ASTR 10, Vista College, Spring 2004

Instructors: Dr. Korpela

What Was Important - Material for Exam #3

April 22

• Interstellar medium: Stuff between the stars. 75% hydrogen, 25% helium, less than 1% other stuff (this is ~ the same as the sun)
• Evidence for ISM: dark clouds of gas/dust that block light (dark nebula)
• Evidence for gas:
  • narrow absorption lines in stellar spectra
  • emission at a wavelength of 21-cm from cold, neutral hydrogen
  • a hot nebula that is excited or ionized can glow due to radiation produced in emission lines (emission nebula). The color of the nebula is dependent on the wavelength of the emission lines (pink/red)
• Evidence for dust:
  • Dust radiates in infrared
  • Dust can reflect light (reflection nebula, blue)
  • Dust can redden (as well as dim) stars.
• Understand why reflection nebulae are blue (and the sky!).
• Understand why dust can both dim and redden starlight. Know that the dimming effect is less strong in the infrared.
• Understand that a star forms from a giant, cold, 'dense' (by interstellar standards, but not Earthly ones) cloud, which is big enough to form hundreds or thousands of stars.
• Understand that it collapses to a 'protostar', and why it heats up along the way. Gravitational energy is converted to Thermal Energy.
• Protostar is embedded in dusty cloud of gas, so hard to see, even though it is glowing because it is warm.
• The protostar is losing energy and will keep collapsing unless there is an internal energy source. This source is FUSION, and when it begins a star is 'born' on the MAIN SEQUENCE!

• Stellar evolution refers to the changes in a star's structure during its lifetime (not over several generations of stars).
• Know that LEAST massive stars live LONGEST (by a HUGE factor - have some idea of the extremes and the value for the Sun), and why.
• Know that stars spend 90% of their lives on the main sequence, and this is why when we plot the H-R diagram for a population of stars, we see most stars on the main sequence. Understand why later stages of their lives are shorter.
• Know the end products of stars of various masses! (details below)
  • Sun (and stars with mass 0.2 M_sun < M < 4 or 6 M_sun): planetary nebula and C/O white dwarf
  • Cool/dim stars (M < 0.4 M_sun): haven't had time to leave the main sequence
  • Massive stars (M > 8 M_sun): Supernova + neutron star or black hole
• Understand when star becomes a red giant: the core runs out of hydrogen, so can't hold itself up against gravity, so shrinks. This converts gravitational energy to thermal energy and so the core is now hot enough to fuse into Helium (He). The surface layers, paradoxically, expand and cool, so we have a BIG, RED star (you don't need to know the details of how this happens, although the book explains it) A "hydrogen burning shell" generates energy which is transported to the surface layers, which therefore expand. Expansion cools the surface, so we have a BIG, RED star.
• Understand why He requires a higher temperature to fuse, and why the stage of helium `burning' is faster than the hydrogen fusion stage.
• Know that He fusion requires a higher temperature, and that it is less efficient that H fusion at generating energy.
• To compare theory with observation, we look at STAR CLUSTERS. These are groups of stars that formed all at one time (out of the same cloud of gas), and are all at the same distance. Like taking a picture of 12-year-old people to see what 12-year-olds are like, instead of a picture of the whole population. Young clusters - mostly main sequence stars, lowest-mass stars haven't yet reached the main sequence (begun to fuse H). Old clusters - only cool/dim main sequence stars remain; have red giants and white dwarfs. The observations match the predictions!
• For stars like the SUN:
  • A "planetary nebula" forms when the outer layers of the star are puffed off when Helium fusion ends and the surface of the star expands (a second red giant phase). The hot, dense core is left behind and revealed, and shrinks/cools to become a white dwarf.
  • We see planetary nebulae with hot stars in the middle! CONFIRMATION!
  • The Pauli Exclusion Principle states that two identical electrons can't have exactly the same energy. Since possible energy levels for electrons are quantized, in a VERY dense gas, the electron motions cannot be changed, since all the energy levels with lower energy are already full. This pressure can hold up the star against gravity. For stars like the sun, this prevents the temperature from rising high enough to fuse Carbon. This DEGENERATE matter: resists compression; is incredibly dense; has pressure which does NOT depend on temperature.
  • If you add mass to a white dwarf (made out of degenerate matter), the star gets squeezed tighter and gets SMALLER! This results in a prediction of 0 radius for 1.4 solar masses, which clearly imposes a limit on the mass of a White Dwarf (Chandrasekhar limit).
  • White dwarfs are the second most common kind of star. No energy source. The positive ions aren't degenerate, and can cool (slow down) and radiate residual heat. The energy is transported internally via CONDUCTION. In about 10 billion years, they may become too cool/dim to see (the universe isn't yet old enough for this to have happened).
• For lowest-mass stars (M < 0.4 M_Sun) (we'll get to this next week):
  • They fuse H VERY slowly, so are long-lived, and have not yet left the main sequence.
  • They have convection throughout their interior, so new hydrogen is always coming from the outer layers to the core => even longer-lived
  • Eventually (possibly 100s of billions of years) they will run out of energy and the He core will contract into a White Dwarf.
• For High-mass stars (M > 6 or 8 M_Sun):
  • Go through initial phases much as the sun will, but faster
  • Unlike the Sun, as the core contracts after it runs out of He, it gets hot enough to fuse C and O into higher elements
  • Eventually, build up a series of 'onion' layers, with shells of various elements fusing (H-shell is outermost), and a core of Iron (Fe)
  • Recall that Iron is the most tightly bound element, and TAKES energy in either fission or fusion reactions.
  • The iron core can't hold itself up, and contracts.
  • Contraction causes it to heat up (gravitational energy to thermal energy)
  • Various other reactions remove energy from the core (see your book)
  • When the collapsing core becomes > 1.4 M_sun, electron degeneracy can no longer support it, and it collapses VERY quickly. Protons and electrons combine to form neutrons + neutrinos - A NEUTRON STAR is born!
  • Energy from the collapse is transferred to the outer layers of the star, which are blown up.
• Star Stuff:
  • Universe began with mostly H, He. We are Carbon-based. Earth is mostly Silicon-based. All of this was made in stars! Almost anything heavier than H/He was made in stars. Anything heavier than Iron (Gold, Silver, Platinum...) was made in exploding stars! We are made of Star Stuff!
  • Evidence for this is that (1) older stars (formed longer ago) have fewer heavy elements and (2) elements that we believe are only generated in supernovae (like gold) are rare (as would be expected)

• The outer layers of matter are no longer held up, and free-fall towards the core. The core is rebounding, so some energy is transferred to the surface layers as they bounce off.
• In addition, 99% of the energy is in neutrinos, and a little of that energy can be transferred to the matter and further accelerate it.
• This disruption of the outer layers of the star is a SUPERNOVA, and results in a supernova + neutron star (or black hole).
• During this violent explosion, fission and fusion occur, and elements heavier than iron are formed.
• Observational support for Supernovae:
  • Observed supernovae: previously "normal" star suddenly (few days) becomes MUCH more luminous (10^10 L_sun). 1054 AD - Chinese and others saw a SN - bright as full moon for several weeks. There is a nebula where this SN occurred. Tycho Brahe saw one, as did Kepler. Expect 1-2/century in our galaxy, but many are obscured by gas/dust.
  • Observe SN remnants to be expanding
  • Observe Neutron stars in some SN remnants (eg Crab pulsar, see below)
  • SN 1987A: detected neutrinos to confirm a 50-year-old theory of neutron star formation during SN!
  • SN 1987A: saw gamma rays with particular energies that could only have come from short-lived radioactive Cobalt. At IR wavelengths, saw emission lines of freshly-made cobalt, nickel. Theories of how heavy elements are formed in SNe are supported by this.
• Over 1/2 of all stars are in multiple systems. The `Roche Lobe' (teardrop-shaped boundary) determines whether the matter is attracted to one star, the other, or neither. Matter within each `lobe' is gravitationally bound to that star. The teardrop shape is determined by the forces due to the circular orbit and the gravitational forces of the two masses. If you have a system with a main-sequence star and a compact object (WD, NS, BH), when the MS star becomes a red giant, it is possible that its outer layers will no longer be bound to the giant star, but will fall towards the compact object.
• In this mass transfer, angular momentum must be conserved. Spinning objects need to keep spinning. If a figure skater pulls in his/her arms, they spin faster (more times per second). This forces the infalling material into an accretion disk.
• Accretion disk gets hot due to friction and tidal forces, and acts as a brake, ridding the gas of angular momentum and allowing it to fall to the white dwarf (or NS/BH). The more compact the object, the hotter the infalling gas becomes (a marshmallow dropped from a distance of 1 AU onto a Neutron Star releases the energy of a 3-Mton bomb!

Neutron Stars

I've included the most important material in these next 2 sections in a fair amount of detail, but tried to stick to the most important topics in this section. Focus on 1) the characteristics of NS and WD, 2) the evidence for various models, 3) the idea behind the lighthouse model of pulsars.
• Neutron stars: form from collapsing iron core of massive star. Must be > 1.4 solar masses (electron degeneracy can't hold it up). Protons and electrons are forced together into neutrons (and emit neutrinos, which were observed for SN 1987A). Neutrons must also obey the Pauli Exclusion Principle, and neutron degeneracy supports the neutron star. Just like a white dwarf, there is a limit to how much mass this degeneracy can support. For a NS, this limit is somewhere between 2 and 3 solar masses.
• So NS have between 1.4 and 2 or 3 solar masses of material, packed into an object with radius ~ 10 km!
• What do we expect of a neutron star?
  • 1.4 to 3 M_sun in 10-15 km radius
  • expect faint (since very small, so blackbody radiation doesn't have much surface area from which to emit)
  • expect HOT (cool slowly since don't radiate much energy) so radiate most in X-rays.
  • expect to find some in SN remnants (since they form in SN explosions)
  • spin fast (angular momentum is conserved : swirling interstellar cloud had some spin, so stars rotate (observed), and as core collapses, it spins faster)
  • strong magnetic field (stars (like Sun) have magnetic fields - the ionized gas drags the magnetic field with it, so as a star collapses, the magnetic field gets squeezed tighter and so made stronger) - about 10⁹ to 10¹³ times that of the Earth's magnetic field
• Compare NS to WD:
  • Both form from cores of evolved stars once fusion is finished.
  • Both are held up by degenerate particles
  • Both are small and faint
  • WD:
    • between 0.6 and 1.4 solar masses
    • about the size of Earth
    • formed from carbon/oxygen (or sometimes helium) core of low/intermediate mass stars after outer layers become planetary nebula
    • made of electrons + carbon/oxygen nuclei, held up by degenerate electrons
    • cooling - no current energy source, radiating residual heat
  • NS:
    • between 1.4 and 2 or 3 solar masses
    • about 20 km across
    • formed from iron core of massive stars during supernova
    • made of neutrons, held up by degenerate neutrons
    • cooling - no current energy source for blackbody radiation, radiating residual heat
    • BUT the rapid rotation of the strong magnetic field acts like a generator, and drives the production of visible radiation (pulsar). Works for neutron star because they spin faster and have bigger magnetic fields. The energy is taken from the rotation (so they slow down). See below for details.
• Do we see the blackbody radiation of tiny, dim neutron stars? Almost never.

Pulsars

• regular pulses of radio emission, with periods ranging from a few milliseconds to 3.75 seconds (originally 33 ms was lower limit). They slow down by a few billionths of a second per day. Pulses only last about a millisecond.
• Why do we think they must be rotating NS? Process of elimination! There is trouble with all other possibilities. The regular pulses could be due to a) orbits b) vibration and c) rotation. The objects could be i) regular stars ii) white dwarfs or iii) neutron stars. (The key ideas here are that we used process of elimination and that the observed slow-down of pulsars helped nail down the answer. The size limit required by the observed short duration of each pulse is another clue).
  • Orbits won't work for periods of 33 milliseconds (too small and fast - they'll lose energy to quickly)!
  • Vibration: Smaller, stiffer objects vibrate with higher frequencies. (think small bell, high pitch, big bell, low pitch). Hard to get the full range of pulsar periods from one kind of object.
  • Big objects that spin fast will tend to fly apart, so the short pulsar periods indicate the objects are small. If the object is rotating, it must be a neutron star (MS stars and WDs would fly apart)!
  • Rotation can explain the full range of pulse periods.
  • Clincher: Vibrating objects speed up as they lose energy (a pot lid can convince you of this). Rotating objects slow down as they lose energy. Pulsars slow down! So they must be rotating, and they must be neutron stars (because bigger objects would fly apart if they rotated that fast).
• Additional Supporting Evidence:
  • Some are seen associated with SN remnants (as predicted)
  • We think pulsars have strong magnetic fields (because of the kind of emission produced and the particles that are keeping the SN remnants glowing; also because of polarization measurements of the radio beams).
  • Mass estimates are consistent
• Pulsars pulse because they emit a beam that we see intermittently (like a lighthouse). You should understand this lighthouse model - we believe the beam is emitted from the magnetic poles of the pulsar. Not all observers will see a given pulsar, because the beam has to be pointed towards you. In addition, if the magnetic pole is on the spin axis, the pulsar won't pulse because the beam doesn't swing around (if a lighthouse beam pointed up, but the lighthouse still rotated the same way, the beam would ALWAYS point up).
• What makes a pulsar shine? This is harder. A NS spins so fast and has high enough B field that it acts like a generator and creates an electric field around itself (changing magnetic fields generate electric fields and vice versa - this is why we have electromagnetic waves). The field is so intense that it rips charged particles (mostly e-) out of the surface near the poles and accelerates them to high velocity. These accelerated electrons emit photons travelling in the same direction as the electrons. Thus, the photons leave the neutron star in narrow beams emanating from the magnetic poles. If the magnetic axis is tilted with respect to the axis of rotation, then the neutron star will sweep the beams around the sky.
• Notice that our model of pulsars matches the expectations of a neutron star (small, dense, rapidly rotating, strong magnetic field, sometimes found in supernova remnants, mass between 1.4 and 3 solar masses)
• Support for the lighthouse model:
  • the energy the Crab pulsar has lost equals the energy the Crab nebula (SN remnant) needs to keep shining!
  • polarization measurements indicate that the radio emission is coming from a region with a magnetic field like that expected for a spinning neutron star
• Some pulsars are extremely fast! Shortest period is about 1.5 milliseconds (spins 640 times/second) (discovered 1982).

Black Holes

• The escape velocity of an object (speed you need to escape from its gravity) is sqrt(2 G M / R) because as you squeeze the mass into a smaller size (R decreases), its surface gravity (G M m / R²) goes up.
• You can imagine squeezing any object into a small enough volume that the escape velocity is bigger than THE SPEED OF LIGHT! So nothing, not even light, can escape! The radius at which this occurs is called the Schwarzschild radius . Any object smaller than its Schwarzschild radius is a black hole. (R_s = 2 G M / c²)
• In the context of GR, light, when trying to move in a straight line, ends up going in a circle around the black hole because of the curvature of space-time.
• event horizon is the boundary of the region within which we can know nothing about the object because not even light can escape
• A BH is not voracious. As long as you stay outside the event horizon, you can escape (assuming you can go fast enough - there might be technical difficulties). If the Sun were replaced with a BH of the same mass (ie shrink the matter in the Sun to a size smaller than 3km (the Schwarzschild radius of the Sun)), the planets would not waver in their orbits! It would get cold and dark, but the orbits would not change, because orbits depend only on gravity, which depends only on the mass of the object and your distance from it!
• A BH forms when the iron core of a massive star collapses but is too massive to be held up by neutron degeneracy. The way to distinguish between a NS and a BH is by measuring its mass, (which is difficult).
• A BH in a binary star system can acquire mass from a companion star (see above). This material forms an accretion disk, and gets hot, so it emits X-rays. To find a black hole, look for an object bigger than several (say, 5) solar masses that is emitting X-rays! You won't be seeing the BH, but the matter falling into the BH.
• Know that a compact object surrounded by an accretion disk might send out a jet (and in which direction)
• Know that we see objects that (based on these criteria) we believe to be black holes. Know also that this isn't absolute proof of their existence! Perhaps some (as yet undiscovered) form of pressure halts the collapse of these objects?

April 29

Milky Way Galaxy:

• Know the basic components of the Galaxy: Disk, bulge, halo, spiral arms, dark matter corona,
• Know what each component is made of, and their properties
• Understand how we know that we're in the disk of a spiral galaxy (both from visible light observations alone, and then (more easily) from infrared/radio observations).
• Understand how we know we're not in the center (both from visible light observations alone, and then (more easily) from infrared/radio observations).
• Understand how we figure out how far from the center we are: Understand how we find the distances to globular clusters from variable stars (CALIBRATION!)
• Know what we can see by using infrared light instead of visible light. This is because DUST blocks visible light!
• Know that cold hydrogen emits light at a particular radio wavelength - 21cm! This is also not obscured by dust.
• Know that we use infrared or radio observations to help us map the spiral arms in our own galaxy. We DID NOT focus on the spiral structure of our galaxy.
• Know how we measure the mass of a Galaxy! We need to know the orbit of an object around the galactic center. For example, we need to know the Sun's speed around the center, and its distance from the center. Understand how this relates to measuring the mass of Stars, and how it differs.
• Notice that by looking at the Doppler shift of the 21-cm line of hydrogen, we can measure how much mass is inside different radii. Know that the mass keeps increases even as the luminous matter drops off. 90% of the Galaxy's mass is stuff we CANNOT see! We don't even know what much of it is.
• The Halo is full of old stars low in heavy elements. The globular clusters are 13 to 17 billion years old. Orbits of halo stars and clusters are random (like a swarm of bees).
• The disk is full of younger stars with more heavy elements. Open clusters no more than 7 million years old. Orbits of objects in the disk are circular.
• There are two populations of stars: disk, halo (but really it is a gradation from one to the other, not completely distinct populations)
• Heavy elements (heavier than H, He) are produced only in Stars! So it makes sense that the earliest stars formed from material lacking in heavy elements. As their material is mixed back into the interstellar medium (supernovae, planetary nebulae), younger stars will have more heavy elements.
• Galaxy formed from GIANT swirling cloud, which collapsed. As collapse began, clumps formed the globular clusters and halo stars (which explains their random orbits, old age, and low heavy-element abundance). Collapse continued, and conservation of angular momentum forced gas/dust into a disk. Halo objects continued in original orbits. The disk undergoes a continuing process of star formation. (This explains circular orbits, younger age, and increased heavy elements of disk stars).
• A few problems with the above scenario: For example: the youngest globular clusters are at the outer edge of the halo, the bulge contains some of the oldest stars (and in this model, you'd expect bulge to form last), where are the first stars with NO heavy elements? etc.
• Part of the answer may be that our galaxy has cannibalized other, smaller ones. There is possible evidence for this happening right now!
• Know and understand the main evidence for a supermassive black hole at the center of our galaxy (and exactly how such a black hole explains the observations!).
• Understand how we can tell there are spiral arms in our own galaxy (use distances to hot, young, blue stars; open clusters; clouds of gas)
• Understand why spiral arms are related to star formation, and why only young objects (things associated with star formation) are found there. Why are old stars not good tracers of spiral arms?

Science:

• For each theory, imagine I'm in court trying to convince you of my theory - I need to back it up with evidence! Notice that sometimes not all of the evidence quite fits the theory! This might mean the whole theory is wrong, or it might mean the observations are in error, or it might mean that we need to modify or add something to the existing theory. You should be able to apply this to the theory of galaxy formation.
• We talked about the difference between a theory being adequate to explain the observations, and necessary. In the former case, the theory can explain all of the observations (and perhaps better/more simply than another theory), but it isn't the ONLY possibility. The theory is necessary if we have no other theory that can come close to explaining the observations.
• We discussed using the process of elimination to choose between theories. If we have eliminated all but one of our theories because only one fits the observations, then we still need to look further. We may not have thought of all of the possibilities! Has the theory made predictions which have been confirmed by further observations? In this context, think about the theory of pulsars as being associated with rotating neutron stars. In this case, further observations have supported (but never proven!) the theory. On the other hand, in the case of black holes (about 5 solar masses, not the supermassive ones) in binary star systems, we have no additional evidence beyond "it's the only thing we can think of with these properties". It is always possible that some unkown physics halts the collapse, and the object isn't truly a "black hole" as we have defined them.

May 6

• Know the general characteristics of the 3 kinds of galaxies, and that they cover a wide range of sizes, masses, luminosities.
• We know galaxies are far beyond our own galaxy because we can measure their distances.
• Understand why we need to know the distances to galaxies to measure their sizes, luminosities, and masses.
• Masses: understand how we use gravity to measure galaxy masses, and how this leads to the conclusion that we can't see 90% of the mass!
• Understand the idea behind using "standard candles" and "standard rulers" to get distances to galaxies. Understand the idea behind the "distance ladder": we need to calibrate each method using the methods that came before it. Common standard candles include Cepheid variable stars and White-dwarf (Type Ia) supernovae.
• Know what we mean by Hubble's Law. More distant galaxies are moving away from us faster. Understand that we need to measure distances (see above) and recessional velocities (via doppler shifts) for many galaxies to determine the Hubble constant.
• Once we know the Hubble constant, a measurement of the redshift of a distant galaxy is sufficient to give an estimate of its distance.
• Understand that we think Hubble's Law is a result of the expansion of space-time. This expansion carries the galaxies with it! This explanation implies the universe has no center. It does NOT imply that the galaxies themselves are expanding (they are held together by gravity) or that the universe's expansion explains all the relative motions of galaxies. Galaxies also move relative to one another due to their gravitational interactions.
• Know the evidence for galaxy interactions, and why we expect them more often than collisions between stars.
• Understand the role of galaxy interactions/collisions/mergers in the history of galaxy evolution. What is the support for this idea? This is probably not the whole story, however.
• Know the general phenomena observed for "active" galaxies (giant radio lobes, jets, extremely luminous galaxy centers...)
• Know why we believe quasars are the extremely luminous cores of distant galaxies.
• Understand how they both can be explained by the "unified theory": A supermassive black hole surrounded by a rotating accretion disk, with jets.
• Know and understand how galaxy mergers/collisions trigger the unusual "activity" in the galaxy cores, and evidence for this scenario.

May 13

• Understand infinity
• Don't fret over Olbers' Paradox, but notice that Assumptions are important!
• Understand the difference between the universe as a whole (may be infinite in size) and the observable universe (finite in size)
• Understand the basic assumptions of homogeneity, isotropy and universality.
• The Geometry of space-time: understand the 2-d analogies for the closed, flat, and open universes. How can the universe be finite but unbounded?
• Expansion of the universe:
  • Hubble's Law
  • how the redshift of light is explained by the expansion
  • everything expands away from us, but we are NOT at the center of the universe - the universe has neither a center nor an edge (we are at the center of the observable universe)
• Standard model of the Big Bang: Focus on the evidence supporting this model:
  • Hubble's law implies the universe is expanding:
    • How is the Hubble constant related to the age of the universe?
    • Understand how gravity should be slowing the expansion, and how this affects the above.
  • observed hydrogen/helium abundances explained:
    • Understand why nucleosynthesis during the Big Bang produced only light elements
  • cosmic background radiation (CBR) observed;
    • Understand the source of the cosmic background radiation (CBR): When was it emitted? What event caused its emission? How hot was the gas? What temperature is observed (and why)?
• Know that the expansion of the universe, the observed light element abundance, and the observation of the CBR are the key pieces of evidence supporting the Big Bang.
• Understand that the CBR is very uniform, and that it is difficult to explain the observed structure of the universe (quasars already exist at 7% of current age) from such a uniform beginning. Know that 'seeds' (irregularities) grew by gravitational attraction to form the structure we see today. We can only get such early structure if these seeds are dark matter (specifically Cold Dark matter, made up of massive, and slowly moving particles - which means massive neutrinos can't be the only kind of dark matter, or even the most prevalent).
• Is the universe open or closed? Why is this related to the mass and energy density of the universe? What is the fate of the universe in each case?
• Currently, by observing the tiny irregularities in the CBR, we conclude that the universe must be nearly flat. The predictions of Big Bang nucleosynthesis, combined with our measurements of light-element abundances, indicates that "normal" matter can only be 4% of the density required to "close" the universe, or make it flat. Our measurements (by gravity) of dark matter account for another 21% of the required density (notice that this stuff has to be mostly WIMPs or something even more exotic - but not "normal" matter). Where's the other 70%? In 1998, measurements of White-dwarf supernovae hinted that the universe might be accelerating (speeding up its rate of expansion), instead of slowing its rate of expansion due to the mutual gravitational attraction of its matter. The "cosmological constant" describing this "dark energy" of empty space has a mass-equivalent of about 74% of the density required to make the universe flat. Of course, this neat picture might well have some flaws on closer examination!

May 20

• Relativity is an attempt to account for the fact that all observers, regardless of their motion, measure the same value for the speed of light.
• The only way this is possible is if time is not a constant for all observers. The rate at which time passes depends upon how you are moving.
• A clock moving at high rate relative to you runs slower than one not moving with respect to you.
• Length is also dependent on velocity. An object moving with respect to you is contracted along the direction of its motion.
• Things can only be said to be truly simultaneous if they happen at the same time and in the same place.
• One event can cause another only if the time between the events is more than the time it takes light to travel between the two events. All observers regardless of velocity would see these events occur in the same order.
• If two events are separated by less time than the time it would take light to travel between their locations, then one could not have caused the other. The order in which these events occur can be different for different observers.
• Time can be treated like a dimension perpendicular to the spacial dimensions. Velocity rotates the local time axis relative to an observer.
• Twin paradox. Each sees the other's clock running slower, but the moving twin sees the distance traveled as being shorter.