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Early investigations in geology focused on describing landscape features, classifying rocks, minerals, geologic features, and mapping. As explorers returned with discoveries and maps from missions around the world, libraries and museums began to fill with enough materials for people to begin to recognize patterns in geologic data. Most of the early works in modern geology came out of Europe's scientific community. Although many thousands of individuals have contributed important ideas, several people stand out for making important early contributions, often at the risk of their own lives and well-being.

What is Earth Science?

The notion that the Earth was old measured in billions of years has not been all that popular with some religious organizations throughout the ages. Although fossils have been marveled at throughout history, it was heresy to describe them as ancient life forms for instance, Leonardo Da Vinci believed fossils were ancient life forms, older than the stories in the biblical book of Genesis, but he only wrote about it in secrecy. It was was a Danish Catholic bishop, Nicolas Steno , who first promoted science of the origin of fossils and the basic geologic principles associated with the science of stratigraphy.

A fossil is a remnant or trace of an organism of a past geologic age, such as a shell, skeleton or leaf imprint, embedded and preserved in the Earth's crust. The fossils found in ancient layers of strata appear unique to rocks of similar age, wherever they occur. The collective knowledge of fossil evidence from around the world is referred to as the fossil record , and follows a time line through Earth's history. The Science of Stratigraphy Stratigraphy is a branch of geology concerned with the systematic study of bedded rock layers and their relations in time and the study of fossils and their locations in a sequence of bedded rocks.

A stratum is a bed or layer of sedimentary rock having approximately the same composition throughout plural is strata. For example, Figure shows strata exposed in the Grand Canyon. A Scottish physician, James Hutton studied rocks and landscapes throughout the British Isles and promoted a theory he called uniformitarianism. Uniformitarianism theory implies that all geologic phenomena may be explained as the result of existing forces having operated uniformly from the origin of the Earth to the present time. Uniformitarianism is commonly summarized: "The present is the key to the past.

Many scientists of his times promoted a theory of catastrophism. Catastrophism theory implies that major changes in the Earth's crust resulted from catastrophes rather than slow, evolutionary processes. Catastrophism was more in line with religious doctrine common in the 17th and 18th centuries. It is interesting that today, uniformitarianism still applies to most geologic and landscape features, but discoveries have show that the Earth, or large regions of it, have experience great catastrophes , such as asteroid impacts, great earthquakes, super storms, great floods, or volcanic events.

However, these events can be scientifically viewed within the greater context of modern geology. Uniformitarianism explains how observable processes taking place over long periods of time can change the landscape. Examples include:. James Hutton also contributed to a theory of rock formations. A rock formation is the primary unit of stratigraphy , consisting of a succession of strata useful for mapping or description. A rock formation typically consists of a unique lithology rock type that has a relatively defined geologic age and is considered mappable occurs throughout area or region, both on the surface and in the subsurface.

The correlation of rock formations and the fossils they contain from one region to another lead to the development of the geologic time scale Figure and William Smith — used Hutton's theories to create the first geologic map of strata exposed throughout the British Isles. William Smith's map named Delineation of the Strata of England and Wales with part of Scotland published in was the first geologic map of an entire country Figure As nations began to understand the importance of geologic mapping for evaluating their natural resources, the science of geology began to grow.

Once researchers had access to the distribution of materials and landscape features, they began to try to understand how and why landscape features like mountain ranges formed. What could explain the distribution of continents and oceans around the world? Why were some regions rich in certain kinds of mineral resources and others were not?

During the same period, there was an explosion of knowledge was happening in the world of biology. Swedish biologist, Carl Linnaeus began the biological naming scheme of binomial nomenclature, establishing a logical way to chart and classify life forms. Taxonomy gave later scientist a means to classify both modern and ancient life forms. This helped Charles Darwin to first propose a theory of evolution , an essential component to explaining the distribution of fossils through the geologic ages. Layers of strata beds of sedimentary rocks exposed in the Grand Canyon. The geologic time scale provides names to a chronology of established periods of time in the history of Earth and the Universe —time periods range from thousands, millions, and billions of years.

If a second were , years - this classic diagram show the distribution of a different ages of time as if it were all squeezed into a 24 hour day. All of human history would fit in the last fraction of a second! William Smith's geologic map of was the first attempt to map an entire country. British Museum of Natural History.

Beaumont Historical Society. Discussion of the major components of Earth's physical environment involves discussion about the solid materials rocks and landscapes , water resources, and its atmosphere. Each of these are discussed in more detail in following chapters.

In cross-section, the Earth has a central core , a mantle , and the crust Figure A core is the innermost part of a rocky planet or moon. Earth's core , based on geophysical studies, is believed to consist of a mile km thick magnetic metallic inner core that is overlain by a mile km thick zone of dense molten material in the outer core. This is overlain by the Earth's mantle. A mantle is an inner layer of a terrestrial planet or other rocky body large enough to have differentiated in composition by density.

On Earth, the mantle is a highly viscous layer between the outer core and the crust at the surface. A crust is the outermost solid shell of a rocky planet or moon, which is chemically distinct from the underlying mantle. Earth's crust ranges from about 6 to 40 miles thick 10 to 64 km.

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The scientific evidence that reveals the structure of the Earth is discussed in detail in Chapter 7. Water moves through the atmosphere involving evaporation, transport, and precipitation , and flows both on the surface and underground on its journey back to the oceans. The collective actions of water migration is called the hydrologic cycle Figure The term hydrosphere is used to describe all the waters on the Earth's surface, such as oceans, lakes, rivers, and streams discussed in Chapter The cryosphere is the frozen water part of Earth's systems, including all ice trapped in continental glaciers and sea ice discussed in Chapter All life on Earth is associated with water.

The term biosphere is used to describe all the regions of the surface, subsurface, and atmosphere of the Earth and possibly other planets occupied by living organisms. The hydrologic cycle is illustrated in this concept diagram. It was in that Edwin Hubble found dozens of uniquely identifiable variable stars in the Andromeda nebula and then determined that Andromeda was at least 10 time more distant than the most distant stars in the Milky Way. He was first to determine that Andromeda was a separate system which he named a galaxy. The Milky Way is an obvious band of densely distributed stars and clouds of dust visible as a band in the clear night sky Figure Before Hubble's discovery, it was thought to be the Milky Way represented the entire Universe, and that unusual shaped spiral nebulae galaxies were part of the Milky Way.

With Hubble's discovery, it became evident that Earth and the Sun's Solar System was within the greater Milky Way Galaxy, and that the abundance of other galaxies showed that the Observable Universe was drastically much, much larger that was previously known. The Andromeda Galaxy is a spiral galaxy Figure It is the closest large galaxy to our Milky Way Galaxy and is one of the few visible to the naked eye. It is the most distant object in space that can be seen without magnification.

The Andromeda Galaxy can be seen in the northern hemisphere on clear autumn nights. It is located about 2. A light year is the astronomical distance that light can travel in a year; approximately about 9. Andromeda is estimated to contain about 1 trillion stars. Astronomers estimate that the Milky Way and Andromeda galaxies will eventually collide merge in about 4.

A galaxy is a system of millions to trillions of stars, together with gas and dust, held together by gravitational attraction. Deep-space observing telescopes show distant field of galaxies —galaxies and clusters of galaxies can be seen in all directions in distant space. The distance to these objects are in the range of thousands to billions of light years away from Earth.

Figure shows a field of galaxies observed in on small region in deep space. Using images like this, astronomers estimate there may be billion galaxies within the Observable Universe. Galaxies appear as many shapes and sizes, but there are three general classes: spiral , elliptical , and irregular galaxies , but each of these groups are subdivided into classes Figures to Small elliptical galaxies are the most common, and unlike spiral galaxies their stars do not seem to revolve around their galactic centers in an organized way.

The galactic center is where the greatest mass and concentration of stars exist in a galaxy. Irregular galaxies take on many shapes, and many are interpreted as galaxies that have collided or merged under gravitational attraction. The Milky Way Galaxy is probably a spiral galaxy. An irregular galaxy. The Big Bang Theory is a cosmological theory holding that the Observable Universe originated approximately Current scientific though is that originally the material ejected from the Big Bang was too hot for subatomic particles with measurable mass to exist.

It was probably many thousands of years after the Big Bang that it got cool enough for sub atomic particles and then atoms to form, and that gravitational attraction could influence the newly forming matter. Early in the history of the Universe matter began to condense and with time gravitation attraction pulled materials together to form galaxies.

In , the Hubble Space Telescope was able to capture an image of the furthest distant galaxy known, estimated at about What is beyond the Observable Universe is unknown. A star is a self-luminous celestial body consisting of a mass of gas held together by its own gravity. Stars exist in a balance—their internal energy generated by nuclear fusion reactions results in an outflow of energy to the star's surface.

This outward flow of directed gas and radiation pressures is balanced by the inward-directed gravitational forces. Since ancient times, astronomers have been charting stars into constellations —recognizable grouping of starts that appear in the night sky and move with the seasons as the Earth orbits the Sun Figure Although stars in constellation often appear in association by appearance, they may be large distances apart and very greatly in brightness intensity. In addition, stars exist in a wide range of colors, most obvious when observed through telescopes or from space Figure Many stars are clustered together, often sharing a common stellar history Figure Some stars orbit each other relatively close to one another as binary systems Figure Some star systems have multiples stars in orbit around each other.

Among the millions of stars observable in our galaxy, astronomers have been classifying them by size, color, and brightness intensity. Most stars in our galaxy fall into a class called the main sequence of which our Sun belongs Figure Astronomers have developed theories about star formation and the life cycle of stars in their different classes.

With years of observation, abundance of knowledge has been gained about the life cycle of stars Figure Stars and solar systems form in giant interstellar clouds called nebulae. A nebula is an interstellar cloud within a galaxy consisting of gas and dust, typically glowing from radiant energy from stars nearby within them Figures to Nebulae are the birth place of both stars and other objects within solar systems. Nebulae can form from the explosion of stars at the end of their life cycle, expelling gas and matter into interstellar space.

Large nebula eventually begin to contract under the influence of gravity, resulting in the creation of new generations of stars and solar systems. As stars form, gravity draws material in mostly gas and it mass increases until the internal heat and pressure is enough to start nuclear fusion reactions converting hydrogen into helium , igniting a new star. As stars age, they consume their fuel and eventually run out of nuclear fuel. Stars like the Sun may take billions of years to consume their nuclear fuel.

When the fuel runs out, stars collapse under the weight of their own gravity. However, the fate of a star depends upon its mass. Stars up to about seven times the mass of the Sun fall within the main sequence grouping of stars. These go through stages as they consume their fuel. Young stars fuse hydrogen into helium. When stars run out of their hydrogen, the force of gravity causes them to collapse, which increases the heat and pressure within its core.

During this phase of a star's life it will expand and become a red giant. Once the helium in the core of a star is consumed, stars in the main sequence will shed much of their mass into space creating nebula , and the remaining core will shrink and cool and shrink to become a hot remnant called a white dwarf. Stars with masses greater than about seven times the mass of the Sun experience a more spectacular fate.

More massive stars will burn through their fuel much faster than stars of the main sequence because their cores are hotter and under greater pressure. One these massive stars burn through their hydrogen and helium, this increase in heat and pressure allows fusion to convert helium into carbon, then carbon into neon, and then into iron. As the star continues to burn through it's fuel it eventually shuts down because it the fusion process of creating iron actually consumes more energy than it produces and the star looses it balance and collapses under it own gravity.

The collapsing core reaches temperatures in the range of billion degree and the core recoils as a massive explosion called a nova. Great star collapses produce supernova where a star may shed the majority of it mass into space, creating a new nebulae. What happens to the core depends on the mass of the star. Stars about 7 to 20 times the mass of the Sun produce massively dense objects called neutron stars their density is so great that electrons and protons collapse to form a great mass of neutrons.

Stars with masses greater than about 20 times the mass of the Sun may collapse to form black holes. Black holes of so dense that their gravity prevents light from escaping from within their event horizons where matter is pulled into an inner space where nothing escapes. A constellation chart of stars visible in the fall night sky. A view of stars of many different colors in the Alpha Centari region. Color is a reflection of how hot stars are: blue are hottest, red are cooler.

White and yellow are intermediate. The Pleiades star cluster, perhaps the most recognizable constellation, contains over stars and is about light years away and about 13 light years in diameter. Albireo is the name of a binary star system visible about light years distant. Internal structure of the Sun. The Sun's corona is visible during a solar eclipse. Sunspots are relatively dark patches that appear temporarily on the Sun's photosphere Figures and Sunspots are cause by a flux in magnetic fields that appear to inhibit convection. Sunspots usually occur in pairs, like the two ends of a U-shaped magnet.

Sunspots last a few days to a few months before they dissipate. The concentration of sunspots on the solar surface tend to follow an 11 year cycle that also flows a small variation is the total amount of solar energy output. Coronal mass ejections are unusually large eruptions of streaming plasma and radiation composed of charged particles under the influence of solar magnetism.

Eruptions result in the formation of solar flares and prominences arching flares that erupt from the Sun's surface Figures and Plasma streaming from the Sun's corona results is the source of the solar wind, and coronal mass ejections in form of large solar flares and prominences can result in solar storms that can severely impact radio communications and potentially satellites orbiting Earth. Solar storms associated with coronal mass ejections can interfere with radio communications, cause damage to satellites, and impact electrical transmission lines and facilities resulting in power outages.

During strong solar storms long lines of metal like electrical power lines, pipelines, and railroad lines in northern regions can overload with electrical charges which and spark to nearby objects and have been reported to have started brush fires. Because massive solar ejections can be observed, the possible impacts of solar storms can be predicted.

A planet is a large spherical celestial body moving in an elliptical orbit around a star.

Fossils Through Geologic Time

A planetary system is a set of gravitationally bound celestial objects in orbit around a star or star system. Planets with orbiting moons are planetary systems. The Solar System consists of four inner rocky planets , four outer gas planets , and orbiting belts of asteroids , comets , planetesimals , and other objects under the gravitation influence of the Sun. Earth's Moon is the fifth largest of at least known moons orbiting planets in the Solar System Figure The Moon rotates ate the same rate that it revolves around the Earth a synchronous rotation that keeps the same side of the Moon facing Earth.

The Moon lacks an atmosphere, and does not display any active geologic activity such as earthquakes or volcanic eruptions. Like Earth, the Moon has a core, mantle, and a crust; geophysical data suggest the part of the Moon's core and mantle may be molten. The lack of atmosphere has helped to preserve geologic features that date back to early stages in the formation of the Solar System. Most of what we have learned about the physical environment, composition, and origin of the Moon comes from the Apollo Missions between and which culminated in a series of manned Moon landings between and Rock and lunar soil sample collected during those missions have helped resolving many questions and supporting theories about the origin of the Earth and Moon within the Solar System discussed below.

An atom is the smallest unit of a chemical element. Atoms have a nucleus composed of neutrons and protons and has a positive charge. Negatively charged electrons orbit around the nucleus in shell-like layers. Elements have equal balance in numbers of positively charged protons and negatively charged electrons.

Common examples of elements are iron, copper, silver, gold, hydrogen, carbon, nitrogen, and oxygen. Each element is assigned a letter symbol to represent the element for general use, such as in the writing of chemical formulas such as H 2 O used for water. The periodic table is a list of known elements. Of these, 92 are naturally occurring elements prior to development of artificial nuclear research and development. The lightest element, hydrogen , has one proton, whereas the heaviest naturally occurring element, uranium, has 92 protons.

In general elements on the left side of the periodic table Figure are elements classed metals highlighted in gray, green, yellow, and pink , and elements on the right shown in blue are nonmetals. On the far right in orange are a group of elements know as noble gases. A molecule is a group of atoms bonded together, representing the smallest fundamental unit of a chemical compound that can take part in a chemical reaction.

For instance, a molecule of water —chemical formula, H 2 O —is made up of two hydrogen atoms and one oxygen atom Figure Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together in a defined spatial arrangement by chemical bonds. A ll minerals are chemical compounds, but by comparison relatively few compounds are naturally occurring minerals! Chemical bonds are discussed below.

Examples of mixtures include rocks, magma molten rock air, and seawater. Chemical formulas may be simple text designations showing the ratio of elements, or may be represented by graphic means showing relationships orientation and bonding between elements within molecules, as illustrated with caffeine in Figure A field of galaxies. A spiral galaxy. An elliptical galaxy Fig. Our galaxy is about , to , light-years in diameter and contains over billion stars. Our Solar System resides roughly 27, light-years away from the Galactic Center. The light we observe from object in space has travel great distances measured in light years.

This means that distant objects in deep space we see on Earth today have long since changed or moved Figure The Hertzsprung-Russell Diagram illustrates classification of stars based on star size, temperature, and intensity. The life cycle of stars depends primarily on their mass and composition. Illustration of the life cycle of stars from their formation in nebulae to their ultimate fate of collapsing and exploding to form white dwarfs, neutron stars, or black holes, depending on their mass. Carina Nebula , a part of our Milky Way Galaxy where new stars are forming and emerging from a gas and dust cloud in what is commonly called a stellar nursery.

Supernovas are great explosions that partially to completely demolish aging massive stars, releasing new matter and gas to create a new generation of stars in newly created nebula. The Horsehead Nebula , located in the constellation Orion, is , mostly dust. Bright spots in the nebula are associated with newly forming stars.

The Crab Nebula is the remnant of a supernova recorded in A. The Crab Nebula now spans about 10 light years and has a neutron star at its center. The Ring Nebula is located about 2, light years from Earth. The nebula is a gas shroud about a light year in diameter that surround a dying star.

The Hour Glass Nebula discovered by the Hubble Telescope is an unusual young planetary nebula located about 8, light years away. The 4 Inner Rocky Planets Fig. Mercury Fig. Venus Fig. Earth Fig. Jupiter Fig. Saturn Fig. Uranus Fig. Chapter 1 - Introduction to Earth Science. Click on images throughout this website for a larger view.

What is Earth Science? Geology is the study of the Earth. The scientific study of the origin, history, and structure of the Earth. The structure of a specific region of the Earth's crust. And, the scientific study of the origin, history, and structure of the solid matter of a celestial body. Historical geology is dependent on concepts and order of events related to deep time, as defined by a geologic time scale. Hydrology is the branch of science of the Earth's water resources, especially its movement in relation to land. Oceanography is the branch of science concerned with the physical and biological properties of the world's oceans, seas, and coastal marine environments.

Meteorology is the branch of science concerned with atmospheric processes and phenomena, including weather. Astronomy is the branch of science that concerns celestial objects in space, and physical Universe as a whole. The physical environments of other planets and objects in the Solar System provide insights into what is happening here on Earth utilizing space-based observation of the Earth's systems earth, water, and air.

Note that astronomy and astrology are not the same. Astrology is the metaphysical study of the movement of celestial objects and how their motions are used to interpret their influence on human affairs. Astrology is not discussed in this course. What do earth scientists do? What is the difference between earth sciences and geology? The term earth science is a broad term that integrates many aspects of science, and includes geology. Geology is an older discipline that primarily focuses of the solid earth, earth materials and resources, and processes shaping the Earth's surface.

Geologists consider themselves earth scientists, but not all earth scientists are geologists. However, both earth science and geology involves close collaboration with chemists, physicists, geographers, mathematicians, hydrologists, biologists, environmentalists, etc. Much of the modern work of earth sciences involved data collection and computer modeling such as manipulating satellite images and data. Many Federal and State organizations employ earth scientists. Many geologists find employment through the Federal Government's employment website: www.

For instance, in California, many earth scientists are employed within the branches of the California Department of Conservation , and are involved in all aspects of water resource management, earthquakes and other natural hazard investigations, coastal and marine resources, mines and mineral resources, etc. Many science teachers in public schools have degrees in earth science and related fields! The Scientific Method The scientific method is how scientific ideas are tested and validated and applies to research conducted in nearly all professions.

Define science, observation, hypothesis, fact, theory, scientific law, and scientific methods. Science is the systematic knowledge of the physical or material world gained through observation and experimentation. The overall goal of science is to understand how the natural world works. The fundamental assumption of science is that the natural world behaves in a consistent and predictable manner.

The scientific method involves the observation of phenomena, the formulation of a hypothesis concerning the phenomena, experimentation to demonstrate the truth or falseness of the hypothesis, and a conclusion that validates or modifies the hypothesis. Observation is the act of noting and recording something, such as a phenomenon , with instruments, in order to gain information. An example is the collection for data for temperature, oxygen levels, and pollutants in seawater at different depths in a harbor to monitor water quality for sea life protection.

A fact is knowledge or information based on real occurrences; something demonstrated to exist or known to have existed. A hypothesis is a tentative explanation for an observation, phenomenon, or scientific problem that can be tested by further investigation. An example of the testable hypotheses: Observed high levels of certain types of bacteria in seawater samples from a harbor might be linked to an influx of raw sewage leaking from a nearby sewage treatment facility.

A theory is a set of statements or principles devised to explain a group of facts or phenomena, especially one that has been repeatedly tested or is widely accepted and can be used to make predictions about natural phenomena. Note that in science the word theory means something far more certain and concrete than the popular use of the word, which we can define as an assumption based on limited information.

Established scientific theories are based on vast amounts of information and knowledge, giving us high confidence that they are correct. Science is dynamic. As new information becomes available based on new methods of analysis, observations, experimentation, facts scientific theories can be modified, expanded, or even rejected as newly tested information and ideas become available.

Making assumptions can be a dangerous thing! An assumption is a thing or idea that is accepted as certain to happen, without proof. Misinterpreted observations can easily be used as proof or evidence in helping to establish a fact or resolve the truth of a statement. However, assumptions are often used as guiding principles in decision making when proof or facts are not resolved or accepted. Classic assumptions in history include ideas such as the Earth is flat , or the Earth is the center of the Universe.

Throughout history, political, religious, economic special interests, and strongly-held societal beliefs have been used as underlying assumptions; sometimes they hold true, others are often proven wrong by new scientific evidence. The term educated guess a hypothesis based on some related knowledge and experience, and therefore likely to be correct may be no more than an assumption.

Example 1: Attendance vs. Grade This example is a very valuable start to a college course! Use the scientific method to evaluate the data on this table comparing two variable factors : student attendance number of classes missed in an introductory science class compared with final grades of students in three classes. Discuss observations , facts , assumptions, hypotheses , and theories. How can these hypotheses be tested? What other factors not listed might explain observable facts? What would it take to make these hypotheses into a proven theory?

Example 2: Beach Sand vs. River Sand A common assignment used in introductory geology courses is to examine and describe characteristics similarities and differences in the nature of river sand and beach sand. Use the scientific method to make observations using these four microscope images of sand samples 2 from river deposits, 2 from beach deposits. Use observations to make hypotheses about why the sample have identifiable characteristics unique to their origin.

Can you make some hypotheses about some of the changes that occur as sand gradually migrates from source areas in upland regions to where sand accumulates on beaches along coastlines? Can you come up with suggestions for experiments to test these hypotheses that would support a theory of the character and origin of sand in different environmental settings? Special note : this topic is covered in more detail in later chapters. Important Concepts In Chemistry and Physics The following sections provide basic background information that are essential to understanding the physical and chemical properties of matter, particularly related to natural earth materials rocks, seawater, air, organic matter, etc.

Basic chemistry concepts needed to be understood for this geology course include:. A conceptual view of an atom. Atoms are composed of protons, neutrons , and electrons. The periodic table of the elements is an arrangement of the elements based on atomic number number of protons in an atom. Graphic illustration of a water molecule composed of two hydrogen atoms bonded to an oxygen atom. Chemical formulas for the caffeine molecule text and illustration versions.

Chemical Bonds Molecular compounds are held together on an atomic level by chemical bonds. Chemical bonds are persistent forces of attraction between atoms or molecule caused by electrostatic forces positive or negative charges or the sharing of electrons between bonded atoms. Three types of chemical bonds include ionic bonds , metallic bonds , and covalent bonds. The types of chemical bond influence the physical properties of the molecular compounds they form.

Ionic Bonds Molecular compounds held together by ionic bonds are salts. An ionic bond is a chemical bond between two oppositely charged ions. Typically, metals lose valence electrons loose electrons in their outer shell of orbiting electrons to become positively charged cations , whereas the nonmetal accepts electrons to become negatively charged anions. Salts readily dissolve in water as their charged ions are attracted to parts of water molecules that can also have positive and negative charges. As water evaporates, the ions dissolved in water will precipitate again as salts Figures and Natural salts like halite NaCl and gypsum CaSO 4 are generally soft minerals and can precipitate from and dissolve in water.

Metallic Bonds Metals are held together by metallic bonds. Compounds with metallic bonds transmit electricity. With metallic bonds, the valence electrons disassociated from orbiting a single atom and become more of a cloud electrons that surround the positively charged nuclei of interacting metallic ions.

Metalloids are intermediate between those of metals and solid nonmetals. Although most elements are metals all those on the left and center parts of the Periodic Table , only a few elements occur naturally in metallic form including gold, platinum, copper, iron, and mercury in liquid form. Examples if minerals that are metalloid compounds include pyrite FeS 2 and magnetite Fe 3 O 4 Figure Covalent Bonds Molecular compounds held together by covalent bonds are non-metallic compounds.

Covalent bonds occur when two or more atoms share orbiting electrons, creating more stability in the valence shell of electrons between the bonding elements. These materials can form crystal complexes and do not transmit electricity and tend to be harder, more durable compounds. For instance, most gem minerals are non-metallic compounds with covalent bonds.

The mineral quartz SiO 2 is a non-metallic crystalline compound see Figure Van der Waals Force and Friction Van der Waals forces bonds are weak, nonspecific forces between molecules and include attractions and repulsions between atoms, molecules, and surfaces. Van der Waals forces are responsible for friction and what makes water sticky adhesive to objects. Salt crystals are held together by ionic bonds. Salt compounds dissolve in and precipitate from water. This view shows salt crystals precipitating on a dry lakebed in Death Valley, California.

Metallic bonds occur in metallic minerals like native copper and gold and metalloid minerals like magnetite and pyrite. Most minerals are non-metallic crystalline compounds held together by covalent bonds and will not transmit electricity. Isotopes and Radioactivity Many elements have one or more isotopes.

Isotopes are of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties. Some isotopes are not stable and ultimately break down or change into other elements. We call such isotopes r adioactive. Many elements have both stable and radioactive isotopes.

For example, the element carbon has 3 isotopes: 12 C and 13 C are stable, whereas 14 C is unstable and will undergo radioactive decay. All there isotopes have 6 protons, but have 6, 7, and 8 neutrons, respectively. In the natural environment there are 80 different elements that have one or more isotopes. Of these, at least stable isotopes that have never been observed to decay. Another 50 isotopes are radioactive these isotopes are called radionuclides.

In most naturally occurring materials the amount of radioactive isotopes is relatively insignificant in measurable concentrations Figure However, with the invention of nuclear weapons, and the numerous nuclear bomb test through the s to the present, and accidents involving poorly designed nuclear power plants, there are now many more radioactive isotopes loose in the environment.

The mixing of these radionuclides in the air, water, and sediments dilute their concentrations, but also disperse them to all regions of the world. For example, the Fukushima Daiichi nuclear disaster associated with the massive earthquake and tsunami in Japan released large amounts of radiation into the marine environment around Japan. The Chernobyl disaster of in the Ukraine released large amounts of radioactive material into the region and atmosphere. Radioactive elements that occur in rocks and minerals include isotopes of potassium, thorium, radium, and uranium. A geiger counter us used to measure materials for radioactivity.

This mean field approach to dynamo theory has been used for decades to study the magnetism of stars, planets, and galaxies. A good overview for the solar case is provided in the review by Charbonneau In general, the solutions to the mean-field equations are classified according to which effects dominate the production of poloidal and toroidal field. One problem arose when helioseismology revealed that the differential rotation profile was nearly conical at mid-latitudes e.

Partly motivated by these difficulties, and also by the fact that magnetic buoyancy instability might lead to the loss of fields amid the convection zone more rapidly than they are regenerated see, e. Later, Charbonneau and MacGregor developed a mean-field model incorporating all the elements that today form part of standard interface dynamo theory, including a solar-like differential rotation, a tachocline, and field generation occuring in spatially distinct regions with toroidal field built mainly in the tachocline and poloidal field built in the convection zone.

Many later papers have built on this basic idea, with various refinements. In our discussion so far, helical convection has been presumed to be the main physical mechanism behind the production of poloidal field from toroidal field with rising convective eddies stretching the field and systematically twisting it, as proposed by Parker b. But other effects can build poloidal field from toroidal as well.

As recognized by Babcock and explored by Leighton , , the decay of tilted active regions at the Solar surface is also a source term for poloidal field, and indeed there is now strong evidence that the reversal of the surface poloidal field is triggered by this decay see, e. These have been partly driven by increasing realization of the strong links between emerging active regions and the reversal of the global field see, e. Almost simultaneously models also began to include the effects of meridional circulation: e. The meridional circulation plays a pivotal role in the behavior of this model and many others like it, by transporting poloidal field from regions near the surface to the bottom of the convection zone, where it is converted into toroidal field by shear Jouve and Brun b.

At the most fundamental level, there is still uncertainty over the extent to which mean-field dynamo theory is applicable to the Sun at all, given that the former in the incarnations usually adopted formally assumes conditions that manifestly do not occur in the Solar interior see, e. Much attention is now focused on the interaction between small-scale growing modes of the dynamo and large-scale ones, and the mediation of these by shear see, e.

We will return to discussion of some of these issues in Sect. Even within the specific framework of mean-field dynamo theory, however, central open questions involve the relative importance of the tachocline, meridional circulations, induction by helical convection, turbulent diffusivity, and magnetic pumping—which the astute reader will have noticed are most of the elements involved in the dynamo in the first place. It seems safe to say that at present, hybrid mean-field models incorporating all evident sources of poloidal field give the best agreement with observations see, e.

In light of the central role that meridional flows play in many of these models e. We will return briefly to these measurements in Sect. Many of the mean-field concepts developed for the solar dynamo have naturally been applied to the more general stellar dynamo problem as well. As in the solar case, there is little consensus regarding which effects are likely to be most important for which stars, so we note only a few broad points.

So, too, does the evident link between surface magnetism as traced by, e. Together, these suggest that for stars across a broad swath of the H-R diagram, both convection and rotation possibly including internal differential rotation play major roles in building the field, whether directly or indirectly. The observational suggestion that cycle periods and rotation are linked see, e. Clearly the surface magnetism is sensitive to both convection and rotation at some level, but how these all conspire to yield the observed trends is not yet clear.

For recent efforts, see for example Blackman and Owen and Blackman and Thomas Together, these would suggest that more rapid rotation should imply longer cycle periods if the flux transport dynamo were dominant unless for instance the advection path is modified to be shorter by considering multi-cellular flows. So depending on the profiles of the various physical ingredients used in this class of mean field dynamo models different trends can be obtained that can be directly confronted to observational ones.

Finally, we note that it is of course possible—and indeed likely—that different classes of dynamo models may more closely approximate the behaviour that arises in stars of different masses and ages. More generally, even if some stars are well-described within the confines of MFT, others may not be; for example as discussed more thoroughly in Sect. In this section, we have discussed a variety of different dynamo mechanisms, including some that fit within the bounds of mean-field theory and others that do not. Ideally, we would be able to list observational features that clearly distinguish these models from one another.

Key testable elements might include the rotational dependence of different models, their propensity to exhibit magnetic cycles and the period of such cycles , and the strength and morphology of the magnetism. Unfortunately, the situation is not so clear cut. Many broad classes of models make similar predictions about the nature of the observable magnetism, or can be adjusted to do so; meanwhile some of the other conceptual models discussed above have not yet been developed to the point where they can really be compared to observations.

Part of the problem is that the properties of the observable field may ultimately encode more information about the way in which the field saturates nonlinearly than the way it which it is built kinematically. A light-hearted summary of some observable features of selected dynamo models and objects. See text for discussion and details. The entries in this table require some explanation. For a thorough summary, we again refer to Brandenburg and Subramanian and Charbonneau By the former, we really mean any model in which the nonlinear effect of strong fields is crucial in subsequent field evolution; the latter refers to the chaotic stretching of field lines described above.

Finally, for comparison we also summarize what is found in 3D global MHD simulations as described in Sect. Clearly, in a summary of this form some important details are lost, so the next few paragraphs provide some clarifications about the spatial structure, rotational dependence, and temporal variability of these models. First, consider the spatial structure of the fields.

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  8. The global-scale simulations and the Sun both exhibit power on a broad range of scales; in simulations, as described in Sect. Global simulations exhibit an enormous variety of behavior, with cyclical, steady, or chaotic solutions all possible see Sect. The Sun, of course, exhibits a regular magnetic cycle with large-scale patterns of field emergence and propagation—though it also possesses small-scale magnetism that contains enormously more energy than that in the large-scale field.

    Not all observed stellar magnetic fields owe their existence to contemporary dynamo action. As noted above, the characteristic Ohmic decay time for large-scale magnetism in a star is typically of order Gyr or more. A relic field, produced for instance as part of the star formation process or by dynamo action on the pre-main-sequence phase, might therefore persist throughout the entire main-sequence lifetime of all but the least massive stars.

    Several recent reviews have discussed aspects of such fields; see, in particular, the recent review by Braithwaite and Spruit for an overview of field evolution in non-convective stars. We note here only a few brief points regarding the strengths such fields might reach, their stability over time, and some aspects of their appearance at the stellar surface. The field strengths that could be reached in principle are quite high: for example, simulations of the collapse of magnetized molecular clouds, adopting reasonable initial values of the mass-to-flux ratio see, e.

    How such strong fields would interact with convection occurring on the pre-main-sequence is unclear, but for example Moss argued that at least some of the field implanted by the star formation process would survive to the main sequence. At the opposite extreme, it is not entirely clear what would set the minimum possible strength of fossil fields. In all cases, a central role is played by whether the field configurations are stable for intervals comparable to the main-sequence lifetime of the star, so we turn to that topic next.

    Cartoons illustrating the instability of purely toroidal and poloidal fields. If differential rotation is initially present, then in principle the energy in this flow might be tapped, to amplify an initially weak magnetic field. Magnetic buoyancy instabilities should also occur at sufficiently strong field strengths, of course, but in the presence of strong stratification Spruit , argued the Tayler instability would arise first. These might then be stretched anew, allowing the dynamo to progress, ultimately at the expense of the kinetic energy in the differential rotation, unless this is actively maintained by some other agent.

    Various technical complications, largely beyond the scope of this review, may render this mechanism somewhat more complex than it at first seems. For the conceptually related problem of determining the mean emf arising from magnetic buoyancy instabilities, see for example Davies and Hughes Ultimately, to help elucidate the circumstances under which such dynamo action may occur, the character of the resulting fields, and their consequences e.

    Sunspots have been observed for centuries but it is only during the modern era that a clear link between their darkness and the presence of strong magnetic fields inhibiting convective heat transport has been made. Currently it is believed that the origin of magnetic sunspots is due to the emergence of magnetic flux ropes created by turbulence and shear, either in the tachocline as often assumed Parker b , or in the near surface shear layer Brandenburg An alternative to the rise of magnetic flux rope has been proposed by Stein and Nordlund They consider the rise of a uniform horizontal field through a convective layer and observe the formation of intense field concentration akin to a spot.

    It remains to be seen if such a scenario can lead to the formation of a penumbra around the magnetic spot and flow like the evershed effect Rempel Complex sunspot groups of mixed polarities associated to active regions are ideal locations for eruptive events such as flares or CMEs. Understanding flux emergence through the convective granular surface into the chromosphere and the associated sunspot magnetic topology and dynamics is thus key to better characterize solar activity.

    In earlier studies the concept of thin magnetic flux tube was used Spruit ; Spruit and Ballegooijen ; Spruit and Roberts and magnetic ropes were rising in a quiescent atmosphere. In the more recent numerical simulations, fully developed convective flows act on the magnetic structures, resulting in more complex evolution and spatial structuring of the emerging flux. Shown on the left is the longitudinal component of the magnetic field with red denoting positive polarity rendered with magnetic field lines that form a large scale magnetic wreaths around the equator.

    We note the clear radial rise of the structure. We refer the interested reader to the Living Review by Fan for a thorough discussion of the physical processes associated to flux emergence and for a detailed accounting of the various theoretical and numerical studies done on this topic. Sunspots can be used as prototypes of star spots as discussed in detail in Schrijver Solar surface flux transport or photometric models have been used to reproduce the solar magnetic flux and light modulations over the year cycle and can be extended to other stars e.

    Indeed by analogy to the dimming of light that sunspots create as they pass on the surface of the Sun, light modulation in photometric observations of stars have been associated to starspots. It is an ill-posed problem. Many configurations of spot number, size or distribution can reproduced a given light curves, but Monte-Carlo techniques or Bayesian techniques can help to find the optimal solutions.

    These models do not generally seek to understand the physics formation, structure and evolution of star spots, in contrast to the 3-D MHD simulations discussed above. Still they can provide useful information on stellar spot distribution size, number, location.

    Top inversion of the 3-D structure of a starspot on AU Mic using spectropolarimetric technique at various line depth formation. A field of 3. Image reproduced by permission from Berdyugina , copyright by ASP. Filled and open circles represent the dominant and secondary active longitudes respectively. We note in each hemisphere two bands roughly degree of longitude apart, with altering intensity levels known as the flip-flop phenomenon. Other important questions naturally arise: How intense and large can starspots be? Can they emerge at different latitudes, closer to the polar region than in solar case?

    Spectropolarimetric maps have recently brought partial answers to these questions. For instance young active stars which spin rapidly seem to harbor large polar spots Strassmeier ; Schrijver and Title Strassmeier even reported, in the evolved K0III primary star of XX Tri, a giant star spot larger than the whole Sun and more than 10, times larger than the largest sunspot ever recorded. Hence all evidence indicates that starspots are ubiquitous in active stars and that they can be detected at all latitudes, with a tendency for fast rotators to harbor polar spots.

    They confirm that when the rotation of the star is fast, star spots emerge at high latitude, forming large polar caps. We refer to Berdyugina , Strassmeier for recent overviews of starspots, their size, lifetime, ocurrence and even their radial structure by using various spectral lines to probe various heights within the stellar atmosphere. We show in Fig. We also refer to the work of Berdyugina and Usoskin for an analysis of active longitudes e. This must come about when both activity sites reach an equivalent level of intensity in the observed field.

    It has been named the flip-flop phenomenon. The active longitude needs to be tracked by substracting off the drift due to the surface differential rotation. In Fig. As stars evolve on the main sequence a complex feedback loop operates between their level of magnetic activity and their rotation rate.

    Through magnetic wind braking solar-like stars spin down as they age old solar-like stars being on average slow rotators. The change of magnetic field amplitude and possibly geometry over the secular evolution of stars has been named magnetochronology in echo to the term used for rotational evolution.

    We have discussed in the previous sections in detail how stellar dynamos operate and we will summarize the recent findings through nonlinear numerical simulations in the next sections. Here we wish to discuss briefly the current status of stellar wind models, in particular of solar-like stars for which the main driver is thermal pressure, and how magnetic field amplitude and geometry influence the corona and the torque applied by stellar winds.

    Stellar rotation history shown using observations of open clusters and 2-layers stellar rotation models. The solid and dash lines correspond to the convection and radiative interior rotation evolution. We note the convergence of the rotational evolution curves by the age of the Sun shown as an open circle.

    Another important property deduced from observations of the rotation rate of stars in open clusters is that their spin down time scale seems to depend on stellar mass. For instance, it is observed that F-type stars spin down faster than M-type stars until they reach the converged sequence e. On that converged sequence, when stars are no more in the saturated rotation regime, the braking time scale seems to be larger for F-type stars. Such a change of behavior could for instance be explained by different levels of braking efficiency by stellar winds.

    These models help understanding the rotational evolution of stars in the large, but for instance for low mass stars some difficulty remains Brown Stellar spin-down time scale in Myr for saturated and unsaturated rotation state versus stellar mass. Note that 3 group of curves green , blue and black out of 5 are showing the same overall behavior: a longer spin down time scale for increasing stellar mass in the unsaturated state and by contrast a decreasing time scale in the saturated rotational regime.

    Influence of rotation and magnetic geometry on stellar wind structure and velocity profile. Top row slow rotators, bottom row fast rotators. Note also the collimation of the magnetic field line at high latitude due to the pressure gradient of the longitudinal field. It gets closer to the star as the field geometry becomes more complex.

    It also moves closer to the surface due to the magneto-centrifugal effect that contributes more and more efficiently to accelerate the wind the faster the star rotates. This effect is just analogous to the motion of a bead free to move on a swinging rope: it will tend to move to its end with a speed that will increase as the rope rotates faster and faster. Left 2.

    Shown is the solar wind speed computed at 15 solar radius, with dark tones denoting slow speed. Another important ingredient of realistic stellar wind model is the physical description of the acceleration region, e. Hence, a better description of the thermodynamics of the low corona and transition region is key. Some first attempts to do so have been reported in Schwadron and McComas , Suzuki and Si , Cranmer and Saar and references therein. Stellar winds also change on short time scales, as for instance in the Sun during the rising and declining phases of the year cycle see Fig. PFSS-like models easily reconstruct the large scale coronal magnetic field geometry, by setting an open source surface at 2.

    As shown in Fig. Magnetic Prandlt versus magnetic Reynolds numbers parameter space diagram. Numerical simulations are in the upper left corner , while laboratory experiments are in the lower left. The Sun is in the lower right corner , the most extreme one. More likely and less likely route for future numerical simulations are tentatively indicated.

    At a certain level of abstraction, all stars share certain unifying physical features that likely control the production of magnetic fields: they rotate, they are spherical, they are generally very good conductors throughout most of their interiors. Many groups have therefore turned to simulations that explore field generation in idealized objects sharing these basic properties, in the hope that many features of the idealized problem may prove to be robust, while necessarily ignoring other attributes peculiar to one type of star or another.

    Other models have chosen to focus on specific objects or problems in more detail, capturing for example surface granulation with great fidelity, while missing other aspects e. We will discuss examples of both types of simulations below, but have chosen to organize our discussion by object i. We have chosen this organisational approach partly because so many different elements change in going from one type of object to another—aspect ratio, location of the convection zone, level of energy input, etc.

    Further, many authors have chosen to frame their simulations as being relevant to one type of object or another, rather than as abstract fluid mechanical problems, and our categorisation below reflects this. We must caution, though, that while the basic results of any given simulation are not usually controversial most of the dynamo codes in use today are solving the MHD equations under similar approximations , their relevance to stars or planets is less clear-cut.

    We will return to this issue in specific instances below. First, we recall the most basic properties that, from a fluids perspective, separate one star from another. Though essentially the same processes operate at some level in all convective stars, the balance between them changes. Particularly great effects appear to come from the geometry of the system, from the relative influence of rotation relative to other effects buoyancy driving or viscosity, for example , and from stratification. In a fully-convective M-dwarf, by comparison, the same elements are all present but their relative importance is altered: convection occurs in the full sphere and is weaker, since it is required to carry less energy outwards , rotation is usually much more significant in the dynamics, and the stratification is quite strong.

    Other, subtler effects related to heat transport can play roles as well: in young stars and very low-mass objects, for example, the luminosity is partly from gravitational contraction and is a strong function of time, and we might expect this to lend some peculiarities to the dynamo process. This, for example, means that a fully convective M-dwarf is not precisely analogous to a pre-main-sequence star, though the two share many similarities. Put another way: even an isentropic low-mass stellar interior would, assuming radiative opacities from a typical 1-D stellar model, have a non-negligible radiative flux in some regions.

    These broad differences help motivate our discussion of simulations below. Before describing the results of these simulations, a few comments on the numerical methods and codes used to produce them are appropriate. Historically, many workers studying turbulent flows have turned to spectral methods e. Broadly, these have long been attractive because of their excellent convergence properties: for smooth functions they converge exponentially as the number of modes is increased in contrast to, e.

    However, they are typically less well-suited to problems with sharp discontinuities e. Still, for convection in main-sequence stars or planets—which remains comfortably subsonic in most instances—spectral methods remain very popular, and many of the results quoted below employ this basic technique, though finite-difference and finite-volume methods are also in use. Conversely, many codes developed for broader astrophysical use go to great lengths to capture shocks or other discontinuities, but do not converge as rapidly with increasing resolution.

    For a recent summary of some of these, see Hopkins A brief description of several of the codes in broad use today can be found in Sect. This procedure is straightforward for standard problems, e. In our summary of simulations below, we have generally chosen to present, first and uncritically, what different simulations have shown, and only later to comment on why so many different solutions have been found, and what this implies for the magnetism of real stars.

    Such commentary can be found, for example, in Sect. The Sun, and fluid convection in stars and planets generally, was one of the earliest targets of numerical simulation in astrophysics, and an early application of numerical MHD specifically. This array of research tasks has required a commensurate array of computational approaches: some models choose to focus on a localized region and incorporate radiative transfer allowing remarkably detailed comparison with observations , while others have adopted a coarser description of the dynamics allowing simulations that extend over larger spatial and temporal intervals.


    We will focus in this review primarily on the global-scale simulations, noting only a few key results from smaller-scale and more realistic calculations. This is, we hasten to add, not because the latter are less useful or illuminating—indeed, the agreeement between observations and simulations of near-surface convection, for example, is stunning. Global simulations of solar convection began with the calculations by Peter Gilman and collaborators e. At first the models were Boussinesq and linear; later calculations, beginning with the work of Gary Glatzmaier Glatzmaier , adopted the anelastic approximation Ogura and Phillips ; Gough , which essentially filters out sound waves but includes the overall density stratification.

    The flows modeled were complex and time-dependent, even if still fairly laminar. With the advent of increasing computational power, simulations began to explore flows less constrained by the effects of viscosity and thermal and magnetic diffusivity, and to encompass stronger density stratifications. The basic approach pioneered by Gilman and Glatzmaier has continued to flourish in the past few decades, and several codes in wide use today borrow at some level from this legacy: e.

    A few other anelastic codes were developed independently e. The recently-developed Rayleigh code described in Featherstone and Hindman a also adopts the same basic principles as these earlier code, and is as of this writing planned for public release in Other groups have tackled the global-scale convection problem using fully compressible methods—see, e.

    Broadly, there has been a pleasing concordance between the results from these different groups and codes: all agree, more or less, on the sense of angular momentum transport in various parameter regimes, all agree that both cyclical and steady solutions to the dynamo problem are possible in some cases, and so forth. Though it is sometimes difficult to compare results from the models precisely—e.

    In most cases these have modeled only the convective unstable envelope, but some calculations e. The simulations described here seek to capture some of the large-scale attributes of solar flows and magnetic fields. Every simulation resolves only a finite range of spatial scales, from the overall size of the system being modeled down to a smaller level set by numerical limitations.

    With this caveat firmly in place, we note some features that have emerged robustly from a variety of simulations.

    The ‘first’ stars

    Image reproduced by permission from Gilman , copyright by AAS. The magnetism in these simulations was intense and small-scale within the convection zone, but was accompanied by somewhat larger-scale, more organized structures with clear antisymmetric parity below its base. A sampling of these results is shown in Fig. These simulations did not, however, show any reversals of polarity at all, much less an orderly cycle. The fields imprint through both the convective envelope and part of the stable region below it, and are strongest just below the interface between these regions.

    These represented, at the time, the closest contact any global simulation had yet made with the cyclical solar dynamo. But several major discrepancies with observations persisted: most significantly, no equatorward migration of the magnetic field was obtained, and the poloidal and toroidal fields appeared to oscillate in phase whereas in the Sun they are phase-lagged. Other simulations including a simulated tachocline have likewise produced cyclical fields—see, e. Below and in Sect. A wide variety of simulations, intended to model global-scale Solar convection and magnetism in various ways, have as summarized above yielded magnetic fields with large-scale spatial and temporal organization.

    Here we discuss a few broad issues raised by such simulations, and highlight some particularly recent developments that bear on these issues. First, note that while some of the simulations quoted above suggest that a tachocline of shear may be helpful for building large-scale organized fields, it is equally clear that within the parameter regimes probed by many global-scale simulations organized fields are sometimes possible without this layer, too. Examples going back to the early work by Gilman and collaborators abound. Why some of these simulations have cycles and others do not, and what sets the period of any cycles that are present, is not yet well understood.

    That is, it shows some of the symmetry properties expected from simple mean-field models, it exhibits cycles and latitudinal propagation that obey some form of the Parker—Yoshimura rule, its production is linked in part to the helicity of the turbulence, and so forth.

    But all other things being equal, more complex flows often produce more complex fields: i. Determining whether the nonlinearly saturated state in the numerical simulations, which are capturing only the largest scales of motion, bear much resemblance to the state that would result at much higher Rm —and if so, why—is not an easy matter.

    Shown are color contours using Mollweide projection of the radial velocity with a zoom illustrating the increasing small scale aspect of convective flows near the surface left panels ; A, C, E and of the longitudinal component of the magnetic field near the base of the convective envelope right panels ; B, D, F. But the future of solar dynamo theory is probably not as dark—nor present simulations so divorced from reality—as some of these results might suggest. These are sampled in Fig. The parameter regimes reached in these calculations are, however, still somewhat more extreme than can be achieved in most global full-sphere simulations.

    These are also sampled in Fig. Taken together with some of the results quoted above, these results suggest that all coherence is not lost as the simulations march towards higher Rm , and indeed that in some cases higher Rm might help enable large-scale dynamo action rather than act as an impediment to it. To summarise: One theme that emerges from much of the above is that strong rotation as opposed to merely some rotation to break symmetry and shear are generically very helpful, and perhaps essential, to large-scale dynamo action as observed in the Sun and other stars.

    Many specific details about the strength of fields, their spatial morphology, and their time variability are still uncertain, but several of the basic results are not in serious dispute, and are reproduced by independent codes and groups studying disparate physical regimes. To wit: 1 More rapid rotation promotes large-scale field generation.

    This might seem unhelpful in the present context we know how rapidly the Sun rotates! A quantitative, predictive theory that encompasses all these results is not yet available. In the following sections, we will see how these dynamical processes play out in models of other stars as well. Image reproduced by permission from von Rekowski and Brandenburg , copyright by Wiley. Right scaling of differential rotation contrast versus Reynolds number in a model of a young solar-like star.

    What impact does the high rotation rate have on turbulent convection, mean flows and dynamo action in stars? These simulations share common features with simulations of solar-like stars discussed in Sect. Young stars rotate fast and for some period of their infancy are fully convective. They found that differential rotation amplitudes in the models are sensitive to the degree of turbulence of the convection zone, a more turbulent state yielding a stronger differential rotation, but that effect tends to saturate see Fig.

    The differential rotation profile becomes more cylindrical for faster rotation, even though the thermal wind is strengthening, but not enough to compensate the increased spin rates. Bessolaz and Brun a have looked at the influence of the aspect ratio on turbulent convection and resulting mean flows in a young star, see Fig.

    They show that larger aspect ratio yield more solar-like differential rotation e. They showed that in order to have a weak dipole as observed by spectropolarimetric techniques one must choose carefully the set of fluid parameters.

    Pulsating Variable Stars

    Left surface radial convective velocity for a young, rapidly rotating star, red tones correspond to upflows, from Bessolaz and Brun a ; right 3-D dynamo simulations of a young solar like-star BPtau and comparison with observed field Bessolaz and Brun b. During the fully convective phase of PMS stars, dynamo action is building intense magnetic fields. Moss argues that more massive stars tend to conserve their fossil field more easily than later type stars for which turbulent convection motions have more time to tangle the field to small scales, hence speeding up their Ohmic diffusive decay.

    Models of solar-like stars: Left 1-D stellar model computed with the CESAM code Morel showing the mass contained in the convective envelope of solar-like stars versus stellar mass, computed for 4 mass bins: 0. Right Color contours of the meridional streamfunction achieved in stellar convection models of G-K stars rotating at the solar rate realized with the ASH code. The images have been scaled to take into account the relative stellar radius difference between a G0 and K7 star. Red tones correspond to counter-clockwise circulation.

    This large variation of mass content and aspect ratio has direct consequences for heat and angular momentum transport in the convective envelope of solar-like stars, as shown for instance for the meridional circulation realized in 4 different modelled stars in Fig. We note that the latitudinal extent and the number of circulation cells per hemisphere vary significantly from one model to another see also Featherstone and Miesch As we will now see this is due primarily to the relative influence of the Coriolis force on the convective flow.

    Models with 0. Solar-like—Antisolar-like differential rotation transition in 3-D numerical simulations of rotating global convection. As of today, there are too few 3-D nonlinear dynamo simulations see below that possess a regular magnetic cycle to be able to assess the sensitivity to parameter change of the cycle period. There is, however, evidence that the large scale unicellular meridional circulation often assumed in conceptual Solar dynamo models is unlikely to carry over to other solar-like stars, since 3-D global stellar convective models often exhibit many meridional circulation cells per hemisphere cf.

    Another important trend to explain for stars is their differential rotation profile internal and surface and how it varies with spectral types. As discussed in Sect. But what states do they settle into? Three stellar masses and three rotation rates are being shown. We illustrate in Fig. Larger differential rotation contrasts are found in F-type stars compared to M-type stars. Both these global trends are recovered in numerical simulations as can be seen in Fig. Here depending on the observational studies considered see Sect.

    This comes about from the feedback from the Lorentz force on the mean flow. Butterfly diagram time—latitude plot of toroidal magnetic field in various dynamo simulation of solar-like stars. Various dynamo states as a function of the magnetic Prandlt number Pm. We clearly see the chaotic modulation of the year cycle as Pm is lowered. Image reproduced by permission from Bushby , copyright by the authors. Top left 3-D rendering of the toroidal magnetic field displaying two magnetic wreaths of opposite polarity.

    Top right evolution of the magnetic parity symmetric vs anti-symmetric state with respect to the equator at two depths 0. It is well known in the dynamo community that Pm is another important parameter to study see, e. We can gain insights by turning to nonlinear mean field dynamo studies such as those of Tobias , Moss and Brooke , Bushby This is due to the various magnetic, velocity and diffusive time scales that leads to a highly time dependent behavior when there are far apart as it is the case for low Pm number.

    We illustrate the occurrence of such intermittent dynamo states in Fig. Further, this low Pm simulation also possesses an intermittent state of lower magnetic energy reduction by a factor of 3 as illustrated in Fig. The presence of a tachocline helps organizing the magnetic field at the base of the convection zone as discussed in Sect. Overall, multi-D numerical simulations of convection and dynamo in solar-like stars have recently made tremendous progresses.

    Most observational trends are recovered qualitatively, if not necessarily quantitatively, and cyclic dynamo solutions are now within reach in 3-D global convection simulations. Left to future work is a full assessment of how dynamo action and the magnetic cycle period are controlled including grand minima as stellar parameters are changed.

    We have seen that the large scale mean flows vary significantly so we expect the magnetic activity to do the same; recent publications as surveyed here confirm that this is indeed the case. In comparison to the vast array of models that have attempted to capture elements of the solar dynamo, the literature on dynamos in much lower-mass stars or brown dwarfs is rather limited. In the past few years, there has been a growing awareness that dynamos in these objects may have more in common with those in gaseous planets than with dynamos in say upper-main-sequence stars.

    Below, we briefly review both the sparse literature on low-mass stars specifically, and note some of the most significant parallels with ongoing work in the planetary dynamo community. Their models considered fully convective spheres using a Cartesian grid-based finite-difference code the Pencil code, used widely for other problems in astrophysical MHD. The fields contained structure over a range of spatial scales, with the largest-scale field seemingly quite dominant.

    The models were only weakly stratified, with the central density a factor of about three greater than that at the photosphere, and the influence of rotation as quantified by the Rossby number was comparatively mild. Later, Browning conducted anelastic simulations of the interior of a 0. These models included a stronger density stratification with the surface density about a hundredth that in the interior , and considered a range of different turbulent diffusivities and resolutions, effectively spanning models that ranged from very laminar convection to reasonably complex flows with Reynolds numbers based on the large-scale flows of order at most a few hundred.

    The resulting dynamo-generated fields typically attained strengths of order equipartition relative to the rotating frame , in this case implying fields of a few kG strength. Differential rotation was established in hydrodynamic cases with a solar-like pattern of fast equator and slow poles but wiped out in the MHD ones, mainly as a result of strong Maxwell stresses exerted by the magnetism. A sampling of results from global-scale 3D simulations of convection in fully convective low-mass stars.

    Images reproduced by permission, copyright by AAS. These three distinct sets of global simulations are sampled in Fig. Right fraction of power dissipated Ohmically, as a function of rotational influence, in a sample of Boussinesq simulations Schrinner Images reproduced by permission, copyright by the authors. In many respects, dynamo action in fully convective stars is probably as akin to what occurs in gaseous planets as it is to dynamo action in more massive Solar-like stars.

    The geometry, the strong role of rotation, and the relatively leisurely convective flows all resemble the planetary regime as much as the Solar one. These parallels only go so far: for example, a typical early M-dwarf is still an extremely good conductor throughout its interior i. Still, we draw here on simulations of planetary dynamos as examples of the dynamics that can occur when convection, rotation, and magnetism meet in a deep spherical domain. One of the clearest and most compelling results concerns the influence of rapid rotation on the geometry of the dynamo-generated magnetism.

    These results are sampled in the left panel of Fig. In these parameter regimes—namely, unstratified convection with fixed temperature contrast—more rapid rotation clearly leads to more dipolar fields. Similar results were reported earlier by Sreenivasan and Jones , who effectively varied the influence of inertia by altering the Prandtl number at fixed Ra and Ek. There is still no to our view particularly compelling theory of why the dipole fraction in these simulations scales with rotation rate in this way.

    This behavior is sampled in Fig. Finally, it is also clear that simulations in this regime i. Simulations showing dipolar and multipolar morphologies, as a function of supercriticality and density stratification. Grey region shows regime in which predominantly dipolar solutions are found; blue squares correspond to multipolar dynamos, red circles to dipolar ones, and black crosses to decaying solutions. But it is also clear that the magnetism is influenced by stratification, by the criticality and vigor of the convection, by the geometry, and by interaction with a zonal flow.

    An example of this is sampled in Fig. Other papers have examined the influence of the mass distribution e. Clearly, many different effects conspire to influence the magnetism: strong rotation helps build ordered dipolar fields; strong stratification, or high levels of turbulence as encapsulated in various ways by Re , Rm , and Ra can counteract this to some extent. How these combine in the asymptotically high- Ra , high- Re regime is not totally clear; perhaps more troublingly, it is not always clear even which numerical simulations among those that are tractable today most accurately probe this regime.

    As one example, it is currently possible to conduct calculations at high Rm , or to run calculations in which rotation dominates over inertial forces, but it is difficult to do both at the same time. Because the Rossby number Ro is the ratio of inertial to Coriolis terms, and the Reynolds number is the ratio of inertial to viscous terms, it is computationally easier to address the low- Ro limit—rapid rotation, relative to inertia—if the Reynolds number is also low, and vice versa.

    But simulations are now starting to bridge the gap between these different regimes, and we believe that the most significant findings noted here—including the strong role of rotation, mediated by stratification and turbulence—are likely to be robust. Stars of more than about 1. In this section we discuss some aspects of the core convection occurring in these stars, and the dynamics of the thick stable layer above it, relegating most analysis of convection occurring in the envelopes of such stars to Sect.

    The envelope convection is, after all, solar-like in geometry, even if dissimilar in some other respects. These regions of core convection rotate, and are hot enough to be excellent conductors, so a generic expectation is that they will also act as dynamos. Whether such dynamos might have any observable impact at the surface is another matter, as discussed below. Here we highlight some features of the convective flows in such objects, and the resulting magnetism, as revealed by simulations. Earlier 2-D simulations were conducted by Deupree , and mean-field dynamo models were calculated by Charbonneau and MacGregor Other authors have also considered 1-D models of massive stars to follow the buoyant rise of magnetic structures based on the thin flux tube approximation, see Sect.

    The core convective flows are strikingly different from those realized in the near-surface convection zone of Solar-like stars Sect. These rapid velocities suggest that in many cases the flows are only weakly influenced by rotation, since the Rossby number is then greater than unity except in objects rotating at at least a few percent of the breakup velocity.

    On the other hand, the flows are larger-scale both relative to the size of the system and in absolute terms than in near-surface convection, with the convection here appearing as broad upflows and downflows of low spherical harmonic degree. This is in keeping with the large density scale heights that prevail in these regions; further, there is little evident asymmetry between upflows and downflows again in sharp contrast to what is observed at the surface of the Sun , since neither strong density stratification nor radiative cooling effects which can lead to narrower downflows are present.

    The flows can transport angular momentum as well as heat, and in some cases this this leads to pronounced differential rotation. Broadly, these findings are consistent with trends found in simulations of solar-like stars by Gilman and collaborators in the s and s see Sect. The core convective motions do not, in general, stop precisely at the point where the entropy stratification becomes stable. The extent of the overshooting, and the extent to which it modifies the background stratification, typically depends on a variety of factors including the filling factor of overshooting flows and their Peclet number.

    In most semi-analytical models, the extent of the overshooting region is typically taken to be a fraction of a pressure scale height at the core boundary; broadly, we would summarize the simulations as being consistent with this, but many uncertainties about the stratification within this region, its overall extent, and its dependence on latitude remain. Surprisingly few simulations have addressed the problem of overshooting from convective cores specifically i.

    Much more numerical work has focused on the case where the stable region underlies the convective one—see, e. Magnetic fields and flows in a simulation of dynamo action by core convection in an A-type star. Left overall magnetic field line rendering, showing the toroidal field present in the radiative envelope and the accompanying poloidal field threading the convective core.

    Middle streamlines of columnar flows, with blue tones indicating northward motion and yellow indicating southward. Right kinetic energy red and magnetic energy blue in the equatorial plane at a particular instant in the simulation, viewed from the pole. The evolution of fields and flows in the stable envelope, meanwhile, has been studied in simulations by Braithwaite and Spruit and follow-on papers, as described below; see review by Braithwaite and Spruit In some cases these simply shape a pre-existing field, whereas in others it may be that dynamo action is possible.

    Broadly, the evolution of the magnetism in these simulations confirms many of the analytical expectations highlighted in Sect.

    If differential rotation is initially present, this represents a potential source of free energy, which can in some cases be tapped to amplify an initially weak magnetic field Spruit ; whether this ultimately results in self-sustaining dynamo action is still a matter of some debate. But modeling the full dynamo loop as envisioned by Spruit , and refined in later papers—see, e.

    More generally, the simulations have suggested that the interaction between the different instabilities and flow fields present—including the Tayler instability as envisioned in Spruit , but also for example the magnetorotational instability MRI and the magnetic buoyancy of toroidal fields—can be quite intricate.

    Of course, real massive star cores do have stable stratification, and it is very likely that this will change which modes are preferred in any given instance since radial motions are then strongly suppressed by the stratification, as noted in Spruit , Finally, though not directly intended to model massive stars, we also note that other authors have modeled the same instabilities in other contexts; e. In the stably stratified envelopes of massive stars, buoyancy acts as a restoring force: parcels of fluid displaced upwards quickly find themselves denser and cooler than their surroundings, and so sink; in general the result is an oscillation with a frequency limited by the Brunt-Vaisalla frequency of the medium.

    In the context of massive stars, such motions are likely to be excited both by turbulent overshooting from the core, and by shear stress from the convection. A variety of numerical simulations have attempted to gauge the properties and consequences of these waves. Gravity wave excitation in simulations of massive stars. Shown are temperature and vorticity perturbations left , middle in simulations from Rogers Image reproduced by permission, copyright by AAS.

    The establishment and strengthening of shear by the waves, and some of their possible implications for massive stars, have been studied numerically in depth by, e. Some of their results from Rogers are sampled in Fig. The simulations summarized here, together with basic theory, allow us to draw a few conclusions about the dynamics occurring in the interiors of massive stars. The cores of these stars host vigorous convection, which can act effectively as a magnetic dynamo.

    As a consequence, we expect that every main-sequence massive star possess interior magnetism, and in many cases the field strengths reached may be quite high. The convective flows overshoot into the surrounding stable envelope, mixing material and together with the core convection itself exciting gravity waves that propagate through the envelope. The complex interaction of these waves—with shear, with magnetism and rotation, and with each other—will certainly transport angular momentum and energy within the star; but the exact amplitude and spectrum of the waves, and the form of the rotation profile that ultimately arises as the end state of this interaction, remains somewhat uncertain.

    Magnetism within the stable layer itself is likely ruled mostly by the evolution of the MHD instabilities noted above Tayler, MRI that act, for example, to convert initially purely toroidal fields to mixed poloidal—toroidal ones; if there is differential rotation present, this in turn can amplify the fields so produced, and dynamo action is likely possible in some cases.

    This process, too, has broad implications for angular momentum transport within massive stars on and off the main sequence, and so in turn for their evolution. Several authors have, for example, employed various analytical or semi-analytical prescriptions for the angular momentum transport by a possible Tayler—Spruit dynamo, or by gravity waves, and studied the implications for, e.

    Our ability to forecast what all this implies for observations at the stellar surface is more limited, and many uncertainties remain. The strong magnetic fields generated in the core might begin to rise buoyantly through the envelope, but because this region is stably stratified this rise occurs slowly, mediated by radiative heating into the rising flux tubes MacGregor and Cassinelli Further, as noted in MacDonald and Mullan , compositional gradients that are likely to be present in the star can act to slow this rise, so that it may be difficult for tubes to arrive at the surface within a main-sequence lifetime.

    If they did survive to the surface, it is not at all clear what form the surface field would then take, since we currently have no effective theory of how often, where, or in what multitudes such flux tubes might be produced within the core. Given these issues, and the nature of the surface magnetic trends discussed in Sect. In this case, the surface field arises essentially as the end state of the instabilities described here and in Sect.

    See Sect. Similarly, the gravity waves induced at the core-envelope boundary may well have observable consequences at the surface.