Author Topic: More astronomy stuff  (Read 436 times)

Offline HenryC

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More astronomy stuff
« on: August 19, 2015, 09:55:54 PM »
If you fire a shotgun, the buckshot is all traveling in more or less the same direction, and at roughly the same speed, relative to the shooter.  On the the other hand, an observer riding on any  one of those pellets would note that the rest of the shot is moving relative to his pellet at speeds much lower than the velocity of the cloud of shot relative to the ground. Furthermore, that pellet-borne observer would note that the other pellets are moving relative to his in random directions and speeds, even though the entire load of buckshot shares a common direction and speed away from the shooter. This is a good way to visualize the motions of stars relative to the sun in the solar neighborhood, that is, within several hundred parsecs (pc) from the sun.  "Parsec" is short for "parallax second".

Stars in our galaxy orbit the galactic nucleus, most of them (like our sun) in the galactic plane, which is a thin disk about 30,000 pc across and 1000 pc thick.  In the solar neighborhood the motion of most stars is dominated by the general rotation of the galactic disk, with some random velocities called proper motion superimposed on that, just as the cloud of buckshot consists of individual shot traveling together but moving slightly relatively to each other.  This mean motion of the solar neighborhood is called the Local Standard of Rest (LSR), and consists of about 255 km/sec, clockwise about the galactic nucleus as viewed from the north.  It corresponds roughly to the Sun's orbital velocity around the Milky Way Galaxy.

A parsec is equal to about 3.26 light years, or 3.086 X 10^13 km, and is the distance in space at which an Astronomical Unit (AU) subtends a second of arc, or 1/3600th  of a degree.  So when viewed from a distance of exactly one pc, the Earth-Sun distance is exactly one second of arc.  This is an enormous distance when you consider that an AU, the average distance from the Earth to the Sun, is about a hundred and fifty million kilometers.  Light years are helpful for laymen to visualize distances in the Galaxy, but this essay should illustrate why astronomers find the pc more convenient in their cocktail napkin calculations.  It is also helpful to keep in mind that in the solar neighborhood, stars are roughly a pc apart.  There are 50 known stellar systems (many of these are multiple stars) within 5 pc of the Sun. 

Our nearest stellar neighbor, the Alpha Centauri triple system, is 4.36 light years, or 1.34 pc away.  This corresponds to a parallax of 1/1.34" or 0.747".  The parallax, the distance a star seems to shift across the distant stellar background as the Earth revolves about its sun, is the reciprocal of the distance in parsecs.  An object one AU in size subtends 1" of arc at a distance of 1 pc.  It is 0.5" of arc in size at 2 pc.  0.33" at 3 pc and so on.  There are no stars (except our sun) less than a pc away from us, so all stellar parallaxes are less than 1".  It gives you some idea of the distance scales if you consider 1 pc = 206,265 AU.

In stellar catalogs, the parallax, or apparent yearly shift in a star's coordinates measured by trigonometric methods as Earth circles its sun, is usually listed in seconds of arc, and taking the reciprocal gives the distance in parsecs.  This convention is so widespread that distances are often listed this way, even when the star is so distant other methods than geometric triangulation are needed to establish its distance.  So for example, the bright red supergiant Betelgeuse  is listed in catalogs with a parallax of  0.007" which corresponds to a distance of 142.9 pc, too far to be measured by geometric parallax methods.  Even today, only a few dozen stellar distances are known to better than 1% precision.  In astronomy 10-20 percent precision is considered excellent!

Relatively nearby stars have another property which can be measured with purely geometric methods, the proper motion.  Take a photograph of a stellar field, wait a few years or decades and then take another, and careful measurements will show nearby stars seem to move with respect to more distant ones (after you correct for parallax, and several other effects I won't get into ).  Distant stars may be moving too, but they are so far away you have to wait long periods of time between pictures to get measurable shifts in position, and photography just hasn't been around that long! 

Parallax and proper motion are among the few effects which can be measured directly, without any intervening assumptions or theoretical guesswork, so they are our most dependable measurement of distance.  Unfortunately, the precision with which we can measure these tiny angles rapidly deteriorates with distance.  They are extremely important because they represent the ground truth, the baseline, or fundamental measurements upon which everything else is based.  Beyond a few hundred light years, all our distance ideas (which also influences our size and brightness measurements) are based on a house of cards of interlocking pyramidal  assumptions.  Every time we improve our local parallax and proper motion techniques the cumulative effect propagates up the distance scale all the way out to the edge of the red horizon.

Proper motion is not a true physical property of the star.  After all, a star could be moving very fast, but if it were moving directly toward or away from us, it would exhibit no proper motion at all.  Strictly speaking, proper motion is motion across our line of sight, any component of the stars motion at right angles to the plane of the sky (called radial velocity) will not show up with purely geometric measurements.  Knowledge of a stars actual movement requires knowledge of its motion along the line of sight as well as across it. Fortunately, radial velocity can be determined accurately using spectroscopic methods and at any distance.

Proper motion is also distance-dependent.  It is much easier to see and measure for nearby stars than it is for distant ones.  In fact, stars with large proper motions are generally suspected to be close to us, although we know this is not always the case--a very nearby star traveling alongside the Sun in a parallel orbit, or one traveling directly towards us would exhibit no proper motion.

The largest known proper motion is that of Barnard's Star, 10.358"/year, or about one full moon of angle every two centuries. According to the catalogs, this object has a parallax of 0. 54551", which corresponds to a distance of slightly over 1.8 pc.  Even for an object that close, this star is really moving very fast.  At its distance, this proper motion corresponds to a velocity of 18.6 AU/yr or 2.79 X 10^9 km/yr, or 88 km/sec relative to the LSR.  Barnard's Star also boasts a radial velocity of -111 km/sec (moving away from us)which suggests that it is not part of the normal galactic disk drift, but an interloper from the galactic halo whose orbit is only penetrating the disk at an acute angle.  Nearby stars moving along with the Sun have at most a few km/sec velocity relative to the the Sun.  It is observations like this that led to the discovery of distinct stellar populations, resident in the disk and halo, whose age, composition and other physical properties were correlated with their dynamical behavior--(a clue to their origins?) So simple calculations of these fundamental catalog measurements sometimes lead to profound astrophysical insights.  The Galaxy consists of two major stellar populations, a younger disk population, and a much older halo population in random orbits about the nucleus. 

Another nearby example is Kapteyn's Star (3.91 pc distant), a radial velocity of  +245 km/sec (approaching) and a proper motion which translates to a velocity across the line of sight at that distance of  161 km/sec.  These high-velocity stars are like high-powered rifle bullets flying through our cloud of buckshot, just passing through. Compare these numbers to a typical star drifting alongside us, participating in the general rotation of the spiral arm.

Alpha Centauri has a proper motion of 3.170 "/yr and multiplying by its distance (1.34 pc) tells it moves 4.2478 AU across our line of sight every year.  Multiply by 1.5x10^8 km/AU to get that in km/yr,  then divide by the number of sec/yr (365.25x24x60x60) to get a cross line of sight velocity of about 20 km/sec.  The radial velocity is -26 km/sec (away from us).

In spite of these extreme velocities, the galaxy is so vast that the stars appear frozen in place, we can stare at them for lifetimes and discern no motion.  Our life spans are just blips, we are staring at an instantaneous photograph of an explosion.

The "fixed stars", aren't.