Hack13.Describe the Brightness of an Object
Hack 13. Describe the Brightness of an Object
When speaking of brightness, magnitude and surface brightness are two terms you'll hear a lot. Understand what these terms mean and how they relate to one another. For astronomy, the primary purpose of a binocular or telescope is to gather light, allowing you to see dimmer objects than are visible to the naked eye. Before you begin observing, it's essential to understand the limits of your viewing apparatus, be it the naked eye, a binocular, or a telescope. Otherwise, you could spend hours looking for objects so dim you'll never be able to see them. Figure 2-3. Robert, smoking while preserving his night vision The magnitude of an object is a numerical quantification of its brightness. Ancient observers first categorized stars by their brightness, describing the brightest stars as being "of the first magnitude." Slightly dimmer stars were grouped as second magnitude, and so on, down to the dimmest stars visible to the naked eye, which the ancients described as sixth magnitude. Dimmer objects accordingly have numerically larger magnitudes. The Greek astronomer Hipparchus created the first known star catalog in about 120 BCE. This catalog contained 1,080 stars visible to Hipparchus from his latitude. He organized these stars into constellations, described the position of each star relative to other stars, and rated their brightness from first to sixth magnitude. In about 125 CE, the Egyptian astronomer, cartographer, and geographer Ptolemy updated the Hipparchus catalog in his famous book Mathematical Syntaxis, usually called The Almagest. Ptolemy added a few northerly stars that Hipparchus had missed, and added more southerly stars that were visible from his Alexandria observatory at 31°15'N but had not been visible to Hipparchus in his observatory at 36°15'N on the island Rhodes. The magnitude system used by Hipparchus and Ptolemy is still in use today, with only minor modifications. With the advent of photometers and other scientific instruments capable of measuring brightness accurately, astronomers formalized the magnitude system by defining a hundred-fold difference in brightness as five magnitudes. By definition, then, a first magnitude star is exactly 100 times brighter than a sixth magnitude star, as is, say, a 9th magnitude star versus a 14th magnitude star. The fifth root of 100 is 2.511+, so a star of magnitude 1.0 is about 2.5 times as bright as a star of magnitude 2.0, and a star of magnitude 9.0 is about 2.5 times as bright as a star of magnitude 10.0. Photometers can provide very precise magnitude values. Star charts commonly list magnitudes to the first or second decimal place. For example, one star might be listed as magnitude 2.75 and another as magnitude 2.74. Although such small differences are impossible to detect visually, they are easily discriminated by CCDs and other sensitive instruments.
2.4.1. Types of MagnitudeThe term magnitude is used in different ways to describe different aspects of an object's brightness.
When amateur astronomers mention the magnitude of an object, they almost always mean the apparent visual magnitude. 2.4.2. Magnitude RangesEarly astronomers used magnitudes ranging from one to six to categorize visible stars. Modern astronomers extended the magnitude range on both ends, and they began applying the concept to celestial objects other than stars. The first departure came during the 19th century, when astronomers began measuring the precise brightness of stars. They learned that there was a greater range of brightnesses in stars that had formerly been grouped as "first magnitude" than there was between some first magnitude stars and others classically considered to be second magnitude. That discovery led to the assignment of fractional and negative magnitudes. Magnitudes are rounded in the same way as any other number. For example, any star with a magnitude between 0.5 and 1.49 is called a first-magnitude star, and any star between 2.5 and 3.49 is called a third-magnitude star. The six stars with magnitudes between -0.5 and 0.49 listed in Table 2-1 are called zeroth-magnitude stars. Sirius and Canopus, which are brighter than zeroth magnitude, have no common class name, although we suppose they could be called "negative one magnitude" stars. Table 2-1 lists the common names, Bayer designations, apparent magnitudes, absolute magnitudes (a "v" indicates the star is of variable magnitude), and distances of the 25 brightest stars in the sky, with our own Sun, Sol, shown for comparison. The ancients described all of these stars as "first magnitude."
The differences are striking. Sirius, the brightest star (other than Sol) visible from Earth has an apparent magnitude of -1.45. With an absolute magnitude of 1.4, Sirius is inherently fairly bright, but the real reason for its brilliance is that it's located less than 10 light years from Earth, which in astronomical terms makes it our next-door neighbor. Canopus, the next-brightest star as visible from Earth, has an apparent magnitude of -0.73, 0.72 magnitude dimmer than Sirius, although at -4.7 its absolute magnitude is 6.1 magnitudes brighter than Sirius. Canopus appears dimmer than Sirius because Canopus is located nearly 200 light years from Earth, or about 22 times more distant than Sirius. 2.4.3. Variable MagnitudesAlthough most celestial objects have fixed magnitudes, there are exceptions, which are described in the following sections. 2.4.3.1 Variable starsAll stars vary somewhat in magnitude, in a cycle that may span from seconds to years. But most stars vary in brightness over a very small range and so are considered for practical purposes to be of fixed magnitude. Some stars, called variable stars, vary significantly from their brightest to their dimmest, some times by several magnitudes and sometimes over very short periods. Depending on their apparent minimum and maximum magnitudes and their degree of variability, variable stars may be anything from prominent at all times to quite dim at their maxima and invisible at their minima to prominent at their maxima and quite dim at their minima. Variable stars are grouped into two types, four classes, and several subclasses:
Observing variable stars is popular among amateur astronomers for two reasons. First, variable stars can be observed at any time of night on any day of the year from any site, even urban locations. More important, variable star observing is one of the few disciplines in which amateurs can still make a serious contribution to science. There are many variable stars and the resources of professional astronomers are limited, so they depend upon amateurs to gather data for them. 2.4.3.2 Solar system objectsSolar system objectsLuna, the planets, asteroids, and cometsare inherently of variable magnitude because their orbits vary their positions relative to the Sun and Earth. Comets vary most in magnitude because their orbits may carry them from the outer edges of the solar system to nearly grazing Sol. At dimmest, most comets are invisible in even the largest scopes; at brightest, a spectacular comet may be a naked-eye object during the day. Earth's moon, Luna, also varies dramatically in magnitude, from invisible when new to about -12.6m when full. Other solar system objects vary less in magnitude, although some show significant magnitude variations. With the exception of Pluto, which has a highly variable orbit, planets and asteroids move in elliptical orbits that approximate circles, so their distance from Soland accordingly their illuminationvaries relatively little. The chief determinant of planetary and asteroid variability is therefore the separation between Terra and the planet or asteroid in question, which is determined by their relative positions in their orbits. For example, Mars and Earth reach closest approach about every two years, during which Mars is significantly brighter than at other times. At brightest, Venus has an apparent magnitude of about -4.4, which varies little because it is always quite close to Sol; Jupiter peaks at about -2.7; Mars, about -2.0; and Saturn, about 0.5. Jupiter and Venus both reach negative magnitudes bright enough to be easily visible during full daylight, if you know when and where to look for them. The best time to do that is when one or both of them are near Luna in the daytime sky. For example, Figure 2-4 shows Winston-Salem Astronomical League (WSAL) members Bonnie Richardson, Paul Jones, and Mary Chervenak (left to right) observing the daytime Lunar occultation of Jupiter on 9 November 2004. Figure 2-4. WSAL members observe a daytime Lunar occultation of Jupiter
With Luna as a reference pointthe thin crescent of Luna itself was difficult to locate in the bright daytime skyall of us were able to view Jupiter naked eye as it was occulted by Luna and then again as it egressed. We were also able to view Venus naked eye because it was only 5° or so distant from Luna, and therefore easy to locate. (Knowing exactly where to look is critical for observing planets during the day; you can scan the sky forever and not see the planet, but once you know exactly where it is it pops out at you, so obvious that you can't believe you couldn't see it before.) 2.4.4. Visibility by Magnitude and InstrumentThe range of visible magnitudes depends on many factors, including personal vision, degree of dark adaptation, sky transparency, light pollution, elevation of the observing site, altitude of the star, the cleanliness of your optics, and of course the optical instrument itself. Elevation and altitude can make a major difference because looking through less air allows you to see dimmer objects. The following are approximations and will vary from person to person as well as with differing observing conditions, but they at least give you a reasonable idea of what you might expect to see.
2.4.5. Surface BrightnessThe concept of magnitude is applied both to stars, which are point sources of light, and to extended objects, which have a visible surface area. Because they are point sources, stars cannot be magnified, although the laws of physics mean that stars actually appear as small disks in any real-world telescope. A star under any magnification therefore always has the same apparent brightness, which is determined only by the aperture of the scope you are using to view it. Extended objects, such as nebulae and galaxies are different. Because they have surface area (also called extent), they can be magnified. As you increase the magnification on an object, the apparent size of the object grows larger, but its apparent brightness grows dimmer. For example, if you double magnification, the apparent linear extent of the object doubles, which is to say that it appears twice as large. Doubling the linear size of the object quadruples its area. That means the light the object emits is spread over four times the area, so the apparent brightness of the object is reduced by a factor of four. In the difference between point-source objects and extended objects lies a truth that has frustrated many a beginning astronomer. Although non-astronomers find it difficult to believe, there are in fact many extended objects that are larger than the full moon. The Andromeda Galaxy (M31), for example, is roughly 3° long by 1° wide, versus the half-degree circle of the full moon. In other words, M31 has more than a dozen times the surface area of the full moon. There are many other examples of huge extended objects. Just in the constellation Cygnus, for example, are the North America Nebula (NGC 7000) and the Veil Nebula (NGC 6992), both of which have extents greater than that of Luna. Why, then, don't these objects jump out at us when we are under the night sky? Because they are very, very dim. Or, to put it another way, they have low surface brightness. A beginning astronomer, checking his charts, may note that M31 is listed as magnitude 3.4 (actually, the magnitude of M31 or any extended object depends on which source you use; more on that later in this section). A star of magnitude 3.4 is easily visible from all but the most light-polluted locations, and yet our beginning astronomer can't see M31 and doesn't understand why. The reason is magnitude versus surface brightness. Magnitudes given for extended objects are integrated magnitudes, which are calculated by assuming that all of the light from the extended object has been condensed into a point source. In other words, if M31 were a star instead of a huge extended object, that star would be 3.4m. But M31 is not a star, with its light condensed into an infinitesimally small point. M31 is a gigantic extended object, with its light spread over several square degrees of sky. The concept of surface brightness (abbreviated SBr) attempts to rectify the magnitude versus visibility issue for extended objects. To calculate surface brightness, you determine the apparent extent of an object and distribute the total light emitted by that object evenly over the extent. With the light evenly distributed, you can determine for any point on the object's extent how much light is emitted and what the magnitude of a star would be if it were that bright. For example, the planetarium program Cartes du Ciel lists the magnitude of M31 as 3.40, but its surface brightness as 13.50, or more than 10,000 times dimmer. Similarly, the North America Nebula is listed as 4.00m and 12.63SBr and the Veil Nebula as 7.00m and 13.44SBr. But if M31 were actually as dim as a 13.50m star, it would be impossible to see it with the naked eye, and yet anyone can see M31 naked eye if the site is dark enough. How can that be? There are two answers. Firstly, the human eye can accumulate and integrate light, treating an extended object much the same as it does a point source. When you view M31, your eye accumulates all of the light emitted by the object and presents it to your brain as a soft, dim blur. Secondly, a typical extended object varies greatly in brightness across its extent. Most, like M31, are relatively bright near the center, and increasingly dim near the edges. The brighter areas of some extended objects, including M31, are sufficiently bright to excite the rods (the monochrome-only dim light sensors in your eye) enough to glimpse the object [Hack #11]. Which brings up the reason why the magnitude and surface brightness of extended objects are matters of opinion. Both depend on how you define the extent of an object. Do you use the smaller visual extent, or the much larger photographic extent? Visually, for example, M31 has an extent not much larger than the full moon, depending on how good your dark-adapted vision is and the size of the telescope you use to view it. Photographically, M31 has a much larger extent, on the close order of three square degrees. That's true because long-exposure CCD or film images can reveal dim parts of an object that are beyond the lower threshold of human vision. As you increase the extent of an extended object, you also decrease the integrated magnitude because you are adding light, albeit in very small amounts. But as you increase the extent defined for an object, you also decrease the surface brightness because the area of the object is growing much faster than the amount of light contributed by the additional area. Accordingly, both the integrated magnitude and the surface brightness are, although this sounds odd, a matter of opinion, because both depend entirely on how you define the extent. This disconnect has profound implications for actual observing because it determines whether a particular object in a particular scope is easily visible, visible with difficulty, or not visible at all. Consider, for example, the Messier galaxy pair M81 and M82 in Ursa Major. Cartes du Ciel defines M81 as having an extent of 24.9X11.5 arcminutes, an integrated magnitude of 6.9, but a surface brightness of only 13.4. M82 is given an extent of 10.5X5.1 arcminutes, an integrated magnitude of only 8.4, but a surface brightness of 12.5. In other words, M81 is larger and 1.5 magnitudes brighter but has surface brightness almost a full magnitude dimmer. Actual observations bear this out. Although both galaxies are easy to see under relatively dark skies with even a small scope, M81 is clearly a more difficult object. It is larger, more diffuse, and "feels" dimmer despite its brighter integrated magnitude. Similar issues apply for other extended objects. Our rule of thumb when viewing extended objects is to consider surface brightness and ignore magnitude. We suggest you do the same. |
EAN: 2147483647
Pages: 112