Chapter 5: The K stars: orange giants and brighter dwarfs
Introduction to K stars:
 Bright orange stars
–Arcturus (K1 III), Pollux (K0 III), Aldebaran (bull’s eye, red), Hyades cluster – K giants
 K dwarfs
–61 Cygni, Fainter member of α Centauri pair
 Subgiants & White Dwarfs
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T = (3900 – 5200) K, Cooler
Strong metal lines
Weak CH & CN molecular bands
H line weakens
5.1 Classification :
Spectral features denoting K type:
1) As progress towards earlier subtype (ie. K9 through K0) TiO bands disappear at K5 and H
absorption lines starts appearing in all classes.
2) More ionized gases, so g line of Ca I weakens; H & K lines of Ca II emerge in violet part of
spectrum.
3) Very strong D line of Na I (actually a doublet) weakens.
4) Increasing temperature causes molecules to break up, surviving only tightly bound ones. G band
of CH increases in strength, as go towards class G.
5) In giants, optical CN and infra red CO bands are prominent.
Luminosity estimate:
1) H & Ca I lines (like in M stars) used in later subtypes. Show negative and positive luminosity
effects.
2) Ratio of metallic absorption lines, ionized Strontium & Titanium to Fe I lines. (Fe I shows
positive luminosity effects).
3) Molecular CN bands beginning at 4215 A (CN break) and 3888 A and extending to blue.
If use a single criterion to get luminosity  Errors may arise.
For a new star of unknown class:
1) Use temperature sensitive features to get Draper Class (OBAFGKM).
2) Then using density criterion get luminosity.
3) Once know star is giant or dwarf, can refine it’s temperature class, to get a more correct
estimate.
5.2 Spectroscopic Distances:
L = 4 * * R2 * f
where, f = Flux as seen from earth
R = Distance of star from earth
Magnitude equation :
M = m + 5 – 5 * log(D) - A
where, M = Absolute magnitude of star, m = apparent magnitude as seen from earth (B, blue or V,
violet), A = Extinction, D = Distance of star from earth
MKK classification  Luminosity (M) directly from spectrum.  Hence find D.
Eg. 39 Cancri : Class K0 III => Mv = +0.5. & V = 6.4 = m
 log(D) = 2.2 => 150 pc away
But !!
Giant stars have spread about average --- ,
If 39 Cnc is as bright as  Uma (ie Mv = -0.3), then it would be 50 % farther away.
In a cluster can use several stars or whole main sequence to increase precision.
Only need from before, M of various stars, ie need to calibrate HR diagram and various luminosity
classes against M(visual) with stars whose distances are known in advance.
5.3 K lines and chromospheres:
Chromosphere: Low density, hot gaseous region (above the higher density photosphere, where the
continuum and bulk of absorption lines form).
Chromospheres detected by high resolution spectroscopy of strongest lines. Eg. Fraunhofer H & K
lines of Ca II (H line of Ca II is blended with a hydrogen line so the K Ca II line is better).
Self - reversed / Self - absorbed emission feature (nested spectral lines):
Ca K absorption line of photosphere (K1) - very strong (10 times broader than strongest Fe line).
Chromosphere, (being low density, hot gas) generates emission lines. Narrow, bright K line (K2)
centered at very broad K1 absorption. But chromosphere gas can also become opaque, absorbing some
of it’s own radiation –> narrower absorption (K3) at center of K2.
Such self absorption also seen in B stars.
UV Mg II lines at λ2796 & 2802 (h & k lines, visible only from satellite borne telescopes) - also
exhibit self absorption.
Wilson Bappu effect: 1956, Wilson & Bappu at Mt Wilson: Width of K2 line correlates very well with
visual magnitude of classes G, K, M from dwarfs through supergiants over a magnitude range > 15
mag.  Luminosity & Distance indicator.
Why this correlation ? - not yet understood - maybe origin of chromosphere & mass motions generating
energy.
5.4 Eclipsing supergiants:
Eg of eclipsing binary pairs: Mira variables, Algol (β Persei)
Eclipse analysis give us several spectral parameters:
- time taken by one star to cover another: diameter.
- drop in observed intensity during eclipse: relative surface brightness of 2 stars, hence temperature.
- mass of stars: if spectroscopic binary, then from Doppler shift of spectra obtain orbital velocity and
hence mass
(orbital vel  mass ratio & sizes of semi major axes  use Kepler’s law & center of mass concepts to
get M of stars individually)
but orbital planes of binaries inclined to line of sight by some angle  hence can only get lower limits
to velocities and masses.
If binary eclipses , from light curve get angle of inclination and hence accurate masses.
Eg of eclipsing binary K stars:
1) ζ Aurigae (faintest of the ‘kids’ of Cappella): magnitude = 3.8. Every 972 days B8 5 component
blocked by K4 II giant and intensity decreases by 0.2 mag. Period of eclipse = 2.6 yrs, eclipse
duration = 38 days => very large star system. For ~ 2 weeks before and after totality, can see
extended atmosphere of K star, imposing itself upon spectrum of B companion. Obs tells that K
secondary produces a wind through which it loses mass.
2) 31 & 32 (o1 & o2) Cygni: K2 II + B3 V & K3 Ib + B3 V binaries ; only 1degree apart
3) U Cephei (G8 I + B8) & VV Cephei (M I a + B) : Both telescopic objects
4)  Aurigae
5.5 Composition Variations:
N stars continue into warmer temperature as class R: K0 to M0 runs parallel to sequence R2 to ~R8 /
C0 to C5. R giants - bands of C2 in spectra.
S stars: similar C & O abundances & enhanced quantities of s - process elements, yttrium, zirconium
appeared once to extend into K (& late G type) temp zone, as the barium stars - recognized by Ba II at
λ4554 & strong abs line by strontium , λ 4077 & λ4216 Sr II.
Few ‘mild barium stars’ that are high temp analogues to type MS (between classes M & S). Now
known, Ba stars are binaries –> so probably 1 member of binary has evolved & expanded & has passed
some of its enriched mass onto the other component, showering it with peculiar elements.
Underabundances:
CN break: very sensitive to luminosity . (CN break very strong in giants, almost absent in dwarfs).
Earlier CN break was used to get absolute mag. But now known , some stars (giants by all other
criterion) - wrongly called dwarfs on basis on CN alone . (4215 A break was too weak to classify them
as giants) .
Coz of carbon & Nitrogen abundances, well below solar  metal deficient pop II stars in galactic halo.
CN anomaly: Difference between observed CN strength & that for stars of solar abundance of a given
luminosity.
5.6 Towards lower luminosity:
K giants (more luminous) – Subgiants (class IV) – Dwarfs (less luminous)
Subgiants (stars above MS, but not really giants), 4/5 solar radius. Appear to be evolving from MS
upwards into true lum class III).
In this region above MS get many T Tauri stars:
 odd in nature: emission lines, vary irregularly , - grouped into T associates, found in
conjunction with ISM clouds.
 newly formed, maybe known youngest stars
K dwarfs (6-8 mag) – less than M dwarfs, larger mass, higher MS luminosity
5.7 Parallaxes & Stellar Distances
Parallax
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Semi annual shift of star’s position in sky caused by earth’s revolution around sun
D = (1/) where D =Distance (pc) & = parallax (arc sec)
1st star to have distance measured: 61 Cygni
D < 50 pc, Distances to Sirius, Vega, Arcturus, Pollux
For classes V & III using parallax, can get distances & hence M, can calibrate HR diagram
Distances farther out
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5.8
Hyades cluster
Radiant position: where star will be after millions of yrs
Angle between radiant & present position  Transverse velocity  Distance
Calibrate HR diagram for Hyades with Mv vs spectral class
Add nearby parallax stars also to diagram & use as standard
Get better calibration for visual mag (luminosity) vs distance
Subdwarfs & White Dwarfs
 Subdwarfs
o 1 mag below MS – metal poor, too early / blue by several subtypes
o Classification metal lines weak – get earlier subclass
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White dwarfs
o Several mag below
o Of terrestrial dimensions, & very high density