Semester 1 - Definitions Flashcards
What is the significance of optical wavebands in understanding the structure of the Universe?
Optical wavebands reveal the contrast between galaxies and surroundings, identifying galaxies as fundamental building blocks.
What is Olber’s paradox?
Olber’s Paradox arises from the assumption of an infinite universe, where every line of sight encounters a star, but distant stars appear fainter.
Define intensity and explain its relationship with flux. Why is intensity independent of distance?
Intensity is flux per square arcsec. It’s distance-independent, while the angular size depends on distance and radius.
What are the two main components of the celestial coordinate system?
Right Ascension (alpha) and declination (delta).
How is azimuth measured in the celestial coordinate system?
Azimuth is measured from North in an easterly direction.
What is the Galactic Coordinate System?
The Galactic Coordinate System is a celestial coordinate system used because the Earth and Sun are not at the Galactic centre. It is specified by Galactic Pole (G) and Galactic Centre (C), with coordinates labelled as Galactic longitude (l) and latitude (b).
Why is the Galactic Coordinate System useful?
The Galactic Coordinate System is useful for representing the locations of objects within the Galaxy as seen from Earth.
Why do we define the Local Standard of Rest (LSR)?
The LSR is defined to understand where something is and how fast it is moving.
What is the circular speed of the Sun at the solar radius in the LSR?
V_(0) = 220km/s.
How is the LSR described in terms of the Sun’s motion?
The LSR is an inertial frame centered on the Sun traveling at the circular speed (v0) in the direction of Galactic rotation.
Why is the LSR necessary?
The galactic coordinate system is not convenient for studying the kinematics and dynamics. We need a coordinate system which will account for the sun’s motion around the galaxy. Where a coordinate system centred on the sun is non-inertial with respect to galactic motions.
Describe the cylindrical coordinate system in terms of the galactic coordinate system.
It has the center of the Galaxy as its origin, with radial distance (R), angular coordinate (Θ), and vertical coordinate (z).
Why do we define the Sun as the site of all observations in the Galaxy?
The Earth-Sun distance is much smaller compared to distances on the Galactic scale, allowing us to focus on changes in velocity rather than position.
Are the assumptions about the Sun’s orbit and the LSR valid?
No, the Sun does not follow a simple planar orbit. It is currently moving inward and north away from the Galactic midplane. The constant drift of the Sun from the LSR needs to be considered.
What is peculiar velocity?
Peculiar velocity is the velocity of a star relative to the Local Standard of Rest (LSR). Where the Sun’s peculiar velocity is known as the solar motion.
How is the kinematic centroid defined for a group of disk stars?
For disk stars not drifting perpendicular to the Galactic plane or towards the Galactic center, the kinematic centroid is defined by < u > = 0 and < w > = 0, which holds true for an axisymmetric Galaxy.
Explain the concept of axisymmetric drift.
Axisymmetric drift occurs because a group of stars, observationally selected, tends to lag behind the solar LSR. The mean value of v depends on the distribution of stellar orbits, causing <v> to deviate from zero.</v>
What is the velocity of a star relative to the Sun?
The velocity of a star relative to the Sun is the difference between the star’s peculiar velocity and the solar motion.
What must we consider when quantifying the solar motion components?
Radial variation in star number density in the solar neighbourhood is considered when quantifying the solar motion components. Where a least squares fit is performed to find the solar motion components.
How can Poisson and Laplace’s equations used to study stellar motion in the Galaxy?
The general approach is to use the equations to treat stars collectively, either by considering an effective potential or by treating stars like gas particles with no collisions. Where they are applied inside and outside the stellar distribution.
What potential is considered in the case of Laplace’s equation?
A 1/r^2 potential is considered both inside and outside the distribution in the case of Laplace’s equation.
How is the potential determined outside a uniformly charged sphere?
We can use spherical polar coordinates where there is no dependence on θ or z. Where the boundary condition requires the field to be zero at infinity, so a = 0.
How are potentials with geometries other than simple spheres approached?
The problem is solved in cylindrical coordinates (R, z). Outside the disk, Laplace’s equation is applied. Complex functions, such as those representing galaxies, can be expressed using Bessel functions where the Hankel transform is the analogue of the Fourier transform in cylindrical systems.
How can the potential of a galaxy represent different shapes?
Depending on parameters a and b, the potential can represent anything from a sphere to a razor-thin disc.
What is the gravitational force within any spherical object with density (ρ(r))?
The gravitational force toward the center is the sum of the inward forces from all matter inside that radius.
How is the mass of the Galaxy estimated using velocities?
If we can measure velocities, especially of stars in orbit, we can start to estimate the mass of the Galaxy by balancing gravitational forces.
What is the effect of a single star attracting other stars?
In most cases, the effect of a single star attracting other stars and changing the gravitational potential can be ignored when determining the orbit of that star.
How does the potential change with time as a star moves through a galaxy?
If the mass distribution is static, the potential at position x does not depend on time. As the star moves with velocity, the potential at its location changes according to changes in the gravitational potential dΦ/dt.
How does the potential influence the dynamics of stars in a galaxy?
The gravitational potential makes stars move in orbits. The energy of a star is the sum of its kinetic and potential energy. The kinetic energy cannot be negative, so a star can only escape if its total energy is greater than zero.
What did Oort derive and what is the result of this?
Oort derived a series of relations describing the differential rotation curve of the Galactic disk, showing that differential rotations are observed when looking at distant objects.
Why does the assumption v = rω become invalid in the context of differential rotation?
Differential rotation implies that the object is not solid, leading to the invalidation of the assumption. This implies peculiar motions are no longer valid.
When must we ignore peculiar motions?
Peculiar motions are not allowed when differential rotation becomes significant which occurs when moving away from the Sun by a few hundred parsecs.
What assumptions are made when considering Oort’s constants and differential rotation?
We assume that all stars are precisely located on the galactic equatorial plane, even though this is not entirely accurate. The thinness of the galactic plane allows for this approximation.
How are the relative velocities of stars with respect to the Sun studied in practice?
In practice, the relative velocities are studied by observing the radial or line-of-sight (LOS) velocity and proper motion (μ) of stars in the solar vicinity.
