Physics
Absolute Magnitude
Absolute magnitude is a measure of the intrinsic brightness of a celestial object, such as a star or galaxy. It is defined as the apparent magnitude the object would have if it were located at a distance of 10 parsecs (32.6 light-years) from the observer. Absolute magnitude is useful for comparing the true brightness of objects, regardless of their distance from Earth.
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11 Key excerpts on "Absolute Magnitude"
eBook - PDFAstronomy Methods
A Physical Approach to Astronomical Observations
- Hale Bradt(Author)
- 2003(Publication Date)
- Cambridge University Press(Publisher)
Astronomers with large telescopes can now obtain images of stars as faint as, or fainter than, m V ≈ 25 or even reaching m V ≈ 29 with the Hubble Space Telescope. Astronomers now distinguish between apparent magnitude m and absolute mag-nitude M . The former is the quantity used by Hipparchus; it is simply a measure of the apparent flux density of the star as measured from the earth. In contrast, the Absolute Magnitude is a measure of the luminosity L , the total rate of energy emission by the object; it is independent of distance to the object. Two physically 8.3 Astronomical magnitudes 225 identical stars at different distances from the earth would have the same Absolute Magnitudes but different apparent magnitudes. A star’s magnitude is typically measured over a fairly broad band of frequencies and these are specified as ultraviolet U , blue B , visual V , etc. Precise calibrations in terms of physical units (W/m 2 ) is not simple because a given detection system has an efficiency for photon detection that is a function of frequency, and this function differs for different types of detectors. Since the incoming frequency distribution of photons (spectral shape) differs from one astronomical body to the next, the ratio of responses of two dissimilar detector systems will vary from source to source. Astronomers have thus gone to great pains to adopt standard measurement systems and calibrations for the purpose of accurately measuring broadband fluxes (magnitudes). Apparent magnitude Here we present the definition of the apparent magnitude in terms of the response of a detection system to incoming radiation. Scales of color magnitudes are also defined. Magnitudes and fluxes A typical detector in the IR–optical–UV region has a response that is proportional to the number of photons impinging upon it in a given time.
eBook - PDF- Stan Owocki(Author)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
Before moving on to examine additional properties of stellar radiation, let us first discuss some specifics of how astronomers characterize apparent versus absolute brightness, namely through the so-called magnitude system. This system has some rather awkward conventions, developed through its long history, dating back to the ancient Greeks. As noted in Chapter 1, they ranked the apparent brightness of stars in six bins of magnitude, ranging from m = 1 for the brightest to m = 6 for the dimmest. Because the human eye is adapted to detect 1 In 2018, NASA launched “Parker Solar Probe,” which will eventually fly within about 9R of the solar surface, or about ∼1/20 au. So a key challenge has been to provide the shielding to keep the factor > 400 higher solar-radiation flux from frying the spacecraft’s instruments. 22 3 Stellar Luminosity a large dynamic range in brightness, it turns out that our perception of brightness depends roughly on the logarithm of the flux. In our modern calibration this can be related to the Greek magnitude system by stating that a difference of 5 in magnitude represents a factor 100 in the relative brightness of the compared stars, with the dimmer star having the larger magnitude. This can be expressed in mathematical form as m 2 − m 1 = 2.5 log(F 1 /F 2 ). (3.7) We can further extend this logarithmic magnitude system to characterize the abso- lute brightness, or luminosity, of a star in terms of an Absolute Magnitude. To remove the inherent dependence on distance in the flux F , and thus in the apparent mag- nitude m, the Absolute Magnitude M is defined as the apparent magnitude that a star would have if it were placed at a standard distance, chosen by convention to be d = 10 pc. Since the flux scales with the inverse-square of distance, F ∼ 1/d 2 , the difference between apparent magnitude m and Absolute Magnitude M is given by m − M = 5 log(d/10 pc) , (3.8) which is known as the distance modulus.
eBook - PDF- Lauren V. Jones(Author)
- 2009(Publication Date)
- Greenwood(Publisher)
So, currently, these space telescopes mea- sure a quantity called apparent magnitude, even though they are not human and do not reside on Earth. A star’s brightness depends on how much energy the star is emitting, the size of the star, and the distance the star is from Earth. A star can appear bright because it is giving off a lot of energy, or because it is large, or because it is close. So, if the only information about a star is its apparent magnitude, it is not possible to tell whether a bright star is bright because it gives off a lot of energy, because it is large, or because it is close. 40 • STARS AND GALAXIES Two stars giving off the same amount of energy that are the same size, but have different apparent magnitudes must be at different distances. Knowing apparent magnitude and two out of the three qualities of energy output, dis- tance, or size, will limit the remaining quality. For example, if two stars have the same apparent magnitudes, give off the same amount of energy, and have the same size, they must be at the same distance from Earth. And, two stars with the same apparent magnitude, same size, and same distance from Earth must be giving off the same amount of energy. Absolute Magnitude Absolute Magnitude is a measure of how much energy a star gives off, or how bright a star actually is. This is what is called “luminosity.” The total amount of energy a star gives off is a measure of its luminosity. Luminosity is not dependent on size or distance of the star. So, two stars with the same Absolute Magnitude give off the same amount of energy, but they may be different sizes or different distances from Earth. The Absolute Magnitude or luminos- ity of a star does not provide any information about distance to the star or radius of the star. Alternatively, the Absolute Magnitude of a star is the same as the apparent magnitude of the star if it were located at a distance of 10 parsecs (pc) from Earth.
eBook - PDF- James Binney, Michael Merrifield(Authors)
- 2021(Publication Date)
- Princeton University Press(Publisher)
2.3.3 Absolute Magnitudes The energy flux we receive at the Earth from an object depends on both its intrinsic brightness and its distance. If F is the flux received when the object is at distance D, the flux / that would be received if it were at some other distance d is given by the inverse square law, ' = & F. (2.34) Obviously, the farther away an object is, the fainter it will appear, and to obtain information about the relative intrinsic brightnesses of objects, we must account for differences in their distances from us. We therefore define the Absolute Magnitude M to be the apparent magnitude an object would have if it were located at some standard distance D. From equations (2.27) and (2.34), we see that -M =-2.5log ( | ) =5log (-^). (2.35) m The standard distance D is always taken to be 10 pc, so if d is measured in parsecs, then m -M = 51ogd-5. (2.36) The quantity (m — M) is called the distance modulus of the object. If we know m and d, we can immediately correct for the nonstandard distance of the object and reduce the apparent magnitude m to the Absolute Magnitude M via equation (2.36). Conversely, if we know m and M, we can infer d. Absolute Magnitudes are normally quoted for the visual band and de-noted My-It should be noted that the Absolute Magnitude is not a direct measure of the total energy output (luminosity) of an object, but only of the energy in the V band. To measure total energy output, we use so-called 'bolometric magnitudes,' which will be discussed in §2.3.4. The distance from the Earth to the Sun is 1AU = (1/206, 265) pc. Thus, we know immediately that the distance modulus of the Sun is —31.57 mag and therefore that the Absolute Magnitude of the Sun Mv{0) = +4.83. We shall see in §3.5 that the Sun is a star of rather average intrinsic brightness - 2.3 Magnitudes and colors 57 Table 2.4 Redshifts at which one UBV band is shifted to an-other u B V R U 0 B 0.22 0 0 0 V .51 .24 0 0.
eBook - PDF- Bradley W. Carroll, Dale A. Ostlie(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
Of course, the radiant flux received from an object depends on both its intrinsic luminosity (energy emitted per second) and its distance from the observer. The same star, if located farther from Earth, would appear less bright in the sky. 3 The magnitudes discussed in this section are actually bolometric magnitudes, measured over all wavelengths of light; see Section 3.6 for a discussion of magnitudes measured by detectors over a finite wavelength region. 3.2 The Magnitude Scale 61 Imagine a star of luminosity L surrounded by a huge spherical shell of radius r . Then, assuming that no light is absorbed during its journey out to the shell, the radiant flux, F , measured at distance r is related to the star’s luminosity by F = L 4 πr 2 , (3.2) the denominator being simply the area of the sphere. Since L does not depend on r , the radiant flux is inversely proportional to the square of the distance from the star. This is the well-known inverse square law for light. 4 Example 3.2.1. The luminosity of the Sun is L = 3 . 839 × 10 26 W. At a distance of 1 AU = 1 . 496 × 10 11 m, Earth receives a radiant flux above its absorbing atmosphere of F = L 4 πr 2 = 1365 W m − 2 . This value of the solar flux is known as the solar irradiance , sometimes also called the solar constant . At a distance of 10 pc = 2 . 063 × 10 6 AU, an observer would measure the radiant flux to be only 1 /( 2 . 063 × 10 6 ) 2 as large. That is, the radiant flux from the Sun would be 3 . 208 × 10 − 10 W m − 2 at a distance of 10 pc. Absolute Magnitude Using the inverse square law, astronomers can assign an Absolute Magnitude , M , to each star. This is defined to be the apparent magnitude a star would have if it were located at a distance of 10 pc. Recall that a difference of 5 magnitudes between the apparent magnitudes of two stars corresponds to the smaller-magnitude star being 100 times brighter than the larger-magnitude star. This allows us to specify their flux ratio as F 2 F 1 = 100 (m 1 − m 2 )/ 5 .
eBook - PDF- D. Scott Birney, Guillermo Gonzalez, David Oesper(Authors)
- 2006(Publication Date)
- Cambridge University Press(Publisher)
At the opposite extreme from the monochromatic magnitude is the bolometric magnitude. Bolometric simply means that all the electro- magnetic radiation emitted by a source is included in the measurement. Such magnitudes are indicated with a “bol” subscript. The bolometric correction is the difference between the bolometric magnitude and the magnitude in some passband BC band = m bol − m band For example, the bolometric correction to the visual magnitude is denoted by BC V . The BC V value for the Sun is −0.07 magnitudes. Note that some authors give BC with the opposite sign from that indicated above. In practice the bolometric magnitude is difficult to determine accurately, as it requires that measurements from different instruments be combined. When we wish to compare the luminosities of stars, we must first calculate their Absolute Magnitudes from the measured values of their distances and apparent magnitudes. The Absolute Magnitude is defined as the apparent magnitude a star would have if it were moved to a distance of 10 parsec. The following equation relates the Absolute Magnitude, M, to the distance in parsecs, d, and the apparent magnitude, m m − M = 5 log d 10 = 5 log d − 5 The quantity m − M is called the distance modulus. Table 5.2 gives the distance moduli for several distances, expressed in parsec. For objects more than a few parsec away, interstellar absorption must also be taken into account. Therefore, a more useful form is the apparent distance modulus (m − M) λ = (m − M) 0 + A λ where A λ is the absorption in magnitudes at wavelength λ or in a pass- band. Note that absorption makes an object appear farther than it really is. Note also that the apparent distance modulus is wavelength dependent.
Available until 25 Jan |Learn more- Pankaj Jain(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
It is now obsolete but historically played a very important role in astronomy. We now make more accurate measurements using photometers. Furthermore, standardized broad band filters, centered at different frequencies, are used. Some of the standard filters are U , B , V , and R , which refer to ultraviolet, blue, visual, and red wavelengths, respectively. The apparent magnitudes of these filters are denoted by m U , m B , m V , and m R , 74 An Introduction to Astronomy and Astrophysics respectively. These are also denoted simply as U , B , V , and R , respectively. The effective wavelengths for the U , B , V , and R filters are 365 nm, 445 nm, 551 nm, and 658 nm, respectively. Their full widths at half maximum are 66 nm, 94 nm, 88 nm, and 138 nm, respectively. The visual magnitude m V corresponds closely to the sensitivity of the human eye. There exist several different magnitude systems in astronomy correspond-ing to different choices of the reference flux. One standard system uses the star Vega as a reference and assigns a value equal to 0.03 for all its apparent magnitudes, such as U , B , V , and R . 4.5.2 Absolute Magnitude The apparent magnitude is related to the flux density of an astronomical object. We also need a measure that quantifies the luminosity or intrinsic brightness of an object. This is provided by the Absolute Magnitude, denoted by M . It is defined as the apparent magnitude of an object when it is placed at a distance of 10 pc from the observer. For a source that radiates isotropically, the flux density F ( r ) in vacuum is proportional to 1 /r 2 , where r is the distance of the observer from the source. Hence, F ( r ) F (10) = 10 pc r 2 , (4.23) where F (10) is the flux density at a distance of 10 pc. This implies that m -M = -2 . 5 log 10 F ( r ) F (10) = -2 . 5 log 10 10 pc r 2 = 5 log 10 r 10 pc . (4.24) The difference m -M is called the distance modulus because it is a measure of the distance of the object.
eBook - PDFAstrophysics
Decoding the Cosmos
- Judith Ann Irwin(Author)
- 2007(Publication Date)
- Wiley(Publisher)
[71] (probable error at most 0.03 mag) and on-line sources. b Typical range over a year. c A variable star. d This is the faintest star that could be observed by eye without a telescope. It will vary with the individual and conditions. e At or close to ‘opposition’ (180 from the Sun as seen from the Earth). f ‘Hubble Space Telescope’, from Space Telescope Science Institute on-line documentation. The limiting magnitude varies with instrument used. The quoted value is a best case. g OWL (the ‘Overwhelmingly Large Telescope’) refers to the European Southern Observatory’s concept for a 100 m diameter telescope with possible completion in 2020. 1.6 THE HUMAN PERCEPTION OF LIGHT – MAGNITUDES 21 From Eq. (1.26) and the values from Table 1.1, we have, B B 0 ¼ 1 : 95 0 ¼ 2 : 5 log f B 632 10 11 ð 1 : 28 Þ Solving, this gives f B ¼ 1 : 0 10 9 erg cm 2 s 1 ˚ A 1 for Betelgeuse. Eq. (1.27) can also be used, B ¼ 1 : 95 ¼ 2 : 5 log ð f B Þ 21 : 100 þ 0 : 601 ð 1 : 29 Þ which, on solving, gives the same result. 1.6.2 Absolute Magnitude Since flux densities fall off as 1 r 2 , measurements of apparent magnitude between stars do not provide a useful comparison of the intrinsic properties of stars without taking into account their various distances. Thus the Absolute Magnitude has been introduced, either as a bolometric quantity, M bol , or in some waveband (e.g. M V , M B , etc). The Absolute Magnitude of a star is the magnitude that would be measured if the star were placed at a distance of 10 pc. Since the magnitude scale is relative, we can let the reference star in Eq. (1.25) be the same star as is being measured but placed at a distance of 10 pc, m M ¼ 2 : 5 log f f 10 pc ¼ 5 þ 5 log d pc ð 1 : 30 Þ where we have dropped the subscripts for simplicity and used Eq. (1.9). Here d is the distance to the star in pc. Eq. (1.30) provides the relationship between the apparent and Absolute Magnitudes for any given star. The quantity, m M , is called the distance modulus .
eBook - PDFUnderstanding the Universe
An Inquiry Approach to Astronomy and the Nature of Scientific Research
- George Greenstein(Author)
- 2013(Publication Date)
- Cambridge University Press(Publisher)
In the case of light bulbs, this is measured by the number of watts emitted by the bulb. Astronomers customarily refer to absolute brightness as luminosity, L . The luminosity of a 100-watt light bulb is simply L = 100 watts. For comparison, the luminosity of the Sun is a gigantic L = 4 10 26 watts. • The apparent brightness of that source is the quantity of light that reaches us . Apparent brightness is measured by the number of watts that hits a detector of unit surface area. For instance, if the detector is a telescope, and if the lens of the telescope happens to have a surface area of one square meter, then the apparent brightness would measure how much light enters the telescope. Astronomers customarily refer to apparent brightness as flux, f . Clearly the 100-watt bulb remains a 100-watt bulb even when it is very far away: luminosity (absolute brightness) does not depend on distance . But equally clearly, the apparent brightness of the bulb grows fainter as it is carried farther away: apparent brightness does depend on distance . So the answer to our conundrum is that the absolute brightness of the faraway 100-watt bulb still exceeds that of the nearby 40-watt bulb, but the apparent brightness is far less. Light carries energy: the brightness of a light beam is a measure of how much energy it carries. Specifically, the absolute brightness of a source of light is the amount of light energy it emits per second . The watt, a familiar unit of luminos-ity, is then a measure of energy emitted per second. Similarly, the apparent brightness is the amount of light energy entering a detector of unit surface area per second . ..............................................................................
eBook - ePub- Cesare Barbieri, Ivano Bertini, Elena Fantino(Authors)
- 2020(Publication Date)
- CRC Press(Publisher)
Chapter 17 ). Furthermore, the AU, not the parsec, is the suitable distance unit; moreover, the distance of the objects from the Sun and from the Earth is greatly variable with their ephemerides.Let us indicate with r the distance of the body from the Sun and with Δ its distance from the Earth, both in AU. The Absolute Magnitude H (1,1) is defined as the observed one, when the body is at unit distance from Sun and Earth (the observer) at the opposition; the quantity H (1,1) can be derived from the apparent magnitude at the opposition:H(16.29)(= m1 , 1)(− 5 log r ⋅ Δr , Δ)Or else, if the body is a fully illuminated perfectly reflecting circular disk of diameter 2s and m ⊙ is the apparent magnitude of the Sun (m ⊙ = −26.74 in the visual band),H(16.30)(=1 , 1)m ⊙− 5 log s( AU )= 14.14 − 5 log s( km )For instance, the largest body between Mars and Jupiter, namely, Ceres, has a diameter of 945 km and an average distance from the Sun of 2.75 AU. According to Equation 16.30, it would have H (1,1) ≈ 0.80. However, a body will reflect only a fraction of the light coming from the Sun, according to its surface characteristics (oceans, clouds, rocky or icy terrain, dust-covered land, etc.). Indeed, Ceres has H (1,1) = +3.4, consistent with a reflectivity of 10%.More precise considerations are therefore in order. For instance, the body, as seen from the Earth, might be not entirely illuminated. The observed magnitude will therefore depend on both the surface properties of the body and the observing geometry. The terminator is the line dividing the sunlit hemisphere from the shadowed regions. Let α be the so-called phase angle , namely, the angle between the Sun and the Earth as seen from the body (α = 0° at opposition, 180° at conjunction) and φ (α ) the phase function
eBook - PDFProperties of Double Stars
A Survey of Parallaxes and Orbits
- Leendert Binnendijk(Author)
- 2016(Publication Date)
88. Open clusters. For photometry of open clusters or other rich star fields we make absolute observations. Excellent transpar-ency is necessary, and it must remain constant all night. Dur-ing a particular night the extinction must be determined and the extinction corrections applied. The magnitudes are then reduced to their values outside atmosphere; independent of the atmo-spheric conditions of the various places of observation, all ob-servers should get the same results within the probable errors. This is what is meant by an absolute result; consequently not all 238 Properties of Double Stars stars are measured absolutely and independently of the others. We will measure the stars in an open cluster in a relative way, namely with respect to a small number of standard stars, so that the group as a whole is homogeneous. The observations of one star may proceed as follows: dark current, star plus sky in yellow, star plus sky in blue, sky yellow, sky blue; the sequence is then repeated in reverse. The dark current is measured to see whether it has remained constant during the observation. The sky light may change rather quickly when the moon is rising or setting. By subtraction we easily find star yellow, star blue, and thus the relative deflections. For ex-tinction stars we choose both a red and a blue one which are low in the east or northeast at the beginning of the night's work. If the open cluster is itself situated there, we can often take these extinction stars as standard stars and save some observational work. The sequence for stars of the open cluster may be ar-ranged as follows : radium light, red standard star, blue standard, star 1, star 2, red standard, blue standard, star 3, star 4, radium light. A certain star in the cluster is consequently always closely timed between two standard stars, and the extinction is fre-quently determined.
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