# Presentation: 313812

## Detection of Earth in the Presence of Stellar noise

- Joseph Catanzarite and Michael Shao,
- Jet Propulsion Laboratory, and
- Nicholas Law,
- Caltech Astronomy Department
- 20 December 2007

## Overview

- 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 a severe requirement on the number of measurements needed for radial velocity detection.

## Dynamic starspot model

- 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.

## Flux jitter in the time domain

- Simulation
- RMS = 4.7x10-4

- Observation
- RMS = 4.2x10-4

## Flux jitter in the frequency domain

- The simulation matches the observational data fairly well.

## Starspots cause systematic variation of stellar flux, astrometric centroid and RV

- 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.

## 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.

## Power spectrum of centroid jitter due to starspots, 45° inclination

-  X jitter spectrum is fairly flat for periods longer than a few months.
-  Y jitter increases at longer periods, due to starspot cycle systematics; but this is offset by the planet signal, which increases by about the same factor.

-  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.
-  Varies between 0.5 & 2 μAU per measurement.
-  At 1 year, it’s ~0.7 μAU per measurement.

## Astrometric detection of Earth at 3 pc in sunspot noise, 45° inclination

-  Starspot noise is a factor of 6 below instrument noise.
-  With 11x more measurements, can detect a 0.3 Earth mass planet at 3 pc, or a 1 Earth mass planet at 10 pc, still well above the instrument noise floor.

-  Earth’s signal is 3 μAU
-  Starspot noise ~0.7 μAU per measurement
-  Instrument noise is 4.2 μAU per measurement.
-  Instrument noise floor is 0.025 μas (0.075 μAU at 3 pc) for SIM Planet-Quest, 0.0375 μas for PQ-Light
-  SNR = 3*sqrt(100)/4.2 = 7

## Power spectrum of RV jitter due to starspots, 90° inclination (edge-on)

-  RV signal of Earth is 0.09 m/sec, much smaller than starspot noise.
-  It would take ~2000 measurements at precision of 20 cm/sec to get the same SNR (~7) as for astrometric detection. And that’s assuming the instrumental noise floor is below about 0.5 cm/s.

-  Mean of 80 periodograms sampled 100 times over 5 years, as in a typical observing campaign.
-  Captures RV jitter as a function of frequency.
-  Between 0.3 and 0.7 m/sec per measurement.
-  At 1 year, it’s 0.55 m/sec per measurement

## Conclusion

- Starspot noise doesn’t interfere with astrometric detection of planets down to 0.3 Earth masses orbiting a solar-analog star at mid-habitable zone at 3 pc. This result scales to 1 Earth mass at 10 pc.
- On the other hand, because of starspot noise, radial velocity detection of Earth would require ~2000 measurements.

## Ongoing work

- We are currently extending this study to estimate the effect of starspots on the detection of habitable planets around all the stars in the SIM target list.
- Use existing space-based photometric time series from WIRE, MOST, and Hipparcos to study the flux variability of other main-sequence stars.
- Exploit connections among flux variability, chromospheric activity (from Ca II H&K indices), age and rotation rate to extend our starspot model to other spectroscopic types on the main sequence.