GCSE Astronomy

Stars

Magnitude

For professional astronomers, magnitudes might be viewed as a 'burden of history' (a more scientific measurement of a star's output would be in terms of Watts). But for non-professionals they are very convenient. They allow the stars to be classified in terms of how bright they actually appear to the human eye. The stars were classified by the ancients (more specifically, there are records by Hipparchus from 150 BC) into six levels of magnitude, the first magnitude being the brightest and sixth the dimmest. In the whole sky, there are about 6,000 stars capable of being detected by the unaided eye.

Although these magnitudes appear logical to the human eye there is biological effect operating here which is not operating in line with the 'real' scale. A better known analogy concerns sound. A level of 6 decibels is 10 times as powerful as 5 decibels, but 5 decibels is 10 times as powerful as four decibels, so 6 decibels is actually 100 times as powerful as four decibels. The human ear will not detect this 'real' scale, but will nevertheless consider the decibel scale to be 'logical'.

The crude classification of Hipparchus had been extended into an even more unreliable scale when fainter stars were being discovered by telescope, different observers sometimes assigning magnitudes for the same star differing by as amny as five magnitudes. About 1850, the British astronomer N. Pogson had established a convention, which was adopted by E.C. Pickering of the Harvard Obseravtory and has become the standard. Under this system a difference of one magniude corresponds to a ratio of light intensity equal to the fifth root of 100 (2.512). In other words, a star of a particular magnitude is 'really' 2.5 times as bright as a star of one lower magnitude (when measured in Watts). Using this 'real' scale, a first magnitude star is 2.5⁵ times more powerful than a sixth magnitude star , i.e. it is 100 times as bright.

The 'real' scale, as I have called it, is referred to as luminosity. Since it is measured in Watts, you can see it is really a measure of power.

The ancient classification of magnitude has been modified so that we can now talk about magnitudes in decimals, not just whole numbers. A few bright stars have been re-classified to have negative numbers (as explained already, the lower the magnitude, the brighter the star is). By extension the Sun has a negative magnitude (-26.7). The full moon is about -12.5 and Venus at brightest is about -4.

Limits of Observation

Naked eye	6
Binoculars	about 10
15 cm telescope	13
5 meter telescope	20
Most powerful telescopes	24

So far we have been talking about apparent magnitude . The absolute magnitude . is the magnitude that a star would have if viewed at a standard distance of 10 parsec.

Apparent magnitude and absolute magnitude are related by the following formula

M = m + 5 - 5 log d

where M is absolute magnitude, m is apparent magnitude, d is the distance of the star and log denotes logarithm (to the base 10)

Quick Quiz a)   Star α has a magnitude of 3.0. Star δ has a magnitude of 5. How mant times brighter is α than δ ?   b)  Star β is 2.5 times fainter than star α which has a magnitude of -0.2. What is the magnitude of β ?   c)   The distance to a star is 1000pc. Calculate its absolute magnitude.   d)  Star A appears 6.25 times brighter than star B. Star B has an apparent magnitude of 3.4. What is the apparent magnitude of star A ?   e)  Two stars A and B have the same absolute magnitude. Star B is 10 times further away from Earth than star A. If the apparent magnitude of star A is -0.5, what is the apparent magnitude of star B ?

Twenty-Five Brightest Stars

	Star	Constellation	Type	Absolute Mag.	Distance (LY)
1	Sirius	Canis Major	A	1.5	8.8
2	Canopus	Carinae	F	-4.7	196
3	α-Centauri	Centaurus	G,K	4.1	4.3
4	Arcturus	Bootes	K	-0.3	36
5	Vega	Lyra	A	0.5	26
6	Capella	Auriga	G	-0.6	46
7	Rigel	Orion	B	-8.2	815
8	Procyon	Canis Minor	F	2.7	11
9	Achernar	Eridanus	B	-1.3	127
10	Betelgeuse	Orion	M	-5.9	650
11	Hadar	Centaurus	B	-4.3	390
12	Altair	Aquila	A	2.4	16
13	Aldebaran	Taurus	K	-0.6	69
14	Acrux	Crux	B,B	-3.4,-2.9	260
15	Antares	Scorpio	M,A	-5.0	425
16	Spica	Virgo	B	-2.9	260
17	Formalhaut	Piscis Austrinus	A	2.0	23
18	Pollux	Gemini	K	1.0	36
19	Deneb	Cygnus	A	-6.2	1630
20	Mimosa	Crux	B	-4.5	490
21	Regulus	Leo	B	-0.6	85
22	Adhara	Canis Major	B	-5.0	650
23	Castor	Gemini	A	0.8	46
24	Shaula	Scorpio	B	-3.4	325
25	Bellatrix	Orion	B	-3.3	303

The first four have 'negative' apparent magnitudes.

Sirius   -1.46

Canopus   -0.7

Alpha Centauri   -0.3

Arcturus   -0.04

The first 21 stars, down to Regulus (1.35) are classed as first-magnitude.

Hertzsprung-Russell Diagram

The vertical axis depicts the inherent brightness of a star, often in either of two equivalent ways

• The luminosity (measured in Watts) this measure is NOT shown on the above H-R diagram
• Absolute Magnitude

The horizontal axis is graduated differently to convention and increases from right to left. It represents either of two equivalent measures

• The temperature (here shown in Centigrade but also often shown in Kelvin, i.e. Centigrade (or Celsius) plus 273)
• Spectral Class, ranging across (hottest first) O, B, A, F, G, K, M, R, N, S (Oh Be A Fine Girl Kiss Me Right Now Sweetie)

About 90% of stars fall on the Main Sequence. Originally it was thought that maybe stars started off on the top left of the Main-Sequence and descended down the Sequence as they aged. Nowadays it is known that a star enters the Main Sequence when it starts to burn hydrogen in its core. It enters at a definite place on the Main Sequence and more or less stays at the same location during its entire hydrogen-burning phase.

Note that as you ascend the Main sequence, the mass of the stars increase. This increased mass will mean more hydrogen is being burnt, producing a brighter star, which then means that higher mass stars will have a shorter lifetime on the Main Sequence than less massive stars. This effect is accelerated by the more efficent nuclear reactions that the more massive stars are able to generate.

This particular characteristic can be used to calculate the age of a cluster - a Hertzsprung-Russell diagram for the stars in a cluster will show a definite upper limit for Main Sequence stars (the turn-off point), all stars more massive than this will have ended their hydrogen burning existence already.

And following on from what we have just said, smaller stars are much more numerous than other types of stars.

You can see that the Sun is a G star. These stars have lifetimes of around 10 billion years - the Sun is about halfway thru this lifetime.

Each spectrum class can be broken down into 10 divisions - the Sun appears to be G2, although different values are quoted.

The Hertzsprung Russell Diagram seems to show that the maximum mass for a Main Sequence is about 60 times the Solar Mass. The minimum mass of a star is about 0.1 of a Solar Mass, the mass required to produce nuclear reactions in the core. The surface temperature of stars varies from 2000 to 35,000 degrees.

Population I and Population II Stars

In the 1940s, Walter Baade classified stars into two populations. The naming of these populations appear to be the 'wrong way round' given that they actually concern differences related to age.

Population I stars are younger stars with a relatively high metal content (about 1% by mass).

Population II stars are older. They formed at the time when the Universe was primarily Hydrogen and Helium - it had not been significantly seeded with heavier elements by Supernova explosions.

The difference in metal content, although small, makes a significant difference to the way that stars evolve. To be more precise, it makes a significant difference to the size of stars that are formed - clouds contracting to form population I stars tend to fragment more and proceed to produce smaller stars.

Population II stars predominate in elliptical galaxies and in the center of spiral galaxies i.e. in the bulge and in globular clusters orbiting predominantly in the halo. Population I stars predominate in the spiral arms of spiral galaxies.

Naming

Many of the bright stars have names derived from Arabic and also Greek.

In 1603, Johann Bayer published his Uranometria star atlas which listed stars using letters of the Greek alphabet. In general, the sequence was stated in terms of decreasing magnitude although there are discrepancies, for example α Orionis is Betelgeuse and β Orionis is Rigel, despite Rigel being brighter than Betelgeuse.

In 1725, Flamsteed's catalog Historia Coelestis Britannica appeared which introduced a numerical system, with the sequence running west to east. Under this system Orion is 58 Orionis. This naming also covered fainter stars than Bayer's

Binary Stars

About half of 'observed stars' are binary stars - so actually two-thirds of stars are members of a binary system (if you're still with me).

It was William Herschel in 1802 who first produced a proof that binary systems existed. John Michell had predicted them mathematically in 1767 - he found that the incidence of apparently close pairings of stars was too great for them all to be effects of line of sight.

Some of the better know binaries are

• Alpha Centauri   Furthermore, Proxima Centauri rotates around this double making it a multiple star system

• Mizar   in the Plough, was the first binary to be discovered in 1650, although it wasn't until the work of Herschel that it was recognized as such.

• Albireo   in Cygnus. One is bright yellow (3.1) and the other dimmer and bluish (5.1).

• Sirius   Sirius A actually has a White Dwarf as a companion. Although Sirius is very close to us, Sirius B is very hard to detect.

• Algol   is an eclipsing binary. Its brightness varies in a regular way as one binary blocks off the light from the other. Every 69 hours it dims from second to third magnitude, as was already known to the Arabs before the Middle Ages. The pair cannot be resolved by telescopes on Earth. It lies in Perseus, marking the head of Medusa. It was John Goodricke in 1782 who realized that it was acting in such a strange way because it was a binary. Its light curvve is shown below.

  
  
  

• γ-Andromedae   consisting of an orange component (mag. 2.2) and a blue component (mag. 5.0).

Spectroscopic Binaries is the name applied to binaries whose nature can only be detected via their Doppler Shift.

Variable Stars

Mira (Omicron Ceti) was the first star recognized to be a variable star, in 1596 (by Fabricius). Fabricius actually actually noticed it as a new star, then it disappeared, reappearing in 1609. It is capable of varying in 11 months between second magnitude and tenth magnitude, although the range of variation varies. As is common, a variable star gives its name to a class of stars, if it is found that other stars also behave in the same way - which is the case here. All Mira stars are Red Giants and evidence points to them being stars dying thru pulsations, these pulsations gradually causing the star to lose matter. They are also called long-period variables.

Flare Stars are red dwarfs that flare up briefly for a few minutes and can take only a short time to flare up, e.g. 20 seconds to change by six magnitudes. This activity is unpredictable. Proxima Centauri is a flare star.

A Nova is assumed to be caused by a White Dwarf in a binary star accumulating matter streaming from its companion, resulting in short-lived fusion and an increase in brightness by about 1000 times in a few days followed by a slower decline to original brightness. All novas observed are in binary systems anyway. Related classes are recurrent novae - less powerful but repeated over decades or centuries (only a couple of which ever reached naked-eye visibility), and dwarf novae (also called U Geminorum or SS Cygni stars) which are even smaller outbursts but recur on a time scale of months. These groups are also called cataclysmic variables.

Cepheids see Distance Ladder - Cepheids

W Virginis stars are actually Population II Cepheids. The identication of the different properties between Population II and Population I Cepheids led to a rescaling of the Universe - see Distance Ladder.

Red Supergiants Betelegeuse is a well known variable, see below. Mu Cephei is another, called the Garnet Star. This latter star is actually much more luminous intrinsically than Betelegeuse but much further away. It varies in magnitude between 3.4 and 5.1, with no well-marked period.

The first variable to be discovered in a constellation is given the designation R, the second S and so on until Z. The next variable is called RR, then RS until RZ. Next comes SS to SZ, TT to TZ, etc. etc. until ZZ. Next after that becomes AA - and so until AZ, followed by BB - up until BZ, followed by CC etc. etc. etc, leaving out J, up to QZ. This highly logical system allows 334 stars to be named. Any stars after this are designated with a system just using numbers.

Spectrum

Luminous solids, or liquids and gas under high-pressure will emit a continuous spectrum of all wavelengths. This is the type of spectrum that the Sun will emit allowing rainbow effects when its light is passed thru a prism.

On the other hand, low pressure gas (and this includes gases of what are normally solids or liquids under normal Earth conditions) will emit radiation at discrete values. In other words, it will emit radiation of certain fixed and distinct frequencies. This spectrum will be the signature of a particular substance - different substances have different spectra.

In addition to emitting only at fixed frequencies, a substance will also absorb radiation at the very same frequencies. This is an important feature in astronomy because this behavior will produce dark absorption lines for a substance of the same pattern as the emission lines produced by the very same substance.

Most famously, absorption lines of Sodium can be detected easily in the Sun's spectrum - the famous Fraunhofer Lines. These lines appear dark because they absorb light from the Sun at a particular frequency, later emitting light of the same frequency except that this emission will be in a different direction and so will not be detected by us - we notice a dark line in the spectrum.

Red Dwarfs

And the faint star in the Alpha Centauri system, Proxima Centauri, which is currently the closest star to us, is also a Red Dwarf.

Barnard's Star is a Red Dwarf and was detected in 1916, by E.E. Barnard. It is the star with the largest proper motion. This star is 6 light years away and lies in the constellation of Ophiuchis Its surface temperature is 3000 degrees. Its movement is 10.29 seconds of arc per year - it takes 180 years to move distance roughly equal to full moon.

Wolf 359 in Leo is a Red Dwarf. For a long time it held the record as the least intrinsically luminous star known. Only Alpha Centauri and Barnard's Star lie closer to us.

Brown Dwarfs

These stars are not actually brown - they emit a feeble glow of infra-red.

For a period at least, they were strong candidates for the 'missing' dark matter in the Universe.

Details of Brightest Stars

	Star
1	Sirius	Binary with a White Dwarf companion (the Pup) with a period of 50 years. The White Dwarf was once the more massive of the two. Obviously Sirius is bright to us because it is close - kowever, intrinsically, it is about 23 times brighter than the Sun, and has roughly twice the mass (2.5 to be more precise).
2	Canopus
3	α-Centauri	At 1.33 parsecs (4.3 light years), the nearest star system to us but only visible from South of a latitude of +30°. It is actually a triple star system. The two brightest form a visual binary of period of 80 years, separated by a distance of 24 AU (about the diameter of the Solar System). The brighter of this binary, as a type G2, is very similar to the Sun. The 'third' star, Proxima Centauri is intrinsically very faint being an M type star, and is separated from the other two by about 10,000 AU. This is a typical triple system, i.e. a close binary accompanied by a much more distant third component which is usually less massive and fainter. Various alternative names are also given in some texts (Rigel Kent, Toliman, Bundula) although α-Centauri but I am not sure how often these names are used in practice.
4	Arcturus	Red Giant which is often considered to be bright orange. Four solar masses, 115 times as bright intrinsically. In the last 2000 years its position has changed by over one degree.
5	Vega	bluish, overhead in Summer
6	Capella	spectrum similar to the Sun, but much larger than the Sun. A spectroscopic binary, with both stars evolving into Red Giants. Capella and Vega are the only two first magnitude stars that can reach the zenith as viewed from Britain.
7	Rigel	Has binary companion of 7th magnitude.
8	Procyon	Actually a binary star, with a White Dwarf companion. Its name means 'before the dog' in Greek, indicating that it rises before Sirius.
9	Achernar	at the 'mouth' of the 'river' Eridanus, adjacent to the Magellanic Clouds.
10	Betelgeuse	Red Supergiant. Temperature about 3000K. Diameter is about 1000 times that of the Sun. Some surface features can be detected with telescopes. According to some sources, its name means something like 'armpit of the great one' and it at one of Orion's 'shoulders' (the right one, but to the left as seen by us) - you are however likely to see other stated derivations of the name. Betelgeuse is the only marked variable among the first magnitude starsas well as the 11th brightest star in the sky. It is a well known semi-regular, pulsatingvariable, whose main period appears to be around 5.7 years with shorter periods of 150to 300 days superimposed. It varies in magnitude between 0.4 and 1.2 in cycles of about six years. The star has a peak magnitude of 0.2 in 1933 and again in1942. At minimum brightness, as in 1927 and 1941, the magnitude may drop below 1.2,a difference in light intensity of about two times. The Hubble telescope resolved it into a disk in 1995, the first star to be seen as anything other than a point of light.
11	Hadar	β-Centauri. This along with α-Centauri are pointers to the Southern Cross.
12	Altair	Rotates in 6.5 hours, resulting in its horizontal radius being 1.5 times its vertical radius. Flanked by two stars.
13	Aldebaran	Red Giant. Temperature 3600K, Luminosity 400 solar luminosities. At a distance of 20 parsecs, the more powerful telescopes can just about resolve its disk.
14	Acrux	Lies at the foot of the Southern Cross (in the direction that points towards the Southern Pole.
15	Antares	Red Supergiant, type M, one of the largest stars known with a diameter about 4590 that of the Sun. However, since it has only a mass of 10-15 Solar masses, it is not very dense. Some sources suggest that it could be similar to a very hot vacuum inside. Temperature of around 3000K. Its name means 'rival of Mars'. Binary with a B-type companion.
16	Spica	Found to be a spectroscopic binary in 1889, with an orbital period of 4 days. Absolute magnitude of -3.7, about 1740 times more luminous than the Sun.
17	Formalhaut	southernmost first-magnitude star visible from Britain. In the constellation Southern Fish, it represents the 'fish's mouth into which Aquarius is pouring his water'. Has been quite important for navigation.
18	Pollux	The brighter of the Gemini. Also orange whereas Castor is white.
19	Deneb	its name means 'tail' (i.e. of the Swan). It is a Supergiant, being 60,000 more luminous than the Sun. In contrast to most stars in this list, it is far away, at 1500 light years distance.
20	Mimosa	β Crucis. At the end of the Eastern 'horizontal' of the Southern Cross.
21	Regulus
22	Adhara	Brightest second magnitude star
23	Castor	Found to be a binary star in 1719 - the first to be observed and highly important at the type for showing that gravity was at work elsewhere in the Universe. Since then each component has been found to be a spectroscopic binary. Also a companion star had been discovered which also turned out to be a spectroscopic binary.
24	Shaula
25	Bellatrix	At Orion's 'shoulder' (right one as seen by us)