Habitability of Planets Using Narlikar Index : A Different Approach

 Is our insignificant little planet Earth the only one out there in the universe to be blessed with life? Could we find conscious beings out there in the vast unknown universe? Many such questions and theories exist about extra-terrestrial life , but unfortunately none of them have been proven to be true. So, can we find life on other planets? Well that’s a tough question and since the universe ( or the multiverse ) is so massive, we need to target certain planets in order to find life. That’s exactly the point that we are going to touch in this paper. What is the habitability of planets ? How can we make our eternal quest for life easier ? Which are the planets that presumably have life and how do we find them ? Many such questions would be answered in this paper.

What is habitability, how is it defined and what are the parameters and factors that define it ? The ability of a planet to develop, harbour and maintain an environment suitable to life is termed as planetary habitability. Additionally, environments that do not contain life can also be habitable.

There are many requirements for life such as sunlight, water, minerals etc. Additionally, several criterions must also be met for a planet to be able to host life. Some of these characteristics include mass, radius, spectral class, temperature of the planet, luminosity, biochemicals, composition, orbital properties, chemical reactions etc. Geological, geophysical and astrobiological properties also play a key role in determining the habitability potential of a planet.

The definitions of a habitable planet are based upon our current understanding of the subject and since a lot of research is being done on it, the measures and criterions of habitability can be modified as and when necessary.

The orbital range for water to exist in its liquid form at the surface of the planet is known as the Habitable Zone. These zones are also called Goldilocks Zones. Such zones are ideal for the presence of life. Additionally, habitats on which water is present on the surface is ideal for life.

We propose an index called Narlikar Index, named after the famous Indian Astrophysicist Jayant Narlikar. The Narlikar Index is based upon various parameters on which each of the potential habitable planets can be graded. The Narlikar Index can have values ranging from zero to four. The following table shows the Narlikar Index and its corresponding qualitative value of habitability.

Narlikar Index

Qualitative Value of Habitability

 

 

3-4

Highly Habitable

2-3

Habitable

1-2

Unhabitable

0-1

Highly Unhabitable

 

The objectives of the Narlikar Index are as follows :-

1.       1) To propose a model that will help study potentially habitable planets.

2.      2) To classify astronomical objects more easily.

3.      3)To compare the relative habitability of one planet with respect to the other.

               

The parameters of the Narlikar Index are as follows :-

1) Spectral Class : It is a method of classification of stars based on spectral analysis of its electromagnetic emission spectra, which gives information about the surface temperature and elementary nuclear reactions within the star. This implies that a habitable star must have a temperature between 3700°C to 6700°C which corresponds to late F or G to mid-K spectral class type.

 

2) Mass : Planets with less mass would find it difficult to harbour life for multiple reasons. Planets with a low mass would have a lower force of gravity, which would mean a low escape velocity hereby enabling particles to escape from the atmosphere. Planets lacking a thick atmosphere would also lack biochemical substances that are important for life. They would also have very poor insulation capabilities, providing less protection against dangerous objects such as asteroids. Lack of density of the atmosphere would also prevent water from existing in its liquid form.

 

A planet with a larger mass would also have a larger iron core, making it mineral rich. This iron core would enable an active magnetic field hereby protecting the planet from harmful phenomena such as cosmic radiations. If the planet is not shielded from cosmic radiations and stellar wind, planetary atmosphere would cease to exist. Also, life would be bombarded with ionized particles, making it difficult to survive.

 

3) Radius : Ideally a planet should have a radius between 0.5R to 2.5R for it to host life. Planets having a smaller radius would eventually end up being geologically dead. They would hence lack important life sustaining materials resulting from plate tectonics, earthquakes, volcanoes etc.

R = Radius of planet / radius of Earth.

 

4) Temperature of the Planet : The temperature of a planet influences how quickly atoms and molecules move. Low temperature results in slower chemical reactions, effectively slowing down the speed of many necessary life processes. Low temperatures also make liquid water unavailable as water would be found in its solid state. At high temperatures, DNA and RNA start to break up. Hence, we need a suitable temperature for the planet in the range of -25°C to 100°C.

 

A planet needs to additionally satisfy 4 basic criteria for it to have a high habitability potential :-

1.    It needs to be in the habitable zone of its star.

2.    It cannot be a rogue planet.

3.    It should not be around any kind of neutron star or black hole.

The following tables illustrate the calculations of the Narlikar Index based upon its factors.

A) Radius of Planet

Case 1) Radius of planet ≥ Radius of Earth

 

Radius of Planet

Narlikar Index for Radius

 

 

More than 30R

0

24R to 30R

0.5

18r to 24R

1

15R to 18R

1.5

12R to 15R

2

8R to 12R

2.5

5R to 8R

3

2.5R to 5R

3.5

1R to 2.5R

4

 

Here R = Radius of Planet / Radius of Earth

Case 2) Radius of Planet < Radius of Earth

Radius of Planet

Narlikar Index for Radius

 

 

Less than 0.38R

0

0.38R to 0.40R

0.5

0.40R to 0.41R

1

0.41R to 0.43R

1.5

0.43R to 0.45R

2

0.45R to 0.47R

2.5

0.47R to 0.48R

3

0.48R to 0.50R

3.5

0.50R to 1R

4

 

Here R = Radius of Planet / Radius of Earth

B) Mass of Planet

Case 1) Mass of Planet ≥ Mass of Earth

Mass of Planet

Narlikar Index for Mass

 

 

More than 318M

0

272.72M to 318M

0.5

227.44M to 272.72M

1

182.16M to 227.44M

1.5

136.88M to 182.16M

2

91.6M to 136.88M

2.5

46.32M to 91.6M

3

1.30M to 46.32M

3.5

1M to 1.30M

4

 

Here M = Mass of Planet / Mass of Earth

Case 2) Mass of Planet < Mass of Earth

Mass of Planet

Narlikar Index for Mass

 

 

Less than 0.002M

0

0.002M to 0.06M

0.5

0.06M to 0.10M

1

0.10M to 0.14M

1.5

0.14M to 0.18M

2

0.18M to 0.22M

2.5

0.22M to 0.26M

3

0.26M to 0.30M

3.5

0.30M to 1M

4

 

Here M = Mass of Planet / Mass of Earth

C) Temperature of the Nearest Star

Case 1) Temperature of the Nearest Star ≥ 5200°C

Temperature of the Nearest Star

Narlikar Index for Star Temperature

 

 

More than 50000

0

43810-50000

0.5

37630-43810

1

31440-37630

1.5

25260-31440

2

19100-25260

2.5

12890-19100

3

6700-12890

3.5

5200-6700

4

Note: All temperatures are in °C

Case 2) Temperature of the Nearest Star < 5200°C

Temperature of the Nearest Star

Narlikar Index for Star Temperature

 

 

Less than 2600

0

2600-2770

0.5

2770-2840

1

2840-3010

1.5

3010-3190

2

3190-3360

2.5

3360-3530

3

3530-3700

3.5

3700-5200

4

Note: All temperatures are in °C

D) Average Temperature of the Planet

Case 1) Average Temperature of the Planet ≥ 0°C

Average Temperature of Planet

Narlikar Index for Planet Temperature

 

 

More than 520

0

460 to 520

0.5

400 to 460

1

340 to 400

1.5

280 to 340

2

220 to 280

2.5

160 to 220

3

100 to 160

3.5

0 to 100

4

Note: All temperatures are in °C

Case 2 : Average Temperature of the Planet < 0°C

Average Temperature of the Planet

Narlikar Index for Planet Temperature

 

 

Less than -200

0

-200 to -175

0.5

-175 to -150

1

-150 to -125

1.5

-125 to -100

2

-100 to -75

2.5

-75 to -50

3

-50 to -25

3.5

-25 to 0

4

Note: All values are in °C

Final Narlikar Index ( or simply Narlikar Index ) = ( N1 + N2 + N3 + N4 ) / 4

                Where N = Narlikar Index for Radius

             N2 =  Narlikar Index for Mass

             N3 =  Narlikar Index for Star Temperature

             N4 =  Narlikar Index for Planet Temperature

This index, can in general, be applied to any planet to find its habitability. Let us look at a few planets to get a better understanding of this index.

Narlikar percentage = (Narlikar Index)*25

 

Note: Whenever while calculating the Narlikar Index, if we get Narlikar Index ≤ 3.0, then we divide it by 2.5 to get the actual Narlikar Index.

 

1) Earth : Earth is the only astronomical object that has been discovered to have life with conditions being nearly perfect for a variety of life forms. It performs exceptionally well scoring 4 on the Narlikar Index making it a highly habitable planet.

                Radius : 1R

                Mass : 1M

                Temperature of the Sun : 5500°C

                Average temperature of Earth : 14°C

                Narlikar Index : 4.000

                Narlikar Percentage :  100%

 

2) Kepler-296e : Kepler-296e performs relatively well scoring 3.625 on the Narlikar Index, making it a highly habitable planet orbiting Kepler-296. It is in the Draco constellation.

                Radius : 1.750R

                Mass : 2.96M

                Temperature of Kepler-296 : 3167°C

                Average temperature of Kepler-296e : -6°C

                Narlikar Index : 3.625

                Narlikar Percentage : 90.625%

 

3) Kepler-11b : Kepler-11b performs relatively poorly scoring 1.15 on the Narlikar Index, making it an unhabitable planet orbiting Kepler-11. It is in the Cygnus constellation.

                Radius : 1.83R

                Mass : 2.78M

                Temperature of Kepler-11 : 5563°C

                Average temperature of Kepler-11b : 627°C

                Narlikar Index : 1.15

                Narlikar Percentage : 28.75%

 

4) Kepler-20b : Kepler-20b performs relatively poorly scoring 1.15 on the Narlikar Index, making it an unhabitable planet orbiting Kepler-20. It is in the Lyra constellation.

                Radius : 1.868R

                Mass : 9.7M

                Temperature of Kepler-20 : 5193°C
                Average temperature of Kepler-20b : 741°C

                Narlikar Index : 1.15

                Narlikar Percentage : 28.75%

 

5) Kepler-442b : Kepler-442b performs relatively well on the Narlikar Index scoring 3.750, making it a highly habitable planet orbiting Kepler-442. It is in the Lyra constellation.

                Radius : 1.34R

                Mass : 2.3M

                Temperature of Kepler-442 : 4129°C

                Average temperature of Kepler-442b : -40°C

                Narlikar Index : 3.75

                Narlikar Percentage : 93.75%

 

6) Gliese 667Cc : Gliese 667Cc performs relatively well on the Narlikar Index scoring 3.625, making it a highly habitable planet orbiting Gliese 667C. Gliese 667Cc is most probably tidally locked to a star. It is in the Scorpius constellation.

 

            Radius : 1.54R

            Mass : 3.709M

            Temperature of Gliese 667C : 3427°C

            Average temperature of Gliese 667Cc : 4.3°C

            Narlikar Index : 3.625

            Narlikar Percentage : 90.625%

 

7) Wolf 1061c : Wolf 1061c is also known as  WL 1061c. It performs relatively well on the Narlikar Index scoring 3.25, making it a highly habitable planet orbiting Wolf 1061. It is in the Ophiuchus constellation.

 

            Radius : 1.6R

            Mass : 4.3M

            Temperature of Wolf 1061 : 3069°C

            Average temperature of Wolf 1061c : -50°C

            Narlikar Index : 3.25

            Narlikar Percentage : 81.250%

 

8) Kepler-20e : Kepler-20e was the first planet found that was having a radius smaller than that of Earth while orbiting a sun like star. It orbits around the star Kepler-20. It performs quite poorly on the Narlikar Index scoring 1.2, making it an unhabitable planet orbiting Kepler-20. It is in the Lyra constellation.

                Radius : 0.868R

                Mass : 1.03M

                Temperature of Kepler-20 : 5193°C

                Average temperature of Kepler-20e : 770°C

                Narlikar Index : 1.2

                Narlikar Percentage : 30%

 

9) Kapteyn b : Kapteyn b is the oldest known potentially habitable planet. . It performs relatively well on the Narlikar Index scoring 3.125, making it a highly habitable planet orbiting Kapteyn’s star. It is in the Pictor constellation.

                Radius : 1.6R

                Mass : 4.8M

                Temperature of Kapteyn’s star : 3297°C

                Average temperature of Kapteyn b : -68°C

                Narlikar Index : 3.125

                Narlikar Percentage : 78.125%

 

10) Gliese 832c : Gliese 832c is a tidally locked planet having no plate tectonics. It performs relatively well on the Narlikar Index scoring 3.625, making it a highly habitable planet orbiting Gliese 832. It is in the Grus constellation.

                Radius : 1.5R

                Mass : 5.4M

                Temperature of Gliese 832 : 3347°C

                Average temperature of Gliese 832c : -20°C

                Narlikar Index : 3.625

                Narlikar Percentage :  90.625%

 

The conclusions of the Narlikar Index are as follows :-

1.    A high Narlikar Index is ideal for habitability.

2.    We should target planets with a high Narlikar Index.

3.    The higher the Narlikar Index, the more similar the planet is with Earth.

Pranav Sawant

Anshuman 

 

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