Today Let's Talk about Photometric Systems

Give the definition of photometric system.

A standard photometric system is defined by a list of standard magnitudes and colors measured at specific bandpasses for a set of stars that are well distributed around the sky. 

Observed magnitudes are corrected for the attenuation of the Earth’s atmosphere away from the zenith, and the data is then normally extrapolated to zero airmass (outside of the atmosphere).

However, most of the infrared (IR) broad bands are difficult to extrapolate to zero airmass because of the nonlinear behavior with airmass of the \(H_2O\) absorption (Manduca & Bell 1979) compared to the linear behavior of dust, aerosols and Rayleigh scattering, the major components of optical extinction.

Many astronomical photometric systems have been established over the years by different observers with a variety of detectors and passbands. 

Different standard photometric systems usually measure different wavelength bands.

All photometric systems enable the measurement of absolute fluxes, from which can be inferred particular properties (such as temperature, gravity, and metallicity) of the emitting object, but different systems claim to do it more precisely or more efficiently than other systems and some are better suited for hot stars and others for cool stars.

Photometric systems are usually divided into broad band ( λ < 1000 \(\overset{\circ}{A})\), intermediate band (70  \(\overset{\circ}{A}\) < λ < 400  \(\overset{\circ}{A})\), and  narrow band ( λ < 70 \(\overset{\circ}{A})\).
Another category, the ultra–broad band, has been recently proposed to encompass those survey systems, such as Sloan and Hipparcos, whose bandwidths are wider than the well-known BVRI broad-band system. 

Another important difference between systems relates to whether they are closed or open. 

An open system is one whose originators encourage others to duplicate the passbands and detector system and to use the originator’s standard stars and reduction system for their photometric programs.

A closed system is one where a small group of people control the instrumentation and data reduction and only encourage others to use the results but not to attempt to duplicate the system and observe stars for themselves. 

For obvious reasons, systematic errors and the quality of the data are better controlled in a closed system than an open system. In the past, the main disadvantage of a closed system was that your particular star of interest was often not in the catalog. 

However, with the advent of large-scale sky surveys to faint magnitudes, it is likely that, in the future, photometry for most objects of nterest will be provided by closed photometric systems.

Reference:

STANDARD PHOTOMETRIC SYSTEMS

Michael S. Bessell

Annual Review of Astronomy and Astrophysics, Vol. 43: 293 -336 (Volume publication date September 2005)

Interesting links:
http://spiff.rit.edu/classes/phys445/lectures/colors/colors.html
http://www.starlink.rl.ac.uk/docs/sc6.htx/node10.html

Today Let's Talk about Surface Brightness

Give the definition of surface brightness.

The surface brightness of an extended object, for example a galaxy, is the radiative flux per square arcseconds on the sky.


                                            ------- 
---------------------------- |   D   |
             d                            --------

D= area on the sky in [square arcseconds]
d= distance of the galaxy we're considering [parsecs]

This galaxy subtends an angle alpha on the sky:

\[\alpha =\frac {D}{d}\]

If I measure the luminosity L of all the stars into the area D I've the TOTAL flux:

\[F =\frac {L}{ 4 \cdot \pi \cdot (d)^2}\]

So I can define the surface brightness with this formula ( very important):

\[I = \frac{F}{(\alpha)^2} = \frac{F}{ \big(\frac{D}{d}\big) ^2}=\frac {L}{ (4 \pi \cdot (d)^{2}) \cdot \big(\frac{D}{d}\big)^{2}}=\frac {L}{ 4 \cdot \pi \cdot (D)^2}\]

\[I \bigg[\frac{mag} {arcseconds^2}\bigg]\]

References:
 1)http://asd.gsfc.nasa.gov/David.Davis//courses/phys315/week6/week6.pdf
 2)http://www.astro.spbu.ru/staff/resh/Lectures/lec1.pdf 

Today let's talk about Magnitudes

What's the definition of magnitude?

In astronomy the magnitude is the measure of the brightness of an object in logarithmic scale, measured in a certain band, for example the near IR (Infra-Red) or V (violet).

Define the apparent and absolute magnitude and explain how to link the two.

The apparent magnitude m of a celestial object is the brightness of an object as seen from earth, without the influence of the atmosphere.

The formula to remember is:

\[m_{2} -m_{1} = -\log\bigg(\frac{F_{2}}{F_{1}}\bigg)\]

where F2 is the observed flux in a certain band, for example the V one and F1 and m1 are respectively the reference flux and magnitude calibrated for example with the star Vega.

The absolute magnitude M of a star is the apparent magnitude it would have if it were at 10 parsecs.

I can derive the absolute magnitude from the apparent one if I know the distance, so I use the distance modulus relation:

\[m - M = 5\cdot \log(D) - 5\]

D is measured in parsecs.

Reference: http://en.wikipedia.org/wiki/Magnitude_%28astronomy%29