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Calculating Theoretical Habitable Zones Around Main Sequence and Outlying Star Systems

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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 1 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 2 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 3 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. 4 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. 5 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. 6 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 7 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: 8 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,
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