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Stellar Classification & Planet Detection. Meteo 466. Reading for this week. “How to Find a Habitable Planet”, James Kasting. Chapter 10, 11 & 12. For this lecture, part of Chapter 10 & all of Chapter 11 Cassan et al., Nature (2012) Udry & Santos, Ann. Rev. Astron. Astrophys. (2007) ) .

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reading for this week
Reading for this week
  • “How to Find a Habitable Planet”, James Kasting. Chapter 10, 11 & 12.
  • For this lecture, part of Chapter 10 & all of Chapter 11
  • Cassan et al., Nature (2012)
  • Udry & Santos, Ann. Rev. Astron. Astrophys. (2007))
how bright is a star
How bright is a star ?
  • The brightness of a star is specified in magnitudes.
  • Hipparchus (190 B.C – 120 B.C) based it on how bright a star appeared to the unaided eye.
  • Brightest stars are Magnitude 1 & dimmest stars are Magnitude 6 (barely visible)
  • Refined definition: Difference of 5 magnitudes (1 to 6) corresponds to a factor of 100 times in intensity (flux).

m1 – m2 = -2.5 log(flux2 / flux1)

color apparent magnitude
Color- (apparent) magnitude

Apparent Magnitude: Brightness Measure as seen from Earth

Color: The difference in apparent magnitudes in different filters

color absolute magnitude
Color- (absolute) magnitude

If the distance ‘d’ to the star is known:

Absolute magnitude = app. Magnitude – 5 Log(d)




White dwarfs


Hertzsprung-Russell (HR) Diagram

O and B


Main sequence


G stars


See also The Earth System,

p. 194



Evolution of

Sun like star

Is white-dwarf

“The” end ??


Evolution of Sun like star

Center for Interdisciplinary Exploration and

Research in Astrophysics (CIERA),

Northwestern University


Evolution of 10 MSun star

Center for Interdisciplinary Exploration and

Research in Astrophysics (CIERA),

Northwestern University


Stars in the solar neighborhood

Within 12.5 light years, there are 33 stars. Most of them

Red dwarfs.

Ultimate goal:To find Earth-like planets, if they exist, and to search for evidence of life
    • So, how do we do that?
exoplanet detection methods ordered by the number of detections
Exoplanet detection methods(ordered by the number of detections )


  • Radial velocity (Doppler method)
  • Transits
  • Gravitational microlensing
  • Pulsar planets
  • Astrometric


  • Optical imaging
  • Infrared interferometry
pulsar planets doppler technique in time
Pulsar planets (Doppler technique in time)
  • Alex Wolszczan (1991): 3 planets around pulsar PSR B1257+12
  • Arecibo radio telescope


extrasolar planet geometry
Extrasolar planet geometry
  • One must think about geometry at which the system is
  • being observed
  • Let
  • i = inclination of the planet’s orbital plane with respect to
  • the plane of the sky
  •  = angle of the planet’s orbital planet with respect to the
  • observer
radial doppler velocity
Radial (Doppler) Velocity

radial doppler velocity1
Radial (Doppler) Velocity

Jupiter: K = 12.6 m/s

Earth : K = 0.1 m/s

first detection around sun like star
First detection around sun like star :

51 Pegasi b ~ 0.5 Jupiter (Mayor & Queloz, 1995)

velocity curve for 51 pegasus mayor queloz 1996
Velocity curve for 51 Pegasus(Mayor & Queloz, 1996)
  • Mass of the planet is only a lower limit because the plane of the
  • planet’s orbit is uncertain (Msin I = 0.47 MJin this case)

velocity curve for hd66428
Velocity curve for HD66428
  • More often than not, the velocity curves are not symmetric
  •  orbit is eccentric (e = 0.5 in this case)

rv around m dwarfs
RV around M-dwarfs

Mahadevan et al.(2011)

planetary systems allow for more detailed analysis
Planetary systems allow for more detailed analysis
  • 2 massive planets orbiting HD 168443
  • Planetary masses
    • 8 MJ
    • 18 MJ

HD 69830

b : 0.61 neptune

c : 0.70 neptune

d : 1.07 neptune

gliese 581 system
Gliese 581 system
  • Spectral type: M3V (0.31 M, 0.0135 L)
  • 4 planets discovered by radial velocity:

a (AU)Mass (M)

b 0.041 >15.6

c 0.073 >5.06

d 0.253 >8.3

e 0.028 >1.7

Ref.: S. Udry et al., A&A (2007)

(Image from Wikkipedia)

tentative conclusions for the gliese 581 system
Tentative conclusions for the Gliese 581 system*
  • Gliese 581c (> 5.1 M) is probably not habitable
    • Stellar flux is 30% higher than that for Venus
  • Gliese 581d (>8.3 M) could conceivably be habitable, but it is probably an ice giant
    • Near the (poorly determined) outer edge of the HZ

*Selsis et al., A&A (2007)

*von Bloh et al., A&A (2007)

gliese 581g
Gliese 581g ?
  • Gliese 581g (~ 3 M), “Zarmina’s world”, apparently exists in the HZ (Vogt et al 2010)
  • The Swiss group with HARPS instrument found it doesn’t exist !
planet mass distribution
Planet Mass Distribution

Occurrence rate α M-0.48

(for periods < 50 days)

Howard et al. (2011), Science

packed planetary systems
Packed Planetary systems

Planetary systems form in such a way that the system

could not support additional planets between the orbits of the

existing ones (gaps with stable orbits contain an unseen planet)

Barnes et al.(2005)

Kopparapu et al.


HD 74156 (Barnes et al.2005)

HD 47186 (Kopparapu et al. 2009)

gravitational microlensing
Gravitational microlensing



  • Planets can also be detected by gravitational microlensing
  • This method takes advantage of the fact that, according
  • to general relativity, light rays are bent by a gravitational
  • field
  • -- or, equivalently, space-time is distorted and light travels
  • along straight paths in the distorted reference frame)

a microlensing event
A microlensing event
  • When the lensing star passes in front of the source star, the light
  • from the source star is amplified by a factor of as much as 10-20
  • The typical duration of a microlensing event is minutes to hours

an event with planets
An event with planets
  • If the lensing star has planets, then the light curve can be distorted (i.e., you get spikes)
  • The planets must be near the Einstein ring radius to be detected
    • Typically, the ring radius is outside of the habitable zone, so this technique is not that useful for finding habitable planets

planet mass distribution microlensing
Planet Mass Distribution (Microlensing)


0.5 to 10 AU

5 Earth to 10 Jup

  • The majority of all
  • detected planets have
  • masses below that of
  • Saturn, though the survey
  • sensitivity is much lower
  • for those planets
  • Low-mass planets are
  • thus found to be much more
  • common than giant planets.

Cassan et al.(2012)

planet mass distribution microlensing1
Planet Mass Distribution (Microlensing)
  • 17% of stars host Jupiter mass planets
  • 52% of stars host Neptune mass
  • 62% of stars host Super-Earths
  • On average, every star in the Milkyway has 1.6 planetstwithin 0.5 to 10 AU !!
  • Planets around stars in our Galaxy thus seem to be the rule rather than the exception.
historical astrometry barnard s star
Historical astrometry: Barnard’s star
  • Second closest star to Earth (6 light yrs), in Ophiucus
  • Red dwarf (M3.8)
  • Largest stellar proper motion (10.3”/yr)
    • Moving towards us. Will be closest star (3.8 l.y.) in about 12,000 yrs
  • Discovered by Edward Emerson Barnard (1957-1923)
  • Studied hard by Peter van de Kamp from 1938 until his death in 1995. Thought to have a planet, but this hypothesis was later proved to be incorrect






the sexagesimal system of angular measurement
The sexagesimal system of angular measurement
  • Equivalently, there are 1,296,000 arcsec in a circle

determination of parallax
Determination of parallax
  • A star’s parallax, p,is the angle by which it appears to move as the Earth moves around the Sun
  • A star that moves by 1 arcsecond when Earth moves by 1 AU relative to the Sun is defined to be at at distance of 1parsec
  • 1 pc = 1 AU/sin p

= 3.0857×1013 km

= 3.262 light years

astrometric method
Astrometric method
  • Calculated motion of the Sun from 1960 to 2025, as viewed from a distance of 10 pc, or about 32 light years above the plane of the Solar System, i.e., at i = 0o
  • Scale is in arcseconds
  • You get the actual mass of the planet because the plane of the planet’s orbit can be determined
  • Can do astrometry from the ground, but the best place to do it is in space 


astrometric missions
Astrometric missions
  • Hipparcos1989 – 1993 (ESA)
  • Precise proper motion & parallax for 118,000 stars (1 milli-arc sec)


0.3 micro-arc sec

  • Gaia 2013 (ESA)
  • Parallax for 1 billion stars
  • (20 micro-arc sec)
  • 3-D map of our Galaxy
sim space interferometry mission
SIM – Space Interferometry Mission
  • This mission will do extremely accurate astrometry from space