视星等与面亮度(译)
In astronomy, surface brightness (SB) 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 (MPSAS) in a particular filter band or photometric system.
Measurement of the surface brightnesses of celestial objects is called surface photometry.
在天文学中, 面亮度 (Surface Brightness) 用来度量空间延展天体(extended object), 比如像星系(galaxy)或星云(nebula), 或者夜空背景(night sky background)单位角面积的视亮度(apparent brightness) 或者通量密度(flux density). 一个物体的面亮度取决于它的表面光度密度(luminosity density), 即它的每个单位表面区域发射出的光度. 在可见光及红外天文学(visible and infrared astronomy)中, 面亮度通常在特定滤光波段或者测光系统中, 以每平方角秒的星等标(magnitude scale)进行描述.
对天体(celestial objects)面亮度的测量, 称为面源测光(surface phtometry).
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综合描述(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. The background light is then subtracted from the measurement to obtain the total brightness. The resulting magnitude value is the same as a point-like source that is emitting the same amount of energy. The total magnitude of a comet is the combined magnitude of the coma and nucleus.
总星等(total magnitude)是诸如星云、星系、星团或彗星一类延展天体的亮度度量. 它可以通过对整个天体区域的光度求和, 或者使用应用了不同尺寸光阑或狭缝的光度计(photometer)来进行测量, 然后减去背景光得到总亮度. 得到的星等值与发射同等能量的点状光源(point-like source)相同. 彗星的总星等是慧发(coma)和彗尾(nucleus)的合成星等(combined megnitude).
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. In general, in order to adequately assess an object’s visibility one needs to know both parameters.
天体的视星等(apparent magnitude)通常是一个积分值(integrated value) —— 如果指明一个星系的星等为 12.5, 那么意味着我们从这个星系看到光的量, 与一颗同为 12.5 星等的恒星(star)相同. 然而, 一颗恒星非常的小, 在大多数观测中它实际上是一个点光源(point source) (剑鱼座 R(R Doradus)是角直径(angular diameter)最大的恒星, 它的角直径是 0.057 ± 0.005 角秒(arcsec)). 但是一个星系可能延展至几角秒或者角分(arcminutes). 因此, 在大气辉光背景(airglow background)下, 星系比恒星更难看到. 如果一个天体是点状的或很小的, 视星等是一个很好的可见度(visibility)指标, 但是如果天体非常大, 那么面亮度则是一个更好的指标. 大或小的评判取决于特定的观测条件, 并且遵循里科定律(Ricco’s low). 通常, 为了充分地评价一个天体的可见度, 同时需要这两个参数.
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计算面亮度(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
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. 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.
面亮度通常使用“星等每平方角秒”描述. 因为星等是对数的, 面亮度是不能简单通过星等除以面积来计算. 而是, 对于一个总星等或累积星等(integrated magnitude)为 $m$ 的光源, 可视面积扩展至 $A$ 平方角秒, 面亮度 $S$ 通过如下公式计算获得:
对于天体来说, 面亮度类似于光度学的亮度(luminance), 不随着距离的改变而改变: 一个天体与我们距离越远, 就变得越暗淡, 同时它的视觉面积也相应地变小. 用几何学术语(geometrical terms)来说, 一个临近物体发射出一定量的光, 辐射通量随着与物体距离的平方值减小而减小, 它的立体角(solid angle)或可视区域相对应的物理面积也在以等比例减小, 最终结果是面亮度不变. 对于星云或星系一类的延展天体, 这个特性就允许我们借助距离模数(distance modulus)或光度距离(luminosity distance), 由面亮度估算空间距离.