Dr. Whitney Shane, MIRA's Charles Hitchcock Adams Fellow
There arc many kinds of variable stars, and new categories and subcat-egories are being invented on what seems to be a daily basis. We have even reached the point where some stars are classified as variable when they show no variability whatsoever, but might be variable if only the circumstances were a little different.
Leaving aside these strange catego-ries, the most reliable of the variable stars are the eclipsing stars, which are not generally intrinsically variable at all, and the various kinds of Cepheid variables. The latter are pulsating stars, and, with some exceptions, they behave in a most orderly and predictable manner.
The prototype of this large class is Delta Cephei, visible high in the northern fall sky. Its range in brightness of about one magnitude and its period of about five days make it an easy, if not very rewarding, object for even the most inexperienced variable star observed It can be found near the south-east boundary of the rather inconspicuous constellation Cepheus, about 20 degrees east of Cassiopeia.
A useful property of Cepheids is that other things being equal, which they almost never are, they adhere very closely to a relation between period of variation and some measure of the intrinsic luminosity. This may be the mean or the minimum or whatever one finds convenient. This makes them valuable as distance indicators, and they have been used in this way for almost 100 years to extend the galactic distance scale to our nearest extragalactic neighbors. A recent large project using the Space Telescope has ex-tended this, with great accuracy, to include galaxies as far away as the Virgo Cluster.
Initially it was assumed, in the absence of better information, that all Cepheids followed the same period-luminosity relation. This led to significant errors in the extragalactic distance scale and thus in estimates of the age of the universe, which at one time appeared to be less than that of the Earth! We now understand that the Ceph-eids which we commonly find in the Galaxy are of a different type than those which were initially identified in our com-panion galaxies, the Magellanic Clouds. The differences lie in the age and chemical composition, which in turn influence the period-luminosity relation. We have learned to be careful to determine this separately for Cepheids of different types.
A plot showing the variation of Delta Cephi's radial velocity over time.
Until very recently direct distance determinations by trigonometric parallax could not be extended as far as even the nearest Cepheids, so we had to rely on indirect methods. A few Cepheids are located in galactic clusters, whose distances can be inferred in a variety of ways, all depending upon the measurement of the same or closely related quantities, velocities, in linear and angular measure. The linear velocity, measured by spectrograph, is independent of distance, whereas the apparent motion, or angular velocity, is inversely proportional to the distance.
A clever variation upon this method is applicable to pulsating stars. The apparent brightness of a star is propor-tional to its apparent size, or the (very small) area on the sky which it covers. Thus from the change in brightness, after correction for temperature changes, we can determine the ratio of largest to smallest size. From spectroscopic mea-surements of the inward and outward velocity of the atmo-sphere of the star, we can measure the difference between the largest and smallest size. Knowing the ratio and the differ-ence between two numbers, we can calculate both numbers. Now, knowing the actual size of the star, we can use the temperature to calculate its absolute luminosity, which is what we need. Simple as it sounds, the calculation does require a good model of the stellar atmosphere, which introduces a whole new set of complications.
Your correspondent has a particular interest in the above method as applied to Delta Cephei because, in the distant past, he determined the radial velocity variation of this star from a series of observations all made with the same instru-ment and extending over a period of almost 50 years. It turned out that the velocity variation was just as stable and reliable as everyone had hoped. More recent observations with much greater accuracy have confirmed this result for Delta Cephei and a number of other well known Cepheids.
Stable as they are, Cepheids do undergo gradual period changes as they slowly use up their energy sources and evolve. These changes can best be measured from accurate photometry over long periods. The changes are predicted from stellar evolution calculations, and their measurement gives us a rare opportunity to test the validity of these calculations as well as our models of stellar interiors.
This year's best opportunity to observe Mercury Will be during the first days of November, when it will be well up in the eastern sky before sunrise. The opportunity is enhanced by the fact that it will be within one degree of Venus during this period and thus much easier to find than usual.
Venus will be low in the eastern sky in the morning hours and can be observed until early December, when it will be lost in the dawn.
We have had all summer to observe the close opposition of Mars, but it seems to be reluctant to leave us, remaining visible in the south-west evening sky throughout the quarter. A lunar occultation on October 23 will be visible only from South America and Africa.
Jupiter rises before midnight at the beginning of the quarter, as it nears opposition, which will occur on New Years Day. It will be stationary on November 2 and well placed for observation later in the quarter.
Saturn reaches opposition on December 3 and is thus well placed for observation during the entire quarter. Saturn will be occulted by the Moon on October 7, November 3, and December 3 and 30. The two December occultations should be visible from our area.
The fall sky is full of meteor showers, and none has attracted more attention recently than the Leonids. They have been much written about in this column and never fail to disappoint. This year again a dramatic show is predicted, despite the fact that the parent comet is now well beyond Perihelion. The Leonid stream is filamentary so we may expect multiple peaks, distributed over a period of 24 hours starting around noon on November 17. A peak in the early morning hours of November 18 is most promising for observers in our area. A much stronger peak, predicted for a few hours later, should occur after sunrise. As we know, however, such detailed predictions are very uncertain, and observations at any time during a few days around November 18 should be rewarding. The Moon is a few days past new and will be no problem.
The Orionids should be visible, starting in the late evening, for about a week around October 21, when the main peak should occur. A secondary peak is suspected a few days earlier. Again, the Moon will not interfere. The Alpha Monocerotids, visible for a few days around November 21, are usually very weak, but they occasionally produce a dramatic outburst.
The Geminids, which rival the Perseids in intensity, should peak during the early evening of December 13 and, in the absence of any moonlight, will provide excellent observing opportunities.
The only bright comet currently visible is C/2001 A2 (LINEAR), which reached fourth magnitude in June, when it had already split into three pieces. After being visible only from the Southern Hemisphere in the early summer; it will now have returned to the north, but it is expected to fade very rapidly.
An annular solar eclipse will take place on December 14. The annular phase will touch land only in Central America, where it will be visible mainly from Costa Rica. From our area, it will be seen during the early afternoon as a partial eclipse with a magnitude less than 20 per cent.
A penumbral lunar eclipse during the early morning hours of December 30 will bring the year to a festive close. The entire eclipse will be visible from our area, and the maximum will occur at about 2:30. Penumbral eclipses are seldom dramatic, but this one will be deep enough that the shading in illumination of the lunar disk should be very clear.
The lovely open cluster NGC 7790 was captured electronically by Dr. Arthur Babcock with the MIRA 36" telescope on the night of December 19th, 2000. This Galactic cluster is found in Cassiopeia and is famous for its luminous Cepheid variables which are critical stepping stones to the inter-galactic distance scale.
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Last updated 3/8/02 DMC