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Dominant group/Learning resource

This subpage of dominant group is exploratory. The ongoing original research project focused on dominant group is uncovering knowledge and producing understanding about this two-word phrase. Each aspect of this process produces potential learning resources.

As the exploration continues, this subpage includes these potential learning resources, organizes them, and determines, if necessary, through experimentation, what is needed to produce the learning resource.

Dominant group occurs in primary sources that are or have been state-of-the-art contributions in almost every field or subject in which original research takes place. Seeing the two-word phrase is almost synonymous with original research, including in psychology, because the phrase is an identifier of something important.

Dominant groups
Examples from primary sources are to be used to prove or disprove each hypothesis. These can be collected per subject or in general.

 * Accident hypothesis: dominant group is an accident of whatever processes are operating.
 * Artifact hypothesis: dominant group may be an artifact of human endeavor or may have preceded humanity.
 * Association hypothesis: dominant group is associated in some way with the original research.
 * Bad group hypothesis: dominant group is the group that engages in discrimination, abuse, punishment, and additional criminal activity against other groups. It often has an unfair advantage and uses it to express monopolistic practices.
 * Control group hypothesis: there is a control group that can be used to study dominant group.
 * Entity hypothesis: dominant group is an entity within each field where a primary author of original research uses the term.
 * Evolution hypothesis: dominant group is a product of evolutionary processes, such groups are the evolutionary process, produce evolutionary processes, or are independent of evolutionary processes.
 * Identifier hypothesis: dominant group is an identifier used by primary source authors of original research to identify an observation in the process of analysis.
 * Importance hypothesis: dominant group signifies original research results that usually need to be explained by theory and interpretation of experiments.
 * Indicator hypothesis: dominant group may be an indicator of something as yet not understood by the primary author of original research.
 * Influence hypothesis: dominant group is included in a primary source article containing original research to indicate influence or an influential phenomenon.
 * Interest hypothesis: dominant group is a theoretical entity used by scholarly authors of primary sources for phenomena of interest.
 * Metadefinition hypothesis: all uses of dominant group by all primary source authors of original research are included in the metadefinition for dominant group.
 * Null hypothesis: there is no significant or special meaning of dominant group in any sentence or figure caption in any refereed journal article.
 * Object hypothesis: dominant group is an object within each field where a primary author of original research uses the term.
 * Obvious hypothesis: the only meaning of dominant group is the one found in Mosby's Medical Dictionary.
 * Original research hypothesis: dominant group is included in a primary source article by the author to indicate that the article contains original research.
 * Primordial hypothesis: dominant group is a primordial concept inherent to humans such that every language or other form of communication no matter how old or whether extinct, on the verge of extinction, or not, has at least a synonym for dominant group.
 * Purpose hypothesis: dominant group is written into articles by authors for a purpose.
 * Regional hypothesis: dominant group, when it occurs, is only a manifestation of the limitations within a region. Variation of those limitations may result in the loss of a dominant group with the eventual appearance of a new one or none at all.
 * Source hypothesis: dominant group is a source within each field where a primary author of original research uses the term.
 * Term hypothesis: dominant group is a significant term that may require a 'rigorous definition' or application and verification of an empirical definition.

Assessing importances
“How important is the proposed [or ongoing original research] activity to advancing knowledge and understanding within its own field or across different fields?”

Bad groups
In practice, depending upon the scientist's intent, dominant group may be the bad group that engages in monopolistic practices, or socially negative behavior such as discrimination, abuse, punishment, and additional possible criminal activity against other demographic groups.

In a society a dominant group often has an unfair advantage such as numbers, military power, or assets and money.

Causative force for change
This exploratory investigation into dominant group and its usage has the potential to demonstrate that dominant group, when identified is a causative force for change, requires further investigation.

Cessation of use
This exploratory investigation into dominant group and its usage has the potential to demonstrate that dominant group should be no longer used as a scientific/technical term because its meanings are unclear and vague, should this actually be the case.

Control groups
Studies and experiments concerning dominant group are likely to require the need for a control group.

For the conclusions drawn from the results of an experiment to have validity, it is essential that the items or patients assigned to treatment and control groups be representative  of the same population. In some experiments, such as many in agriculture or psychology,  this can be achieved by randomly assigning items from a common population to one of the treatment and control groups.

Data mining test standard
"[T]wo-word glossary items are the most common technical terms". Dominant group is a likely two-word glossary item captured by data mining algorithms. A first-principle's demonstration that dominant group is a two-word scientific/technical term yields one test standard for data mining algorithms to find.

Dominant group of two-word scientific terms
As a two-word scientific/technical term, is dominant group a member of the dominant group of two-word scientific/technical terms?

Empirical identifiers
Dominant group can serve as an empirical identifier in observations. At one extreme, it is 100 % of the effect or phenomenon under study. At the other, it is a minority group effect that perhaps has some natural or artificial advantage.

Experiments
Empirical or predictive uses of dominant group per its likely meaning may be informative regarding fields where its occurrence is minimal.

Evolutionary process
Hypothesis: As an evolutionary process, a dominant group may be a force for extinction by driving a number of other groups to extinction. As a force for extinction a particular dominant group may also through its actions on other groups ultimately produce its own extinction event. This departure from a zone then allows other groups to fill the niche.

Hypothesis: As an evolutionary process, a dominant group may be a force for speciation when spatial or temporal dispersion creates diversity and isolation which may eventually produce new groups

Hypothesis: In every field for which it has been used, dominant group is a force for extinction of other groups while being a force for speciation of new effects within that field?

Changes in the characteristics or properties of a region may force the dominant group into extinction; thereby, making room for the next dominant group. However, some changes may not allow a dominant group to emerge. Additionally, properties of dominance may be appearance only. No competition for resources may have occurred.

Inhibiting or moderating force
This exploratory investigation into dominant group and its usage has the potential to demonstrate that dominant group identifies an inhibiting or moderating force that works against 'high-risk, high-reward' "research with an inherent high degree of uncertainty and the capability to produce a major impact on important problems in biomedical/behavioral research", or in other scientific/technical fields.

Lectures
Subpages of dominant group are not allowed to be lectures, but a category for lectures has been created. A lecture about dominant group the two-word scientific/technical term may help focus any possible or pending NSF proposal and delineate methods to evaluate hypotheses. The lecture would be a part of the course elements of terminology.

Dominant species occurs about 2 1/2 times more often than dominant group suggesting it as another possible lecture/article topic.

Regions is another likely lecture/article topic applicable to dominant group.

The field of dominant group appears to be regions, or the science of regions. Within a region in any science, including the social sciences, there may be a dominant group. Each region is defined by its limits. These limits in turn may allow for a dominant group. Change the limits (characteristics) for any region and the dominant group may go extinct. If a regional genome in biology lacks the potency to take advantage of any change in regional characteristics, there will be no dominant biological group.

Bad groups appears to be one of the characteristics attached to dominant groups. The members of the bad group engage in socially negative behavior such as discrimination, abuse, punishment, and additional possible criminal activity against other demographic groups, including monopolistic practices. These bad groups always have an unfair advantage such as numbers, military power, or assets and money, financial and political power. Even worse these groups seem to have lost their sense of humanity and definitely do not believe that we are all in this together.

Letter of interest
Although a letter of intent may not be required before an unsolicited proposal is submitted to NSF, a letter of interest to the respective program manager usually is. Such a letter is similar to a letter of intent, but is designed to assess directly by request whether or not the program manager has sufficient interest in the proposal topic to proceed with either the letter of intent or the formal proposal submission.

One such letter of interest (Dominant group/Letter of interest/NSF - Linguistics Program) has been sent.

NEH does not require a letter of interest because it uses grants.gov.

Lexical pragmatics
The term lends itself to lexical pragmatics.

From a metadefinitional point of view each use of "dominant group" has a relationship between members of the dominant group, a population from which the dominant group is a subset, a criterion for dominance, and a region, range, distribution or "in their own country". But, each of these four structures may have their meaning in the context within which the author or speaker places the two-word technical term "dominant group".

Two-word terms
"The compound two-word term is employed to give more precision than either word alone would have, not being exact synonyms. And each word indicates the sense in which the other is used." Bold added.

The image at right is part of human history. And, human history is a two-word term.

Oldest two-word terms
It (or one of its relative synonyms) may be one of the oldest two-word terms. Some of its synonyms predate 1826: for example, the phrase “die Dominanten Religionen von ganz Europa” occurs in 1726.

One of the synonyms, patrician class, or classicus, comes from the early Roman Republic, some 2600 b2k.

Origin
The proposed activity consists of finding the origin of dominant group or one of its relative synonyms. The fundamental concepts encompassed by the totality of relative synonyms may have very early origins in primitive languages.

1826 (Kirby): "Groups, according to their range, may be denominated either predominant, dominant, sub-dominant, or quiescent."

1840 (Shuckard): "The Ants and the Staphylini have been supposed to represent each other in the tropical and temperate zones. In the temperate zone, and especially in our own country, the Staphylini are a dominant group, and the ants a secondary one."

1857 (Tocqueville): “The fact that a group is egoistic and dominant proves that it is well formed and that it approaches the make-up of a man.”

1859 (Darwin): The earliest use is on page 343, “The dominant species of the larger dominant groups tend to leave many modified descendants, and thus new sub-groups and groups are formed.”

1860 (Darwin): “Under the many conditions of life which this world affords, any group which is numerous in individuals and species and is widely distributed, may properly be called dominant" [a dominant group]. [Letter 110. To W.H. Harvey, August, 1860]

1944 (Simpson): "In the history of life it is a striking fact that major changes in the taxonomic groups occupying various ecological positions do not, as a rule, result from direct competition of the groups concerned in each case and the survival of the fittest, as most students would assume a priori. On the contrary, the usual sequence is for one dominant group to die out, leaving the zone empty, before the other group becomes abundant." . "GG Simpson's so-called evolutionary species concept contains undefinable criteria and is useless in praxis.

1960 (Huxley): "Improved organization gives biological advantage. Accordingly, the new type becomes a successful or dominant group. It spreads and multiplies and differentiates into a multiplicity of branches. This new biological success is usually achieved at the biological expense of the older dominant group from which it sprang or whose place it had usurped."

1971 (Travis): The earlier theory of evolutionary progressivism (Social Darwinism) puts forth several concepts including "dominant group".

2001 (Mayr): "Other previously dominant groups of organisms that also became extinct at the end of the Cretaceous are many marine taxa, such as most nautiloids and the ammonities, both of whom had been previously highly successful organisms." Page 320: "Ernst Mayr is the biologist largely responsible for shaping the modern synthesis of genetics and evolutionary theory."

Original research identifier
Dominant group serves as an indicator that original research has been conducted, especially when it appears in a primary source.

Own field
The first question to answer is "What is dominant group's own field?"

It is a scientific or technical term, specifically a two-word scientific or technical term. Its overall field is linguistics, or technical language, terminology. It is and refers to an entity. An overall field allowing application to other fields is regions or the science of regions, usually spatial, but not necessarily always spatial. Spatial science or the science of space may be the appropriate field for dominant group.

The identification of its own field may result; thereby, in allowing differentiation of other fields so as to determine how knowledge is advanced across those different fields. It's like "differential equations". Although differential equations is a subject within mathematics, its spread to other subjects such as physics with ensuing use advanced knowledge within physics.

Proof of concept
Within the development of a science or technology is the need to prove that something works. "Dominant group" has successfully demonstrated itself to be a concept, two-word phrase, and ultimately a two-word technical term that is beyond jargon.

Questionnaires
Several learning resources are available in a mostly completed form to benefit an original research effort. These include survey design, questionnaire, hints for designing effective questionnaires, survey research and design in psychology, questionnaire (Wikipedia), statistical survey (Wikipedia), and Questionnaire (Wiki Commons).

An external link is Survey design images (tagged on delicious).

Why do scientists outside biology (especially evolution or entomology) use the term?

Quizzes
It may be an enjoyable learning activity to compose several quizzes focused on important aspects of dominant group and its usages.

Radiance
Fields have been found for which as yet the term is not known to occur. Are there any demographic factors limiting its radiance?

Regions
Region is most commonly found as a term used in terrestrial and astrophysics sciences also an area, notably among the different sub-disciplines of geography, studied by regional geographers. Regions consist of subregions that contain clusters of like areas that are distinctive by their uniformity of description based on a range of statistical data, for example demographic, and locales. In astrophysics some regions have science-specific terms such as galactic clusters.

Term tests
"Dominant group" occurs in a number of articles on several of the Wikimedia Foundation's projects, including Wikibooks, Wikimedia meta wiki, Wikipedia, Wikiquote, and Wikisource. The inclusion of the two-word technical term within articles on these resources allows students to explore attribution, copyright, and the legal implications of quotation use.

Theory of definition
This two-word technical term may be unique in its versatility across fields of science and technology. Yet, it may have a relatively simple definition, specifically a metadefinition, within which are subconcepts into which plugin definitions are made so that a specific observational fact may be reported in the primary literature of science and technology.

Two-word scientific terms
Usually scientific and technical are thought of as synonyms, but they are not exact synonyms. Scientific relates to application of the scientific method, whereas, technical refers to technology, especially using facts from applied science.

Dominant group, when used in scientific/technical primary sources appears to be more of a scientific two-word term than a technical one.

Two-word technical terms
"Two-word terms [are] determined not to be of interest in the context of the whole document collection either because they do not occur frequently enough or because they occur in a constant distribution among different documents [deviation-based approach]."

Two-word technical terms meeting these two criteria may not be significant enough.

Usages
Determining why scientists outside biology use the term, may contribute to understanding how science makes conceptual advances.

Hypotheses

 * 1) Learning how not to become a member of a patrician class or other dominant group is for the better good of humanity.

title: Dominant group/Learning resource


text: File:Poster.png

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: File:Poster.png


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Creating Accessible Courses/Set up a course website and communications

Many people don't use Wikiversity as the primary location for their course, or for effective communications either. Instead they use it to keep documentation and develop resources that will be used in another primary website. That primary website for the course might be an organisation or institution website, or their own professional website as an independent practitioner.

We will assume you are an independent practitioner looking for simple to use tools for setting up a primary and central website for your course, and for opening up communication channels for people taking your course.

The website
There are several free and easy services you can use to establish a website, without the need for expertise in website design and production. Many people use Google Sites, Blogger or Wordpress.com for examples. Services like these afford more control on layout of the site - so improving its usability and focus to an intended audience is easier and in the hands of the developer. They also facilitate easy domain name registration like yourcourse.com for example, and additional communication and information management features.

In this project we will use Blogger to set up a course website.

 * 1) Register an account with Blogger.com and "Start a Blog", naming it as you would name your course (subject to name availability).
 * 2) Create the first blog post, announcing the course website, linking to the Wikiversity development space, and outlining your intentions
 * 3) In the Pages settings for your blog, create pages for the course outline, contact information, assignments, and key resources. The home page will remain your blog space for announcements and news updates.
 * 4) In the Layout settings for your blog, add and remove "gadgets" as you think useful
 * 5) In the Template settings, apply the design you prefer. You may consider using a professional web designer to help you with this
 * 6) In the general Settings, go through the range of settings to ensure your time zone, comment moderation and alerts, and other setting are as you need
 * 7) In the Other section of the Settings, export your blog every week or month for backup. This file can be used to import your site into other services like Wordpress.com
 * 8) Consider the benefit of registering a domain name for your site. This can be simply done through Basic section of the Settings

 * Links and resources
 * Blogger Help
 * Video help
 * Wikipedia article about Blogger
 * Networked Blogs - How to auto post from your website to Facebook and Twitter

Communications
So far we have dealt mainly with the information side of your course, starting with the outline on Wikiversity, going through the management of the information and resources, and into a course website. But Communication is critical in many courses, and there are a number of tools that may prove useful for facilitating or enhancing communications in your course.

 * 1) Face to face communication is obviously a valuable and important method of communicating, but a luxury or even barrier for some. Online, or Internet based communication is a luxury or barrier to many as well. Consider how you might use print formats and the postal service in unique and interesting ways, such as Chain letter, Postcards and Penpals. Post may be a slower method of communicating through text and media, but has unique and interesting aspects that may be worth appreciating.
 * 2) Before you set up communication channels for your course, consider the pros and cons of joining with existing channels. Depending on your subject matter and methods, using existing forums may be a way to make use of the expertise in those forums, and encourage Legitimate peripheral participation as a learning method.
 * 3) Consider setting up a Facebook page for your course, and setting it so the announcements you make on your course website automatically cross post onto the Facebook page
 * 4) Look into the same for Google+ "Pages" and/or "Communities"
 * 5) Consider the use of Skype or Google Hangouts both to communicate with people via video, but also to bring in guest speakers, live stream events and/or record sessions
 * 6) For many people, an email forum is an effective way to run online, text based discussion forums. Google groups is a good service for this
 * 7) Youtube, Twitter, LinkedIn, Facebook and many other such services have communication features that are central to their service. Consider ways to use these features in your course.

 * Links and resources
 * Wikipedia article about Chain letters
 * Wikipedia article about Postcards
 * Wikipedia article about Penpals
 * Google Groups Help
 * Google+ Help
 * Facebook Help


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User:Dross4565/enes100/My Work 2

Write problem/project Goal
restarted car hack project. this time we want to build MPGuino (arduino that reads mpg from any vehicle).

My First Task
research mpguinos, learn what they are, how they work, how to set up arduino to make it a MPGuino. Learn how to solder wires, where to put wires on arduino to MPGuino faceplate. What wires to solder on car to connect to arduino.

Summary of actual work over first weekend
Researched how the MPGuino read the MPG in a car. Started getting the wires and taking apart the computer screen. Helping build the MPGuino by soldering the computer screen and plugging wires into the screen to get it to read.

Week1 Narrative
Started to assemble the MPGuino using the website help MPGuino Assemble. and started learning how the arduino read the MPG from the vehicle using this website MPGuino Workspace.

My Second Task
Research more options with mpguino, learn what else we can do with it instead of just building the software. Start soldering car wires and attach arduino to computer screen monitor.

Summary of actual work over second weekend
searched for other projects that were used with the mpguino. found project that could tie car hack one project [|Car Hack 1] into this project. Started back up with controlling the fuel injection module within the car using arduino and OBD connector.

Week2 Narrative
Researched different options/projects used with the mpguino that we could use instead of just building software and reading of the car's mpg. Which is lame. Found that you can install red and green led lights to computer screen being used with mpguino to signal whether the mpg for the car is the same, better, or worse than the initial depending on which lights on the screen light up. Here is the link to that idea: LED Lights for MPGuino. In seeing this, I immediately was reminded of this group's first car hack project in trying to write programs through the arduino to control the engine of the car. [|Car Hack 1] So, what if I could write a program to control the fuel injection module within the engine of are vehicle using the same arduino that would read the MPG of the vehicle then signal whether the MPG is better than the initial or if I wrote the wrong program and made the MPG worse? This will allow any engineer to write his/her own program within the arduino and attempt to better the MPG than the previous program. Competition between engineers is love. While farthering the project, I can make the project everlasting and make it into a "game". write the wrong MPG code, get a red light on the computer screen. Write the right code, get just the green light on the computer screen. Write a program that gives the same result as the previous program, both the red and green LED lights come on the screen.

My Third task
continue creating the programs using the project from the group's first project to try to control the fuel injection module in the vehicle. Write the code to signal the LED lights to come on at a certain point on the computer screen and help solder the arduino wires to add the LED lights to the computer backscreen and to build the MPGuino.

Summary of actual work over third weekend
Couldn't solder the wires to change the LED lights on the computer screen because didn't have the opportunity to meet with group members to get a the materials in one place, seeing as I wasn't in the possession of the computer screen at the time. So tried to work on fuel injection module and codes for the LED lights.

Week3 Narrative
Because I did not have the possession of the printer screen going to be used in our project I had to improvise, but first I started to create codes with the arduino program using LED Codes has a outline/guideline. First, i had to order the spare lcd shield LCD Shield so I only experiment with the coding in the arduino to use for our actual LCD screen. The actual LED shield attaches directly to the arduino while the LCD screen we are using for this project we soldered on using wires. I also began fiddling with the arduino to control the fuel injector for the car we are using. First, I had to order the fuel injector and the ssr to control it to be able to connect it to the arduino. SSR order Toyota Corolla Fuel Injector but as u can see the fuel injector for the car used in this project was expensive so I went to the junkyard to grab one for $10 out of totaled vehicle.

My Fourth task
Now that I have all the materials needed. Going to start experimenting with the codes to keep the fuel injector opened for as long as I want to so that I could have my final result similar to this video Arduino with fuel injector. I also want to perfect the turning on and off of the different lights within the LCD shield for the arduino to display the increasing or decreasing of the MPG the vehicle has received after uploading the codes to control the fuel injector from the arduino through the OBD to the ecu to the fuel injector within the vehicle. I will try to post videos of my attempts rather they be successful or failures.

Summary of actual work over fourth weekend
Received fuel injector and SSR, connected both to arduino. Started writing codes for both the fuel injection valve and for the LCD monitor on the arduino.

Week4 Narrative
Tested the codes for the arduino to the fuel injector using the same codes for the arduino light structure in order to make easier the timing of how long I wanted the fuel injection to be opened when acceleration on the car's gas pedal has been pushed down. I took the idea from the motor experiment we did when first being "experienced" with the arduino in our engineering class. I also tried to play around with the lighting within the LCD screen Multicolor LCD arduino after installing a multicolor LED light as the backlight. Now trying to get the LCD to signal a red or blue light depending if the MPG is better than the original MPG or not using this as a Tutorial. Gotten to the point where I could make the lights behind the LED light up, but haven't gotten to test if lights will light up when I wanted them to. Now in the process of rewiring the MPGuino to the SSR and the fuel injector using the fuel injection program and the lighting program at the same time.

Complete Team Page
Car Hack 2

title: User:Dross4565/enes100/My Work 2


title: File:Sampling.2.B.BandPass.20120321.pdf


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User:Mattski au/PLE

"I wish life was not so short,' he thought. 'Languages take such a time, and so do all the things one wants to know about" J.R.R. Tolkein

I have begun using Wikiversity to enhance my learning and motivation for my university degree. I begun this Personal Learning Environment alongside my blog, and so far have found it useful in keeping me on track. As I near the end of my degree, I find the "same-old" university class style quiet boring and uninteresting, hence I find using wikiversity provides me with a little more motivation by adding a 'practical application' value on my current studies.

BA/BSci(Psych), Fourth (and Hypothetically Final Academic) Year
Although a little late in the uptake, the involvement of Wikiversity alongside my university course came at the most critical point of my degree - the last leg of the race. However, with the current plan of continuing my education still on the horizon, I plan to use wikiversity with those learning journeys as well. For more info about my university journey, check out my blog.

Group Work:
 * Mindfulness Training Program
 * Mindfulness Training Program - (six weeks)

Literature and Law:
 * Tutorial Report on Free Culture

Curatorship:
 * Item 1

Learning:
 * Item 1

Lit. Studies:
 * Item 1

title: User:Mattski au/PLE


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Talk:Wind Turbine/Howard Community College/Spring2012/p1501KEP

project grading
 * 90 points .. good job ... need tutorials finished ... Kyle's diode stuff is a tutorial .. needs to be put on a tutorial page


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User:Marshallsumter/Radiation astronomy2/Superluminals

In the diagram at right, the black line is the shock wave of Cherenkov radiation, shown only in one moment of time. This double image effect is most prominent for an observer located directly in the path of a superluminal object (in this example a sphere, shown in grey). The right hand bluish shape is the image formed by the blue-doppler shifted light arriving at the observer—who is located at the apex of the black Cherenkov lines—from the sphere as it approaches. The left-hand reddish image is formed from red-shifted light that leaves the sphere after it passes the observer. Because the object arrives before the light, the observer sees nothing until the sphere starts to pass the observer, after which the image-as-seen-by-the-observer splits into two—one of the arriving sphere (to the right) and one of the departing sphere (to the left).

Faster-than-light (also superluminal or FTL) communications and travel refer to the propagation of information or matter faster than the speed of light. Under the special theory of relativity, a particle (that has rest mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons).

On the other hand, what some physicists refer to as "apparent" or "effective" FTL   depends on the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations in less time than light could in normal or undistorted spacetime. Although according to current theories matter is still required to travel subluminally with respect to the locally distorted spacetime region, apparent FTL is not excluded by general relativity.

Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was [apparently] predicted before it was observed by Martin Rees and can be explained as an optical illusion caused by the object partly moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light. Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.

Notations
Notation: let the symbol VLBI stand for Very Long Baseline Interferometry.

Superluminals
NGC 2903 is a barred spiral galaxy in the constellation of Leo, first documented by William Herschel in 1784. Although it is bright and fairly large, easily seen in binoculars, it escaped the attention of Charles Messier and his associate Pierre Mechain. On a large scale, NGC 2903 lies within the Virgo Supercluster which includes the Milky Way and Andromeda galaxies. Except for dwarf elliptical galaxy UGC 5086, at a distance of 2 million ly, it has no near neighbors, and does not belong to any local galaxy cluster. Such isolated galaxies, undisturbed by gravitational fields of large neighbors, are called "field galaxies", constitute 10-20% of the total galaxy population, and follow different evolutionary pathways than "cluster galaxies". Unaffected by major tidal forces and mergers, large field galaxies are most commonly low-surface-brightness (LSB) spirals with delicate and symmetrical spiral arm structure, and usually with low star formation rates (SFR). However, NGC 2903 is far from quiescent. Although its energy output is insufficient to qualify it as an active galactic nucleus (AGN), the nucleus is still bright in all bands, from radio waves to X-rays, suggesting the presence of a central supermassive black hole (SMBH) with polar jets and an accretion disk. Photometric and spectroscopic analysis of the central region reveals increased star formation rates generated by interstellar medium turbulence initiated by radiation pressure and feedback outflows from the central SMBH. The turbulence then extends outward, augmented by stellar winds and supernovae, enhancing new star formation further afield. The distinct blue floccules in the spiral arms represent "OB associations", huge clusters of very hot young stars.

From its measurable properties it can be calculated that NGC 2903 is about 26 million ly distant, and 100,000 light years in diameter, roughly 30% smaller than the Milky Way, and proportionally less luminous. Several interesting features within the galaxy are marked on the annotated image. Some sources define object NGC 2905 as a bright region near the nucleus, at the S end of the bulge. Opinions differ whether the object is a large collection of stars or a very hot ionized hydrogen (Hii) region. Meanwhile, both NED and SIMBAD extragalactic databases list NGC 2905 simply as a duplicate identifier for the main galaxy, NGC 2903. At the NE extremity of the galaxy there is evidence of a curved luminous region which does not seem to be a part of the spiral arm. I speculate it may be a small satellite galaxy in the process of merging, stretched into a "stellar stream" by the tidal forces of the main galaxy. Computer models show that stellar streams can persist through multiple galactic orbits, for billions of years, before they are ultimately dispersed into anonymity. Gaps in stellar streams are thought to be caused by encounters with dark matter overdensities (subhalos) within the galactic halo. At the W perimeter of the galaxy, ULX marks the location of an ultra-luminous X-ray source. Such objects can be associated with intermediate-mass black holes (IMBH), and may emit optical transients during the periods of more active accretion.

Numerous distant galaxies are visible on close inspection of the background, many of which have no identifier. Of the more prominent ones, the most formidable is SDSS J093239.53+214555.7, a hyperluminous giant galaxy, at least 160,000 ly in diameter, lying at a distance around 3.2 billion ly. Near the threshold of the limiting magnitude are seen three quasars (QSOs). The most remote is QSO B0929+2128, nearly 3,000 times brighter than the Miky Way, whose light travelled 10.9 billion years before reching us. When its photons were emitted, the quasar was receding at 251,428 km/s (relativistic or redshift recession velocity). In the present epoch, it lies at a "comoving = proper distance" of 18.7 billion ly, receding at a superluminal "proper recession velocity" of 405,052 km/s. The quasar is now located well beyond the "cosmic event horizon". Since the space between us is expanding faster than its light is moving toward us, the photons it is presently emitting can never reach us.

Def. having a speed greater than light is called a superluminal.

Def. having a speed equal to that of light is called a luminal.

Def. having a speed less than light is called a subluminal.

Here's a theoretical definition:

Def. having an acceleration (or deceleration) that produces speeds which cross the speed of light is called a transluminal.

"The waves cannot accelerate particles to transluminal velocities."

Mediums
Numerous distant galaxies are visible on close inspection of the background, many of which have no identifier. Of the more prominent ones, the most formidable is SDSS J093239.53+214555.7, a hyperluminous giant galaxy, at least 160,000 ly in diameter, lying at a distance around 3.2 billion ly. Near the threshold of the limiting magnitude are seen three quasars (QSOs) listed in the chart below the image.

Def. the nature of the surrounding environment is called a medium.

Cherenkovs
A typical Čerenkov telescope produces a "flash of light" image which appears as a bright spot with an angular resolution of about 1°.

With a single telescope displaying a single image of the event, it is difficult to reconstruct its exact geometry and trace the energy of the primary gamma photon. To improve the angular resolution it is necessary to resort to the stereoscopic technique observing the same event from different angles using several telescopes placed at optimal distance from each other.

In this way, by combining the images obtained, it is possible to trace the trajectory of the swarm of particles and therefore define the axis and the vertex of the Čerenkov cone, essential data for determining the energy and direction of arrival of the gamma photon.

Magnetic Cherenkov radiation
"There is in fact also “magnetic” Cherenkov radiation from a pure magnetic dipole having no net electric charge".

Askaryan effect
The Askaryan effect is the phenomenon whereby a particle traveling faster than the phase velocity of light in a dense dielectric (such as salt, ice or the lunar regolith) produces a shower of secondary charged particles which contain a charge anisotropy and thus emits a cone of coherent radiation in the radio or microwave part of the electromagnetic spectrum. It is similar to the Cherenkov effect.

Theoretical superluminal astronomy
"The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally (see comoving distance for a discussion of different notions of 'velocity' in cosmology). Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10−36 seconds after the Big Bang to around 10−33 seconds), when the universe may have rapidly expanded by a factor of around 1020 to 1030.

There are many galaxies visible in telescopes with red shift numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually. However, because the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future, because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light-years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light-years away, but the signal would never reach us if the event was more than 16 billion light-years away.

“Observed variations concerning the brightness distributions in four extragalactic radio sources were so rapid that the apparent transverse velocity of expansion is greater than the velocity of light.”

“Maps of the radio structure of the quasar 3C273 provide evidence of a superluminal expansion during the period 1977-1980. The superluminal expansion might be attributed to the movement of a single knot away from the nucleus along the jet. The apparent constant velocity of 10 times the speed of light is an important constraint on theories of apparent superluminal expansion.”

Objects
"Tracking the features within small-scale jets has revealed interesting complications. The paths are not always radial to the nucleus, usually taken as the source with the flattest spectrum in ambiguous cases. This is based on the general principle that synchrotron spectra are flattened at lower frequencies by self-absorption, so the densest plasma will have a flat or inverted spectrum. An interesting case is 3C 345 [at right], in which emission features repeatedly appear off the core and follow fairly consistent nonradial paths. [...] a new component appears in late 1985, brightens, and moves outward changing its relative position angle in the process".

Electromagnetics
"The emission of electromagnetic radiation from a superluminal (faster-than-light in vacuo) charged particle [is such] that no physical principle forbids emission by extended, massless superluminal sources. A polarization current density (dP/dt; see Maxwell's fourth equation) can provide such a source; the individual charged particles creating the polarization do not move faster than c, the speed of light, and yet it is relatively trivial to make the envelope of the polarization current density to do so."

The "emitted radiation has many unusual characteristics, including: (i) the intensity of some components decays as the inverse of the distance from the source, rather than as 1/(distance)2 (i.e. these components are non-spherically-decaying); (ii) the emission is tightly beamed, the exact direction of the beam depending on the source speed; and (iii) the emission contains very high frequencies not present in the synthesis of the source. Note that the non-spherically decaying components of the radiation do not violate energy conservation. They result from the reception, during a short time period, of radiation emitted over a considerably longer period of (retarded) source time; their strong electromagnetic fields are compensated by weak fields elsewhere [1]."

The "emission occupies a very small polar angular width of order 0.8 degrees in the far field. Based on these findings, we suggest that a superluminal source could act as a highly directional transmitter of MHz or THz signals over very long distances."

"The magnetic field is well-ordered in many jets, as shown by polarization measurements. Synchrotron radiation can be very highly polarized (50%) if the field is globally ordered, and some sources [approach] this level. The electric vectors show clear structure and alignment; an especially common pattern is for the field lines to be along the jet in the inner portions and transition to an azimuthal configuration farther out. This is seen in [PKS0521-36 at 2 cm]."

Weak forces
"[C]harged particles moving faster than light through the vacuum emit Cherenkov radiation. How can a particle move faster than light? The weak speed of a charged particle can exceed the speed of light."

Emissions
"Seyfert galaxies were originally noted for the strength and broadening of their emission lines, and as a class were later characterized by the high ionization states of many of the atomic and ionized species producing these lines. This composite spectrum of the archetypal Seyfert NGC 4151 shows the wide variety of emission lines present, from the Lyman limit at 912 A to the mid-infrared at about 9 microns. It uses spectra taken with apertures several arcseconds in size, so as to reproduce the usual spectrum mixing broad and narrow-line components. From 912-1800 A, the data come from the Shuttle-borne Hopkins Ultraviolet Telescope; from 1800-3200 A, from the mean of three measurements by the International Ultraviolet Explorer (IUE) taken at similar brightness levels; from 3200-4000A, from an observation at Kitt Peak National Observatory, with the continuum rescaled to match the adjacent spectra; from 4000-8000 A, a CCD observation obtained at the Lick Observatory 3-m Shane telescope by Alexei Filippenko; from 8000 A to 1 microns, an observation using the same telescope by Donald Osterbrock and collaborators, carefully corrected for atmospheric absorption; from 0.9-2.4 microns, measurements by Rodger Thompson at Steward Observatory's 2,3-m Bok telescope, and on into the infrared, from the Infrared Space Observatory provided by Eckhard Sturm. Because NGC 4151 is irregularly variable, some of the spectral components have been scaled to make the various pieces match for this presentation (so the relative strengths of lines in very different spectral regions may not be accurate)."

"Some of the most prominent emission lines are marked for reference. The permitted lines - those that can be produced at high densities by astronomical standards - show both brad and narrow components. The strongest of these are the hydrogen recombination lines, such as Lyman alpha at 1216 A, H-beta at 4861, and H-alpha at 6563, plus the strong ultraviolet lines of C IV at 1549 and Mg II at 2800. Other features produced only by very rarefied gas at densities of 1000 atoms per cubic centimeter or so - the forbidden lines, denoted by brackets - arise in regions with less velocity structure and are narrower. Some strong examples are [O III] at 4959 and 5007 A, [O II] at 3727, [Ne V] at 3426, and [S III] at 9060 and 9532."

"The spectra of active galactic nuclei are noteworthy in showing species with a large range in ionization at once, from neutral ions such as [O I] and [N I] to highly ionized cases such as [Ne V] and [O VI]. Even hot stars such as light up gaseous nebulae in our galaxy cannot ionize gas as highly as these ions require, so that both a strong source of hard radiation and a wide range in gas density must be present to see such spectra."

Absorptions
"NGC 4151 is a bit unusual in showing strong absorption in several lines, especially Lyman alpha and C IV. The absorption is blueshifted with respect to the line centers, so that it arises in some kind of wind or other gaseous outflow."

Meteors
"[S]uperluminal motion for each of [two] knots, [in the BL Lacertae object OJ 287 is suggested] at an angular speed of 0.28 mas yr-1, corresponding to βapp = vapp/c ≃ 3.3h-1 (for z = 0.306, H0 = 100h km s-1 Mpc-1, and q0 = 0.5)." "Superluminal motion for each knot, with an apparent velocity ~3.3h-1c, is suggested by the polarization data. The polarizations of C [the core] and K2 [knot two] changed markedly over the year between observations."

Subsequent VLBI "observations of the total intensity structure of the BL Lacertae object OJ 287 have been made with an angular resolution of 7 x 1 mas at λ6 cm. The source consists of a core and three knots in a VLBI jet at position angle θ ≃ -100°. Previously suspected superluminal motion in the outer two knots at βapph ≃ 3 ... has been confirmed."

For the speeds in units of c, β = v/c, "[i]n the usual interpretation of superluminal motion, the apparent velocity is given by
 * $$\beta_{app} = { \beta_{jet} \sin \phi \over 1 - \beta_{jet} \cos \phi },$$

where βjetc is the jet velocity, and the jet makes an angle Φ to the line of sight."

In April 2010, radio astronomers working at the Jodrell Bank Observatory of the University of Manchester reported an unknown object in M82. The object has started sending out radio waves, and the emission does not look like anything seen anywhere in the universe before. There have been several theories about the nature of this unknown object, but currently no theory entirely fits the observed data. It has been suggested that the object could be a "micro quasar", having very high radio luminosity yet low X-ray luminosity, and being fairly stable. However, all known microquasars produce large quantities of X-rays, whereas the object's X-ray flux is below the measurement threshold. The object is located at several arcseconds from the center of M82. It has an apparent superluminal motion of 4 times the speed of light relative to the galaxy center.

Electrons
Cygnus A (Third Cambridge Catalogue of Radio Sources 3C 405) is a radio galaxy, and one of the strongest radio sources in the sky, along with Cassiopeia A, and Puppis A were the first "radio stars" identified with an optical source; of these, Cygnus A became the first radio galaxy; the other two being nebulae inside the Milky Way. It is a double source, contains an active galactic nucleus and a supermassive black hole at the core with a mass of 2.5 ± .7 x 109 solar mass.

"Many objects with jets, especially the powerful FR II radio sources with long and highly collimated jets, show hot spots - compact enhancements in brightness of the lobes. Cygnus A [at right] is a prime example. These may in turn have internal structure, and often have the flattest spectra (thus most energetic particle populations) in the extended lobes. They have been pictures as encounter surfaces between the jet flows and a mostly unseen surrounding medium, with compression of the magnetic field occurring and thus vastly increased emissivity. Some (such as Pictor A) have such high-energy electron populations that sychrotron emission continues through the optical into the X-ray regime."

Cygnus A "is the most powerful radio galaxy on our corner of the Universe, used as a point of departure for studying radio galaxies at great distances. At a redshift z=0.0565 (distance of about 211 Mpc or 700 million light-years), its nature remains mysterious enough. The first photographs of Cygnus A showed two clumps of luminous material, which led [to the speculation] that the radio emission was somehow linked to a galaxy collision. [Or,] a poorly resolved version of Centaurus A, bisected by a thick dust lane. The HST image shown as an inset [in the image at right] reveals much detail, but doesn't quite clear the matter up. We see dust and an odd Z-shaped pattern. Much of this light in some regions comes not from stars, but from gas ionized by the nucleus. This is a narrow-line radio galaxy, but infrared and polarization measurements show that from some directions it would appear as a broad-line object and perhaps as a quasar, so that there is plenty of radiation in some directions to light up the gas."

"Cygnus A is an excellent example of the Fanaroff-Riley (FR) type II radio sources, characterized by faint, very narrow jets, distinct lobes, and clear hot spots at the outer edges of the lobes, often where the jets intersect the outer edges. These are in general more powerful radio sources than the FR I objects [...], with the difference being frequently attributed to faster (relativistic?) motion of the jet material in the stronger FR II sources. The radio/optical overlay highlights the extent of the radio source beyond the central galaxy, extending 140 kpc (500,000 light-years) if we see it sideways."

Radio images show two jets protruding in opposite directions from the galaxy's center, extending many times the width of the portion of the host galaxy which emits radiation in the visible. At the ends of the jets are two lobes with "hot spots" of more intense radiation at their edges, formed when material from the jets collides with the surrounding intergalactic medium.

In 2016, a radio transient was discovered 460 parsecs away from the center of Cygnus A, between 1989 and 2016, the object, cospatial with a previously-known infrared source, exhibited at least an eightfold increase in radio flux density, with comparable luminosity to the brightest known supernova, but, the rate of brightening is unknown, the object has remained at a relatively constant flux density since its discovery, consistent with a second supermassive black hole orbiting the primary object, with the secondary having undergone a rapid accretion rate increase, where the inferred orbital timescale is of the same order as the activity of the primary source, suggesting the secondary may be perturbing the primary and causing the outflows.

Neutrinos
"Because neutrinos are electrically neutral, conventional Cherenkov radiation of superluminal neutrinos does not arise or is otherwise weakened. However neutrinos do carry electroweak charge and ... may emit Cherenkov-like radiation via weak interactions when traveling at superluminal speeds."

"[S]uperluminal neutrinos may lose energy rapidly via the bremsstrahlung [Cherenkov radiation] of electron-positron pairs $$(\nu \rightarrow \nu + e^- + e^+).$$"

Assumption:

"muon neutrinos with energies of order tens of GeV travel at superluminal velocity."

For "all cases of superluminal propagation, certain otherwise forbidden processes are kinematically permitted, even in vacuum."

Consider

 * $$ \nu_{\mu} \rightarrow \begin{bmatrix}

{\nu_{\mu} + \gamma} & (a) \\ {\nu_{\mu} + \nu_e + \overline\nu_e } & (b) \\ {\nu_{\mu} + e^+ + e^-} & (c) \end{bmatrix} $$

"These processes cause superluminal neutrinos to lose energy as they propagate and ... process (c) places a severe constraint upon potentially superluminal neutrino velocities. ... Process (c), pair bremsstrahlung, proceeds through the neutral current weak interaction."

"Throughout the shower development, the electrons and positrons which travel faster than the speed of light in the air emit Cherenkov radiation."

"High energy processes such as Compton, Bhabha, and Moller scattering, along with positron annihilation rapidly lead to a ~20% negative charge asymmetry in the electron-photon part of a cascade ... initiated by a ... 100 PeV neutrino".

Gamma rays
Tachyonic γ rays have not been observed directly as of 2007.

"The tachyonic spectral densities generated by ultra-relativistic electrons in uniform motion are fitted to the high-energy spectra of Galactic supernova remnants, such as RX J0852.0−4622 and the pulsar wind nebulae in G0.9+0.1 and MSH 15-52. ... Tachyonic cascade spectra are quite capable of generating the spectral curvature seen ... Estimates on the electron/proton populations generating the tachyon flux are obtained from the spectral fits"

"Tachyonic radiation implies superluminal signal transfer [1-7], the energy quanta propagating faster than light in vacuum, in contrast to rotating superluminal light sources emitting vacuum Cherenkov radiation [8, 9]."

"The existence of superluminal energy transfer has not been established so far, and one may ask why. There is the possibility that superluminal quanta just do not exist, the vacuum speed of light being the definitive upper bound. There is another explanation, the interaction of superluminal radiation with matter is very small, the quotient of tachyonic and electric fine-structure constants being q2/e2 ≈ 1.4 x 10-11 [5], and therefore superluminal quanta are hard to detect."

X-rays
There is a cut-off frequency above which the equation $$\cos\theta=1/(n\beta)$$ cannot be satisfied. Since the refractive index is a function of frequency (and hence wavelength), the intensity does not continue increasing at ever shorter wavelengths even for ultra-relativistic particles (where v/c approaches 1). At X-ray frequencies, the refractive index becomes less than unity (note that in media the phase velocity may exceed c without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as gamma rays) would be observed. However, X-rays can be generated at special frequencies just below those corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonance frequency (see Kramers-Kronig relation and anomalous dispersion).

Opticals
"Measurements of the polarization of the light near the nucleus of NGC 1068, a nearby and prototypical type 2 Seyfert, provided strong evidence that it actually contains a type 1 nucleus which is blocked from our direct view by an obscuring ring or torus of material. The nucleus produces a radio jet at right angles to this hypothesized torus, which must lie almost at right angles to the galaxy's disk plane. Recent VLBI observations may have detected this torus, as shown in this montage. HST images are used to show the galaxy as a whole and the conelike illumination pattern of highly ionized gas which must see the nucleus directly, then the radio jet and finally a tiny structure which has the right size, orientation, and temperature to be the obscuring disk. If this in fact the obscuring material, this is an important piece of evidence for the unified scheme for Seyfert galaxies. This is simply the notion that many type 2 Seyferts would be type 1 objects if we could see them from the proper direction, nearly along the axis of the torus so that our view is not blocked. These special directions are often marked by both radio jets and cones of intense radiation, which we see either as they ionize ambient gas or are reflected from clouds rich in dust that happen to lie within the cones."

Blues
The frequency spectrum of Cherenkov radiation by a particle is given by the Frank–Tamm formula. Unlike fluorescence or emission spectra that have characteristic spectral peaks, Cherenkov radiation is continuous. Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter wavelengths) are more intense in Cherenkov radiation. This is why visible Cherenkov radiation is observed to be brilliant blue. In fact, most Cherenkov radiation is in the ultraviolet spectrum—it is only with sufficiently accelerated charges that it even becomes visible; the sensitivity of the human eye peaks at green, and is very low in the violet portion of the spectrum.

At right is an example of Cherenkov radiation. "Cherenkov radiation (also spelled Čerenkov) is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium.

Reds
"[M]ultiwavelength observations of the superluminal X-ray transient GRO J1655-40 [have been performed] during and following the prominent hard X-ray outburst of 1995 March-April."

"The red color of the optical counterpart with E(B - V) = +1.3 ± 0.2, as recently determined by deep 200 nm Hubble Space Telescope (HST) observations in 1995 May (Horne et al. 1996), indicates significant absorption in the direction of GRO J1655-40 (see also B95a). Spectroscopic CTIO observations of GRO J1655-40 carried out in early 1995 May revealed Doppler-shifted high-excitation emission lines superposed on an F-type or early G-type stellar absorption spectrum (Bailyn et al. 1995b, hereafter B95b)."

Radios
"Historically, the connection between radio loud [RLQs] and radio quiet quasars [RQQs] has been unclear, but new studies are pointing toward a similarity in the physical mechanisms of core radio emission in the two classes. Both classes appear to have similar core spectral index distributions, including or inverted cores in RQQs, both have compact VLBI cores, and both appear to be about equally time-variable. This suggests that RQQs possess beamed, relativistic jets like those in RLQs. If RQQs are really lower power cousins of RLQs, the jets in RQQs should show superluminal motions. With the advent of very high sensitivity VLBI using the High Sensitivity Array, it should now be possible to detect the parsec-scale jets in RQQs and measure component speeds."

GW170817
"The binary neutron-star merger GW1708171 was accompanied by radiation across the electromagnetic spectrum2 and localized2 to the galaxy NGC 4993 at a distance3 of about 41 megaparsecs from Earth. The radio and X-ray afterglows of GW170817 exhibited delayed onset4–7, a gradual increase8 in the emission with time (proportional to t0.8) to a peak about 150 days after the merger event8, followed by a relatively rapid decline9,10."

The "compact radio source associated with GW170817 exhibits superluminal apparent motion between 75 days and 230 days after the merger event. This measurement breaks the degeneracy between the choked- and successful-jet cocoon models and indicates that, although the early-time radio emission was powered by a wide-angle outflow8 (a cocoon), the late-time emission was most probably dominated by an energetic and narrowly collimated jet (with an opening angle of less than five degrees) and observed from a viewing angle of about 20 degrees. The imaging of a collimated relativistic outflow emerging from GW170817 adds substantial weight to the evidence linking binary neutron-star mergers and short γ-ray bursts."

Very "long-baseline interferometry (VLBI) observations with the High Sensitivity Array (HSA)—which consists of the Very Long Baseline Array (VLBA), the Karl G. Jansky Very Large Array (VLA) and the Robert C. Byrd Green Bank Telescope (GBT)—75 and 230 days after the GW170817 merger event [...] indicate that the centroid position of the radio counterpart of GW170817 changed from a right ascension of RA = 13 h 09 min 48.068638(8) s and declination of dec. = −23° 22′ 53.3909(4)′′ to RA = 13 h 09 m in 48.068831(11) s and dec. = −23° 22′ 53.3907(4)′′ between these epochs (1σ uncertainties in the last digits are given in parentheses). This implies an positional offset between the two observations of 2.67±0.19±0.21 mas in RA and 0.2±0.6±0.7 mas in dec. (1σ uncertainties; statistical and systematic, respectively; [...]). This corresponds to a mean apparent velocity of the source of the radio counterpart along the plane of the sky of βapp = 4.1 ± 0.5, where βapp is in units of the speed of light, c (1σ, including the uncertainty in the source distance). [...] Our VLBI data are consistent with the source being unresolved at both day 75 and day 230. Given the VLBI angular resolution and the signal-to-noise ratio of the detection, this puts an upper limit on the size of the source in both epochs of about 1 mas (0.2 pc at the distance of NGC 4993) in the direction parallel to its motion and 10 mas perpendicular to its motion [...]."

"Although superluminal motion is seen frequently in active galactic nuclei and micro-quasars, it is extremely rare in extragalactic explosive transients. Superluminal motion has been measured in only one such transient: the long-duration γ-ray burst GRB 03032924. GRB 030329 had a measured superluminal expansion of βapp ≈ 3–5, but no proper motion, whereas GW170817 has measured proper motion, but no expansion. Although both were relativistic events of comparable energies, these differences suggest different geometries and/or viewing angles."

Gaseous objects
"These images [at right] both depict the same area - the region of ionized gas around the nucleus of the bright Seyfert galaxy NGC 4151. In one case, the observations used a narrow-band filter to isolate the bright gaseous emission of doubly ionized oxygen - [O III] - at 5007 Angstroms, while the other used a diffraction grating to spread the light at each point into a spectrum. The color coding was used to indicate this and to show the direction of spectral dispersion, though the wavelength range spanned by the observation would not produce a vivid color range visually. The brilliant nucleus is spread into a horizontal line, producing radiation at all wavelengths in the form of a continuum. In the dispersed image, a single cloud of gas with small internal motions will have a single Doppler shift, and will have the same appearance as in the filtered image, perhaps with a position shift due to its overall Doppler shift with respect to the average. However, a parcel of gas with a large velocity dispersion, such as one might see in a turbulent situation or near a shock front, will be preferentially smeared along the wavelength direction (left-right in this depiction). Careful comparison of these two images shows that there are many such regions, mostly located in the locations close to where the galaxy's small radio jets emerge from the nucleus. These radio jets lie approximately along the axes of the twin emission-line cones. This connection between rapid local gas motions and the emerging jets has been interpreted as evidence that much of the "turbulent" motion in the outer regions of Seyfert nuclei is powered by the radio jets, as they transfer energy to their surroundings."

"The emission-line image shows clearly the biconical region where most of the ionized gas appears, in support of a `beaming picture" for the various kinds of Seyfert nuclei. It poses an interesting puzzle, however, because to get this plan view we must be outside the cones, but we see the broad-line region and thus classify NGC 4151 as a type 1 Seyfert - in fact, it was the prototype of the class. Thus, there are directions outside these cones where we can have a fairly clear view of the core, so the simple mental picture of a solid torus and clear views along its axis cannot be taken quite literally."

Hydrogen
"Superluminal speeds are associated with a phenomenon known as anomalous dispersion, whereby the refractive index of a medium (such as an atomic gas) increases with the wavelength of transmitted light. When a light pulse – which is comprised of a group of light waves at a number of different wavelengths – passes through such a medium, its group velocity can be boosted to beyond the velocity of its constituent waves."

"As pulsars spin, they emit a rotating beam of radiation that flashes past distant observers at regular intervals like a lighthouse beacon."

"Several factors are known to affect the pulses. Neutral hydrogen can absorb them, free electrons can scatter them and an additional magnetic field can rotate their polarization. Plasma in the interstellar medium also causes dispersion, which means pulses with longer wavelengths are affected by a smaller refractive index."

"Using the Arecibo Observatory in Puerto Rico, they took radio data of the pulsar PSR B1937+21 at 1420.4 MHz with a 1.5 MHz bandwidth for three days. Oddly, those pulses close to the center value arrived earlier than would be expected given the pulsar's normal timing, therefore appearing to have traveled faster than the speed of light."

"The cause of the anomalous dispersion for these pulses [...] is the resonance of neutral hydrogen, which lies at 1420.4 MHz."

Interstellar medium
"In far-distant quasars and galaxies, millions or even billions of light-years away, the gravitational energy of supermassive black holes is capable of accelerating "jets" of subatomic particles to speeds approaching that of light. The VLA has observed such jets for many years. In some of these jets, blobs of material have been seen to move at apparent speeds greater than that of light -- a phenomenon called superluminal motion. The apparent faster-than-light motion actually is an illusion seen when a jet of material is travelling close to -- but below -- the speed of light and directed toward Earth."

"In the Spring of 1994, Felix Mirabel from Saclay, France, and Luis Rodriguez, from the National Autonomous University in Mexico City, were observing an X-ray emitting object called GRS 1915+105, which had just shown an outburst of radio emission. This object was known to be about 40,000 light-years away, within our own Milky Way Galaxy -- in our own cosmic neighborhood. Their time series of VLA observations, seen in this image, showed that a pair of objects ejected from GRS 1915+105 were moving apart at an apparently superluminal speed. This was the first time that superluminal motion had been detected in our own Galaxy."

"This surprising result showed that the supermassive black holes at the centers of galaxies -- black holes millions of times more massive than the Sun -- have smaller counterparts capable of producing similar jet ejections. GRS 1915+105 is thought to be a double-star system in which one of the components is a black hole or neutron star only a few times the mass of the Sun. The more-massive object is pulling material from its stellar companion. The material circles the massive object in an accretion disk before being pulled into it. Friction in the accretion disk creates temperatures hot enough that the material emits X-rays, and magnetic processes are believed to accelerate the material in the jets."

"Since Mirabel and Rodriguez discovered the superluminal motion in GRS 1915+105, several other Galactic "microquasars" have been discovered and studied with the VLA and the VLBA. In 1999, NRAO astronomer Robert Hjellming turned the VLA toward a bursting microquasar within 24 hours of a reported X-ray outburst. Working with X-ray observers Donald Smith and Ronald Remillard of MIT, Hellming found that this object is a microquasar only 1,600 light-years away, making it the closest black hole to Earth yet discovered."

"Microquasars within our own Galaxy, because they are closer and thus easier to study, have become invaluable "laboratories" for revealing the physical processes that produce superfast jets of material. For discovering this new class of celestial object, Mirabel and Rodriguez received the prestigous Bruno Rossi Prize of the American Astronomical Society in 1997."

"On the far side of our Galaxy, gas clouds explode away from a small black hole. This might seem peculiar, as black holes are supposed to attract matter. But material falling toward a black hole collides and heats up, creating an environment similar to a quasar that is far from stable. In the [at second right] time-lapse sequence, micro-quasar GRS1915 expels bubbles of hot gas in spectacular jets. These computer enhanced radio images show one plasma bubble coming almost directly toward us at 90 percent the speed of light, and another moving away. Each of the four frames marks the passage of one day. Originally detected on October 29th, these bubbles have now faded from view."

In the second image down on the right is shown a time-lapse sequence, where each of the four frames marks the passage of one day, as the micro-quasar GRS1915 expels bubbles of hot gas in spectacular jets at apparently superluminal speeds.

Milky Way
"Researchers using the Very Large Array (VLA) have discovered that a small, powerful object in our own cosmic neighborhood is shooting out material at nearly the speed of light -- a feat previously known to be performed only by the massive cores of entire galaxies. In fact, because of the direction in which the material is moving, it appears to be traveling faster than the speed of light -- a phenomenon called "superluminal motion.""

BL Lacertae objects
A BL Lacertae object or BL Lac object is a type of active galaxy with an active galactic nucleus (AGN) and is named after its prototype, BL Lacertae. In contrast to other types of active galactic nuclei, BL Lacs are characterized by rapid and large-amplitude flux variability and significant optical polarization.

All known BL Lacs are associated with core dominated radio sources, many of them exhibiting superluminal motion.

Intergalactic medium
"The very fast neon nova GK Persei rivalled the brightness of Vega at the peak of its outburst in 1901 (see Bode, O’Brien & Simpson 1994, and references therein). Early observations showed it to possess optical nebulosities on arcminute scales apparently expanding at super-light velocities and subsequently explained as light echoes (Kapteyn 1902). Indeed, it was the first astronomical source in which such motion was observed and one of only three novae where such an effect has been noted (the other two being V732 Sgr (Swope 1940) and V1974 Cyg (Casalegno et al. 2000) - see next section)."

"The 1901 nova outburst was therefore the first of ultimately very many that this system will undergo."

"The classical nova GK Persei ... has turned out to be the longest lived and most energetic among the classical novae and appears more like a supernova remnant (SNR) in miniature but evolving on human timescales."

"Images made with the Very Long Baseline Array (VLBA) radio telescope show the mysterious X-ray nova in Scorpius as it ejected blobs of material at tremendous speeds over the period from August 18 to September 22, 1994. Some of these blobs appear to be moving faster than the speed of light -- an illusion created by both the great actual speed of the blobs and their direction of travel with relation to the Earth."

"This object was discovered by the Compton Gamma Ray Observatory "

Relativistic jets
In the images at right are the effects of charged particles apparently moving six times the speed of light.

"We see almost a dozen clouds which appear to be moving out from the galaxy's center at between four and six times the speed of light. These are all located in a narrow [relativistic] jet of gas streaming out from the region of the black hole at the galaxy's center".

"We believe this apparent speed translates into an actual velocity just slightly below that of light itself."

"The speeds reported are two to three times faster than the fastest motions previously recorded in M87, the only nearby galaxy to show evidence for superluminal motion."

"This discovery goes a long way towards confirming that radio galaxies, quasars and exotic BL Lac objects are basically the same beast, powered by super massive black holes, and differ only in orientation with respect to the observer".

"Here we have, for the first time, a fairly normal radio galaxy with both excellent evidence for a super-massive black hole, as well as superluminal jet speeds similar to those seen in distant quasars and BL Lac objects."

"This is the first time superluminal motion has been seen with any optical telescope, and this discovery was made possible by the extremely fine resolution obtained by Hubble".

"The structure of relativistic jets in [active galactic nuclei] AGN on scales of light days reveals how energy propagates through jets, a process that is fundamental to galaxy evolution."

Their lengths can reach several thousand or even hundreds of thousands of light years. The hypothesis is that the twisting of magnetic fields in the accretion disk collimates the outflow along the rotation axis of the central object, so that when conditions are suitable, a jet will emerge from each face of the accretion disk. If the jet is oriented along the line of sight to Earth, relativistic beaming will change its apparent brightness. The mechanics behind both the creation of the jets and the composition of the jets are still a matter of much debate in the scientific community; it is hypothesized that the jets are composed of an electrically neutral mixture of electrons, positrons, and protons in some proportion.

A relativistic jet emitted from the AGN of M87 is traveling at speeds between four and six times the speed of light.

"The term 'superluminal motion' is something of a misnomer. While it accurately describes the speeds measured, scientists still believe the actual speed falls just below the speed of light."

"It's an illusion created by the finite speed of light and rapid motion".

"Our present understanding is that this 'superluminal motion' occurs when these clouds move towards Earth at speeds very close to that of light, in this case, more than 98 percent of the speed of light. At these speeds the clouds nearly keep pace with the light they emit as they move towards Earth, so when the light finally reaches us, the motion appears much more rapid than the speed of light. Since the moving clouds travel slightly slower than the speed of light, they do not actually violate Einstein's theory of relativity which sets light as the speed limit."

Active galactic nuclei
For active galactic nuclei (AGNs) "bright jet features typically exhibit apparent superluminal speeds and accelerated motions."

AGN "jets with the fastest superluminal speeds all tend to have high Doppler boosted radio luminosities. [...] there is a correlation between intrinsic jet speed and intrinsic (de-beamed) luminosity".

The AGN showing superluminal motion in B1950 are
 * 1) 0003+380 S4 0003+38 J0006.1+3821 z=0.229 quasar
 * 2) 0003-066 NRAO 005 ... z=0.3467 BL Lac
 * 3) 0007+106 III Zw 2 ... z=0.0893 radio galaxy
 * 4) 0010+405 4C +40.01 ... z=0.256 quasar
 * 5) 0015-054 PMN J0017-0512 J0017.6-0510 z=0.226 quasar
 * 6) 0016+731 S5 0016+73 ··· z=1.781 quasar
 * 7) 0048-097 PKS 0048-09 J0050.6-0929 z=0.635 BL Lac
 * 8) 0055+300 NGC 315 ··· z=0.0165 radio galaxy
 * 9) 0059+581 TXS 0059+581 J0102.7+5827 z=0.644 quasar
 * 10) 0106+013 4C +01.02 J0108.6+0135 z=2.099 quasar
 * 11) 0109+224 S2 0109+22 J0112.1+2245 z=0.265 BL Lac
 * 12) 0109+351 B2 0109+35 ··· z=0.450 quasar
 * 13) 0110+318 4C +31.03 J0112.8+3208 z=0.603 quasar
 * 14) 0111+021 UGC 00773 ··· z=0.047 BL Lac
 * 15) 0116-219 OC -228 J0118.8-2142 z=1.165 quasar.

At right is a radio image of quasar S4 0003+38. This object was image on March 9 and December 1, 2006, March 28 and August 24, 2007, May 1 and July 17, 2008, March 25, 2009, and July 12, 2010. From its movement as it was leaving its source in µas y-1, S4 0003+38 before it left its source was moving at 2.62±0.84c, left its source at a back projected date of 2003.01±0.24, continued accelerating to 4.63±0.32c, then began to decelerate successively at each observation epoch from 0.67±0.20, 0.36±0.32, to 0.16±0.26.

The second image at right is of apparent superluminal motion in NGC 315. In both of these images the apparent motion is rectilinear or close to it. NGC 315 is a low-luminosity radio galaxy.

The third image at right shows the approximate radial motion of the jet component versus the core.

"Inward motions are rare (2% of all features), are slow (< 0.1 mas per y), are more prevalent in BL Lac jets, and are typically found within 1 mas of the unresolved core feature. [...] Considering only the AGN with a known redshift, the inward components of 1458+718 [fourth at right] are the only ones which appear significantly superluminal, ranging from 1.4 c to 4.6 c. With the exception of 1458+718, 2021+614, and 2230+114, the inward motions all occur within ∼ 1 mas of the core, in typically the innermost component. In particular, the innermost two jet components of two TeV-emitting BL Lacs in our sample: 0219+428 (3C 66A) [at fifth right] and 1219+285 (W Comae) are both inward-moving. The small velocities and core separations of these moving components may indicate that the core is not a stable reference point in these two jets."

The line in the image for 1458+718 connects the two components. The "the apparent inward motion [...] of [the] two component [is] in a complex emission region located ∼ 25 mas south of the core in this compact steep spectrum quasar. [There is] one additional component in this complex [...] that is also moving inward, in a non-radial direction."

"The moving features are generally non-ballistic, with 70% of the well-sampled features showing either significant accelerations or non-radial motions."

"A substantial number of components showed no significant acceleration, but had non-radial motion vectors. [...] This is in stark contrast to the kinematics of features in stellar (Herbig-Haro) jets, which are well described by ballistic models [...] Of the 739 components with statistically significant (≥ 3σ) speeds, 38% exhibited significant non-radial motion, implying non-ballistic trajectories.".

The "acceleration [is resolvable into] terms μ⊥ and μǁ in directions perpendicular and parallel, respectively, to the mean angular velocity direction φ."

"[S]ignificant parallel accelerations [are] seen in roughly one third of our sample, and significant perpendicular accelerations in about one fifth of our sample."

"VLBA images of the jet in the broad-line radio galaxy 3C 111. The picture shows the variable parsec-scale structure of the jet in this active galactic nucleus. The features observed correspond to ejected plasma regions traveling at relativistic speeds. Those appear to be larger than the speed of light due to projection effects. The sixteen images are spaced by their relative time intervals. The images show that a major radio flux-density outburst in 1996 was followed by a particularly bright plasma ejection associated with a superluminal jet component. This major event was followed by trailing features in its evolution. A similar event is seen after mid 2001. The jet dynamics in this source is revealed: a plasma injection into the jet beam leads to the formation of multiple shocks that travel at different speeds downstream (ranging from 3c to 6c) and interact with each other and with the ambient medium. This is in agreement with numerical relativistic magnetohydrodynamic structural and emission simulations of jets."

"Images were taken at 15 GHz with the full Very Long Baseline Array as part of the 2cm Survey/MOJAVE collaboration. The observing runs usually last 8 hr and the total observing time on source is approximately 50 minutes. The typical dynamic range in the images is of 1000:1 (the lowest shown flux density is typically of 1-2 mJy/beam). The images are convolved with a common restoring beam of 0.5x1.0 milliarcseconds (P.A. of 0 deg). The image alignment is (arbitrary) to the brightness peak. The superluminal speeds of the features in the jet were determined from a detailed analysis of multiple Gaussian model fits to the observed visibilities."

Quasars
"Superluminal motion in quasar 3C279 is shown [at right] in a "movie" mosaic of five radio images made over seven years. The stationary core is the bright red spot to the left of each image. The observed location of the rightmost blue-green blob moved about 25 light years from 1991 to 1998, hence the changes appear to an observer to be faster than the speed of light or "superluminal". The motion is not really faster than light, the measured speed is due to light-travel-time effects for a source moving near the speed of light almost directly toward the observer. The blue-green blob is part of a jet pointing within 2 degrees to our line of sight, and moving at a true speed of 0.997 times the speed of light. These five images are part of a larger set of twenty-eight images made with the VLBA and other radio telescopes from 1991 to 1997 to study the detailed properties of this energetic quasar." The images are in the K band, 1.2 cm, 22 GHz.

"A time ordered sequence of images of the microquasar GRO J1655-10, with earlier times at the top and later times underneath. This sequence covers a month in the life of the microquasar, as imaged by the VLBA. GRO J1655-40 is a binary system in which the outer envelope of the normal star is overflowing onto its black hole companion. The accreting matter swirls into a rapidly rotating disk as it falls towards the black hole; near the center, some of this matter is "squirted out" perpendicular to the disk, at relativistic speeds (i.e, speeds approaching the speed of light). The radio emission associated with these relativistic jets is what we see here. The intrinsic speed of these jets is about 90% of the speed of light. Because the jets are moving almost as fast as the radiation they emit, the approaching jet appears to move even faster, and the apparent motions range up to 1.3 times the speed of light."

"VLBA images [are] at 1.6 GHz. Images made from data collected in August and September, 1994. Top image from Aug 18-19; next one from Aug 22-23; next Aug 25-26; next Aug 25-26; next Sep 1-2; next Sep 8-9; next Sep 12-13; and last Sep 20-21."

"It is generally accepted that the blazar phenomenon is due to the anisotropic boosting of the radiation along the direction of motion which gives rise to an apparent enhanced luminosity at all wavelengths if the observer is located close to the direction of motion. There are many observations which support this interpretation including the one sided appearance of blazar jets and the rapid flux density variability observed at many wavelengths. However, the only direct observations of relativistic motion are at radio wavelengths when motion close to the line of sight produces a compression of the time frame resulting in apparent superluminal motion. High resolution interferometric radio images are able to measure such motions which are typically less than one milliarcsecond per year."

The "details of the kinematics [of superluminal source motions] have remained elusive. One of the problems is, that contrary to indications of early observations (e.g., Cohen et al. 1977), the radio jets often do not contain simple well defined moving components. Instead, the jets may show a complex brightness distribution with regions of enhanced intensity that may brighten and fade with time. Some features appear to move; others are stationary, or may break up into two or more separate features, and it is often unclear how these moving features are related to the actual underlying relativistic flow."

The third image at right "shows the distribution of apparent linear velocity for the 157 components contained in our full sample that have well-determined motions. This includes 104 quasar components, 31 BL Lac components, and 22 components associated with the nucleus of an active galaxy."

This image "is in marked contrast to early discussions of superluminal motion, which indicated typical values of γ in the range 5 to 10 (Cohen et al. 1977, Porcas 1987). [...] Most of the sources in our sample are quasars and their velocity distribution is peaked near low values of v/c between zero and ten, but there is a tail extending out to v/c ~ 34. Features associated with the active nuclei of galaxies all appear to have motions in the range 0 < v/c < 8, while the BL Lac objects appear more uniformly distributed over the entire range from 0 to 35."

Double-lobed quasars
The "detection of superluminal motion in the central component of the double-lobed quasar 3C 245 [is shown above in the Objects section above.] This object has a strong nucleus (S = 0.91 Jy at 5 GHz; [an] extended, steep-spectrum emission [and] is intermediate between lobe-dominated (R < 1) and core-dominated (R > 1) objects. [Where R is the ratio of compact to extended flux density at an emitted frequency ν = 5 GHz.]" The object was observed at five successive epochs: 1981.76, 1983.11, 1983.78, 1984.95, and 1986.17.

"The apparent separation of the centroids of [each lobe] changes from 0.33 mas to 0.46 mas between epochs 4 and 5; [...] The milliarcsecond-scale structure of 3C 245 may be interpreted as a typical "core-jet" source, [...] The jet components [...] are aligned, within the errors, with a one-sided jet on a scale of ~ 10-30 mas, which in turn is aligned with the inner knots of a curved arcsecond jet [...] z = 1.029 [...] the curvature (~ 20°) in the arcsecond-scale jet is moderate for extragalactic radio sources. [...] moderate apparent curvature is expected in a source with small intrinsic curvature aligned at a fairly small angle to the line of sight, θ."

The "strong, rapid variability provides evidence for bulk relativistic motion. [...] The proper motion of 0.11 ± 0.05 mas yr-1 [...] translates into an apparent transverse velocity [of] (3.1 ± 1.4) [c]. The apparent velocity in 3C 245 lies between that of the other of two known steep-spectrum, double-lobed superluminal quasars (4.5 [c] for 3C 179, [and] 1.3 [c] for 3C 263 [...] The average apparent velocity in the three steep-spectrum, double-lobed quasars is half that in the seven best-studied, strongly core-dominated superluminal quasars"

A "linear-correlation coefficient test using these 10 quasars shows a correlation of βapp with R significant at the 96% level".

Recent history
The recent history period dates from around 1,000 b2k to present.

"VLBI (very-long-baseline interferometry) observations between 1971 and 1983 have been used to determine the positions of the 'core' of the quasar 3C345 relative to the more distant compact quasar NRAO512 with a fractional uncertainty as small as two parts in a hundred million. The core of 3C345 appears stationary in right ascension to within 20 arc microsec/yr, a subluminal bound corresponding to 0.7c. The apparent velocities of the jets are superluminal, up to 14c in magnitude."

Physics
A relativistic jet coming out of the center of an active galactic nucleus is moving along AB with a velocity v. We are observing the jet from the point O. At time $$t_1$$ a light ray leaves the jet from point A and another ray leaves at time $$t_2$$ from point B. Observer at O receives the rays at time $$t_1^\prime$$ and $$t_2^\prime$$ respectively.

 * $$AB \ = \ v\delta t$$
 * $$AC \ = \ v\delta t \cos\theta$$
 * $$BC \ = \ v\delta t \sin \theta$$
 * $$t_2-t_1 \ = \ \delta t$$

 * $$t_1^\prime = t_1 + \frac{D_L+v\delta t \cos\theta}{c}$$
 * $$t_2^\prime =t_2+ \frac{D_L}{c}$$

 * $$\delta t^\prime = t_2^\prime - t_1^\prime = t_2 - t_1 - \frac{v\delta t \cos\theta}{c} = \delta t - \frac{v\delta t \cos\theta}{c} = \delta t (1-\beta \cos\theta)$$, where $$\beta=\frac{v}{c}$$

 * $$\delta t = \frac{\delta t^\prime}{1-\beta\cos\theta}$$

 * $$BC \ = \ D_L\sin\phi \approx \phi D_L = v\delta t \sin \theta \Rightarrow \phi D_L = v\sin\theta\frac{\delta t^\prime}{1-\beta\cos\theta}$$

Apparent transverse velocity along CB, $$v_T = \frac{\phi D_L}{\delta t^\prime}=\frac{v\sin\theta}{1-\beta\cos\theta}$$

 * $$\beta_T = \frac{v_T}{c} = \frac{\beta\sin\theta}{1-\beta\cos\theta}$$

 * $$\frac{\partial\beta_T}{\partial\theta} = \frac{\partial}{\partial\theta} \left[\frac{\beta\sin\theta}{1-\beta\cos\theta}\right] = \frac{\beta\cos\theta}{1-\beta\cos\theta} - \frac{(\beta\sin\theta)^2}{(1-\beta\cos\theta)^2} = 0$$

 * $$\Rightarrow \beta\cos\theta (1-\beta\cos\theta)^2 = (1 - \beta\cos\theta) (\beta\sin\theta)^2$$

 * $$\Rightarrow \beta\cos\theta (1-\beta\cos\theta) = (\beta\sin\theta)^2 \Rightarrow \beta\cos\theta - \beta^2\cos^2\theta = \beta^2sin^2\theta \Rightarrow \cos\theta_{max} = \beta$$

 * $$\Rightarrow \sin\theta_{max} = \sqrt{1-\cos^2\theta_{max}} = \sqrt{1-\beta^2} = \frac{1}{\gamma}$$, where $$\gamma=\frac{1}{\sqrt{1-\beta^2}}$$

 * $$\therefore \beta_T^{max} = \frac{\beta\sin\theta_{max}}{1-\beta\cos\theta_{max}} = \frac{\beta/ \gamma}{1-\beta^2} = \beta\gamma$$

If $$\gamma \gg 1$$ (i.e. when velocity of jet is close to the velocity of light) then $$\beta_T^{max} > 1$$ despite the fact that $$\beta < 1$$. And of course $$\beta_T > 1$$ means apparent transverse velocity along CB, the only velocity on sky that we can measure, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal.

Observatories
"For the 1989.29 VLBI observation we simultaneously used the VLA [above center] at 5 GHz in its normal B-configuration synthesis mode to obtain an image of the large scale structure of 3C390.3 with angular resolution of 1.2". We observed the source nearly continuously for 14 hours, except for a 5 min observation of 1803+784 as a phase and amplitude calibrator twice per hour."

Detectors
Most Cherenkov detectors aim at recording the Cherenkov light produced by a primary charged particle. Some sensor technologies explicitly aim at Cherenkov light produced (also) by secondary particles, be it incoherent emission as occurring in an electromagnetic particle shower or by coherent emission, example Askaryan effect.

Cherenkov radiation is not only present in the range of visible light or UV light but also in any frequency range where the emission condition can be met i.e. in the radiofrequency range.

Different levels of information can be used. A binary information can be based on the absence or presence of detected Cherenkov radiation. The amount or the direction of Cherenkov light can be used. In contrast to a scintillation counter the light production is instantaneous.

Cherenkov threshold detectors have been used for fast timing and Time of flight measurements in particle physics experiments. More elaborate designs use the amount of light produced. Recording light from both primary and secondary particles, for a Cherenkov calorimeter the total light yield is proportional to the incident particle energy.

Using the light direction are differential Cherenkov detectors. Recording individual Cherenkov photon locations on a position-sensitive sensor area, RICH detectors then reconstruct Cherenkov angles from the recorded patterns. As RICH detectors hence provide information on the particle velocity, if the momentum of the particle is also known (from magnetic bending), combining these two informations enables the particle mass to be deduced so that the particle type can be identified.

A Ring-imaging Cherenkov (RICH) detector is a device that allows the identification of electrically charged subatomic particle types through the detection of the Cherenkov radiation emitted (as photons) by the particle in traversing a medium with refractive index $$ n $$ > 1. The identification is achieved by measurement of the angle of emission, $$ \theta_c $$, of the Cherenkov radiation, which is related to the charged particle's velocity $$ v $$ by

$$ \cos \theta_c = c/nv, $$

where $$c$$ is the speed of light.

The LHCb experiment on the Large Hadron Collider uses two RICH detectors for differentiating between pions and kaons. The first (RICH-1) is located immediately after the Vertex Locator (VELO) around the interaction point and is optimised for low-momentum particles and the second (RICH-2) is located after the magnet and particle-tracker layers and optimised for higher-momentum particles.

The Alpha Magnetic Spectrometer device AMS-02, recently mounted on the International Space Station uses a RICH detector in combination with other devices to analyze cosmic rays.

Cherenkov detectors
A Cherenkov (Čerenkov) detector is a particle detector using the mass-dependent threshold energy of Cherenkov radiation. This allows a discrimination between a lighter particle (which does radiate) and a heavier particle (which does not radiate).

It is a more advanced form of scintillation counter. A particle passing through a material at a velocity greater than that at which light can travel through the material emits light. This is similar to the production of a sonic boom when an airplane is traveling through the air faster than sound waves can move through the air. This light is emitted in a cone about the direction in which the particle is moving. The angle of the cone, $$\scriptstyle \theta_c $$, is a direct measure of the particle's velocity through the formula

 * $$\cos \theta_c = \frac{c}{nv}$$,

where $$\scriptstyle c$$ is the speed of light, and $$\scriptstyle n $$ is the refractive index of the medium. Alternatively, if the momentum of the particle is known (from magnetic bending) the Cherenkov's information on the particle's velocity enables the mass to be deduced so that the particle can be identified.

Cherenkov telescopes
The project involves over 28 countries and over 170 research institutes, with over 1000 scientists and engineers expected to work on its initiation and subsequent operations. With its unprecedented energy coverage and angular resolution it will provide astronomers a deep insight into our high-energy Universe. The CTA has decided to start negotiations with the two sites — Aar in Namibia and ESO’s Paranal–Armazones site in Chile — keeping Leoncito in Argentina as a third option.

The Cherenkov telescopes do not actually detect the gamma rays directly but instead detect the flashes of visible light [Cherenkov radiation] produced when gamma rays are absorbed by the Earth's atmosphere.

Hypotheses

 * 1) Astronomical objects observed to be traveling transversely at superluminal speeds are traveling transversely at superluminal speeds.
 * 2) As most observable matter seems to be subluminal and normal, perhaps superluminal matter is mostly antimatter.


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