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ASTR 5610, Majewski [SPRING 2016]. Lecture Notes

ASTR 5610 (Majewski) Lecture Notes


FLUXES, MAGNITUDES, COLORS, AND FILTER SYSTEMS

This web page overlaps substantially, but not completely, with a similar discussion in my class notes for ASTR511: Astronomical Techniques, which you can access here, and here. You will be expected to know the material on these latter two sites, as well as additional material here. Most new subtopics added here will be in brown font.


SOME RADIOMETRIC TERMS

A variety of terms are used in the discussion of the electromagnetic energy output of sources and well as in radiative transfer. It is useful to clarify some of these expressions as we will meet them in this course:

The astronomical flux quantities are usually quoted for at the top of the Earth's atmosphere.

Note that in the above definitions we have given no specificity as to the wavelengths or energies of the individual photons or light.

More commonly we work with fluxes at specific energies.

The actual energy flux received by an Earthbound instrument really given by:

OR:

where:

fλo = stellar flux incident on Earth atmosphere

Tλ = transmission of atmosphere

Rλ = efficiency of telescope + detector

Sλ = transmission function of filter

fλo depends not only on how bright something is -- its luminosity -- but on its distance d:


Constancy of Detected Surface Brightness

In astronomy, of course, we don't have access to full Ω solid angle of power emitted from a radiating surface; we only see that fraction of the power received on our telescope+detector.

Note that as the distance to the source increases, the solid angle the telescope intercepts from each patch on the source diminishes as 1 / r2 for same area, a (i.e. power received in each pixel of detector goes down as 1 / r2 ).

But, as distance increases, the amount of source area in the telescope field of view goes up as r2.

So, the viewed total area, A, of the extended source contributing power to our telescope makes up for less solid angle per each dA intercepted.

Thus, the "surface brightness" (detected power/arcsec2) of an extended source is independent of the source distance!

Surface brightness is a distance-independent quantity.


Magnitudes

Magnitudes are a brightness scale, a logarithmic representation of the spectral flux density.

History of the concept of magnitudes:


Relative Photometry

Measuring the brightness of one star compared to another is called relative photometry.

Because observations in astronomy are difficult to do absolutely (they are typically made under "field conditions", where Earth atmospheric transmission varies with time and with equipment having a wide range of wavelength sensitivities), it is more natural to make measurements by comparison of one source to another with the same equipment and close in time.

We have seen the Pogsonian system which gives the following permutations of the same equations above:


Absolute Photometry

When we care about the magnitude of a star on set magnitude scale, this is absolute photometry.

When we care about the magnitudes (and fluxes) of stars on a set, universal scale, this is absolute photometry.

Setting up a universal magnitude system means defining for the equation

a set flux value f2 corresponding to m2.

Then we can evolve to a definition of magnitudes that looks like:

Several approaches to this problem have now evolved.

The most common is the Vega-Based System, where, by convention, we chose the star Vega ( Lyrae) to be 0 mag in all filters. Then:

Note: Can use any measure of brightness for f* - e.g., different filters giving different wavelength ranges observed, and constant only depends on measuring the same set of wavelengths in the Vega spectrum.

The advantage of this system is that one can use any measure of brightness for f* -- e.g., different detectors with different filters yielding different spectral response -- and one can obtain the magnitude of the test star simply by using the same equipment and atmospheric conditions to measure fVega .

The disadvantages of this system are:


Two other magnitude systems that have evolved are:


  • The AB Magnitude System

    An alternative magnitude scale gaining popularity is the "AB" or "ABν" magnitude system, which is not based on Vega, but instead assumes the CONSTANT in the above equation is always the same for all filtered magnitudes.

  • The "STMAG" System


  • Intercomparison of Magnitude Systems


    Magnitudes and Distances


    Absolute Magnitudes and the Distance Modulus


    Extinction by Dust

    View towards the Galactic Center showing the dark foreground dust extinction. From apod.gsfc.nasa.gov/ apod/ap051004.html. Copyright and credit Serge Brunier.
    Robert Trumpler (1930) showed existence of interstellar absorption by comparing distances of clusters from the brightnesses of their stars to geometric distances from the cluster sizes (i.e., assuming a standard linear size for open clusters). The latter method always gave closer distances.

    Trumpler's analysis of the extinction for 100 open clusters. From Trumpler 1930, PASP, 42, 214.
    • Therefore, stars get dimmer both due to distance and because some light gets absorbed, scattered by dust along line-of-sight.
    • Worse problem near Galactic plane, where it is thicker and lumpier.
    • (Top) Nidever-Majewski dust extinction map near the Galactic plane using 2MASS+Spitzer observations in a small section of the GLIMPSE survey area. (Bottom) Current best dust map by Schlegel et al. (1992). (Middle) Molecular CO cloud map in same region, showing how dust and gas are connected physically.
    • To account for this dust extinction we can write the distance modulus equation more accurately as:

    • Deriving the extinction terms is non-trivial, and we shall return to this later in the semester.
    We are generally working in a certain filter system, so important to identify the filter; e.g. in the case of no extinction:
  • --> It is especially important to identify the filter in the case that there is any extinction, because A = A(λ).


    Magnitude Naming Conventions with Filters

    When stating a magnitude measurement it is important to specify to which bandpass the flux measurement pertains.

    Stellar population studies make use of numerous filter systems for various problems.

    There are, of course, some standard passbands agreed upon by the astronomical community as particularly astrophysically meaningful/useful.

    The naming of magnitudes by the bandpass follows certain conventions.


    Colors, Color Indices

    In astronomy, we define the colors of stars quantitatively, on the basis of numerical color indices.


    Bolometric Fluxes/Colors

    A major aspect of stellar populations research as well as the study of stellar evolution is the comparison of theoretical models of stellar interiors/atmospheres and their evolution with real data in the color-magnitude diagram.

    A big problem with connecting stellar evolution models to observational data is that the former predict total, or bolometric, luminosities over all frequencies, while we only measure fluxes in specific wavelength regions/passbands.

    We define the bolometric magnitude as the total magnitude of a source measured by an ideal detector with perfect quantum efficiency for all wavelengths.

    In practice, it is hard to measure the B.C.X.

    Conversion from the theoretical to observational plane also tricky and generally takes several tacks:

    1. Use models of stellar atmospheres coupled to stellar interiors models to predict bolometric corrections --> colors and magnitudes.
      • Requires detailed knowledge of line transitions in each element present, line opacities, oscillator strengths, etc.
      • Most famous are the Kurucz models (see this site for one of many versions on the web).

        The Kurucz models approximate the stellar atmosphere as plane parallel.
      • More recently, 3-D spherical atmospheres models have been developed, such as the MARCS models (see this site).

      One artificially "observes" the models to get colors and B.C.'s.

      Then you adjust models to match to data on observed stars when possible, or use the comparison to calculate corrections.

    2. For a given model Mbol and Teff find the observed star with the most similar properties.

      Assign the spectral energy distribution shape (i.e., stellar atmosphere output or spectrum) of the observed star to the model and use it to calculate B.C.'s and colors.

    3. Typically a blending of both of methods is used.

      • See the Bessell, Castelli & Plez (1997) reference above as an example.

    Mass to Light Ratios


    Surface Brightness in Magnitudes


    What sorts of things do color indices measure?


    Standard Photometric Systems

    We design photometric systems to maximize information that can be gleaned from extremely low resolution spectroscopy, i.e., photometry.

    Astronomy has developed a number of standard broad/intermediate band photometric filter systems designed specifically to address certain types of astrophysical problems.

    From Mihalas & Binney, Galactic Astronomy.
    From top to bottom, the Johnson/Kron-Cousins bandpass system, the Thuan-Gunn system, the Sloan Digital Sky Survey system, and the Stromgren system. From Mike Bolte's web notes: http://www.ucolick.org/~bolte/AY257/ay257_2.pdf. The arrows point to the UV atmospheric cutoff near 3100-3300 Å and the NIR silicon bandgap cut-off.

    The most commonly used system in optical astronomy is the UBVRI system, which was originally defined as follows:

    The Johnson version of the RI filters are not commonly used today, as we will discuss below.



    The Johnson-Morgan UBV System

    The UBV system was originally designed by Johnson and Morgan (1953) to understand stars (particularly hot stars).



    The RI Extension to the Johnson-Morgan UBV System

    In the 1960s, Johnson (and later others) extended the UBV system to the red and infrared, with R,I,J,K,L,M,N.... bands.

    In the optical, then, we have the UBVRI broadband system.



    Other Filter Systems of Note

    Particularly useful are photometric systems that can not only gauge temperature and metallicity, but are tuned to be sensitive to other stellar properties, like the stellar gravity (i.e., luminosity class), or even age. Some of these systems are described below.

    Stebbins-Whitford 6 Color System A competing, once popular alternative to the Johnson-Morgan system also designed around photoelectric photometry and spanning a similarly large range of wavelength is the Stebbins and Whitford 6 Color System.


    Washington Filter System

    The Washington C, M, T1, T2 filters (thick lines left to right) compared to the standard UBVRI system (thin lines). From Bessell (2001, PASP, 113, 66).

    Stromgren-Crawford Intermediate Band System


    DDO System

    The intermediate band DDO system consists of strategically selected filters that aid in measuring stellar properties for later stellar types.


    Thuan-Gunn System

    Another passband system of note is the Thuan-Gunn system:


    Infrared Systems

    The near- and mid-infrared uses slightly modified Johnson bands.


    Previous Topic: Stellar Motions: Parallax, Proper Motion, Radial Velocity and Space Motion Lecture Index Next Topic: Spectral Typing & CMDs

    Filter curves taken from http://www.ast.cam.ac.uk/AAO/local/www/ras/rgo/appendix_c.html. All other material copyright © 2003, 2006, 2008, 2010, 2012, 2014, 2016 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 551 and Astronomy 5610 at the University of Virginia.