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Astrometric Detection of Exo-Earths
Astrophysical noise in astrometry and RV
M. Shao, G. Marcy, C. Beichman, J. Catanzarite, N. Law,
V. Makarov, W. Traub
Topics
• SIM-Lite Introduction, detection of 1 Mearth planets in the habitable
zone.
• Double blind test, astrometric and RV detection of planets (random
noise assumed 0.82uas, 1m/s at each epoch, 5yrs astrometry, 15yrs
RV)
• Star spots and their effect on astrometric and RV measurements,
using our Sun as a target star. (making a quantitative connection
between photometric variability and Astrometric and RV variability)
• Is our Sun a typical star? A comparative look at Corot data and
SOHO/Virgo data.
• A double blind test, RV, and astrometry with star spot noise
SIM Will Test Theories of Planet Formation
Terrestrial planets in
Habitable Zone
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Double Blind Study
• 5 “theory” teams to generate multiple planet systems (provides a
list of planets (mass, period, eccentricity, coplanarity etc.)
• Data generation team. Introduces randomized Euler rotations and
orbital phases, pm and prlx, and generated the Astrometric and RV
observables. 5 yrs of astrometric data (consistent with SIM), 15
years of RV data 1m/s (~8 obs/yr). Time sampling was “randomized”
and included Sun avoidance for both SIM and RV measurements.
• ~400 fake planetary systems were generate, 48 systems were
selected randomly to be solved by the “Analysis teams”.
• In addition to the “random” planetary system there were several
solar system clones (with randomized orbital parameters).
• 5 Analysis teams (4 produced solutions)
– Casertano, Sozzetti et al (STScI, INAF/CFA)
– Fischer et al (SFSU)
– Kasdin et al (Princeton)
– Muterspaugh et al (Berkeley)
– Internal SIM team (JPL, Cornell, U Texas)
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Planet Population in Study (48 stars)
Huge number of asteroids were
include, could not be detected,
did not interfere with detection of
planets.
Asteroids
Earths
Saturns
Neptunes
Jupiters
There were 95 planets with
orbital period < 5 yrs, mass >
0.1 Mearth.
Previously, we knew that an
SNR= 5.8 was needed to
detect a planet (with 1% FAP)
SNR = a / (s * sqrt(N_obs))
a = semi-major axis
s = single epoch noise
Fig 2 Mass Distribution of 581 Objects
52 of the 95 planets had SNR >
5.8 ,theoretically detectable in
“solo” systems.
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Results of Double Blind Test
• Completeness. (what fraction of planets with SNR>5.8 were
detected in a multiplanet environment)?
• Confidence. (If we made a “claim” that we found a planet, how often
were we right?)
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Impact of Star Spots on Astrometry and RV
Example:
Spot area 10-3, Sun @ 10pc
Astrometry
Spot bias
0.25 uas
Earth @1AU amp
0.3 uas
RV
1 m/s
0.1m/s
Total_noise2 =Instrument 2 + Photon2 + Stellar_N2
Time scale: Instrument sqrt(T) till systematic
Photon
sqrt(T)
Stellar
sqrt(T/ ~1 week)
• We apply a dynamic starspot model to estimate the impact of
starspot noise on the detection of Earth via astrometric and radial
velocity techniques.
• We find that for the Earth-Sun system, starspots
– do not appreciably interfere with astrometric detection.
– impose severe requirements on the number of measurements
and duration of an observing campaign needed for radial velocity
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detection.
Dynamic starspot model
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Assumptions
– All of the Sun’s visible flux variation is due to dark starspots.
– On average there are three starspots of equal area on the Sun’s surface
at any time.
– The birth of starspots is a Poisson process in time.
Adjustable parameters:
– Lognormal distribution of starspot lifetimes (2 parameters)
– Starspot area (1 parameter)
Model includes effects of
– Area projection and limb-darkening
– Systematic latitude drift with solar cycle “Maunder Butterfly pattern”
– Inclination of stellar rotation axis with respect to the line of sight.
Each starspot is specified by its creation date, lifetime, latitude, and area.
Each starspot is propagated in time as the star rotates.
Drive the total daily starspot area with the 30-year record of sunspot
numbers, that overlaps the space-based TSI (total solar irradiance) record.
Tune the model parameters to approximately match the Sun’s observed flux
variations.
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Flux jitter in the time domain
Simulation
RMS = 4.7x10-4
5 yr
Observation
RMS = 4.2x10-4
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Maunder Butterfly Pattern
• An 11-year sunspot cycle is included in the simulation.
• Sunspots occur at higher latitudes at the beginning of the cycle.
• As the cycle progresses sunspots become more likely to appear
at lower latitudes.
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Flux jitter in the frequency domain
Construct a star spot model, that
matches the power spectrum of
photometric fluctuations.
Use that model to calculate the
astrometric and RV noise caused
by the star spots.
Goal is to be able to estimate
Astrometric and RV noise from
photometric noise
Note that photometric noise at high freq (5 min ~ 3x10-3 hz) are
orders of magnitude smaller than at 10-6 hz. It’s much easier to find a
planet with a 1 day period than with a 10 day period.
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Starspots cause systematic variation of stellar flux,
astrometric centroid and RV
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The effect depends on inclination and
latitude.
In the tangent plane: X is along the
direction of the line of nodes, Y is
along the projected direction of the
star’s rotation axis.
In general, the jitter in the X centroid
and RV are zero-mean, but the jitter in
the Y centroid is not.
The bias in the Y centroid is worst for
the case of 45° inclination.
Typical starspot lifetimes* are about
a week so (roughly speaking)
starspot noise
– Is correlated for measurements
separated by less than a week.
– Is independent for
measurements separated by
over a week.
*The starspot represented in the figure above is
persistent, for the purpose of illustration only.
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Astrometric jitter due to starspots
Mean of 80 periodograms
sampled 100 times over 5
years, as in a typical
observing campaign.
Captures noise in the
astrometric centroid as a
function of frequency
The noise power at 1 year
period is 0.006 uAU2
Noise is 0.08 uAU for the
ensemble of 100
measurements, or 0.8 uAU
per measurement
At 10 pc, astrometric jitter is
0.08 uas per measurement
Astrometric detection of Earth at 3 pc in sunspot noise, 45°
inclination
• Earth’s signal is 3 μAU
• Starspot noise is 0.7 μAU
per measurement.
• Instrument noise is 3 μAU
per measurement, at 3 pc.
• Instrument noise floor
– SIM PlanetQuest:
0.025 μas, or
0.075 μAU at 3 pc
– SIM PlanetQuest Light:
0.038 μas, or
0.113 μAU at 3 pc
• SNR = 3*sqrt(100)/4.2 ~ 7
• At distances of 3 pc and beyond, instrument noise dominates starspot noise, so that
– Starspot noise doesn’t interfere with astrometric detection of Earth (see periodogram, above).
– Even correlated starspot noise is generally not problematic: the noise average for groups of
10 or so measurements taken within a week is well above the starspot noise.
• SIM PlanetQuest (or SIM PlanetQuest Light) could detect a 0.3 Earth mass planet in the habitable zone at 3 pc, 14
with the 1000 measurements allowed by the noise floor.
RV jitter due to starspots
Mean of 80 periodograms
sampled 100 times over 5
years, as in a typical
observing campaign.
Captures RV jitter due to
starspots as a function of
frequency
The noise power at 1 year
period is 0.002 (m/s)2
Noise is 0.045 m/s for the
ensemble of 100
measurements
RV jitter is 0.45 m/s per
measurement
RV and Ast Sun @10pc Summary
• Equiv ast noise ~0.08 uas
• Equiv RV noise ~0.45m/s
0.3uas signature
0.09m/s signature
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How Quiet is the Sun, How Quiet are most stars?
• 12 years of total solar irradiance (SOHO/Virgo) to measure the
photometric stability of the sun
• Looked at ~104 stars from Corot, 140 days of photometric
data.
• Removed obvious artifacts and calculated the rms fluctuations
for each star.
– Slope removal, median filter (for spikes)
• Looked at distribution of rms fluctuations
• Tried to estimate instrumental effects by looking at the
quietest stars. (this limits what we can say about how quiet
stars in the field are relative to the Sun.)
• Given instrumental limitations, and reasonable assumptions
on the distribution of stellar variability, what can we say about
how stable the Sun is relative to most stars?
Our Sun from SOHO/Virgo
Total Solar irradiance
Over ~12.3 years
Rms over 12.3 yrs
4.2e-4
RMS over ~75 days
~2e-4.
5 yr time span
Any astrometric or RV campaign to look for Earths (~1AU)
will have an observing campaign lasting 5 yrs or longer.
There are short (1~2) year periods during the sun spot cycle
when the sun in very quiet, but a 5~15 year, astrometric or
RV campaign will see the “average” sun.
Corot Data (flux vs time)
Had a Slope
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•
The slope is instrumental, not from the
star
Also, there are numerous jumps from
“hot” pixels, higher dark current due to
cosmic ray events at “edges” of pixels.
Light Curves for 70 of 104 Stars (common slope evident)
Remove Slope, Median Filter
Common slope across all 104 light
curves were removed.
Median filter (in green) removed most
of the single point glitches. (Cosmic ray
hits in pixels adjacent to area used for
photometry?) Median filter does not
remove the steps.
Steps attributed to “Hot” pixels, also
seen on HST and other spacecraft.
Increased dark current from cosmic ray
damage at edges of pixels. Did not try
to “fix” hot pixels, this noise limited the
photometric precision and ultimately
what we can say about our Sun versus
other stars.
Data in 2nd ½ also much noisier and
omitted in calculated rms.
RMS of all 104 stars
The RMS of all 104 stars is
larger than the sun (over ~100
day period). But much of this
may be due to hot pixels and
other instrumental effects.
SUN
How can we separate
instrumental vs astrophysical
fluctuations? (or rather how
well can we separate the two?
0.01%
0.1%
1%
10%
The Quietest (29) Stars
If we look at the distribution of
rms fluctuations for stars that are
perfectly stable, we will find the
distribution of instrumental noise.
The quietest stars are NOT
perfectly quiet, so this distribution
represents a pessimistic
assesment of the stability of the
Corot data.
How can we interpret the distribution of
fluctuations of the 104 stars?
But it seems that hot pixels will
produce ~0.1% fluctuations most
of the time. The instrument is
never quieter than 3e-4 and
rarely noiser than 3e-3.
What do we want to know? The distribution of variability of stars. (eg 4% of stars
will fluctuate by > 1%, 20% of stars fluctuate >0.3% etc.
Discussion
• Because instrumental effects peak at ~0.1% and are non-trivial even
at 0.2%, if a star’s rms is <0.2% we can’t say for certain that that is
due primarily to astrophysical effects.
– 40% of stars have rms > 0.2%
– The other 60% are more stable than 0.2%. But can we say
anything about what % of stars are more stable than 0.02%?
– We can make some “reasonable assumptions” and see what the
consequences of those assumptions are.
• What are reasonable assumptions, on the parent distribution of
stars? (what are unreasonable assumptions?)
Possible Distributions
(40% >0.2%)
SUN
0.02%
~100 days
40% of stars
Gaussian distribution(s)
~40% of stars > 0.2%
~2.5% of stars < 0.02%
~7% of stars < 0.02%
60% of stars <0.02% would require
a very unusual distribution (2 hump)
Rectangular Distribution
40% of stars > 0.2% variable
0% stars < 0.02%
Stars whose intrinsic variability is
< 0.15% may look like 0.15% in
this Corot data set.
Two Hump (Camel) Distribution
• 60% of stars are quieter than ~0.2%. The data does not contradict
the statement that 60% of all stars are quieter than the Sun. But the
statement 60% of stars are quieter than 0.2% rms does not imply
that 60% of all stars are also quieter than 0.02%.
• For the statement 60% of stars are quieter than the Sun to be true,
the parent distribution must have 0% of stars whose variability is
between 0.2% and 0.02%. A two humped “camel” distribution.
The red dotted line, which is a
distribution consistant with 40%
> 0.2% but decreases
monotonically would have ~14%
stars quieter than the Sun.
Very likely only 10~15% of stars
are quieter than the Sun.
Likely ~40% stars < 0.06~0.08%
Must deal with stars ~3 times
noisier than the Sun
Is the Other Evidence the Sun is Unusually Quiet?
• Solar like stars obey a relation between chromospheric activity and
photometric variability down to a level ~1 mmag. The photometric
variability of the Sun measured from space shows that it is the
quieter than the ~25 stars in this survey.
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Photometric Variablity Consistant with Measured
RV Variability
RV Precision / Noise
Keck/HIRES
Eta-Earth Survey stars
GKM
Chromospherically quiet
~10-100 observations each
HARPS
Mayor and Udry, 2008,
Phys. Scr. T130, 014010
Correlated Noise
• When measurements are limited by
systematic error, increased integration
time won’t improve accuracy. Noise that
decrease with 1/sqrt(T) has a flat power
spectrum.
• Star spots are one example of “non-white noise
• The astrometric and RV noise for short period planets is quite
small. Because the RV bias from a star spot is roughly constant
over a few days. But when looking for planets with periods of > 1
month, the effect of star spots is much larger.
• Photometric variability (on ~10hr time scales for transits) of
the sun is ~2e-5 but is ~5e-4 on time scales of ~1 month
• For Sun like stars, spot noise is correlated on time scales of 1~2
weeks. Accuracy of RV/Astrometry measurement improve as
• 1/sqrt(T/ 1week)
• If the spot noise is ~1m/s detecting a 10cm/s signal at
SNR=5~6 will take 3600 weeks 50~65 years
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Summary, Next Steps
• Photometric variations on the surface of a star affect both RV and
astrometry in basically the same way.
• Relative to a planet in a 1yr orbit, the star spot noise for RV is ~10X
larger than for Astrometry. (short periods favor RV, long periods
favor Astrometry)
• For the Sun the astrometric noise is ~0.5m/s and ~0.08uas at each
epoch. (This noise becomes “random” for epochs separated by
longer than ~ 1 week.)
• Preliminary analysis of ~100 stars observed by Corot shows that
~40% of the stars are ~10X or more variable than the Sun. Most
likely only 10~15% of stars are quieter than the Sun. To be able to
detect Earth-like planets around a majority of stars, will likely have to
deal with star spot noise 2~3 times worse than the sun.
• We’ve extended the data generation codes for our double blind test,
to include multiple planet systems with star spot and instrument
noise of various levels. Ready to start a double blind study of
astrometry and RV detection of exo-Earths in the presence of
instrument noise, and star spot noise.
Being Prepared
• Simulation of RV and astrometric observations with both instrument
noise and astrophysical noise from star spots/groups.
– Simulate data for star spot noise that is 1,3,5X solar levels.
– Expected instrument noise for both astrometry and RV.
0.1m/sec (100 min) for RV and 1uas/1000 sec for astrometry
– Insert multiplanet system typical of the planet systems in the
double blind study.
– Determine which planets could be found with 1,3,5X solar levels
of spot noise
• NASA has also asked a double blind study for imaging.
– Imaging of multiple planet systems
– Speckle noise, local/exo-zodi,
– Inner working angle (planets not observable all the time)
– 1st image and orbit determination
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– Imaging alone, imaging with astrometry
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