Absolute magnitude
In
Absolute magnitudes of stars generally range from approximately −10 to +20. The absolute magnitudes of galaxies can be much lower (brighter).
The more luminous an object, the smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100n/5. For example, a star of absolute magnitude MV = 3.0 would be 100 times as luminous as a star of absolute magnitude MV = 8.0 as measured in the V filter band. The Sun has absolute magnitude MV = +4.83.[1] Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8.[2]
As with all astronomical
An object's absolute bolometric magnitude (Mbol) represents its total
Stars and galaxies
In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light-years, 308.57 petameters or 308.57
Some stars visible to the naked eye have such a low absolute magnitude that they would appear bright enough to outshine the planets and cast shadows if they were at 10 parsecs from the Earth. Examples include Rigel (−7.0), Deneb (−7.2), Naos (−6.0), and Betelgeuse (−5.6). For comparison, Sirius has an absolute magnitude of only 1.4, which is still brighter than the Sun, whose absolute visual magnitude is 4.83. The Sun's absolute bolometric magnitude is set arbitrarily, usually at 4.75.[4][5] Absolute magnitudes of stars generally range from approximately −10 to +20. The absolute magnitudes of galaxies can be much lower (brighter). For example, the giant
Apparent magnitude
The Greek astronomer Hipparchus established a numerical scale to describe the brightness of each star appearing in the sky. The brightest stars in the sky were assigned an apparent magnitude m = 1, and the dimmest stars visible to the naked eye are assigned m = 6.[7] The difference between them corresponds to a factor of 100 in brightness. For objects within the immediate neighborhood of the Sun, the absolute magnitude M and apparent magnitude m from any distance d (in parsecs, with 1 pc = 3.2616 light-years) are related by
For objects at very large distances (outside the Milky Way) the luminosity distance dL (distance defined using luminosity measurements) must be used instead of d, because the
The absolute magnitude M can also be written in terms of the apparent magnitude m and stellar parallax p:
Examples
Rigel has a visual magnitude mV of 0.12 and distance of about 860 light-years:
Vega has a parallax p of 0.129″, and an apparent magnitude mV of 0.03:
The Black Eye Galaxy has a visual magnitude mV of 9.36 and a distance modulus μ of 31.06:
Bolometric magnitude
The absolute
Classically, the difference in bolometric magnitude is related to the luminosity ratio according to:[7]
- L⊙ is the Sun's luminosity (bolometric luminosity)
- L★ is the star's luminosity (bolometric luminosity)
- Mbol,⊙ is the bolometric magnitude of the Sun
- Mbol,★ is the bolometric magnitude of the star.
In August 2015, the
Resolution B2 defines an absolute bolometric magnitude scale where Mbol = 0 corresponds to luminosity L0 = 3.0128×1028 W, with the zero point
Following Resolution B2, the relation between a star's absolute bolometric magnitude and its luminosity is no longer directly tied to the Sun's (variable) luminosity:
- L★ is the star's luminosity (bolometric luminosity) in watts
- L0 is the zero point luminosity 3.0128×1028 W
- Mbol is the bolometric magnitude of the star
The new IAU absolute magnitude scale permanently disconnects the scale from the variable Sun. However, on this SI power scale, the nominal solar luminosity corresponds closely to Mbol = 4.74, a value that was commonly adopted by astronomers before the 2015 IAU resolution.[10]
The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude Mbol as:
Solar System bodies (H)
H | Diameter |
---|---|
10 | 36 km |
12.7 | 10 km |
15 | 3.6 km |
17.7 | 1 km |
19.2 | 510 m |
20 | 360 m |
22 | 140 m |
22.7 | 100 m |
24.2 | 51 m |
25 | 36 m |
26.6 | 17 m |
27.7 | 10 m |
30 | 3.6 m |
32.7 | 1 m |
For planets and asteroids, a definition of absolute magnitude that is more meaningful for non-stellar objects is used. The absolute magnitude, commonly called , is defined as the apparent magnitude that the object would have if it were one astronomical unit (AU) from both the Sun and the observer, and in conditions of ideal solar opposition (an arrangement that is impossible in practice).[12] Because Solar System bodies are illuminated by the Sun, their brightness varies as a function of illumination conditions, described by the phase angle. This relationship is referred to as the phase curve. The absolute magnitude is the brightness at phase angle zero, an arrangement known as opposition, from a distance of one AU.
Apparent magnitude
The absolute magnitude can be used to calculate the apparent magnitude of a body. For an object reflecting sunlight, and are connected by the relation
By the law of cosines, we have:
Distances:
- dBO is the distance between the body and the observer
- dBS is the distance between the body and the Sun
- dOS is the distance between the observer and the Sun
- d0, a AU, the average distance between the Earth and the Sun
Approximations for phase integral q(α)
The value of depends on the properties of the reflecting surface, in particular on its roughness. In practice, different approximations are used based on the known or assumed properties of the surface. The surfaces of terrestrial planets are generally more difficult to model than those of gaseous planets, the latter of which have smoother visible surfaces.[13]
Planets as diffuse spheres
Planetary bodies can be approximated reasonably well as
By contrast, a diffuse disk reflector model is simply , which isn't realistic, but it does represent the opposition surge for rough surfaces that reflect more uniform light back at low phase angles.
The definition of the geometric albedo , a measure for the reflectivity of planetary surfaces, is based on the diffuse disk reflector model. The absolute magnitude , diameter (in
Example: The Moon's absolute magnitude can be calculated from its diameter and geometric albedo :[18]
More advanced models
Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models to predict apparent magnitudes based on known or assumed properties of the body.[13] For planets, approximations for the correction term in the formula for m have been derived empirically, to match observations at different phase angles. The approximations recommended by the Astronomical Almanac[20] are (with in degrees):
Planet | Referenced calculation[21] | Approximation for | |
---|---|---|---|
Mercury | −0.4 | −0.613 | |
Venus
|
−4.4 | −4.384 |
|
Earth | − | −3.99 | |
Moon[22] | 0.2 | +0.28 |
|
Mars
|
−1.5 | −1.601 |
|
Jupiter
|
−9.4 | −9.395 |
|
Saturn
|
−9.7 | −8.914 |
|
Uranus
|
−7.2 | −7.110 | (for ) |
Neptune
|
−6.9 | −7.00 | (for and ) |
Here is the effective inclination of
Example 1: On 1 January 2019,
Example 2: At
Earth's
Asteroids
If an object has an atmosphere, it reflects light more or less isotropically in all directions, and its brightness can be modelled as a diffuse reflector. Bodies with no atmosphere, like asteroids or moons, tend to reflect light more strongly to the direction of the incident light, and their brightness increases rapidly as the phase angle approaches . This rapid brightening near opposition is called the
In 1985, the
where
- the phase integral is and
- for or , , , and .[25]
This relation is valid for phase angles , and works best when .[26]
The slope parameter relates to the surge in brightness, typically 0.3 mag, when the object is near opposition. It is known accurately only for a small number of asteroids, hence for most asteroids a value of is assumed.[26] In rare cases, can be negative.[25][27] An example is 101955 Bennu, with .[28]
In 2012, the -system was officially replaced by an improved system with three parameters , and , which produces more satisfactory results if the opposition effect is very small or restricted to very small phase angles. However, as of 2022, this -system has not been adopted by either the Minor Planet Center nor Jet Propulsion Laboratory.[13][29]
The apparent magnitude of asteroids
Cometary magnitudes
The brightness of comets is given separately as total magnitude (, the brightness integrated over the entire visible extend of the
The activity of comets varies with their distance from the Sun. Their brightness can be approximated as
For example, the lightcurve of comet
Comet | Absolute magnitude [35] |
Nucleus diameter |
---|---|---|
Comet Sarabat |
−3.0 | ≈100 km? |
Comet Hale-Bopp |
−1.3 | 60 ± 20 km |
Comet Halley |
4.0 | 14.9 x 8.2 km |
average new comet | 6.5 | ≈2 km[36] |
C/2014 UN271 (Bernardinelli-Bernstein) |
6.7[37] | 60–200 km?[38][39] |
289P/Blanpain (during 1819 outburst) | 8.5[40] | 320 m[41] |
289P/Blanpain (normal activity) | 22.9[42] | 320 m |
The absolute magnitude of any given comet can vary dramatically. It can change as the comet becomes more or less active over time or if it undergoes an outburst. This makes it difficult to use the absolute magnitude for a size estimate. When comet 289P/Blanpain was discovered in 1819, its absolute magnitude was estimated as .[40] It was subsequently lost and was only rediscovered in 2003. At that time, its absolute magnitude had decreased to ,[42] and it was realised that the 1819 apparition coincided with an outburst. 289P/Blanpain reached naked eye brightness (5–8 mag) in 1819, even though it is the comet with the smallest nucleus that has ever been physically characterised, and usually doesn't become brighter than 18 mag.[40][41]
For some comets that have been observed at heliocentric distances large enough to distinguish between light reflected from the coma, and light from the nucleus itself, an absolute magnitude analogous to that used for asteroids has been calculated, allowing to estimate the sizes of their nuclei.[43]
Meteors
For a
See also
- Araucaria Project
- Hertzsprung–Russell diagram – relates absolute magnitude or luminosity versus spectral color or surface temperature.
- Jansky radio astronomer's preferred unit – linear in power/unit area
- List of most luminous stars
- Photographic magnitude
- Surface brightness – the magnitude for extended objects
- Zero point (photometry) – the typical calibration point for star flux
References
- NASA Goddard Space Flight Center. Retrieved 25 February 2017.
- doi:10.1086/382905.
- doi:10.1086/177785.
- S2CID 189937884.
- S2CID 16400466.
- ISSN 0004-637X.
- ^ ISBN 978-0-321-44284-0.
- ISBN 978-3662043561
- ^ "IAU XXIX General Assembly Draft Resolutions Announced". Retrieved 8 July 2015.
- ^ Bibcode:2015arXiv151006262M
- ^ CNEOS Asteroid Size Estimator
- ^ Luciuk, M., Astronomical Magnitudes (PDF), p. 8, retrieved 11 January 2019
- ^ ISBN 9783662530450.
- Bibcode:1907Obs....30...96W
- ^ Bruton, D., Conversion of Absolute Magnitude to Diameter for Minor Planets, Stephen F. Austin State University, archived from the original on 23 July 2011, retrieved 12 January 2019
- ^ The factor can be computed as , where , the absolute magnitude of the Sun, and
- (PDF) from the original on 9 October 2022.
- ^ Albedo of the Earth, Department of Physics and Astronomy, retrieved 12 January 2019
- ^ Luciuk, M., Albedo – How bright is the Moon?, retrieved 12 January 2019
- ^ S2CID 69912809.
- ^ "Encyclopedia - the brightest bodies". IMCCE. Retrieved 29 May 2023.
- ^ Cox, A.N. (2000). Allen's Astrophysical Quantities, fourth edition. Springer-Verlag. p. 310.
- ^ JPL Horizons (Ephemeris Type "OBSERVER", Target Body "Venus [299]", Observer Location "Geocentric [500]", Time Span "Start=2019-01-01 00:00, Stop=2019-01-02 00:00, Step=1 d", QUANTITIES=9,19,20,24), Jet Propulsion Laboratory, retrieved 11 January 2019
- ^ Minor Planet Circular 10193 (PDF), Minor Planet Center, 27 December 1985, retrieved 11 January 2019
- ^ Bibcode:1987A&AS...68..295L
- ^ Bibcode:2007JBAA..117..342D, retrieved 11 January 2019
- ^ JPL Horizons (Version 3.75) (PDF), Jet Propulsion Laboratory, 4 April 2013, p. 27, retrieved 11 January 2013
- ^ JPL Small-Body Database Browser – 101955 Bennu, Jet Propulsion Laboratory, 19 May 2018, retrieved 11 January 2019
- hdl:10138/228807
- Bibcode:2016PDSS..246.....H.
- ^ Guide to the MPES (PDF), Minor Planet Center, p. 11, retrieved 11 January 2019
- Bibcode:1976NASSP.393..410M
- ^ Comet C/2011 L4 (PANSTARRS), COBS, retrieved 11 January 2019[permanent dead link]
- ^ Minor Planet & Comet Ephemeris Service (C/2011 L4, ephemeris start date=2013-03-10), Minor Planet Center, retrieved 11 January 2019
- ^ Kidger, M. (3 April 1997), Comet Hale-Bopp Light Curve, NASA JPL, retrieved 31 May 2019
- Bibcode:1990acm..proc..327H.
- ^ "JPL Small-Body Database Browser: (2014 UN271)" (2021-08-08 last obs.). Jet Propulsion Laboratory. Retrieved 15 September 2021.
- ^ "The Largest Comet Ever Found Is Making Its Move Into a Sky Near You". The New York Times. 28 June 2021. Retrieved 1 July 2021.
- ^ Farnham, Tony (6 July 2021). "Comet C/2014 UN271 (Bernardinelli-Bernstein) exhibited activity at 23.8 au". The Astronomer's Telegram. Retrieved 6 July 2021.
- ^ a b c Yoshida, S. (24 January 2015), "289P/Blanpain", aerith.net, retrieved 31 May 2019
- ^ doi:10.1086/500390. Retrieved 31 May 2019.
- ^ a b 289P/Blanpain (2013-07-17 last obs.), Jet Propulsion Laboratory, 18 May 2019, retrieved 31 May 2019
- Bibcode:2004come.book..223L, archived(PDF) from the original on 9 October 2022
- ^ "Glossary – Absolute magnitude of meteors". International Meteor Organization. Retrieved 16 May 2013.
- NASA Jet Propulsion Laboratory. Retrieved 16 May 2013.
External links
- Reference zero-magnitude fluxes Archived 22 February 2003 at the Wayback Machine
- International Astronomical Union
- Absolute Magnitude of a Star calculator
- The Magnitude system
- About stellar magnitudes Archived 27 October 2021 at the Wayback Machine
- Obtain the magnitude of any star – SIMBAD
- Converting magnitude of minor planets to diameter
- Another table for converting asteroid magnitude to estimated diameter