Maximized Yields for Coronagraphs and Starshades

Christopher Stark STScI

cstark@stsci.edu

1

Calculating Yield with a DRM Code

2DRM

HZ

ExoEarth Yield Estimated via Completeness

IWA

3

Too faint

τ

•  Completeness, C = the chance of observing a given planet around a given star if that planet exists (Brown 2004)

•  Yield = ηEarth Σ C

•  Calculated via a Monte Carlo simulation with synthetic planets

4

Maximizing Yield by Optimizing Observations

C

Optimizing exposure times can potentially double yield

Optimized Exposure Times

HZ

ExoEarth Yield Estimated via Completeness

IWA

5

Too faint

τ

•  Revisiting same star multiple times can increase total completeness

•  Can optimize number of visits and delay time between visits

6Optimized revisits increase yield by additional 35-75%

Maximizing Yield by Optimizing Revisits

Optimized Revisits

Result: A Static Optimized Observation Plan

7

Alpha Cen

Beta Pic

Eps Eri

Starry McStarface

Visit 1 Visit 2 Visit 3 Visit 4

t2=100 s t1=100 s t3=100 s t4=100 s Δt21=0.3 yr Δt32=0.2 yr Δt43=0.1 yr

t2=300 s t1=300 s t3=200 s Δt21=0.5 yr Δt32=0.2 yr

t2=400 s t1=500 s Δt21=0.4 yr

Occurrence rate of Earth-sized planets in the habitable zone of Sun-like stars

ηEarth = 0.1 (Published estimates of ηEarth range from ~0.03 – 1.0)

Habitable Zone 0.75 – 1.77 AU for Sun-like star (Somewhat wide/optimistic)

Planet characteristics Earth twins on circular orbits

Amount of “exozodiacal” dust obscuring the planet

nexozodis = 3 × our own zodiacal dust (Best-case future upper limit from LBTI observations)

8

Astrophysical Assumptions in Yield Models

•  End-to-end throughput = 0.2 •  Noise floor, Δmagfloor = 27.5 •  OWA = 15 λ/D •  Diffraction-limited Airy pattern PSF •  No detector noise •  1 year of total exposure time •  1 additional year of total overheads •  Up to 10 visits allowed to each star 9

Baseline Coronagraph Mission Parameters

Detection Coronagraph

Designed for fast searches

λ  = 0.55 µm Δλ = 20% SNR = 7

IWA = 3.6 λ/D Contrast, ζ = 10-10

2 Coronagraphs: Characterization Coronagraph

Designed to detect water

λ  = 1.0 µm Spectral Res. = 50

SNR = 5 IWA = 2.0 λ/D

Contrast, ζ = 5×10-10

10

What Telescope/Instrument Parameters Matter?

Yield most strongly depends on aperture. Moderately weak exposure time dependence.

Yield ∝ Dφ

Yield ∝ tφ

11

What Telescope/Instrument Parameters Matter?

D2 dependence: roughly equal contributions from collecting area, IWA, and PSF solid angle.

Yield ∝ Dφ

Yield ∝ tφ

12

IWA matters more than contrast when treating both linearly. OWA doesn’t matter much. Noise floors with Δmag > 26.5 are unnecessary.

Coronagraph Scaling Relationships What Telescope/Instrument Parameters Matter?

13

Coronagraphs yield linearly proportional to ηEarth. Moderately strong dependence on exoEarth albedo.

Weak dependence on exozodi level.

Impact of Astrophysical Assumptions

14

Details of an Optimized Observation Plan: Number of Stars & Number of Observations

Optimization results in hundreds of stars and thousands of observations—code is skimming off gibbous phase planets. Don’t worry! The # of observations can be greatly reduced with only small impact on yield. Overheads will ultimately

limit # of observations.

15

Details of an Optimized Observation Plan: Stellar and Planet Vmag distribution

D = 12 m

D = 4 m

D = 12 m

D = 4 m

16

Details of an Optimized Observation Plan: Stellar Angular Diameter Distribution

Peak of distribution not linearly proportional to D. Larger apertures access smaller stars.

Distributions weighted by completeness

D = 12 m

D = 4 m

17

D = 8 m

Details of an Optimized Observation Plan: Stellar Type and Distance Distribution

18

Details of an Optimized Observation Plan: Detection & Characterization Time Distribution

D = 12 m

D = 4 m

D = 12 m

D = 4 m

V band spectra R = 70 SNR = 10 No detector noise

V band Detection Time (days) Characterization Time (days)

0 yr 5 yr

Starshade Optimization: Exposure Time & Fuel Are Connected

19

Optimizing Starshades: Balancing Time with Fuel

0 yr 5 yr2 yr1 yr

Coronagraph Optimization: Simple Time Budgeting

20

Optimizing Starshades: Balancing Time with Fuel

We search the 5-dimensional parameter space controlling starshade yield to maximize yield

•  End-to-end throughput = 0.65 •  Noise floor, Δmagfloor = 27.5 •  OWA = Infinite •  Diffraction-limited Airy pattern PSF •  No detector noise •  5 yr mission: Optimized exposure/slew time balance, no overheads •  <5 visits per star, no optimization of revisit time •  Islew = 3000 s, Isk = 300 s, Thrust = 10 N (!) •  Delta IV Heavy payload limit of 9800 kg to S-E L2 •  Optimized starshade design from Eric Cady 21

Baseline Starshade Mission Parameters

Detection Bandpass

λ  = 0.55 µm Δλ = 40% SNR = 7

IWA = 60 mas Contrast, ζ = 10-10

1 starshade Characterization Bandpass

λ  = 1.0 µm Spectral Res. = 50

SNR = 5 IWA = 60 mas

Contrast, ζ = 10-10

22

Maximized Yields for Starshades

0 2 4 6 8 10Telescope Diameter, D (m)

0

5

10

15

ExoE

arth

Can

dida

te Y

ield q = 0.11

62/5967/66 69/69 60/60

51/5143/43

28/28

12/40/0

q = 0.62

159/98

191/148

208/184

221/210232/224

240/236

248/248

241/241

240/240

q = 0.65

179/106

228/156

244/191

270/241

284/258295/270

307/292

312/296

315/311

20 40 60 80 100IWA (mas)

0

5

10

15

ExoE

arth

Can

dida

te Y

ield q = 4.30

0/0 0/0 0/0

69/69

114/114157/131 166/128

q = ï0.00

72/72

118/118

161/161 208/184 248/185283/174

315/169

q = ï0.29

117/117

169/169205/199

244/191279/184

298/180

329/170

10ï11 10ï10 10ï9

Contrast, c (×10ï10)

0

5

10

15Ex

oEar

th C

andi

date

Yie

ld q = 0.06

32/32

51/5169/69 81/81

97/73

q = ï0.07

186/184 202/193208/184

235/166

250/124

q = ï0.07

230/203 237/198244/191

265/181

299/137

44

68

92

115

Dss (m

)

44

68

92

115

Dss (m

)Yield is moderately sensitive to aperture size and turns over

at large D; an optimum aperture size exists.

SLS

23

Yield vs Instrument Optical Parameters

Small IWA = fuel hungry; Large IWA = planets unobservable. An optimum IWA exists.

24

Yield vs Launch Mass

D = 4 m

D = 2 m

D = 6 m

D = 4 m

D = 2 m

Starshade performance highly dependent on launch mass budget, i.e. fuel mass.

Falcon

9

Delta

IVH

SLS

Falcon

9

Delta

IVH

SLS

IWA = 40 mas IWA = 60 mas

25

Compared to coronagraph, starshade yield more robust to astrophysical sources of photometric noise! This is because

yield is partially limited by fuel.

Impact of Astrophysical Assumptions

26

Details of an Optimized Observation Plan: Spectral Type & Visit Distribution

Starshade optimization chooses similar targets to coronagraphs, but observes them more deeply and only a

couple of times.

27

Direct Comparison of Baseline Coronagraph & Baseline Starshade Yields

Assumes identical astrophysical assumptions, science goals, and observational “rules.”

Need to examine the impact of the rules.

n = 3 zodis n = 60 zodis

SLS

Falcon 9

Delta IV H SLS

Falcon 9

Delta IV H

Coronagraph

Coronagraph

28

Future Work

•  Run yield calculations for actual coronagraph designs:

www.starkspace.com/yield_standards.pdf

•  Compare coronagraph & starshade yields for a variety of astrophysical scenarios, science goals, and observational approaches

•  Produce a code capable of dynamic observation plans (learns as the mission progresses)

•  Support Exoplanets Standards Team analysis of decadal studies

29

Backup Slides

30

Falcon 9 Delta IV Heavy SLS Block 1

ηEarth

???

Choosing a Powerful Null Result in the Search for Life

Number of habitable

zones (HZs) surveyed

Frequency of Earth-

sized rocks in the HZ

Yield of “exoEarth

candidates”

Fraction of Earth-sized HZ rocks with life

Yield of living

planets

× = flife× =

To guarantee at least 1 Earth-like planet at confidence level C

32

How Does One Choose a Yield Goal?

Must rely on blind selection counting. The probability P of x successes out of n tries, each with probability p of success, is given

by the binomial distribution function…

33flife

ExoE

arth

Can

dida

te Y

ield

Choosing a Powerful Null Result in the Search for Life

ExoEarth candidate yield required to constrain flife

34

Lower Limits on Aperture Size

If ηEarth = 0.1, detecting >30 exoEarth candidates requires D ≳ 11 m.

Amountofexozodiacaldust(×solarzodiacal

amount)

35

Larger Apertures Can Improve Characterization

Reconstruction of Earth’s land:sea ratio from disk-averaged time-resolved EPOXI observations.

12-m 8-m 4-meter

Exposure Time for Earth at 10 pc

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time (days)

0.09 0.08 0.07 0.06 0.05

Refl

ectiv

ity

Measuring rotational period and mapping planet

Ford et al. 2003

Require S/N~20 (5% photometry) to detect ~20% variations in reflectivity.