Directly imaging habitable planets around M-type stars with ELTs

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Extremely Larget Telescopes (ELTs): the fastest and easiest path toward direct imaging and characterization of potentially habitable planets

Abstract

The unprecedented angular resolution soon to be offered by extremely large telescopes (ELTs), together with recently developed high contrast imaging techniques (coronagraphy and wavefront control), will enable direct imaging and spectroscopic characterization of potentially habitable planets around nearby M-type stars. While the habitable zones of M stars is challenging to resolve, the planet to star contrast and the apparent brightness of the planet are highly favorable, thus providing the only reliable opportunity for direct imaging and spectroscopic characterization of habitable planets from the ground.

The key to imaging and characterizing such planets lies in the ability to perform high contrast imaging (approximately 1e-5 raw contrast) at $\approx$ 1 λ/D with high photometric efficiency. Technical solutions to this challenge now exist, as illustrated by the recent development of a full throughput coronagraph concept offering sub-λ/D inner working angle at high contrast on segmented apertures, and schemes to achieve the necessary level of pointing and low order wavefront error control. Demonstrations of these key techniques are ongoing in laboratories and on ground-based telescopes, already yielding encouraging results. We conclude that a highly specialized, but relatively simple, high contrast imaging system can be build for ELTs within this decade, and that it would likely provide the first opportunity to acquire high quality spectra of habitable planets, before space-based telescope can provide similar capabilities for brighter F-G-K type stars.

1. Introduction

Characterization of potential habitable planets around other stars to the level required for identification of biological activity requires relatively high quality spectroscopy.

In Section 2, the expected first-order observational characteristics (planet contrast, separation and apparent luminosity; star brightness) of rocky planets in the habitable zones of nearby stars are established. Using these parameters, section 3 shows that rocky planets around M-type stars can be observed with ELTs in reflected light provided that (1) a coronagraph operating with a 1 λ/D inner working angle can be used and (2) wavefront sensing can be performed efficiently on low-order aberrations. These two requirements are then discussed in more detail in sections 4 (coronagraphy) and 5 (wavefront control and calibration).

2. Rocky planets in the habitable zones of nearby stars

2.1. Input catalogs

• The Gliese Catalog of Nearby Stars 3rd edition (CNS3) containing all stars known to be within 25 parsecs of the Sun as of 1991. This catalog is the primary source of targets for this work, and contains the position the spectral type, apparent magnitude (V band), colors (B-V, R-I) and parallax for each target.
• Near-IR photometry is obtained from the 2MASS point source catalog.
• The northern 8-parsec sample [Reid, Hawley & Gizis, 1995] countains bolometric luminosities and colors (B-V, V-R, V-I) for targets in the 8-parsec sample and is used to establish empirical photometric relationships that can be applied to the full sample, as detailed in the next sections

2.2. Star bolometric luminosity, planet angular separation and contrast

Blue fit (B-V < 1.2):

fitblue(x) = ab + bb*x + cb*x**2 + db*x**3

degrees of freedom    (FIT_NDF)                        : 20
rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.0321603
variance of residuals (reduced chisquare) = WSSR/ndf   : 0.00103429

Final set of parameters            Asymptotic Standard Error
=======================            ==========================

ab              = -0.121112        +/- 0.03043      (25.12%)
bb              = 0.634846         +/- 0.2317       (36.5%)
cb              = -1.01318         +/- 0.4267       (42.12%)
db              = 0.125024         +/- 0.217        (173.6%)

fitred(x) = ar + br*x + cr*x**2 + dr*x**3 + er*x**4

degrees of freedom    (FIT_NDF)                        : 73
rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.250859
variance of residuals (reduced chisquare) = WSSR/ndf   : 0.0629302

Final set of parameters            Asymptotic Standard Error
=======================            ==========================

ar               = -43.9614         +/- 20.91        (47.56%)
br               = 115.958          +/- 54.3         (46.83%)
cr               = -110.511         +/- 51.86        (46.93%)
dr               = 44.7847          +/- 21.63        (48.29%)
er               = -6.74903         +/- 3.327        (49.29%)

Fig 1: Bolometric correction as a function of B-V color for the 8-pc sample. The blue and red fits are used for B-V < 1.1 and B-V > 1.1 respectively. [eps]

The bolometric luminosity (referenced to the Sun) for each star is then derived from the absolute magnitude M_V and the bolometric correction BC():

Lbol = 2.51188643-(MV-4.83) + (BC - BCSun)	(1)

with BC_Sun = -0.076.

The planet is then placed sqrt(L_bol) AU from the star, and its angular separation is computed using the star parallax.

Fig 2: Angular separation vs reflected light contrast for SuperEarths (2x Earth diameter), assuming each star in the sample has such a planet. [eps]

Fig 3: Angular separation vs reflected light contrast for SuperEarths (2x Earth diameter), assuming each star in the sample has such a planet (detail). [eps]

2.1.2. Apparent magnitudes in V, R, and I bands

 
degrees of freedom    (FIT_NDF)                        : 76
rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.0741659
variance of residuals (reduced chisquare) = WSSR/ndf   : 0.00550058

Final set of parameters            Asymptotic Standard Error
=======================            ==========================

a               = 0.0207711        +/- 0.07513      (361.7%)
b               = 0.571443         +/- 0.233        (40.78%)
c               = -0.157074        +/- 0.2176       (138.5%)
d               = 0.147305         +/- 0.06183      (41.97%)

degrees of freedom    (FIT_NDF)                        : 76
rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.1921
variance of residuals (reduced chisquare) = WSSR/ndf   : 0.0369025

Final set of parameters            Asymptotic Standard Error
=======================            ==========================

a               = 0.221522         +/- 0.1946       (87.84%)
b               = 0.0067191        +/- 0.6036       (8984%)
c               = 0.906601         +/- 0.5636       (62.17%)
d               = 0.000695602      +/- 0.1601       (2.302e+04%)

2.1.3. Apparent magnitudes in J, H and K bands

This study assumes that planet imaging is performed in the near-IR with adaptive optics. To estimate the contribution of photon noise, the near-IR brightnesses of both the stars and their planets are required

Apparent J, H and K magnitudes for the stars are extracted from the 2MASS catalog. In the few cases (1% of the targets) where Gliese catalog entries do not have a match in the 2MASS catalog (usually because they are too faint or they are close companions), 4th order polynomial fits of the V-J, V-H and V-K colors as a function of B-V color are derived from the list of targets that are matched in both catalogs, and then applied to those for which no near-IR flux measurement exists. In this case, the standard deviation in the J, H, and K magnitudes are 0.36, 0.41 and 0.36 respectively (these values are sufficiently small to not significantly affect planet detectability estimates).

Since the planet albedo is assumed independent of wavelength, the planet to star contrast in the near-IR is the same as computed for visible light. No thermal emission is assumed (this is a conservative assumption in K band).

3. Observability of rocky planets in reflected light

3.1. First cut at observation constraints for ELTs

• Angular separation. The separation must be sufficiently larger than the inner working angle (IWA) of the coronagraph.
• Contrast. The planet-to-star contrast must be above the detection limit, which is itself a function of both wavefront correction performance, coronagraph performance, PSF calibration accuracy, and uncorrelated noises (photon noise mostly).
• Star brightness. The star brightness has a strong impact on the wavefront correction quality: faint stars do not produce sufficient light for accurate and fast wavefront measurements.
• Planet brightness. The planet brightness must be above the photon-noise detection limit.

These detectability constraints are highly coupled. For example, the contrast limit is usually a steep function of the angular separation, and both the star brightness and planet brightness strongly affect the contrast limit. The interdependencies between these limits are function of the instrument design and choices (wavefront control techniques, observation wavelength). To easily identify how instrumental trades affect detectability of habitable exoplanets, first cut limits are first applied to construct a small list of potential targets.

The first cut limits are shown in the table above. The number of targets kept is mostly driven by the contrast and separation limits, and to a lesser extent by the planet brightness limit. The planet brightness limit is derived from a required SNR=10 detection in 10mn exposure in a 0.05 μm wide effective bandwidth (equivalent to a 15% efficiency for the whole H-band) on a 30-m diffraction limited telescope, taking into account only sky background and assuming all flux in a 20mas wide box is summed. The assumed sky background (continuum + emission) is m_H = 14.4 mag/arcsec² [E-ELT sky background model, ESO] and [Cuby et al. 2000].

D=30 -> 700 m2
background = 16412 ph / sec / um / m2 / arcsec2 -> 230 ph/sec on the 20mas box
With N photon/sec from source: SNR(t) = N sqrt(t) / sqrt(N + 230) 
With t = 600 sec -> SNR = 24.5 N / sqrt(N+230)
SNR = 10 ->  N = 6.3 ph/sec
flux = 6.3 ph/sec = 0.18 ph/sec/um/m2 -> mH = 26.8

Fig 4: Planet apparent brightness in H-band as a function of system distance. The mH=26.8 flux limit adopted excludes planets beyond 20pc. plot [0:20][28:19] "./cat1.dat" u 1:($26-2.5*log10($10)) w p ps 0.4 pt 7 [eps]

The target list after applying the first cut limit consists of 274 entries. Figure x shows that this lists consists mostly of relatively faint (mV~10) late-type (V-R ~ 1 to 1.5) main sequence stars. Two notable exceptions are the 40 Eri B and Sirius B white dwarfs, clearly visible in fig x as much bluer (V-R ~ 0) than the rest of the sample.

Fig 5: ELT exoplanet targets stars visible light brightness and color. [eps]

3.2. List of most favorable targets

• Angular separation at maximum elongation > 15 mas
• Contrast > 1e-7
• Planet brightness m_H < 24, allowing spectroscopy

4. High efficiency coronagraphy at small IWA on segmented apertures

4.1. Proof of existence of a full efficiency coronagraph working within the telescope diffraction limit: the PIAACMC concept

4.2. Expected performance and manufacturability

5. Wavefront control for high contrast imaging near the telescope's diffraction limit

5.1. Optimal wavefront sensing strategy

Fig 6: Planet contrast as a function of star I-band magnitudes for the ELT exoplanet sample and the top targets. [eps]

5.2. Expected contrast limit

The raw PSF contrast is estimated in Figure x for a m_I target. In the 10 to 20 mas angular separation range where most of the exoplanets are imaged, the contrast is limited by time lag in the loop and photon noise, and the other fundamental limits to raw contrast (scintillation and atmospheric chromaticity effects) are much smaller. With a high efficiency wavefront sensor able to take advantage of the telescope's diffraction limit, the expected raw PSF contrast at these small separations is approximately 1e-5, provided that the servo lag is no more than about 0.1 ms. This unusually low servo lag can be achieved with a high WFS sampling frequency (>10 kHz), and/or the use of predictive wavefront control techniques. Figure x also shows that a seeing-limited WFS such as the SHWFS is very inefficient at these small angular separations, and would be a poor choice for the system, even if it operates at its photon-noise limit with no loop servo lag other than the one imposed by photon noise.

Fig 7: Raw contrast in a Extreme-AO corrected PSF on a 30-m telescope. The WFS is assumed to be operating at the diffraction limited sensitivity on a mI=8.5 target, with a 0.05 μm effective spectral bandwidth. For comparison, the photon-noise limited raw contrast limit for a SHWFS is also shown (upper curve). Several closed loop effective delays have been considered. [eps]

The analytical model used to estimate raw contrast was also tested for an 8-m diameter telescope under the same conditions. For a 1 kHz system with a diffraction-limited wavefront sensor on an 8-m telescope, the raw contrast at 0.1" is 3e-4 (limited by servo lag), and it is 3e-5 at 0.5". These numbers are consistent with the goals of the future Extreme-AO systems on such telescopes.

The detection contrast limit is more difficult to estimate for this system, as a range of PSF calibration techniques could be used (spectral or polarimetric differentiation for example). For simplicity, it is assumed here that spectral or polarimetric PSF calibration techniques are not used, and that the detection limit is imposed by speckle structure in the long-exposure image and photon noise. It is also assumed that static and slow speckles that are not due to the atmosphere are removed by focal plane wavefront control, a scheme that has already demonstrate control and removal of static coherent speckles at the 3e-9 contrast level in the presence of much stronger dynamic speckles.

The PSF halo consists of rapid atmospheric speckles at the 1e-5 contrast level with a lifetime of no more than one millisecond (speckles of longer duration are suppressed by the AO loop). In a one-hour observation, this fast component can thus average to 5e-9 contrast assuming that the AO system has removed correlation on timescales above 1ms. In addition to these fast speckles, chromatic non-common path errors and scintillation create a speckle halo contribution at the 1e-6 contrast level. Since this component is not controlled by the AO system, its coherence time is longer, at up to about 100ms in the near-IR. A 1-hr long observation will average this component by a factor ~200, to 5e-9 contrast level. Finally, photon noise in a 1-hr exposure for a m_H star and a 1e-5 raw contrast will set a 1e-9 contrast limit for a 0.05 μm effective spectral bandwidth. Combined together, the 3 effects lead to a detection contrast limit just below 1e-8 for a 1hr long exposure.

5.3. Stellar angular size

5.4. Pointing and low order aberrations control

• Pointing jitter needs to be sufficiently small to allow detection and characterization of exoplanets in the presence of the photon noise created by coronagraphic leaks. For a 1e-5 allowable raw contrast at the coronagraph's IWA, the pointing jitter should be no more than about two percent of the telescope diffraction limit, or 0.2 mas. This is similar to the angular radius of most stars in the sample: the largest angular radius in the top targets is 0.5mas (Proxima Centauri), so reducing the pointing jitter below 0.2 mas will in fact not bring significant performance improvement, as the coronagraph will be designed to tolerate this level of jitter in order to accommodate stellar angular size.
• Pointing calibration on longer timescales should be accurate to about 0.01 mas to support 1e-8 calibrated contrast level.

6. Instrument design, technologies required

• Given that the ExAO system needs to operate fast (10 kHz or faster) but does not need to clean the PSF halo over a large range of angles, it consists of a ultra fast low actuator count system (~12 x 12 actuators) placed after a conventional facility AO system. The conventional AO system's role is to provide a diffraction-limited PSF, and will require many actuators for an ELT, but can run relatively slowly (~kHz). The ExAO system achieves its speed and sensitivity over a small number of modes to keep its computational bandwidth and pixel read rate manageable. This architecture (slow tweeter followed by fast woofer) is opposite to current ExAO systems for which the second AO layer has a higher actuator count.
• Since the two AO system have different functions and very different temporal bandwidth, there is no need for communication between the two systems. The planet imaging instrument does therefore not need to interface with the facility AO system, simplifying development, testing and operation.
• A fast sensor dedicated to pointing and focus is implemented within the coronagraph.
• The coronagraph allows direct imaging at λ/D inner working angle
• The science camera - an integral field spectrograph - is designed for fast readout, compromising with field of view and spectral resolution. The fast readout (second or faster) allows efficient active suppression of slow speckles that are due to non-common path errors in the system.

Figure 8: Possible system architecture for an experiment aimed at imaging habitable planets around nearby M-type stars with an ELT.

Conclusions

Direct imaging of habitable planets around nearby M-type stars with ELTs appears to be feasible thanks to new techniques that allow high contrast imaging at small angular separation. While these planets are too close to be resolved by current telescopes, an ELT able to acquire high contrast imaging in the 10mas to 30mas separation range can image them, and their relatively high brightness would allow for spectroscopic investigations. For the top targets, Earth-size habitable exoplanet may even be detected.

The technologies required to achieve this goal exist, even though several key technologies have only recently been identified and not yet demonstrated at the required performance level in laboratories or on sky. The next decade will be extremely valuable to mature these techniques toward an integrated system that can be ready when ELTs begin science operations. Experimental systems on 8-m telescopes, such as the Subaru Coronagraphic ExtremeAO (SCExAO) instrument, are rapidly maturing the techniques proposed required for this goal, and should continue to do so through this decade. Given the unusual requirements of such a system and the relatively small number of targets, a focused instrument (more akin to a science experiment than a facility instrument) should be developed instead of a general purpose extreme-AO system similar to the current generation of ExAO systems on 8-m class telescopes. This would allow for a relatively simple system with a rapid development schedule and moderate cost - an approach that would allow ELTs to acquire the first high quality spectra of nearby M-type habitable planets. This science goal is complementary to future space mission operating in visible light, which will need to target exoplanets at more challenging contrast levels around Sun-like stars due to limited angular resolution.