Part 3: Practical measurements of flux#
Useful units#
Measuring flux is not as simple as pointing a telescope and photometer at a star and recording a value. Flux varies by wavelength because stars radiate more intensely at some wavelengths than others. Therefore, we can use units which accommodate that reality. One such set of units is watts per square centimeter per micrometer (or nanometer) of wavelength.
\(\phi=\frac{\frac{W}{m^2}}{\mu m}=\frac{W}{m^2\cdot \mu m}\)
Another one is:
\(\phi=\frac{ergs}{s\,cm^2\,\mu m}\) written linearly as:
\(\phi=ergs\cdot s^{-1} cm^{-2} \mu m^{-1}\)
This represents the ergs per second which cross a sensor per square centimeter for each micrometer of wavelength. An erg is a small unit of energy, as in \(1\,W=1 \frac{J}{s}=10^7\,\frac{ergs}{s}\). It's from the Greek word ergon (ἔργον), meaning work.
Wavelength bands#
The bands U, B, V, R, I, J, H, and K are part of the standard photometric system used in astronomy. They correspond to different ranges of the electromagnetic spectrum, with U being the shortest wavelength and K being the longest.
- U-band (ultraviolet at about 350-400 nm)
- B-band (blue at about 400-500 nm)
- V-band (visual at about 550-600 nm)
- R-band (red at about 600-700 nm)
- I-band (infrared at about 800-900 nm)
- J-band (infrared at about 1.2 - 1.3 micrometers)
- H-band (infrared at about 1.6 - 1.7 micrometers)
- K-band (infrared at about 2.2 micrometers)
These are some standard bands or filters, but there are numerous others. An important set of filters lately is from the Gaia satellite flux data:
- The "BP" or "Blue Photometer" band at 330-680 nm.
- The "RP" or "Red Photometer" band at 640-1000 nm.
- The "G" or "Green" band at 535-1050 nm.
Some other important photometery systems include the Johnson and Sloan Digital Sky Survey systems.
| Johnson | Sloan |
|---|---|
| U (infrared) at 364 nm | u' (ultraviolet) at 354 nm |
| B (blue) at 442 nm | g' (blue-green) at 475 nm |
| V (visual) at 540 nm | r' (red) at 622 nm |
| i' (near infrared) at 763 nm | |
| z' (far infrared) at 905 nm |
Examine this example from a paper about calibrating the flux of the reference star Vega (Colina, et al., 1996):
| filter | wavelength \(\mu m\) | magnitude | flux \(ergs\cdot s^{-1} cm^{-2} \mu m^{-1}\) |
|---|---|---|---|
| U | 3735 | 0.030 | \(4.22\times 10^{-9}\) |
| B | 4443 | 0.035 | \(6.20\times 10^{-9}\) |
| V | 5483 | 0.035 | \(3.55\times 10^{-9}\) |
| R | 6855 | 0.075 | \(1.92\times 10^{-9}\) |
| I | 8637 | 0.095 | \(9.39\times 10^{-10}\) |
Notice that the magnitudes vary by wavelength. Ultraviolet is the brightest, blue and visual (green) are slightly dimmer, red is much dimmer, and infrared is the dimmest wavelength. Using the wavelengths presented in the table, here are the approximate filter colors (note that the UV and IR are not visible colors):
To read more about star colors, have a look at Part 5: Colors and temperatures of stars
References#
Colina, L., Bohlin, R., & Castelli, F. (1996, April 22). Absolute Flux Calibrated Spectrum of Vega. Space Telescope Science. Retrieved January 13, 2023, from https://www.stsci.edu