GLOBAL MAPPING OF EARTH-LIKE EXOPLANETS FROM SCATTERED LIGHT CURVES

Scattered lights from terrestrial exoplanets provide valuable information about their planetary surface. Applying the surface reconstruction method proposed by Fujii et al. to both diurnal and annual variations of scattered light, we develop a reconstruction method of land distribution with both longitudinal and latitudinal resolutions. We find that one can recover a global map of an idealized Earth-like planet on the following assumptions: (1) cloudlessness, (2) a face-on circular orbit, (3) known surface types and their reflectance spectra, (4) lack of atmospheric absorption, (5) known rotation rate, (6) a static map, and (7) the absence of a moon. Using the dependence of light curves on planetary obliquity, we also show that the obliquity can be measured by adopting the χ2 minimization or the extended information criterion. We demonstrate the feasibility of our methodology by applying it to a multi-band photometry of a cloudless model Earth with future space missions such as the occulting ozone observatory (O3). We conclude that future space missions can estimate both the surface distribution and the obliquity at least for cloudless Earth-like planets within 5 pc.

[1]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[2]  R. Gilliland,et al.  Detection of an Extrasolar Planet Atmosphere , 2001, astro-ph/0111544.

[3]  Xavier Bonfils,et al.  A super-Earth transiting a nearby low-mass star , 2009, Nature.

[4]  Teruyuki Nakajima,et al.  Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system , 1983 .

[5]  Adam Burrows,et al.  Phase Functions and Light Curves of Wide-Separation Extrasolar Giant Planets , 2005 .

[6]  E. Kokubo,et al.  Formation of Terrestrial Planets from Protoplanets. II. Statistics of Planetary Spin , 2007 .

[7]  W. Menke.  Geophysical data analysis , 1984 .

[8]  S. Seager,et al.  PHOTOMETRIC LIGHT CURVES AND POLARIZATION OF CLOSE-IN EXTRASOLAR GIANT PLANETS , 2000 .

[9]  W. Press,et al.  Numerical Recipes in Fortran: The Art of Scientific Computing.@@@Numerical Recipes in C: The Art of Scientific Computing. , 1994 .

[10]  Margaret Turnbull,et al.  Detectability of planetary characteristics in disk-averaged spectra II: synthetic spectra and light-curves of earth. , 2006, Astrobiology.

[11]  J. Fortney,et al.  Resolving the Surfaces of Extrasolar Planets with Secondary Eclipse Light Curves , 2006, astro-ph/0601092.

[12]  Harold F. Levison,et al.  On the Character and Consequences of Large Impacts in the Late Stage of Terrestrial Planet Formation , 1999 .

[13]  David Charbonneau,et al.  A map of the day–night contrast of the extrasolar planet HD 189733b , 2007, Nature.

[14]  Pin Chen,et al.  Submitted to the Astrophysical Journal Letters Molecular Signatures in the Near Infrared Dayside Spectrum of , 2022 .

[15]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[16]  M. Mayor,et al.  An extended upper atmosphere around the extrasolar planet HD209458b , 2003, Nature.

[17]  Nicolas B. Cowan,et al.  Inverting Phase Functions to Map Exoplanets , 2008, 0803.3622.

[18]  G. Kitagawa,et al.  Generalised information criteria in model selection , 1996 .

[19]  N. J. Woolf,et al.  The Spectrum of Earthshine: A Pale Blue Dot Observed from the Ground , 2002 .

[20]  L. Colina,et al.  Absolute Flux Calibrated Spectrum of , 1996 .

[21]  Darren M. Williams,et al.  Seasonality on terrestrial extrasolar planets: inferring obliquity and surface conditions from infrared light curves , 2004 .

[22]  Margaret Turnbull,et al.  Detectability of planetary characteristics in disk-averaged spectra. I: The Earth model. , 2006, Astrobiology.

[23]  William H. Press,et al.  Numerical Recipes in Fortran 77 , 1992 .

[24]  H. N. Russell.  On the light variations of asteroids and satellites , 1906 .

[25]  G. Kitagawa,et al.  Bootstrapping Log Likelihood and EIC, an Extension of AIC , 1997 .

[26]  Gautam Vasisht,et al.  The presence of methane in the atmosphere of an extrasolar planet , 2008, Nature.

[27]  L. Arnold,et al.  A test for the search for life on extrasolar planets - Looking for the terrestrial vegetation signature in the Earthshine spectrum , 2002, astro-ph/0206314.

[28]  P. R. Goode,et al.  Vegetation Signature in the Observed Globally Integrated Spectrum of Earth Considering Simultaneous Cloud Data: Applications for Extrasolar Planets , 2006, astro-ph/0604420.

[29]  W. Menke.  Geophysical data analysis : discrete inverse theory , 1984 .

[30]  S. Seager,et al.  Characterization of extrasolar terrestrial planets from diurnal photometric variability , 2001, Nature.

[31]  S. Fukuda,et al.  COLORS OF A SECOND EARTH: ESTIMATING THE FRACTIONAL AREAS OF OCEAN, LAND, AND VEGETATION OF EARTH-LIKE EXOPLANETS , 2009, 0911.5621.

[32]  J. Chambers.  Making More Terrestrial Planets , 2001 .

[33]  Jonathan Tennyson,et al.  Water vapour in the atmosphere of a transiting extrasolar planet , 2007, Nature.

[34]  J. Kasting,et al.  Habitable planets with high obliquities. , 1996, Icarus.

[35]  et al,et al.  The CoRoT space mission : early results Special feature Transiting exoplanets from the CoRoT space mission VIII . CoRoT-7 b : the first super-Earth with measured radius , 2009 .

[36]  Webster Cash,et al.  CONSTRUCTION OF AN EARTH MODEL: ANALYSIS OF EXOPLANET LIGHT CURVES AND MAPPING THE NEXT EARTH WITH THE NEW WORLDS OBSERVER , 2009 .

[37]  S. Seager,et al.  ALIEN MAPS OF AN OCEAN-BEARING WORLD , 2009, 0905.3742.

[38]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[39]  N. J. Kasdin,et al.  Analyzing the Designs of Planet-Finding Missions , 2009, 0903.4915.

[40]  S. Seager,et al.  Identifying the Rotation Rate and the Presence of Dynamic Weather on Extrasolar Earth-like Planets from Photometric Observations , 2008, 0802.1836.

[41]  D. Pollard,et al.  Extraordinary climates of Earth-like planets: three-dimensional climate simulations at extreme obliquity , 2003, International Journal of Astrobiology.