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Astrometric Detection of Exoplanets. Stellar Motion. There are 4 types of stellar „motion“ that astrometry can measure:. 1. Parallax (distance): the motion of stars caused by viewing them from different parts of the Earth‘s orbit 2. Proper motion: the true motion of stars through space

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slide2

Stellar Motion

There are 4 types of stellar „motion“ that astrometry can measure:

1. Parallax (distance): the motion of stars caused by viewing them from different parts of the Earth‘s orbit

2. Proper motion: the true motion of stars through space

3. Motion due to the presence of companion

4. „Fake“ motion due to other physical phenomena

slide3

Galileo was the first to try measure distance to stars using a 2.5 cm telescope. He of course failed.

Brief History

  • Astrometry - the branch of astronomy that deals with the measurement of the position and motion of celestial bodies
  • It is one of the oldest subfields of the astronomy dating back at least to Hipparchus (130 B.C.), who combined the arithmetical astronomy of the Babylonians with the geometrical approach of the Greeks to develop a model for solar and lunar motions. He also invented the brightness scale used to this day.
  • Hooke, Flamsteed, Picard, Cassini, Horrebrow, Halley also tried and failed
slide4

Modern astrometry was founded by Friedrich Bessel with his Fundamenta astronomiae, which gave the mean position of 3222 stars.

  • 1838 first stellar parallax (distance) was measured independently by Bessel (heliometer), Struve (filar micrometer), and Henderson (meridian circle).
  • 1887-1889 Pritchard used photography for astrometric measurements
slide5

Mitchell at McCormick Observatory (66 cm) telescope started systematic parallax work using photography

  • Astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. Astrometric applications led to the development of spherical geometry.
  • Astrometry is also fundamental for cosmology. The cosmological distance scale is based on the measurements of nearby stars.
slide6

Astrometry: Parallax

Distant stars

1 AU projects to 1 arcsecond at a distance of 1 pc = 3.26 light years

slide7

Astrometry: Parallax

So why did Galileo fail?

q= 1 arcsecond

1 parsec = 3.08 ×1018 cm

d = 1 parsec

d = 1/q, d in parsecs, q in arcseconds

f = F/D

F

D

slide8

360o · 60´ ·60´´

206369 arcsecs

2 p F

F

Astrometry: Parallax

So why did Galileo fail?

D = 2.5cm, f ~ 20 (a guess)

Plate scale =

=

F = 500 mm

Scale = 412 arcsecs / mm

Displacement of a Cen = 0.002 mm

Astrometry benefits from high magnification, long focal length telescopes

slide9

Astrometry: Proper motion

Discovered by Halley who noticed that Sirius, Arcturus, and Aldebaran were over ½ degree away from the positions Hipparchus measured 1850 years earlier

slide10

Astrometry: Proper motion

Barnard is the star with the highest proper motion (~10 arcseconds per year)

Barnard‘s star in 1950

Barnard‘s star in 1997

slide11

D

To convert to an angular displacement you have to divide by the distance, D

Astrometry: Orbital Motion

a1m1 = a2m2

a1 = a2m2 /m1

a2

×

a1

slide12

q =

P2/3

m

D

M2/3

Astrometry: Orbital Motion

The astrometric signal is given by:

This is in radians. More useful units are arcseconds (1 radian = 206369 arcseconds) or milliarcseconds (0.001 arcseconds) = mas

m

a

q =

M

D

m = mass of planet

M = mass of star

a = orbital radius

D = distance of star

Note: astrometry is sensitive to companions of nearby stars with large orbital distances

Radial velocity measurements are distance independent, but sensitive to companions with small orbital distances

slide13

Astrometry: Orbital Motion

With radial velocity measurements and astrometry one can solve for all orbital elements

slide14

• Orbital elements solved with astrometry and RV:

P - period

T - epoch of periastron

w - longitude of periastron passage

e -eccentricity

  • • Solve for these with astrometry
      • - truesemi-major axis

i - orbital inclination

  • W - position angle of ascending node
  • m - proper motion

p- parallax

  • • Solve for these with radial velocity
  • g - offset
  • K - semi-amplitude
slide15

-

a

(

1

e

)

2

s

i

n

i

P

K

1

=

A

w

p

× 4.705

2

a

b

s

All parameters are simultaneously solved using non-linear least squares fitting and the Pourbaix & Jorrisen (2000) constraint

  • a = semi major axis
  • = parallax

K1 = Radial Velocity amplitude

P = period

e = eccentricity

slide16

So we find our astrometric orbit

But the parallax can disguise it

And the proper motion can slinky it

slide18

Astrometric Detections of Exoplanets

The Challenge:

for a star at a distance of 10 parsecs (=32.6 light years):

slide19

The Observable Model

Must take into account:

  • Location and motion of target
  • Instrumental motion and changes
  • Orbital parameters
  • Physical effects that modify the position of the stars
slide21

The Importance of Reference stars

Example

Focal „plane“

Detector

Perfect instrument

Perfect instrument at a later time

  • Reference stars:
  • Define the plate scale
  • Monitor changes in the plate scale (instrumental effects)
  • Give additional measures of your target

Typical plate scale on a 4m telescope (Focal ratio = 13) = 3.82 arcsecs/mm = 0.05 arcsec/pixel (15 mm) = 57mas/pixel. The displacement of a star at 10 parsecs with a Jupiter-like planet would make a displacement of 1/100 of a pixel (0.00015 mm)

slide22

They can have their own (and different) parallax

2. They can have their own (and different) proper motion

Good Reference stars can be difficult to find:

3. They can have their own companions (stellar and planetary)

4. They can have starspots, pulsations, etc (as well as the target)

slide24

In search of a perfect reference.

You want reference objects that move little with respect to your target stars and are evenly distributed in the sky. Possible references:

K giant stars V-mag > 10.

Quasars V-mag >13

Problem: the best reference objects are much fainter than your targets. To get enough signal on your target means low signal on your reference. Good signal on your reference means a saturated signal on your target→ forced to use nearby stars

slide25

Barnard´s star

Astrometric detections: attempts and failures

To date no extrasolar planet has been discovered with the astrometric method, although there have been several false detections

slide29

Scargle Periodogram of Van de Kamp data

False alarm probability = 0.0015!

Frequency (cycles/year)

A signal is present, but what is it due to?

slide30

New cell in lens installed

Lens re-aligned

Hershey 1973

Van de Kamp detection was most likely an instrumental effect

slide32

Gatewood 1996:

At a meeting of the American Astronomical Society Gatewood claimed Lalande 21185 did have a 2 Mjupiter planet in an 8 yr period plus a second one with M < 1 Mjupiter at 3 AU. After 16 years these have not been confirmed.

Lalande 21185

Gatewood 1973

slide35

The first space interferometer for astrometric measurements:

The Fine Guidance Sensors of the Hubble Space Telescope

slide36

Fossil Astronomy at its Finest - 1.5% Masses

MTot =0.568 ± 0.008MO

MA =0.381 ± 0.006MO

MB =0.187 ± 0.003MO

πabs = 98.1 ± 0.4 mas

HST astrometry on a Binary star

slide37

Image size at best sites from ground

HST is achieving astrometric precision of 0.1–1 mas

slide38

One of our planets is missing: sometimes you need the true mass!

B

HD 33636 b

P = 2173 d

msini = 10.2 MJup

Bean et al. 2007AJ....134..749B

i = 4 deg → m = 142MJup

= 0.142 Msun

slide39

GL 876

M- dwarf host star

Period = 60.8 days

slide42

The mass of Gl876b

  • The more massive companion to Gl 876 (Gl 876b) has a mass Mb = 1.89 ± 0.34 MJup and an orbital inclination i = 84° ± 6°.
  • Assuming coplanarity, the inner companion (Gl 876c) has a mass Mc = 0.56 MJup
slide43

The Planet around e Eridani

Cambel and Walker : e Eri was a „probable variable“

slide45

What the eye does not see a periodogram finds:

Radial Velocities

Period = 6.9 years

Activity indicator

FAP ≈ 10–9

slide47

e Eri

p = 0.3107 arcsec (parallax)

a = 2.2 mas (semi-major axis)

i = 30° (inclination)

X-displacement (arc-seconds)

Y-displacement (arc-seconds)

Mass (true) = 1.53 ± 0.29 MJupiter

slide52

-

a

(

1

e

)

2

s

i

n

i

P

K

1

=

A

w

p

× 4.705

2

a

b

s

Brown Dwarf

slide63

The Purported Planet around Vb10

Up until now astrometric measurements have only detected known exoplanets. Vb10 was purported to be the first astrometric detection of a planet. Prada and Shalkan 2009 claimed to have found a planet using the STEPS: A CCD camera mounted on the Palomar 5m. 9 years of data were obtained.

slide64

Vb 10

Control star

slide65

Control star

Control star

slide71

The RV data does not support the previous RV model. The only way is to have eccentric orbits which is ruled out by the astrometric measurements.

slide72

“Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.”

– Richard Feynman

Taken with a different slit width!

Is there something different about the first point?

slide73

Radial Velocity

Astrometry

1. Measure a displacement of a spectral line on a detector

1. Measure a displacement of a stellar image on a detector

2. Thousands of spectral lines (decrease error by √Nlines)

2. One stellar image

3. Hundreds of reference lines (Th-Ar or Iodine) to define „plate solution“ (wavelength solution)

3. 1-10 reference stars to define plate solution

4. Reference lines are stable

4. Reference stars move!

Comparison between Radial Velocity Measurements and Astrometry.

Astrometry and radial velocity measurements are fundamentally the same: you are trying to measure a displacement on a detector

slide74

Space: The Final Frontier

  • Hipparcos
    • 3.5 year mission ending in 1993
    • ~100.000 Stars to an accuracy of 7 mas
  • Gaia
    • 1.000.000.000 stars
    • V-mag 15: 24 mas
    • V-mag 20: 200 mas
    • Launch 2011 2012 2013
slide77

GAIA Detection limits

Casertano et al. 2008

detection

Parameters determined

Red: G-stars Blue: M Dwarfs

slide78

Number of Expected Planets from GAIA

8000 Giant planet detections

4000 Giant planets with orbital parameters determined

1000 Multiple planet detections

500 Multiple planets with orbital parameters determined

slide79

40 mas

Our solar system from 32 light years (10 pcs)

1 milliarcsecond

In spite of all these „problems“GAIA has the potential to find planetary systems

slide80

Summary

  • Astrometry is the oldest branch of Astronomy
  • It is sensitive to planets at large orbital distances → complimentary to radial velocity
  • Gives you the true mass
  • Least successful of all search techniques because the precision is about a factor of 1000 to large.
  • Will have to await space based missions to have a real impact
slide81

Small proper motion

Large proper motion

Sources of „Noise“

Secular changes in proper motion:

Perspective effect

slide82

2vr

dm

mp

=

dt

AU

vr

dp

p2

=

dt

AU

In arcsecs/yr2 and arcsecs/yr if radial velocity vr in km/s, p in arcsec, m in arcsec/yr

(proper motion and parallax)

slide85

Sources of „Noise“

Relativistic correction to stellar aberration:

No observer motion

observer motion

q = angle between direction to target and direction of motion

1

v3

v

1

v2

(

)

+

sin2q

1 + 2 sin2q

aaber≈

sin q

sin2q

6

c3

c

4

c2

=

=

=

20-30 arcsecs

1-3 mas

~ mas

slide86

Sources of „Noise“

Gravitational deflection of light:

4 GM

y

adefl=

cot

2

Roc2

M = mass of perturbing body

Ro = distance between solar system body and source

c, G = speed of light, gravitational constant

y = angular distance between body and source

slide89

Spots :

y

x

Brightness centroid

slide90

Astrometric signal of starspots

Latitude = 10o,60o

Latitude = 10o,0o

2 spots radius 5o and 7o, longitude separation = 180o DT=1200 K, distance to star = 5 pc, solar radius for star

Horizontal bar is nominal precision of SIM