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Can we find Earth-mass planets orbiting our nearest star, α Centauri?. John Hearnshaw, University of Canterbury, Christchurch, NZ. Humboldt Symposium University of Otago Dunedin 29 January 2010. Harlow Shapley (1885-1972) Harvard College Observatory.

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Can we find Earth-mass planets

orbiting our nearest star,

α Centauri?

John Hearnshaw,

University of Canterbury,

Christchurch, NZ

Humboldt Symposium

University of Otago


29 January 2010


Harlow Shapley (1885-1972)

Harvard College Observatory

“Millions of planetary systems must exist.

Whatever the method of origin, planets

may be the common heritage of all stars …

“Our kind of chemistry, the chemistry of our Sun, our Earth,

is the common chemistry of the universe…

“On some of these planets is there actually life? Or is that

biochemical operation strangely limited to our planet? …

“Is life thus restricted? Of course not. We are not alone.”

Harlow Shapley in a lecture on

‘Religion in an age of science’ at

Vanderbilt University, spring 1958.


The masses of planets

Jupiter mass planets: 1 MJ = 10-3MSun

Earth-mass planets: 1 ME = MJ = MSun

1 A.U. = 1 astronomical unit = Earth-Sun distance

= 150 million km.

  • No Earth-mass planets have yet been detected, but
  • a few planets slightly bigger than the Earth have been
  • found.
  • Mainly they are much closer than the Earth-Sun
  • distance (= 1 AU) so very hot.

Three ways of finding Earth-like planets

  • The Doppler method: periodic radial-velocity
  • variation of a star, detected spectroscopically
  • 346 planets orbiting 294 stars discovered since 1995
  • Most are Jupiter-mass objects (~300 MEarth )
  • Lowest mass is Gliese 581e (mass ≥ 1.94 MEarth) at 0.03 AU
  • Note also Gliese 581 d (mass ≥ 7.1 MEarth) at 0.22 AU
  • (Mayor et al. June 2009)

Radial-velocity (Doppler) method

HD114762: original data of

Latham et al. (small dots),

and more precise data from

McDonald (Cochran et al.)

(large dots).

51 Pegasi: Marcy and Butler

mp sin i (mJ) = 11.0 0.47

a (AU) = 0.3 0.05

P (days) = 84.03 4.22

e = 0.334 0.00


Three ways of finding Earth-like planets

  • 2. Transits of planets across disk of a star
  • 62 planets detected by precise photometry
  • First was HD209458 (Charbonneau et al. 2000)
  • Typical change in light ~ 10-4 to 10-5
  • Smallest is CoRoT-7b: size = 1.7 REarth; mass = 4.8 MEarth
  • a = 0.017 AU; P = 0.85 d (20.5 h) (Leger et al. Aug 2009)

Finding planets by the transit method

The principle of planet detection by the transit technique.

Jupiter would cause a fall in brightness of the Sun by

~1% if it was in a transit event for a distant observer.



  • Launch 5 March 2009
  • Search for planetary transits
  • Monitor >100,000 stars for 4 yr
  • continuously and simultaneously
  • Stars are brighter than mV = 14
  • Sensitivity to Earth-size planets as
  • well as gas giants

Kepler satellite


KEPLER: planet sensitivity region

and the habitable zone

Kepler search area

as function of stellar

mass and orbital

semi-major axis.


Three ways of finding Earth-like planets

  • 3. Microlensing
  • Nine planets found, first in 2004
  • Lowest mass objects:
  • (i) OGLE-05-BLG-390Lb, mass = 5.4 MEarth
  • at 2.1 AU (projected on sky plane)
  • (ii) MOA-07-BLG-192Lb, mass = 3.2 MEarth
  • at 0.62 AU

Microlensing light curves for two lens stars with

low mass planets

Left: light curve of


Below: light curve of



α Centauri: position in the sky

Right ascension: A: 14h 39m 36.4951s B: … 35.0803s

Declination: A: -60° 50′ 02.308 B: … 13.761″

Hence: culminates at midnight in early May

In NZ (lat 44°S), lower culmination at altitude 15° (Nov).


α Centauri: name and brightness

Names: α Centauri, Rigil Kent, Rigil Kentaurus, Toliman

Distance: d = 1.34 parsecs = 4.37 light-yr ~ 40 × 1012 km


When viewed by naked eye as a single star, V = –0.27,

α Centauri is the 3rd brightest star in the sky.

α CentauriA (V = +0.01) is 4th brightest after Sirius,

Canopus and Arcturus.

α CentauriB (V = 1.33) is 21st brightest in visual

apparent magnitude.


α Centauri: a double star

  • α Centauri is a double star with star A similar to the Sun
  • and star B a little cooler than the Sun
  • Orbital elements:
  • Period P = 79.91 yr
  • Eccentricity e = 0.52
  • Semi-major axis a = 23.4 A.U. (separation varies between
  • Inclination i = 79° 11.2 and 35.6 AU)

α Centauri: a double star

Angular separation of stars varies from 2 to 22 arc sec

2008: 8.3

2009: 7.5

2016: 4.0

max separation:

1995, 2075

closest approach:

1955, 2035


α Centauri: the stellar components


apparent mag mV +0.01 1.33

luminosity L 1.6 0.45

mass M 1.10 0.91

radius R 1.227 0.865

temperature Teff (K) 5790 5260

(of surface)

age (billions of yr) 6.52±0.3 6.52±0.3

relative sizes of α Cen

components and the Sun


Stability of planetary orbits

in α Cen AB

Wiegert & Holman found stable orbits inside 2.34 AU, but unstable 3 to 70 AU from each star, provided i = 0° (coplanar with binary orbit).

Planets in inclined orbital planes are much

less stable.

Beyond 75 AU from the barycentre, stable orbits are again possible.


Habitable zone planets

The habitable zone of a star is the zone

where a planet can have liquid water.

More precisely, the continuously

habitable zone about a star

is the zone in which an Earth-like planet

will undergo neither a runaway greenhouse

effect in the early stages of its history nor

runaway glaciation after it develops an oxidizing atmosphere.

For α Centauri A: habitable zone 1.1 – 1.3 AU (1 from A)

For α Centauri B: habitable zone 0.5 – 0.9 AU (0.6

from B)


Habitable zones

The relative sizes of habitable zones around four of the

nearest stars. Sirius A, alpha Centauri A and B, and Proxima

Centauri. At this scale, the habitable zone around the

red dwarf Proxima is so small that it is only about the size of

the full stop at the end of this sentence.


Habitable zone planets

for α Centauri A and B


Can planets form in the α Cen system?

An example of planet

formation in a circumstellar disk

around α CenB. The disk is initially

populated by 600 lunar-mass

planetary embryos in nearly circular

orbits. The radius ofeach circle is

proportional to the size of the object.

After 200 Myr four planets have

formed. One planet has about

themass of Mercury and is at a=

0.2 AU, two 0.6ME planetsform at

a= 0.7 and a= 1.8 AU, and a 1.8 ME

planet formsat a= 1.09 AU.

Javiera Guedes et al ApJ 679, 1582 (2008)


The detection of planets

by the Doppler method

K = velocity amplitude of star’s ‘wobble’ caused by planet

mp = mass of planet in Jupiter or Earth masses

M* = stellar mass in solar mass units

a = size of planetary orbit in AU

i = inclination of orbit to line of sight (i = 90º is edge on)


α Centauri: Existing upper mass limits for planets

The study of M. Endl et al. (2001) looked for periodic

RV variations in α CenA and B, and found no planets.

Typical velocity precision ~ 10 m/s.

For α CenA and α CenB: No Jupiter-mass planets were


Conclusion: There are no Jupiters in α Centauri!


The challenge of detecting

Earth-mass planets

Earth-mass planets require velocity precision of ~ 1 m/s.

The table gives velocity amplitudes of α Cen A and B

for 1 ME and 10 ME planets in orbits of different size, a.

α Cen A

α Cen B

Earth super-Earth

Earth super-Earth


Sample spectra of α Cen B through I2 cell showing

thousands of fine I2 lines superimposed on stellar spectrum

Recorded by JBH at Mt John 2009 Jan 24



High Efficiency and Resolution Canterbury

University Large Echelle Spectrograph


Two spectra of ζ TrA (F9 V)

showing a 15 km/s shift in

the stellar lines


ζ TrA: a test spectroscopic binary

Two spectra of ζ TrA (F9 V)

showing a 15 km/s shift in

the stellar lines


Spectral Instruments

4k × 4k CCD camera

on Hercules Dec 2006


Latest developments in

the Hercules instrument

  • Tests of an iodine vapour cell (S. Barnes, M. Endl)
  • The cell was placed at the Cassegrain focus just before
  • the fibre entrance. I2 absorption lines superimposed on
  • stellar spectrum act as a precise wavelength calibration.
  • Cell length 15 cm
  • Iodine vapour temperature 50.0 ± 0.1 °C.

2009 April data for α Cen A showing a

precision of 2.68 m/s from 963 observations

using iodine cell


Why observe α Centauri from

Mt John Observatory New Zealand?

  • We have a high resolution spectrograph able to
  • deliver 1 m/s precision on late-type star velocities.
  • We have a 1-m telescope with enough time available
  • for an intensive observing program over several years.
  • We are the only observatory in the world able to
  • observe α Centauri all year, even in November and
  • December when α Cen passes through lower culmination
  • (altitude ~ 15°). In Chile, Australia, S Africa the lower
  • culmination is at altitude 0° and the observing season
  • is 9 to 10 months through large air mass.

What do we need to do to detect

Earth-mass planets?

For K ~ 1 m/s, about 300 spectra at S/N 300:1 over

about 3 years, with σ ~ 2.5 m/s to detect super-Earths.

For K ~ 0.1 m/s, about 30,000 spectra (or more)

at S/N 300:1 over about 3 years, with σ ~ 2.5 m/s to detect

Earths-mass planets.

Typical exposure times for this S/N, using R = 70,000:

α Cen A: ~40 s

α Cen B: ~ 2 min in typical 2 arc s seeing.


α Centauri program: progress in last year

  • From 2008 August to 2009 October we have acquired
  • Hercules spectra with an iodine cell as follows:
  • α Centauri A: 6536 spectra
  • α Centauri B: 3359 spectra
  • Observers: Kilmartin, Hearnshaw and Barnes.
  • S/N ratio ~ 300:1
  • Our aim is to increase the rate of acquisition of spectra
  • in 2010.

How precisely do the positions of Doppler

line shifts need to be measured?

  • Hercules pixel size = 15 μm ≡ 1.2 km/s
  • A precision of 1 m/s requires measuring line position
  • to 1 in 300 million.
  • A 1 m/s velocity shift ≡ a line displacement of ~ 12 nm
  • (~ 10–3 pixels!) on the CCD detector.
  • A 10 cm/s shift ≡ 1.2 nm ~ 10-4 pixels
  • ~ 5 × diameter of a Si atom in the CCD chip.

Semi-empirical RV data for α Cen A.

Based on actual spectra taken April 2009, but (a) reproduced over

a 4-yr period; (b) with an 8 cm/s 370-d period signal added; (c)

binned into 17 equally spaced bins (each of about 3 weeks)


RV simulation on α Cen A to find

a one Earth-mass planet at 1 A.U.

The simulation assumed 11,500 spectra per year each with σ = 3 m/s.

The planet induces a signal with K = 8 cm/s, P = 370 d. The power

spectrum shows this planet is easily detectable, even after 2 years!


Can we send a space probe to α Centauri

to confirm the existence of a planet?

  • Answer: Yes, may be!
  • If we can travel at 0.1c (30,000 km/s), the journey would
  • take about 50 years.
  • To reach that speed, we need to
  • accelerate at 0.04 m/s2 for 25 years,
  • and then decelerate for another 25 yr.
  • To do that we need a light sail driven
  • by radiation pressure (sunlight or lasers)
  • Sail area needed ~25 km2
  • Technology may be available in 50 yr
  • from now. Arrival at α Cen ~ 100 yr from
  • now. Return of first images 4.3 yr after
  • that.