# Surface brightness

In astronomy, surface brightness quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on its surface luminosity density, i.e., its luminosity emitted per unit surface area. In visible and infrared astronomy, surface brightness is often quoted on a magnitude scale, in magnitudes per square arcsecond in a particular filter band or photometric system.

Measurement of the surface brightnesses of celestial objects is called surface photometry.

## General description

The total magnitude is a measure of the brightness of an extended object such as a nebula, cluster, galaxy or comet. It can be obtained by summing up the luminosity over the area of the object. Alternatively, a photometer can be used by applying apertures or slits of different sizes of diameter.[1] The background light is then subtracted from the measurement to obtain the total brightness.[2] The resulting magnitude value is the same as a point-like source that is emitting the same amount of energy.[3]

The apparent magnitude of an astronomical object is generally given as an integrated value—if a galaxy is quoted as having a magnitude of 12.5, it means we see the same total amount of light from the galaxy as we would from a star with magnitude 12.5. However, a star is so small it is effectively a point source in most observations (the largest angular diameter, that of R Doradus, is 0.057 ± 0.005 arcsec), whereas a galaxy may extend over several arcseconds or arcminutes. Therefore, the galaxy will be harder to see than the star against the airglow background light. Apparent magnitude is a good indication of visibility if the object is point-like or small, whereas surface brightness is a better indicator if the object is large. What counts as small or large depends on the specific viewing conditions and follows from Ricco's law.[4] In general, in order to adequately assess an object's visibility one needs to know both parameters.

## Calculating surface brightness

Surface brightnesses are usually quoted in magnitudes per square arcsecond. Because the magnitude is logarithmic, calculating surface brightness cannot be done by simple division of magnitude by area. Instead, for a source with a total or integrated magnitude m extending over a visual area of A square arcseconds, the surface brightness S is given by

${\displaystyle S=m+2.5\cdot \log _{10}A.}$

For astronomical objects, surface brightness is analogous to photometric luminance and is therefore constant with distance: as an object becomes fainter with distance, it also becomes correspondingly smaller in visual area. In geometrical terms, for a nearby object emitting a given amount of light, radiative flux decreases with the square of the distance to the object, but the physical area corresponding to a given solid angle or visual area (e.g. 1 square arcsecond) decreases by the same proportion, resulting in the same surface brightness.[5] For extended objects such as nebulae or galaxies, this allows the estimation of spatial distance from surface brightness by means of the distance modulus or luminosity distance.

## Relationship to physical units

The surface brightness in magnitude units is related to the surface brightness in physical units of solar luminosity per square parsec by

${\displaystyle S({\rm {mag}}/{\rm {arcsec}}^{2})=M_{\odot }+21.572-2.5\log _{10}S(L_{\odot }/{\rm {pc}}^{2}),}$

where ${\displaystyle M_{\odot }}$ and ${\displaystyle L_{\odot }}$ are the absolute magnitude and the luminosity of the Sun in chosen color-band[6] respectively.

Surface brightness can also be expressed in candela per square metre using the formula [value in cd/m2] = 10.8×104 × 10(-0.4*[value in mag/arcsec2]).

There is an online calculator available here http://unihedron.com/projects/darksky/magconv.php?ACTION=SOLVE&txtMAGSQA=21.83

## Examples

A truly dark sky has a surface brightness of 2×10−4  cd m−2 or 21.8 mag arcsec−2.[7]

The peak surface brightness of the central region of the Orion Nebula is about 17 Mag/arcsec2 (about 14 millinits) and the outer bluish glow has a peak surface brightness of 21.3 Mag/arcsec2 (about 0.27 millinits).[8]

## References

1. ^ Daintith, John; Gould, William (2006). The Facts on File dictionary of astronomy. Facts on File science library (5th ed.). Infobase Publishing. p. 489. ISBN 0-8160-5998-5.
2. ^ Palei, A. B. (August 1968). "Integrating Photometers". Soviet Astronomy. 12: 164. Bibcode:1968SvA....12..164P.
3. ^ Sherrod, P. Clay; Koed, Thomas L. (2003). A Complete Manual of Amateur Astronomy: Tools and Techniques for Astronomical Observations. Astronomy Series. Courier Dover Publications. p. 266. ISBN 0-486-42820-6.
4. ^ Crumey, Andrew (2014). "Human contrast threshold and astronomical visibility". Monthly Notices of the Royal Astronomical Society. 442: 2600. arXiv:1405.4209. Bibcode:2014MNRAS.442.2600C. doi:10.1093/mnras/stu992.
5. ^ Sparke & Gallagher (2000, § 5.1.2)
6. ^ Absolute magnitudes of the Sun in different color-bands can be obtained from Binney & Merrifield (1998) or Absolute Magnitude of the Sun in Several Bands Archived 2007-07-18 at the Wayback Machine
7. ^ Based on the equivalence 21.83 mag arcsec−2 = 2×10−4  cd m−2, from description of a "truly dark sky", Section 1.3 of Crumey, A. (2014). Human contrast threshold and astronomical visibility. MNRAS 442, 2600–2619.
8. ^ Clark, Roger (2004-03-28). "Surface Brightness of Deep Sky Objects". Retrieved 2013-06-29.. The conversion to nits is based on 0 magnitude being 2.08 microlux.

### General references

Andromeda XXI

Andromeda XXI (And 21, And XXI) is a moderately bright dwarf spheroidal galaxy about 859 ± 51 kiloparsecs (2.80 ± 0.17 Mly) away from the Sun in the constellation Andromeda. It is the fourth largest Local Group dwarf spheroidal galaxy.

This large satellite of the Andromeda Galaxy (M31) has a half-light radius of nearly 1 kpc.The discovery arose from the first year data of a photometric survey of the M31/M33 subgroupings of the Local Group by the Pan-Andromeda Archaeological Survey (PAndAS). This survey was conducted with the Megaprime/MegaCam wide-field camera mounted on the Canada-France-Hawaii Telescope.

Andromeda XXI appears as a spatial overdensity of stars. It has red giant branches at the distance of M31/M33, and follows metal-poor, [Fe/H]=-1.8 when plotted in a color-magnitude diagram.

Although moderately bright (MV=-9.9 ± 0.6), it has low surface brightness. This indicates that numerous relatively luminous M31 satellites remain undiscovered.

Antlia 2

Antlia 2 (Ant 2) is a low-surface-brightness dwarf satellite galaxy of the Milky Way at a galactic latitude of 11.2°. It spans 1.26° in the sky just southeast of Epsilon Antliae. The galaxy is similar in size to the Large Magellanic Cloud, despite being 10,000 times fainter. Antlia 2 has the lowest surface brightness of any galaxy discovered and is ~ 100 times more diffuse than any known ultra diffuse galaxy. It was discovered by the European Space Agency's Gaia spacecraft in November 2018.

Crater 2 Dwarf

Crater 2 is a low-surface-brightness dwarf satellite galaxy of the Milky Way, located approximately 380,000 ly from Earth. Crater 2 was identified in imaging data from the VST ATLAS survey.The galaxy has a half-light radius of ∼1100 pc, making it the fourth largest satellite of the Milky Way. It has an angular size about double of that of the moon.

Dwarf spiral galaxy

A dwarf spiral galaxy is the dwarf version of a spiral galaxy. Dwarf galaxies are characterized as having low luminosities, small diameters (less than 5 kpc), low surface brightnesses, and low hydrogen masses. The galaxies may be considered a subclass of low-surface-brightness galaxies.

Dwarf spiral galaxies, particularly the dwarf counterparts of Sa-Sc type spiral galaxies, are quite rare. In contrast, dwarf elliptical galaxies, dwarf irregular galaxies, and the dwarf versions of Magellanic type galaxies (which may be considered transitory between spiral and irregular in terms of morphology) are very common.It is suggested that dwarf spiral galaxies can transform into dwarf elliptical galaxies, especially in dense cluster environments.

The effective radius (${\displaystyle R_{e}}$) of a galaxy is the radius at which half of the total light of the system is emitted. This assumes the galaxy has either intrinsic spherical symmetry or is at least circularly symmetric as viewed in the plane of the sky. Alternatively, a half-light contour, or isophote, may be used for spherically and circularly asymmetric objects.

${\displaystyle R_{e}}$ is an important length scale in de Vaucouleurs ${\displaystyle {\sqrt[{4}]{R}}}$ law, which characterizes a specific rate at which surface brightness decreases as a function of radius:

${\displaystyle I(R)=I_{e}\cdot e^{-7.67\left({\sqrt[{4}]{\frac {R}{R_{e}}}}-1\right)}}$

where ${\displaystyle I_{e}}$ is the surface brightness at ${\displaystyle R=R_{e}}$. At ${\displaystyle R=0}$,

${\displaystyle I(R=0)=I_{e}\cdot e^{7.67}\approx 2000\cdot I_{e}}$

Thus, the central surface brightness is approximately ${\displaystyle 2000\cdot I_{e}}$.

Galactic disc

A galactic disc is a component of disc galaxies, such as spiral galaxies and lenticular galaxies. Galactic discs consist of a stellar component ( composed of most of the galaxy's stars) and a gaseous component (mostly composed of cool gas and dust). The stellar population of galactic discs tend to exhibit very little random motion with most of its stars undergoing nearly circular orbits about the galactic center. Discs can be fairly thin because the disc material's motion lies predominantly on the plane of the disc (very little vertical motion). The Milky Way's disc, for example is approximately 1 kpc thick but thickness can vary for discs in other galaxies.

Low Surface Brightness galaxy

A low-surface-brightness galaxy, or LSB galaxy, is a diffuse galaxy with a surface brightness that, when viewed from Earth, is at least one magnitude lower than the ambient night sky.

Most LSBs are dwarf galaxies, and most of their baryonic matter is in the form of neutral gaseous hydrogen, rather than stars. They appear to have over 95% of their mass as non-baryonic dark matter. There appears to be no supernova activity in these galaxies.Rotation curve measurements indicate an extremely high mass-to-light ratio, meaning that stars and luminous gas contribute only very little to the overall mass balance of an LSB. The centers of LSBs show no large overdensities in stars, unlike e.g. the bulges of normal spiral galaxies. Therefore, they seem to be dark-matter-dominated even in their centers, which makes them excellent laboratories for the study of dark matter.

In comparison to the high-surface-brightness galaxies, LSBs are mainly isolated field galaxies, found in regions devoid of other galaxies. In their past, they had fewer tidal interactions or mergers with other galaxies, which could have triggered enhanced star formation. This is an explanation for the small stellar content.

LSB galaxies were theorized to exist in 1976 by Mike Disney.

Malin 1

Malin 1 is a giant low surface brightness (LSB) spiral galaxy. It is located 1.19 billion light-years (366 Mpc) away in the constellation Coma Berenices, near the North Galactic Pole. As of February 2015, it is arguably the largest known spiral galaxy, with an approximate diameter of 650,000 light-years (200,000 pc), six and a half times the diameter of our Milky Way. It was discovered by astronomer David Malin in 1986 and is the first LSB galaxy verified to exist. Its high surface brightness central spiral is 30,000 light-years (9,200 pc) across, with a bulge of 10,000 light-years (3,100 pc). The central spiral is a SB0a type barred-spiral.Malin 1 is peculiar in several ways: its diameter alone would make it the largest barred spiral galaxy ever to have been observed.Malin 1 was found later to be interacting with two other galaxies, Malin 1B and SDSS J123708.91+142253.2. Malin 1B is located 46,000 light-years (14,000 pc) away from the high surface brightness central spiral of Malin 1, which may be responsible for the formation of the galaxy's central bar. Meanwhile, SDSS J123708.91+142253.2 is located within the huge, faint halo of Malin 1 and might have caused the formation of the extended low surface brightness disc through tidal stripping.

Observations by Galaz et al. in April 2014 revealed a detailed view of the spiral structure of Malin 1 in optical bands. The galaxy exhibits giant and very faint spiral arms, with a thickness of up to one-third the diameter of the Milky Way. Other details, such as possible stellar streams and formation regions, are revealed as well.

NGC 1090

NGC 1090 is a barred spiral galaxy located in the constellation Cetus.

NGC 1090 has a pseudo inner ring. The disc has a very low surface brightness.

This galaxy has been the site of two known supernovae (in 1962 and 1971).

NGC 1090 is not part of a galaxy group, even though it appears close to NGC 1087, M-77 (NGC 1068), NGC 1055, NGC 1073, and five other small irregular galaxies.

The distance to NGC 1090 is approximately 124 million light years and its diameter is about 144,000 light years.

NGC 1264

NGC 1264 is a low-surface-brightness barred spiral galaxy located about 145 million light-years away in the constellation Perseus. The galaxy was discovered by astronomer Guillaume Bigourdan on October 19, 1884. NGC 1264 is a member of the Perseus Cluster.

NGC 296

NGC 296 is a low surface brightness unbarred spiral galaxy in the constellation of Pisces. The designation NGC 295 is sometimes mistakenly used for NGC 296.

NGC 3794

NGC 3794, also cataloged in the New General Catalogue as NGC 3804, is a low-surface-brightness galaxy in the constellation Ursa Major. It is very far from Earth, with a distance of about 68,470,000 light-years (20,990,000 pc).

NGC 3821

NGC 3821 is a low surface brightness spiral galaxy and a ring galaxy about 270 million light-years away in the constellation Leo. The galaxy was discovered by astronomer William Herschel on April 26, 1785 and is a member of the Leo Cluster.

NGC 3883

NGC 3883 is a large low surface brightness spiral galaxy located about 330 million light-years away in the constellation Leo. NGC 3883 has a prominent bulge but does host an AGN. The galaxy also has flocculent spiral arms in its disk. It was discovered by astronomer William Herschel on April 13, 1785 and is a member of the Leo Cluster.

NGC 45

NGC 45 is a low surface brightness spiral galaxy in the constellation of Cetus. It was discovered on 11 November 1835 by the English astronomer John Herschel.

Unlike the Milky Way, NGC 45 has no clear defined spiral arms, and its center bar nucleus is also very small and distorted. NGC 45 thus does not have a galactic habitable zone. For the Milky Way, the galactic habitable zone is commonly believed to be an annulus with an outer radius of about 10 kiloparsecs and an inner radius close to the Galactic Center, both of which lack hard boundaries.

NGC 5774

NGC 5774 is an intermediate spiral galaxy approximately 71 million light-years away from Earth in the constellation of Virgo. It was discovered by Irish engineer Bindon Stoney on April 26, 1851.NGC 5774 belongs to a small group of galaxies, together with nearby NGC 5775 and IC 1070.

It has been classified as a "low surface brightness" (LSB) galaxy, but its central surface brightness is 5 times brighter than the brightest LSB galaxies.

It has a multiple spiral pattern with bright blue knotty structure all along the arms.It is an extremely low star forming galaxy with five X-ray sources plus three ultraluminous X-ray source candidates.

NGC 765

NGC 765 is an intermediate spiral galaxy located in the constellation Aries. It is located at a distance of circa 220 million light years from Earth, which, given its apparent dimensions, means that NGC 765 is about 195,000 light years across. It was discovered by Albert Marth on October 8, 1864. The galaxy has an extensive hydrogen (HI) disk with low surface brightness, whose diameter is estimated to be 240 kpc (780,000 light years).

NGC 779

NGC 779 is a spiral galaxy seen edge-on, located in the constellation Cetus. It is located at a distance of circa 60 million light years from Earth, which, given its apparent dimensions, means that NGC 779 is about 70,000 light years across. It was discovered by William Herschel on September 10, 1785.NGC 779 features a bright nucleus and an elliptical or boxy bulge. It is seen with high inclination. The inner arms are tightly wound and form an inner pseudoring with high surface brightness. A break is seen at the northwest side of the pseudoring and may be due to dust extinction. The disk has lower surface brightness and is smooth, with no pronounced star-forming knots. The spiral pattern of the galaxy gas been described either as multiple-armed or grand-design two-armed spiral.NGC 779 forms a small galaxy group with UGCA 024, known as the NGC 779 group. NGC 779 is considered to be part of the Cetus II cloud, which also includes NGC 584, NGC 681, NGC 720, and their groups, although it could also lie in the foreground.The galaxy is included in the Herschel 400 Catalogue. It lies about five degrees northeast from Zeta Ceti. It can be seen with a small telescope at moderate magnification, with its core being more easily detected.