ASTR2110 Exam 2

the ones with asterisks *** are the topics highlighted by Mallory in discussion

Hydrogen series; what final energy level is each associated with?

Lyman

Balmer

Paschen

Brackett

Lyman: n = 1

Balmer: n = 2

Paschen: n = 3

Brackett: n = 4

What do the greek letters mean in relation to a hydrogen series? α, β, γ, etc

counts the steps from up from the lower level (change in n)

α = n + 1

β = n + 2

γ = n + 3

Example: Balmer β, final n=2, initial n=4

Difference between permitted and forbidden transitions?

Permitted: transitions that obey specific “selection rules”

Forbidden: transitions that do NOT follow “selection rules”; Note that forbidden transitions can occur, they just require special circumstances

Which atomic processes cause emission?

Which ones cause absorption?

Emission:

Absorption:

What’s excitation and de-excitation; what can cause it?

Excitation: atom absorbs energy → electron goes to a higher energy level

photoexcitation - absorbs a photon

collisional excitation - collision with another atom/free electron

De-excitation: atom loses energy → electron goes to lower energy state

radiative de-excitation - emits photon

collisional de-excitation - a collision that carries away energy

Photoionization and Recombination

***What does the Maxwell-Boltzmann distribution describe?

It shows the distribution of the velocities/kinetic energies of particles that interact through collisions

***What is the mean energy per particle regardless of mass?

(3/2)kT

***In thermal equilibrium, how is a more massive particle’s movement affected?

it moves slower

***Why is there a critical radius (the “potato” radius) below which bodies are irregular (not spherical)?

To become spherical, self-gravity must overcome the elastic strength set by chemical bond

***Even though the Sun holds 99.8% of the mass in the Solar System, where is most of the angular momentum?

In the giant planets

***Evidence that the Solar System formed in a disk?

1. All planets orbit in same direction, in a thin plane, with nearly circular orbits

2. Most planets rotate in same direction as they orbit, and moons orbit in the same direction as planets spin

3. Almost all the mass is near the center (Sun) and almost all the angular momentum is on the outside (mostly in Jupiter)

***Can we observe protoplanetary disks?

Yes! We can observe them directly around young stars

***What is the general process of solar system formation?

Molecular cloud begins to collapse

Gas spins-up and flattens into an accretion disk,

Solids (metals) condense and hit each other

Planetesimals grow by collisional sticking of condensed solids

Why do eclipses do not occur at every new and full Moon?

Because the moon’s orbit is inclined relative to the ecliptic

***Why has the development of adaptive optics (AO) systems been so important for ground based astronomy?

It undoes the blurring effect from earth’s atmosphere and lets the telescope approach the diffraction limit at near infrared wavelengths

***What is the wavelength size range for each type of light on the EM spectrum?

Gamma: less than 0.01 nm

X-ray: 0.01 nm to 10 nm

Ultraviolet: 10 nm to ~400 nm

Visible: ~400 nm to ~750 nm

Infrared: ~700 nm to 1 mm

Microwave: 1 mm to 1 m

Radio: above 1 m

***What are the mechanisms that broaden a spectral line?

1. Natural Width - due to the Heisenberg Uncertainty Principle, there is always some amount of time that an electron with naturally decay to a lower energy state on its own

2. Thermal Doppler Broadening - caused by Maxwell-Boltzmann random thermal motion, where particles motion is affected by temperature. As particles move towards and away from your line of sight, their wavelength get red/blue shifted affecting the spectral line

3. Turbulent Broadening - Similar to thermal Doppler broadening, except happening on a larger scale where macroscopic currents/winds/etc cause the movements of the particles

***How is the Doppler Shift related to line-of-sight velocity v?

Particles moving towards you (positive v) have a higher frequency - blueshifted

Particles moving away from you (negative v) have a lower frequency - redshifted

***What is the relationship between spectral peaks and temperature?

Wien’s Law: the peak wavelength is inversely related to temperature →

• hotter objects emit radiation at higher frequency, higher energy, shorter wavelength

• cooler objects emit radiation at a lower frequency, lower energy, longer wavelength

Difference between total, partial, and annular solar eclipses?

Total: The moon completely blocks the face of the sun from the Earth

Partial: the sun, moon, and earth are not perfectly aligned, so only a part of the sun gets covered by the moon

Annular: the moon passes between the earth and the sun, but its near the furthest point in its orbit away from earth, so it doesn’t completely cover the sun

What is local thermodynamic equilibrium?

All particles have the same kinetic energies per particle. Local means the temperature can vary with location and time.

What is thermodynamic equilibrium?

Why do eclipses require a new or full moon?

It has to do with the moon’s position in its orbit relative to the earth and sun; an eclipse depends on the alignment of the earth-moon-sun system to be in a line.

Why are total solar eclipses visible only from a narrow track, while total lunar eclipses are visible from the entire night side of earth?

Solar eclipse: due to the position of the moon being between the sun and earth, the moon is much smaller than earth and so it’s umbra only casts a small shadow on the surface of the earth

Lunar eclipse: the earth is between the sun and moon, and because the earth is much bigger than the moon, the earth has a much large umbra that casts a shadow on the moon and further in the moons orbit

Why does an eclipsed moon appear red?

Rayleigh scattering + reflection: bluer wavelengths get scattered away easier when hitting molecules in the earth’s atmosphere, and then the atmosphere on the edges of the earth bend redder wavelengths towards the moon

Basic inventory of the solar system?

In order:

The Sun →

Terrestrial Planets: Mercury, Venus, Earth, Mars (mainly rocky composition, less H/He and Ices) →

Asteroid Belt (small irregularly shaped bodies with rocky composition) →

Jovian Planets: Jupiter, Saturn (gas giants with mainly solar H/He composition) and Uranus, Neptune (ice giants with mainly ice composition and less H/He) →

Dwarf Planets: Pluto, Ceres, Makemake, etc. (spherical, but not massive enough to clear their orbital neighborhood of other objects) →

Kuiper Belt (past the orbit of Neptune, thick disk of icy bodies, density too low to form planets) →

Oort Cloud (roughly spherical cloud of icy bodies at 100,000 AU, made of billions of comets)

Difference between orbital and rotational angular momentum?

• Orbital is the angular momentum in the plane the body orbits: L = 2πa²m/P√1 − e² ˆz with eccentricity e, semimajor axis a, and period P was found to be

• Rotational is the momentum of the body itself rotating: L = kMR²w where w = 2pi/rotation Period

What is obliquity?

It is the angle between the planet’s spin axis and its orbital plane

Obliquity of 90 degrees means the spin axis is perpendicular.

Greater than 90 degrees means the planet rotates in the opposite sense from its orbit.

What’s inclination?

The angle between the orbital plane and some other reference plane

When to use the formula for angular resolution WITHOUT the 1.22?

When the question mentions interferometers, combining multiple telescopes together, an array of telescopes. B in the formula is the baseline, the distance between the telescopes

What does the radiative transfer equation mean in principle?

dI/dx = j - n(sigma)I

How the intensity of radiation (light) changes through a medium as it interacts with matter

Change in intensity = Gains - losses

What is optical depth?

Measure how transparent a medium is to parts of the electromagnetic spectrum

Ex 1: Starlight passes through interstellar gas which absorbs some wavelengths, so large optical depth and it’s harder to see some forms of light

Ex 2: atoms and molecules in Earth’s atmosphere absorbs radiation (only optical, near infrared, and radio can be done on ground telescopes)

What is limb darkening on the sun?

The sun’s outer edges appear redder than the center. This happens because when you look at the sun’s center, you’re looking through more, hotter layers. Looking at the edges, you’re looking at an angle that only sees the cooler parts of the sun’s layers.

What are sunspots?

Sunspots are cooler, darker regions on the Sun's surface (photosphere) caused by intense magnetic fields that inhibit the convective flow of hot gas from the interior.

What is the period of sunspots increasing/decreasing, and what are some features of it?

The period is every 11 years. When its maximum, man sunspots are visible, and at minimum, barely any sunspots. Throughout the cycle, the locations change shown in a butterfly diagram, where the sunspots start at the mid-poles and migrate towards the equator

Why do sunspots come in pairs?

The magnetic field of the spots make a loop that goes inside to outside, and the place where the loop crosses the sun’s surface is where the sunspots are visible.

What’s magnetic reconnection and how does it power solar flares?

when magnetic fields pointing in opposite direction get close together, they can reconnect. when they reconnect, it kind of snaps and shoots plasma confined in the field out into space, causing a solar flare.

What’s a prograde orbit?

when the body rotates in the same direction as its orbit (so earth rotates counterclockwise viewed from north pole, and also orbits the sun counterclockwise).

Most planets are prograde, except venus which rotates opposite (retrograde) and uranus which spins on its side.

Why are sunspots cooler than the surrounding surface?

The intense magnetic fields that cause the sunspots block flow of heat to the area, causing it to be cooler.

The total pressure on the outside has to equal the pressure of the gas and the pressure of the magnetic field pushing outward. Make use of magnetic pressure formula and the ideal has law formula. Since sunspots have such high mag fields, thus mag pressure, there needs to be less gas pressure to keep it all contained so because less gas, less density, and with ideal gas law, less temperature.

Difference between umbra and penumbra?

Umbra is the darkest part of the shadow, cone shaped

penumbra is the lighter, outer fringe of the shadow where light it only partially blocked

What is “seeing”?

Turbulence in the atmosphere causes diffraction that leads to twinkling of stars.

for good sights on earth that blurs about 1 arcsecond

Ways to improve angular resolution?

Use a larger diameter telescope

observe in shorter wavelengths

What is the Rayleigh Criterion?

The limit of angular resolution where something is JUST resolvable enough. Note: even if a telescope reaches it’s diffraction limit, other things like atmospheric turbulence n whatnot may still prevent it working as well as it could on the ground.