Probably: and particularly if by now you are an enthusiastic observer enthralled with the antics of the stars. So let's take advantage of the situation and perambulate amongst two of the most unusual objects in our galaxy, 041619 T Tauri, and 155037 RU Lupi, two stars that represent the carefree conduct of cosmic youth. Both stars are irregular variables and represent stars that are observed in clouds of gas called diffuse nebulae.

T Tauri

Let's begin with T Tauri, the easier of the two, a star that can be watched easily from northern latitudes in the frigid evenings of winter.

If you can find the Hyades, you can find T Tauri. Moving from Delta to 64 Tauri to 4th magnitude 68 Tauri, you proceed to the northeast until you reach Epsilon Tauri, a 3.6 magnitude star (Fig. 22.1). Slightly to the southwest of Epsilon is a group of four stars in the shape of a malformed kite. I use this group as a guide to T Tauri.

Notice the magnitude range of 9.3 to 13.5; I have observed T Tauri for several years and I have never once seen it go fainter than magnitude 10.6 nor brighter than the mid 9s. Most observers have reported it hovering just brighter than 10th magnitude.

But that's only part of the story. T Tauri occasionally can flicker.

A simple curriculum model is cyclic in nature. It begins with aims and objectives. These lead to a choice of content (knowledge, skills, applications, and attitudes). These choices are instilled in the students through effective teaching and learning methods. The teaching and learning are then evaluated and assessed, leading to feedback that is used to improve every part of the cycle.

In previous chapters, we have addressed many parts of this cycle: aims and objectives (implicitly), curriculum content, teacher education, and education research in general. We have not explicitly discussed how teachers should assess students' learning, but we assume that this is part of effective teacher education.

Classroom teaching uses many tools. Elsewhere in this book, we address some of the more innovative ones. There are others, of course, some old and some new. Probably the oldest is the lecture, which can still be effective if it is interactive in the sense of involving questioning - the Socratic approach. There is the blackboard (or white-board) - still a flexible tool. There are the students' notes and notebooks; students can often internalize material by writing it or drawing it. Textbooks have evolved with the times, and now often come with a whole constellation of ancillaries, including a website. Textbooks can be the main support mechanism for both student and teacher.

There are audio-visuals. Wall charts and posters are useful, since they often stay in place for years, and make a permanent imprint on the students' minds. There are overhead transparencies and, looking back a decade or a few, 35 mm slides, filmstrips, and lantern slides. Films, videos, and DVDs (to give an evolutionary sequence) are useful.

The integral role of planetariums in engaging the public on issues in astronomy is addressed in On the role of planetariums by Anthony P. Fairall from Cape Town, South Africa.

Probably in excess of 100 million persons, mainly youngsters, pass through the world's planetariums each year, by far the largest, and arguably the most influential, conveyance of astronomy to the general public. However, while some planetariums have close ties to the research world, and even to IAU Commission 46, they are by far the exception and not the rule. In general, the planetarium community operates independently of the stakeholders represented at this conference.

While much of planetarium activity shares a common mission with the IAU Commission on Astronomy Education and Development, there are significant deviations: since the main market driving the planetarium world is clearly throughput, some planetariums emphasize entertainment and novelty more than the teaching of astronomy. There is also an unfortunate tendency in smaller planetariums, where lecturers are weak on science, to overemphasize star lore and constellations. In the author's opinion, the gap between the teaching of astronomy, as seen from the research world of the IAU, and teaching of astronomy, as seen from the planetarium world, badly needs closing.

In winter, we draw inward as the frigid weather and short days beckon us away from the stars and towards the armchair. This is an unfortunate loss for northern hemisphere observers who forego the unparalleled richness and diversity of the sky at this time of year, a sky that dares us to defy the inside comforts and go outside and watch. This is a time of challenge.

With its stunning belt and sword regions, Orion is the first area we would look to for possible variables, and we will not be disappointed! Orion's Great Nebula harbors some of the most fascinating variables of the entire sky. Lurking within the nebula are some 50 variable stars, 10 of which are bright enough to be observed with a 15 cm (6-inch) telescope.

With a telescope, winter offers a host of unparalleled, delightful stars that are infrequently observed because of the clouds and the cold. U Geminorum, which can rocket from 14.2 to 8.8 in a few hours, is a highlight of winter observing.

Observing hints for cold weather

A winter night can be a devastating experience, which under no circumstances should be taken lightly. During his search for trans-Neptunian planets, one quiet, wind-free night, Pluto discoverer Clyde Tombaugh opened the shutter of the 13-inch telescopic camera and began an exposure. He had been out already for some time and looked forward to the chance to sit back and watch the telescope do his work for him.

Educating students using robotic telescopes

Case Rijsdijk: Robotic telescopes are an oxymoron – how much time in terms of human resources is needed to maintain a telescope?

Jayant Narlikar: Our center, the Inter-University Center for Astronomy and Astrophysics (IUCAA), in Pune, India, uses the Internet to operate a small telescope at Mt. Wilson, California, for school children at Pune. There is a time difference of 12½ hours, which makes it possible for the schoolchildren to use direct observing methods. I think all such groups that use the Internet for remote observing by schoolchildren should get together and exchange their experiences. It would help to have an email directory of such groups.

Nick Lomb: Remote-controlled telescopes are an important new teaching resource. However, we need to make observation with them as exciting as possible. We suggest real-time observing with contact with an observer at the telescope. Adding “bells and whistles” such as a webcam showing the motor of the telescope would be most useful. A second problem is overcoming teacher reluctance to try new technology as well as training them to have enough astronomical background and technical knowledge to operate the telescope.

Gravitational wave detectors LIGO[2, 34], Virgo[78, 4, 503] shown in Figure 16.1, GEO[147, 601] and TAMA[15] are broad band detectors, sensitive in a frequency range of about 20–2000 Hz. The laser interferometric detectors are based on Michelson interferometry, and have a characteristic right angle between their two arms for optimal sensitivity for spin-2 waves[476]. At low frequencies (approximately less than 50 Hz), observation is limited by unfiltered seismic noise. In a middle band of up to about 150 Hz, it is limited by thermal noise and, at high frequencies above a few hundred Hz, by shot noise[495]. The design bandwidth of these detectors is chosen largely by the expected gravitational wave frequencies emitted in the final stages of binary neutron star coalescence, i.e. frequencies up to a few hundred Hz produced by compact stellar mass objects. At these frequencies, the detectors operate in the short wavelength limit, wherein the signal increases linearly with the length of the arms. It is therefore advantageous to build detectors with arm lengths as long as is practically feasible, given that many noise sources are independent of the arm length.

Gravitation is induced by the stress-energy tensor of matter and fields via curvature. This four-covariant description contains the Newtonian limit of weak gravity and slow motion. Subject to conservation of energy and momentum, this leads uniquely to the Einstein equations of motion, up to a cosmological constant. These equations admit a Lagrangian by the associated scalar curvature, as described by the Hilbert action.

Curvature of spacetime displays features similar to that of the sphere, as in the previous chapter. It generalizes to four-dimensional spacetime as in the discussion of the gravitational field of a star.

Spacetime curvature is described by the Riemann tensor. Given a metric, and so the light cones at every point of spacetime, the Riemann tensor is defined completely by the metric up to its second coordinate derivatives. Both the Riemann tensor and the metric, each in different ways, contain time-independent gravitational interactions, including the Newtonian limit of weak gravity, as well as gravitational radiation.

The Riemann tensor has various representations which bring about different aspects of spacetime.

Parallel transport over a closed loop. Continuing the discussion of parallel transport on the sphere, consider vectors carried along closed curves in spacetime.

While variable-star observing is a specialized branch of observational astronomy, the basic procedures of patience and care that apply to all observing also work with variables.

Plan your program in advance, but be flexible, since the sky often offers surprises. Choose your variable carefully. Is the star likely to be visible through your telescope, or is it obviously too faint? At the other extreme, is your star so bright that observing it is a waste of your precious telescope time?

Telescope

Telescope size

This is more of a consideration than most observers realize. In a sense, each variable star has its own best combination of telescope and eyepiece. The general rule is to use only enough power and magnification to see the variable clearly but not have it so bright that it is hard to estimate. Ideally, the variable should be about two magnitudes brighter than the faintest star you can see with your telescope. If it is much fainter than that, you will have a problem seeing the star, and if the variable is several magnitudes brighter, so many photons will enter your eye that its sensitivity to subtle magnitude variations will be affected.

At minimum, a star might be fair game for most telescopes smaller than 30 cm (12 inches), but as the star brightens you could use a smaller telescope. (When discussing a telescope size, I refer to the size of the mirror or objective lens.)

What else does the sky have that varies? Besides stars, there are other objects worth noting. Some are easily visible, and others are beyond the reach of all but the most powerful telescopes and detectors. They range in distance from a few million kilometers to billions of light years.

Variable nebulae

In the constellation of Monoceros is a variable star called R. It varies irregularly by about half a magnitude around 11. However, the star is usually very hard to see. The reason is that it is embedded in a nebula which also varies in brightness! This object is known as Hubble's variable nebula, NGC 2261, after the Mount Wilson astronomer who, in 1916, discovered that it varies in brightness, size, and even shape. The variation does not seem to follow the brightness changes in R Mon, and they do not occur with any regularity.

R Monocerotis and its nebula probably represent a planetary system in an early stage of formation. At least two other variable nebulae are known, NGC 1555 in Taurus, and a tiny wisp in Corona Austrina, NGC 6729, the home of R Coronae Austrinae (see Section 29.8).

Active galaxies

Innocently displaying some irregular brightness changes are a number of objects that have recently been identified as the cores of galaxies. The Seyfert galaxies are spiral galaxies with starlike nuclei that are very bright and slightly variable.

Introduction

In 1944, three years before India became independent of British rule, Jawaharlal Nehru wrote in his now famous book Discovery of India:

He then went on to express the hope that “Only when we are politically and economically free will the mind function normally and critically.” India became independent in 1947 with Nehru as the first Prime Minister, a post that he held for nearly 17 years. Ever an advocate of science and technology as the means of progress, he encouraged establishment of a good scientific infrastructure and also looked after achieving industrial growth. However, what has been the net outcome so far as human resources are concerned? Now we are well into the sixth decade after independence: where do we stand vis-à-vis Nehru's expectations of rational thinking?

This season is variable time, with a cast of variables probably better than at any other time during the year. We still have the fine variables of the Milky Way, while toward the east, a different group of variables is gaining prominence.

This is also the time to get your fellow astronomy-club members excited about the challenging field of variables. Fall is the time for renewal in many northern-hemisphere astronomy clubs, where after the summer break, monthly programs and dark-of-the-Moon star parties are taking place once again. If you are fanatical about variables, you may be aware that this field of observing is not the most popular among the amateurs who attend astronomy club meetings. Observations of the changing light output of these distant suns are perceived to lack the luster of the Messier hunt or the glossy galaxy photo, and even the thrill of the meteor watch. Now is the time to insist that variables are fun.

Now we can observe Algol in all its glory, and use it as a motivation to start observing other eclipsing binaries. Two other easily found, easily observed stars are Delta Cephei, and its neighbor Mu Cephei, a huge red-giant sun with totally irregular and unpredictable variations.

Another exciting star is RU Pegasi, a dwarf nova. You never know exactly when the next outburst will take place! While RU Peg may be one of the most exciting stars of fall, it surely is not the most famous.

Gamma-ray bursters are serendipitously discovered transients of nonthermal emissions of cosmological origin. They come in two varieties: (a) short bursts with durations of a few tenths of a second, and (b) long bursts with durations of a few tens of seconds. The latter are now observed in association with supernovae, while no such association is observed for the former. The parent population of Type Ib/c supernovae may well represent the outcome of binary evolution of massive stars, such as SN1993J. In light of these observations, a complete theory is to explain GRBs as a rare kind of supernovae. Long-duration GRB-supernovae require a baryon-poor inner engine operating for similar durations, for which the most promising candidate is a rapidly rotating Kerr black hole. Formed in core collapse of a massive star, the black hole is parametrized by its mass, angular momentum, and kick velocity (M, JH, K).

At low kick velocity K, core-collapse produces a high-mass and rapidly rotating black hole. The Kerr solution predicts a large energy reservoir in angular momentum. Per unit of mass, this far surpasses the energy stored in any baryonic object, including a rapidly rotating neutron star.