing the particular frequencies emitted by the atoms, which are indicative of that atom’s nature (i.e. whether it has the ‘fingerprint’ of hydrogen or helium)

Absorbtion

Spectrum

A series of dark bands on a coloured background. These bands correspond to the frequencies that the atoms absorbed as the energy passed through them, and are indicative of the ‘jump’ made by the electrons up through the energy shells. Each element absorbs its own unique set of frequencies, which are the same frequencies that it will produce in an emission spectrum.

Absorption occurs in a hydrogen atom when the electron absorbs an incoming photon of discrete energy that allows it to jump to a

higher energy shell. Though the electron falls to its ground state almost instantly, the atom’s spherical shape means that the energy is re-radiated in all directions, meaning that the light of that

particular frequency has a significantly less intensity than the other frequencies, and hence appears as a darker ‘gap,’ relative to the incident light.

star can be compared to the absorption spectrum of known

elements using correlation methods to ascertain the composition of the star. From analysing a star’s spectrum we can determine its:

1)

Surface Temperature

2)

Speed of Approach / Retreat (Doppler Effect)

3)

Density

4)

Chemical Composition

Spectroscopy has made numerous contributions to

astronomy including:

1) Identification of elements in the atmosphere of stars and galaxies

2) Detection of invisible astrometric binary ‘partners’ due to recognition of the Doppler shift

3) Detection of the expansion of the universe

4)

Discovery of the helium in the sun before it was discovered on Earth.

Spectroscope

(Spectrometer)

A device used to illustrate the visual spectrum of a star for

the observer, using either a prism or diffraction grating.

Bohr’s Model

Used to explain spectra emission. When an atomic of hydrogen is excited by an incoming photon of energy, the electron is energised and ‘jumps’ to a higher energy level. The electron then (almost immediately) falls back to its ground state, releasing the energy it absorbed as a discrete photon of energy of a particular frequency, corresponding to a particular wavelength or colour. The falling electron only emits frequencies that correspond to how far it falls through the energy shells. Because this happens many times per second with many billions of atoms, it is assumed that the electrons fall down in every possible arrangement through the energy levels, so that a number of different discrete frequencies are released.

Spectrograph

Instrument used to photograph a spectrum.

Spectrogram

A visual photographic image of a spectrum.

Collimated

Made into a parallel beam (within spectroscopy)

Quasar

a.k.a. Quasi-stellar radio source/ Galactic Nucleus -- Distant ‘starlike’ source that exhibit strong red-shifts. They emit enormous amounts of energy – especially radio waves.

Emission Spectra

As an object is heated, it changes colour from red, orange, yellow, blue and eventually white. When viewed through a spectroscope, a continuous spectrum is seen, illustrating all of the colours in a smooth gradient. As Planck’s black body curves show, each object radiates all of the frequencies in different proportions, according to its heat and irrespective of its composition.

Absorbtion Spectra

(See Definition)

Spectrometers

are devices used to visually observe spectra.

There are two types of spectroscopes: Prism and Diffraction Telescopes --

1) Prism Spectroscopes - light from a source passes through a slight and collimated. The light is the dispersed by a prism, each frequency being refracted by a different amount (e.g. red bends more than blue)Another lens focuses the coloured pattern onto a detector or screen (e.g. photographic plate) appearing as a gradient of colours transitioning from red to blue– dark absorption bands become visible where light of particular frequencies have been absorbed by atoms during the light’s journey:

One ERROR associated with prism spectroscopes is that they absorb some of the radiation. The glass of the prism, for example, absorbs ultraviolet and infrared

frequencies.

2)

Diffraction Spectroscope – Light from a source passes through a collimator before striking a reflection grating that disperses and focuses one particular frequency of light

into a photomultiplier. The grating can be rotated to allow the observation of each individual frequency discretely.

Alternatively, a transmission grating is used to slightly diffract the collimated light passing through it, so that only a very narrow frequency band strikes the photomultiplier

at any one time. The grating can again be rotated to allow the observer to examine the intensities of different frequencies. Numerous miniature slits in the diffraction grating

cause interference between the light causes the different wavelengths to spread out into a spectrum.

Stellar Spectra

Astronomical Spectra can be produced from 4 main sources:

1) Stars – A star’s spectra is directly related to its surface temperature, according to Planck’s black body radiation curves. The spectrum of a star is an absorption spectrum, which reveals what elements are surrounding the immediate atmosphere of the star that the EMR has to pass through.

2) Emission Nebulae – The heat and light energy emitted by a protostar core strikes the atoms that are within a nebula cloud (mostly hydrogen, nitrogen and oxygen) causing them to become excited and emit energy of a particular frequency – resulting in the acquirement of an emission spectrum of the gasses surrounding a protostar.

3) Galaxy Spectra – Spectrometers gather a blend of different spectra from galaxies, as they are composed of stars, planets, nebula and quasars. Most galaxies exhibit red-shift, indicating their movement away from our planet. Galaxy spectra have absorbtion bands that indicate the presence of molecular hydrogen, nitrogen, carbon and silicon, as well as other forms of EMR from the entire spectrum – radio waves and infrared in particular.

4) Quasars – Stellar objects that emit massive amounts of all types of spectra (radio waves, x-rays, light) This allegedly occurs when gas is being swallowed by a black hole, the gravitational energy being converted to kinetic.

Key Features of Stellar Spectra

A stellar spectrum is the spectrum of EMR emitted by a star. The star’s surface temperature determines the spectral pattern formed –hydrogen absorption lines are the dominant type observed, while calcium and sodium may also be observed. The type of EMR and hence spectrum produced by a star, however, is independent of its composition. It depends entirely upon the surface temperature of the star.

To produce a line in the visible spectrum, an electron must be in the 2nd energy level when it absorbs a photon. Too little energy (low surface temperature) equates to weaker absorption lines (less electrons are excited sufficiently to absorb the photons.) Too much energy will ionise the atoms, stripping their electrons and no absorption lines will be visible. To produce HYDROGEN absorption lines, the stars temperature must be 4 000K-12 000K To produce HYDROGEN absorption lines, the stars temperature must be 15000K – 30000K The strongest intensity emission from a star will peak in the frequency that corresponds to the blackbody curve associated with its surface temperature.

From observing the strength (boldness) of the Hydrogen absorption lines, we can ascertain a star’s surface temperature and assign it a spectral class – a letter from O, B, A, F, G, K, M. Each class has 10 divisions (e.g. F4, G5, K9). This can be determined by comparing the star’s emission intensity in each frequency band with other stars of known spectral class – or by comparing the emission intensity to a black body curve and observing in what frequency the star’s emission spectra peaks.

Spectral Class Colour Surface

Temperature (K) Spectral Features

O

Blue

30 000

Strong lines of ionised helium. Doubly Ionised Oxygen, Nitrogen &

Carbon lines

Ionised He, Weak H

B

Blue-white

15 000

Neutral Helium lines more prominent. Hydrogen lines stronger than on O class. Neutral He, Weak H

A

White

10 000

H-lines most prominent. Ionised Mg, Si, Fe, Ca appear Strong H

F

White-yellow

7000

H-lines are weaker than A class – neutral metals are stronger Weak H, metals (Ca, Fe)

G

Yellow

5000

Lines of ionised calcium are strongest feature. H-lines are weak. Lines of many neutral metallic ions present.

Strong Metals (Ca)

K

Orange

4000

Neutral metal lines most prominent. H-lines virtually non-existent.

Strong metals (CH and CN)

M

Red

3000

Molecular bands are most prominent. Titanium oxide bands

are very prominent.

What Spectra Reveals about a Star

1) Structure – Emission lines indicate that the star’s emission is proceeding unimpeded; Absorption lines indicate that the star is surrounded by gas that absorbs the EMR.

2) Chemical Composition – Comparing stellar spectra with spectra of elements on Earth with known spectral lines – correlating the 2 spectral patterns to determine what elements are present.

3) Rotational / Translational Velocity – The observance of red-shift / blue-shift of a star’s spectral pattern indicates the motion of the star away from / towards Earth. The displacement of the line from its regular position is an indication of the speed at which the star is moving away from / toward earth (i.e. greater red-shift means moving away faster.) The rotational velocity of a star can be determined by pointing a spectrometer at the approaching or receding end of a star as it spins, and observing the degree to which red/blue shift occurs. The star’s period and hence speed can then be calculated. 4) Density – Under the influence of gravity, atoms possess more energy due to the extra

density and gravitational pull of a nearby star. Undisturbed, the atom absorbs emission as per usual. Dwarf stars, with high density, produce broad absorption lines; supergiants with less dense atmospheres produce narrow absorption lines.

5) Surface Temperature – According to Planck’s black body curves, there is a direct link between the colour of a star and its surface temperature. The dominant wavelength emitted by a star indicates the star’s temperature.

Typical Astronomical Spectra

Stars – produce continuous spectra with superimposed absorption lines (appear as ‘divets’) Doppler shift may be identifiable – stars are capable of receding from / approaching Earth. Emission Nebulae – Releases light as a dominant frequency – almost always characteristic pink of hydrogen and orange-yellow glow of helium. Gas cloud EMISSION energy of specific frequency according to the elements present (most hydrogen & helium.) Little Doppler effect is observable – Nebulae rarely move.

Galaxies – Continuous spectrum of superimposed ABSORBTION lines of NUMEROUS elements from different types of stars. Doppler effect is evident – galaxies show great red shift because they are receding from earth a great rate (universe is expanding.) There are a few spikes corresponding to the most abundant elements in the galaxy (hydrogen, helium.) Quasars – Enormous amounts of EMR EMISSION in all spectrums. Very large Doppler shifts – very far away and moving away at a fast rate. Large emission ‘spikes’ occur – usually hydrogen excited by enormous energy release from the quasar.

Practical: Using a hand-held Spectroscope

AIM: To observe the spectra of sunlight and that of a sodium vapour lamp using

a hand-held spectroscope.

SAFETY: Do not look directly at the sun- to measure sunlight just look outside

METHOD:

1. Point the hand-held spectroscope outside and look into the lens. A bright

continuous spectra should be observed, showing colours from red to blue.

2. Next, point the spectroscope at a sodium lamp source and observe two

bright orange lines form on the spectra.

RESULTS: A continuous spectrum was visible from sunlight and two distinctly

brighter orange lines were also present in the sodium lamp’s spectra.

ERRORS: The room was not darkened when viewing the spectra of the sodium

lamp, meaning that other spectra were visible (sunlight was still present.)

4. Photometric Measurements (Absolute Magnitude)

Apparent

Magnitude (m)

(Apparent

Brightness)

The brightness of a star as it appears from earth.

On a magnitude scale, seemingly BRIGHT stars are ranked

with negative values, while fainter stars are given high

positive values (e.g. ranking system 1

st

 100

th

brightest)

Each increase of m by 1.0 corresponds to a decrease in

apparent

brightness

by

a

factor

of

2.512

(e.g. m=1 is 100 times brighter than m=6)

Absolute

Magnitude (M)

(Absolute

Brightness)

A comparative measure of the amount of light a star emits

(a measure of the star’s true luminosity.) The absolute

magnitude would be the apparent magnitude of the star if

all stars were placed at a distance of 10 parsecs from earth

– so that the only factor affecting their brightness is their

size. The most negative values equate to the brightest stars.

Luminosity

The amount of light energy radiated by a luminous object.

The intrinsic brightness of a star. (i.e. Absolute magnitude)

Brightness Ratio

How many times brighter one star is in comparison to

Distance modulus

The value of m – M of a star (difference between apparent

and absolute brightness)

Colour Index

(B – V)

Measuring the apparent magnitude in two different colours

(Blue / Yellow) allows one to find the Colour Index which is

associated with a particular spectral class (proportional to

temperature) C.I. ranges from –0.6 to +2.0 (bluered)

Hence C.I. may be considered a measure of a star’s redness

(white stars have a C.I. = 0)

Photographic

Magnitude (B)

The magnitude of a star measured by a photographic plate

or blue filter, which is more sensitive to short-wavelength

light (400nm / more BLUE light) Blue stars hence appear

brighter (lower magnitude) upon a photographic plate.

Yellow-sensitive film is used to obtain photographic

magnitude.

Visual Magnitude

(V)

The magnitude of a star measured by the human eye or a

yellow-green filter, which is more sensitive to

long-wavelength light (550nm / yellow-green)

The brightness ratio of 2 stars is equal to 2.512 to the power of the magnitude difference:

= 2.512

m2 – m1

Where… I1/2 = brightness of star 1/2

m1/2 = magnitude of star 1/2

*The ratio is an expression of how many times brighter the top star is than the bottom star (i.e. a ratio of 1.5 means that I1 is 1.5x brighter than I2 ) – star 1 compared to star 2

The same formula can also be applied to determine the absolute magnitude ratio by replacing m2 and m1 with M2 and M1 :

= 2.512

M2 – M1

Where… I1/2 = absolute brightness of star ½

M1/2 = absolute magnitude of star 1/2

 If a star is exactly 10 parsecs away: absolute brightness = apparent brightness

 If a star is closer than 10 parsecs away, it is apparently brighter than its absolute brightness. Since low integers equate to high brightness (numerical ranking)

apparent brightness < absolute brightness

(the star needs to be pushed away to 10pc, numerically increasing its brightness rank to its absolute rank [e.g. from -1  6] )

 If a star is further than 10 parsecs away, its apparent brightness > absolute brightness (the star needs to be pulled closer to 10pc, decreasing its brightness value to its absolute [e.g. brightness 6  -1] )

Rearranging the formulas that are used to determine apparent and absolute brightness, we can formulate an equation that expresses the difference in apparent and absolute magnitude of a single star in terms of distance of the star from earth:

m – M = 5 – 5

where… m = apparent brightness of star M = absolute brightness of star

D = distance of star from Earth in parsecs (pc)

PRACTICAL: Filters and Photometric Measurements

1. Each student provided with TWO PHOTOGRAPHS of the star cluster M67; one taken with a YELLOW FILTER (VISUAL) and the other with a BLUE FILTER.

2. Particular stars in the cluster were labelled A-P, and a plastic overlay with a reference scale was used to assign an apparent magnitude value to each star in each photograph 3. This data was tabulated in a table similar to that below:

STAR BLUE MAGNITUDE (B) VISUAL MAGNITUDE (V) COLOUR INDEX (B-V) A

4. The results were then graphed with Visual Magnitude (V) on the vertical axis and Colour Index (B-V) on the horizontal Axis.

Photoelectric Photometry vs. Photographic Photometry

Photometry is a method by which the brightness of a star is ascertained. An

apparent luminosity value or rank can be assigned to each star using two

methods (though the latter is more accurate):

Photographic

Photometry

A measurement of the apparent luminosity of a star based

upon visual comparisons of star images on photographic

plates.

This method is less accurate because there is an element of

error when determining visually from an image. The stars

brightness also cannot be calibrated, because of the

complex

size/density-brightness

relationship.

Photoelectric

Photometry

(Photoelectric effect to calculate the apparent magnitude)

Light from a star is captured by a photomultiplier, that

converts the weak light signal into a strong electric current.

Photons of light enter through a thin glass window into an

excavated tube, striking a photocathode. Photoelectrons

are emitted as per the photoelectric affect and an applied

voltage

accelerates

the

photoelectrons

down

photomultiplier, bouncing off dynodes as it goes. The

output pulse is a measurable current proportional to the

light input.

The fast response and proportional nature of the current

makes

it

an

effective

detector

of

starlight.

(e.g. Accuracy + Sensitivity)

5. Binary Stars

Binary Star

A stellar system in which two stars orbit around each other.

(e.g. Alpha Centauri)

There are 4 types of Binary Stars:

Visual Binary

Two stars that can be resolved with the naked eye or

through the use of a telescope.

Astrometric

Binary

A star that appears to regularly ‘wobble’ – the star has an

invisible partner that is exerting a gravitational pull upon

the star, causing it to ‘wobble’ about its centre of mass.

Used as evidence for black holes.

Spectroscopic

Binary

These stars cannot be resolved visually. Using a

spectroscope, such binary stars demonstrate red shift

(moving away) or blue shift (moving closer) as per the

Doppler effect.

(This is because the star in orbit is moving away from us or towards us, and its spectral lines hence appear shifted to either the red or blue end of the spectrum. This can only be observed when the star is moving away or towards the observer, not when the star is moving across the observer’s vision.)

The star

needs to be observed over a sustained period so that the

shifting can be confirmed as occurring at regular intervals.

(The size of the gap between a spectral line’s normal and

red shifted position indicates the speed at which the star is

moving away.)

Eclipsing Binary

When the orbital plane of the binary system is edge-on, the

observer will observe changes in light intensity as one of

the stars eclipses the other. This is only considered in the

context of visual binaries. When the light intensity of the

star is plotted as a function of time, the intensity is at its

maximum as both stars are visible, then decreases greatly

as the brightest star eclipses the other. Then full brightness

is restored before brightness decreases slightly when the

brighter star partially eclipses the other.

(Square dips in the graph indicate that the system is

completely edge-on and total eclipses are occurring.

Curved dips indicate partial eclipses when the orbiting

system both stars are at least partially visible at all times.)

Importance of Binary Stars for Determining Stellar Masses

Astronomers need to determine the mass of a star to better understand its spectral class and chemical composition. Because binary systems are held together by gravity, which acts a centripetal force towards a common centre of mass, the mass of a binary system can be calculated if the orbital period and distance of separation is known. This is because the stars within a binary system have to obey Kepler’s 3rd Law:

Rearranging this formula, and splitting the total mass of the system (M) into m1 + m2 …

M = m

1

+ m

2

=

Where r is STAR SEPARATION (metres between stars 1 and 2)

m1/2 is the mass of star ½ (kg)

M is the total mass of the system (kg)

T is the orbital period of the binary second (seconds) Employing these calculations, however, lend themselves to numerous errors:

 Simplified formula to assume perfectly circular orbit (orbit is actually elliptical)

 Measurements do not have a great degree of accuracy (only calculates powers of 10)

Variable Star

A star that’s brightness alters periodically over time due to

the influence of an internal factor (intrinsic) or external

factor (extrinsic)

Intrinsic Variable

A star that displays regular or irregular changes in

brightness

due

to

some

change

within

itself.

(e.g. Nova, chemical composition, pulsating star)

Extrinsic Variable

A star with varying brightness caused by some external

factor (e.g. astrometric binary ‘wobble’ due to invisible

partner)

Periodic

Variable star whose brightness alters in a regular, repeated

pattern over time. Cepheids are examples of periodic

intrinsic variables that have varying luminosity as they

expand and contract in a regular pattern due to their own

gravitational and chemical forces. Most extrinsic variables

occur periodically.

Non-periodic

The brightness of non-periodic variables alters irregularly

with time. Nova and supernova are examples – they are

eruptive variables that exhibit no regular pattern in their

varying brightness as they collapse.

Cepeid Variables are intrinsic, periodic variables that have varying luminosity

as they expand and contract in a regular pattern due to their own gravitational

and chemical forces. This regular change in brightness is due to the changing

surface temperature of the star, which becomes hotter as it contracts (denser =

more kinetic energy) and cooler as it expands (bigger = more gravity.)

The period of a Cepheid variable is related to its average luminosity

(period-luminosity relationship) Cepheids with a longer period (60 days max) are more

luminous (i.e. lower luminosity value) than those with shorter periods (2 days

min) Many Cepheids are present in the Small and Large Magellanic Clouds.

This means that the luminosity of a star can be ascertained if the star’s period of

variation (the time taken in seconds for the brightness pattern to perform a

complete cycle) is known. Once the luminosity of the star is determined through

the use of a luminosity-period graph (above), the luminosity can be compared

to the apparent brightness in order to calculate the distance to the Cepheid:

m – M = 5 – 5

Understanding the period-luminosity relationship allows astronomers to

calculate the distances to distant galaxies containing Cepheids by examining

their period, calculating their luminosity, calculating the distance modulus using

the apparent brightness and hence calculating the distance using the above

equation. This method has been instrumental in astronomers’ exploration of the

universe.

2

nd

Hand Data: Impact of technology on Astronomy



The development of electronic data collection, storage and computation

technology has greatly improved the efficiency and accuracy with which

astronomers perform their observations.



Cosmic Background Explorer (COBE); Chandra X-ray Telescope; Hubble Space

Telescope; etc;

Practical: Computer Simulation of Eclipsing Binaries



An online applet was used to simulate the motion and corresponding apparent brightness of eclipsing binary systems when observed from different angles. Many of the intrinsic and extrinsic factors influencing the system could be altered, and the effects upon the apparent brightness observed.

+ves:

+ Allows us to observe a simplified model of a binary system from different angles + Allows us to manipulate intrinsic and extrinsic factors that influence the stars’ apparent brightness (orbital radius, surface temperature, size, density, star radius etc;) + Provides a luminosity-period graph that illustrates how the brightness varies periodically over time (curved for partial overlap + square graphs for complete overlap)

-ves

- Simplification of the model: represents circular orbit, not elliptical - Does not allow students to simulate non-periodic variables - Does not account for how the luminosity is calculated from the period (circumvents calculations)

6. Life Cycle of Stars

Planetary Nebula

Massive cloud of dust and Hydrogen ions, atoms and molecules. Planetary nebula may be dark or bright if illuminated by a protostar from within. Massive planetary nebula, containing more material, form larger stars (blue giants.) Planetary nebula are the remnants of previous stars gone nova.

Protostar

A dust cloud with a hot, dense core that illuminates the surrounding dust particles, making the entire system appear luminous and colourful.

Main Sequence

A star with varying brightness caused by some external factor (e.g. _{astrometric binary ‘wobble’ due to invisible partner)}

p-p reaction

A 3-step reaction occurring in main sequence stars cooler than Sol:

C.N.O reaction

Faster reaction undergone by large main sequence stars – another reaction that fuses Hydrogen to produce Helium that uses higher activation energy. Carbon is present as a catalyst that speeds the reaction – partial contributor to the short lifespan of main sequence stars

Protostar

A protostar forms when the gas and dust in a planetary nebula congeal on a centre of mass. This core grows due to accretion, becoming denser and converting the GPE of the system into KE. The system becomes a protostar when the GPE balances the KE of the core. The protostar’s bright core usually illuminates the nebula as it continues to contract and grow hotter. A protostar behaves like a non-periodic intrinsic variable, plotted in the top-right of the H-R diagram due to its size. When the core’s temperature reaches 8millionoK, fusion reactions begin and the ZAMs stabilises.

Sol

The name given to our own G2, yellow-coloured, medium-sized sun. It has a luminosity of 1, to which all of the other stars are assigned comparative luminosity values.

Helium Flash

Large stars transition slowly from main sequence  red giants. Smaller main sequence stars, however, experience a sudden onset of helium fusion as they transition rapidly to red giants, resulting in a “Helium Flash.”

Blue Main

Sequence Stars

Possess 30x as much fuel as our sun and are 10,000x as luminous. They only survive a few million years due to their quick decay. There are no old blue stars. Large stars have an abundance of Hydrogen.

Yellow Main

Sequence Star

A star like our sun lasts 10 billion years. Appear brighter from earth as the human eye is more sensitive to yellow light than blue light.

Red main

Sequence Stars

(red dwarfs)

Possess much less fuel than our sun and use it very slowly. They have lifetimes 100’s of billions of years. (90% of main sequence stars are old red dwarfs that have not yet expired due to coolness)

Positron Decay

A type of radiation decay in which an atom loses a positively charged electron, a neutrino and energy. The product is an atom of the same atomic weight with one less atomic number (proton.)

ZAMs

Zero Age Main Sequence –when a protostar reaches 8million oK

Electron

Degeneracy

Phenomenon causing the collapse of massive stars.

Stellar Wind

A stream of radiated energy and fast particles emitted from a star.

Stellar Formation

 Dust particles within a planetary nebula, heated by solar winds, begin to congeal due to attractive forces between the minute particles

 The surrounding dust particles converge upon an exponentially growing core. The energy possessed at this stage is in the form of gravitational potential energy (GPE)

 Gravity causes the cold (no kinetic energy) dust cloud to collapse upon the core, generating heat (GPE  Kinetic Energy) The surrounding dust cloud absorbs energy from the mass (thermal, EMR) and radiates it into space, aiding the contraction.

(Massive protostars form more rapidly than small stars – heat increases reaction rate)

 The star continues to collapse until a balance is attained between the radiation pressure and gravity – it is now named a protostar. The time taken to progress to this stage is about 1 million years. The surrounding nebula cloud is dispersed by stellar winds produced by the protostar, preventing additional matter adding to the star.

 At this stage, due to its low heat and density, the mass appears red-giant-like: bright, cool and not dense. The protostar is not undergoing nuclear reactions, but is behaving as a bright, non-periodic intrinsic variable star.

 Because the kinetic/heat energy within the star is insufficient to counter the inward contraction of gravity, the star continues to contract, becoming less luminous but also hotter and denser. The surrounding planetary nebula (dust cloud) also spins faster with the steadily-heating star. Dust particles converge quickly into masses which become stars, which fragment to form orbiting planets – solar systems are formed.

 When the core temperature reaches 8 million oK, it begins fusing Hydrogen to Helium – becoming a ZAMS – Zero Age Main Sequence Star

 The ZAMS quickly stabilises when a balance is attained between gravity (which condenses and heats the star) and internal fusion reactions (which push outward and prevent further contraction.) To progress to this stage for a star of 1 solar mass usually takes about 50 million years.

Key Stages of a Star’s Life

1. Material in a planetary nebula congeals and collapses into a core due to

gravitational attraction, forming a hot core of matter. This luminous core

lights up the surrounding dust cloud. The luminous cloud with its hot core is

known as a protostar. The increasing density and heat of the core generates

stellar winds that prevent the addition of matter. The core itself appears red

giant-like, being large, red and cool. The star continues to contract slowly,

becoming hotter and more dense.

2. Once the core temperature reaches 8 million, the star begins fusing Hydrogen to Helium – becoming a ZAMS – Zero Age Main Sequence Star. Where the ZAMS enters the main sequence is dependent upon its mass. The ZAMS quickly stabilises when a balance is attained between gravity (which condenses and heats the star) and internal fusion reactions (which push outward and prevent further contraction.) The surrounding nebula cloud is dispersed by stellar winds produced by the main sequence, preventing additional matter adding to the star.

3.

The main sequence may be a large, hot blue star if it was formed from a large nebula, or a cool, small yellow-red main sequence star like our own sun. 90% of a star’s lifespan is spent as a main sequence, undergoing hydrogen fusion. The star only consumes 15% of its Hydrogen reserves before nova, bequeathing hydrogen for the daughter stars to fuse. The mass of the star determines the position in which it enters the main sequence. All main sequence stars migrate slightly along the main sequence throughout the duration of their existence, becoming slightly brighter and hotter towards the end of their life as a main sequence star. Large, hot blue stars have a shorter lifespan than small, yellow-red stars.

4.

Once the star’s helium content reaches 12%, fusion of Hydrogen ceases. Without the outward push of the hydrogen fusion reaction, the star collapses, becoming much hotter and denser. This induces Helium fusion, the energy of which pushes the surface of the star outwards – causing the star to expand to a large, cool star known as a red giant. Large main sequence stars may become a supergiant. There are no old blue stars, as blue is an indicator of extremely high temperatures which equate to a rapid rate of decay.

5. A star’s life ends when it exhausts is fuel and is unable to fuse any lighter elements to form heavier ones. The fusion reactions cease and the star collapses under its own gravity, an event known as Nova. The nova of small stars forms white dwarfs, small, hot dense stars that are the remnants of the star’s core. They are luminous due to the kinetic energy they still possess after nova. Larger stars go supernova, becoming a super-dense pulsar star or a black hole.

 Blue Main Sequence Stars

Star Fuel Reactions

There are 2 main reactions that occur within a main sequence star, depending on its size: Proton-proton chain reaction: P-p reactions are the dominant type of reaction within smaller, cooler main sequence stars like our own sun. P-p reactions require lower activation energy to proceed. P-p reactions fuse 4 hydrogen nuclei (protons) into helium in 3 steps:

1) Two H-atoms (protons) combine to produce Heavy Hydrogen (deuterium) nucleus – a positron (positively charged electron), a neutrino (v) and energy are also released. 2) Heavy hydrogen fuses with another hydrogen atom to produce a neutron-deficient

Helium atom – gamma radiation and energy are also released

3) Two of the neutron-deficient Helium atoms fuse together to form a stable Helium atom, 2 Hydrogen nucleuses (protons) and energy.

Carbon-Nitrogen-Oxygen Reaction (CNO): CNO reactions dominate within large, hot, blue main sequence stars, plotted on the left of the HR-Diagram. This reaction has a much higher activation energy, but still accomplishes the production of Helium from the fusion of Hydrogen. Carbon atoms are present as catalysts for the 6-step reaction:

The CNO reaction is much faster than the p-p reaction, causing the hotter, larger blue stars to expire faster. This is also why the CNO reaction releases heat faster.

The core Helium content reaches 15%, the star transitions to a red giant or supergiant and begins undergoing Triple-alpha reactions to fuse Helium into heavier elements (such as carbon and iron.) Three helium atoms combine to form Carbon, and Carbon and Helium atoms combine to form oxygen:

3 4He2  12C6 + gamma + energy

Star Clusters

Depending on their age, star clusters may be either open star clusters or globular clusters:

 Open Star Clusters are NEWCLUSTERS – they have no red giants or white dwarfs in them. The stars of open clusters are just babies – all main sequence stars. (e.g. Pleiades)

 Globular Clusters are OLD CLUSTERS - typically globe shaped with millions of distant suns. Many older stars – red giants and white dwarfs – are present, because hotter, bluer stars age faster than the cooler main sequence stars. (e.g. Omega Centauri) – Visually, a globular cluster appears as a ‘blot’ of light at the centre, that disperses as it moves out.

Hotter, larger stars age quicker – they use up their fuel faster and progress through their life stages quicker.

Determining the Age of a Star using H-R Diagrams

The age of a star can be determined by examining the cluster of which it is part:

 All the stars in a cluster are about the same age and distance

 Open Clusters are young, sparse clusters consisting of a few hundred loosely bound stars. Open cluster stars have spectra that reveal and abundance of metals.

 Globular clusters contain hundreds of thousands of stars bound together in a rough sphere. Globular clusters have a fewer metallic spectral lines.

Open Cluster Globular Cluster MB type stars occupy the main sequence

(most of the stars are main sequence)

Only the lower portion of the main sequence is present (cooler stars age slower)

No Red Giants / White Dwarfs Many red giants / White dwarfs / highly luminous, large stars

Stellar masses > 0.1M All stellar masses <0.8M

 In open clusters, young, hot stars occupy the main sequence.

 Larger stars have a shorter ‘incubation’ period – take less time to form

 Stars greater than 8 solar masses go onto form other heavier elements until Fe is formed

Star Death

A star dies when fusion reactions in the core cease and the outward pressure of radiation is insufficient to balance the compression of gravity.

Stars of comparable size to our sun (1-5 solar masses) undergo the following death:

 Once the red giant stage has ended, the star unleashes numerous ‘bursts’ of luminosity as it disperses layers of its atmosphere. These gases ejected from the star appear as ‘rings’ known as planetary nebula, from which new stars form.

 The core collapses into a white dwarf – heat and energy condensed into a small, dense mass that still possesses kinetic energy to keep it spinning. It cools very slowly due to its small surface area.

Massive stars (5-8 solar masses) undergo the following death:

 Supergiant star has fused lots of lighter elements into heavier ones, the heaviest being Iron. The core collapses catastrophically, increasing the brightness of the star

dramatically in its supernova stage.

 A neutron star forms if the star was 1.4 solar masses +