Calculating Theoretical Habitable Zones Around Main Sequence and Outlying Star Systems

Stephen Southard

12/2/2020

PHY 481

B.S. Physics

Advised by Dr. Neil Comins

Table of contents

Abstract……………………………………………………………………………………………3

1 Introduction………………………………………………………………………………….…..5

1.1 Background……………………………………………………………………………5

1.2 Objectives……………………………………………………………………………..6

2 Habitable Zones………………………………………………………………………………....8

2.1 Theory and Mathematics……………………………………………………………...8

2.2 Example Data of the Sun…………………………………………………………….12

2.3 Evolution of the Sun…………………………………………………………………13

3 Main-Sequence Stars…………………………………………………………………………..19

3.1 M-Type………………………………………………………………………………19

3.2 K-Type……………………………………………………………………………….23

3.3 G-Type………………………………………………………………………....…….26

3.4 F-Type……………………………………………………....………………………..29

3.5 A-Type……………………………………………………………………………….31

3.6 B-Type…………………………………………………………………………….....34

3.7 Discussion of Error…………………………………………………………………..37

4 Supergiants……………………………………………………………………………………..38

4.1 Background…………………………………………………………………………..38

4.2 Red Supergiants……………………………………………………………………...39

4.3 Blue Supergiants……………………………………………………………………..42

4.4 Yellow Supergiants…………………………………………………………………..46

5 White and Brown Dwarfs……………………………………………………………………...49

5.1 Background…………………………………………………………………………..49

5.2 Habitability around White and Brown dwarfs……………………………………….50

5.3 White Dwarfs………………………………………………………………………...50

5.4 Brown Dwarfs………………………………………………………………………..53

6 Conclusions…………………………………………………………………………………….55

Citations………………………………………………………………………………………….57

Abstract

Habitable zones around star systems are a key interest in the development and search for exterrestrial life and exoplanets. A star’s habitable zone is set by an inner and outer boundary, a radial shell where water can be in a liquid form on planetary surfaces. In order to find the boundaries of a given system, luminosity of the host star is required. By using empirical bolometric constants it is possible to calculate the luminosity of main-sequence stars. By obtaining a star’s apparent magnitude, the magnitude of the brightness as it is measured from

Earth, we are able to calculate the absolute visual magnitude of that same star, or how bright the star appears at a standard distance of 32.6 light-years, or 10 parsecs. This allows comparison of a close star, i.e the Sun, and a target star that are at far relative distances from each in order to determine the luminosity, or stellar flux of the target star. The absolute visual magnitude is used along with a bolometric constant correction based on the spectral class of the target star in order to determine its luminosity. With constants for stellar flux measured at inner and outer radii, in order to replicate the insolation that Earth receives in our solar system, the theoretical inner and outer bounds of the habitable zone can be determined for main-sequence stars in the Milky Way.

Luminosity of main-sequence stars increases as the Hertz-Russell diagram is climbed, thus formulating a basis for the size of the habitable zones. M-type stars, such as TRAPPIST-1, have small and compact habitable zones (0.0224 to 0.0323 AU), whilst a B-type star, such as Tau

Scorpii (142.49 to 205.79 AU), will have a wide and grotesque zone that encompasses a large stellar area. Habitable zones are not limited to just main-sequence stars, however, as habitable zones are theoretically possible around any star where the flux is sufficient to replicate Earth-like

conditions, even supergiant stars. Supergiant stars are capable of extremely large stellar habitable zones, such as Zeta Puppis (859.7 to 1238.53 AU). However, even in “ideal” zones of, the habitability of planets can be limited. Very-low luminous stars, for example, require very tight orbits which can translate to tidal heating or a susceptibility to solar flares, whereas high-luminous stars have to potential to leave planets ravaged by high stellar winds and ultraviolet radiation which can damage DNA and prevent life from developing. Short lifespans on some types of stars do not give life adequate time to develop, variability can cause planets to lack stable conditions that are required, and unknown factors of planetary development around white and brown dwarfs are all measures of uncertainty in the possibilities of Earth-like conditions outside the solar system.

Chapter 1

Introduction

1.1 Background

Our galaxy, and further beyond that, the Universe, is an extraordinary place, full of science, exciting phenomenon, and mysteries. One of the most highly disputed topics in the astronomical field is whether or not humankind is alone. Earth is a mere grain of sand in the scheme of the universe. To be the only bastion of life seems highly unlikely. Life on Earth begins and relies on one very important substance: water. Hence, the search for habitable planets can be narrowed to those that could possibly have that same life enriching resource. This idea is where the habitable zone itself was born. A perfect range, where water can remain in its liquid

1 form on the planetary surface, while being neither fully frozen or evaporated. The standard definition of a habitable zone is the range of distances from a star in which liquid water could exist on planetary surfaces, and therefore it is technically the region around a star where conditions are favorable, and required, for life. The habitable zone is effectively a radial shell

2 around a given star, with an inner and outer edge. The inner boundary of the zone is at the edge of a “runaway” greenhouse zone. A planet inside of the inner edge would succumb to an infinite greenhouse effect due to greenhouse gases trapping incoming infrared radiation, thus causing increasing temperatures, leading to surface water evaporating away. The outer edge is subsequently the opposite. As the outer edge is approached, surface temperatures continue to drop. Outside the outer edge, greenhouse gases cease to be able to sufficiently warm the planet, leaving all surface water frozen, thus leaving the planet far too cold to support life.

This energy from stars can be denoted as the stellar flux, or radiant flux emitted by the

2 star. Flux is defined as the energy per unit time emitted from a source (the observed star) over 3 optical wavelengths. In astronomical terms, we denote this flux as the luminosity of a star, or the intrinsic brightness. Habitable zones are based solely on the luminosity of the host star of any given system. Luminosity is measured in two different ways, through a finite waveband (visual), or across the entire electromagnetic spectrum, bolometric luminosity being the latter. The brighter the star, the more energy it emits. The more energy the star emits, the further away the habitable zone is from the star.

1.2 Objectives

The main objective of this project is to model and understand the mathematical and theoretical basis for habitable zones. This is done through calculations and physical modeling of many different star systems ranging from low luminosity to very high, as well as discussing factors that may affect planet habitability in the zones.

Therefore the objectives are:

1. Modeling of theoretical habitable zones of main-sequence stars of different spectral

classes

2. Model and show the habitable zone of our solar system over the next 5 billion years

3. Modeling of theoretical habitable zones of outlying stars not belonging to the

main-sequence (Supergiants, White Dwarfs, and Brown Dwarfs)

4. Discuss the physical factors affecting habitability in main-sequence and outlying stars

habitable zones

Chapter 2

Habitable Zones

2.1 Theory and Mathematics

The process of calculating habitable zones begins with data, particularly apparent brightness, and distance. A variety of databases, stellar catalogues, and publications were used in attempts to get accurate information. The SIMBAD Astronomical database provides basic data, cross-identifications, and measurements for astronomical objects outside the solar system. The

Hipparcos catalogue was designed to help pinpoint stellar position and measurements with high precision, and the NASA Star and Exoplanet Database (NStED) collates and cross-correlates astronomical data particularly on stellar information regarding exoplanets and data of the host star, mainly stellar parameters of positions, magnitudes, and temperatures.

As stated above, the habitable zone shell around a given star is based on the luminosity of

3 the host star. Inner and outer radii of the habitable zone may be computed by equations (1) and (2) below:

In these equations, ri and ro represent the distance from the star to the inner and outer radius of

4 the habitable zone, respectively. There are two constant values used, 1.1, and 0.53. These values represent the stellar flux that defines the boundary conditions of the habitable zone. These values help calculate the habitable zone to the point where the planets receive conditions nearly similar to that of Earth in the solar system.

In order to calculate the habitable zone radius around the desired host star, the luminosity of the star itself needs to be calculated first. For these calculations the bolometric magnitude

(Mbol) of the desired star is used as a comparison material to the bolometric magnitude of the Sun. Bolometric magnitude is a measure of brightness and flux of a star that takes into account all electromagnetic radiation across all wavelengths. By using bolometric magnitudes it allows us to have a more accurate calculation, since we are accounting for all forms of energy that

5 planets may experience in the habitable zone. By using generalized bolometric constant corrections for the respective spectral class main-sequence star we are observing, absolute

magnitude (Mv) can be converted to the absolute bolometric magnitude (Mbol) using equation (3) below.

5 Table 1. Generalized bolometric corrections based off Habits and Heintze (1981)

6 For the above expression, Mv, the absolute visual magnitude, is needed. Absolute visual magnitude is a measure of luminosity on an inverse logarithmic scale. It is the apparent magnitude of the star when placed at exactly 10 parsecs, or 32.6 light-years from Earth. The more luminous the star, the smaller numerical value for its absolute magnitude. By considering

the stars at a fixed distance, the intrinsic brightnesses of different stars can be compared. Mv is generally attributed to the ‘absolute visual magnitude’, for brightness between a wavelength range of 4000 to 7000 angstrom.. In order to determine the absolute visual magnitude, we need

the observed brightness, or the apparent magnitude (mv), as well as the distance to the object we are observing, in parsecs. Apparent magnitude is the brightness as measured by someone here on

Earth, at the given distance the object is. It works in the same way that absolute magnitude does, an inverse logarithmic. the brighter the object, the lower the magnitude number. A magnitude of

7 1.0 corresponds to a value of 2.512, or Pogson’s Ratio, thus a star of magnitude 2.0 will be 2.512 times brighter than a star of magnitude 3.0, and so on. By having both the apparent

6 magnitude, and the distance to the object in parsecs, equation (4) can be used to find the absolute visual magnitude.

By taking the calculated values, we are able to calculate the luminosity based on the

8 bolometric magnitude values. Using equation (5) the luminosity of the target star in terms of the luminosity of the Sun can be calculated:

In equation (5), all values are calculated, except for Mbol, Sun. The bolometric magnitude of the Sun is constant, estimated between 4.72 - 4.75. The constant is determined by the logarithmic relationship between the Sun’s luminosity (in watts) and the zero point luminosity, which is a

28 fixed value, 3.0128x10 watts .

2.2 Example Data of the Sun

9 The Sun is used as the basis of measurement for stellar data. The Sun’s radius, 696,342

10 28 km, is defined as 1 R☉, and the Sun’s luminosity, 3.828x10 watts, is 1 L☉. These relationships give as an approximation to measure other stellar objects in terms of what we already understand. Below is the habitable zone measure of the Sun at present time:

Fig. 1 Representation of the habitable zone of the Sun, a G Type Main-sequence star with

1 R☉ and 1 L☉. Habitable Zone Range of 0.9534 AU to 1.373 AU

2.3 Evolution of the Sun

(Fig. 1) is a representation of the Sun’s habitable zone at the current point of its life cycle. As a G type star, the Sun over the course of its life cycle converts hydrogen into helium. As the Sun burns away more and more hydrogen, it’s luminosity, and also its radius, will steadily increase, roughly by around 1%~ every 110 million years or so. This resulting change will have a direct impact on the habitable zone, which is directly proportional to the luminosity of the Sun.

Fig 2. Luminosity of the Sun over the next 5~ billion years from 1 L☉ at present time to 1.563479 L☉ at 4.95 billion years

Fig. 3 Representation of the habitable zone

of the Sun (+550 million years),

1.05101 L ☉ Habitable Zone Range .977478 AU to

1.408203 AU

Fig. 4 Representation of the habitable zone of

the Sun (+990 million years), 1.09277 L ☉ Habitable Zone Range .9996176 AU to

1.435907AU

As the Sun’s luminosity increases, the habitable zone is pushed outwards to account for the increased stellar flux. (Fig. 4) represents the habitable zone 990 million years in the future.

At this point, Earth’s orbit at 1 AU is no longer well off the inner edge, as it was in (Fig. 1).

While Earth is still technically in the habitable zone, Earth’s physical attributes would be quite different, with higher surface temperatures due to further increases in greenhouse gases in the atmosphere. By 990 million years, Mars is beginning it’s slow approach to the outer edge.

Fig. 5 Representation of the habitable zone of the Sun (+1.98 billion years),

1.195134 L☉, Habitable Zone Range 1.042346 AU to 1.501655 AU

(Fig. 5) displays another billion years in the future from (Fig. 4), 1.98 billion years from present time. At this time Earth is far beyond the inner edge, in turn causing the planet to be a moist greenhouse, with all surface water having evaporated off. Mars on the other hand, has just reached the outer edge of the zone, while most likely still being far too cold for human life, it is the start of a new era for the red planet.

Fig. 6 Representation of the habitable zone of the Sun (+3.08 billion years),

1.320169 L☉, Habitable Zone Range 1.095515 AU to 1.578253 AU

Fig. 7 Representation of the habitable zone of the Sun (+4.4 billion years),

1.487597 L☉, Habitable Zone Range 1.16291 AU to 1.67534 AU

Two further time jumps are depicted in (Fig. 6) and (Fig. 7), jumps to 3.08 billion and 4.4 billion years respectively. In these depictions, the habitable zone continues to move further away from

Earth, and closer to Mars, which is ideally becoming a warmer and sustainable planet. Mars from this point will have roughly 600 million years or so to settle in the habitable zone before the Sun undergoes a drastic change at roughly 5 billion years. At approximately the 5 billion years, the

Sun will run out of hydrogen, thus beginning it’s helium burning process, drastically increasing the Sun’s radius as it expands into a red giant. As it expands, its outer layers will consume Mercury and Venus, and possibly Earth. It is still debated whether or not our planet will be engulfed, or whether it will orbit dangerously close to the star. During the Sun’s billion roughly

year lifetime as a red giant, the habitable zone will expand outward even more, and planets in the outer solar system could be part of a habitable zone. The Sun’s last shift will happen as it shrinks significantly when it becomes a white dwarf, although there would not be any planets orbiting close enough at this point to benefit from such a zone.

Chapter 3

Main-Sequence Stars

3.1 M-Type Main-Sequence

Out of all the stars in the galaxy, M-type main-sequence are the most common. They

12 account for roughly 76% of all main-sequence stars in the solar neighborhood . Most of these class M-type stars exist as red dwarfs, some of the smallest, coolest, and dimmest stars we can observe (as depicted in Fig. 8, which plots the absolute visual magnitude (Mv) over the

13 main-sequence spectral classes). Radii of M-type dwarfs generally range from 8% R ☉ to 62% R☉, luminosity from 0.015% L☉ to 7.2%☉, and temperature from 2,300 to

3,800 K.

Three class M-type star systems were modeled. These stars were chosen either for being spectral standards that represent ideall M-type stars, or as known stars with planetary systems (such as the TRAPPIST-1). Two plots for each respective star are shown below, a plot of the habitable zone with respect to the radius of the star, the other with Earth’s orbit with respect to the star.

Fig. 9 HZ around TRAPPIST-1 M-Type Star (d=12.43pc)

mv=18.4, Mv=17.92, 0.00053 L☉, .1192 R☉

Fig. 10 Earth’s orbit in the TRAPPIST-1 System

Fig. 11 HZ around Gliese 581 M-Type Star (d=6.26pc)

mv=10.55, Mv=11.57, 0.011 L☉, .299 R☉

Fig. 12 Earth’s orbit in the Gliese 581 System

Fig. 13 HZ around HIP 57050 M-Type Star (d=11pc)

mv=13.765, Mv=13.55, 0.0018 L☉, 0.4 R☉

Fig. 14 Earth’s orbit in the HIP 57050 System

These plots illustrate the dimness associated with stars of this spectral class. A planet in a habitable zone around a M-type star orbits far closer to its parent star than Earth does to its star, in order to theoretically receive the same planetary conditions present on Earth. Due to such close proximity to the parent star, planetary systems in M-Type star systems can become tidally locked in orbit, causing runaway greenhouse effects due to tidal heating, as well as being more vulnerable to solar flares, which can greatly affect the development of life.

3.2 K-Type Main-Sequence

12 K-type main-sequence stars, or orange dwarfs, are the second most common main-sequence star in the solar neighborhood, accounting for roughly 12% of stars. Generally they are orangish and slightly cooler than the Sun. Orange dwarfs are considerably larger and

brighter than red dwarfs, with radii usually ranging from ~0.7 R☉ to ~0.96 R☉, and luminosity 5 ranging from ~0.08 L☉ to ~0.6 L☉. Surface temperatures on these stars are measured between 3,900 to 5,200 K.

14 K-type stars are the ideal type star for planetary development in habitable zones. These stars remain stable on the main sequence for a long period of time (18 to 34 billion years), thus leaving plenty of time for life to develop on planets orbiting ideal stars. They are also more abundant than G-type (Sun-type stars), and overall emit less ultraviolet radiation as well.

Three K-type star systems were selected, two of them being “anchor” points for the

M-type classification system (Epsilon Eridani and Sigma Draconis). These stars have remained unchanged over the years, and hence are prime examples for this classification.

Fig. 15 HZ around Epsilon Eridani K-Type Star (d=3.2pc)

mv=3.736, Mv=5.83, 0.36 L☉, 0.735 R☉

Fig. 16 HZ around Sigma Draconis K-Type Star

(d=5.7pc)

mv=4.674, Mv=5.89, 0.51 L☉, 0.776 R☉

Fig. 17 HZ around HD 219134 K-Type Star (d=6.55pc)

mv=5.574, Mv=6.46, 0.26 L☉, 0.778 R☉

Overall, K-type stars are ideally one of the most likely for extraterrestrial life being present in their habitable zones. Less ultraviolet radiation, as well as being a safe distance from the host star, helps negate tidal locking and solar flare problems associated with M-type stars. By plotting

Earth’s orbit relative to the stars, the distance (to the outer edge) is much more reasonable

(compared to M-type), and in the case of Sigma Draconis (Fig. 16), it is near the outer edge.

Therefore there is a high likelihood of an Earth-like world orbiting a K-type star system.

3.3 G-Type Main-Sequence

G-Type, Sun-like, or yellow dwarfs are the third most common spectral classification

12 among the main-sequence. They make up roughly 7.5% of the main-sequence stars in the solar

15 neighborhood. Typical G-type stars generally range from 0.96 R☉ to 1.4 R☉ in radius, 0.6 L☉ to

5 L☉ in luminosity, and 5300 to 5980 K in temperature. Four G-Type stars were modeled, two of which being known star systems with planets,

Kepler-22 and Kepler-452, one with suspected planetary systems in the habitable zone, Tau Ceti,

1 and one with no confirmed planets currently, Kappa Ceti.

1 Fig. 18 HZ around Kappa Ceti G-Type Star (d=9.14pc)

mv=4.84, Mv=5.03, .78 L☉, 0.95 R☉

Fig. 19 HZ around Kepler-22 G-Type Star (d=195.7pc)

mv=11.664, Mv=5.2, .67 L☉, 0.979 R☉

Fig. 20 HZ around Kepler-452 G-Type

Star (d=561pc)

mv=13.426, Mv=4.68, 1.069 L☉, 1.11 R ☉

Fig. 21 HZ around Tau Ceti G-Type Star (d=3.7pc)

mv=3.5, Mv=5.66, .608 L☉, .793 R☉

One factor that all these star systems have in common is their similarities to the Sun. (Fig 18)

1 depicts Kappa Ceti, a Sun-like with no confirmed planets, although it is still a good candidate for terrestrial planets. It has Earth’s orbit in a favorable position in the rough center of its

16 habitable zone, and has served as a stable anchor point for G-type stars . The Kepler-22 system has received attention for its once thought “super-Earth” exoplanet, Kepler-22b, which is roughly

17 twice the size of Earth . It orbits its habitable zone in roughly the same spot that Earth orbits the Sun, however a confirmed highly elliptical orbit causes variance in surface temperatures.

Kepler-452 is a near solar twin, with near identical characteristics in stellar flux and radius. It has one orbiting exoplanet, Kepler-452b depicted in (Fig 20), the first potentially rocky

18 “super-Earth” , orbiting slightly further in the zone than where Earth’s orbit would be. This exoplanet is currently one of the most Earth-likes discovered so far by Kepler. The last system,

Tau Ceti, while being slightly dimmer and smaller radially than the Sun, still possesses many characteristics that support habitable planets. It has an estimated 7 (4 confirmed) planets orbiting it, with most of them being potentially outside the habitable zone range.

3.4 F-Type Main-Sequence

F-Type stars, or yellow-white dwarfs, are the fourth most common spectral class among the main-sequence. They are more luminous, hotter, and physically larger than G-type stars.

Radially they range from roughly 1.2 R☉ to 2.0 R☉ or even larger. They range from ~3 L☉ to ~4

5 L☉, and generally have surface temperatures between 6,000 and 7,600 K. The increased stellar flux will push the zone outward much further away than that of where the Earth would normally be with respect to the star.

Fig. 22 HZ around Beta Virginis F-Type

Star (d=10.93pc)

mv=3.604, Mv=3.261, 3.83 L☉, 1.681 R☉

Fig. 23 HZ around Iota Piscium

F-Type Star (d=13.71pc)

mv=4.13, Mv=3.45, 3.698 L☉, 1.595 R ☉

3 Fig. 24 HZ around Pi Orionis F-Type Star (d=8pc) mv=3.16, Mv=3.494, 3.093 L☉, 1.236 R ☉

The three F-type stars depicted here all have relatively similar stellar characteristics, fitting those of anchor points for F-type spectral classification. The possibility of life existing on F-type stars is currently disputed. Compared to G-type stars, F-type emit much more intense light, and have a shorter stellar lifespan, thus leaving less time for development. F-types emit much higher ultraviolet radiation than G, K, and M-type stars, which has a direct negative impact on DNA

19 molecules . A hypothetical planet in the habitable zone of a F-type is estimated to receive roughly 2.5 to 7.1 times more UV light than Earth, thus requiring sufficient atmospheric

19 shielding for life to be protected . With a robust ozone layer, life could technically survive around one of these or similar star systems.

3.5 A-Type Main-Sequence

A-type main sequence are the fifth most common, they make up roughly 0.625% of the

12 main-sequence stars in the stellar neighborhood . A-type stars are generally bright, often seen

20 with the naked eye, and usually white or bluish-white in nature. Radially speaking, A-type stars range from 1.55 R☉ to 1.87 R☉ and can be greater. Luminosities can vary greatly in A-type stars, ranging from 15 L☉ to much higher in the range of 70 L☉+. Temperatures typically range from 7,100 to 9,700 K.

Three stars, all being spectral standards for A-type classification, Gamma Ursae Majoris,

Vega, and Fomalhau, were modeled.. All three stars have large variance in their luminosities between each other.

Fig. 24 HZ around Gamma Ursae

Majoris A-Type Star (d=25.5pc)

mv=2.438, Mv=0.405, 70.14 L☉, 3.04 R ☉

Fig. 25 HZ around Vega A-Type

Star (d=7.7pc)

mv=0.026, Mv=0.5935, 44.7

L☉, 2.59 R☉

Fig. 26 HZ around Fomalhaut A-Type Star (d=7.7pc)

mv=1.16, Mv=1.72, 15.84 L☉, 1.842 R☉

While A-Type stars possess a habitable zone, the possibility of life developing around a A-type star is relatively slim. A-type stars are young (typically a few hundred million years old) and

21 have shorter lifespans of around a billion years . With short lifespan compared to that of K, and G-type stars, the time window for development of life is rather short. As lifespans are short, stars

22 of this classification will leave the main-sequence long before most K, G, or F-type stars .

3.6 B-Type Main-Sequence

B-type stars are very luminous and hot, much more than A-type stars. Due to this stellar nature, they have relatively short lives that end in violent supernova events, ultimately resulting in the creation of either black holes or neutron stars. B-type stars range from 2.7 R☉ to 10 R☉

23 radially, and the luminosity of these stars range from 100 L☉ to 1,000,000 L☉. Temperatures are high, compared to other main-sequence stars, ranging from

10,000 to 30,000 K.

Fig. 27 HZ around 29 Persei

B-Type Star (d=200pc)

mv=5.16, Mv=-1.31

1682 L☉ 3.9 R☉

Fig. 28 HZ around Tau Scorpii

B-Type Star (d=150pc)

mv=2.82, Mv=-4.2, 22334 L ☉ 6.5 R ☉

Fig. 29 HZ around Omega Scorpii

B-Type Star (d=145pc)

mv=3.95, Mv=-1.85, 9100 L ☉ 6.6 R ☉

Fig. 30 Earth’s Orbit around Omega Scorpii system

(Fig 27), (Fig 28), and (Fig 29) depict the habitable zones around these three B-type stars. As stated, the possibility of life developing in these zones is relatively nonexistent, due to the unpredictable nature of this spectral classification.

3.7 Discussion of error

Habitable zones calculated during this project were done using bolometric magnitude through the use of bolometric constant corrections. Bolometric corrections as stated earlier in this report are used to translate the absolute visual magnitude to its bolometric magnitude. The use of tabulations of empirical bolometric corrections has general errors associated with it. Bolometric corrections are set while the zero point is arbitrary, while the bolometric magnitude of the Sun used in combination with such tables cannot be chosen arbitrarily in this same matter. Therefore there is some innate error involved, generally low for most main-sequence stars (a percent or two).

Bolometric corrections in general can get complicated regarding spectral classification and luminosity classification. Some complications can be resolved through the use of

5 generalized tabulations, based on compilations of effect temperatures for different spectral classifications (which was used for this project), at the possibility of some small degree of uncertainty in calculations.

Chapter 4

Supergiants

4.1 Background

The term of giant star was first termed to represent the stars appearing in the top distinct

25 regions of the Hertzsprung-Russell Diagram (Fig. 8). Larger and more luminous stars (in respect to main-sequence) were coined giants, while subsequently it became apparent that significantly larger and more luminous stars existed, thus dubbing the term supergiant.

Supergiants generally are massive (usually 30 R☉ to 500 R☉, or even in excess of 1000

R☉) , extremely luminous (1000 L☉ to over 1,000,000 L☉), and have masses roughly an order of magnitude higher than the Sun, although generally lower surface gravity (particularly in red supergiants), which causes the star to be unstable and experience rapid mass loss and pulsations.

Theoretically, habitable zones around supergiants are possible. Habitable zones in this case would have to be hundreds of astronomical units away from the host star in order to have the same insolation that the Earth does around the Sun, however. A side factor is variability.

Most supergiant stars are either semiregular variables, or irregular variables, which causes photometric variability in the luminosities. Constant changes in luminosity, would severely

26 affect the development of life, even if a planet were to be orbiting in the zone. Supergiant stars also produce strong stellar winds, requiring planets to have a strong magnetosphere, in order to protect a planet’s atmosphere from being eroded away. Lastly, being late stage stars (evolved from main-sequence) as well as having very short lifespans of generally less than a 100 million

years. This simply doesn’t give life the adequate time to develop as it would around main-sequence stars.

The main problem with modeling supergiant stars is the large amount of uncertainty

involved. Uncertainties of many thousand L☉ cause massive shifts in the theoretical zone around a given giant. All supergiants were modeled using the same distance scale as well as having uncertainty considered in both a minimum and maximum zone.

4.2 Red Supergiants

Red supergiants are generally cooler and some of the largest stars we know of. There is a

27 some-what defined upper limit for luminosity and radius regarding them however. Luminosities of red supergiants generally cap out at around 630,000 L☉, and radii at 1500 R☉, while temperatures generally range around or below 4,100 K. Stars with greater luminosity and radius would simply be too unstable to form. The three red supergiants selected to model were

Betelgeuse, a well known red supergiant, as well as two larger supergiants,

Mu Cephei, and KY Cygni.

Fig. 31 HZ around Betelgeuse RSG

(d=168pc)

28 1 20000 ± 30000 L☉, 770 ± 80 R☉ (Min HZ: 286.04 to 412.08 AU) (Max HZ: 369.27 to 532.00 AU)

Fig. 32 Earth’s Orbit with respect to

Betelgeuse

Fig. 33 HZ around Mu Cephei RSG

(d=940pc)

29 3 11500 ± 28500 L☉, 1340 ± 80 R☉ (Min HZ: 507.22 to 730.73 AU) (Max HZ: 555.96 to 800.94 AU)

Fig. 34 Earth’s Orbit with respect to

Mu Cephei

Fig. 35 HZ around KY Cygni RSG

(d=1068pc)

30 2 00000 ± 70000 L ☉ 1046 ± 374 R ☉ (Min HZ: 343.78 to 495.26 AU) (Max HZ: 495.43 to 713.75AU)

Fig. 36 Earth’s Orbit with respect to KY Cygni

4.3 Blue Supergiants

Blue supergiants, unlike red supergiants have very high temperatures (10,000 to 50,000

K), while also being extremely luminous. Evolved from high-mass stars, they are physically smaller than red supergiants radially, and are just as luminous, if not more. Blue supergiants

range from around 20 R☉ to 80 R☉, and luminosity can range up to a 1,000,000 L☉. These types of stars are relatively rare in the cosmic scheme, and have short lifespans of generally less than

~10 million years. Three blue supergiants were chosen to be modeled, Rigel, one of the largest

blue supergiants known, Zeta Puppis, one of the most luminous stars in the Milky Way, and UW

Canis Majoris, a prime example of a blue supergiant.

Fig. 37 HZ around Rigel BSG

(d=260pc)

30 1 20000 ± 25000 L ☉ 78 ± 7 R ☉ (Min HZ: 293.88 to 423.37 AU) (Max HZ: 363.07 to 523.05 AU)

Fig. 38 Earth’s Orbit with respect to

Rigel

Fig. 39 HZ around Zeta Puppis BSG

(d=330pc)

32 8 13000 ± 100000 L ☉ 20 ± 6 R ☉ (Min HZ: 776.36 to 1118.46 AU) (Max HZ: 547.72 to 1347.95 AU)

Fig. 40 Earth’s Orbit with respect to

Zeta Puppis

Fig. 41 HZ around UW Canis

Majoris BSG (d=1500pc)

33 2 90000 ± 40000 L ☉ 15 ± 4 R ☉ (Min HZ: 476.73 to 686.80 AU) (Max HZ: 547.72 to 789.08 AU)

Fig. 42 Earth’s Orbit with respect to

UW Canis Majoris

4.4 Yellow Supergiants

Yellow supergiants much like all other supergiants, are a group of highly luminous, grostoque stars. They are cooler than blue supergiants but warmer than red supergiants.

Temperatures in these supergiants range generally (4,000 to 7,000 K). Luminosities of yellow

supergiants exceed 1,000 L,, with some up above 100,000 L☉. Radially yellow supergiants range

34 from 30 R to several hundred R☉ . As with all supergiant class stars, these evolved from the main-sequence, mainly from F-type or G-type stars, and have a short lifespan measured in millions of years. Two yellow supergiants were chosen to be modeled, Delta Canis Majoris, an anchor for yellow supergiant classification, and Alpha Leporis, an older, dying star, with an impending supernova in ~1 million years.

Fig. 43 HZ around Delta Canis

Majoris YSG (d=490pc)

35 8 2000 ± 10000 L ☉ 215 ± 70 R ☉ (Min HZ: 255.84 to 368.58 AU) (Max HZ: 289.20 to 416.64 AU)

Fig. 44 Earth’s Orbit with

respect to Delta Canis Majoris

Fig. 45 HZ around Alpha

Leporis YSG (d=680pc)

36 3 2000 ± 5000 L ☉ 15 ± 4 R ☉ (Min HZ: 156.67 to 225.71 AU) (Max HZ: 183.40 to 264.22 AU)

Fig. 46 Earth’s Orbit with

respect to Alpha Leporis

Chapter 5

White and Brown Dwarfs

5.1 Background

White and brown dwarfs stars are two extraordinary stellar objects. White dwarfs being stellar core remnants, and brown dwarfs being essentially failed stars, not possessing enough

37 mass to trigger sustained nuclear fusion of hydrogen in their cores . White dwarf stars are final stage remnants of main-sequence or giant stars. They no longer possess material to undergo fusion reactions, and therefore have no source of energy production. White dwarfs are held together by electron degeneracy pressure, which causes them

38 to be extremely dense (e.g. a mass of 1 M☉ would have a volume comparable to the Earth) . With no source of energy, they are very hot when formed, with temperatures ranging as high as

40,000 K while cooling to 8,000 K or below as they age. When formed they produce large amounts of strong ultraviolet radiation from the star, which dispurses as they cool. White dwarfs have very long lifespans (up to ~10 billion years), and are theoretically thought to become black

39 dwarfs (theoretical stellar remnant of a white dwarf) at the end of their lifespan . Brown dwarfs were theorized to exist, but were not discovered until roughly the

40 mid-1990s. They have low mass, estimated generally between 13 to 80 Jupiter masses . They have very low surface temperatures (in stellar terms) ranging from 300 to 2,800 K. Much like white dwarfs, as brown dwarfs do not undergo fusion, also cooling down over time. Due to the nature of the star, brown dwarfs do not emit much visible light, mainly emitting light in the

41 infrared range .

5.2 Habitability around White and Brown dwarfs

Although they are considered stellar remnants, white and brown dwarfs are bright enough to support a habitable zone. Since they become cool and less luminous over time, they are

42 unique, with their habitable zones moving inward as opposed to outwards . As these stars have very low luminosity, this leads to close proximity of the habitable zone to the host star, thus creating the risk of tidal-locked heating with the star (similar to M-type stars), which can lead to runaway greenhouse effects, regardless of the habitable zone location. High ultraviolet emissions

42 also lead to habitability concerns with planets orbiting white dwarfs . Brown dwarfs are more unknown, since observational data does not map ultraviolet emissions or early activity very well.

Although no terrestrial planets have been discovered around white dwarfs or brown dwarfs, there is no reason to believe they technically do not exist. Habitability around these types of stars has received less attention than around hydrogen burning stars. Specifically, Brown dwarfs have received less attention because few are known, and it is still unknown if planets can

42 form around them . Work has been done to technically confirm brown dwarfs can support

43 habitable zones, specifically due to gravitational heating, due to slow contractions .

5.3 White dwarfs

White dwarf stars are not very luminous objects, with luminosities ranging from ~0.05

L☉ or less, and radially ranging from ~0.008 R☉ to ~0.2 R☉. As stated above, they have very long lifespans of up to ~10 billion years, very close habitable zone ranging, and release a large amount of ultraviolet radiation, particularly in the beginning of their lifespans, which can

complicate the development of life. I chose to model two white dwarf stars, a well known Sirius

B (one of the most luminous white dwarfs), and Procyon B, a relatively faint white dwarf. Both stars are binary elements in their parent systems.

Fig. 47 HZ around Sirius B (d=2.64pc)

44 ~ 0.056 L ☉ 0.0084 ± 0.00025 R ☉ with respect to Earth’s orbit

Fig. 48 HZ around Procyon B

(d=3.51pc)

45 ~ 0.000049 L ☉ 0.01234 ± 0.00032 R ☉

Fig. 49 Earth with respect to

Procyon B

5.4 Brown dwarfs

As with white dwarfs, brown dwarfs are not luminous, even less so than white dwarfs.

Typical luminosities are estimated to be around ~0.00001 L☉, with radii ranging around 0.06 R☉ to 0.12 R☉, with some being higher (like Teide 1 being modeled below). It is speculated that Brown dwarfs have long lifespans, measured in billions or potentially trillions of years. One

46 brown dwarf, Teide 1, was modeled. This was the first brown dwarf to be verified, in 1995 . Tiede 1 is estimated to be young on the cosmic scale, around 120 million years old.

Fig. 50 HZ around Tiede 1 (d=120pc)

47 ~ 0.0006 ± 0.0001 L ☉ ~0.37985 R ☉

Fig. 51 Earth with respect to Tiede 1

Chapter 6

Conclusions

Overall, theoretical calculations for a habitable zone can be made for any star capable of supplying orbiting planets with flux that is relatively the same as the insolation that Earth receives. There are clear limitations to the habitability around some star classifications.

Particularly higher luminosity stars with high ultraviolet radiations, short lifespans, and high variability. This also extends to stars with very-low luminosity, where habitability could succumb to high temperatures due to tidal-heating, and solar flare damage due to proximity of the host star. K, G, and F-type stars are thought to have the highest probability of developing life in some nature. This is especially true of K-type stars which are of particular interest in the search for extraterrestrial life, due to their long lifespans on the main-sequence, and low ultraviolet radiation emissions, even less than our own Sun. K-type stars are also the most common main-sequence star after M-type. Other stars types, particularly white and dwarf stars require future research on development of planets to determine feasibility of exoplanet research in these systems.

This science boils down to the calculations of habitable zones, which are dependent on luminosity assumptions, through the use of accurate bolometric corrections for given star classifications, to which a uniform scale for corrections has not yet been standardized.

Bolometric corrections are a substantial part of measuring the emissions of particularly ultraviolet radiation, and a large portion of infrared light. Habitable zones are also solely based on replicating the insolation that Earth receives from the Sun,

Constraints and Considerations

Theoretical research itself does not have many constraints, but translating theoretical calculations into precise and accurate measurement can.. Humankind’s knowledge of stars, planets, the galaxy, etc. changes constantly. Habitable zone theory is somewhat limited by proven knowledge of exoplanets. Even the habitable zone in our solar system is still debated, therefore accuracy stating the true habitable zone around a distant star is still future research. Future direct imaging of exoplanets, spectra analysis of atmospheric conditions, and correct interpretation of possible biomarker gases will be critical in determining the correct and precise habitable zones.

Considerations can be made in regards to socioeconomics and politics. Space exploration and investment in such has been a topic of discussion for many years. Many argue that there are enough problems on Earth that outward looking into the reaches of space is not a concern. Space exploration and research is a long-term investment. However, society’s greatest advancements come through research, development, and hard work. Many say investments in scientific research are investments in the betterment of humanity, even if it is not always an easy path to see. Advancements are sometimes not realized until years or generations after.

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