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.
How are radial and transverse motions considered for a star(s)?
If the distance to a star is known, its proper motion becomes its transverse motion. The angular velocity curve is defined, and line-of-sight velocity and proper motions are expressed in terms of this angular velocity.
Why did Oort derive a set of equations for the proper motion and line of sight velocity?
Measuring the distance is challenging, especially for distant stars where the ISM makes viewing difficult. Because of these limitations Oort derived a set of equations, valid only in the region near the sun.
What does Oort’s constant A describe?
Oort’s constant A measures the local shear of a galaxy known as the radial velocity gradient. It describes how much the Milky Way is not rotating as a rigid disk. Where A is zero if Ω is constant.
What does Oort’s constant B measure, and what information does it provide about the Galactic Disk?
Oort’s constant B measures the angular momentum gradient, representing the vorticity of material in the Galactic Disk. It indicates the tendency for material to circulate about any given point.
How is the large-velocity structure of the Galactic Disk studied?
The large-velocity structure is studied by observing Vlos as a function of Galactic longitude (l) to determine Ω(R). We also use the hydrogen 21-cm line as it can penetrate virtually the entire Galaxy.
What limitations are associated with using HI probes to determine the line of sight velocity?
Determining the distance to the emitting region is difficult. The method involves selecting the largest radial velocities along each measurement path. However, the approach breaks down near galactic longitudes of 90° and 270°, as Vlos becomes insensitive to changes in distance.
How is the rotation curve of the Milky Way expected to behave according to theoretical predictions?
The rotation curve is expected to drop off as Θ ∝ R^(-1/2), assuming most of the mass is interior to the solar circle. However, observations show that the curve does not drop off as expected, indicating a significant amount of mass beyond the solar circle.
What do unexpected features in the Milky Way rotation curve lead to in terms of theoretical explanations?
Unexpected features in the rotation curve, such as its possible increase beyond the solar circle, lead to theories involving dark matter in the Galactic halo and Modified Gravity.
How do rotation curves of other spiral galaxies compare to the Milky Way’s rotation curve?
Similar rotation curves to the Milky Way have been measured for other spiral galaxies. They exhibit a rapid rise in rotation up to a few scale lengths from the center, followed by nearly flat rotation curves beyond that point.
What are the components of the Milky Way?
The Component Model suggests that the Milky Way consists of several components: Central Bulge, Stellar Halo, and Dark Matter Halo. Rigid-body rotation near the center, a local maximum due to combined effects of all three matter components, and eventual flat rotation at large distances are observed.
How is the Virial Theorem applied to understanding the dynamics of galaxies?
The Virial Theorem states that the sum of twice the time-averaged kinetic energy (T) with the time-averaged potential energy (U) in a bound system is equal to zero. It is applied to galaxies, star clusters, and clusters of galaxies to understand the dynamics and their constituent parts.
Describe the relaxation time.
The relaxation time is the time taken for a star’s velocity to be significantly changed by two-body interactions. It is given when Δv = v and is estimated by considering strong and weak encounters between stars.
What are strong encounters, and how do they influence galactic dynamics?
Strong encounters are defined as interactions where the change in potential energy is larger than or equal to the initial kinetic energy at the closest approach. These encounters are very rare in the Galactic disc due to the large separation between stars, and their impact on the dynamics of stars can be ignored.
What is the significance of weak encounters in stellar systems?
Weak encounters provide only a tiny perturbation to the motions of stars in a stellar system but are more likely to occur than strong encounters, making them more important in practice.
What is the impact parameter?
The impact parameter, b, determines the distance of closest approach.
What are the scales for weak and strong encounters and what is the relaxation time for a weak encounter?
The maximum scale for weak encounters is the size of the system (R), while the minimum for a strong encounters is 1AU. The relaxation time for weak encounters is much greater than the age of the Universe.
Why are weak encounters important for globular clusters but not for galaxies?
Weak encounters are important for globular clusters due to their relatively small scale, but for galaxies, with larger scales, stars are collisionless systems, and weak encounters are not significant. Galaxies are defined by the collisionless Boltzmann equation.
Describe the process of violent relaxation.
Violent relaxation is a process in which the continually changing gravitational potential causes the orbits of stars to change in a system that is not in equilibrium. It results in virializing a galactic system.
What are the three classifications of galaxies proposed by Hubble?
Hubble proposed the Hubble Sequence, classifying galaxies into three primary categories: Ellipticals (E), Spirals (S), and Irregulars (Irr). Spirals can be normal (S) or barred (SB), and lenticular galaxies can be normal (SO) or barred (SBO).
What is Hubble’s tuning-fork diagram, and how did he interpret it in terms of galactic evolution?
Hubble arranged his morphological sequence in the form of a tuning-fork diagram, representing the evolutionary stages in a galaxy’s life. He thought elliptical galaxies were early-stage, and spirals were late-stage, but this theory was later proven wrong.
How did we learn Hubble’s theory of galactic evolution was incorrect?
Measuring the rotation speeds of galaxies reveals that Hubble’s theory of galactic evolution was incorrect. The high rotational velocities observed in spiral galaxies are not consistent with the idea that elliptical galaxies are slowly rotating and spontaneously speeding up.
How are elliptical galaxies classified, and what factors influence their apparent ellipticity?
Elliptical galaxies are classified based on how round or flat they look. The number after the ‘E’ describes the degree of ellipticity. Apparent ellipticity depends on the location of the observer with respect to the galaxy.
What is the Firehose Instability?
The Firehose Instability is a gravitational instability where elliptical galaxies with morphology > E7 become unstable. It causes oscillations in the system and can disrupt bars and spirals, with the gravitational potential acting as a restoring force causing a return to the original spiral.
Describe spiral galaxies and their shape.
Spiral galaxies are shaped like spirals with arms winding into a bright central bulge. Barred spiral galaxies have a bright line or bar running through their centers, while normal spiral galaxies lack a central bar.
How are spiral galaxies further classified based on the winding of their spiral arms?
Spiral galaxies are further classified based on the tightness of their spiral arms. Symbols such as ‘a’ represent a tightly wound spiral galaxies, while ‘c’ represents a loosely wound spiral galaxies. For example, the Milky Way is likely an SBbc galaxy.
Describe a Lenticular galaxy.
Lenticular galaxies are halfway between spiral and elliptical galaxies. They have a central bulge but no arms and their masses and luminosities are comparable to larger ellipticals.
How are irregular galaxies characterized, and what is a common cause of their formation?
Irregular galaxies have disorganized structures and are frequently the result of two galaxies colliding with each other.
What are the different theories regarding the formation of galaxies?
Galaxies can form through the primordial collapse of individual gas clouds or through hierarchical clustering, where smaller galaxies cluster to form larger ones. Secular evolution depends on internal processes.
What causes the difference in appearance between spiral and elliptical galaxies?
The difference in appearance between spiral and elliptical galaxies may be related to the speed of star formation. If spiral galaxies are formed over a long period where their remaining gas collapses and settles into a disk. If elliptical galaxies are formed all at once then the stars remain in their spherical distribution.
What is passive evolution?
Passive evolution occurs in isolated elliptical galaxies without mergers, interactions, or ongoing star formation. Blue stars evolve into red stars without a change in morphological type.
What are the potential outcomes of interactions and mergers in galaxies?
Interactions and mergers may or may not produce new stars. Interactions without new star formation result in a change in morphological type but not luminosity. Those producing new stars result in changes in both morphological type and luminosity.
What is the galactic luminosity function?
The galactic luminosity function (Φ(M)) helps study the distribution of galaxy luminosities and understand galactic evolutionary processes.
What is the Malmquist Bias, and how does it impact astronomical surveys?
The Malmquist Bias arises from the limiting magnitude of telescopes, introducing bias in observed galaxy populations. It affects the distribution of galaxy luminosities causing the measured mean absolute magnitude to be shifted from the true mean.
What does the Schechter function tell us?
The Schechter function tells us that the number of galaxies drops monotonically with increasing luminosity.
Describe the free parameters of the Schechter function.
At the faint end Φ(M) decreases exponentially with M. brighter than M* or L* theres a sharp break and the number of bright galaxies fall sharply in number density. Alpha determines the slope of the luminosity function at the faint end of the range and Φ* sets the over-all normalisation of the function.
Why is measuring galaxy surface brightness challenging?
Galaxy luminosities are harder to measure than stellar luminosities due to their extended nature and lack of well-defined edges leading to difficulties in measuring the surface brightness.
What is the concept of isophotes, and how are galaxies characterized by their isophotal diameters?
Isophotes are lines connecting points of equal brightness on a galaxy. Lacking sharp edges, galaxies are characterized by their isophotal diameters, representing the diameter at which a particular brightness level is reached.
Describe measuring the night sky brightness at the galaxies location.
Directly measuring night sky brightness at the galaxy’s location is challenging. It is often inferred from other empirical measures due to the brightness of the night sky usually surpassing that of the galaxy being observed.
What are the environmental and instrumental factors that cause challenges in measuring galaxy surface brightness.
Environmental factors include air glow, zodiacal light, faint stars and extragalactic light. Instrumental factors inclue flat fielding issues, vignetting, detector thermal noise, readout noise, and atmospheric seeing.
How does the brightness of the night sky vary, and what factors influence it?
The brightness of the night sky varies with location, galactic and ecliptic latitude, and longitude. It can be characterized by parameters such as (B-V), where a reddish hue indicates a higher value.
What are the four steps involved in making measurements of galaxy surface brightness?
- Determine the sensitivity of each pixel in the imaging device.
- Flat-field the image to correct for vignetting.
- Subtract the contribution of the night sky from the image.
- Integrate over the area of the image and express the result as an apparent magnitude.
How can errors in estimating the night-sky brightness impact the interpretation of galaxy brightness profiles?
Overestimation of the night-sky brightness can lead to plausible but incorrect brightness profiles. Small errors in night-sky brightness can result in significant errors in derived surface brightness.
What is ‘seeing’?
Seeing is the blurring of images caused by atmospheric conditions. The point-spread function (PSF) describes the probability density that a photon will hit the imaging device at a point offset by the effects of seeing.
How does the point-spread function (PSF) impact the observed surface brightness of galaxies?
The PSF introduces an apparent core of nearly constant apparent surface brightness, which can be mistaken for real features in theoretical galaxy models. The central isophotes may appear rounder than those further out, leading to potential misinterpretations.
Why is deprojection necessary?
Deprojection allows for the inference of the distribution of stars in the Galaxy. It is needed to recover luminosity density profiles from projected surface brightness.
Describe the modfiied Hubble law.
The modified Hubble Law relates luminosity density to surface brightness. However, it may not work well at large radii, predicting a divergence in total luminosity at radius R, which is inconsistent with observations.
Describe the de Vaucouleurs Law.
The de Vaucouleurs Law or the R^1/4 surface-brightness law, provides a good fit for most galaxies. The general form ensures that half the total luminosity comes from R < Re.
Describe a disk galaxy.
A disk galaxy is characterized by a conspicuous disk. It can also possess an elliptical-like bulge or bar. The disk may exhibit pronounced spiral structure, and there is often a significant quantity of dust present, making it non-transparent in all wavelength bands.
How does dust in a galaxy affect its apparent luminosity?
A dust-filled galaxy appears less luminous when seen edge-on. This is because light has to traverse a longer column of dust to reach the observer, making it liable to be absorbed or scattered en route. This introduces a bias into observational data, impacting the perceived luminosity of edge-on galaxies.
What photometric effects are caused by the presence of dust in galaxies?
Blue light is scattered more strongly than red light by dust. This leads to color and brightness asymmetries between the near and far sides of a galaxy. Studying these effects can help determine the direction of rotation.
Describe the surface-brightness profile in disk galaxies.
Surface-brightness profiles of disk galaxies are often fitted using a combination of the exponential law and the R^1/4 law . The crossover point of these two laws is critical, where the disk component’s slope may be significantly smaller than that of the bulge component.
What challenges arise in studying the central bulges in a disk galaxy edge-on?
The vertical profiles of the disk in near edge-on galaxies are frequently well-fitted with exponential profiles. It is challenging to distinguish between the existence of a central bulge or a thick disk in such views.
How is the disk-to-bulge ratio calculated, and what does it quantify?
The bulge fraction (B/T) can be calculated from fitted data where B represents the bulge’s luminosity, and T is the total luminosity. B/T is tightly correlated with Hubble type and quantifies the classification of galaxies based on the prominence of the bulge.
