astrophysics - Why don't stars in globular clusters all orbit in the same plane?

Globular clusters like Omega Centauri certainly don't seem to be very coplanar at all.

In other words, why doesn't the explanation at Why are our planets in the solar system all on the same disc/plane/layer? (quoted below) apply here?

We haven't ironed out all the details about how planets form, but they almost certainly form from a disk of material around a young star. Because the disk lies in a single plane, the planets are broadly in that plane too.

But I'm just deferring the question. Why should a disk form around a young star? While the star is forming, there's a lot of gas and dust falling onto it. This material has angular momentum, so it swirls around the central object (i.e. the star) and the flow collides with itself. The collisions cancel out the angular momentum in what becomes the vertical direction and smear the material out in the horizontal direction, leading to a disk. Eventually, this disk fragments and forms planets. Like I said, the details aren't well understood, but we're pretty sure about the disk part, and that's why the planets are co-planar.

Answer

Because the stars each form from their own region of the cloud. Each star forming event is separate* from the other stars that are not in the same orbital plane. All the stars are not in a disk like the planets are. This PDF (OBSERVATIONS AND THEORY OF STAR CLUSTER FORMATION) may give you the answers you are looking for.

Furthermore, the Solar System is dominated by one single mass, the Sun, which means that to most planets, the solar system is approximately a two-body problem. This is not the case in a globular cluster, in which the stars are all of more or less comparable size. N-body systems are notoriously chaotic, so even if the stars had started out in ordered motion (which they haven't), their orbits would be highly unstable, and the cluster would quickly be relaxed into a virial system.

*notwithstanding multiple star systems that do form around each other, but this only applies to a limited number of stars compared to the millions in the cluster.

thermodynamics - Is heat always associated with Light?

I have found that light always produces heat. The only cases I think heat is absent with light is Fluorescence and Phosphorescence (maybe because they emit low energy but maybe the heat is still present?). So my question is: Is heat energy always present when light is emitted, specially for bright light(more energy)?

If some example or any links can be provided, then it will be very helpful.

Answer

Thermal radiation is emitted by any surface having a temperature higher than absolute zero. So the short answer to your question is yes. Light (electromagnetic radiation) of any frequency will heat surfaces that absorb it. In case of Fluorescence, the emitted light has a longer wavelength (lower frequency), and therefore lower energy, so that's why you feel the heat is absent.

quantum mechanics - Second order degenerate perturbation theory

What is a good resource to learn about higher degree degenerate perturbation theory - one that involves mathematics that isn't much more advanced than first order perturbation theory? I've looked around and I've only found Sakurai talk about it but he uses projections operators and other fancy mathematics. Also, does anyone have any examples of it being used?

quantum field theory - LSZ reduction theorem derivation in Weinberg QFT

When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions, $$ G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} \langle |\hat {T}\left( \hat {O}_{l}(x_{1})\hat {A}_{2}(x_{2})...\hat A_{n}(x_{n})\right) |\rangle , \quad (1) $$ where $\hat {O}_{l}(x)$ transforms under the irreducible representation of the Lorentz group as some free field $\hat {\Psi}_{l}(x)$. By insertion between $\hat {O}_{l}(x_{1})$ and $\hat {A}_{2}(x_{2})$ functional unit $$ \sum_{i, \sigma}\int d^{3}\mathbf p | (\mathbf p , \sigma )_{i}\rangle \langle (\mathbf p , \sigma )_{i}| $$ and by allocation of one-particle states from it he have "reduced" (with some hints) $(1)$ to the form $$ G(q_{1},...,q_{n}) \to f(q)\sum_{\sigma}\langle | \hat {O}_{l}(0)| (\mathbf q_{1}, \sigma )\rangle \times $$

$$ \times \int d^{4}x_{2}...e^{-iq_{2}x_{2}-...}\langle (\mathbf q_{1}, \sigma ) |\hat {T}\left( \hat {A}(x_{2})...\right) | \rangle \delta (q_{1} + ... + q_{n}). \qquad (2) $$ Here $f(q)$ contains the pole of the first order $\frac{1}{q^{2} - m^{2} - i\varepsilon}$ and $q = q_{1} + ... + q_{r}$.

After that he says that in $(2)$ there is equality $\hat {O}_{l}(0)| (\mathbf q_{1}, \sigma )\rangle = \frac{1}{\sqrt{(2 \pi )^{3}}}Nu^{\sigma}_{l}(\mathbf q_{1})| \rangle $.

So I have the question: why was factor $N$ (in comparison with free field-like expression $\hat {O}_{l}(0)| (\mathbf q_{1}, \sigma )\rangle = \frac{1}{\sqrt{(2 \pi )^{3}}}u^{\sigma}_{l}(\mathbf q_{1})| \rangle $) appeared? What is its physical sense? Is its appearance connected with the fact that $| \rangle$ doesn't refer to the "usual" vacuum? Can you also comment this statement, if you please?

mass - How is light affected by gravity?

Light is clearly affected by gravity, just think about a black hole, but light supposedly has no mass and gravity only affects objects with mass.

On the other hand, if light does have mass then doesn't mass become infinitely larger the closer to the speed of light an object travels. So this would result in light have an infinite mass which is impossible.

Any explanations?

Answer

In general relativity, gravity affects anything with energy. While light doesn't have rest-mass, it still has energy --- and is thus affected by gravity.

If you think of gravity as a distortion in space-time (a la general relativity), it doesn't matter what the secondary object is. As long as it exists, gravity affects it.

quantum mechanics - How "things" radiate electromagnetic radiation?

How things radiate electromagnetic radiation? I don't ask why they radiate (higher temperature than 0K) but how they radiate this electromagnetic waves?

Answer

There are two ways of getting electromagnetic radiation from matter.

Matter is usually neutral, the electrons and protons are equal in number to each other and any fields are spill over giving rise to Van der Waals forces which bind neutral atoms into molecules etc.

At this micro level nature is quantum mechanical. That means that all electrons are in energy levels some of which energy levels are practically a continuum, i.e. the difference between them is very small. This means that vibrations of the atoms and molecules in their solid structure, as an example, will excite by kinematics these levels and fall back by the emission of a photon ( de-excitation); the ensemble of these photons gives rise to black body radiation. When the temperature is high the corresponding energy levels have larger gaps, and the photons are of higher energy.

A filament lamp has high enough temperature to emit visible light . Liquids have similar behavior, gases only have molecular energy levels and vibrations but the process is the same. Kinetic energy from temperature is transformed into photons from de-excitations .

The bulk of light we see comes from this mechanisms, even the light from the sun.

There are the LED lights, again a quantum mechanical effect, but of different origin:

"when electrons cross the junction from the n- to the p-type material, the electron-hole recombination process produces some photons in the IR or visible in a process called electroluminescence."

The second way of getting light is how the other answers state, by accelerating charges, ions and electrons, as in sparks and lightning, plasma etc.

lateral thinking - Where did you end up? [Part 2!]

Follow the clues and tell me where you are in the end.

1. You are here


2. The birthplace


3. The biggest child


4. The first letter of it's name


5. Go left

Note: This one is harder, and has the requirement that you have to live in US/Canada or assume that you do.

Hint:

You need to make the Canada/US for clue #5

This is part 2 of a series of puzzles, part 1 can be found here: Where did you end up? [Part 1] feel free to join in the fun!

Answer

You are here:

Puzzling.SE

The Birthplace:

Area 51

The Biggest Child:

Graphic Design

The First Letter of it's Name:

G

Go Left:

F