12

The half light radius is the radius from within which half the luminosity emerges. "Deprojected" means that the authors must have fitted some model to the 2D distribution of light, which can then be mathematically deprojected to give them a 3D model for luminosity as a function of radius, that they can then integrate to give a number for the half light ...


10

The Ca triplet in the near infrared are extremely strong resonance absorption lines. They are by far the strongest features in the near infrared spectra of cool G,K,M type dwarfs and giants, which will be the majority of the stars observed by the Gaia RVS. The Ca triplet lines are so strong that even in low metallicity halo stars, that have little Ca in ...


10

Definition of the velocity dispersion From the title of your question, I'm unsure whether you actually know what "dispersion" means: The dispersion of some numbers is the spread around their mean, usually taken to mean their standard deviation. If you measure the velocity of several light sources (from the Doppler shift of their spectral lines) that are ...


10

I assume you're asking about central supermassive black holes (SMBHs, one per galaxy), not stellar-mass black holes. The answer is yes, but what actually happens is the two SMBHs have to merge first, and then the resulting combined SMBH can sometimes be ejected from the combined (merged) galaxy. [Edited to add: Since you've updated the question with a ...


9

Yes. The velocities you list (X, Y, …) are all velocities with respect to some reference frame. But all reference frames are arbitrary, and you can always define a reference frame where the velocity of some object is exactly zero, as long as it's not accelerating. For instance, Earth's velocity in the Sun's reference frame is X, but in its own reference ...


8

Hands down it's Jupiter. It has both the largest radius and faster rotational velocity of the planets, and smaller objects will not be able to compete with that huge radius. Jupiter's rotational velocity is approximately 13.4 km/s (with some variation due to wind currents, as it is a gas), which can be determined both from Doppler shifts of reflected ...


7

The ESA states it pretty clearly (although their figure of 855.2 nm is incorrect; it should be 866.2 nm): The RVS wavelength range, 847-874 nm, has been selected to coincide with the energy-distribution peaks of G- and K-type stars which are the most abundant RVS targets. For these late-type stars, the RVS wavelength interval displays, besides numerous ...


7

Photons are massless. This doesn't depend on their energy, so doesn't depend on their frequency or wavelength. Massless particles travel at the speed of light. Even if we abandon particles and look at classical electrodynamics, we find that the speed of an electromagnetic wave (in vacuum) has a fixed value. It doesn't depend on wavelength. Gravitational ...


7

You will always get a "stable" orbit if the stars have less than escape velocity relative to each other. (unless you are modelling the stars as having non-zero radii so they can collide) The stars will enter into elliptical orbits around a barycentre. But I guess you want a circular orbit. For a circular orbit the speed $v$ is given by $$v^2=GM/r$$...


7

To generalise from James K's answer, which gives the condition for a circular orbit... The condition for the binary to remain bound is that the total energy of the system, which is the sum of the potential energy $V$ and the kinetic energy $T$ (as evaluated in a centre-of-momentum frame) is less than zero. $$T+V < 0$$ Considering the system as two point ...


6

As Einstein realized and like you correctly state, you indeed can't measure the speed of an object by itself since it has to be measured relative to something else. As a logic result, if you ask the question "How fast is X moving?", you will have to specify that you want the speed with respect to another object because motion cannot be measured without a ...


6

I'd like to know a little more about the geometry of the ship's trajectory. I would be asking for clarification in comments but I don't know how to put images in comments. A good distance away the ship is moving nearly a straight line with regard to the large mass. As the ship gets closer the path gradually bends towards the large mass. If you're still a ...


6

According to Cropper and Katz 2011 part 2.2, the RVS working group considered other bands, but the ~850 nm band is relatively unaffected by absorption in the Earth's atmosphere, facilitating ground-based preparation and follow-up. In addition to the strong Ca II triplet, this band is rich in lines enabling study of astrophysical quantities other than radial ...


5

The reason is detailed in depth in this pdf, which contains the following diagram: Some key quantities: $R_0$: Distance from the observer to the center of the Milky Way $R$: Distance from target gas to the center of the Milky Way $V_0$: Velocity of the observer with respect to a certain reference frame $V$: Velocity of target gas with respect to the same ...


5

No, black holes are not the only cause of HVSs, although it is thought to be the most common mechanism. Hyper velocity stars are believed to be caused when binary stars come close enough to a supermassive black hole for one of the pair to be captured while the other star is ejected at high velocity. This appears to the main mechanism for HVSs. See for ...


5

In short, the escape velocity from the region we find ourselves in the milky way is 544 Km/s +- 10%. This number, and an extensive explanation of how it was calculated can be found on a paper called The RAVE Survey: Constraining the Local Galactic Escape Speed Also important to consider is the fact that we already are at aproximately 220 Km/s because of ...


5

You can't without assuming something about the overall velocity. The radial velocity is one component of a velocity vector; you are missing the other two components, which could in principle be anything. However, you could assume that as open clusters are mostly quite young and members of the Galactic disc population, that they are moving in the disc on ...


4

The rest frame for measuring (astronomical) speeds and velocities depends on the context and purpose. A geocentric frame, based on the Earth's centre of mass might be appropriate for objects in orbit around the Earth. A heliocentric reference frame, centred on the Sun, is often used when describing the line of sight velocities of astronomical objects, but ...


4

Before I start, let me just say that this topic is vastly more complicated than you've presented and what I will be showing. The trouble here is that ultimately, everything you've done and I will do (to a lesser extent) uses approximations and assumptions. Because of this, it can sometimes be hard to understand the true underlying physics when looking at ...


4

Hubble velocities The Universe expands and carries galaxies away from each other with a relative velocity proportional to the distance between them. This is Hubble's law, and if the Universe is infinitely large, there is no limit to how fast two galaxies may recede from each other. In our observable Universe, the most distant galaxy observed (GN-z11; Oesch ...


4

Yes, and in fact a mechanism somewhat like this has probably dumped a large number of BHs into intergalactic space. Black holes tend to settle towards the center of galaxies (an effect of dynamical friction). As they settle, they "cool" by evaporation. The chaos of BHs orbiting the center of mass all interact, especially when two of them approach closely. ...


4

The first part of this question is already answered at How Do we know about redshift? Regarding the second part, measuring tangential velocity is much harder, and indeed impossible for stars that are far away. Basically the method is to observe the position of the star very accurately compared to very distant stars which are assumed not to be moving and ...


4

The vis-viva equation is commonly written like this: $$v^2 = GM\left(\frac{2}{r} - \frac{1}{a}\right)$$. For $r=a(1-e)$: $$v = \sqrt{GM\left(\frac{2}{a(1-e)} - \frac{1}{a}\right)} = \sqrt{GM\frac{1}{a}\left(\frac{2}{1-e}-1\right)} = \sqrt{GM\frac{1}{a}\left(\frac{1+e}{1-e}\right)}$$. The derivation of the vis-viva equation is not at all trivial and ...


3

The radial velocity curve of a star in a binary system (with another star or a planet) is defined through 6 free parameters $$V_r(t) = K\left(\cos(\omega + \nu) +e \cos \omega \right) + \gamma,$$ where $K$ is the semi-amplitude, $\gamma$ is the centre of mass radial velocity, $\omega$ is the usual angle defining the argument of the pericentre measured from ...


3

The question itself is wrong, actually. There is no such thing as absolute velocity, which is what you're assuming in your question. Velocity is always relative to a frame of reference. Your speed relative to your chair is zero, but it's not zero relative to the airplanes flying over your house. When you say "a point in space where nothing is moving and ...


3

The $v_{GSR}$ in the linked paper seems to be the radial velocity (RV, in $km.s^{-1}$) with respect to the GSR. This information is mentioned in the Abstract section. I don't know exactly what kind of coordinates you have and how exactly are your velocities expressed (Cartesian vectors?), but what you probably need to do is to convert the velocity vector of ...


3

Chris, you are actually on the verge of understanding how special relativity works. You're very close. You only need to take one extra step. to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer" This is correct. Absolute space, as in newtonian physics, does not exist. Same for ...


3

What you do is predict the orbital velocity for a more realistic hypothesised mass distribution. There is an easy analytic solution for a disc. More complicated distributions require a numerical solution. If you get far enough outside an arbitrary mass distribution, then that solution will asymptotically look similar to $v_{\rm circ} = \sqrt{GM/r}$. ...


3

Two techniques immediately spring to mind. For the stars you detect, you can compare their colours and luminosities (Gaia provides photometric colours and distances) with what you expect for a star of that type at that distance. The difference between what you expect and what you observe tells you the reddening and extinction caused by interstellar dust, ...


3

If we are talking about any significant celestial bodies, then it will be the relative velocities of a pair of merging black holes. The typical relative velocity due to the orbital speed of the black hole components just before merger is greater than half the speed of light. Nothing comes close to that on a galactic scale. Typical peculiar velocities for ...


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