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ASTR 313, Majewski [FALL 2008]. Lecture Notes

ASTR 313 (Majewski) Lecture Notes


FILTERS AND COLOR INDICES

REFERENCE: Chapters 5 (especially pages 84-93) and 10 of Birney et al.

Filters

We often wish to measure the light flux from a star in only restricted wavelength ranges. To do this, we rely on devices that permit only the desired wavelengths to reach our detector called filters.

  • Typically:
    • Glass - colored (Schott) or interference
    • Dyed gelatin - colored (Kodak)
    • Chemical suspension (e.g. CuSO4) liquid
  • That absorbs/reflects certain wavelengths and transmits others.
  • Different properties depending on:

    • chemicals in glass/gelatin - absorptive properties (bandgaps!)

    • in interference filter, layers of dielectric with different indices of refraction that cause destructive/constructive interference at certain wavelengths.

      If a thin transparent medium (air or glass) is placed between two partly reflective coatings, we can develop multiple reflections in that space. Constructive interference will occur for transmitted light that is twice (or some other even multiple of) the wavelength of the space, while other wavelengths will be attenuated. This is useful for building filters tuned to narrow wavelength ranges.
      • THOUGHT PROBLEM: Why would the transmitted wavelength through an interference filter change if we tilted the filter?

      • THOUGHT PROBLEM: Why does the transmitted wavelength through an interference filter used with a telescope depend on the f/ratio of the telescope?

      Note a common mistake when installing filters at the telescope: Because many kinds of filters (especially interference filters) reflect light -- have to look through to see transmitted color, not be fooled by the color of light reflecting off of the filter.


Terminology associated with filters and their transmission properties (see figure):

  • Transmission curve (or response curve): Percentage of incident light transmitted as a function of wavelength.

  • Bandpass (or passband): Range (how many Angstroms wide) of transmitted wavelengths. Often measured as the FWHM of the transmission curve.

    Note, in astronomy we have some rough categories commonly used to describe the FWHM of the bandpass:

    • broadband -- ~1000 Å wide

    • intermediate band -- ~100 Å wide

    • narrow band -- ~10 Å wide

  • Central wavelength: λcentral = midpoint between λ1 and λ2, where:

  • Peak wavelength: Wavelength of maximum transmission (not necessarily central wavelength).

  • Effective wavelength: The "central" wavelength when weighted by S(λ), as follows:

  • Cut-on or longpass filter: Transmits light beyond a certain wavelength.
  • Cut-off or shortpass filter: Transmits light shortward of a certain wavelength.
  • Note: Harder to make well, often have "red leaks".

  • Dichroic filter: Reflects certain wavelengths, transmits other wavelengths. Make as an interference filter with one layer totally reflective.
  • Schott names - The most commonly used colored glass transmission filters are made by the Schott company in Germany.

    • "Cut-off" filters are designated by two letters that give the color of the glass.

      • UG - ultraviolet glass
      • BG - blue glass
      Schott filter curves for UG and BG filters commonly used in astronomy. Note the red leaks in some of the filters, which can be a problem if your detector is sensitive in the red/IR but you are not interested in seeing those wavelengths.

      Note that these are "cut-off" only in the sense that they cut-off in the optical, where CCDs and other optical detectors work -- but they also cut-off on the UV side so these are not "cut-off" in the true sense shown above.

    • Cut-on filters are designated by two letters that give the color of the glass and three numbers which are the more exact wavelength (in nanometers) of the cut-on point.
      • GG - gelb (yellow) glass
      • OG - orange glass
      • RG - rot (red) glass
      Some Schott filters showing their cut-on wavelength designations.

    • Note: cut-on, cut-off filters often used to define only one side of a photometric bandpass, detector or atmosphere defines other.
    • On left: definition of U band by atmospheric transmission and UG glass. On right: definition of photographic blue (J) band by GG 385 cut-on filter and photographic sensitivity of Kodak IIIa-J emulsion.

    • Note use of copper sulfate solutions and crystals to make better blue passbands.


Other types of Filters

  • Neutral density - "grey", i.e., equal amount of light reduction at all wavelengths (e.g., for bright object viewing).
  • Actual neutral density curves for filters made by Jenoptik (see http://www.jenoptik-los.de/optik/english/filter/jenoperm/jenoperm401.html).

  • Polarizing filter
    • Only allows light through of certain polarization
    • Made with aligned, long-chain molecules. Waves that are polarized in direction of chains can excite electrons in molecules and get preferentially absorbed.

    • Example, polaroid sunglasses used to block ground surface glare, which is highly polarized:

    • In astronomy, often used to measure magnetic fields in space.

      Oblong dust grains align along magnetic flux lines; reflect/scatter light preferentially in certain planes of polarization.

Magnitude Naming Conventions with Filters

As may now be clear, we can measure the light in a multitude of restricted wavelength regions.

    Note: Spectroscopy is the limit when we measure the flux in a large number of very fine, adjacent wavelength bands.

When stating a magnitude measurement it is important to specify to which bandpass the flux measurement pertains. Of the infinite possibilities for bandpasses, most often we elect to use a standard set agreed upon by the astronomical community as astrophysically meaningful.

The naming of magnitudes by the bandpass follows certain conventions.

  • The simplest way to keep things clear is to always use small "m" to denote apparent magnitudes and large "M" for absolute magnitudes.

    We then subscript with the community-agreed-upon name for the passband. E.g.:

    • Apparent V (visual) magnitude is written as "mV".

    • Absolute V (visual) magnitude is written as "MV".

    • Apparent B (blue) magnitude is written as "mB".

    • Absolute B (blue) magnitude is written as "MB".

    • Apparent magnitude in the DDO51 filter is written as "mDDO51".

    • Absolute magnitude in the DDO51 filter is written as "MDDO51".

    • Apparent magnitude in the Stromgren u filter is is written as "mu".

    • Absolute magnitude in the Stromgren u filter is is written as "Mu".

      etc.

  • But often astronomers shorthand this convention, by writing the apparent magnitude by the name of the filter itself:

    • Apparent V (visual) magnitude can also be written as simply "V".

    • Apparent B (blue) magnitude can also be written as simply "B".

    • Apparent magnitude in the DDO51 filter can also be written as simply "DDO51".

    • Apparent magnitude in the Stromgren u filter can also be written as simply "u".

    DON'T BE CONFUSED BY THIS!

    • Apparent magnitudes are often (but not always) written in shorthand with capital letters (like B and V) after the names of the filters or their bandpass.

    • One way to avoid confusion between apparent and absolute magnitudes based on capital versus little letters is to remember that astronomers always write absolute magnitudes in the "MV" style to be clear that what is meant is an absolute magnitude. Any magnitude not written in this style is likely an apparent magnitude.


Colors, Color Indices

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

  • Suppose we measure fluxes in two different filters:

  • We make a color index by:

    A color index is simply a statement of the difference in the magnitude of a source as measured in two different filters.

  • We generally write the color index as letters that denote filters, e.g.:
  • Note that the above equation shows that (in the absence of dust effects) the color of a source is the same whether we use apparent or absolute magnitudes to make the color index.

    This is because the distance effects cancel when measuring colors (i.e., the magnitudes in both filters increase by the same amount when the distance to the source is increased) -- the color is the same when discussing absolute or apparent magnitude differences.

  • By convention we pick cA - cB based on Vega (A0V type star) so that for Vega:
  • AB system (e.g. HST) uses cA= cB = same constant for all filters (and color of Vega is therefore not necessarily 0, because of the -2.5() term above.
  • Note conventions:
    • Typically write colors with shorter wavelength passband first, e.g.:
      • B - V
      • U - B
      • f25 - f60 (IRAS)
      • J - K (NIR)
    • In this way, smaller numbers always mean "bluer", larger "redder":
      • C.I. < 0 means "bluer than Vega" (in this color system)
      • C.I. > 0 means "redder than Vega" (in this color system)

What sorts of things do color indices measure?

  • Temperature
    • Stars are similar to Blackbodies (perfect radiation - hole in wall of oven)
    • Energy emitted by unit area of BB:
    • Star of radius R:
    • The hotter the star, the more luminous at radius R
    • Wien's Law - hotter stars are bluer:
    • Appropriate filters
    • F1 > F2 for hotter star (m1 - m2 small)

      F1 < F2 for cooler star (m1 - m2 large)

  • Other filters can be tuned to measure things such as:
    • Absolute magnitude - Hβ filter in Stromgren system

      The Hβ filter is useful for determining the absolute magnitudes of main sequence type stars.

    • Surface gravity of star - giant or dwarf - e.g. DD051 centered on gravity-sensitive Mgb lines and the MgH band of lines.
    • Metal abundance of star - measure strength of absorption in certain Δλ, e.g.,

      • U band measures "metals" broadly in UBV system (see below)
      • more specific "carbon" measurement from Washington C filter centered on CN, CH bands.
    • Coronal activity in stars - emission lines
    • The image of the Sun during an eclipse passed through a prism shows that the outer parts of the Sun (the corona) -- where flares and prominences are made -- emits light in certain emission lines. Each image here corresponds to a picture of the Sun in one wavelength. The most prominent image here is the Halpha (6563 Å) emission line. From http://www.astrosurf.com/buil/us/eclipse.htm.

    • Hot gas content in galaxies - emission line galaxies, emission lines, HII regions
    • This image of the Rosette Nebula (NGC2237) is a composite of images taken in three narrow band filters that center on the wavelengths of some primary sources of emission from the nebula: Halpha (6563 Å shown as red), OIII oxygen (4959 and 5007 Å shown as green) and SII sulfur (6716/6731 Å -- but, shown here as the blue). This nebula is huge and covers more than six times the size of the full moon. T.A.Rector, B.A.Wolpa, M.Hanna, KPNO 0.9-m Mosaic, NOAO/AURA/NSF (for details see Conditions of Use)

      Spectrum of the Orion Nebula showing that it gives most of its light in specific emission lines. From http://members.cts.com/cafe/m/mais/Planetary%20Nebula.htm.

    • Active nuclei - emission lines - QSOs, Seyferts
    • Spectrum of a quasar, showing its prominent, but wide, emission lines. From http://www.seds.org/~rme/qsospec.htm.

    • Redshift of galaxies/quasars:
    • Two of the highest redshift (most distant) objects known are these quasars discovered by multifilter photometry in the Sloan Digital Sky Survey. The bottom quasar is at higher redshift. Can you guess what signature was used to identify these objects as special from among the millions of objects that SDSS took pictures of? From http://skyserver.fnal.gov/en/sdss/discoveries/discoveries.asp.


Standard Photometric Systems

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

The most commonly used system in optical astronomy is the UBVRI system:

The UBV system was originally designed by Johnson and Morgan in the 1950s to understand stars.

  • The V band is meant to simulate and perpetuate measurements historically made by the human eye, to which it approximately matches.
  • The B band approximates the blue sensitivity of the original photographic emulsions on typical stars.
    • In older references, you will often see so-called "mpg" magnitudes -- corresponding to magnitudes of stars as measured on photographic films.

  • The B-V color (or the older mpg - mV color) provides a measure of the temperature of stars.
  • Johnson and Morgan realized that much more information was possible by adding a third filter in the ultraviolet.

    • Coincidentally, the 1P21 photomultiplier was just getting popular and was sensitive at the U, B and V wavelengths.
    • All three filters of the actual UBV filter system were designed with this photomultplier in mind.
    • Obviously, the U-B color can tell you about the relative temperature of stars. See above figure.
    • But the real advantage of the U band is that is sensitive to a part of the spectrum -- the ultraviolet -- where metals have spectral lines.
    • ASIDE: WHAT IS A "METAL" TO AN ASTRONOMER??

      • Since most of the universe is made up of hydrogen and helium, astronomers lump together all other elements into one category called "metals". This includes all elements from lithium on up, whether or not they have true metallic properties (e.g., as we discussed earlier this semester.
    • Since many "metallic" lines exist in the ultraviolet, a star with a high abundance of metals will have more absorption lines in the ultraviolet and, consequently, will give off less flux in the ultraviolet.
    • Thus, the U band designed to measure the line strength of metals in stars, which are concentrated to a large extent in the ultraviolet.
    • Thus, the U-B color gives a measure of:

      • the temperature of the star, and
      • the metallicity of a star.
      Since U-B measures both simultaneously, in order to see the metallicity effect separated from the temperature effect, we can make a "two-color diagram" where we use the B-V color to sort stars by temperature, whereas the other axis shows the metallicity effects.

      Two-color diagram from Wildey, Burbidge, Sandage, and Burbidge (1962, ApJ, 135, 94) showing the line-blanketing effects of increasing metal line absorption (stars get redder in U-B when they have more metals). The locus of stars of different temperatures from 5500 to 10000 K and with metal abundances like the Sun is shown as the bottom curve. The other curvy lines show the locus of stars of different temperatures but with 0.1 and 0.01 the metals as the Sun. These stars are bluer (i.e., more UV flux) than metal rich stars of the same B-V color (i.e., temperature).

    • Metal poor stars have a bluer U-B (i.e. more UV flux) at a given B-V (i.e. temperature) than metal-rich stars.
      • In the graph above, the fact that the line-blanketing vectors are not straight up and down shows that there is a small metallicity effect in the B filter as well, and changes in metallicity affect the B-V color too. But the steeper than 45 degree angle shows that U-B is more strongly changed than B-V for a given change in metals.
    • We say that metal-poor stars show an "Ultraviolet Excess" (comparatively more UV flux) than metal-rich stars - which have a lot more absorption lines in ultraviolet
    • Definition of "metallicity":
      • As mentioned above, we lump all elements other than hydrogen and helium together as "metals".
      • An assumption (not always a good one) is that when we change the abundance of one metal species (e.g., iron) the relative abundance of other metals (e.g., carbon, nitrogen, calcium) change in the same proportion.
      • Astronomers commonly use iron as tracer of the total metal content under the assumption that all metals change abundance in proportion to how Fe changes in abundance (not always true!!)
      • In this scheme, we describe the "metallicity" of a star with the symbol [Fe/H], which describes how many iron atoms there are to every hydrogen atom.

        The square braces mean this is a logarithmic scale and also that this is a comparison to the ratio of iron to hydrogen in the Sun:

        [Fe/H] = log[n(Fe)/n(H)]* - log[n(Fe)/n(H)]Sun

      • We can write other ratios, like:

        [Ca/H] = log[n(Ca)/n(H)]* - log[n(Ca)/n(H)]Sun

        [O/Fe] = log[n(O)/n(Fe)]* - log[n(O)/n(Fe)]Sun

        but in general "metallicity" will refer to [Fe/H].
      • We can relate [Fe/H] to the amount of "ultraviolet excess" in a rather direct way.
  • Later, Johnson 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.

    • It was found that the UBV system did not work well for very cool stars, like K and M spectral types, and these very red stars were easier to study at redder wavelengths. So the V, R and I bands are often used to study these kinds of stars.
    • Unfortunately, the use of these redder filters has caused some confusion in the astronomical community, because a number of different R and I filters have been adopted:

      • The original Johnson RI bands are really no longer used.
      • But a horrible mess of R and I filters have been substituted in the past.

      • Most astronomers tend to use the Cousins RI bands with the Johnson-Morgan UBV.

One other passband system of note is the Thuan-Gunn system:

  • Invented by UVa faculty member Trinh Thuan and James Gunn.
  • Often used for galaxy work.
  • The u and v filters measure the strength of the "Balmer jump".
  • The g-r color measures temperature, but the g and r bands are designed to avoid prominent wavelengths where the night sky emits light, so the sky becomes darker in these filters and increases the contrast for faint objects.
  • Basis of the filter system used in the Sloan Digital Sky Survey.


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Interference filter image from http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/intfilt.html. Polarizer filter images from http://www.physicsclassroom.com/Class/light/U12L1e.html. Filter curves taken from http://www.ast.cam.ac.uk/AAO/local/www/ras/rgo/appendix_c.html. All other material copyright © 2002,2006,2008 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 313 at the University of Virginia.