S-type star

From Wikipedia, the free encyclopedia

 

W Aquilae is an S-type star and Mira variable with a close companion resolved by the Hubble Space Telescope.

 

An S-type star (or just S star) is a cool giant with approximately equal quantities of carbon and oxygen in its atmosphere. The class was originally defined in 1922 by Paul Merrill for stars with unusual absorption lines and molecular bands now known to be due to s-process elements. The bands of zirconium monoxide (ZrO) are a defining feature of the S stars. 

The carbon stars have more carbon than oxygen in their atmospheres. In most stars, such as class M giants, the atmosphere is richer in oxygen than carbon and they are referred to as oxygen-rich stars. S-type stars are intermediate between carbon stars and normal giants. They can be grouped into two classes: intrinsic S stars, which owe their spectra to convection of fusion products and s-process elements to the surface; and extrinsic S stars, which are formed through mass transfer in a binary system.

The intrinsic S-type stars are on the most luminous portion of the asymptotic giant branch, a stage of their lives lasting less than a million years. Many are long period variable stars. The extrinsic S stars are less luminous and longer-lived, often smaller-amplitude semiregular or irregular variables. S stars are relatively rare, with intrinsic S stars forming less than 10% of asymptotic giant branch stars of comparable luminosity, while extrinsic S stars form an even smaller proportion of all red giants.

Spectral features

Cool stars, particularly class M, show molecular bands, with titanium(II) oxide (TiO) especially strong. A small proportion of these cool stars also show correspondingly strong bands of zirconium oxide (ZrO). The existence of clearly detectable ZrO bands in visual spectra is the definition of an S-type star.

The main ZrO series are:

• α series, in the blue at 464.06 nm, 462.61 nm, and 461.98 nm
• β series, in the yellow at 555.17 nm and 571.81 nm
• γ series, in the red at 647.4 nm, 634.5 nm, and 622.9 nm

The original definition of an S star was that the ZrO bands should be easily detectable on low dispersion photographic spectral plates, but more modern spectra allow identification of many stars with much weaker ZrO. MS stars, intermediate with normal class M stars, have barely detectable ZrO but otherwise normal class M spectra. SC stars, intermediate with carbon stars, have weak or undetectable ZrO, but strong sodium D lines and detectable but weak C₂ bands.

S star spectra also show other differences to those of normal M class giants. The characteristic TiO bands of cool giants are weakened in most S stars, compared to M stars of similar temperature, and completely absent in some. Features related to s-process isotopes such as YO bands, SrI lines, BaII lines, and LaO bands, and also sodium D lines are all much stronger. However, VO bands are absent or very weak. The existence of spectral lines from the period 5 element Technetium (Tc) is also expected as a result of the s-process neutron capture, but a substantial fraction of S stars show no sign of Tc. Stars with strong Tc lines are sometimes referred to as Technetium stars, and they can be of class M, S, C, or the intermediate MS and SC.

Some S stars, especially Mira variables, show strong hydrogen emission lines. The H_β emission is often unusually strong compared to other lines of the Balmer series in a normal M star, but this is due to the weakness of the TiO band that would otherwise dilute the H_β emission.

Classification schemes

The spectral class S was first defined in 1922 to represent a number of long-period variables (meaning Mira variables) and stars with similar peculiar spectra. Many of the absorption lines in the spectra were recognised as unusual, but their associated elements were not known. The absorption bands now recognised as due to ZrO are clearly listed as major features of the S-type spectra. At that time, class M was not divided into numeric sub-classes, but into Ma, Mb, Mc, and Md. The new class S was simply left as either S or Se depending on the existence of emission lines. It was considered that the Se stars were all LPVs and the S stars were non-variable, but exceptions have since been found. For example, π¹ Gruis is now known to be a semiregular variable.

The classification of S stars has been revised several times since its first introduction, to reflect advances in the resolution of available spectra, the discovery of greater numbers of S-type stars, and better understanding of the relationships between the various cool luminous giant spectral types.

Comma notation

The formalisation of S star classification in 1954 introduced a two-dimensional scheme of the form SX,Y. For example, R Andromedae is listed as S6,6e.

X is the temperature class. It is a digit between 1 (although the smallest type actually listed is S1.5) and 9, intended to represent a temperature scale corresponding approximately to the sequence of M1 to M9. The temperature class is actually calculated by estimating intensities for the ZrO and TiO bands, then summing the larger intensity with half the smaller intensity.

Y is the abundance class. It is also a digit between 1 and 9, assigned by multiplying the ratio of ZrO and TiO bands by the temperature class. This calculation generally yields a number which can be rounded down to give the abundance class digit, but this is modified for higher values:

• 6.0 – 7.5 maps to 6
• 7.6 – 9.9 maps to 7
• 10.0 – 50 maps to 8
• > 50 maps to 9

In practice, spectral types for new stars would be assigned by referencing to the standard stars, since the intensity values are subjective and would be impossible to reproduce from spectra taken under different conditions.

A number of drawbacks came to light as S stars were studied more closely and the mechanisms behind the spectra came to be understood. The strengths of the ZrO and TiO are influenced both by temperature and by actual abundances. The S stars represent a continuum from having oxygen slightly more abundant than carbon to carbon being slightly more abundant than oxygen. When carbon becomes more abundant than oxygen, the free oxygen is rapidly bound into CO and abundances of ZrO and TiO drop dramatically, making them a poor indicator in some stars. The abundance class also becomes unusable for stars with more carbon than oxygen in their atmospheres.

This form of spectral type is a common type seen for S stars, possibly still the most common form.

Elemental intensities

The first major revision of the classification for S stars completely abandons the single-digit abundance class in favour of explicit abundance intensities for Zr and Ti. So R And is listed, at a normal maximum, with a spectral type of S5e Zr5 Ti2.

In 1979 Ake defined an abundance index based on the ZrO, TiO, and YO band intensities. This single digit between 1 and 7 was intended to represent the transition from MS stars through increasing C/O ratios to SC stars. Spectral types were still listed with explicit Zr and Ti intensity values, and the abundance index was included separately in the list of standard stars.

Abundance index criteria and estimated C/O ratio

Abundance index	Criteria	C/O ratio
1	TiO ≫ ZrO and YO	< 0 .90
2	TiO ≥ ZrO ≥ 2×YO	0 .90
3	2×YO ≥ ZrO ≥ TiO	0 .93
4	ZrO ≥ 2×YO > TiO	0 .95
5	ZrO ≥ 2×YO, TiO = 0	> 0 .95
6	ZrO weak, YO and TiO = 0	~ 1
7	CS and carbon stars	> 1

Slash notation

The abundance index was immediately adopted and extended to run from 1 to 10, differentiating abundances in SC stars. It was now quoted as part of the spectral type in preference to separate Zr and Ti abundances. To distinguish it from the earlier abandoned abundance class it was used with a slash character after the temperature class, so that the spectral class for R And became S5/4.5e.

The new abundance index is not calculated directly, but is assigned from the relative strengths of a number of spectral features. It is designed to closely indicate the sequence of C/O ratios from below 0.95 to about 1.1. Primarily the relative strength of ZrO and TiO bands forms a sequence from MS stars to abundance index 1 through 6. Abundance indices 7 to 10 are the SC stars and ZrO is weak or absent so the relative strength of the sodium D lines and C_s bands is used. Abundance index 0 is not used, and abundance index 10 is equivalent to a carbon star Cx,2 so it is also never seen.

Abundance index criteria and estimated C/O ratio

Abundance index	Criteria	C/O ratio
MS	Strongest YO and ZrO bands just visible
1	TiO ≫ ZrO and YO	< 0 .95
2	TiO > ZrO	0 .95:
3	ZrO = TiO, YO strong	0 .96
4	ZrO > TiO	0 .97
5	ZrO ≫ TiO	0 .97
6	ZrO strong, TiO = 0	0 .98
7 (SC)	ZrO weaker, D lines strong	0 .99
8 (SC)	No ZrO or C2, D lines very strong	1 .00
9 (SC)	C2 very weak, D lines very strong	1 .02
10 (SC)	C2 weak, D lines strong	1 .1:

The derivation of the temperature class is also refined, to use line ratios in addition to the total ZrO and TiO strength. For MS stars and those with abundance index 1 or 2, the same TiO band strength criteria as for M stars can be applied. Ratios of different ZrO bands at 530.5 nm and 555.1 nm are useful with abundance indices 3 and 4, and the sudden appearance of LaO bands at cooler temperatures. The ratio of BaII and SrI lines is also useful at the same indices and for carbon-rich stars with abundance index 7 to 9. Where ZrO and TiO are weak or absent the ratio of the blended features at 645.6 nm and 645.0 nm can be used to assign the temperature class.

Asterisk notation

With the different classification schemes and the difficulties of assigning a consistent class across the whole range of MS, S, and SC stars, other schemes are sometimes used. For example, one survey of new S/MS, carbon, and SC stars uses a two-dimensional scheme indicated by an asterisk, for example S5*3. The first digit is based on TiO strength to approximate the class M sequence, and the second is based solely on ZrO strength.

Standard stars

This table shows the spectral types of a number of well-known S stars as they were classified at various times. Most of the stars are variable, usually of the Mira type. Where possible the table shows the type at maximum brightness, but several of the Ake types in particular are not at maximum brightness and so have a later type. ZrO and TiO band intensities are also shown if they are published (an x indicates that no bands were found). If the abundances are part of the formal spectral type then the abundance index is shown. 

Comparison of spectral types under different classification schemes

Star	Keenan (1954)	Keenan et al. (1974)	Ake (1979)	Keenan-Boeshaar (1980)
R Andromedae	S6,6e:	Zr4 Ti3	S4,6e	S8e Zr6	4	S5/4.5e	Zr5 Ti2
X Andromedae	S3,9e	Zr3 Ti0	S2,9e:	S5.5e Zr4	5	S5/4.5e	Zr2.5 Tix
RR Andromedae	S7,2e:	Zr2 Ti6.5	S6,2e:	S6.5e Zr3 Ti6	2	S6/3.5e	Zr4+ Ti4
W Aquilae	S4,9:	Zr4 Ti0	S3,9e:			S6/6e	Zr6 Ti0
BD Camelopardalis	S5,3	Zr2.5 Ti4		S3.5 Zr2.5 Ti3	2	S3.5/2	Zr2+ Ti3
BH Crucis			SC8,6:			SC4.5/8-e	Zr0 Tix Na10:
Chi Cygni	S7,1e:	Zr0-2 Ti7	S7,2e	S9.5 Zr3 Ti9	1	S6+/1e = Ms6+	Zr2 Ti6
R Cygni	S3.5,9e:	Zr3.5 Ti0	S3,9e	S8e Zr7 Ti3:	4	S5/6e	Zr4 Tix
R Geminorum	S3,9e:	Zr3 Ti0	S3,9e	S8e Zr5	5	S4/6e	Zr3.5 Tix

Formation

There are two distinct classes of S-type stars: intrinsic S stars; and extrinsic S stars. The presence of Technetium is used to distinguish the two classes, only being found in the intrinsic S-type stars.

Intrinsic S stars

Stellar properties as a 2 M_☉ solar-metallicity red giant evolves along the TP-AGB to become an S star and then a carbon star

 

Intrinsic S-type stars are thermal pulsing asymptotic giant branch (TP-AGB) stars. AGB stars have inert carbon-oxygen cores and undergo fusion both in an inner helium shell and an outer hydrogen shell. They are large cool M class giants. The thermal pulses, created by flashes from the helium shell, cause strong convection within the upper layers of the star. These pulses become stronger as the star evolves and in sufficiently massive stars the convection becomes deep enough to dredge up fusion products from the region between the two shells to the surface. These fusion products include carbon and s-process elements. The s-process elements include zirconium (Zr), yttrium (Y), lanthanum (La), technetium (Tc), barium (Ba), and strontium (Sr), which form the characteristic S class spectrum with ZrO, YO, and LaO bands, as well as Tc, Sr, and Ba lines. The atmosphere of S stars has a carbon to oxygen ratio in the range 0.5 to < 1. Carbon enrichment continues with subsequent thermal pulses until the carbon abundance exceeds the oxygen abundance, at which point the oxygen in the atmosphere is rapidly locked into CO and formation of the oxides diminishes. These stars show intermediate SC spectra and further carbon enrichment leads to a carbon star.

Extrinsic S stars

The Technetium isotope produced by neutron capture in the s-process is ⁹⁹Tc and it has a half life of around 200,000 years in a stellar atmosphere. Any of the isotope present when a star formed would have completely decayed by the time it became a giant, and any newly formed ⁹⁹Tc dredged up in an AGB star would survive until the end of the AGB phase, making it difficult for a red giant to have other s-process elements in its atmosphere without technetium. S-type stars without technetium form by the transfer of technetium-rich matter, as well as other dredged-up elements, from an intrinsic S star in a binary system onto a smaller less-evolved companion. After a few hundred thousand years, the ⁹⁹Tc will have decayed and a technetium-free star enriched with carbon and other s-process elements will remain. When this star is, or becomes, a G or K type red giant, it will be classified as a Barium star. When it evolves to temperatures cool enough for ZrO absorption bands to show in the spectrum, approximately M class, it will be classified as an S-type star. These stars are called extrinsic S stars.

Distribution and numbers

Stars with a spectral class of S only form under a narrow range of conditions and they are uncommon. The distributions and properties of intrinsic and extrinsic S stars are different, reflecting their different modes of formation. 

TP-AGB stars are difficult to identify reliably in large surveys, but counts of normal M-class luminous AGB stars and similar S-type and carbon stars have shown different distributions in the galaxy. S stars are distributed in a similar way to carbon stars, but there are only around a third as many as the carbon stars. Both types of carbon-rich star are very rare near to the galactic centre, but make up 10% – 20% of all the luminous AGB stars in the solar neighbourhood, so that S stars are around 5% of the AGB stars. The carbon-rich stars are also concentrated more closely in the galactic plane. S-type stars make up a disproportionate number of Mira variables, 7% in one survey compared to 3% of all AGB stars.

Extrinsic S stars are not on the TP-AGB, but are red giant branch stars or early AGB stars. Their numbers and distribution are uncertain. They have been estimated to make up between 30% and 70% of all S-type stars, although only a tiny fraction of all red giant branch stars. They are less strongly concentrated in the galactic disc, indicating that they are from an older population of stars than the intrinsic group.

Properties

Very few intrinsic S stars have had their mass directly measured using a binary orbit, although their masses have been estimated using Mira period-mass relations or pulsations properties. The observed masses were found to be around 1.5 – 5 M_☉ until very recently when Gaia parallaxes helped discover intrinsic S stars with solar-like masses and metallicities. Models of TP-AGB evolution show that the third dredge-up becomes larger as the shells move towards the surface, and that less massive stars experience fewer dredge-ups before leaving the AGB. Stars with masses of 1.5 – 2.0 M_☉ will experience enough dredge-ups to become carbon stars, but they will be large events and the star will usually skip straight past the crucial C/O ratio near 1 without becoming an S-type star. More massive stars reach equal levels of carbon and oxygen gradually during several small dredge-ups. Stars more than about 4 M_☉ experience hot bottom burning (the burning of carbon at the base of the convective envelope) which prevents them becoming carbon stars, but they may still become S-type stars before reverting to an oxygen-rich state. Extrinsic S stars are always in binary systems and their calculated masses are around 1.6 – 2.0 M_☉. This is consistent with RGB stars or early AGB stars.

Intrinsic S stars have luminosities around 5,000 – 10,000 L_☉, although they are usually variable. Their temperatures average about 2,300 K for the Mira S stars and 3,100 K for the non-Mira S stars, a few hundred K warmer than oxygen-rich AGB stars and a few hundred K cooler than carbon stars. Their radii average about 526 R_☉ for the Miras and 270 R_☉ for the non-miras, larger than oxygen-rich stars and smaller than carbon stars. Extrinsic S stars have luminosities typically around 2,000 L_☉, temperatures between 3,150 and 4,000 K, and radii less than 150 R_☉. This means they lie below the red giant tip and will typically be RGB stars rather than AGB stars.

Mass loss and dust

Extrinsic S stars lose considerable mass through their stellar winds, similar to oxygen-rich TP-AGB stars and carbon stars. Typically the rates are around 1/10,000,000th those of the sun, although in extreme cases such as W Aquilae they can be more than ten times higher.

It is expected that the existence of dust drives the mass loss in cool stars, but it is unclear what type of dust can form in the atmosphere of an S star with most carbon and oxygen locked into CO gas. The stellar winds of S stars are comparable to oxygen-rich and carbon-rich stars with similar physical properties. There is about 300 times more gas than dust observed in the circumstellar material around S stars. It is believed to be made up of metallic iron, FeSi, silicon carbide, and forsterite. Without silicates and carbon, it is believed that nucleation is triggered by TiC, ZrC, and TiO₂.

Detached dust shells are seen around a number of carbon stars, but not S-type stars. Infrared excesses indicate that there is dust around most intrinsic S stars, but the outflow has not been sufficient and longlasting enough to form a visible detached shell. The shells are thought to form during a superwind phase very late in the AGB evolution.

Examples

BD Camelopardalis is a naked-eye example of an extrinsic S star. It is slow irregular variable in a symbiotic binary system with a hotter companion which may also be variable.

The mira variable Chi Cygni is an intrinsic S star. When near maximum light, it is the sky's brightest S-type star. It has a variable late type spectrum about S6 to S10, with features of zirconium, titanium and vanadium oxides, sometimes bordering on the intermediate MS type. A number of other prominent Mira variables such as R Andromedae and R Cygni are also S-type stars, as well as the peculiar semiregular variable π¹ Gruis.

The naked-eye star ο¹ Ori is an intermediate MS star and small amplitude semiregular variable with a DA3 white dwarf companion. The spectral type has been given as S3.5/1-, M3III(BaII), or M3.2IIIaS.

Asymptotic giant branch

From Wikipedia, the free encyclopedia

 

H–R diagram for globular cluster M5, with known AGB stars marked in blue, flanked by some of the more luminous red-giant branch stars, shown in orange

     Asymptotic giant branch (AGB)      Upper red-giant branch (RGB)      Horizontal branch (HB)      RR Lyrae variable (RR)      End of main sequence, subgiant branch, and lower RGB

The asymptotic giant branch (AGB) is a region of the Hertzsprung–Russell diagram populated by evolved cool luminous stars. This is a period of stellar evolution undertaken by all low- to intermediate-mass stars (0.6–10 solar masses) late in their lives.

Observationally, an asymptotic-giant-branch star will appear as a bright red giant with a luminosity ranging up to thousands of times greater than the Sun. Its interior structure is characterized by a central and largely inert core of carbon and oxygen, a shell where helium is undergoing fusion to form carbon (known as helium burning), another shell where hydrogen is undergoing fusion forming helium (known as hydrogen burning), and a very large envelope of material of composition similar to main-sequence stars.

Stellar evolution

A sun-like star moves onto the AGB from the Horizontal Branch after core helium exhaustion

 

A 5 M_☉ star moves onto the AGB after a blue loop when helium is exhausted in its core

 

When a star exhausts the supply of hydrogen by nuclear fusion processes in its core, the core contracts and its temperature increases, causing the outer layers of the star to expand and cool. The star becomes a red giant, following a track towards the upper-right hand corner of the HR diagram. Eventually, once the temperature in the core has reached approximately 3×10⁸ K, helium burning (fusion of helium nuclei) begins. The onset of helium burning in the core halts the star's cooling and increase in luminosity, and the star instead moves down and leftwards in the HR diagram. This is the horizontal branch (for population II stars) or red clump (for population I stars), or a blue loop for stars more massive than about 2 M_☉.

After the completion of helium burning in the core, the star again moves to the right and upwards on the diagram, cooling and expanding as its luminosity increases. Its path is almost aligned with its previous red-giant track, hence the name asymptotic giant branch, although the star will become more luminous on the AGB than it did at the tip of the red giant branch. Stars at this stage of stellar evolution are known as AGB stars.

AGB stage

The AGB phase is divided into two parts, the early AGB (E-AGB) and the thermally pulsing AGB (TP-AGB). During the E-AGB phase, the main source of energy is helium fusion in a shell around a core consisting mostly of carbon and oxygen. During this phase, the star swells up to giant proportions to become a red giant again. The star's radius may become as large as one astronomical unit (~215 R_☉).

After the helium shell runs out of fuel, the TP-AGB starts. Now the star derives its energy from fusion of hydrogen in a thin shell, which restricts the inner helium shell to a very thin layer and prevents it fusing stably. However, over periods of 10,000 to 100,000 years, helium from the hydrogen shell burning builds up and eventually the helium shell ignites explosively, a process known as a helium shell flash. The luminosity of the shell flash peaks at thousands of times the total luminosity of the star, but decreases exponentially over just a few years. The shell flash causes the star to expand and cool which shuts off the hydrogen shell burning and causes strong convection in the zone between the two shells. When the helium shell burning nears the base of the hydrogen shell, the increased temperature reignites hydrogen fusion and the cycle begins again. The large but brief increase in luminosity from the helium shell flash produces an increase in the visible brightness of the star of a few tenths of a magnitude for several hundred years, a change unrelated to the brightness variations on periods of tens to hundreds of days that are common in this type of star.

Evolution of a 2 M_☉ star on the TP-AGB

 

During the thermal pulses, which last only a few hundred years, material from the core region may be mixed into the outer layers, changing the surface composition, a process referred to as dredge-up. Because of this dredge-up, AGB stars may show S-process elements in their spectra and strong dredge-ups can lead to the formation of carbon stars. All dredge-ups following thermal pulses are referred to as third dredge-ups, after the first dredge-up, which occurs on the red-giant branch, and the second dredge up, which occurs during the E-AGB. In some cases there may not be a second dredge-up but dredge-ups following thermal pulses will still be called a third dredge-up. Thermal pulses increase rapidly in strength after the first few, so third dredge-ups are generally the deepest and most likely to circulate core material to the surface.

AGB stars are typically long-period variables, and suffer mass loss in the form of a stellar wind. Thermal pulses produce periods of even higher mass loss and may result in detached shells of circumstellar material. A star may lose 50 to 70% of its mass during the AGB phase.

Circumstellar envelopes of AGB stars

Formation of a planetary nebula at the end of the asymptotic giant branch phase.

 

The extensive mass loss of AGB stars means that they are surrounded by an extended circumstellar envelope (CSE). Given a mean AGB lifetime of one Myr and an outer velocity of 10 km/s, its maximum radius can be estimated to be roughly 3×10¹⁴ km (30 light years). This is a maximum value since the wind material will start to mix with the interstellar medium at very large radii, and it also assumes that there is no velocity difference between the star and the interstellar gas. Dynamically, most of the interesting action is quite close to the star, where the wind is launched and the mass loss rate is determined. However, the outer layers of the CSE show chemically interesting processes, and due to size and lower optical depth, are easier to observe.

The temperature of the CSE is determined by heating and cooling properties of the gas and dust, but drops with radial distance from the photosphere of the stars which are 2,000–3,000 K. Chemical peculiarities of an AGB CSE outwards include:

• Photosphere: Local thermodynamic equilibrium chemistry
• Pulsating stellar envelope: Shock chemistry
• Dust formation zone
• Chemically quiet
• Interstellar ultraviolet radiation and photodissociation of molecules – complex chemistry

The dichotomy between oxygen-rich and carbon-rich stars has an initial role in determining whether the first condensates are oxides or carbides, since the least abundant of these two elements will likely remain in the gas phase as CO_x. 

In the dust formation zone, refractory elements and compounds (Fe, Si, MgO, etc.) are removed from the gas phase and end up in dust grains. The newly formed dust will immediately assist in surface catalyzed reactions. The stellar winds from AGB stars are sites of cosmic dust formation, and are believed to be the main production sites of dust in the universe.

The stellar winds of AGB stars (Mira variables and OH/IR stars) are also often the site of maser emission. The molecules that account for this are SiO, H₂O, OH, HCN, and SiS. SiO, H₂O, and OH masers are typically found in oxygen-rich M-type AGB stars such as R Cassiopeiae and U Orionis,^[16] while HCN and SiS masers are generally found in carbon stars such as IRC +10216. S-type stars with masers are uncommon.

After these stars have lost nearly all of their envelopes, and only the core regions remain, they evolve further into short-lived preplanetary nebulae. The final fate of the AGB envelopes are represented by planetary nebulae (PNe).

Late thermal pulse

As many as a quarter of all post-AGB stars undergo what is dubbed a "born-again" episode. The carbon–oxygen core is now surrounded by helium with an outer shell of hydrogen. If the helium is re-ignited a thermal pulse occurs and the star quickly returns to the AGB, becoming a helium-burning, hydrogen-deficient stellar object. If the star still has a hydrogen-burning shell when this thermal pulse occurs, it is termed a "late thermal pulse". Otherwise it is called a "very late thermal pulse".

The outer atmosphere of the born-again star develops a stellar wind and the star once more follows an evolutionary track across the Hertzsprung–Russell diagram. However, this phase is very brief, lasting only about 200 years before the star again heads toward the white dwarf stage. Observationally, this late thermal pulse phase appears almost identical to a Wolf–Rayet star in the midst of its own planetary nebula.

Stars such as Sakurai's Object and FG Sagittae are being observed as they rapidly evolve through this phase.

Super-AGB stars

Stars close to the upper mass limit to still qualify as AGB stars show some peculiar properties and have been dubbed super-AGB stars. They have masses above 7 M_☉ and up to 9 or 10 M_☉ (or more). They represent a transition to the more massive supergiant stars that undergo full fusion of elements heavier than helium. During the triple-alpha process, some elements heavier than carbon are also produced: mostly oxygen, but also some magnesium, neon, and even heavier elements. Super-AGB stars develop partially degenerate carbon–oxygen cores that are large enough to ignite carbon in a flash analogous to the earlier helium flash. The second dredge-up is very strong in this mass range and that keeps the core size below the level required for burning of neon as occurs in higher-mass supergiants. The size of the thermal pulses and third dredge-ups are reduced compared to lower-mass stars, while the frequency of the thermal pulses increases dramatically. Some super-AGB stars may explode as an electron capture supernova, but most will end as an oxygen–neon white dwarf. Since these stars are much more common than higher-mass supergiants, they could form a high proportion of observed supernovae. Detecting examples of these supernovae would provide valuable confirmation of models that are highly dependent on assumptions.

Hertzsprung–Russell diagram

From Wikipedia, the free encyclopedia

 

An observational Hertzsprung–Russell diagram with 22,000 stars plotted from the Hipparcos Catalogue and 1,000 from the Gliese Catalogue of nearby stars. Stars tend to fall only into certain regions of the diagram. The most prominent is the diagonal, going from the upper-left (hot and bright) to the lower-right (cooler and less bright), called the main sequence. In the lower-left is where white dwarfs are found, and above the main sequence are the subgiants, giants and supergiants. The Sun is found on the main sequence at luminosity 1 (absolute magnitude 4.8) and B−V color index 0.66 (temperature 5780 K, spectral type G2V).

 

An HR diagram showing many well known stars in the Milky Way galaxy

 

The Hertzsprung–Russell diagram, abbreviated as H–R diagram, HR diagram or HRD, is a scatter plot of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their stellar classifications or effective temperatures. More simply, it plots a star's luminosity (brightness) against its temperature (color). 

The diagram was created circa 1910 by Ejnar Hertzsprung and Henry Norris Russell and represents a major step towards an understanding of stellar evolution. 

The related color–magnitude diagram (CMD) plots the apparent magnitudes of stars against their color, usually for a cluster so that the stars are all at the same distance.

Historical background

In the nineteenth-century large-scale photographic spectroscopic surveys of stars were performed at Harvard College Observatory, producing spectral classifications for tens of thousands of stars, culminating ultimately in the Henry Draper Catalogue. In one segment of this work Antonia Maury included divisions of the stars by the width of their spectral lines. Hertzsprung noted that stars described with narrow lines tended to have smaller proper motions than the others of the same spectral classification. He took this as an indication of greater luminosity for the narrow-line stars, and computed secular parallaxes for several groups of these, allowing him to estimate their absolute magnitude.

In 1910 Hans Rosenberg published a diagram plotting the apparent magnitude of stars in the Pleiades cluster against the strengths of the calcium K line and two hydrogen Balmer lines. These spectral lines serve as a proxy for the temperature of the star, an early form of spectral classification. The apparent magnitude of stars in the same cluster is equivalent to their absolute magnitude and so this early diagram was effectively a plot of luminosity against temperature. The same type of diagram is still used today as a means of showing the stars in clusters without having to initially know their distance and luminosity. Hertzsprung had already been working with this type of diagram, but his first publications showing it were not until 1911. This was also the form of the diagram using apparent magnitudes of a cluster of stars all at the same distance.

Russell's early (1913) versions of the diagram included Maury's giant stars identified by Hertzsprung, those nearby stars with parallaxes measured at the time, stars from the Hyades (a nearby open cluster), and several moving groups, for which the moving cluster method could be used to derive distances and thereby obtain absolute magnitudes for those stars.

Forms of diagram

There are several forms of the Hertzsprung–Russell diagram, and the nomenclature is not very well defined. All forms share the same general layout: stars of greater luminosity are toward the top of the diagram, and stars with higher surface temperature are toward the left side of the diagram. 

The original diagram displayed the spectral type of stars on the horizontal axis and the absolute visual magnitude on the vertical axis. The spectral type is not a numerical quantity, but the sequence of spectral types is a monotonic series that reflects the stellar surface temperature. Modern observational versions of the chart replace spectral type by a color index (in diagrams made in the middle of the 20th Century, most often the B-V color) of the stars. This type of diagram is what is often called an observational Hertzsprung–Russell diagram, or specifically a color–magnitude diagram (CMD), and it is often used by observers. In cases where the stars are known to be at identical distances such as within a star cluster, a color–magnitude diagram is often used to describe the stars of the cluster with a plot in which the vertical axis is the apparent magnitude of the stars. For cluster members, by assumption there is a single additive constant difference between their apparent and absolute magnitudes, called the distance modulus, for all of that cluster of stars. Early studies of nearby open clusters (like the Hyades and Pleiades) by Hertzsprung and Rosenberg produced the first CMDs, a few years before Russell's influential synthesis of the diagram collecting data for all stars for which absolute magnitudes could be determined.

Another form of the diagram plots the effective surface temperature of the star on one axis and the luminosity of the star on the other, almost invariably in a log-log plot. Theoretical calculations of stellar structure and the evolution of stars produce plots that match those from observations. This type of diagram could be called temperature-luminosity diagram, but this term is hardly ever used; when the distinction is made, this form is called the theoretical Hertzsprung–Russell diagram instead. A peculiar characteristic of this form of the H–R diagram is that the temperatures are plotted from high temperature to low temperature, which aids in comparing this form of the H–R diagram with the observational form.

Although the two types of diagrams are similar, astronomers make a sharp distinction between the two. The reason for this distinction is that the exact transformation from one to the other is not trivial. To go between effective temperature and color requires a color–temperature relation, and constructing that is difficult; it is known to be a function of stellar composition and can be affected by other factors like stellar rotation. When converting luminosity or absolute bolometric magnitude to apparent or absolute visual magnitude, one requires a bolometric correction, which may or may not come from the same source as the color–temperature relation. One also needs to know the distance to the observed objects (i.e., the distance modulus) and the effects of interstellar obscuration, both in the color (reddening) and in the apparent magnitude (where the effect is called "extinction"). Color distortion (including reddening) and extinction (obscuration) are also apparent in stars having significant circumstellar dust. The ideal of direct comparison of theoretical predictions of stellar evolution to observations thus has additional uncertainties incurred in the conversions between theoretical quantities and observations.

Interpretation

An HR diagram with the instability strip and its components highlighted

 

Most of the stars occupy the region in the diagram along the line called the main sequence. During the stage of their lives in which stars are found on the main sequence line, they are fusing hydrogen in their cores. The next concentration of stars is on the horizontal branch (helium fusion in the core and hydrogen burning in a shell surrounding the core). Another prominent feature is the Hertzsprung gap located in the region between A5 and G0 spectral type and between +1 and −3 absolute magnitudes (i.e. between the top of the main sequence and the giants in the horizontal branch). RR Lyrae variable stars can be found in the left of this gap on a section of the diagram called the instability strip. Cepheid variables also fall on the instability strip, at higher luminosities. 

The H-R diagram can be used by scientists to roughly measure how far away a star cluster or galaxy is from Earth. This can be done by comparing the apparent magnitudes of the stars in the cluster to the absolute magnitudes of stars with known distances (or of model stars). The observed group is then shifted in the vertical direction, until the two main sequences overlap. The difference in magnitude that was bridged in order to match the two groups is called the distance modulus and is a direct measure for the distance (ignoring extinction). This technique is known as main sequence fitting and is a type of spectroscopic parallax. Not only the turn-off in the main sequence can be used, but also the tip of the red giant branch stars.

Diagram's role in the development of stellar physics

HR diagrams for two open clusters, M67 and NGC 188, showing the main-sequence turn-off at different ages

 

Contemplation of the diagram led astronomers to speculate that it might demonstrate stellar evolution, the main suggestion being that stars collapsed from red giants to dwarf stars, then moving down along the line of the main sequence in the course of their lifetimes. Stars were thought therefore to radiate energy by converting gravitational energy into radiation through the Kelvin–Helmholtz mechanism. This mechanism resulted in an age for the Sun of only tens of millions of years, creating a conflict over the age of the Solar System between astronomers, and biologists and geologists who had evidence that the Earth was far older than that. This conflict was only resolved in the 1930s when nuclear fusion was identified as the source of stellar energy. 

Following Russell's presentation of the diagram to a meeting of the Royal Astronomical Society in 1912, Arthur Eddington was inspired to use it as a basis for developing ideas on stellar physics. In 1926, in his book The Internal Constitution of the Stars he explained the physics of how stars fit on the diagram. The paper anticipated the later discovery of nuclear fusion and correctly proposed that the star's source of power was the combination of hydrogen into helium, liberating enormous energy. This was a particularly remarkable intuitive leap, since at that time the source of a star's energy was still unknown, thermonuclear energy had not been proven to exist, and even that stars are largely composed of hydrogen, had not yet been discovered. Eddington managed to sidestep this problem by concentrating on the thermodynamics of radiative transport of energy in stellar interiors. Eddington predicted that dwarf stars remain in an essentially static position on the main sequence for most of their lives. In the 1930s and 1940s, with an understanding of hydrogen fusion, came an evidence-backed theory of evolution to red giants following which were speculated cases of explosion and implosion of the remnants to white dwarfs. The term supernova nucleosynthesis is used to describe the creation of elements during the evolution and explosion of a pre-supernova star, a concept put forth by Fred Hoyle in 1954. The pure mathematical quantum mechanics and classical mechanical models of stellar processes enable the Hertzsprung–Russell diagram to be annotated with known conventional paths known as stellar sequences — there continue to be added rarer and more anomalous examples as more stars are analysed and mathematical models considered.