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LabNotes

This is the laboratory notebook of the PHL, a preprint and technical blog space of ideas and progress reports that could be later incorporated into peer-review research. Its content is mostly oriented to scientists, specially to those involved in our projects. However, many of the entries contain links to images and software that could be of interest to the general scientific community, educators, and public. You can subscribe to it via RSS.
  • Not all habitable planets are equally ‘habitable’ So far we know of up to 20 potentially habitable planets around other stars out of nearly 2,000 planets that have been detected and confirmed. We expect to find ...
    Posted Mar 12, 2014, 7:39 AM by Abel Mendez Torres
  • Surface Temperature of Planets The mean global surface temperature of a planet in a circular orbit is given by (adapted from Qiu et al., 2003): (1) where Ts = mean global surface temperature (K ...
    Posted Jan 7, 2014, 6:22 AM by Abel Mendez Torres
  • A New Large Batch of Earth-like Worlds Candidates The NASA Kepler added 1,089 new objects of interest from the Q1-16 release to its KOI database. All are objects of interest pending further verification (not dispositioned) to ...
    Posted Jan 4, 2014, 7:10 AM by Abel Mendez Torres
  • Spatial and Temporal Averages for Elliptical Orbits Mean orbital values for distance, stellar flux, and equilibrium temperature can be computed with respect to spatial or temporal coordinates. Spatial averages are usually calculated with respect to the mean ...
    Posted Jan 4, 2014, 8:50 AM by Abel Mendez Torres
  • SER: First Look at Pluto The Scientific Exoplanets Renderer (SER) is our core software to generate photorealistic-looking images of planets such as the ones for the Visible Paleo-Earth and the Habitable Exoplanets Catalog ...
    Posted Nov 13, 2013, 10:02 AM by Abel Mendez Torres
  • Occurrence of Earth-like planets around GKM Stars Here we combine and interpret results from Kopparapu (2013) and Petigura et al. (2013) on the occurrence of Earth-like planets around red-dwarf (type M) and Sun-like (type ...
    Posted Nov 5, 2013, 8:47 AM by Abel Mendez Torres
  • New Kepler Potential Planet Transit Signals The NASA Kepler team released a revised global list of 16,285 potential planet transit signals (formally known as Threshold-Crossing Events or TCE) from quarters one to sixteen, the ...
    Posted Nov 4, 2013, 8:03 AM by Abel Mendez Torres
  • 50th Anniversary of the Arecibo Observatory The Arecibo Observatory (AO) was inaugurated November 1, 1963. To recognize its 50th year of service to the scientific community, the AO is having a science symposium, “50 Years of ...
    Posted Oct 27, 2013, 7:20 PM by Abel Mendez Torres
  • A Binomial Nomenclature for Common Names of Exoplanets When naming exoplanets create common names for both the stellar system and the exoplanetsThere are nearly one thousand exoplanets already confirmed and many more waiting for confirmation. The general ...
    Posted Sep 27, 2013, 12:20 AM by Abel Mendez Torres
  • About 40 potentially habitable worlds by the end of 2015? We started with just two planets in our Habitable Exoplanets Catalog almost two years ago on December 2011. At that time having a catalog for just two planets was overkill ...
    Posted Sep 20, 2013, 3:12 AM by Abel Mendez Torres
  • One-AU Exoplanets Most known exoplanets are within one astronomical unit (AU) from their stars, a bias of our detection methods. Here are graphical representations of 417 stellar systems with planets within one ...
    Posted Aug 12, 2013, 1:01 PM by Abel Mendez Torres
  • Earth from Near and Deep Space The Cassini spacecraft on Saturn and the Messenger spacecraft on Mercury are taking images of Earth in July 19, 2013. From their vantage point Earth will be just a few ...
    Posted Jul 23, 2013, 3:07 AM by Abel Mendez Torres
  • Statistics of Nearby Earth-like Planets Around M-dwarfs Stars Here is an analysis on the frequency, number, distance, and probability of Earth-like planets (Earth-size within the habitable zone) around M-dwarf stars within 10 parsecs (~33 light ...
    Posted Apr 8, 2013, 1:20 AM by Abel Mendez Torres
  • Transits of Earth-like Exoplanets and Exomoons Here are a few transit simulations of Earth-like planets with and without moons (Figures 1-3) including Avatar's Pandora (Figure 4). All simulations assume long cadence observations (every ...
    Posted Apr 29, 2013, 12:31 AM by Abel Mendez Torres
  • Summary of the Limits of the New Habitable Zone The new habitable zone (Kopparapu et al., 2013) has a narrow and wide definition (Figure 1). The narrower 'conservative habitable zone' is bounded by the 'moist greenhouse' and 'maximum greenhouse ...
    Posted Apr 8, 2013, 12:39 AM by Abel Mendez Torres
  • Conferencia en el IITF El Prof. Abel Méndez ofrecerá una conferencia sobre planetas habitables en el Instituto Internacional de Dasonomía Tropical el jueves, 21 de marzo de 2013 a las 2:30 PM. Para ...
    Posted Mar 19, 2013, 1:20 AM by Abel Mendez Torres
  • Limits of the New Habitable Zone Here are some limits of the new habitable zone (HZ) for main sequence stars (Table 1) from Kopparapu et al. (2013) for six parameters: distance from star (Table 2), stellar ...
    Posted Mar 17, 2013, 9:59 PM by Abel Mendez Torres
  • TCE01: Terrestrial Climatology and Ecology Initial test of reading, plotting, and estimate of NPP. These files are part of a study of terrestrial climatology and ecology and are only intended for the scientisits working on ...
    Posted Mar 17, 2013, 3:01 PM by Abel Mendez Torres
  • KOI-172.02: An excellent candidate for a “Venus-twin” (Reposted from PaleBlue.blog.) It seems that we have our latest "Earth twin candidate." This time, the planet is in orbit around a star very similar to our Sun. It ...
    Posted Jan 14, 2013, 7:56 PM by Abel Mendez Torres
  • The New Potential Habitable Exoplanets Candidates of NASA Kepler We evaluated the new release of 2740 NASA Kepler Candidates and identified 10 new candidates for potential habitable exoplanets from the previous batch. We also noticed that nine of the ...
    Posted Jan 11, 2013, 4:19 PM by Abel Mendez Torres
  • Current NASA Kepler Confirmed Planets This is a list of 132 confirmed planets by the NASA Kepler mission. The list combines both the Kepler Team and the general scientific community detections. All Kepler stars systems ...
    Posted Jan 10, 2013, 3:30 PM by Abel Mendez Torres
  • Exoplanets @ AAS 221 Here are the presentations program and press information for the 221st American Astronomical Society Meeting (AAS 221) from January 6 to 10, 2013. Below are three press conferences related to ...
    Posted Jan 4, 2013, 2:48 PM by Abel Mendez Torres
  • HEC Dump Files for Confirmed Planets, Kepler Candidates, and TCE Here are the HEC Dump Files with the basic statistics as of Jan 3rd, 2013 for Confirmed Exoplanets, NASA Kepler Candidates, and NASA Kepler TCE. They are used as a ...
    Posted Jan 4, 2013, 7:52 AM by Abel Mendez Torres
  • Science Definition Team for the 2020 Mars Science Rover Call for Letters of Application for Membership on the Science Definition Team for the 2020 Mars Science Rover  Solicitation Number: Posted Date:FedBizOpps Posted Date:Recovery and Reinvestment Act Action ...
    Posted Dec 23, 2012, 9:54 AM by Abel Mendez Torres
  • Planetary Habitability @ AGU 2012 Here is a list of the sessions related to planetary habitability that will be presented in the AGU Fall meeting 2012, from December 3 to 7, 2012 in San Francisco ...
    Posted Nov 30, 2012, 10:06 AM by Abel Mendez Torres
  • Annual Arecibo Observatory Scientific Conference Image Credit: Arecibo ObservatoryIMPORTANT: THIS ACTIVITY HAS BEEN POSTPONEDDecember 27 & 28, 2012 Arecibo Observatory, Arecibo, Puerto Rico Overview We cordially invite Puerto Rican astronomers with interests in astronomy ...
    Posted Dec 20, 2012, 7:59 AM by Abel Mendez Torres
  • Exoplanets at the DPS Annual Meeting Here are the exoplanet oral and poster presentations at the 44th annual meeting of the Division for Planetary Sciences (DPS) of the American Astronomical Society (AAS) in Reno, Nevada, 14 ...
    Posted Oct 14, 2012, 7:32 PM by Abel Mendez Torres
  • Exoplanets and Astrobiology at EPSC These are the presentations related to exoplanets and astrobiology at the European Planetary Science Congress 2012, IFEMA-Feria de Madrid, 23–28 September 2012, Madrid, Spain.Oral Program EX1Observations ...
    Posted Sep 25, 2012, 8:22 AM by Abel Mendez Torres
  • AGU Fall Meeting 2012 Here are most of the proposed sessions related to astrobiology, in no particular order, as part of the next AGU Fall Meeting from December 3-7, 2012 on San Francisco ...
    Posted Jul 8, 2012, 12:15 PM by Abel Mendez Torres
  • 84 New Kepler Exoplanet Candidates Ofir and Dreizler (2012) did an independent analysis to 64 stellar systems from the NASA Kepler dataset. They found 84 new exoplanets candidates in these systems increasing the number of ...
    Posted Aug 7, 2012, 7:10 PM by Abel Mendez Torres
  • Exoplanet Presentations at AAS 220th Here is a list of various sessions with exoplanet presentations on the 220th Meeting of the American Astronomical Society from June 10-14, 2012 in Anchorage, Alaska. Check the ...
    Posted Oct 21, 2012, 2:44 PM by Abel Mendez Torres
  • Reference and Color Calibration for the Visible Daily-Earth This is test image that we are using as landmasses reference and color calibration for the Visible Daily-Earth. It shows computer generated global views of Earth as seen from ...
    Posted Jun 4, 2012, 8:37 PM by Abel Mendez Torres
  • Eclipse of May 20-21, 2012 Here is the shadow over Earth near the maximum during the Annular Solar Eclipse of May 20-21, 2012. This image was generated during a color test of our Visible ...
    Posted Jun 4, 2012, 8:38 PM by Abel Mendez Torres
  • Visible Daily-Earth: May 16, 2012 This is a test of the code for our new Visible Daily-Earth project where we will have a true-color global picture of Earth generated daily from geostationary satellites ...
    Posted Jun 4, 2012, 8:39 PM by Abel Mendez Torres
  • Earth Live We are working in a project to put online current daily global satellite images of Earth in true-color (colors as seen by the human eye). Unfortunately, satellites that have ...
    Posted Jun 4, 2012, 8:40 PM by Abel Mendez Torres
  • Three Hot Subterran Exoplanets around KOI-961 Here are some quick stellar and planetary properties (Tables 1 and 2) for the three exoplanets system KOI-961 plus the basic habitability assessment with the Habitable Zone Distance (HZD ...
    Posted Jun 30, 2012, 11:10 AM by Abel Mendez Torres
  • AAS 219 Press Conference: Extraordinary Exoplanets Here are the abstracts of the presentations related to the AAS 219 press conference Extraordinary Exoplanets schedule on Wednesday, January 11, 2012 at 1:00 PM CST (3:00 PM ...
    Posted Jan 11, 2012, 10:15 AM by Abel Mendez Torres
  • Exoplanets with the Most Earth-like Interiors This is a list of exoplanets with the most Earth-like interiors ranked by the Interior Earth Similarity Index (iESI), a measure of how an exoplanet size and bulk density ...
    Posted Aug 11, 2012, 1:56 PM by Abel Mendez Torres
  • Habitability Assessments using Habitable-Space Metrics One of the main problems of measuring habitability, the suitability of an environment to support life, is how to connect the dependency of many environmental variables with life. The best ...
    Posted Jun 30, 2012, 11:16 AM by Abel Mendez Torres
  • Habitable Zone Atmosphere (HZA): A habitability metric for exoplanets The Habitable Zone Atmosphere (HZA) is a measure of the potential of an exoplanet to hold a habitable atmosphere. Most life forms requires some basic atmospheric ingredients like carbon dioxide ...
    Posted Jun 30, 2012, 11:49 AM by Abel Mendez Torres
  • Habitable Zone Composition (HZC): A habitability metric for exoplanets The Habitable Zone Composition (HZC) measures how compatible for life is the bulk composition of an exoplanet within the habitable zone. Life requires a variety of elements from volatiles to ...
    Posted Jul 1, 2012, 11:24 AM by Abel Mendez Torres
  • Standard Mass-Radius Relation for Exoplanets We are trying to develop a standard mass-radius relationship for exoplanets to predict the most likely value from the other. There are very high uncertainties in predicting radius from ...
    Posted Jun 30, 2012, 11:54 AM by Abel Mendez Torres
  • Updates on Kepler-22 b during the First Kepler Science Conference Dec05: The recent confirmation of Kepler-22 b (KOI-087) does not qualify as a potential habitable exoplanet in the Habitable Exoplanets Catalog. It is in the habitable zone of ...
    Posted Jun 30, 2012, 11:56 AM by Abel Mendez Torres
  • Data Comparison of Confirmed Exoplanets with Kepler Candidates Here we show a simple statistical comparison of data for confirmed exoplanets (exoplanet.eu) and Kepler candidates (Borucki et al., 2011). This analysis was done as a quality test of ...
    Posted Oct 29, 2011, 6:22 AM by Abel Mendez Torres
  • Exoplanets Continuously Within the Habitable Zone There are 83 exoplanets in the habitable zone (HZ) in the currently known 694 exoplanets, but many exhibit wide elliptical orbits that take them just inside or outside the edges ...
    Posted Jun 30, 2012, 12:02 PM by Abel Mendez Torres
  • The Night Sky of Exoplanets We are developing software code to generate photorealistic visualizations of star fields. The code uses information from the stars to generate their visual appearance from any vantage point including relative ...
    Posted Jun 30, 2012, 12:06 PM by Abel Mendez Torres
  • The Periodic Table of Exoplanets This table summarizes in eighteen thermal-mass categories most of the current known exoplanets (as of October 2011). Planets are divided in six mass classes as mercurians, subterrans, terrans, superterrans ...
    Posted Jun 30, 2012, 12:08 PM by Abel Mendez Torres
  • The Apparent Brightness and Size of Exoplanets and their Stars One thing that we are trying to reproduce for the Habitable Exoplanets Catalog is the visual appearance of exoplanets and stars. This includes the color, brightness, and size of the ...
    Posted Jun 30, 2012, 12:10 PM by Abel Mendez Torres
  • Location and Relative Size of Exoplanets on the Night Sky This is a visualization of the location and relative size of current 690 confirmed exoplanet on the night sky, using equatorial coordinates with a rectangular projection. The constellation outlines are ...
    Posted Jun 30, 2012, 12:12 PM by Abel Mendez Torres
  • A Stellar System Map for Exoplanets Here we created a stellar map of 564 exoplanets systems from the latest database of confirmed exoplanets from the Extrasolar Planets Encyclopaedia. The map helps to visualize the relative distance ...
    Posted Jun 30, 2012, 12:19 PM by Abel Mendez Torres
  • Latest List of Potential Habitable Exoplanets and Exomoons We finally identified potential habitable exoplanets and exomoons from three catalogs. This was the first step in the construction of our Habitable Exoplanets Catalog (HEC). No exomoons have been detected ...
    Posted Oct 1, 2011, 8:32 PM by Abel Mendez Torres
  • Earth Around a Red Star The current potential habitable exoplanets, HD 85512 b and Gliese 581 d, orbit red stars. HD 85512 is a K5V and Gliese 581 is a M3V type star, both dimmer ...
    Posted Sep 26, 2011, 1:18 PM by Abel Mendez Torres
  • Earth "Real" Blues Our vision is not only limited by the energy range on the visible spectrum but also by its sensitivity to particular colors. The eyes are more adapted to see green ...
    Posted Sep 26, 2011, 7:29 AM by Abel Mendez Torres
  • Current Number of Habitable Exoplanets: 16 There are now two potential habitable exoplanets out of the confirmed 687, and 14 out of the published 1235 Kepler candidates. The original Kepler paper by Borucki et al. (2011 ...
    Posted Sep 24, 2011, 7:46 PM by Abel Mendez Torres
  • Only 39 Kepler Planet Candidates in the Habitable Zone Last April 2011 the Kepler Mission Team published a paper describing 1235 new planet candidates (Borucki et al., 2011). They argue that 56 of those where in the habitable zone ...
    Posted Sep 22, 2011, 6:36 AM by Abel Mendez Torres
  • The Exoplanet's Stars We are developing a code to automatically generate updated diagrams and visualizations from various exoplanets catalogs for the Habitable Exoplanet Catalog. Here is a test showing the mass, temperature, and ...
    Posted Sep 18, 2011, 10:11 PM by Abel Mendez Torres
  • The Habitability of "Tatooine" Kepler-16 (AB) b Kepler-16 (AB) b, an exoplanet with a Saturn-like mass, Venus-like orbit, and Mars-like temperatures.Kepler-16 (AB) b, aka "Tatooine," is the first exoplanet detected around ...
    Posted Sep 17, 2011, 12:39 PM by Abel Mendez Torres
  • Habitability Metrics and Classifications for Exoplanets Various habitability metrics can be used to assess and compare the potential for life, as we know it, of exoplanets. The main idea behind these metrics is to simplify the ...
    Posted Sep 6, 2011, 6:50 AM by Abel Mendez Torres
  • The Surface Pressure of Earth-like Exoplanets The total mass of the atmosphere of a planet is very easy to approximate from the surface pressure and radius of the planet, using a simple multiplication of pressure by ...
    Posted Aug 26, 2011, 10:31 PM by Abel Mendez Torres
  • A Mass Classification for both Solar and Extrasolar Planets We will need a simple way to communicate results as part of the Habitable Exoplanets Catalog. Our Habitable Exoplanet Classification focus only on habitable planets and a broader classification will ...
    Posted Oct 2, 2011, 11:18 AM by Abel Mendez Torres
  • The Mass and Radius of Potential Exomoons We barely have the capability to detect Earth-size exoplanets, less moons around them. Small exomoons will be atmosphere-less bodies, like our own Moon that shares with Earth the ...
    Posted Sep 30, 2011, 10:35 AM by Abel Mendez Torres
  • Habitable Zone Distance (HZD): A habitability metric for exoplanets The search for life in the universe requires methods to identify and characterize habitable planets in other stars. The concept of habitable zones (HZ) around stars provides the easiest procedure ...
    Posted Jul 30, 2012, 2:17 PM by Abel Mendez Torres
  • A Thermal Planetary Habitability Classification for Exoplanets Current and future observations by ground and orbital missions will be able to identify habitable exoplanets. As a first assessment, the surface temperature of Earth-like exoplanets is used as ...
    Posted Aug 9, 2011, 10:06 AM by Abel Mendez Torres
  • Vegetation, Ice and Deserts of the Paleo-Earth In our previous post we discussed the distribution of landmasses of the Paleo-Earth. Here we used the Visible Paleo-Earth (VPE) datasets to estimate the global surface coverage of ...
    Posted Jul 29, 2011, 3:46 AM by Abel Mendez Torres
  • Habitability of the Paleo-Earth as a Model for Earth-like Exoplanets The Phanerozoic is the last Eon of Earth history, from 542 million years ago to today. This was the period when large and complex life started to populate the ocean ...
    Posted Aug 6, 2011, 3:05 AM by Abel Mendez Torres
  • Distribution of landmasses of the Paleo-Earth Our planet shows different features as it rotates along its axis, sometimes dominated by land and others by ocean. Land areas are distributed predominantly in the Northern Hemisphere (68%) relative ...
    Posted Jul 8, 2011, 6:53 AM by Abel Mendez Torres
  • The Distribution of Complex Life in the Last 540 Million Years Following our previous post for the paleo-distribution of life, here we show two animations of the distribution of complex life in the last 540 million years based on the ...
    Posted Jul 1, 2012, 7:19 PM by Abel Mendez Torres
  • The Global Paleo-Distribution of Life 120 Ma We will be doing a simple habitability analysis of Earth in the last 750 million years as part of the Visible Paleo-Earth (VPE) project. We are using the fossil ...
    Posted May 30, 2011, 3:26 AM by Abel Mendez Torres
  • Seasonal Surface Temperatures of Dark Earth The Visible Paleo-Earth (VPE) project provides a unique set of data about the evolution of Earth in the last 750 million years that can be used not only to ...
    Posted May 12, 2011, 9:43 PM by Abel Mendez Torres
  • Analysis of the Distribution of Land and Oceans Here we present a quick analysis of the distribution of landmasses from the data generated as part of our Visible Paleo-Earth project. Previous post (here and here) showed the ...
    Posted May 12, 2011, 9:43 PM by Abel Mendez Torres
  • More Preliminary Analysis of Paleomaps Here are six more analysis of paleomaps for the periods 90, 150, 170, 560, 690, and 750 million years ago. For an explanation of the figures see previous post. These ...
    Posted Apr 11, 2011, 4:17 AM by Abel Mendez Torres
  • Preliminary Analysis of Paleocontinents Distribution We are studying Earth's paleoclimate and paleogeography as a base model to characterize future observations of Earth-like exoplanets. We are particularly interested in interpreting the diurnal and seasonal ...
    Posted Apr 2, 2011, 6:24 AM by Abel Mendez Torres
  • Using REDUCE as a computer algebra system (CAS) There are many computer algebra systems (CAS) available for doing math intensive operations. I needed one in MacOS and Linux/Unix platforms for complex operations, and potentially in an iPad ...
    Posted Mar 24, 2011, 3:25 AM by Abel Mendez Torres
  • Conversion from RBG to greyscale images. The following images show the result of converting an RGB image to greyscales using the rgb2grey IDL function (code below). This function is being used to calculate light curves and ...
    Posted Mar 10, 2011, 3:46 PM by Abel Mendez Torres
  • Nearby Stellar Density These plots show some simple statistics for our stellar neighborhood using the HYG Stellar Database v2.0, which combines stellar data from the Hipparcos Catalog, the Yale Bright Star Catalog ...
    Posted Mar 15, 2011, 1:02 PM by Abel Mendez Torres
  • References related to Paleo-Earth, exoplanets light curves, and color This is a reference list of web resources related to ‎the project Simulations of Light Curves from Earth-like Exoplanets‎. This list contains links of introductory materials, research articles, software ...
    Posted Mar 10, 2011, 2:49 PM by Abel Mendez Torres
Showing posts 1 - 76 of 76. View more »

Not all habitable planets are equally ‘habitable’

posted Mar 12, 2014, 7:30 AM by Abel Mendez Torres   [ updated Mar 12, 2014, 7:39 AM ]

So far we know of up to 20 potentially habitable planets around other stars out of nearly 2,000 planets that have been detected and confirmed. We expect to find many more in the following decades. Unfortunately, we are very far from really understanding the potential for life of these planets since we know very little of them.

We have a rough idea or their size and temperature and that tells us how likely are they to support liquid water, a necessity for life as we know it. However, we also need to understand their atmosphere, water content, climate, and many other factors that are still out of reach of our observational technology, these planets are very far away.

A habitable planet does not mean that it is actually inhabited, only that it might support life, at least microbial life. It might be hard to imagine a planet able to support life yet not inhabited, but that is a possibility. Some might be better than others since their habitability depends on complex physical and chemical interactions. If some already have life, well, that is another complication.


Almost Home is a 3D computer-animated family film by DreamWorks Animation scheduled for release on November 26, 2014.

Surface Temperature of Planets

posted Jan 4, 2014, 9:49 AM by Abel Mendez Torres   [ updated Jan 7, 2014, 6:22 AM ]

The mean global surface temperature of a planet in a circular orbit is given by (adapted from Qiu et al., 2003):

(1)

where Ts = mean global surface temperature (K), L* = star luminosity (solar units), a = semi-major axis, f = atmosphere redistribution factor (e.g. = 1 for fast rotators and f = 2 for tidally locked planets without atmospheres)A = bond albedo, and g = normalized greenhouse effect), and To = 278.5 K. The normalized greenhouse effect is defined as (Raval & Ramanathan, 1989):

(2)

where G = greenhouse effect (W/m2) or greenhouse forcing, and Teq = equilibrium temperature (K). Both A and g are numbers between 0 and 1 that are necessary to understand the temperature of planets. They do not only depend on the surface and atmospheric properties of the planet but also on the surface temperature. For example, Raval & Ramanathan (1989) determined the terrestrial g for clear-skies globally, but for a particular month (April 1985), as:

(3)

where Ts = sea surface temperature (SST), and only valid for temperatures between 275 K to 300 K. Eq. 1 can be easily extended to elliptical orbits assuming that both A and g are nearly constants as function of eccentricity (i.e. constant with orbital changes of Ts). Table 1 show some approximate values of A and g for Venus, Earth, and Mars.

Table 1. Necessary data to calculate the surface temperature of Venus, Earth, and Mars from Eq. 1. Solar luminosity L = 1.0 and f = 1. This solution can be extended to exoplanets given appropriate estimates of A and g.

Planet a, Semi-Major Axis (AU)  A, bond albedo g, greenhouse
Venus 0.723 0.750 0.990
Earth 1.000 0.300 0.397
Mars 1.524 0.250 0.086

References

  • Qiu, J., Goode, P. R., Pallé, E., Yurchyshyn, V., Hickey, J., Rodriguez, P. M., ... & Koonin, S. E. (2003). Earthshine and the Earth's albedo: 1. Earthshine observations and measurements of the lunar phase function for accurate measurements of the Earth's Bond albedo. Journal of Geophysical Research,108 (D22), 4709.
  • Raval, A., & Ramanathan, V. (1989). Observational determination of the greenhouse effect. Nature342 (6251), 758-761.

A New Large Batch of Earth-like Worlds Candidates

posted Dec 23, 2013, 3:36 AM by Abel Mendez Torres   [ updated Jan 4, 2014, 7:10 AM ]

The NASA Kepler added 1,089 new objects of interest from the Q1-16 release to its KOI database. All are objects of interest pending further verification (not dispositioned) to be included among their current 3,603 exoplanets candidates. The new batch includes up to 172 potentially habitable exoplanets, the largest number ever in any previous data release. However, they might be harder to confirm since most are not part of multi-planet systems or don't have many transit events. The table below lists these 172 objects sorted by Earth similarity (i.e. ESI). Those with ESI above 0.90 are particularly the most interesting ones. Check here for some definitions used in this table.

--------------------------------------------------------------------------------------------------
            Name              pClass  hClass   M(EU)   R(EU) P(days)  D(lyr)  Teq(K)   Ts(K)   ESI
--------------------------------------------------------------------------------------------------
     KOI-5330.01       K-Warm Terran       M    0.97    0.99    40.9   973.9    265.    299.  0.94
     KOI-5123.01       G-Warm Terran       M    1.28    1.09   288.9  1873.9    265.    300.  0.94
     KOI-5494.01       G-Warm Terran       M    1.83    1.24   223.5  1124.4    255.    291.  0.92
     KOI-5927.01       G-Warm Terran       M    1.83    1.24   436.4  1533.5    245.    282.  0.91
     KOI-5958.01    G-Warm Subterran       M    0.49    0.79   226.5   515.1    245.    276.  0.90
     KOI-3447.01    K-Warm Subterran       M    0.42    0.75    31.5   520.1    253.    283.  0.90
     KOI-5161.01  G-Warm Superterran       M    2.12    1.31   289.8   983.8    262.    299.  0.90
     KOI-5060.01       G-Warm Terran       P    1.46    1.14   290.4   888.8    235.    270.  0.88
     KOI-5560.01  G-Warm Superterran       M    2.12    1.31   365.0  1040.1    241.    278.  0.88
     KOI-5737.01  G-Warm Superterran       M    2.66    1.43   376.2  1833.4    254.    292.  0.87
     KOI-5806.01  G-Warm Superterran       M    2.21    1.33   313.8   970.0    271.    309.  0.87
     KOI-5627.01  G-Warm Superterran       M    2.90    1.48   244.0  1822.6    257.    295.  0.86
     KOI-5670.01  F-Warm Superterran       M    2.39    1.37   542.2  2340.4    239.    276.  0.86
     KOI-4996.01       F-Warm Terran       M    1.60    1.18   358.5  1597.9    280.    316.  0.86
     KOI-5957.01       G-Warm Terran       P    1.53    1.16   371.5   702.6    230.    265.  0.85
     KOI-5499.01  G-Warm Superterran       M    2.21    1.33   122.6  1965.3    279.    316.  0.84
     KOI-5147.01  G-Warm Superterran       M    3.26    1.55   471.4  1067.4    267.    305.  0.83
     KOI-5846.01  G-Warm Superterran       M    2.61    1.42   199.1  1713.8    278.    316.  0.83
     KOI-5610.01  F-Warm Superterran       M    3.71    1.64   495.4  2233.7    248.    287.  0.82
     KOI-5210.01       G-Warm Terran       M    1.83    1.24   126.0  1924.7    286.    323.  0.82
     KOI-5389.01  G-Warm Superterran       M    3.45    1.59   365.7  1053.9    241.    279.  0.82
     KOI-5840.01  F-Warm Superterran       M    3.87    1.67   460.8  1818.0    249.    288.  0.82
     KOI-5097.01  G-Warm Superterran       P    2.76    1.45   329.7  1859.0    232.    270.  0.81
     KOI-5975.01  F-Warm Superterran       P    2.24    1.34   545.5   902.7    228.    265.  0.81
     KOI-5200.01  G-Warm Superterran       M    4.15    1.72   357.8  1951.6    248.    288.  0.81
     KOI-5377.01  G-Warm Superterran       T    2.00    1.28   251.0  1488.6    288.    325.  0.81
     KOI-5232.01  F-Warm Superterran       M    4.30    1.75   476.4  2239.9    261.    300.  0.80
     KOI-5270.01  F-Warm Superterran       P    2.80    1.46   606.9  1900.9    229.    267.  0.80
     KOI-5395.01  G-Warm Superterran       M    4.53    1.79   601.1  1924.3    254.    294.  0.80
     KOI-5861.01  F-Warm Superterran       M    4.59    1.80   452.4  2135.3    256.    295.  0.80
     KOI-5646.01  F-Warm Superterran       M    4.42    1.77   386.6  1652.2    267.    307.  0.79
     KOI-5824.01  G-Warm Superterran       P    3.66    1.63   247.5  2704.4    233.    272.  0.79
     KOI-4940.01  K-Warm Superterran       M    4.37    1.76    84.6  1249.4    271.    310.  0.79
     KOI-5087.01  G-Warm Superterran       M    3.93    1.68   651.1  1260.1    234.    273.  0.79
     KOI-5949.01  F-Warm Superterran       M    4.99    1.87   559.8  1873.4    249.    289.  0.78
     KOI-5506.01  F-Warm Superterran       P    3.46    1.59   641.6  2638.4    230.    268.  0.78
     KOI-5421.01  G-Warm Superterran       M    4.84    1.84   370.9  1886.4    266.    306.  0.78
     KOI-5491.01  F-Warm Superterran       M    4.09    1.71   480.2  2456.0    235.    274.  0.78
     KOI-5777.01  G-Warm Superterran       M    5.06    1.88   372.3  2898.9    249.    289.  0.78
     KOI-5465.01  G-Warm Superterran       P    3.22    1.54   476.8  1740.7    227.    266.  0.78
     KOI-5475.01  F-Warm Superterran       P    3.84    1.66   448.3  1196.0    232.    271.  0.78
     KOI-5227.01  G-Warm Superterran       M    5.22    1.91   371.6  1988.8    259.    299.  0.78
     KOI-5938.01  F-Warm Superterran       M    5.34    1.93   545.2  1597.3    257.    297.  0.78
     KOI-5904.01    G-Warm Subterran       P    0.46    0.77   322.5   448.7    219.    250.  0.77
     KOI-5959.01  G-Warm Superterran       T    3.66    1.63   251.5  2450.8    284.    323.  0.77
     KOI-5357.01  F-Warm Superterran       M    5.16    1.90   520.6  2443.3    243.    283.  0.77
     KOI-5422.01  F-Warm Superterran       M    4.64    1.81   360.6  1982.7    274.    314.  0.77
     KOI-5920.01  F-Warm Superterran       M    5.28    1.92   471.4  2342.2    265.    304.  0.77
     KOI-5856.01  G-Warm Superterran       M    4.07    1.71   259.3  2543.3    281.    320.  0.77
     KOI-5165.01  F-Warm Superterran       M    4.70    1.82   369.7  2362.9    274.    314.  0.77
     KOI-5679.01  F-Warm Superterran       P    2.52    1.40   615.9  1387.3    221.    258.  0.77
     KOI-5843.01  G-Warm Superterran       M    4.93    1.86   331.8  1996.4    273.    313.  0.77
     KOI-5788.01  F-Warm Superterran       M    4.04    1.70   242.5  2871.1    283.    322.  0.77
     KOI-5194.01  F-Warm Superterran       T    2.32    1.35   287.5  2036.3    297.    334.  0.77
     KOI-5176.01  G-Warm Superterran       T    3.05    1.51   215.7  1303.6    292.    330.  0.76
     KOI-5767.01  F-Warm Superterran       M    5.81    2.01   386.6  3155.8    259.    299.  0.76
     KOI-5870.01    K-Warm Subterran       P    0.44    0.76   132.1   494.1    217.    247.  0.76
     KOI-5536.01  G-Warm Superterran       P    3.87    1.67   392.7  2576.3    226.    265.  0.76
     KOI-5455.01  G-Warm Superterran       M    5.63    1.98   292.1  3003.9    267.    307.  0.76
     KOI-5948.01  G-Warm Superterran       P    3.36    1.57   398.5  1427.5    222.    261.  0.76
     KOI-5453.01  G-Warm Superterran       M    4.70    1.82   190.7  2475.1    280.    320.  0.75
     KOI-5715.01  G-Warm Superterran       M    6.14    2.06   190.0  2805.2    260.    300.  0.75
     KOI-5623.01  F-Warm Superterran       M    6.17    2.07   583.7  3402.7    249.    289.  0.75
     KOI-5068.01  F-Warm Superterran       T    3.69    1.64   385.3  1740.2    290.    329.  0.75
     KOI-5413.01  G-Warm Superterran       M    5.46    1.95   428.4  1882.1    236.    276.  0.75
     KOI-5674.01  G-Warm Superterran       M    5.52    1.96   231.5  2496.0    274.    314.  0.75
     KOI-5202.01  F-Warm Superterran       P    4.48    1.78   535.9  2865.3    227.    266.  0.74
     KOI-5185.01  G-Warm Superterran       M    6.29    2.09   419.9  2805.1    266.    306.  0.74
     KOI-5000.01  G-Warm Superterran       M    6.60    2.14   249.6  2652.5    249.    290.  0.74
     KOI-5326.01  F-Warm Superterran       M    5.87    2.02   506.8  1482.0    275.    315.  0.74
     KOI-5819.01  G-Warm Superterran       P    2.03    1.29   381.4  1459.0    212.    249.  0.74
     KOI-5530.01  F-Warm Superterran       T    4.44    1.77   591.4  2236.5    289.    329.  0.74
     KOI-5844.01  G-Warm Superterran       P    5.22    1.91   345.0  2254.1    230.    269.  0.74
     KOI-4990.01  F-Warm Superterran       M    7.03    2.21   561.1  1452.3    255.    296.  0.73
     KOI-5120.01  G-Warm Superterran       M    6.91    2.19   250.5  2749.5    246.    286.  0.73
     KOI-5256.01  F-Warm Superterran       P    5.57    1.97   588.1  2856.9    231.    271.  0.73
     KOI-5589.01  G-Warm Superterran       M    7.09    2.22   376.6  2669.6    247.    287.  0.73
     KOI-5239.01  G-Warm Superterran       P    5.34    1.93   351.0  2888.5    228.    267.  0.73
     KOI-5973.01  F-Warm Superterran       T    5.46    1.95   419.9  1578.8    285.    325.  0.72
     KOI-5306.01  F-Warm Superterran       M    6.69    2.15   681.0  1454.7    274.    314.  0.72
     KOI-5056.01  G-Warm Superterran       M    6.17    2.07   222.8  2308.5    279.    320.  0.72
     KOI-5969.01  K-Warm Superterran       M    7.59    2.30   163.8  1718.2    250.    291.  0.72
     KOI-5878.01  G-Warm Superterran       M    7.65    2.31   211.5  2790.7    251.    292.  0.72
     KOI-5653.01  K-Warm Superterran       P    6.23    2.08   188.7  1894.6    231.    272.  0.72
     KOI-5893.01  G-Warm Superterran       P    3.77    1.65   405.6  2365.5    216.    255.  0.72
     KOI-5545.01       G-Warm Terran       P    1.15    1.05   541.1  1378.7    206.    241.  0.72
     KOI-5541.01  G-Warm Superterran       M    7.78    2.33   339.6  2549.6    250.    291.  0.72
     KOI-5017.01  G-Warm Superterran       P    5.16    1.90   492.3  1469.6    224.    264.  0.72
     KOI-4933.01  F-Warm Superterran       M    7.84    2.34   452.1  3788.7    254.    295.  0.72
     KOI-5558.01  F-Warm Superterran       M    7.77    2.33   428.1  4311.8    260.    301.  0.72
     KOI-5047.01  F-Warm Superterran       T    5.69    1.99   326.7  3040.0    287.    327.  0.71
     KOI-5065.01  F-Warm Superterran       M    7.47    2.28   523.4  4662.7    240.    280.  0.71
     KOI-5237.01  G-Warm Superterran       P    5.46    1.95   380.4  2761.0    224.    264.  0.71
     KOI-5002.01  F-Warm Superterran       T    5.93    2.03   399.5  1590.7    286.    326.  0.71
     KOI-5505.01  G-Warm Superterran       P    4.09    1.71   323.8  1581.8    216.    256.  0.71
     KOI-5276.01  G-Warm Superterran       M    7.03    2.21   220.7  2579.8    235.    275.  0.71
     KOI-5903.01  G-Warm Superterran       M    8.22    2.40   253.8  2785.1    253.    294.  0.71
     KOI-5888.01  G-Warm Superterran       M    7.40    2.27   190.9  2875.3    273.    314.  0.71
     KOI-5362.01  G-Warm Superterran       M    7.59    2.30   150.7  2257.6    271.    312.  0.71
     KOI-5592.01  F-Warm Superterran       M    7.78    2.33   482.5  3586.5    241.    282.  0.71
     KOI-5386.01  F-Warm Superterran       P    5.86    2.02   575.4  2867.1    225.    266.  0.71
     KOI-5879.01  K-Warm Superterran       P    2.48    1.39    88.5   953.1    209.    246.  0.71
     KOI-5447.01  G-Warm Superterran       M    8.03    2.37   322.6  1172.8    265.    306.  0.71
     KOI-5489.01  F-Warm Superterran       T    6.48    2.12   370.5  2409.3    284.    324.  0.71
     KOI-5851.01  F-Warm Superterran       M    7.28    2.25   322.2  3075.3    277.    318.  0.70
     KOI-5462.01  F-Warm Superterran       T    5.75    2.00   371.3  2632.4    290.    331.  0.70
     KOI-5896.01  G-Warm Superterran       P    3.61    1.62   434.3  2096.0    212.    251.  0.70
     KOI-5144.01  G-Warm Superterran       M    8.03    2.37   491.1  2583.8    241.    281.  0.70
     KOI-5035.01  K-Warm Superterran       P    6.78    2.17   115.2  1547.9    229.    270.  0.70
     KOI-5319.01  F-Warm Superterran       T    5.81    2.01   590.4  2250.0    291.    331.  0.70
     KOI-5657.01  F-Warm Superterran       T    5.63    1.98   284.7  2745.5    293.    333.  0.70
     KOI-5796.01  F-Warm Superterran       M    8.10    2.38   495.9  3109.5    239.    280.  0.70
     KOI-4986.01  G-Warm Superterran       P    3.51    1.60   444.1  2112.3    211.    249.  0.70
     KOI-5889.01  F-Warm Superterran       M    7.40    2.27   374.4  5030.4    280.    320.  0.70
     KOI-4931.01  G-Warm Superterran       P    5.16    1.90   579.8  2471.4    218.    258.  0.69
     KOI-5236.01  F-Warm Superterran       M    8.41    2.43   550.9  1605.3    240.    281.  0.69
     KOI-5196.01  F-Warm Superterran       T    5.46    1.95   392.5  1424.0    297.    337.  0.69
     KOI-5687.01  G-Warm Superterran       P    3.24    1.55   513.1  1926.0    208.    247.  0.69
     KOI-4994.01       G-Warm Terran       P    0.79    0.92   528.1   662.0    201.    234.  0.69
     KOI-5042.01  F-Warm Superterran       M    8.35    2.42   538.3  5005.6    237.    277.  0.69
     KOI-5916.01    K-Warm Subterran       P    0.19    0.58   100.4   207.8    211.    238.  0.69
     KOI-5810.01  G-Warm Superterran       M    8.16    2.39   425.6  2336.0    278.    319.  0.69
     KOI-5140.01  F-Warm Superterran       M    8.22    2.40   484.6  2964.0    277.    318.  0.69
     KOI-5089.01  F-Warm Superterran       T    5.93    2.03   545.6  1218.5    296.    336.  0.68
     KOI-5303.01       G-Warm Terran       P    1.87    1.25   438.6  1073.8    202.    238.  0.68
     KOI-4988.01  G-Warm Superterran       M    8.54    2.45   484.2  2047.2    235.    276.  0.68
     KOI-5492.01  G-Warm Superterran       P    5.01    1.87   368.5  1802.9    214.    254.  0.68
     KOI-5356.01  F-Warm Superterran       T    7.78    2.33   326.4  3774.2    283.    324.  0.68
     KOI-5874.01  G-Warm Superterran       T    7.09    2.22   287.3  1770.4    289.    329.  0.68
     KOI-5473.01  G-Warm Superterran       P    7.09    2.22   549.4  2816.9    223.    263.  0.67
     KOI-5755.01  G-Warm Superterran       P    4.42    1.77   388.7  2000.8    210.    249.  0.67
     KOI-5299.01  G-Warm Superterran       T    6.97    2.20   211.0  3074.6    293.    334.  0.67
     KOI-5693.01  F-Warm Superterran       P    6.36    2.10   612.9  2590.8    217.    258.  0.67
     KOI-5703.01  G-Warm Superterran       T    7.72    2.32   247.4  1508.7    290.    331.  0.67
     KOI-5067.01  G-Warm Superterran       T    8.79    2.49   219.9  1897.1    282.    323.  0.67
     KOI-5199.01  G-Warm Superterran       P    7.78    2.33   501.5  2621.6    224.    264.  0.67
     KOI-5268.01  G-Warm Superterran       P    8.03    2.37   474.2  3476.6    225.    265.  0.66
     KOI-5398.01  G-Warm Superterran       P    4.20    1.73   551.2  2153.7    206.    245.  0.66
     KOI-5556.01  G-Warm Superterran       P    5.16    1.90   632.0  1458.6    210.    250.  0.66
     KOI-5091.01  G-Warm Superterran       P    7.34    2.26   328.8  3001.6    219.    259.  0.66
     KOI-5562.01    G-Warm Subterran       P    0.48    0.78   438.0   382.8    197.    228.  0.65
     KOI-5595.01       K-Warm Terran       P    1.72    1.21   208.0   878.8    196.    232.  0.65
     KOI-5135.01  G-Warm Superterran       P    7.15    2.23   314.8  2576.5    217.    258.  0.65
     KOI-5188.01  F-Warm Superterran       T    8.86    2.50   455.2  1460.1    290.    331.  0.65
     KOI-5367.01  G-Warm Superterran       P    7.59    2.30   503.0  1828.7    217.    258.  0.65
     KOI-5229.01  F-Warm Superterran       T    7.97    2.36   364.6  3532.5    298.    338.  0.64
     KOI-5391.01  G-Warm Superterran       P    7.39    2.27   368.7  1740.9    215.    256.  0.64
     KOI-5442.01  G-Warm Superterran       P    3.39    1.58   512.1  1353.7    198.    237.  0.64
     KOI-5775.01  G-Warm Superterran       P    6.54    2.13   492.2  3239.8    209.    250.  0.63
     KOI-5789.01  G-Warm Superterran       P    5.34    1.93   383.3  1220.0    203.    242.  0.62
     KOI-5978.01  K-Warm Superterran       P    7.53    2.29   364.2  1955.7    209.    250.  0.62
     KOI-5793.01       G-Warm Terran       P    1.69    1.20   507.5   757.9    189.    225.  0.62
     KOI-5130.01  G-Warm Superterran       P    6.97    2.20   370.1  2603.1    206.    247.  0.61
     KOI-5170.01  K-Warm Superterran       P    6.36    2.10   149.5  1115.1    202.    242.  0.60
     KOI-5559.01  G-Warm Superterran       P    2.70    1.44   586.6  1082.0    189.    227.  0.60
     KOI-5009.01  G-Warm Superterran       P    5.81    2.01   360.0  1861.9    200.    240.  0.60
     KOI-5399.01  G-Warm Superterran       P    8.86    2.50   466.9  2598.2    210.    251.  0.60
     KOI-5366.01  G-Warm Superterran       P    3.51    1.60   574.7  1322.3    191.    229.  0.60
     KOI-5741.01  G-Warm Superterran       P    7.47    2.28   362.1  2639.2    203.    244.  0.59
     KOI-5809.01       K-Warm Terran       O    1.42    1.13   216.1   562.5    183.    219.  0.59
     KOI-5749.01  K-Warm Superterran       P    8.41    2.43   282.0  1883.1    204.    245.  0.58
     KOI-5643.01  G-Warm Superterran       P    4.48    1.78   570.0  1769.4    190.    230.  0.58
     KOI-5258.01  G-Warm Superterran       P    7.59    2.30   452.3  2679.6    199.    240.  0.57
     KOI-5645.01  G-Warm Superterran       P    8.10    2.38   580.9  4097.2    200.    241.  0.57
     KOI-5829.01  G-Warm Superterran       P    6.97    2.20   583.9  2412.0    196.    237.  0.57
     KOI-5871.01  G-Warm Superterran       P    7.03    2.21   623.3  2142.1    196.    237.  0.57
     KOI-4961.01  K-Warm Superterran       P    7.59    2.30   349.0  2048.4    198.    239.  0.57
     KOI-5570.01  G-Warm Superterran       P    7.47    2.28   574.7  2236.0    196.    237.  0.56
     KOI-5467.01  G-Warm Superterran       P    8.54    2.45   502.8  2565.7    199.    240.  0.56
     KOI-5540.01  G-Warm Superterran       P    6.36    2.10   643.4  2564.4    192.    232.  0.56
     KOI-5103.01  G-Warm Superterran       P    8.41    2.43   586.9  3445.0    198.    239.  0.56
     KOI-5884.01  G-Warm Superterran       P    4.48    1.78   588.6  1189.6    185.    224.  0.55
     KOI-5203.01  K-Warm Superterran       P    4.37    1.76   367.7  1613.8    184.    224.  0.55
     KOI-4957.01  K-Warm Superterran       O    2.12    1.31   105.5   642.6    176.    213.  0.54
     KOI-5649.01  G-Warm Superterran       P    8.73    2.48   426.9  1861.0    187.    228.  0.51
     KOI-5538.01  G-Warm Superterran       P    8.79    2.49   485.6  2848.6    187.    228.  0.51
     KOI-5764.01  K-Warm Superterran       O    6.60    2.14   286.1  1431.0    180.    221.  0.51
     KOI-5725.01  K-Warm Superterran       P    8.67    2.47   351.2  2035.5    185.    226.  0.50
--------------------------------------------------------------------------------------------------

Spatial and Temporal Averages for Elliptical Orbits

posted Dec 16, 2013, 5:45 AM by Abel Mendez Torres   [ updated Jan 4, 2014, 8:50 AM ]

Mean orbital values for distance, stellar flux, and equilibrium temperature can be computed with respect to spatial or temporal coordinates. Spatial averages are usually calculated with respect to the mean anomaly (E) or true anomaly (θ). Temporal averages are calculated with respect to time (t) or the eccentric anomaly (M). It is often assumed that the mean equilibrium temperature of a planet in an elliptic orbit can be simply calculated from its mean distance or flux, but this is not correct. 

We calculated analytic solutions for both the spatial and temporal averages of distance, flux, and equilibrium temperature (Méndez et al., 2014, in preparation). Here a is the semi-major axis, e is the eccentricity, L is the stellar luminosity, A is the planet's bond albedo, and To = 278.5 K (i.e. the equilibrium temperature of Earth for zero albedo). A factor f is related to the effectiveness of atmospheric circulation and how the energy absorbed is transferred from the planet’s day to night sides (e.g. f = 1 for fast rotators and f = 2 for tidally locked planets without atmospheres)For convenience, the formulas derived here use 'exoplanet units' where distances are in AU, flux in solar units, and temperature in kelvins.

Mean Spatial Distance, Flux, and Equilibrium Temperature


(1)


(2)

(3)

Here r̅ , F̅, and T̅eq are the mean spatial values (i.e. with respect to the true anomaly) for planet distance, stellar flux, and planet equilibrium temperature. E is the complete elliptic integral of the second kind of the argument within parenthesis.

Mean Temporal Distance, Flux, and Equilibrium Temperature


(4)

(5)


(6)

Here <r>, <F>, and <Teq> are the mean temporal values (i.e. with respect to time) for planet distance, stellar flux, and planet equilibrium temperature. E is the complete elliptic integral of the second kind of the argument within parenthesis.

All the previous equations become the well known expressions for circular orbits for e = 0, where there is no difference between spatial or temporal averages. For most applications the temporal averages are the ones necessary. Eq. 1, 4, and 5 are well known expressions (William and Pollard, 2002Perryman, 2011). Eq. 2, 3, and 6 are new derivations, but only Eq. 6 has practical implications. Eq. 4, 5, and 6 were also verified with a numerical simulation.

Using the Mean Temporal Equilibrium Temperature


The time-average stellar flux (Eq. 5) can't be used to calculate the time-average equilibrium temperature (Eq. 6) as if often assumed. The stellar flux increases to infinity as the eccentricity of the planet approaches one. However, the equilibrium temperature does not change accordingly, actually it decreases with eccentricity approaching a minimum of about 90% the value for a circular orbit. This seems contradictory but the stellar flux increases with 1/r2 while the equilibrium temperature with 1/√r. Therefore, the following expressions should not be used to calculate the average equilibrium temperature from the average distance or stellar flux since they produces large errors (>>10%) for highly eccentric orbits:

(7)

where <r> is given from Eq. 4 and <F> is given from Eq. 5. These expression suggests that the equilibrium temperature increases with an increase in stellar flux due to eccentricity but it is quite the opposite. 

Eq. 6 is the analytic solution to the equilibrium temperatures for eccentric orbits. Errors from assuming a circular orbits can be up to 10% for highly eccentric orbits. Still, this is not a large error compared with larger uncertainties associated with f and A. Summarizing, given the equilibrium temperature for circular orbits, the equilibrium temperature for elliptical orbits is:

(8)

where the equilibrium temperature for circular orbits Teqc is given by:

(9)

and T* and R* are the effective temperature and radius of the star.

Notes


  • There are many math libraries which include calculations for complete elliptic integral functions (e.g. Mathematica and GSL). The following expression could be used to simplify the calculation of Eq. 6 or 8. Errors from this approximation are less than 1% (less than 0.5% for e < 0.5).
(10)
  • The last part of Eq. 9 does not use the same 'exoplanets units' as the other equations since it requires the same units for both a and R*.
  • If either f or A depend on insolation, then Eq. 6 needs to be rederived, probably as a numerical solution.
  • The factor f has different definitions among the scientific literature. See for example Perryman, 2011 and López-Morales and Seager, 2007.
  • Please note that the correct implementation of E(x) with GSL elliptic functions is gsl_sf_ellint_Ecomp(sqrt(x)), it requires first the square root of the argument.

SER: First Look at Pluto

posted Nov 13, 2013, 9:34 AM by Abel Mendez Torres   [ updated Nov 13, 2013, 10:02 AM ]

The Scientific Exoplanets Renderer (SER) is our core software to generate photorealistic-looking images of planets such as the ones for the Visible Paleo-Earth and the Habitable Exoplanets Catalog. SER was developed to simulate complex stellar transit events and interpret planetary light curves. It takes as little information from a planet as available to automatically create representations. The more input given the more the images become more scientific than artistic representations.

Here with used SER to create a basic representation of Pluto (Figure 1 and 2) given its albedo maps obtained by Buie et al. (2010A, 2010Bfrom the Hubble Space Telescope (Figure 3). We will keep generating better and better representations as we get more data from Pluto, specially from New HorizonsWe also plan to produce more creative versions by adding more surface features. It will be fun to compare our progress, starting from our first image, until the final close-up pictures of Pluto on July 2015.


Figure 1. This representation of Pluto combines real and synthetic data to create a more photorealistic look. The image shows a possible scenario of Pluto that preserves the original basic albedo features. It uses a false color palette (similar to Triton) for only one of the two channels of the HST filters (F435W). Credit: PHL @ UPR Arecibo, NASA HST.


Figure 2. Equirectangular projection of the Pluto map shown in Figure 1. Data for the south pole was extrapolated since it was not available in the original HST data. Credit: PHL @ UPR Arecibo, NASA HST.

http://hubblesite.org/newscenter/archive/releases/2010/06/image/a/

Figure 3. This is the most detailed view to date of the entire surface of the dwarf planet Pluto, as constructed from multiple NASA Hubble Space Telescope photographs taken from 2002 to 2003. Credit: NASA, ESA, and M. Buie (Southwest Research Institute).

Occurrence of Earth-like planets around GKM Stars

posted Nov 5, 2013, 8:12 AM by Abel Mendez Torres   [ updated Nov 5, 2013, 8:47 AM ]

Here we combine and interpret results from Kopparapu (2013) and Petigura et al. (2013) on the occurrence of Earth-like planets around red-dwarf (type M) and Sun-like (type G and K) stars, respectively. Both studies used NASA Kepler results. Based on their occurrence estimates we calculated the mean separation and 95% confidence distance for the solar neighborhood (<10pc). These numbers suggest that there is over a 95% probability of finding an Earth-like planet around a Sun-like star in the solar neighborhood. The probability is higher for those around M-dwarf stars.

Table 1. Occurrence (ηE), separation (δ), and 95% confidence distance (d95%) of Earth-like planets (0.5 — 2.0 RE in the HZ) around M-dwarfs and GK stars. The study of Petigura et al. (2013) only considered 1.0 — 2.0 RE planets. Calculations assume that there are 198 stellar systems with M-dwarf stars and 50 with GK-stars in the solar neighborhood (<10pc).

 

 

M-dwarfs (Kopparapu, 2013)

GK stars (Petigura et al., 2013)

Habitable Zone Definition

a (AU)*

ηE

δ(ly)

dE 95% (ly)

ηE

δ(ly)

dE 95% (ly)

Conservative (1)

0.99 — 1.69

0.51 +0.10/-0.20

6.25

10.1

0.086 ± 0.03

17.9

28.9

Empirical (1)

0.75 — 1.84

0.61 +0.07/-0.15

5.89

9.51

0.14 ± 0.05

15.2

24.6

Simple Flux (2)

0.5 — 2

0.22 ± 0.08

13.1

21.1

Desert-H2 Planets (3)

0.38 — 10

0.52 ± 0.19

9.8

15.9

HZ References: (1) Kopparapu et al., 2013; (2) Petigura et al., 2013; (3) Zsom et al., 2013; Pierrehumbert and Gaidos, 2011

Table Notes:
a = semi-major axis (values shown for G stars, check here for other types of stars).
ηE (eta Earth) = fraction of Earth-like planets per star.
δ(delta Earth) = mean distance between stellar systems with Earth-like planets.
d95% = 95% confidence distance for an Earth-like planet.

New Kepler Potential Planet Transit Signals

posted Nov 4, 2013, 8:00 AM by Abel Mendez Torres   [ updated Nov 4, 2013, 8:03 AM ]

The NASA Kepler team released a revised global list of 16,285 potential planet transit signals (formally known as Threshold-Crossing Events or TCE) from quarters one to sixteen, the four years of operation of Kepler (Table 1). This list already includes most of the 3,602 Kepler Objects of interest (KOI) with 170 Kepler Confirmed Planets.

Additional analysis is necessary to confirm the planetary nature of the over 12,000 remaining TCE objects. Many of these transits signals are expected to be false alarms, specially for long periods objects such as those orbiting within the habitable zone (HZ).

Nearly 1,500 TCE objects match our standard criteria for potentially habitable planets (planet size 0.4 — 2.6 Earth radii orbiting within the empirical HZ), but only about 20% of them might turn out to be real planets, still a large number. Nevertheless, this analysis provides some upper limits to interesting objects in the Kepler TCE sample (Table 2).

Table 1. Summary statistics of some planetary and stellar characteristics of the new 16,285 TCE list.
---------------------------------------------------------------------------
                      Property         MIN         AVG         MAX    Count
---------------------------------------------------------------------------
           Planet Radius (EU):        0.00       15.53     5312.00    16285
         Planet Period (days):        0.50      197.33      707.28    16285
  Planet Semi-Major Axis (AU):      0.0101      0.5349      2.3200    16285
        Planet Temperature(K):       63.10      875.85    14200.00    16285

               Star Mass (SU):        0.09        1.06        3.71    16285
             Star Radius (SU):        0.12        4.18      219.50    16285
         Star Temperature (K):     2661.00     5715.10    15896.00    16285
         Star Luminosity (SU):      0.0006     48.2446  14036.8495    16285
---------------------------------------------------------------------------
EU = earth units, SU = solar units

Table 2. Basic analysis of the TCE objects. 
----------------------------------------------------------------------------
Habitable Exoplanets Catalog (HEC) Statistics
  Data Source: NASA Kepler Threshold Crossing Events (TCE)
  [Nov  4, 2013] Planetary Habitability Laboratory (phl.upr.edu) 
----------------------------------------------------------------------------
                         Stellar Systems  9743
                              Exoplanets 16285
              Exoplanets in the Hot Zone 10982 (67.4%)
 Exoplanets in the Warm 'Habitable' Zone  3646 (22.4%)
             Exoplanets in the Cold Zone  1657 (10.2%)
                            Unclassified     0 ( 0.0%)
          Potential Habitable Exoplanets  1486 ( 9.1%)
   Expected Potential Habitable Exomoons   185 ( 1.1%)
                               Eta Earth  15.3 %
----------------------------------------------------------------------------

--------------------------------------------------------------------
Number of Multiple Systems
--------------------------------------------------------------------
     1      2      3      4      5      6     7      8      9     10
  6520   1832    537    292    228    204    93     30      3      4
  66.9   18.8    5.5    3.0    2.3    2.1   1.0    0.3    <0.1  <0.1
--------------------------------------------------------------------

-----------------------------------------------------------------------
Planetary Class
-----------------------------------------------------------------------
Mercurian    Subterran     Terran    Superterran    Neptunian    Jovian
42           327           1382      5766           5063         3355
0.3          2.0           8.5       35.4           31.1         20.6
-----------------------------------------------------------------------

----------------------------------------
Hot Zone
            Category     Count   Percent
----------------------------------------
          Mercurians        19       0.1
          Subterrans       274       1.7
             Terrans      1123       6.9
        Superterrans      3664      22.5
          Neptunians      2695      16.5
             Jovians      2858      17.5
----------------------------------------

----------------------------------------
Warm 'Habitable' Zone
            Category     Count   Percent
----------------------------------------
          Mercurians         3       0.0
          Subterrans        29       0.2
             Terrans       117       0.7
        Superterrans      1340       8.2
          Neptunians      1760      10.8
             Jovians       396       2.4
----------------------------------------

----------------------------------------
Cold Zone
            Category     Count   Percent
----------------------------------------
          Mercurians        20       0.1
          Subterrans        24       0.1
             Terrans       142       0.9
        Superterrans       762       4.7
          Neptunians       608       3.7
             Jovians       101       0.6
----------------------------------------

References

50th Anniversary of the Arecibo Observatory

posted Oct 21, 2013, 2:15 PM by Abel Mendez Torres   [ updated Oct 27, 2013, 7:20 PM ]


The Arecibo Observatory (AO) was inaugurated November 1, 1963. To recognize its 50th year of service to the scientific community, the AO is having a science symposium, 50 Years of Scientific Achievement and Future Directions at Arecibo Observatory, at the Angel Ramos Foundation Visitor Center. The event will be held Monday & Tuesday, October 28-29, 2013, beginning at 8:30 AM each day. Current and past users of the William E. Gordon telescope and other scientific equipment, as well as leaders of its Education and Outreach programs are invited.


Symposium Agenda


Day 1: Monday, October 28, 2013

07:30 AM    Breakfast
08:30 AM    Welcome and Key Note 1: Arecibo: A personal history and future directions  Rich Behnke
09:00 AM    Key Note 2: Evolution of the William E. Gordon 305 m — Don Campbell
09:30 AM    Key Note 3: From Appleton to Arecibo and Beyond — John Matthews
10:00 AM    Break
10:30 AM    Whistler wave interaction experiments at Arecibo Observatory — Min-Chang Lee
10:45 AM    Understanding Pulsars with Arecibo, Past, Present & Future — Joanna Rankin
11:00 AM    Arecibo Observatory: A Long Life with Very Long Baselines — Leonid Gurvits
11:15 AM    Exploration of Atmosphere and Geospace with LIDAR  Xinzhao Chu
11:30 AM    Key Note 4: Living and working with the Arecibo radio telescope — Alex Wolszczan
12:00 PM    50ish Years of SETI at Arecibo — Dan Wertheimer
12:15 PM    Arecibo-Mini-RF Bistatic Observations of the Moon — Ben Bussey (presented by Lynn Carter)
12:30 PM    LUNCH
01:15 PM    Key Note 5: My Love Affair with Arecibo— Carl Heiles
01:45 PM    Achieving electron temperature measurements using the plasma line of incoherent scatter — Mike Sulzer
02:00 PM    Zeeman Splitting in High-Latitude Molecular Clouds — Allison Smith
02:15 PM    The Arecibo Airglow Observatory or Photometer Shack - Which was it?  John Meriwether and Fred Herrero
02:30 PM    Searching for almost nothing in the 21cm line — Jay Lockman
02:45 PM    The ALFA Ultra Deep Survey — Wolfram Freudling
03:00 PM    Lower thermospheric wind estimates from dual-beam incoherent scatter radar measurements — Dave Hysell
03:15 PM    Break
03:45 PM    Key Note 6: Arecibo Observatory: Lab in the Sky Ionosphere Challenges - Then and Now — Herb Carlson
04:15 PM    From MM to MMXII - raising Arecibo's sensitivity to the next level — Ganesh Rajagopalan
04:30 PM    Penn State Software-Defined Radar Research at Arecibo: Initiatives and Challenges — Julio Urbina
04:45 PM    The New Arecibo HF Facility Dual Array Cassegrain Antenna — Jim Breakall
05:00 PM    Ammann & Whitney's History with the Telescope — Jim Gould
05:15 PM    Early Ionospheric Experiments at the Arecibo Observatory — A. J. Ferraro
05:30 PM    The Life and Times of the Mini-Gregorian — Loris Magnani
05:45 PM    ASAP Group Discussion on AO Future
06:30 PM    Dinner
                Key Note After Dinner — Sheldon Reynolds 

Day 2: Tuesday, October 29, 2013

07:30 AM    Breakfast
08:30 AM    Key Note 7: A Butterfly Fluttered Its Wings, And Lo! - A Great Observatory Emerged!- Frank Drake
09:00 AM    The Arecibo Remote Command Center — Rick Jenet
09:15 AM    Observing the full incoherent scatter spectrum with the Arecibo radar — Asti Bhatt
09:30 AM    A new era of tests of general relativity with Arecibo — Paulo Freire
09:45 AM    Accurate Arecibo Decimetre Flux Densities from the Solar System to the Edge of the Universe — Dave Jauncey
10:00 AM    From Dead to Habitable Exoplanets at Arecibo — Abel Méndez
10:15 AM    GoldenEye's view of the ISM in the Milky Way — Snezana Stanimirovic
10:30 AM    Break
11:00 AM    Key Note 8: Planetary Geology with the Arecibo radar: Impacts and Explosive Volcanism — Lynn Carter
11:30 AM    50 years of lunar observation — Tommy Thompson
11:45 AM    Near-Earth Asteroid Radar Extravaganza — Lance Benner
12:00 PM    Planetary Radar Observations at Arecibo: Current Work and Future Directions — Mike Nolan
12:15 PM    Radio Spectroscopy of Comets — Amy Lovell
12:30 PM    Reflections on Arecibo by a (Non-Radio) Astronomer — Jonathan Lunine
12:45 PM    Lunch
01:30 PM    Key Note 9: Reflections on Discovery of the First Binary Pulsar — Joe Taylor
02:00 PM    Measuring the rise and fall times of HF-induced irregularities at Arecibo in the 1980s — Anthea Coster
02:15 PM    The Arecibo Galactic Environments Survey — Robert Minchin
02:30 PM    Innovating Airglow - Facilitating the Aeronomy Ecosystem — John Noto
02:45 PM    The Crab Pulsar: Enigmas — Tim Hankins
03:00 PM    New, uniquely sensitive AO + DRAO images - gateway to another Arecibo future — Phil Kronberg
03:15 PM    Plans for an HF imaging Array in Aguadilla, Puerto Rico — Brett Isham
03:30 PM    Break
04:00 PM    A VLBI Resolution of the Pleiades Distance Controversy — Carl Melis
04:15 PM    The Magnificent Magnetic Mysterium Megamasers! — Tim Robishaw
04:30 PM    The ALFA Zone of Avoidance Survey — Travis McIntyre
04:45 PM    Arecibo and the renaissance of meteor aeronomy — Lars Dyrud
05:00 PM    Gravitational Waves at Arecibo — Andrea Lommen
05:15 PM    Boston University Aeronomy Research at the Arecibo Observatory — Steve Smith
05:30 PM    Key Note 10: Gas and Galaxies – Arecibo’s contributions over the past 50 years — Karen O'Neil
06:00 PM    Depart

Press Contact

José (Tony) Acevedo
Public Relations & Communications, Arecibo Observatory
Tel. (787) 878.2612 x228

A Binomial Nomenclature for Common Names of Exoplanets

posted Sep 27, 2013, 12:09 AM by Abel Mendez Torres   [ updated Sep 27, 2013, 12:20 AM ]

When naming exoplanets create common names for both the stellar system and the exoplanets


There are nearly one thousand exoplanets already confirmed and many more waiting for confirmation. The general astronomy community is interested on naming exoplanets with the help of the general public (1). Individual naming of such discoveries is a time consuming labor but both usable by the scientific community and general public.

Simple procedures for the individual naming of thousands or even millions of objects are nothing new to science. For example the binomial nomenclature by genera and species in Biology has been used to name over 1.2 million species and has the potential to name more than the estimated 8.7 million species on Earth (2). These are used as scientific names, equivalent to the catalog names in astronomy, but in many cases are easier to remember and even used as common names (i.e. E. coli).

We propose a similar binomial nomenclature for exoplanets to create simple hierarchical common names. The first part of the name is the stellar system and the second part is the individual planet name. If the stars have already a common name then it is used as the stellar system names (i.e. Fomalhaut). The planets or other stars of the system are named with the usual alphabetical letters until a proper name is given.

This procedure reduces the complexity of the catalog star names until the planets are individually named. As an hypothetical example, the planet Alpha Centauri B b, could become Alcen-B Rakhat, where Alcen is the name of the stellar system, B denotes the second star of the system, and Rakhat the name of the planet. The actual selection process of the individual names for the system and planets are out of the scope of this proposal.

Therefore, any exoplanet naming campaign should concentrate first efforts on naming the stellar systems of interest and then any individual planets, avoiding naming exoplanets before the stellar systems. The stellar names could also be used to guide the naming of its planets. Our suggestion describes a minimum effort plan for naming exoplanets and provides a logical and hierarchical system not much different from the current catalog names, but for common names too.

In the end, it is expected that some exoplanets will be better known by their full name (using both system and planet names) and others just by their individual name. A new definition of planets that includes both solar and extrasolar planets would also be appropriate before any naming campaign (3).

References

About 40 potentially habitable worlds by the end of 2015?

posted Sep 20, 2013, 3:12 AM by Abel Mendez Torres


We started with just two planets in our Habitable Exoplanets Catalog almost two years ago on December 2011. At that time having a catalog for just two planets was overkill and we were not expecting much change anyway until many years, but we were surprised. We ended the first years with seven and now we have twelve, and the year is not over yet. That certainly exceeded our expectations. The exoplanets field was moving much faster toward the detection of smaller Earth-size planets by both the radial velocity and transit methods. A catalog is now a necessary tool to track these discoveries.

The 2010's is the decade when we finally started to discover potentially habitable worlds (the exception is Gliese 581d discovered on 2007). We have enough data now to give some preliminary prediction on the expected number of habitable exoplanets to be discovered in the next years. If we follow the present trend (Figure 1) there could be a total of 21 by 2014 and 38 by 2015. That still sounds like too many for just two years but there are 36 waiting for confirmation from the NASA Kepler mission alone. Similar predictions can be derived for the total number of confirmed exoplanets (Figure 2). Lets wait and see what happens.
Figure 1. Cumulative number of potentially habitable exoplanets detected in the last four years (red dots). The data was fitted with an exponential function (blue line) included at the top of the plot. The fit predicts reaching about 21 exoplanets by 2014 and 38 by 2015. Predictions for longer periods are much more uncertain. Data source is available in Table 1.
Figure 2. Cumulative number of confirmed exoplanets detected in the last 22 years (red dots). The data was fitted with an exponential function (blue line) included at the top of the plot. The fit predicts reaching over 1,000 exoplanets by the end of 2013 and over 1,500 by 2015. Predictions for longer periods are much more uncertain. Data source is available in Table 1.

Table 1. Number per year and cumulative (total from all previous years) of discovered confirmed exoplanets and those potentially habitable. Data from the PHL's Exoplanet Catalog. The year 2011 was a good year for exoplanet discoveries. Figures 1 and 2 show the cumulative data plotted.

 

Confirmed

Potentially Habitable

Year

Per Year

Cumulative

Per year

Comulative
1989 1 1
1990 0 1
1991 0 1
1992 3 4
1993 0 4
1994 0 4
1995 1 5
1996 6 11
1997 0 11
1998 7 18
1999 11 29
2000 19 48
2001 14 62
2002 30 92
2003 27 119
2004 31 150
2005 33 183
2006 29 212
2007 61 273 1 1
2008 61 334 0 1
2009 81 415 0 1
2010 114 529 1 2
2011 189 718 2 4
2012 147 865 3 7
2013
109
974
5
12

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