Schools and educational systems play an integral role in individuals’ lives as well as society as a whole, sociologists and educators view that role from many diverse points of view. Functionalists believe that education equips people to perform different functional roles in society. Conflict theorists view education as a means of widening the gap in social inequality. Feminist theorists point to evidence that sexism in education continues to prevent women from achieving a full measure of social equality. Symbolic
interactionists study the dynamics of the classroom, the interactions between students and teachers, and how those affect everyday life. In this section, you will learn about each of these perspectives and review familiar and new theorist such as Piaget, Gardner and Kimberlé Crenshaw.
Functionalism
Functionalists view education as one of the more important social institutions in a society. They contend that education contributes two kinds of functions: manifest (or primary) functions, which are the intended and visible functions of education; and latent (or secondary) functions, which are the hidden and unintended functions.
Manifest Functions
There are several major manifest functions associated with education. The first is socialization. Beginning in preschool and kindergarten, students are taught to practice various societal roles. The French sociologist Émile Durkheim (1858–1917), who established the academic discipline of sociology, characterized schools as “socialization agencies that teach children how to get along with others and prepare them for adult economic roles” (Durkheim 1898). Indeed, it seems that schools have taken on this responsibility in full.
This socialization also involves learning the rules and norms of the society as a whole. In the early days of compulsory education, students learned the dominant culture. Today, since the culture of the United States is increasingly diverse, students may learn a variety of cultural norms, not only that of the dominant culture.
School systems in the United States also transmit the core values of the nation through manifest functions like social control. One of the roles of schools is to teach students conformity to law and respect for authority. Obviously, such respect, given to teachers and administrators, will help a student navigate the school environment. This function also prepares students to enter the workplace and the world at large, where they will continue to be subject to people who have authority over them. Fulfillment of this function rests primarily with classroom teachers and instructors who are with students all day.
Education also provides one of the major methods used by people for upward social mobility. This function is referred to associal placement. College and graduate schools are viewed as vehicles for moving students closer to the careers that will give them the financial freedom and security they seek. As a result, college students are often more motivated to study areas that they believe will be advantageous on the social ladder. A student might value business courses over a class in Victorian poetry because she sees business class as a stronger vehicle for financial success.
Latent Functions
The educational setting introduces students to social networks that might last for years and can help people find jobs after their schooling is complete. Of course, with social media such as Facebook and LinkedIn, these networks are easier than ever to maintain. Another latent function is the ability to work with others in small groups, a skill that is transferable to a workplace.
The educational system, especially as experienced on university campuses, has traditionally provided a place for students to learn about various social issues. This was definitely apparent when the nation went into lock downs and online learning. Students were learning how to navigate and develop relationships with their peers, siblings and families in different ways than before. There were also movements happening within the United States and abroad related to social justice, equity, voting rights, fair pay, health care and many more which were unified with the purpose of changing the political climate of the country.
Manifest and Latent Functions of Education according to functionalist theory, education contributes both manifest and latent functions.
Manifest Functions: Openly stated functions with intended goals
Latent Functions: Hidden, unstated functions with sometimes unintended consequences
Socialization
Courtship
Transmission of culture
Social networks
Social control
Group work
Social placement
Creation of generation gap
Cultural innovation
Political and social integration
Another role of schools, according to functionalist theory, is that of sorting, or classifying students based on academic merit or potential. The most capable students are identified early in schools through testing and classroom achievements. Such students are placed in accelerated programs in anticipation of successful college attendance.
Conflict Theory
Conflict theorists do not believe that public schools reduce social inequality. Rather, they believe that the educational system reinforces and perpetuates social inequalities that arise from differences in class, gender, race, and ethnicity. Where functionalists see education as serving a beneficial role, conflict theorists view it more negatively. To them, educational systems preserve the status quo and push people of lower status into obedience.
The fulfillment of one’s education is closely linked to social class. Students of low socioeconomic status are generally not afforded the same opportunities as students of higher status, no matter how great their academic ability or desire to learn. Picture a student from a working-class home who wants to do well in school. On a Monday, he’s assigned a paper that’s due Friday. Monday evening, he has to babysit his younger sister while his divorced mother works. Tuesday and Wednesday, he works stocking shelves after school until 10:00 p.m. By Thursday, the only day he might have available to work on that assignment, he’s so exhausted he can’t bring himself to start the paper. His mother, though she’d like to help him, is so tired herself that she isn’t able to give him the encouragement or support he needs. And since English is her second language, she has difficulty with some of his educational materials. They also lack a computer and printer at home, which most of his classmates have, so they have to rely on the public library or school system for access to technology. As this story shows, many students from working-class families have to contend with helping out at home, contributing financially to the family, poor study environments and a lack of support from their families. This is a difficult match with education systems that adhere to a traditional curriculum that is more easily understood and completed by students of higher social classes.
Such a situation leads to social class reproduction, extensively studied by French sociologist Pierre Bourdieu. He researched how cultural capital, or cultural knowledge that serves (metaphorically) as currency that helps us navigate a culture, alters the experiences and opportunities available to French students from different social classes. Members of the upper and middle classes have more cultural capital than do families of lower-class status. As a result, the educational system maintains a cycle in which the dominant culture’s values are rewarded. Instruction and tests cater to the dominant culture and leave others struggling to identify with values and competencies outside their social class. For example, there has been a great deal of discussion over what standardized tests such as the SAT truly measure. Many argue that the tests group students by cultural ability rather than by natural intelligence.
The cycle of rewarding those who possess cultural capital is found in formal educational curricula as well as in the hidden curriculum, which refers to the type of nonacademic knowledge that students learn through informal learning and cultural transmission. This hidden curriculum reinforces the positions of those with higher cultural capital and serves to bestow status unequally.
Conflict theorists point to tracking, a formalized sorting system that places students on “tracks” (advanced versus low achievers) that perpetuate inequalities. While educators may believe that students do better in tracked classes because they are with students of similar ability and may have access to more individual attention from teachers, conflict theorists feel that tracking leads to self-fulfilling prophecies in which students live up (or down) to teacher and societal expectations (Education Week 2004).
To conflict theorists, schools play the role of training working-class students to accept and retain their position as lower members of society. They argue that this role is fulfilled through the disparity of resources available to students in richer and poorer neighborhoods as well as through testing (Lauen and Tyson 2008).
IQ tests have been attacked for being biased—for testing cultural knowledge rather than actual intelligence. For example, a test item may ask students what instruments belong in an orchestra. To correctly answer this question requires certain cultural knowledge—knowledge most often held by more affluent people who typically have more exposure to orchestral music. Though experts in testing claim that bias has been eliminated from tests, conflict theorists maintain that this is impossible. These tests, to conflict theorists, are another way in which education does not provide opportunities, but instead maintains an established configuration of power.
Feminist Theory
Feminist theory aims to understand the mechanisms and roots of gender inequality in education, as well as their societal repercussions. Like many other institutions of society, educational systems are characterized by unequal treatment and opportunity for women. Almost two-thirds of the world’s 862 million illiterate people are women, and the illiteracy rate among women is expected to increase in many regions, especially in several African and Asian countries (UNESCO 2005; World Bank 2007).
Women in the United States have been relatively late, historically speaking, to be granted entry to the public university system. In fact, it wasn’t until the establishment of Title IX of the Education Amendments in 1972 that discriminating on the basis of sex in U.S. education programs became illegal. In the United States, there is also a post-education gender disparity between what male and female college graduates earn. A study released in May 2011 showed that, among men and women who graduated from college between 2006 and 2010, men out-earned women by an average of more than $5,000 each year. First-year job earnings for men averaged $33,150; for women the average was $28,000 (Godofsky, Zukin, and van Horn 2011). Similar trends are seen among salaries of professionals in virtually all industries.
When women face limited opportunities for education, their capacity to achieve equal rights, including financial independence, are limited. Feminist theory seeks to promote women’s rights to equal education (and its resultant benefits) across the world.
Grade Inflation: When is an 'A' Really a 'C'?
Consider a large-city newspaper publisher. Ten years ago, when culling résumés for an entry-level copywriter, they were well assured that if they selected a grad with a GPA of 3.7 or higher, they’d have someone with the writing skills to contribute to the workplace on day one. But over the last few years, they’ve noticed that A-level students don’t have the competency evident in the past. More and more, they find themselves in the position of educating new hires in abilities that, in the past, had been mastered during their education.
This story illustrates a growing concern referred to as grade inflation—a term used to describe the observation that the correspondence between letter grades and the achievements they reflect has been changing (in a downward direction) over time. Put simply, what used to be considered C-level, or average, now often earns a student a B, or even an A.
Why is this happening? Research on this emerging issue is ongoing, so no one is quite sure yet. Some cite the alleged shift toward a culture that rewards effort instead of product, i.e., the amount of work a student puts in raises the grade, even if the resulting product is poor quality. Another oft-cited contributor is the pressure many of today’s instructors feel to earn positive course evaluations from their students—records that can tie into teacher compensation, award of tenure, or the future career of a young grad teaching entry-level courses. The fact that these reviews are commonly posted online exacerbates this pressure.
Other studies don’t agree that grade inflation exists at all. In any case, the issue is hotly debated, with many being called upon to conduct research to help us better understand and respond to this trend (National Public Radio 2004; Mansfield 2005).
Symbolic Interactionism
Symbolic Interactionism sees education as one way that labeling theory is seen in action. A symbolic interactionist might say that this labeling has a direct correlation to those who are in power and those who are labeled. For example, low standardized test scores or poor performance in a particular class often lead to a student who is labeled as a low achiever. Such labels are difficult to “shake off,” which can create a self-fulfilling prophecy (Merton 1968).
In his book
High School Confidential
, Jeremy Iverson details his experience as a Stanford graduate posing as a student at a California high school. One of the problems he identifies in his research is that of teachers applying labels that students are never able to lose. One teacher told him, without knowing he was a bright graduate of a top university, that he would never amount to anything (Iverson 2006). Iverson obviously didn’t take this teacher’s false assessment to heart. But when an actual seventeen-year-old student hears this from a person with authority over her, it’s no wonder that the student might begin to “live down to” that label.
The labeling with which symbolic interactionists concern themselves extends to the very degrees that symbolize completion of education. Credentialism embodies the emphasis on certificates or degrees to show that a person has a certain skill, has attained a certain level of education, or has met certain job qualifications. These certificates or degrees serve as a symbol of what a person has achieved, and allows the labeling of that individual.
Indeed, as these examples show, labeling theory can significantly impact a student’s schooling. This is easily seen in the educational setting, as teachers and more powerful social groups within the school dole out labels that are adopted by the entire school population.
Gardner’s Multiple Intelligences Theory
, of which there are currently nine so-called intelligences, listed as follows. (Note: number nine is pretty new on Professor Gardner’s evolving list and is yet to be included in most representative graphics, such as the one below.)
musical-rhythmic and harmonic
visual-spatial
verbal-linguistic
logical-mathematical
bodily-kinesthetic
interpersonal
intrapersonal
naturalist
existential.
Critical Race Theory (CRT)
Kimberle Williams Crenshaw—who coined the term Critical Race Theory defined as "a practice of interrogating the role of race and racism in society that emerged in the legal academy and spread to other fields of scholarship.” (Crenshaw, 2011) This describes this theory as a verb. Here's an example of what this looks like in practice.
Critical Race Theory in Education
Ladson-Billings and Tate (1995) introduced CRT to education by arguing that race has remained undertheorized, and although race has been examined "as a powerful tool for explaining social inequity, the intellectual salience of this theorizing has not been systematically employed in the analysis of educational inequality" (p. 50). After Ladson-Billings and Tate's (1995) seminal article on CRT in education, many authors have applied CRT to educational research (Solorzano, 1998; Tate, 1997).
There are five tenets that CRT scholars have developed that guide the examination of educational equity and racial justice:
Centrality of Race and Racism
:
CRT research within an education context should center race and racism, as well as the intersections of other forms of oppression, such as gender, class, and sexual orientation.
Challenge to the Dominant Perspective
:
CRT in education challenges dominant culture perspectives and centers historically marginalized perspectives.
Commitment to Social Justice:
CRT is consistently rooted in social justice outcomes.
Valuing Experiential Knowledge:
CRT builds on the oral traditions and narratives of Black, Indigenous, and people of color (BIPOC) communities when discerning social inequities.
Interdisciplinary: CRT asserts that scholarly research should reflect multiple perspectives (Solorzano & Bernal, 2001).
Critical Race Theory has also received criticisms by the educational systems as shame blaming or not the history which should be shared in our schools and classrooms.
Critical Reflection and Application Time
What did you hear the General in the video above say and what are your thoughts and feelings of what was said?
In what ways is education shaped by the theories we learned in this chapter, what examples would you add to each of the theories to provide deeper understanding?
Summary
The theories offer insight into how we understand education and how schools play a role in the development of child within Bronfenbrenner's Bio-Ecological Systems Theory. . Functionalists view education as an important social institution that contributes both manifest and latent functions. Functionalists see education as serving the needs of society by preparing students for later roles, or functions, in society. Conflict theorists see schools as a means for perpetuating class, racial-ethnic, and gender inequalities. In the same vein, feminist theory focuses specifically on the mechanisms and roots of gender inequality in education. The theory of symbolic interactionism focuses on education as a means for labeling individuals. Piaget's cognitive development describes the stages of thinking from individual to interpersonal based on interactions and experiences. Gardner incorporates the way we learn based on our diverse array of intelligences. Critical Race Theory calls us to act and identify race and racism in the communities we live and engage as educators.
Education Week
. 2004. “Tracking.”
Education Week
, August 4. Retrieved February 24, 2012.
Godofsky, Jessica, Cliff Zukin, and Carl Van Horn. 2011.
Unfulfilled Expectations: Recent College Graduates Struggle in a Troubled Economy
. New Brunswick, NJ: Rutgers University.
Iverson, Jeremy. 2006.
High School Confidential
. New York: Atria.
Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465–491. doi.org/10.2307/1163320
Lauen, Douglas Lee and Karolyn Tyson. 2008. “Perspectives from the Disciplines: Sociological Contribution to Education Policy Research and Debate.”
AREA Handbook on Education Policy Research
. Retrieved February 24, 2012.
National Public Radio. 2004. “Princeton Takes Steps to Fight ‘Grade Inflation.’”
Day to Day
, April 28.
Mansfield, Harvey C. 2001. “Grade Inflation: It’s Time to Face the Facts.”
The Chronicle of Higher Education
47(30): B24.
Merton, Robert K. 1968.
Social Theory and Social Structure
. New York: Free Press.
Solorzano, D. G. (1998). Critical race theory, race and gender microaggressions, and the experience of Chicana and Chicano scholars. International Journal of Qualitative Studies in Education, 11(1), 121–136.
Solorzano, D. G., & Bernal, D. D. (2001). Examining transformational resistance through a critical race and LatCrit theory framework: Chicana and Chicano students in an urban context.
Urban education
,
36
(3), 308-342.
Tate, W. F., IV. (1997). Critical race theory and education: History, theory, and implications. In M. Apple (Ed.), Review of research in education (Vol. 22., pp. 195–247). American Educational Research Association.
UNESCO. 2005.
Towards Knowledge Societies: UNESCO World Report
. Paris: UNESCO Publishing.
World Bank. 2007.
World Development Report
. Washington, DC: World Bank.


6.5B: Weber’s Model for Bureaucracy
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Learning Objectives
- Describe Weber’s ideal type of bureaucracy and his concept of the “iron cage”
Weberian bureaucracy was a term coined by Max Weber, a notable German sociologist, political economist, and administrative scholar, who contributed to the study of bureaucracy, administrative discourses, and literature during the mid-1800s and early 1900s. In his 1922 masterpiece, Economy and Society, Weber described many ideal types of public administration and governance. His critical study of the bureaucratization of society was one of the most enduring parts of this work. It was Weber who began the study of bureaucracy and whose works led to the popularization of this term. Many aspects of modern public administration date back to him. This is epitomized in the fact that a classic, hierarchically-organized civil service is still called a “Weberian civil service. ”
Weber listed the following as preconditions for the emergence of bureaucracy: the growth in size and density of the population being administered, the growth in complexity of the administrative tasks being carried out, and the existence of a monetary economy requiring a more efficient administrative system. As a result of the development of communication and transportation technologies, like telegraphs and automobiles, a more efficient administration became not only possible but demanded by the public. Accompanying this shift was an increasing democratization and rationalization of culture. This resulted in public demands for a new administrative system that treated all humans equally. Weber’s ideal bureaucracy is characterized by the following:
- hierarchical organization
- delineated lines of authority with fixed areas of activity
- action taken on the basis of, and recorded in, written rules
- bureaucratic officials with expert training
- rules implemented by neutral officials
- and career advancement depending on technical qualifications judged by organization, not individuals
Rational-Legal Authority
Weber identified in bureaucracies a rational-legal authority in which legitimacy is seen as coming from a legal order. The majority of modern bureaucratic officials and political leaders represent this type of authority. However, while recognizing bureaucracy as the most efficient form of organization, and perhaps indispensable for the modern state, Weber also saw it as a threat to individual freedoms. For Weber, the implementation of bureaucracies in government was a kind of rationalization, in which traditional motivators for behavior were cast aside. Instead of utilizing traditions, emotions, or values to motivate behavior, in a bureaucracy, people used rational calculation. Regarding Western societies, Weber called this increasing rationalization an “iron cage” that trapped individuals in systems based solely on efficiency, rational calculation, and control. In his theory, the “iron cage” is the one set of rules and laws that we are all subjected to. According to Weber, the shift from old forms of mobility, like kinship, to new forms, like strict, legal rules, was a direct result of the growth of bureaucracy and capitalism.
Key Points
- Weber listed several preconditions for the emergence of bureaucracy: the growth in size of the population being administered, the growth in complexity of the administrative tasks being carried out, and the existence of a monetary economy requiring a more efficient administrative system.
- Weber identified in bureaucracies a rational-legal authority in which legitimacy is seen as coming from a legal order and the laws enacted within it. This is contrasted with traditional forms of authority, which arose from phenomena like kinship.
- Rationalization describes a transition in society, wherein traditional motivators of behavior, like values, beliefs, and emotions, are replaced with rational calculations.
- Weber termed the increasing rationalization in Western societies an “iron cage” that traps individuals in systems based solely on efficiency, rational calculation and control.
Key Terms
- Rational-legal authority : A form of leadership in which the authority of an organization or a ruling regime is largely tied to legal rationality, legal legitimacy and bureaucracy.
- ideal type : An ideal type is not a particular person or thing that exists in the world, but an extreme form of a concept used by sociologists in theories. For example, although there is not a perfectly “modern” society, the term “modern” is used as an ideal type in certain theories to make large-scale points.
- iron cage : a theory proposed by Max Weber which argues that rationalization and rules trap humans in a figurative “cage” of thought based on rational calculations


8.5A: Phenotypic Analysis
- Distinguish between phenotypic characteristics for Bacteria, Archaea and Eukaryotes
Microorganisms are very diverse. They include bacteria, fungi, algae, and protozoa; microscopic plants (green algae); and animals such as rotifers and planarians. Most microorganisms are unicellular (single-celled), but this is not universal.
Single-celled microorganisms were the first forms of life to develop on earth, approximately 3 billion–4 billion years ago. Further evolution was slow, and for about 3 billion years in the Precambrian eon, all organisms were microscopic. So, for most of the history of life on earth the only forms of life were microorganisms. Bacteria, algae, and fungi have been identified in amber that is 220 million years old, which shows that the morphology of microorganisms has changed little since the Triassic period. When at the end of the 19 th century information began to accumulate about the diversity within the bacterial world, scientists started to include the bacteria in phylogenetic schemes to explain how life on earth may have developed. Some of the early phylogenetic trees of the prokaryote world were morphology-based. Others were based on the then-current ideas on the presumed conditions on our planet at the time that life first developed.
Microorganisms tend to have a relatively rapid evolution. Most microorganisms can reproduce rapidly, and microbes such as bacteria can also freely exchange genes through conjugation, transformation, and transduction, even between widely-divergent species. This horizontal gene transfer, coupled with a high mutation rate and many other means of genetic variation, allows microorganisms to swiftly evolve (via natural selection) to survive in new environments and respond to environmental stresses.
The relationship between the three domains (Bacteria, Archaea, and Eukaryota) is of central importance for understanding the origin of life. Most of the metabolic pathways, which comprise the majority of an organism’s genes, are common between Archaea and Bacteria, while most genes involved in genome expression are common between Archaea and Eukarya. Within prokaryotes, archaeal cell structure is most similar to that of Gram-positive bacteria.
Phenotypic Methods of Classifying and Identifying Microorganisms
Classification seeks to describe the diversity of bacterial species by naming and grouping organisms based on similarities. Microorganisms can be classified on the basis of cell structure, cellular metabolism, or on differences in cell components such as DNA, fatty acids, pigments, antigens, and quinones.
There are some basic differences between Bacteria, Archaea, and Eukaryotes in cell morphology and structure which aid in phenotypic classification and identification:
- Bacteria: lack membrane -bound organelles and can function and reproduce as individual cells, but often aggregate in multicellular colonies. Their genome is usually a single loop of DNA, although they can also harbor small pieces of DNA called plasmids. These plasmids can be transferred between cells through bacterial conjugation. Bacteria are surrounded by a cell wall, which provides strength and rigidity to their cells.
- Archaea: In the past, the differences between bacteria and archaea were not recognized and archaea were classified with bacteria as part of the kingdom Monera. Archaea are also single-celled organisms that lack nuclei. Archaea in fact differ from bacteria in both their genetics and biochemistry. While bacterial cell membranes are made from phosphoglycerides with ester bonds, archaean membranes are made of ether lipids.
- Eukaryotes: Unlike bacteria and archaea, eukaryotes contain organelles such as the cell nucleus, the Golgi apparatus, and mitochondria in their cells. Like bacteria, plant cells have cell walls and contain organelles such as chloroplasts in addition to the organelles in other eukaryotes.
The Gram stain, developed in 1884 by Hans Christian Gram, characterizes bacteria based on the structural characteristics of their cell walls. The thick layers of peptidoglycan in the “Gram-positive” cell wall stain purple, while the thin “Gram-negative” cell wall appears pink. By combining morphology and Gram-staining, most bacteria can be classified as belonging to one of four groups (Gram-positive cocci, Gram-positive bacilli, Gram-negative cocci, and Gram-negative bacilli). Some organisms are best identified by stains other than the Gram stain, particularly mycobacteria or Nocardia, which show acid-fastness on Ziehl–Neelsen or similar stains. Other organisms may need to be identified by their growth in special media, or by other techniques, such as serology.
While these schemes allowed the identification and classification of bacterial strains, it was unclear whether these differences represented variation between distinct species or between strains of the same species. This uncertainty was due to the lack of distinct structures in most bacteria, as well as lateral gene transfer between unrelated species. Due to lateral gene transfer, some closely related bacteria can have very different morphologies and metabolisms. To overcome this uncertainty, modern bacterial classification emphasizes molecular systematics, using genetic techniques such as guanine cytosine ratio determination, genome-genome hybridization, as well as sequencing genes that have not undergone extensive lateral gene transfer, such as the rRNA gene.
Key Points
- The relationship between the three domains ( Bacteria, Archaea, and Eukaryota) is of central importance for understanding the origin of life. Most of the metabolic pathways are common between Archaea and Bacteria, while most genes involved in genome expression are common between Archaea and Eukarya.
- Microorganisms are very diverse. They include bacteria, fungi, algae, and protozoa; microscopic plants, and animals. Single-celled microorganisms were the first forms of life to develop on earth, approximately 3 billion–4 billion years ago.
- The Gram stain characterizes bacteria based on the structural characteristics of their cell walls. By combining morphology and Gram-staining, most bacteria can be classified as belonging to one of 4 groups (Gram-positive cocci, Gram-positive bacilli, Gram-negative cocci, and Gram-negative bacilli).
- There are some basic differences between Bacteria, Archaea, and Eukaryotes in cell morphology and structure which aid in phenotypic classification and identification.
Key Terms
- Gram stain : A method of differentiating bacterial species into two large groups (Gram-positive and Gram-negative).
- microorganism : An organism that is too small to be seen by the unaided eye, especially a single-celled organism, such as a bacterium.
- domain : In the three-domain system, one of three taxa at that rank: Bacteria, Archaea, or Eukaryota.


18: The Cardiovascular System - Blood
Chapter Objectives
- Identify the primary functions of blood, its fluid and cellular components, and its physical characteristics
- Identify the most important proteins and other solutes present in blood plasma
- Describe the formation of the formed element components of blood
- Discuss the structure and function of red blood cells and hemoglobin
- Classify and characterize white blood cells
- Describe the structure of platelets and explain the process of hemostasis
- Explain the significance of AB and Rh blood groups in blood transfusions
- Discuss a variety of blood disorders
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- 18.0: Prelude to Blood
- Single-celled organisms do not need blood. They obtain nutrients directly from and excrete wastes directly into their environment. The human organism cannot do that. Our large, complex bodies need blood to deliver nutrients to and remove wastes from our trillions of cells. The heart pumps blood throughout the body in a network of blood vessels.  The cellular elements—referred to as the formed elements—include red blood cells, white blood cells, and cell fragments called platelets. The extracellular matrix, called plasma, makes blood unique among connective tissues because it is fluid. This fluid, which is mostly water, perpetually suspends the formed elements and enables them to circulate throughout the body within the cardiovascular system.
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- 18.2: Production of the Formed Elements
- Although one type of leukocyte called memory cells can survive for years, most erythrocytes, leukocytes, and platelets normally live only a few hours to a few weeks. Thus, the body must form new blood cells and platelets quickly and continuously. Your body typically replaces the donated plasma within 24 hours and it takes about 4 to 6 weeks to replace the blood cells. The process by which this replacement occurs is called hemopoiesis, or hematopoiesis.
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- 18.3: Erythrocytes
- The erythrocyte, commonly known as a red blood cell (or RBC), is by far the most common formed element: A single drop of blood contains millions of erythrocytes and just thousands of leukocytes. Specifically, males have about 5.4 million erythrocytes per microliter (µL) of blood, and females have approximately 4.8 million per µL. In fact, erythrocytes are estimated to make up about 25 percent of the total cells in the body.
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- 18.4: Leukocytes and Platelets
- The leukocyte, commonly known as a white blood cell (or WBC), is a major component of the body’s defenses against disease. Leukocytes protect the body against invading microorganisms and body cells with mutated DNA, and they clean up debris. Platelets are essential for the repair of blood vessels when damage to them has occurred; they also provide growth factors for healing and repair.
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- 18.5: Hemostasis
- Platelets are key players in hemostasis, the process by which the body seals a ruptured blood vessel and prevents further loss of blood. Although rupture of larger vessels usually requires medical intervention, hemostasis is quite effective in dealing with small, simple wounds. There are three steps to the process: vascular spasm, the formation of a platelet plug, and coagulation (blood clotting). Failure of any of these steps will result in hemorrhage—excessive bleeding.
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- 18.6: Blood Typing
- Blood transfusions in humans were risky procedures until the discovery of the major human blood groups by Karl Landsteiner, an Austrian biologist and physician, in 1900. Until that point, physicians did not understand that death sometimes followed blood transfusions, when the type of donor blood infused into the patient was incompatible with the patient’s own blood. Blood groups are determined by the presence or absence of specific marker molecules on the plasma membranes of erythrocytes.


14.6: Nervous System Worksheet
1. The diagram below is of a nerve cell or neurone.
- i. Add the following labels to the diagram.
- Axon; Myelin sheath; Cell body; Dendrites; Muscle fibres ;
- ii. If you like, colour in the diagram as suggested below.
- Axon - purple;
- Myelin sheath - yellow;
- Cell body - blue;
- Dendrites - green;
- Muscle fibres – red;
- iii. Now indicate the direction that the nerve impulse travels.
2. There are three different kinds of neurone or nerve cell. Match each kind with its function.
- A. Motor neuron; B. Sensory neuron; C. Relay neuron;
| Kind of neurone | Function |
|---|---|
| ................................... |
The nerve cell that carries impulses from a sense receptor to the brain or spinal cord. |
| .................................... | The nerve cell that connects sensory and motor neurons |
| ..................................... |
The nerve cell that transmits impulses from the brain or spinal cord to a muscle or gland |
3. Match the descriptions in the table below with the terms in the list.
- A. Synapse; B. Axon; C. Myelin sheath; D. Nerve impulse; E. Sense receptor; F. Response;
- G.Reflex; H. Cell body; I. Dendrite; J. Nerve; K. Neurotransmitter; L. Axon terminal
| Term | Function |
|---|---|
| .............................. | 1. The long fibre that carries the nerve impulses. |
| .............................. | 2. A bundle of axons. |
| .............................. | 3. The connection between adjacent neurons. |
| ............................... |
4. The chemical secreted into the gap between neurons at a synapse. |
| ............................... | 5. A rapid automatic response to a stimulus. |
| ............................... |
6. The covering of fatty material that speeds up the passage of nerve impulses. |
| ................................... |
7. The structure at the end of an axon that produces neurotransmitters to transmit the nerve impulse across the synapse. |
| ................................ | 8. The high speed signals that pass along the axons of nerve cells. |
| ................................ |
9. The branching filaments that conduct nerve impulses towards the cell. |
| ..................................... |
10. The sense organ or cells that receive stimuli from within and outside the body. |
| ..................................... | 11. The reaction to a stimulus by a muscle or gland. |
| ..................................... | 12.The part of the nerve cell containing the nucleus. |
4. The diagram below shows a cross-section of the spinal cord. Add the following labels to the diagram.
- Central canal; White matter; Dorsal root; Grey matter; Ventral root; Skin;
- Muscle; Sensory neuron; Relay neuron; Motor neuron; Pain receptors in skin
5.
- a) List in order the 3 different neurons involved in a reflex arc from the stimulus to the response.
| Stimulus | ........................... | ........................... | ........................... | Response |
|---|
- b) Name 3 different reflexes found in animals.
Reflex 1..............................
Reflex 2..............................
Reflex 3..............................
6. The diagram below shows the nervous system of a horse. Add the following labels.
- Brain; Spinal cord; Cranial nerves; Spinal nerves; Sciatic nerve; Nerves of the autonomic nervous system; Vagus nerve; Network of nerves to forelimb.
7. Indicate whether the following parts of the nervous system are part of the Central Nervous System CNS) or the Peripheral Nervous System (PNS).
| Part of nervous system | CNS or PNS? |
|---|---|
| Brain | ........................ |
| Autonomic nervous system | ........................ |
| Spinal nerves | ........................ |
| Spinal cord | ........................ |
| Cranial nerves | ......................... |
8. The diagram below shows a section of a dog’s brain. Add the labels in the list below and, if you like, colour in the diagram as suggested.
- Cerebellum - blue;
- Spinal cord - green;
- Medulla oblongata - orange;
- Hypothalamus - purple;
- Pituitary gland - red;
- Cerebral hemispheres – yellow.
9. Match the descriptions below with the terms in the list. You may need to use some terms more than once.
- A. Cerebral hemispheres; B. White matter; C. Cerebellum; D.Medulla oblongata; E. Hypothalamus; F. Pituitary; G. Grey matter; H. Meninges; I. Ventricles; J. Cerebrospinal fluid; K. Sulcus; L. Carotid artery
| Term | Description |
|---|---|
| ............................. | 1. Controls water balance and body temperature. |
| .............................. | 2. Where the respiratory rate is controlled. |
| ............................... |
3. Where posture, balance and voluntary muscle movements are controlled. |
| ............................... |
4. Contains centres governing mental activity, including intelligence, memory, and learning. |
| ............................... |
5. The tough fibrous envelope enclosing the brain and spinal cord. |
| ............................... | 6. The “master” gland of the endocrine system. |
| ............................... | 7. Responsible for instigating voluntary movements. |
| ............................... | 8. The fluid that surrounds the brain and spinal cord. |
| .............................. | 9. Composed of cell bodies and nuclei. |
| .............................. | 10. Composed of axons. |
| ............................... |
11. Where the sensations of sight, sound, taste etc. are interpreted. |
| ................................ | 12. Spaces in the brain filled with cerebral spinal fluid. |
| ................................ | 13. A fold in the cerebral cortex. |
| ................................. | 14. The artery that supplies the brain with oxygenated blood. |
10. Match the descriptions below with the parts of the nervous system in the list. You may need to use some terms more than once.
- A. Autonomic nervous system; B. Central nervous system; C. Peripheral nervous system;
- D. Parasympathetic nervous system; E. Sympathetic nervous system
| Description | Part of the nervous system |
|---|---|
|
1. Part of the nervous system that is composed of the brain and the spinal cord. |
........................ |
|
2. Part of the nervous system that is composed of the cranial and spinal nerves. |
.......................... |
|
3. The part of the peripheral nervous system that regulates the activity of the heart and smooth muscle. |
........................... |
|
4. The part of the autonomic nervous system that increases heart and respiratory rates, increases blood flow to the skeletal muscles and dilates the pupils of the eye. |
............................ |
|
5. The part of the autonomic nervous system that increases gut activity and decreases heart and respiratory rates. |
............................ |
11. Name the nerves described below using the choices in the list.
- Olfactory nerve; Sciatic nerve; Vagus nerve; Optic nerve; Vestibular nerve
| Nerve | Description |
|---|---|
| .......................... |
1. The 8th cranial nerve that carries impulses from the organs of balance and hearing to the brain. |
| ........................... |
2. The 2nd cranial nerve that carries nervous impulses from the retina of the eye to the brain. |
| ............................ | 3. The largest nerve in the body serving the muscles of the leg. |
| ............................ |
4. The 1st cranial nerve that carries impulses from the organ of smell in the nose to the brain. |
| .............................. |
5. The 10th cranial nerve that supplies the pharynx, lungs, heart, stomach and most of the abdominal organs. |


41.3.12: Chapter 13
Case Study
1.
b.
Fluoxetine has a stimulant effect and may interfere with sleep if taken close to bedtime. Therapeutic effects take 4–6 weeks.
2.
a.
If someone has an undiagnosed bipolar disorder, placing them on an antidepressant without a mood stabilizer can induce mania.
Review Questions
1.
b.
The drug blocks muscarinic receptors and causes anticholinergic effects. This results in reduced salivation (xerostomia), decreased peristalsis (constipation), and relaxation of the detrusor muscle, causing urinary retention.
2.
b.
Rapid, pressured speech is a classic sign of mania. If the drug level is considered subtherapeutic, this means it is not working favorably. The other options indicate the manic behavior is being well managed.
3.
c.
This demonstrates the child’s ability to remain focused on the task at hand.
4.
c.
The brain has to adapt to these types of drugs. Although a person can feel some benefit in 2 weeks, full effects can take 4–6 weeks. It is important to emphasize this to the client or else they will simply stop taking the drug.
5.
b.
Tremors, pseudoparkinsonism, and akinesia are extrapyramidal side effects that can occur with haloperidol.
6.
d.
Whole milk and aged cheeses are high in tyramine and therefore should be avoided.
7.
c.
Clozapine can cause a significant decrease in the neutrophil count, increasing the risk of infection. Also, abrupt discontinuation of clozapine can result in significant complications for client treatment. To ensure the client does not have a gap in the treatment, this is a modification to the REMS program.
8.
c.
This is a norepinephrine dopamine reuptake inhibitor.
9.
a.
Zolpidem is useful for initiating sleep (sleep latency) and ensuring the client stays asleep during the night.
10.
a.
Because this drug is a stimulant, it should not be taken near the evening or it will interrupt sleep.


7.5: Embryonic Development of the Axial Skeleton
Learning Objectives
- Discuss the two types of embryonic bone development within the skull
- Describe the development of the vertebral column and thoracic cage
The axial skeleton begins to form during early embryonic development. However, growth, remodeling, and ossification (bone formation) continue for several decades after birth before the adult skeleton is fully formed. Knowledge of the developmental processes that give rise to the skeleton is important for understanding the abnormalities that may arise in skeletal structures.
Development of the Skull
During the third week of embryonic development, a rod-like structure called the notochord develops dorsally along the length of the embryo. The tissue overlying the notochord enlarges and forms the neural tube, which will give rise to the brain and spinal cord. By the fourth week, mesoderm tissue located on either side of the notochord thickens and separates into a repeating series of block-like tissue structures, each of which is called a somite . As the somites enlarge, each one will split into several parts. The most medial of these parts is called a sclerotome . The sclerotomes consist of an embryonic tissue called mesenchyme, which will give rise to the fibrous connective tissues, cartilages, and bones of the body.
The bones of the skull arise from mesenchyme during embryonic development in two different ways. The first mechanism produces the bones that form the top and sides of the brain case. This involves the local accumulation of mesenchymal cells at the site of the future bone. These cells then differentiate directly into bone producing cells, which form the skull bones through the process of intramembranous ossification. As the brain case bones grow in the fetal skull, they remain separated from each other by large areas of dense connective tissue, each of which is called a fontanelle (Figure \(\PageIndex{1}\)). The fontanelles are the soft spots on an infant’s head. They are important during birth because these areas allow the skull to change shape as it squeezes through the birth canal. After birth, the fontanelles allow for continued growth and expansion of the skull as the brain enlarges. The largest fontanelle is located on the anterior head, at the junction of the frontal and parietal bones. The fontanelles decrease in size and disappear by age 2. However, the skull bones remained separated from each other at the sutures, which contain dense fibrous connective tissue that unites the adjacent bones. The connective tissue of the sutures allows for continued growth of the skull bones as the brain enlarges during childhood growth.
The second mechanism for bone development in the skull produces the facial bones and floor of the brain case. This also begins with the localized accumulation of mesenchymal cells. However, these cells differentiate into cartilage cells, which produce a hyaline cartilage model of the future bone. As this cartilage model grows, it is gradually converted into bone through the process of endochondral ossification. This is a slow process and the cartilage is not completely converted to bone until the skull achieves its full adult size.
At birth, the brain case and orbits of the skull are disproportionally large compared to the bones of the jaws and lower face. This reflects the relative underdevelopment of the maxilla and mandible, which lack teeth, and the small sizes of the paranasal sinuses and nasal cavity. During early childhood, the mastoid process enlarges, the two halves of the mandible and frontal bone fuse together to form single bones, and the paranasal sinuses enlarge. The jaws also expand as the teeth begin to appear. These changes all contribute to the rapid growth and enlargement of the face during childhood.
Development of the Vertebral Column and Thoracic cage
Development of the vertebrae begins with the accumulation of mesenchyme cells from each sclerotome around the notochord. These cells differentiate into a hyaline cartilage model for each vertebra, which then grow and eventually ossify into bone through the process of endochondral ossification. As the developing vertebrae grow, the notochord largely disappears. However, small areas of notochord tissue persist between the adjacent vertebrae and this contributes to the formation of each intervertebral disc.
The ribs and sternum also develop from mesenchyme. The ribs initially develop as part of the cartilage model for each vertebra, but in the thorax region, the rib portion separates from the vertebra by the eighth week. The cartilage model of the rib then ossifies, except for the anterior portion, which remains as the costal cartilage. The sternum initially forms as paired hyaline cartilage models on either side of the anterior midline, beginning during the fifth week of development. The cartilage models of the ribs become attached to the lateral sides of the developing sternum. Eventually, the two halves of the cartilaginous sternum fuse together along the midline and then ossify into bone. The manubrium and body of the sternum are converted into bone first, with the xiphoid process remaining as cartilage until late in life.
View this video to review the two processes that give rise to the bones of the skull and body. What are the two mechanisms by which the bones of the body are formed and which bones are formed by each mechanism?
HOMEOSTATIC IMBALANCES
Craniosynostosis
The premature closure (fusion) of a suture line is a condition called craniosynostosis. This error in the normal developmental process results in abnormal growth of the skull and deformity of the head. It is produced either by defects in the ossification process of the skull bones or failure of the brain to properly enlarge. Genetic factors are involved, but the underlying cause is unknown. It is a relatively common condition, occurring in approximately 1:2000 births, with males being more commonly affected. Primary craniosynostosis involves the early fusion of one cranial suture, whereas complex craniosynostosis results from the premature fusion of several sutures.
The early fusion of a suture in primary craniosynostosis prevents any additional enlargement of the cranial bones and skull along this line. Continued growth of the brain and skull is therefore diverted to other areas of the head, causing an abnormal enlargement of these regions. For example, the early disappearance of the anterior fontanelle and premature closure of the sagittal suture prevents growth across the top of the head. This is compensated by upward growth by the bones of the lateral skull, resulting in a long, narrow, wedge-shaped head. This condition, known as scaphocephaly, accounts for approximately 50 percent of craniosynostosis abnormalities. Although the skull is misshapen, the brain still has adequate room to grow and thus there is no accompanying abnormal neurological development.
In cases of complex craniosynostosis, several sutures close prematurely. The amount and degree of skull deformity is determined by the location and extent of the sutures involved. This results in more severe constraints on skull growth, which can alter or impede proper brain growth and development.
Cases of craniosynostosis are usually treated with surgery. A team of physicians will open the skull along the fused suture, which will then allow the skull bones to resume their growth in this area. In some cases, parts of the skull will be removed and replaced with an artificial plate. The earlier after birth that surgery is performed, the better the outcome. After treatment, most children continue to grow and develop normally and do not exhibit any neurological problems.
Chapter Review
Formation of the axial skeleton begins during early embryonic development with the appearance of the rod-like notochord along the dorsal length of the early embryo. Repeating, paired blocks of tissue called somites then appear along either side of notochord. As the somites grow, they split into parts, one of which is called a sclerotome. This consists of mesenchyme, the embryonic tissue that will become the bones, cartilages, and connective tissues of the body.
Mesenchyme in the head region will produce the bones of the skull via two different mechanisms. The bones of the brain case arise via intramembranous ossification in which embryonic mesenchyme tissue converts directly into bone. At the time of birth, these bones are separated by fontanelles, wide areas of fibrous connective tissue. As the bones grow, the fontanelles are reduced to sutures, which allow for continued growth of the skull throughout childhood. In contrast, the cranial base and facial bones are produced by the process of endochondral ossification, in which mesenchyme tissue initially produces a hyaline cartilage model of the future bone. The cartilage model allows for growth of the bone and is gradually converted into bone over a period of many years.
The vertebrae, ribs, and sternum also develop via endochondral ossification. Mesenchyme accumulates around the notochord and produces hyaline cartilage models of the vertebrae. The notochord largely disappears, but remnants of the notochord contribute to formation of the intervertebral discs. In the thorax region, a portion of the vertebral cartilage model splits off to form the ribs. These then become attached anteriorly to the developing cartilage model of the sternum. Growth of the cartilage models for the vertebrae, ribs, and sternum allow for enlargement of the thoracic cage during childhood and adolescence. The cartilage models gradually undergo ossification and are converted into bone.
Interactive Link Questions
View this video to review the two processes that give rise to the bones of the skull and body. What are the two mechanisms by which the bones of the body are formed and which bones are formed by each mechanism?
Answer: Bones on the top and sides of the skull develop when fibrous membrane areas ossify (convert) into bone. The bones of the limbs, ribs, and vertebrae develop when cartilage models of the bones ossify into bone.
Review Questions
Q. Embryonic development of the axial skeleton involves ________.
A. intramembranous ossification, which forms the facial bones.
B. endochondral ossification, which forms the ribs and sternum
C. the notochord, which produces the cartilage models for the vertebrae
D. the formation of hyaline cartilage models, which give rise to the flat bones of the skull
Answer: B
Q. A fontanelle ________.
A. is the cartilage model for a vertebra that later is converted into bone
B. gives rise to the facial bones and vertebrae
C. is the rod-like structure that runs the length of the early embryo
D. is the area of fibrous connective tissue found at birth between the brain case bones
Answer: D
Critical Thinking Questions
Q. Discuss the processes by which the brain-case bones of the skull are formed and grow during skull enlargement.
A. The brain-case bones that form the top and sides of the skull are produced by intramembranous ossification. In this, mesenchyme from the sclerotome portion of the somites accumulates at the site of the future bone and differentiates into bone-producing cells. These generate areas of bone that are initially separated by wide regions of fibrous connective tissue called fontanelles. After birth, as the bones enlarge, the fontanelles disappear. However, the bones remain separated by the sutures, where bone and skull growth can continue until the adult size is obtained.
Q. Discuss the process that gives rise to the base and facial bones of the skull.
A. The facial bones and base of the skull arise via the process of endochondral ossification. This process begins with the localized accumulation of mesenchyme tissue at the sites of the future bones. The mesenchyme differentiates into hyaline cartilage, which forms a cartilage model of the future bone. The cartilage allows for growth and enlargement of the model. It is gradually converted into bone over time.
Q. Discuss the development of the vertebrae, ribs, and sternum.
A. The vertebrae, ribs, and sternum all develop via the process of endochondral ossification. Mesenchyme tissue from the sclerotome portion of the somites accumulates on either side of the notochord and produces hyaline cartilage models for each vertebra. In the thorax region, a portion of this cartilage model splits off to form the ribs. Similarly, mesenchyme forms cartilage models for the right and left halves of the sternum. The ribs then become attached anteriorly to the developing sternum, and the two halves of sternum fuse together. Ossification of the cartilage model into bone occurs within these structures over time. This process continues until each is converted into bone, except for the sternal ends of the ribs, which remain as the costal cartilages.
Glossary
- fontanelle
- expanded area of fibrous connective tissue that separates the brain case bones of the skull prior to birth and during the first year after birth
- notochord
- rod-like structure along dorsal side of the early embryo; largely disappears during later development but does contribute to formation of the intervertebral discs
- sclerotome
- medial portion of a somite consisting of mesenchyme tissue that will give rise to bone, cartilage, and fibrous connective tissues
- somite
- one of the paired, repeating blocks of tissue located on either side of the notochord in the early embryo


1.5: Visualization and manipulation of satellite images
Most of this course will deal with the typical kind of ‘satellite image’ you might see on the news or on Google Earth, in other words the kind of image produced by passive optical sensors. These images can in many ways be considered to be similar to the photos you take with your phone, so you can do similar things to them to make them better. Except in the context of remote sensing ‘better’ doesn’t mean photoshopping them to remove red eyes and create more vibrant colours, it means showing them in ways that help interpreting them better for specific purposes. This is a form of scientific visualization , a process in which displaying data helps explore and understand them. The reason exploring data visually can be more useful than running them through a computer algorithm is that humans are exceptionally adept at interpreting spatial patterns. As an example, just imagine you’re walking through a field in Eastern Canada and see the scene below. You are immediately able to realize that the dark part of the image seems ‘out of place’ and thus might be important, the shape suggests to you that it is a large animal, and you can bring all kinds of context (the time of year, the environment, the fact that bears are known to live in the area) to help in your interpretation of what is going on.
29: People are exceptionally good at recognizing structures in images, and while computer vision is in rapid development, the human brain still often outperforms artificial intelligence in this field. A Bear In The Woods by Linda Tanner, Flickr, CC BY-NC-ND 2.0 .
Un-enhanced greyscale display
A lot goes on behind the scenes when you display an image on a computer screen. To look at the details we will take the simplest possible example first, an 8-bit greyscale image, but keep in mind that the same principles apply to data of different kinds. An 8-bit greyscale image (commonly, but misleadingly, also called a black-and-white image) corresponds to a single two-dimensional data layer with values ranging from 0 to 255. Digitally, the image file (e.g. a jpg, png, tif, or other image file) contains a bunch of numbers, as well as some information about the dimensions of the image. In the example below, the image contains 16 pixels arranged in 4 rows and 4 columns, and a value between 0 and 255 is associated with each cell. This is the Digital Number (DN) value. Most computer screens are able to display 256 different intensities of light, and use three colours (red, green and blue) to do so, which enables the production of 256 * 256 * 256 = 16.8 million colours. Think of there being three little ‘coloured light guns’ inside each pixel in the computer screen, which determine how much light to produce, of each colour, in each pixel. When displaying greyscale images, the intensity of light produced in red, green, and blue is all the same, allowing 256 shades of grey. The darkest of these (0 light intensity in red, 0 in green, and 0 in blue) produces a black colour on the screen, and the brightest (255 in red, 255 in green and 255 in blue) produces white. The example shown in Figure 30 is thus the simplest visualization (on the right) of the DN values in the file (on the left).
30: Single-layer greyscale image, showing the digital numbers on the left, and their visualization on the right. By Anders Knudby, CC BY 4.0 .
Un-enhanced true-colour display
Most images have more than a single data layer, and can thus be used to produce colour images. Phone cameras record image files with three layers, corresponding to red, green, and blue, so visualizing these files is easy with the three ‘colour guns’ in your computer screen. A true-colour visualization is, not surprisingly, one in which you display the ‘red’ data layer using the red ‘colour gun’, and so on. For example:
31: DN values in the red, green, and blue bands, and their direct display in a true-colour composite. By Anders Knudby, CC BY 4.0 .
Un-enhanced false-colour display
Most passive optical sensors on satellites record light in more than three ‘bands’, and thus produce image files with more than three data layers. Some of these bands may be different shades of visible light (e.g. violet), while others, such as infrared and ultraviolet, fall outside the spectrum that is visible to humans. To show such data, false-colour visualizations are used. The name false-colour simply states that what is shown does not represent what the images area would look like to a human, it does not imply that there is anything wrong with the image (in fact false-colour displays are very useful). False-colour displays come in many flavours – just imagine the number of different combinations of three bands you can make with data from a sensors that has more than 200 bands… The most common false-colour visualization is often called ‘colour-infrared’, and it displays a ‘near-infrared’ band using the red colour gun, a ‘red’ band using the green colour gun, and a ‘green’ band using the blue colour gun. Figure 32 provides a side-by-side comparison of true-colour and a false-colour display of a Landsat image containing Zanzibar Town.
32: True-colour and colour-infrared displays of a Landsat image containing Zanzibar Town. By Anders Knudby, CC BY 4.0 .
Image enhancement
In the preceding examples, we have imagined that the images always contained values between 0 and 255, neatly providing the 256 different possible values that the colour guns in a typical computer screen can display. There are two situations in which using the DN value found in the image file directly to determine the intensity of light produced by a colour gun is not the best option:
- Not all sensors record data using 8 bits per pixel (per colour). For (older) sensors that use less than 8 bits, or (newer) sensors that use more than 8 bits, a conversion between the DN value and the intensity with which it should be displayed is typically necessary.
- If the sensor has produced an image over a particularly bright or dark area, or at least if such an area is of specific interest, the values found over that area (e.g. between 50 and 80) can be displayed using a wider range of intensities on the screen (e.g. between 20 and 110), thus improving the visual contrast over the area of interest.
To better understand these issues, we need to consider how the DN values are stored in computer memory. We will consider a single pixel and its DN value for a single band. For an 8-bit sensor, this DN value is stored in 8 bits, each of which can either be ON (1) or OFF (0). The value is encoded as illustrated in Figure 33. In that example, the bits representing values of 128, 32, 16, 8 and 2 are all ON, while the others are OFF. The DN value of the pixel is therefore calculated as 128 + 32 + 16 + 8 + 2 = 186. The range of possible values with 8 bits goes from 0 (all bits are OFF) to 255 (all bits are ON), for a total of 256 possible values. In fact, the number of possible values, given the number of bits, is easily calculated as 2 n , where n is the number of bits.
33: This example illustrates an 8-bit pixel with the value 186. By Anders Knudby, CC BY 4.0 .
This is the reason why sensors that use fewer than 8 bits to store the DN for each pixel cannot produce 256 different values. However, just for the sake of argument, if we were to display 4-bit DN values (DN values ranging between 0 and 15) directly without transformation, we would only see very dark shades of grey (no actual sensors record information using only 4 bits, but the first Landsat sensors used only 6 bits, and the issue is the same).
On the other hand, sensors that use 12 bits to store each DN value (as many modern sensors do), contain values ranging from 0 to 2 12 -1 = 4095. To display this range of values, we need to transform them to all fit between 0 and 255, which is most easily done by simply dividing by 16 and rounding down. Note that in this case, while the computer screen is not capable of displaying the data in all its detail, image processing algorithms will still be able to make use of it.
Things get more interesting when we have an image in which a specific range of values are of greatest interest. A common example is the kind of image seen in Figure 32, which contains some water (very dark), land (relatively dark and largely green), and clouds (very bright). Unless we are specifically interested in studying the clouds in this image, we don’t really need to be able to distinguish between pixels with DN values of 245 vs. 250 vs. 255. What we can do, then, is to display all ‘bright’ pixels that we don’t really care about with the same colour (white), and thus ‘reserve’ more of the different brightnesses with which we can display pixels for the DN values we care more about. Mathematically, this means creating a table that translates each DN value, for each band, into an equivalent brightness value with which it is going to be displayed on screen. Graphically, we can show this as done below in Figure 34, where the DN values are shown on the x axis, and the brightness with which they are displayed is shown on the y axis. The blue line represents the direct use of the DN value, without contrast enhancement. The orange line represents a linear contrast enhancement, in which all DN values less than 50 are displayed with a brightness of 0, and all DN values greater than 240 are displayed with a brightness of 255. This allows us to use the remaining 254 possible brightness values to better display the smaller differences between pixels with DN values between 50 and 240. The grey line is a square root transformation that keeps some contrast along the entire range of DN values, but focuses on displaying differences between pixels with low DN values, at the expense of those with high DN values. Examples of what such contrast enhancement can look like in practice are shown in Figures 35-37:
34: Three options for displaying 8-bit data. By Anders Knudby, CC BY 4.0 .
35: No contrast enhancement. By Anders Knudby, CC BY 4.0 .
36: Linear contrast enhancement using the minimum and maximum values of the image in place of 50 and 240 in the above example. By Anders Knudby, CC BY 4.0 .
37: Contrast enhancement known as histogram equalization. This is mathematically more complex than the examples shown above, but often provides good results. By Anders Knudby, CC BY 4.0 .
Pan-sharpening
When you watch Hollywood movies and the CIA analyst or the surprisingly good-looking police officer clicks a button to ‘enhance’ footage from a surveillance camera, thus revealing facial features from what was previously a blurry blob, well, that’s Hollywood. The thing about images is that they are just data, and you can’t make detail (new data) appear where none exists in the original data. There’s a funny explanation of this general idea here . However, with some satellite imagery there is one kind of ‘enhancement’ that actually kind of works (although it wreaks havoc in subtle ways on the image radiometry). The technique in question is called pan-sharpening, which refers to the fact that most passive optical satellite sensors have a ‘pan-chromatic’ band that records data on brightness across all the visible bands and at higher spatial resolution than the individual colour bands. For example, the sensors on Landsat satellites 4-7 have blue, green and red bands, all with 30 meter spatial resolution, and a pan-chromatic band that records blue and green as well as red light, with 15 meter spatial resolution. For modern high-resolution sensors, the difference in spatial resolution is even greater, with WorldView-2 having colour bands at 2 meter resolution and a pan-chromatic band at 50 cm resolution. Broadly speaking, we can therefore combine the colour information from the individual colour bands with the spatial detail from the pan-chromatic band, to get something like what you see in Figure 38.
There are several algorithms that can be used to perform this operation, and each employs a different set of assumptions and rules for how to generate colour information for each of the pixels in the pan-sharpened image. While context determines which algorithm is superior for a given image, the results of most algorithms are impressive and can greatly aid in visual interpretation of satellite imagery. Most commercial image processing software packages have one or more algorithms for pan-sharpening, so while the process itself is fairly complex, actually applying it to an image is done with the click of a button.
Band ratios and other band math
The previous sections have mostly dealt with different ways of displaying the DN values found in each band – in greyscale or colour, directly or transformed through contrast enhancement, pan-sharpened or not. An alternative is to create new bands using a process commonly called ‘Band Math’.
For example, we might want to produce a band that quantifies how ‘red’ something is. The problem with the original ‘red’ band in a typical satellite image is seen by comparing the ‘red’ DN values from the top left part of Figure 31 with the colours shown in the bottom right part of the same figure. Arguably, the pixel that is in the top left corner is what most people would consider ‘red’, but the two pixels with the highest DN values in the ‘red’ band are the yellow and white pixels (both have ‘red’ DN values of 255). Despite their high ‘red’ DN value, these pixels do not appear ‘red’ because they also have high DN values in one or more of the other colours. To better quantify the ‘red’ appearance of each pixel, we can calculate something called the ‘red chromatic coordinate’ (RCC). For each pixel, this is calculated as RCC = Red / (Red + Green + Blue), where Red, Green and Blue represent the respective DN values in each pixel. As you can see from the calculations in Figure 39, the red pixel in the top left corner has a higher RCC value than any of the other pixels, followed by yellow pixel next to it (because yellow is ‘close to’ red). Note that band math operates on each pixel individually, and completes the same mathematical operation on all pixels in an image. In doing so, it produces a new band that is a function of the original bands. Other common uses of band math is to calculate ‘band ratios’, such as the vegetation index called the ‘Simple Ratio’ that is calculated as SR = NIR / Red, where NIR is a value (ideally the TOA reflectance) in the near-infrared band, and Red is the same value in the red band. Because healthy plants reflect near-infrared light very effectively, while they absorb most red light (and thus reflect very little red light for the sensor to detect), areas with vegetation tend to have high reflectance and DN values in the near-infrared band and low values in the red band. This leads areas with vegetation to have very high Simple Ratio values, and this band ratio can therefore be used to quickly and easily produce a visualization that helps people distinguish between vegetated and un-vegetated areas. An even more popular vegetation index is the Normalized Difference Vegetation Index (NDVI), which is calculated as NDVI = (NIR – Red) / (NIR + Red).
Band math can be used to calculate new bands with any combination of input bands you can think of, and different kinds of band math are used, among many other applications, to monitor global deforestation , track seasonal changes in snow cover, map water depth, and monitor urban sprawl.
Tasseled cap transformation (TCT)
A particular application of band math called the tasseled cap transformation has been developed for Landsat data, and is now commonly used to produce a standardized and readily interpretable set of bands from the original data. It was originally developed for an instrument called Landsat MSS (which does not operate anymore), and has since been updated for Landsat TM (the sensors on Landsat 4 and 5), ETM+ (the sensor on Landsat 7), and OLI (the passive optical sensor on Landsat 8). The idea behind the tasseled cap transformation is to produce three new bands, ‘greenness’, ‘brightness’ and ‘wetness’, that describe the actual variations in those parameters across the image. In a typical satellite image of a rural landscape, areas covered by water (blue dots) and bare soil (red dots) will form a “line” in two-dimensional (NIR / RED) space, while vegetation (green dots) will lie away from the line and various stages of plant growth together will form a shape roughly like a tasseled cap (Figure 40). The three new bands are created by effectively rotating the axes of the coordinate system, so ‘brightness’ is determined along the ‘line of soils’ in Figure 40, ‘greenness’ is determined along an axis that departs from the line of soils and increases in value as it moves toward the top of the ‘tasseled cap’, and ‘wetness’ is determined along a third axis (not shown in Figure 40) perpendicular to the first two. An example of the results, based on an IKONOS image from Idaho, USA, is shown in Figure 41. In practical terms, each component of the tasseled cap is calculated as a weighted sum of the values in the original bands. For example, for Landsat TM data, the ‘brightness’ is calculated as BR = 0.3037 * BLUE + 0.2793 * GREEN + 0.4343 * RED + 0.5585 * NIR + 0.5082 * SWIR1 + 0.1863 * SWIR2 (SWIR1 and SWIR2 are two shortwave infrared bands also present on Landsat TM sensors).
40: The principle of the tasseled cap transformation. Bare soils of varying brightness fall along a line when plotted with their values in the RED and NIR bands, while vegetation of increasing density is found within the ‘cap’, up and left from the line of soils. Vegetation at various growth stages, growing on soils of different brightness, thus form a shape that looks like a tasseled cap. The original formulation of the tasseled cap included a third dimension, using the green band. Tasseled Cap Transformation for bright and dark soil by Gurkengräber (adapted from Richards and Jia), Wikimedia Commons, CC BY-SA 4.0 .
41: An example of the tasseled cap transformation applied to an IKONOS image from Idaho, USA. tcap_example by Jason Karl, The Landscape Toolbox, CC0 1.0 .
Principal Components Analysis (PCA)
42: A two-dimensional example of Principal Components Analysis. GaussianScatterPCA by Nicoguaro, Wikimedia Commons, CC BY 4.0 .
The last kind of band math we will look at in this chapter is similar to the tasseled cap transformation in that the calculation involves a weighted sum of the original bands, but it is different in the sense that the weights are determined from the properties of the image itself, and as such they vary from image to image. Figure 42 provides a good illustration of how it works. We can imagine that each points in the scatter plot is a pixel from our image, and that it is plotted according to its value in one band on the x-axis and another band on the y-axis. It is clear from the distribution of points in Figure 42 that points with high values in the one band tend to also have high values in the other band, and that most of the distribution of the points runs along an imaginary line from the bottom left to the top right of the plot. The orientation of this imaginary line is called the first principal component (PC 1 ), and is illustrated with the longest arrow. But there is also some variation orthogonally (perpendicular) to PC 1 . This is the orientation of the second principal component, PC 2 , illustrated with the shorter arrow. Depending on how many bands are in an image, one could continue to find new such lines in the third, fourth etc. dimensions, each oriented along the greatest distribution of points in any orientation perpendicular to all previous principal components. In Figure 42 the original data set had only two dimensions, so two principal components were created. The length of each arrow corresponds to the amount of total distribution captured by each principal component, and it is clear that PC 2 has captured rather little of the distribution in the original points. This can be interpreted as PC 2 containing very little information, and often the higher-numbered principal components can be removed entirely with little loss of information. With this knowledge, new bands can be created, in which the value of each pixel is no longer its DN value in the original bands, but rather its value along each of the principal component axes. This is the main strength of PCA: that it allows you to transform the data into a smaller number of bands (thus taking up less hard disk space, and allowing quicker reading and processing) without losing much information. Research has even shown that for some kinds of images (e.g. a cloud-free Landsat image of an agricultural area), specific principal components tend to correspond to specific environmental variables, such as soil humidity, vegetation cover, and so on. However, a note of caution is important here. Because the orientation of the principal components (the arrows in Figure 42) depend on the distribution of the totality of pixel values in each individual image, the principal component values of a pixel are not directly interpretable, and may vary dramatically between images, even for identical pixels. PCA can thus help you to reduce the data volume of an image, but it destroys (or at least complicates) interpretation in the process. Another really good explanation of PCA, including an animated scatterplot that I think explains things really well, is found here .


3.1: Vector Spaces
1 View Vector Spaces on YouTube
In multivariable, or vector calculus, a vector is defined to be a mathematical construct that has both direction and magnitude. In linear algebra, vectors are defined more abstractly. Vectors are mathematical constructs that can be added and multiplied by scalars under the usual rules of arithmetic. Vector addition is commutative and associative, and scalar multiplication is distributive and associative. Let \(\text{u}\), \(\text{v}\), and \(\text{w}\) be vectors, and let \(a\), \(b\), and \(c\) be scalars. Then the rules of arithmetic say that
\[\text{u} + \text{v} = \text{v} + \text{u},\quad \text{u} + (\text{v} + \text{w}) = (\text{u} + \text{v}) + \text{w};\nonumber \]
and
\[a(\text{u}+\text{v})=a\text{u}+a\text{v},\quad a(b\text{u})=(ab)\text{u}.\nonumber \]
A vector space consists of a set of vectors and a set of scalars that is closed under vector addition and scalar multiplication. That is, when you multiply any two vectors in a vector space by scalars and add them, the resulting vector is still in the vector space.
We can give some examples of vector spaces. Let the scalars be the set of real numbers and let the vectors be column matrices of a specified type. One example of a vector space is the set of all three-by-one column matrices. If we let
\[\text{u}=\left(\begin{array}{c}u_1\\u_2\\u_3\end{array}\right),\quad\text{v}=\left(\begin{array}{c}v_1\\v_2\\v_3\end{array}\right),\nonumber \]
then
\[w=a\text{u}+b\text{v}=\left(\begin{array}{c}au_1+bv_1 \\ au_2+bv_2 \\ au_3+bv_3\end{array}\right)\nonumber \]
is evidently a three-by-one matrix, so that the set of all three-by-one matrices (together with the set of real numbers) forms a vector space. This vector space is usually called \(\mathbb{R}^3\).
A vector subspace is a vector space that is a subset of another vector space. For example, a vector subspace of \(\mathbb{R}^3\) could be the set of all three-by-one matrices with zero in the third row. If we let
\[\text{u}=\left(\begin{array}{c}u_1\\u_2\\0\end{array}\right),\quad\text{v}=\left(\begin{array}{c}v_1\\v_2\\0\end{array}\right),\nonumber \]
then
\[\text{w}=a\text{u}+b\text{v}=\left(\begin{array}{c}au_1+bv_1\\au_2+bv_2\\0\end{array}\right)\nonumber \]
is evidently also a three-by-one matrix with zero in the third row. This subspace of \(\mathbb{R}^3\) is closed under scalar multiplication and vector addition and is therefore a vector space. Another example of a vector subspace of \(\mathbb{R}^3\) would be the set of all three-by-one matrices where the first row is equal to the third row.
Of course, not all subsets of \(\mathbb{R}^3\) form a vector space. A simple example would be the set of all three-by-one matrices where the row elements sum to one. If, say, \(\text{u} =\left(\begin{array}{ccc}1&0&0\end{array}\right)^{\text{T}}\), then \(a\text{u}\) is a vector whose rows sum to \(a\), which can be different than one.
The zero vector must be a member of every vector space. If \(\text{u}\) is in the vector space, then so is \(0\text{u}\) which is just the zero vector. Another argument would be that if \(\text{u}\) is in the vector space, then so is \((−1)\text{u} = −\text{u}\), and \(\text{u} − \text{u}\) is again equal to the zero vector.
The concept of vector spaces is more general than a set of column matrices. Here are some examples where the vectors are functions.
Consider vectors consisting of all real polynomials in \(x\) of degree less than or equal to \(n\). Show that this set of vectors (together with the set of real numbers) form a vector space.
Solution
Consider the polynomials of degree less than or equal to \(n\) given by
\[p(x)=a_0+a_1x+a_2x^2+\cdots +a_nx^n,\quad q(x)=b_0+b_1x+b_2x^2+\cdots +b_nx^n,\nonumber \]
where \(a_0,\: a_1,\cdots , a_n\) and \(b_0,\: b_1,\cdots , b_n\) are real numbers. Clearly, multiplying these polynmials by real numbers still results in a polynomial of degree less than or equal to \(n\). Adding these polynomials results in
\[p(x)+q(x)=(a_0+b_0)+(a_1+b_1)x+(a_2+b_2)x^2+\cdots +(a_n+b_n)x^n,\nonumber \]
which is another polynomial of degree less than or equal to \(n\). Since this set of polynomials is closed under scalar multiplication and vector addition, it forms a vector space. This vector space is designated as \(\mathbb{P}_n\).
Consider a function \(y = y(x)\) and the differential equation \(d^3y/dx^3 = 0\). Find the vector space associated with the general solution of this differential equation.
Solution
From Calculus, we know that the function whose third derivative is zero is a polynomial of degree less than or equal to two. That is, the general solution to the differential equation is
\[y(x)=a_0+a_1x+a_2x^2,\nonumber \]
which is just all possible vectors in the vector space \(\mathbb{P}_2\).
Consider a function \(y = y(x)\) and the differential equation \(d^2y/dx^2 + y = 0\). Find the vector space associated with the general solution of this differential equation.
Solution
Again from Calculus, we know that the trigonometric functions \(\cos x\) and \(\sin x\) have second derivatives that are the negative of themselves. The general solution to the differential equation consists of all vectors of the for
\[y(x)=a\cos x+b\sin x,\nonumber \]
which is just all possible vectors in the vector space consisting of a linear combination of \(\cos x\) and \(\sin x\).


 But do they actually exist? And how do we go about looking for something that is many light years away, only about a few dozen kilometers across (if a stellar black hole), and completely black? It turns out that the trick is not to look for the black hole itself but instead to look for what it does to a nearby companion star.
As we saw, when very massive stars collapse, they leave behind their gravitational influence. What if a member of a double-star system becomes a black hole, and its companion manages to survive the death of the massive star? While the black hole disappears from our view, we may be able to deduce its presence from the things it does to its companion.
Requirements for a Black Hole
So, here is a prescription for finding a black hole: start by looking for a star whose motion (determined from the Doppler shift of its spectral lines) shows it to be a member of a binary star system. If both stars are visible, neither can be a black hole, so focus your attention on just those systems where only one star of the pair is visible, even with our most sensitive telescopes.
Being invisible is not enough, however, because a relatively faint star might be hard to see next to the glare of a brilliant companion or if it is shrouded by dust. And even if the star really is invisible, it could be a neutron star. Therefore, we must also have evidence that the unseen star has a mass too high to be a neutron star and that it is a collapsed object—an extremely small stellar remnant.
We can use Kepler’s law (see Orbits and Gravity) and our knowledge of the visible star to measure the mass of the invisible member of the pair. If the mass is greater than about 3 \(M_{\text{Sun}}\), then we are likely seeing (or, more precisely, not seeing) a black hole—as long as we can make sure the object really is a collapsed star.
If matter falls toward a compact object of high gravity, the material is accelerated to high speed. Near the event horizon of a black hole, matter is moving at velocities that approach the speed of light. As the atoms whirl chaotically toward the event horizon, they rub against each other; internal friction can heat them to temperatures of 100 million K or more. Such hot matter emits radiation in the form of flickering X-rays. The last part of our prescription, then, is to look for a source of X-rays associated with the binary system. Since X-rays do not penetrate Earth’s atmosphere, such sources must be found using X-ray telescopes in space.
In our example, the infalling gas that produces the X-ray emission comes from the black hole’s companion star. As we saw in The Death of Stars, stars in close binary systems can exchange mass, especially as one of the members expands into a red giant. Suppose that one star in a double-star system has evolved to a black hole and that the second star begins to expand. If the two stars are not too far apart, the outer layers of the expanding star may reach the point where the black hole exerts more gravitational force on them than do the inner layers of the red giant to which the atmosphere belongs. The outer atmosphere then passes through the point of no return between the stars and falls toward the black hole.
The mutual revolution of the giant star and the black hole causes the material falling toward the black hole to spiral around it rather than flow directly into it. The infalling gas whirls around the black hole in a pancake of matter called an accretion disk . It is within the inner part of this disk that matter is revolving about the black hole so fast that internal friction heats it up to X-ray–emitting temperatures (see the chapter thumbnail).
Another way to form an accretion disk in a binary star system is to have a powerful stellar wind come from the black hole’s companion.  Some of the ejected gas in the wind will then flow close enough to the black hole to be captured by it into the disk (Figure \(\PageIndex{1}\)).
We should point out that, as often happens, the measurements we have been discussing are not quite as simple as they are described in introductory textbooks. In real life, Kepler’s law allows us to calculate only the combined mass of the two stars in the binary system. We must learn more about the visible star of the pair and its history to ascertain the distance to the binary pair, the true size of the visible star’s orbit, and how the orbit of the two stars is tilted toward Earth, something we can rarely measure. And neutron stars can also have accretion disks that produce X-rays, so astronomers must study the properties of these X-rays carefully when trying to determine what kind of object is at the center of the disk. Nevertheless, a number of systems that clearly contain black holes have now been found.
The Discovery of Stellar-Mass Black Holes
Because X-rays are such important tracers of black holes that are having some of their stellar companions for lunch, the search for black holes had to await the launch of sophisticated X-ray telescopes into space. These instruments must have the resolution to locate the X-ray sources accurately and thereby enable us to match them to the positions of binary star systems.
The first black hole binary system to be discovered is called Cygnus X-1 (see the chapter thumbnail). The visible star in this binary system is spectral type O. Measurements of the Doppler shifts of the O star’s spectral lines show that it has an unseen companion. The X-rays flickering from it strongly indicate that the companion is a small collapsed object. The mass of the invisible collapsed companion is about 15 times that of the Sun. The companion is therefore too massive to be either a white dwarf or a neutron star.
A number of other binary systems also meet all the conditions for containing a black hole. Table \(\PageIndex{1}\) lists the characteristics of some of the best examples.
| Table \(\PageIndex{1}\): Some Black Hole Candidates in Binary Star Systems | |||
|---|---|---|---|
| Name/Catalog Designation 1 | Companion Star Spectral Type | Orbital Period (days) | Black Hole Mass Estimates (\(M_{\text{Sun}}\)) |
| LMC X-1 | O giant | 3.9 | 10.9 |
| Cygnus X-1 | O supergiant | 5.6 | 15 |
| XTE J1819.3-254 (V4641 Sgr) | B giant | 2.8 | 6–7 |
| LMC X-3 | B main sequence | 1.7 | 7 |
| 4U1543-475 (IL Lup) | A main sequence | 1.1 | 9 |
| GRO J1655-40 (V1033 Sco) | F subgiant | 2.6 | 7 |
| GRS 1915+105 | K giant | 33.5 | 14 |
| GS202+1338 (V404 Cyg) | K giant | 6.5 | 12 |
| XTE J1550-564 | K giant | 1.5 | 11 |
| A0620-00 (V616 Mon) | K main sequence | 0.33 | 9–13 |
| H1705-250 (Nova Oph 1977) | K main sequence | 0.52 | 5–7 |
| GRS1124-683 (Nova Mus 1991) | K main sequence | 0.43 | 7 |
| GS2000+25 (QZ Vul) | K main sequence | 0.35 | 5–10 |
| GRS1009-45 (Nova Vel 1993) | K dwarf | 0.29 | 8–9 |
| XTE J1118+480 | K dwarf | 0.17 | 7 |
| XTE J1859+226 | K dwarf | 0.38 | 5.4 |
| GRO J0422+32 | M dwarf | 0.21 | 4 |
Feeding a Black Hole
After an isolated star, or even one in a binary star system, becomes a black hole, it probably won’t be able to grow much larger. Out in the suburban regions of the Milky Way Galaxy where we live (see The Milky Way Galaxy), stars and star systems are much too far apart for other stars to provide “food” to a hungry black hole. After all, material must approach very close to the event horizon before the gravity is any different from that of the star before it became the black hole.
But, as will see, the central regions of galaxies are quite different from their outer parts. Here, stars and raw material can be quite crowded together, and they can interact much more frequently with each other. Therefore, black holes in the centers of galaxies may have a much better opportunity to find mass close enough to their event horizons to pull in. Black holes are not particular about what they “eat”: they are happy to consume other stars, asteroids, gas, dust, and even other black holes.
As a result, black holes in crowded regions can grow, eventually swallowing thousands or even millions of times the mass of the Sun. Ground-based observations have provided compelling evidence that there is a black hole in the center of our own Galaxy with a mass of about 4 million times the mass of the Sun (we’ll discuss this further in the chapter on The Milky Way Galaxy). Observations with the Hubble Space Telescope have shown dramatic evidence for the existence of black holes in the centers of many other galaxies. These black holes can contain more than a billion solar masses. The feeding frenzy of such supermassive black holes may be responsible for some of the most energetic phenomena in the universe (see Active Galaxies, Quasars, and Supermassive Black Holes). And evidence from more recent X-ray observations is also starting to indicate the existence of “middle-weight” black holes, whose masses are dozens to thousands of times the mass of the Sun. The crowded inner regions of the globular clusters we described in Stars from Adolescence to Old Age may be just the right breeding grounds for such intermediate-mass black holes.
Over the past decades, many observations, especially with the Hubble Space Telescope and with X-ray satellites, have been made that can be explained only if black holes really do exist. Furthermore, the observational tests of Einstein’s general theory of relativity have convinced even the most skeptical scientists that his picture of warped or curved spacetime is indeed our best description of the effects of gravity near these black holes.
Summary
The best evidence of stellar-mass black holes comes from binary star systems in which (1) one star of the pair is not visible, (2) the flickering X-ray emission is characteristic of an accretion disk around a compact object, and (3) the orbit and characteristics of the visible star indicate that the mass of its invisible companion is greater than 3 \(M_{\text{Sun}}\). A number of systems with these characteristics have been found. Black holes with masses of millions to billions of solar masses are found in the centers of large galaxies.
Footnotes
1 As you can tell, there is no standard way of naming these candidates. The chain of numbers is the location of the source in right ascension and declination (the longitude and latitude system of the sky); some of the letters preceding the numbers refer to objects (e.g., LMC) and constellations (e.g., Cygnus), while other letters refer to the satellite that discovered the candidate—A for Ariel, G for Ginga, and so on. The notations in parentheses are those used by astronomers who study binary star system or novae.
Glossary
- accretion disk
- the disk of gas and dust found orbiting newborn stars, as well as compact stellar remnants such as white dwarfs, neutron stars, and black holes when they are in binary systems and are sufficiently close to their binary companions to draw off material
Contributors and Attributions
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Andrew Fraknoi (Foothill College), David Morrison (NASA Ames Research Center), Sidney C. Wolff (National Optical Astronomy Observatory) with many contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/astronomy ).