Basic Photometry and Astrometry for GTN Participants

Photometry Lingo
Photometry is the measure of the brightness of astronomical objects. A standard result of photometry is the light curve (a plot of brightness vs. time). Magnitude is a logarithmic measure of the brightness of an object. The magnitude system is defined in such a way that the magnitudes of dim objects are large positive numbers, whereas bright objects have small positive numbers. For extremely bright objects, magnitudes can even be negative. Examples will be helpful: the brightest stars have magnitudes around zero or 1, and the dimmest stars visible in a dark area far from city lights have magnitudes around 6. The full moon has a magnitude of –11, and the sun is at –26. This system applies to visible, IR, and near UV light. The equation used by modern astronomers to define the difference in magnitude between two sources is:

Magnitude Equation

where m1 and m2 are the magnitudes of the two sources, and B1 and B2 are their brightnesses (energy fluxes – see below). The zero-point for the system is the star Vega, which is defined to have a magnitude of zero at all wavebands (colors).

Luminosity: the measured energy emitted each second by a celestial body. This includes all wavelengths of light. Note that this is not necessarily the same as the apparent brightness because two objects with the same luminosity can appear different brightness if they are at different distances. The SI unit for luminosity is watts: the luminosity of the Sun is approximately 4 x 1026 W.

Fluence: the integrated luminosity over some specified time duration, i.e., the total energy emitted over that time. The SI unit for fluence is joules.

Photon Flux: the number of emitted photons that are detected in a given area per unit time. For instance, the number of photons passing through a square meter-sized detector in one second would be the photon flux.

Energy Flux: the energy per second that is deposited onto a given area. For instance, the energy per second deposited on a square-meter sized detector. Since all photons do not have the same energy, the energy flux and photon flux are not necessarily the same. The SI unit for energy flux is watts per square meter [W/m2]. At the top of Earth’s atmosphere, the flux from the Sun is about 1300 W/m2.

Spectrum: the distribution of flux (energy or photons) with energy. Basically, the spectrum of an object is a histogram of the total energy it emits at each photon energy, or if the photon flux is being measured, then the spectrum could be the number of photons emitted at each photon energy.

How to Determine the Brightness of an Object Determining the brightness of an astronomical object using a CCD detector includes several steps. The basic ideas involved are illustrated in our Cookie Cutter Photometry exercise. In short, you must compare your star’s brightness to a reference star (or stars) of known brightness. It’s a bit like measuring the elevation of a point on Earth’s surface with reference to the standard “sea level.” Complete the Cookie Cutter activity to get a basic understanding of how this is done. You can also follow along with the Photometry Tutorial (uses Maxim DL).

 

Astrometry Lingo Astrometry: the determination of positions in the sky of astronomical objects and how those positions change over time. Astrometry involves making a map of objects in sky.
Coordinate Systems Measuring the positions of objects requires the use of a coordinate system of some sort. Here we describe three that you are likely to encounter in making or reducing astronomical observations.

Equatorial Coordinate System: The Equatorial coordinate system is one of the preferred coordinate systems of observational astronomers. The Equatorial coordinate system, like latitude and longitude, is based on measures of angular separation from some arbitrary origin; in the case of latitude and longitude the coordinates are measured from the equator and Greenwich Observatory in London, respectively. In the Equatorial system, the equator is still used (or, rather, its projection up onto the sky), but the other reference point is where the Sun crossed the equator on the Vernal Equinox (the point is called the first point of Aries).The names of the coordinates in the Equatorial system are Right Ascension (RA – similar to longitude, it measures positions east and west) and Declination (Dec – similar to latitude, it measures positions north and south). Declination works exactly like latitude, with the declination of a star being its angular separation from the equator (negative declinations mean the star is south of the equator). Right Ascension is a bit different from longitude: it is measured in hours, minutes and seconds. There are 24 hours of Right Ascension around the sky. Each hour corresponds to 15 degrees of arc. Thus there are 360 degrees around the equator. Can you think of a reason why RA is measured in hours, minutes and seconds rather than degrees, arcminutes and arcseconds? (Hint: How many hours does it take the Earth to rotate through 360 degrees?) RA is really a measure of time!

skymaps
NOTE:
RA: 1 hour = 15 degrees = 60 minutes and 1 minute = 60 seconds (of time)
Dec: 1 degree = 60 arcminutes and 1 arcminute = 60 arcseconds.

Horizon Coordinate System: A coordinate system that is often useful for making astronomical observations is the Horizon system. In this system the coordinates are related to the individual making the observations. An object is located by its altitude above the horizon and by its direction from due north. The altitude is given merely by the angular distance measured perpendicularly from the horizon. The point directly overhead, the zenith has an altitude of 90 degrees, whereas the horizon itself has an altitude of zero. The direction from north is measured in a clockwise sense, with due east having a azimuth angle of 90 degrees. South is 180 degrees, west is 270 degrees and north returns us to 0 or 360 degrees. The Horizon system is often also called the Altitude – Azimuth coordinate system. The control software used to point a telescope must convert RA-DEC coordinates to Alt-Az coordinates so that the telescope will point at the correct position in the sky. The Alt-Az system is also quite important when trying to decide if an object is observable from a given location. Clearly if an object has a negative altitude at some given time, then it is below the horizon and cannot be observed.

Galactic Coordinate System: One final coordinate system you might come across from time to time is the Galactic Coordinate System. Unlike the Equatorial system, Galactic coordinates are not referenced to the Earth and its spin axis. Instead, Galactic coordinates are based on the orientation of the Milky Way. The Galactic system uses longitude and latitude, just as we do on the Earth’s surface. In the case of Galactic coordinates, the “equator” is the plane of the Galaxy. The Galactic latitude of objects is the perpendicular angular distance from the equator, either north or south. The zero-point for longitude is the Galactic center (in the constellation of Sagittarius). You won’t have to know a lot about the Galactic system to use the telescope, but we have mentioned it for completeness.

For additional information about astronomical coordinate systems see the Astronomy Notes website. To learn in detail how to fit an astrometric model, see our astrometry page.

000-017   000-080   000-089   000-104   000-105   000-106   070-461   100-101   100-105  , 100-105  , 101   101-400   102-400   1V0-601   1Y0-201   1Z0-051   1Z0-060   1Z0-061   1Z0-144   1z0-434   1Z0-803   1Z0-804   1z0-808   200-101   200-120   200-125  , 200-125  , 200-310   200-355   210-060   210-065   210-260   220-801   220-802   220-901   220-902   2V0-620   2V0-621   2V0-621D   300-070   300-075   300-101   300-115   300-135   3002   300-206   300-208   300-209   300-320   350-001   350-018   350-029   350-030   350-050   350-060   350-080   352-001   400-051   400-101   400-201   500-260   640-692   640-911   640-916   642-732   642-999   700-501   70-177   70-178   70-243   70-246   70-270   70-346   70-347   70-410   70-411   70-412   70-413   70-417   70-461   70-462   70-463   70-480   70-483   70-486   70-487   70-488   70-532   70-533   70-534   70-980   74-678   810-403   9A0-385   9L0-012   9L0-066   ADM-201   AWS-SYSOPS   C_TFIN52_66   c2010-652   c2010-657   CAP   CAS-002   CCA-500   CISM   CISSP   CRISC   EX200   EX300   HP0-S42   ICBB   ICGB   ITILFND   JK0-022   JN0-102   JN0-360   LX0-103   LX0-104   M70-101   MB2-704   MB2-707   MB5-705   MB6-703   N10-006   NS0-157   NSE4   OG0-091   OG0-093   PEGACPBA71V1   PMP   PR000041   SSCP   SY0-401   VCP550   100-101   70-412   VCP550   LX0-104   000-017   70-461   700-501   70-347   EX200   SSCP   200-120   VCP550   NS0-157   400-201   N10-006   000-080   000-080   70-346   3002   300-101   PMP   640-692   ITILFND   ICBB   70-246   9L0-066