THE SUN AND ITS RELATION TO OTHER STARS

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Stellar astronomyWe’ll discuss properties of solar-type and other stars

– let’s first review some preliminaries:Naming of stars Stellar distance scale: parsecsProperties:

Stellar spectral classesStellar luminosity classesStellar magnitudesStellar colours and relation to Teff

H—R diagram2

Naming of starsStars assigned letters (Greek or Roman) or numbers

and sometimes names (Arabic, Latin, or Greek)The names of most (apparently) brightest stars are

a letter/number followed by the genitive of the Latin name of a constellation, boundaries of which are defined by the IAU, e.g. Betelgeuse = α Orionis, abbreviated α Ori.

Generally brightest 24 stars have Greek letters α, β, γ, δ, ε ... ω

Variable stars given Roman letters (R, S, T, ... Z, then RR, RS, RT, ... RZ, SS, ST, ... SZ, .... ZZ)

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Stellar distance scalesStellar distances are reckoned in parsecs: 1 pc =

the distance at which a star’s annual parallax π = 1 arcsecond, i.e. at the star, the radius of the Earth’s orbit (150 x 106 km) subtends an angle of 1 arcsecond.

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2π

Note: 1 parsec = 3.26 light year = 3.1 x 1013 km

Stellar spectral classes: notation

Visible-light spectra of stars can be arranged in a sequence: O-B-A-F-G-K-M.

This is closely related to the effective temperature:Spectral class Teff (K)

O 40,000B 28,000A 10,000F 7,400G 6,000K 4,900M 3,500

Note: spectral types are subdivided (e.g. B0, B1, B2...B9): spectral classes in this table are B0, A0, etc.

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Stellar Luminosity classes

Stellar spectra also give an indication of whether stars are on the “main sequence” or are evolved, i.e. have reached the end of their main sequence lifetime and have evolved to become giants or supergiants.

Notation for luminosity is: class I (supergiants), II (bright giants), III (giants), IV (subgiants) and V (main sequence/dwarf stars).

The Sun is a G2V star – sometimes called a dG2 star. Its Teff is 5778K.

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Stellar magnitudesIn visible-light range, a star’s apparent brightness defined by

the flux in the spectral region 480—680 nm on a “magnitude” (V) or logarithmic scale.

We define the V magnitude of the star Vega to be V = 0. The V magnitude of any other star is

V = 2.5 [log I(Vega) – log I(star)]where I = energy flux in the 480—680 nm range in SI units:

W m-2. So YZ Canis Minoris (YZ CMi) has V = 11.2: therefore:

I (YZ CMi)/ I (Vega) = 10-11.2/2.5 = 3.3 × 10-5. Note: 5 magnitudes = factor of 100 in brightness.

Magnitudes are on a decreasing flux scale: the brighter the star, the smaller is its apparent magnitude. Some stars have negative magnitudes (e.g. Sirius, V = - 1.45). 7

Absolute magnitudesA star’s absolute magnitude is the apparent

magnitude it has at a distance of 10 pc. Sun’s absolute magnitude MV = + 4.8 (its apparent

magnitude from Earth is mV = -26.7).

For comparison: Sirius has Mv = + 1.4 (brightest star in sky)

α Cen MV = + 4.4 (Sun’s “twin” star)

Proxima Cen MV = 15.5 (nearest star)

Barnard’s star MV = 13.5 (largest proper motion)8

Other visible-light magnitudes

B (“blue”) magnitude is measured by flux in the 380—540 nm range.

U (“ultraviolet”) magnitude is measured by flux in the 300—400 nm range.

Note: U magnitude measures “near” ultraviolet radiation: wavelengths much greater than UV wavelengths measured by spacecraft.Human eye sensitivity (dark-adapted) is approximately 400—630 nm.

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Stellar colours

U, B, V magnitudes of a star are a measure of its brightness in three different wavelength bands.

So U – B and B – V are measures of the star’s “colour”.

In particular B – V is often used as a “proxy” (substitute) for spectral type or effective temperature.

Thus for YZ CMi, spectral type is dM4, B-V = + 1.6 (i.e. V is brighter than B), and Teff = 2900K.

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Hertzsprung-Russell Diagram

HR diagram for nearby stars

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4Mʘ

1Mʘ

0.25 Mʘ

0.5 Mʘ

Stellar masses indicated in units of 1 solar mass = 1 Mʘ

Review of Solar Properties

Compared with most stars in the Milky Way galaxy, Sun has medium mass (1 Mʘ = 2 × 1030 kg).

Sun is mid-way through its life-cycle: age = 4.6 Gyr (expected total lifetime before red giant phase =10 Gyr).

Sun’s interior made up of radiative zone (inner 0.7 Rʘ) and convective zone (outer part, 0.7 – 1.0 Rʘ).

Solar activity: hot corona (temperature rises with height over chromosphere/transition region to corona); active regions (complex magnetic field); flares; coronal mass ejections.

So although photosphere is not very hot (6400 K), its atmosphere (upper chromosphere/corona) is hot and an emitter of ultraviolet, X-ray and radio emission.

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Evidence for solar activity in visible spectrum

The Sun’s visible spectrum has very little evidence of a high-temperature chromosphere, even less of a very hot corona.

The only (very subtle) evidence is that strong absorption spectral lines of ionized Ca (Ca+) – the Ca II H and K lines – have profiles showing small emission peaks, especially over active regions. These peaks arise in the chromosphere.

Wavelengths: Ca II K line 393.4 nm, Ca II H line 396.8 nm.

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Solar-type stars

Many stars with cooler effective temperatures than Sun’s show the Ca II H and K lines as strong emission lines, not absorption lines at all.

Even the Hα and other Balmer lines of H are commonly in emission for such stars.

These stars are normally very dim, cool dwarf stars at the bottom of the H-R diagram – they are called dM stars.

If a dM star has the Hα line in emission, then it is called a dMe star.

There are correspondingly dK and dKe stars

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Properties of dMe starsPhotospheric temperatures may be so low (<3000

K) that molecules form – e.g. TiO (titanium oxide), ZrO (zirconium oxide) plus more usual molecules like H2. (Molecules do exist in the Sun, near the temperature minimum: e.g. H2 and CH.)

Visible-light spectra show emission mostly in red part of spectrum, with strong TiO or ZrO molecular “bands” with strong emission lines – Ca II H and K, Hα and other Balmer lines.

Very often dMe stars are in binary systems, e.g. AT Microscopii, which consists of two dM4.5e stars orbiting around each other.

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Visible-light spectrum of AT Microscopii (dMe,UV Ceti star)

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Hβ

Hγ

Hδ

Ca II H & K

TiO band-heads

From SAAO 1.9 m telescope + spectrograph: 1980

From Bromage et al. (1982)Wavelength in Å (1Å = 0.1 nm)

X-ray and ultraviolet emission from stars

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Spacecraft from the 1970s showed that many stars emit ultraviolet and X-ray radiation.

Many of these stars are similar to the Sun, having “late” spectral types (F, G, K, or M), with effective temperatures ranging from 7400 K or cooler: M5 stars have Teff = 2800 K.

Their UV spectra show emission lines like C IV (155 nm, emitted at ~105 K), He II (30.4 mm, 104 K).

The most intense X-ray emitters are also characterized by large flares, with total flare emission >> the emission from the star itself.

UV & visible-light spectrum of AT Mic

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UV spectrum from IUE satellite SAAO 1.9m tel. spectrum

1Å = 0.1 nm

Short history of Flare Stars

Flare-like brightenings observed optically on certain cool M-type dwarfs: DH Carinae (in 1924) and UV Ceti (in 1948).

These cool stars were also characterized by emission lines in their visible-light spectra, particularly the Ca II H & K lines and Hα lines.

Observations in late 1950s with the Jodrell Bank radio telescope by Lovell and others showed large increases in m-wave radio emission from cool stars including UV Ceti.

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Stellar activity and link to magnetic field

Stellar activity defined by presence of strong chromosphere and corona, and the occurrence of active regions and flares (probably CME’s too).

Stellar activity must be linked to presence of magnetic fields which convey energy from the interior to the atmosphere by either MHD waves or tiny (“nano-”) flares.

The magnetic field is generated by differential rotation and by convection.

So stellar activity has two ingredients: fast stellar rotation and convection.

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Differential rotation and convection

21Differential rotation over a solar cycle (Babcock model).

Convection current carries magnetic field upwards while Coriolis forces twist field (sense shown is for S hemisphere).

Energy transport in stars as a function of Teff

For very hot main sequence stars, whole of stellar interior is fully ionized and energy transport is entirely by radiation.

By spectral class F0 (Teff = 7400K), H is ionized just beneath the stellar surface: radiative transport occurs up to region near surface, then convective transport occurs.

For progressively later (cooler) types (G, K, M), convection becomes increasingly important.

For M stars with Teff < 3500K, whole of star may be convective.

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Stellar activity and spectral typeX-ray coronae and flares are evident in main sequence

stars with spectral type of F0 and later.Very cool stars (M stars of the UV Ceti type) have the

most pronounced flaring activity = “flare stars”.The most active dM and dK stars are those with rapid

rotation rates, which suggest youth (i.e. just formed from gas cloud – older stars lose their angular momentum via stellar winds).

Some B and A stars may also have flares, as do stars with special characteristics, generally binary systems.

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HR diagram for nearby stars

MS stars liable to have coronae

RS, XC

NC

RS = RS CVn binaries.

XC = X-ray coronae

NC = no coronae, just cool winds

dM stars (incl. some dMe stars)

Line source functions

Whether lines are in emission or absorption depends on the source function:S = j/κ = emission coefft./absorption coefft. = processes that create line photons / processes that destroy line photons.

These processes are due to (a) collisions of the emitting atoms with electrons; (b) excitation or de-excitation of emitting atoms with photons from the photospheric radiation field.

If there is a chromosphere, electron collisions become very important.

For flare stars with their dim, red photospheres, the radiation field is not so important.

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Collisionally and photoelectrically controlled lines in solar and stellar spectra

In the Sun, photospheric radiation field is quite strong, so many lines (like Hα and other Balmer lines) are “photoelectrically” controlled, collisions of electrons not important.

Case of Ca II H and K lines slightly different: the chromosphere gives rise to emission line cores since there the lines are collisionally controlled.

But for flare stars, there is a dense chromosphere with much higher temperature (~10,000K) than the photosphere (~3,000K).

This results in nearly all lines (Ca II H and K, Balmer lines (Hα, Hβ etc.) being collisionally controlled, with strong emission peaks formed in the stellar chromosphere.

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Stellar flares

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Flare on Kruger 60B – Kruger 60 is a binary system with two dM stars. Kruger 60B is a flare star. Successive exposures (a to d) are 2 ¼ minutes apart.

60A

60B

(a) (b) (c) (d)

Flare light-curve (U magnitude) on EV Lacertae

28Roizman & Shevchenko (1982)

Balmer line spectrum from flare on AD Leonis (UV Ceti star)

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Spectrum shown is difference of flare and pre-flare spectrum. Balmer lines + Ca II H,K lines + He I (402.6nm) lines all visible. Note 1 Å = 0.1 nm.

Case of AB Doradus (AB Dor)

AB Dor is a young, rapidly rotating dK star – period of rotation is 12 hours (cf. Sun 25-34 days).

Rotation velocity at equator >80 km/s (cf. Sun 2 km/s).

The Einstein X-ray spacecraft found X-ray flares.Rotational modulation in visible-light, suggesting

giant “starspots”. Strong radio emitter. Variable absorption features in Hα line profile

attributed to huge prominences (Collier Cameron).

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Doppler imaging of a stellar prominence: Hα line profile

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Hα line centre is at 656.3 nm = 6563 Å

Velocity from v = Δλ/c

Doppler imaging of a stellar prominence

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Observations of AB Doradus by A. C. Cameron in 1986.

Properties of the clouds in AB Dor’s spectrum

Observations suggest that clouds are like prominences (temperatures 10,000K, electron densities around 1018 m-3).

Prominences appear to co-rotate with star, i.e. revolve around the star in a 12-hour period.

If so, they are probably held in giant magnetic loops extending out to 2.5 x the star’s radius.

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Other active stars: non-solar starsVery young – T Tauri – stars forming out of a

hydrogen cloud often show flaring activity. They appear to be only a few 106 years old.

Flares probably result from blobs of material that cascade into the newly formed star from an accretion disk.

A powerful stellar wind is driven from the main star as it continues to collapse.

The Sun passed through this stage early on its lifetime, with giant flares and solar wind. 34

Model for T Tauri stars

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T Tauri star forms out of gas cloud. Accretion disk supplies mass to the forming star. X-ray flares result from blobs of material falling into star from disk. A powerful stellar wind flows from the main star.

T Tauri and Hind’s nebula

T Tauri is the yellow star in this image, with a nebula (NGC 1555) near by. Both vary with time but not simultaneously. (APOD 26.03.2011)

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W Ursae Majoris (W UMa) stars

Binary star system consisting of two dwarf stars.The two stars are in contact with each other as

they revolve. Material is transferred from the more massive

star to its companion.Orbital periods are < 1 day.Ultraviolet and X-ray observations suggest that

the stars share a common chromosphere and corona.

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Schematic of W UMa system

38Two stars orbit each other in ~ 1 day; mass transfer from more massive to less massive star. Stars share chromosphere/corona.

RS Canum Venaticorum (RS CVn) stars

Binary star systems in which an F or G main sequence star orbits an evolved K subgiant star.

The two stars are tidally locked (rotation period of each star = their orbital period).

Magnetic loop structures may connect the two stars.

Very hot coronae, with temperatures ~50-80 MK.

Giant X-ray flares may occur.39

Scheme for RS CVn star system

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Stars are separate while orbiting each other. Mass transfer from K subgiant to G main sequence star. Corona made up of magnetic loop systems connecting the stars.

Doppler imaging of starspotsOptical light-curve of some active stars show modulation

with same period as the rotation period of the star.Prominent absorption lines (like Hα) may show extra

absorption features which cross the line profile.This can be used to “map” the star’s surface, the extra

absorption features being dark areas on the star’s surface.

This “Doppler imaging” technique has been used to search for starspots.

Possibility that starspot imaging is confused by presence of planets around stars which have a similar modulation pattern (which the Kepler spacecraft is searching for).

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Doppler imaging of starspots: HR1099 (one component of an RS CVn system)

42Observations by S. Vogt & A. Hatzer in 1985

Summary of active starsUV Ceti stars: single (or members of distant binary stars)

showing emission lines in UV and optical regions: evidence of chromospheres/transition regions/coronae. Also strong flares. Like the Sun only “more so”.

T Tauri stars: newly born stars, with accretion disks. Frequent flares arising from blobs of material falling into stars. The Sun had a T Tauri phase early on.

W UMa stars: contact binaries consisting of dwarf stars, with more massive star transferring mass to other star; share chromospheres, coronae. Strong flaring occurs.

RS CVn stars: F or G main sequence star orbiting an evolved K subgiant star with mass transferred to its companion; magnetic loops extend out from each star. Giant flares. Coronal temps. ~50-80 MK. 43

The Sun’s early historyWe saw how the Sun formed from the collapse

of a large cloud of gas.Most probably, several stars formed out of a gas

cloud with mass many times Mʘ -- perhaps 1500 – 3500 Mʘ.

When we look out now (4.6 Gyr after the Sun was formed), there are only a few bright stars that are nearer to the Sun than 10 pc (e.g. Sirius, α Cen, Altair), but lots of very faint dM stars.

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Neighbours of the Sun

45Courtesy: Scientific American

The Sun’s “siblings”: where are they now?

So what happened to the ~1500—3500 stars (assuming average stellar mass = 1 Mʘ)?

The Sun is located about 10 kpc from the centre of the Milky Way Galaxy (galaxy diameter ~ 30 kpc). Its orbital speed is about 234 km/s, and period ~ 270 x 106 yrs = 0.27 Gyr.

So in its 4.6 Gyr lifetime, the Sun will have orbited the Galaxy about 20 times.

In this time, the original star cluster that was formed has spread out into an arc centred on the Galaxy’s centre 46

Milky Way Galaxy

Scheme of the Milky Way galaxy with spiral arms and barred centre. The Sun is 10 kpc from the Galactic Centre, and the whole galaxy has a diameter of 30 kpc.

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SUN

GALACTIC CENTRE 30 kpc

Intriguing possibilityThe Sun’s fellow cluster members are probably

still around, but only ~400 are probably within 1 kpc of the Sun: they could be identified with the ESA Hipparchos spacecraft.

Some meteorites recently analyzed, thought to be leftovers from the formation of the solar system, have Ni60 in them, which can only have been formed from Fe60 within the past 3 Myr. The Fe60 must have been formed, and injected into the meteorites, in < 3Myr.

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A supernova near the Sun?

Where did this material come from? Speculation is that one of the original star cluster members had a large mass and underwent a supernova explosion, distributing the material into the vicinity of the Sun when the Sun was only 2 Myr old.

The supernova might have been only a fraction of 1 pc away.

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Giant flaring on the early Sun?A survey of very young stars in the Orion

Association shows that Sun-like stars can undergo giant flares (total energy >> 1025 J).

Did this happen for the young Sun, i.e. when it was in its T Tauri phase?

It might conceivably explain why the Sun has a very low abundance of Li (which was mostly formed in the Big Bang), only 1/150 times the “cosmic” abundance. Giant flares might have resulted in nuclear reactions that in time broke down Li into H or He. 50

Concluding RemarksSeveral nearby stars have properties like the

Sun’s in terms of “activity”: coronae, chromospheres, active regions, starspots, prominences, and stellar flares.

Some stellar flares are much more energetic than solar flares.

Sun probably formed in a cluster, but original cluster members not very evident.

Possibility that a supernova went off early in the Sun’s history, and that giant flares occurred. 51