PHYS263 - Introduction to Astrophysics

By comparing the periods of the Earth and an interior planet (normally Venus), to which the distance may be radar ranged, and the distance infered using Keppler's laws.

The angle subtended by the apparent motion of a ‘nearby’ star relative to the celestial sphere, caused by the orbit of the Earth around the Sun.

The angular displacement of a "nearby" star relative to a fixed background when the Earth moves by 1 AU (half the angluar change observed over a period of 6 months).

The distance which an object would have to be at to have a parallax angle of 1".

A set of points on a plane such that:
$\mathit{r+r'=2a}$
$\mathit{\frac{x^2}{a}+\frac{y^2}{b}}=1$
Where a is the semi-major axis and b is the semi-minor axis

The ratio between the major axis and the inter-focal distance

Planets orbit the sun in ellipses with the sun at one focus

The line joining the sun and a planet sweeps out equal areas in equal times

The square of the orbital period is proportional to the cube of the average seperation
$\mathit{P^2=ka^3}$

k may be taken as one if P is measured in years and a is measured in AU

The closest point on the orbital path to the object being orbited

The furthest point on an orbital path to the object being orbited

Every body continues in its state of rest or of uniform motion in a straight line unless acted upon by an external net force.

The rate of change of momentum is equal to the net applied force

Every action has an equal and opposite reaction

$\mathit{F=\frac{Gm_1m_2}{r^2}}$

$\mathit{\mu=\frac{m_1m_2}{m_1+m_2}}$

By equating the force under Newton's second law to his second law applied to the reduced mass, Kepler's second law in the general case of non-spherical orbits

$\mathit{U_f-U_i=-\int_{r_i}^{r_f}G\frac{m_1m_2}{r^2}=-\frac{GMm}{r}}$

$m_1r_1=m_2r_2$ where r_n is the distance of the respective body from the barycentre

By considering a circular orbit, the orbital period may be expressed in terms of the tangential velocity. The expression may then be rearranged for the centripetal force, and this equated to the gravitational force.

$\mathit{E=\frac{1}{2}mv^2-\frac{GMm}{r}}$

A closed orbit with the minimum possible energy - it is a perfect circle

A closed orbit with an eccentricitiy 0<e<1

An open orbit with an eccentricity e=1

An open orbit with an eccentricity e>1

23 hours and 56 minutes

Measured Eastwards in the equatorial plane (equivalent to longitude).

Measured as an angle above the R.A (equatorial) plane.

Sexagesimal time (hh:mm:ss)

Either decimal or sexagesimal

$\mathit{\Delta Dec = Dec_1 - Dec_2}$

$\mathit{\Delta RA = (RA_1-RA_2)\cos{Dec_{ Mean}}}$

An intrinsic measure of an object's brightness - normally taken as its overall power output

The total luminosity of an object across all wavelengths

The power recieved per unit area

The flux per unit wavelength or unit frequency

Also known as surface brightness, it is the spectral flux density per steradian.

By integrating the intensity over the sky
$\mathit{S=\int_{\text{sky}}I_v(\theta, \phi)d\Omega}$
Where $\theta$ and $\phi$ are sky coordinates

A logarthmic scale of flux recieved on Earth. The more negative a magnitude, the brighter it is.

18.87

A differene in magnitudes through different filters.

$B-R= m_B-m_R = -2.5 \log_{10}\left(\frac{f_r}{f_b}\right)$

The more negative the colour value, the bluer the object. So the longer wavelength filter magnitude is subtracted from the shorter wavelength magnitude

The magnitude an obejct would have when measured at a distance of 10pc

The distance between the absolute and apparent magntidues $\mathit{\mu=m-M}$

The find the distance to an object

The Optical window, some infra red, and the majority of the radio window

The continuum of thermal radiation emitted by a heated object. The stated formula gives the flux at the surface per steradian, that is power per unit area per wavelength per arc second squared.

1 - integrate the function across the full range of wavelengths to obtain bolometric surface brightness
2 - Integrate the bolometric surface brightness over the area of the sky ($\Omega = 4\pi$) - this gives the Stefan-Boltzman law, which gives the surface flux
3 - Integrate the surface flux across the surface of the star

It is the low frequency (long wavelength) approximation for Planck's law, giving the power emitted per unit area, per steradian, per wavelength.

Radiation produced by non-relativistic charged particles moving in a magnetic field

Radiation emitted by relativistic charged particles moving in a magnetic field

Radiaton emitted by deccelerating matter

$n\rightarrow\infty$

$\mathit{n=1}$

Hydrogen emission series with final level $\mathit{ n=1}$ (in the UV region)

Hydrogen emission series with final level $\mathit n=2$ (in the visible region)

An function of temperature, it predicts the ratio of state occupancy of a heated gas, given information about the degeneracy of the states

A function of temperature, it gives the proportion of singly ionised moecules in a cloud of heated gas. It is a modification of the Boltzmann equation. $N_{II}$ denotes the singly ionised state, and $N_{I}$ or $N$ denote the unionoised state.

1 - An opaque body at T>0k produces a continuous spectrum (black body emission)
2 - A hot gas obscured by a cool gas will produce absorbtion lines
3 - A hot, diffuse gass produces bright, narrow emission lines

The relative motion of objects affecting the wavelength of emitted waves as seen by a "stationary" observer

- Quantum effects (uncertainty principle)
- Thermal doppler broadening
- Turbulent doppler broadening

A system of actuators used to compensate for the "sagging" of large mirrors in different positons

A system of actuators used in conjunction with a live-tracking system, which adapts the shape of the mirror in real-time to compensate for atmospheric disturbances

#photons detected/#photons incident

The positioning of astronomical objects in the sky

The alphabetical ranking of observed stars based on the strength (depth) of their Balmer lines, with A having the strongest lines

O, B, A, F, G, K, M, with O being the largest, brightest, hottest, and most massive ("Oh be a fine girl, kiss me!")

By using the spectral data from multiple different transitions, combined with the Saha and Boltzman equation, the temperature of the star and thus its classifcation may be deduced

>30,000 k

<4,000 k

The absolute luminosity of a star against its temperature

Using the luminosity-temperature relation, we can infer the radius of the star

- The central diagonal line is the main sequence
- A group of large, cold stars are the red giants
- A group of very large cold stars exist above the red giants - these are the supergiants
- Towards the hot side there is a grouping of very small stars: white dwarfs

$0.1 M_{\odot} > M > 100 M _{\odot}$

A relationship between the time averaged potential and kinetic energies of a stable, bounded system
$2\langle K \rangle + \langle U \rangle = 0

- if K>U/2, then the cloud will expand
- if K=U/2, the cloud will continue in its bound state
- if K<U, the cloud will collapse

The critical mass for a cloud of a given temperature, radius, and composition, above which the cloud would collapse

The Initial Mass Function (IMF) describes the number of stars per stellar mass when stars are born

By integrating the IMF across the mass range, the total number of stars formed by a region may be found. It may also be used to find the total mass of the stars formed.

As the stellar cluster ages:
- Stars get stripped away from the main sequence
- It starts with the hottest stars
- The point of departure works its way down the main
sequence
- As small stars evolve slowly the lowest part of the
main sequence on the HR diagram does not change

Population I: young, metal-rich, blue, and in spiral galaxies primarily found in the disk and bulge
Population II: old, metal-poor, red, and in spiral galaxies primarily found in the halo and bulge

The very earliest stars, formed from abundant hydrogen, helium, and deuterium early in the universe. They are predicted to be very large and short lived

Any element heavier than helium

- The outside typically expands and the inner parts collapse, leading to a red giant phase
- The dense, collapsed centre will becoe hot enough to begin nucelar fusion again
- The outer layer is blown off, forming a planetary nebula
- The remaining core cools down to a white dwarf

- It is a body that orbits the Sun (this definition only applies to our Solar System)
- It is large enough for its own gravity to make it round
- It has "cleared its neighbourhood" of smaller objects

- It is a celestial body orbiting the Sun
- It is massive enough to be rounded by its own gravity
- BUT it has NOT cleared its neighbouring region of planetesimals
- It is not a satellite

The ejection of high energy radiation from the sun which often accompany prominences

The ejection of large ammounts of plasma

If the Universe is static, homogenous, and populated by an infinite number of stars then every line of sight
should end with a star. Hence, every line of sight will have a star thus have light leading to the sky being
bright everywhere, but this is not what we observe

- Disk – mainly Pop I;
- Halo – mainly Pop II;
- Bulge – mix of Pop I and II.

A relationship between the pulsation period of Cepheid variables and their luminosity, allowing them to be used as cosmic rulers

A massive, gravitationally bound system of stars, gas, dust, and dark matter, orbiting around a supermassive black hole

Eliptical, spiral, barred spiral, and lenticular (somewhere between eliptical and spiral)

~13.7 Gyr

A solid angle (radian squared) which "cuts out" an area on the surface of a sphere equal to its radius squared - there are thus 4π steradian in a full sphere

The product of a power-law and an exponential function

page 176

- Harassment (lots of low-level interactions with other galaxies)
- Strangulation (prevention of gas inflow)
- Ram pressure stripping (removal of gas by the intracluster medium)

- Winds driven by supernovae
- AGN-driven feedback
- (early on in the Universe: re-ionisation)

The self-regulating processes in which energy, momentum, and matter released by stars and supermassive black holes shape the evolution of their host galaxies