Instability strip

The unqualified term instability strip usually refers to a region of the Hertzsprung–Russell diagram largely occupied by several related classes of pulsating variable stars:[1] Delta Scuti variables, SX Phoenicis variables, and rapidly oscillating Ap stars (roAps) near the main sequence; RR Lyrae variables where it intersects the horizontal branch; and the Cepheid variables where it crosses the supergiants.

RV Tauri variables are also often considered to lie on the instability strip, occupying the area to the right of the brighter Cepheids (at lower temperatures), since their pulsations are attributed to the same mechanism.

HR-diag-instability-strip

Position on the HR diagram

The instability strip intersects the main sequence in the region of A and F stars (1–2 solar mass (M)) and extends to G and early K bright supergiants (early M if RV Tauri stars at minimum are included). Above the main sequence, the vast majority of stars in the instability strip are variable. Where the instability strip intersects the main sequence, the vast majority of stars are stable, but there are some variables, including the roAp stars.

Pulsations

Stars in the instability strip pulsate due to He III (doubly ionized helium).[1] In normal A-F-G stars He is neutral in the stellar photosphere. Deeper below the photosphere, at about 25,000–30,000K, begins the He II layer (first He ionization). Second ionization (He III) starts at about 35,000–50,000K.

When the star contracts, the density and temperature of the He II layer increases. He II starts to transform into He III (second ionization). This causes the opacity of the star to increase and the energy flux from the interior of the star is effectively absorbed. The temperature of the star rises and it begins to expand. After expansion, He III begins to recombine into He II and the opacity of the star drops. This lowers the surface temperature of the star. The outer layers contract and the cycle starts from the beginning.

The phase shift between a star's radial pulsations and brightness variations depends on the distance of He II zone from the stellar surface in the stellar atmosphere. For most Cepheids, this creates a distinctly asymmetrical observed light curve, rising rapidly to maximum and falling slowly back down to minimum.

Other pulsating stars

There are several types of pulsating star not found on the instability strip and with pulsations driven by different mechanisms. At cooler temperatures are the long period variable AGB stars. At hotter temperatures are the Beta Cephei and PV Telescopii, variables. Right at the edge of the instability strip near the main sequence are Gamma Doradus variables. The band of White dwarfs has three separate regions types of variable: DOV, DBV, and DAV (= ZZ Ceti variables) white dwarfs. Each of these types of pulsating variable has an associated instability strip[2][3][4] created by variable opacity partial ionisation regions other than helium.[1]

Most high luminosity supergiants are somewhat variable, including the Alpha Cygni variables. In the specific region of more luminous stars above the instability strip are found the yellow hypergiants which have irregular pulsations and eruptions. The hotter luminous blue variables may be related and show similar short- and long-term spectral and brightness variations with irregular eruptions.

References

  1. ^ a b c Gautschy, A.; Saio, H. (1996). "Stellar Pulsations Across the HR Diagram: Part 2". Annual Review of Astronomy and Astrophysics. 34: 551. Bibcode:1996ARA&A..34..551G. doi:10.1146/annurev.astro.34.1.551.
  2. ^ Beauchamp, A.; Wesemael, F.; Bergeron, P.; Fontaine, G.; Saffer, R. A.; Liebert, J.; Brassard, P. (1999). "Spectroscopic Studies of DB White Dwarfs: The Instability Strip of the Pulsating DB (V777 Herculis) Stars". The Astrophysical Journal. 516 (2): 887. Bibcode:1999ApJ...516..887B. doi:10.1086/307148.
  3. ^ Starrfield, S. G.; Cox, A. N.; Hodson, S. W.; Pesnell, W. D. (1983). "The discovery of nonradial instability strips for hot, evolved stars". The Astrophysical Journal. 268: L27. Bibcode:1983ApJ...268L..27S. doi:10.1086/184023.
  4. ^ Dupret, M. -A.; Grigahcène, A.; Garrido, R.; Gabriel, M.; Scuflaire, R. (2004). "Theoretical instability strips for δ Scuti and γ Doradus stars". Astronomy and Astrophysics. 414 (2): L17. Bibcode:2004A&A...414L..17D. doi:10.1051/0004-6361:20031740.
14 Persei

14 Persei is a single star in the northern constellation Perseus, located roughly 1,900 light years away from the Sun. It is visible to the naked eye as a faint, yellow-hued star with an apparent visual magnitude is 5.43. The object is slowly moving closer to the Earth with a heliocentric radial velocity of −1.2 km/s.The spectral classification of 14 Persei is as a G0 yellow supergiant, but in other respects it appears to be a giant star. The class has been given as G0Ib-II Ca1 CH-1 or G0Ib-IIa Ca1, where the abundance suffixes indicate stronger Calcium lines than expected for its class, or weaker hydrocarbons. Other analyses of the spectrum give a class of G0Ib. Stellar models of 14 Persei yield an estimated mass four times that of the Sun and an age of 162 million years. It has expanded to 57 times the Sun's radius and has a projected rotational velocity of 8.7 km/s. The star is radiating 372 times as much luminosity compared to the Sun from its enlarged photosphere at an effective temperature of 5,624 K.14 Persei has been calculated to lie within the Cepheid instability strip although it is not considered to be variable. Uncertainty in the absolute magnitude means that the star may actually lie near the instability strip but not on it. Small periodic radial velocity variations are seen, but an order of magnitude or more smaller than for Cepheid variables and with longer periods than would be expected for pulsations. The cause of the radial velocity changes and the difference between variable and non-variable stars within the instability strip is unknown.

18 Vulpeculae

18 Vulpeculae is a binary star system in the northern constellation of Vulpecula, located about 489 light years away from the Sun. It is visible to the naked eye as a faint, white-hued star with a combined apparent visual magnitude of 5.51. The system is moving closer to the Earth with a heliocentric radial velocity of −11.7 km/s.This is a double-lined spectroscopic binary system with an orbital period of 9.3 days and a small eccentricity of 0.0116. It is a detached binary with a semimajor axis of 0.14742 ± 0.00047 AU. The system contains a Delta Scuti variable, but the temperature places it to the blue (hotter) side of the δ Scuti instability strip. The combined stellar classification of this system remains unclear, with classes of A3 III, A1 IV, A3 V, and A2 IV being given. The ultraviolet spectrum matches an A3 dwarf star. It shows no spectral peculiarities.

19 Aquilae

19 Aquilae is a single star located 142 light-years (44 parsecs) away from the Sun in the equatorial constellation of Aquila. 19 Aquilae is the Flamsteed designation. It is visible to the naked eye as a dim, yellow-white hued star with an apparent visual magnitude of 5.23. The star is moving closer to the Earth with a heliocentric radial velocity of −46.7 km/s.This object has a stellar classification of F0 III-IV, with the luminosity class matching an evolving star transitioning from the subgiant to a giant stage. Poretti et al. (2003) list it as a suspected Gamma Doradus variable, and it is located near the cooler end of the instability strip on the Hertzsprung–Russell diagram. These spatial coordinates are a source of X-ray emission, which is most likely coming from the star.19 Aquilae is an estimated 2.25 billion years old with a moderately high rate of spin, showing a projected rotational velocity of 57.0 km/s. It has 1.54 times the mass of the Sun and 2.50 times the Sun's radius. The star is radiating 12.8 times the luminosity of the Sun from its photosphere at an effective temperature of 6,784 K.

35 Aquilae

35 Aquilae (abbreviated 35 Aql) is a star in the equatorial constellation of Aquila. 35 Aquilae is its Flamsteed designation though it also bears the Bayer designation c Aquilae. The apparent visual magnitude of this star is 5.8, which means it is a faint star but visible to the naked eye from dark suburban or rural skies. It has an annual parallax shift of 16.34 mas that is caused by the Earth's orbit around the Sun. This yields a distance estimate of 200 light-years (61 parsecs), give or take a 4 light-year margin of error. At this distance, the visual magnitude is diminished by 0.26 from extinction caused by interstellar gas and dust.The spectrum of 35 Aquilae fits a stellar classification of A0 V, indicating it is an A-type main sequence star. Compared to the Sun, it has 210% of the mass and 180% of the radius. As such, it is much brighter than the Sun, emitting 14 times the luminosity from its outer atmosphere at an effective temperature of 8,939 K. This heat causes it to glow with the white-hot hue of an A-type star. 35 Aquilae is spinning rapidly with a projected rotational velocity of 110 km/s.In 1994 it was discovered that 35 Aquilae is a variable star with a pulsation period of just 30 minutes. It was determined to be a Delta Scuti variable, which is a type of star found on the instability strip that undergoes short period pulsations. Observation with the Spitzer Space Telescope shows that 35 Aquilae is radiating an excess level of infrared radiation for a star of its type. This excess may be explained by the heating of nearby interstellar dust belonging to a diffuse cloud of material that the star is passing through. This interaction may also explain the Lambda Boötis categorization for this star.

70 Aquarii

70 Aquarii is a variable star located 425 light years away from the Sun in the equatorial constellation of Aquarius. It has the variable star designation FM Aquarii; 70 Aquarii is the Flamsteed designation. It is near the lower limit of visibility to the naked eye, appearing as a dim, yellow-white hued star with a baseline apparent visual magnitude of 6.19. This star is moving closer to the Earth with a heliocentric radial velocity of –5.8 km/s.This is an F-type main-sequence star with a stellar classification of F0 V. Located in the lower part of the instability strip, it is a Delta Scuti-type variable that ranges in brightness from magnitude 6.16 down to 6.19 with a period of 125 minutes (0.087 days). The star has a high rate of spin, showing a projected rotational velocity of 110 km/s. It has four times the Sun's radius and is radiating 45 times the luminosity of the Sun from its photosphere at an effective temperature of around 7,314 K.

Blue loop

In the field of stellar evolution, a blue loop is a stage in the life of an evolved star where it changes from a cool star to a hotter one before cooling again. The name derives from the shape of the evolutionary track on a Hertzsprung–Russell diagram which forms a loop towards the blue (i.e. hotter) side of the diagram.

Blue loops can occur for red supergiants red giant branch stars, or asymptotic giant branch stars. Some stars may undergo more than one blue loop. Many pulsating variable stars such as Cepheids are blue loop stars. Stars on the horizontal branch are not generally referred to as on a blue loop even though they are temporarily hotter than on the red giant or asymptotic giant branches. Loops occur far too slowly to be observed for individual stars, but are inferred from theory and from the properties and distribution of stars in the H-R diagram.

Classical Cepheid variable

Classical Cepheids (also known as Population I Cepheids, Type I Cepheids, or Delta Cepheid variables) are a type of Cepheid variable star. They are population I variable stars that exhibit regular radial pulsations with periods of a few days to a few weeks and visual amplitudes from a few tenths of a magnitude to about 2 magnitudes.

There exists a well-defined relationship between a classical Cepheid variable's luminosity and pulsation period, securing Cepheids as viable standard candles for establishing the galactic and extragalactic distance scales. Hubble Space Telescope (HST) observations of classical Cepheid variables have enabled firmer constraints on Hubble's law. Classical Cepheids have also been used to clarify many characteristics of our galaxy, such as the Sun's height above the galactic plane and the Galaxy's local spiral structure.Around 800 classical Cepheids are known in the Milky Way Galaxy, out of an expected total of over 6,000. Several thousand more are known in the Magellanic Clouds, with more known in other galaxies. The Hubble Space Telescope has identified classical Cepheids in NGC 4603, which is 100 million light years distant.

HD 84810

HD 84810, also known as l Carinae (l Car), is a star in the southern constellation of Carina. Its apparent magnitude varies from about 3.4 to 4.1, making it readily visible to the naked eye and one of the brighter members of Carina. Based upon parallax measurements, it is approximately 1,600 light-years (490 parsecs) from Earth.From the characteristics of its spectrum, l Carinae has a stellar classification of G5 Iab/Ib. This indicates the star has reached a stage in its evolution where it has expanded to become a supergiant with 169 times the radius of the Sun. As this is a massive star with 8–13 times the mass of the Sun, it rapidly burns through its supply of nuclear fuel and has become a supergiant in roughly 17-19 million years, after spending 15–17 million years as a main sequence star.l Carinae is classified as a Cepheid variable star and its brightness varies over an amplitude range of 0.725 in magnitude with a long period of 35.560 days. The radial velocity of the star likewise varies by 39 km/s during each pulsation cycle. Its radius varies by about 40 R☉ as it pulsates, reaching maximum size as its brightness is decreasing towards minimum.It has a compact circumstellar envelope that can be discerned using interferometry. The envelope has been resolved at an infrared wavelength of 10μm, showing a radius of 10–100 AU at a mean temperature of 100 K. The material for this envelope was supplied by mass ejected from the central star.The period of l Carinae is calculated to be slowly increasing and it is thought to be crossing the instability strip for the third time, cooling as it evolves towards a red supergiant after a blue loop.

Omicron Serpentis

Omicron Serpentis (ο Ser, ο Serpentis) is a solitary star in the Serpens Cauda (tail) section of the equatorial constellation Serpens. Based upon an annual parallax shift of 18.83 mas as seen from Earth, it is located around 173 light years from the Sun. The star is visible to the naked eye with a base apparent visual magnitude of +4.26.This is a white-hued A-type main sequence star with a stellar classification of A2 Va. It is located on the lower instability strip and is classified as a Delta Scuti type variable star. The apparent magnitude of the star varies in the range 4.26−4.27 with a period of 76 minutes, or 0.053 days.The star has an estimated 2.13 times the mass of the Sun and about 2.2 times the Sun's radius. It is about half a billion years old and is spinning with a projected rotational velocity of 112.6 km/s. Omicron Serpentis is radiating 42.6 times the solar luminosity from its photosphere at an effective temperature of 8,972 K.

RU Camelopardalis

RU Camelopardalis, or RU Cam, is a W Virginis variable (type II Cepheid) in the constellation of Camelopardalis. It is also a Carbon star, which is very unusual for a Cepheid variable.

Rapidly oscillating Ap star

Rapidly oscillating Ap stars (roAp stars) are a subtype of the Ap star class that exhibit short-timescale rapid photometric or radial velocity variations. The known periods range between 5 and 23 minutes. They lie in the δ Scuti instability strip on the main sequence.

Rho Phoenicis

Rho Phoenicis (ρ Phoenicis) is a variable star in the constellation of Phoenix. From parallax measurements by the Gaia spacecraft, it is located at a distance of 240 light-years (74 parsecs) from Earth.This star is classified as an F-type giant with a spectral type of F3III, and in the HR diagram it occupies in the lower part of the instability strip. Rho Phoenicis is Delta Scuti variable, changing its visual apparent magnitude between 5.17 and 5.27 with a period of around 0.1–0.2 days. The pulsation period seems to vary in a timescale of weeks, which indicates the star is not a simple radial pulsator. The analysis of the temperature variations over the pulsation cycles also supports this conclusion. It is not clear if the pulsation period really is variable, or if the light curve is simply the sum of multiple stable pulsation frequencies.Stellar evolution models indicate that Rho Phoenicis has about 2.1 times the solar mass and an age of around 1 billion years. This star is shining with 35 times the solar luminosity and has an effective temperature of 6,900 K. Its metallicity is high, with an overall metal abundance 25% greater the solar value. Gaia Data Release 2 discovered a star with the same proper motion and parallax as Rho Phoenicis. It has an apparent magnitude of 14.6 (G band) and is at a separation of 7.9 arcseconds.

SV Vulpeculae

SV Vulpeculae is a Classical Cepheid (δ Cepheid) variable star in the constellation Vulpecula. It is a supergiant at a distance of 8,000 light years.

SV Vulpeculae is a δ Cepheid variable whose visual apparent magnitude ranges from 6.72 to 7.79 over 45.0121 days. The light curve is highly asymmetric, with the rise from minimum to maximum taking more less than a third of the time for the fall from maximum to minimum. The period has been decreasing on average by 214 seconds/year.SV Vulpeculae is a yellow bright supergiant around twenty thousand times as luminous as the sun, with a spectral type that varies from late F to early K. It pulsates and varies in temperature from below 5,000 K to above 6,000 K. The radius is 216.5 R☉ at maximum, and varies from 188 R☉ to 238 R☉ as the star pulsates.The mass of SV Vulpeculae is now near 15 M☉, and is estimated to have been about 17 M☉ when it was on the main sequence. The rate of change of the period and the atmospheric abundances show that the star is crossing the instability strip for the second time. The first instability strip crossing occurs rapidly during the transition from the main sequence to becoming a red supergiant. The second crossing occurs during core helium burning when the star executes a blue loop, becoming hotter for a time before returning to the red supergiant stage.

S Doradus

S Doradus (also known as S Dor) is located 160,000 light-years away, and is one of the brightest stars in the Large Magellanic Cloud (LMC), a satellite of the Milky Way. It is a luminous blue variable and one of the most luminous stars known, but so far away that it is invisible to the naked eye.

V399 Carinae

V399 Carinae (V399 Car, P Carinae, P Car, 195 G. Carinae) is a variable star in the constellation Carina.

The spectral type of V399 Carinae has been variously assigned between A5 and F0, being a bright, luminous supergiant. Its spectrum is described as having a non-photospheric continuum and silicon absorption lines, indicative of high mass loss.V399 Carinae has long been suspected to be variable. A 1981 study of yellow supergiants fit observations to a Cepheid-like light curve with a period of 58.8 days, although the luminosity and spectral type do not place the star near the Cepheid instability strip. It was listed in the General Catalogue of Variable Stars as a possible δ Cep variable. Further observations refined the period to 47.25 days. The Hipparcos catalogue classified V399 Car as a semiregular variable with a period of 88 days and a mean amplitude of only 0.04 magnitudes. An automated classification from Hipparos photometry suggested it is an α Cygni variable. The observed brightness varies from magnitude +4.63 to +4.72.V399 lies amongst the stars of the open cluster IC 2581, by far the brightest member of the cluster. It is about 7,500 light years from Earth assuming it is a member of IC 2581, which is given a 62.9% probability.

V810 Centauri

V810 Centauri is a double star consisting of a yellow supergiant primary (V810 Cen A) and blue giant secondary (V810 Cen B). It is a small amplitude variable star, entirely due to the supergiant primary which is visually over three magnitudes brighter than the secondary.V810 Cen A shows semi-regular variations with several component periods. The dominant mode is around 156 days and corresponds to Cepheid fundamental mode radial pulsation. Without the other pulsation modes it would be considered a Classical Cepheid variable. Other pulsation modes have been detected at 89 to 234 days, with the strongest being a possible non-radial p-mode at 107 days and a possible non-radial g-mode at 185 days.The blue giant secondary has a similar mass and luminosity to the supergiant primary, but is visually much fainter. The primary is expected to have lost around 5 M☉ since it was on the main sequence, and has expanded and cooled so it lies at the blue edge of the Cepheid instability strip. It is expected to get no cooler and may perform a blue loop while slowly increasing in luminosity.V810 Cen was once thought to be a member of the Stock 14 open cluster at 2.6 kpc, but now appears to be more distant. The distance derived from spectrophotometric study is larger than the mean Hipparcos parallax value but within the margin of error.

X Crucis

X Crucis is a classical Cepheid variable star in the southern constellation of Crux.

X Crucis is a pulsating variable star with am extremely regular amplitude and period. Its apparent magnitude varies from 8.1 to 8.7 every 6.22 days. This type of variable is known as a Cepheid after δ Cephei, the first example to be discovered. X Crucis is a population I star and so is a classical or type I Cepheid variable, to be distinguished from older low-mass stars called type II Cepheid variables.Classical Cepheids pulsate radially so that their size varies. X Crucis pulsates in its fundamental mode and its properties indicate that it is crossing the instability strip for the third time as its evolves back to cooler temperatures. Its radius varies by about 5 R☉ during each cycle, approximately 8% of its mean radius. At the same time its temperature varies between 5,180 and 6,029 K. The radius and temperature do not vary in sync, with the smallest size occurring as the temperature is approaching its maximum. The brightness increases rapidly to a maximum when the star is hottest, then decreases more slowly. This is one of the properties that indicate fundamental mode pulsation.

Yellow hypergiant

A yellow hypergiant is a massive star with an extended atmosphere, a spectral class from A to K, and, starting with an initial mass of about 20–60 solar masses, has lost as much as half that mass. They are amongst the most visually luminous stars, with absolute magnitude (MV) around −9, but also one of the rarest with just 15 known in the Milky Way and six of those in just a single cluster. They are sometimes referred to as cool hypergiants in comparison to O- and B-type stars, and sometimes as warm hypergiants in comparison to red supergiants.

Yellow supergiant star

A yellow supergiant star is a star, generally of spectral type F or G, having a supergiant luminosity class (e.g. Ia or Ib). They are stars that have evolved away from the main sequence, expanding and becoming more luminous.

Yellow supergiants are smaller than red supergiants; naked eye examples include Canopus and Polaris. Many of them are variable stars, mostly pulsating Cepheids such as δ Cephei itself.

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