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ASTR 5110, Majewski [FALL 2017]. Lecture Notes

ASTR 5110 (Majewski) Lecture Notes



  • Mihalas & Binney, Galactic Astronomy, Section 2.6.

  • Binney & Merrifield, Galactic Astronomy, Section 2.3.

  • Kitchin, Astrophysical Techniques, Section 3.1, and Section 4.1 (Fabry-Perot part).

  • Hecht, Section 9.1.

  • Bessell et al. (1998), A&A, 337, 321.

  • Bessell (1986), 98, 1303.

  • Thuan & Gunn (1976), PASP, 88, 543.

  • Chapters 7 and 10 of Birney.


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 built based on one of two principles:

  • Substances that absorb/reflect certain wavelengths and transmit others.
    • absorptive properties depend on the matter through which the light passes (e.g., bandgaps)

    • These filters typically use salts, e.g. nickel or cobalt oxides, dissolved in glass, gelatine or even water. For example:

      • Colored glass (Schott and Corning are common vendors for these types of filters)
      • Schott colored glass filters, from Reynard Corporation (
      • Dyed gelatin (e.g., "Wratten" filters available from Kodak)
      • Common Wratten filters, often used in photography. From
      • Chemical suspension (e.g. CuSO4) liquid
    • Typically these are used as broadband filters, allowing >1000 Å to pass.

    • Often have "red leaks" that need to be blocked (see below).

  • Use of interference to define the transmitted wavelengths.

    • Mostly, these types of filters make use of Fabry-Perot etalons, which are pairs of partially reflective surfaces placed parallel to one another with a small separation and filled with a dielectric of a given index of refraction.

      The result is multi-beam interference, with constructive and destructive interference happening on the exiting beams.

      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.
    • Fabry-Perot systems can be used to isolate almost any wavelength of light.

    • The physics of a Fabry-Perot is based on constructive interference that occurs when the path length taken by multiply reflected waves are an integral number of wavelengths, and attenuation of light where the pathlength is not an even multiple number of wavelengths, as shown in this example:


    • In detail, one can vary the phase differences for different wavelengths of light by either varying the spacing between the mirrors, t , the refraction index, n , of the medium between the semi-reflectors, or the angle of incidence of the light to the etalons, α.


    • The path length difference between pairs of successively reflected, emergent rays transmitted to the right is given by (prove this to yourself!)

      Δ(pathlength) = 2 d cos α

      or, if the medium between the etalons is not air, but a substance with index of refraction n, then:

      Δ(pathlength) = 2 n d cos α

      where we have assumed that the rays outside of the etalons are traveling through air, and have accounted for bending of the rays by Snell's Law by including the index of refraction of the medium between the etalons (which, if air, has n=1).

      For constructive interference, we want this pathlength difference to be a multiple number wavelengths, and this gives us the basic Fabry-Perot equation:

      m λ = 2 n d cos α

    • Now, imagine that we collimate the multi-wavelength light from a source, send it through a pair of etalons, and then refocus the image. (Effectively, what we would be doing in this case is replacing the prism or grating of a spectrograph --- a device with a collimator, a wavelength-dispersing element, and then a focuser) with a set of etalons.)

      This is the essence of a Fabry-Perot Interferometer.

      A Fabry-Perot spectrograph. From Astrophysical Techniques, by Kitchin.
      We will get images of the point source, but only at wavelengths that satisfy the Fabry-Perot equation.

      If we were to use a prism or grating to cross-disperse the image of the point source, we would see a wavelength distribution of light at the image that looked something like this:

      From Astrophysical Techniques, by Kitchin.
      The peaks correspond to successive wavelengths for which the light entering the etalons at the specific angle α can have constructive interference.

    • Note that these peaks have a specific width.

      The width of the peaks depends on the reflectivity of the etalons, r, because the reflectivity determines how many bounces the light will make before fading away.

      • More reflections possible means there are more possible, successive rays that can interfere with one another at a given wavelength.

      • This is like the multiple slit interference experiment with monochromatic light.

        Recall what happens to the fringes in an interference pattern for monochromatic light as we add more evenly-spaced slits:

        As we add more slits, the fringes become narrower (more "pure").

      Therefore, as may be seen in the Kitchin figure above, the higher the reflectivity, the narrower are the peaks in the wavelength distribution of transmitted light.

      • Using this method, we can build very high resolution, Fabry-Perot spectrographs, with a resolution, R = λ / Δ λ approaching 107, which is orders of magnitude higher than can be achieved with the usual prisms and gratings used in spectrographs (even echelle spectrographs).

      Another parameter, aside from the resolution R = λ / Δ λ, used to describe the width of these wavelength peaks, called the finesse, is basically the ratio of the separation of adjacent peaks to the half-width of the peak, and is of course a function of the reflectivity of the etalons, r (where reflectivity is given as a fraction of 1):

      finesse = π r 1/2 / ( 1 - r )

      Note the difference in the purity of the lines given by a finesse of 2 compared to a finesse of 10. From
    • Note also that for a single wavelength, it is possible to have multiple orders of output images, corresponding to different even multiples of pathlength difference, m.

    • Therefore, if we illuminate our etalons system with a broad, diffuse source (e.g., the sky), all rays incident on the etalons at a given angle α and wavelength will result in a fringe pattern that has a circular symmetry for that wavelength.

      With a broad diffuse source, the interference bands will therefore yield a set of concentric rings (one ring for each order) for any given wavelength, and which in fact has a fringe spacing given by the Airy function.

      From Optics, Fourth Edition, by Hecht.
    • Clearly, because of the differences in pathlength difference for different incident angles to the etalons, different wavelengths will produce different ring patterns.

    • For a non-diffuse (e.g., a point) source seen through an etalon system, what we would get in a particular focal plane is a wavelength-dispersed image of the source, with that dispersion being a radial variation by wavelength away from the optical axis.

      The basic distortion in wavelength as a function of spatial position is

      λ = λ(0) cos(arctan(r / C)) = λ(0) / sqrt(1 +(r / C)2 )

      λ = λ(0) (1 - (1/2)(r / C)2 ) + (3/8)(r / C)4 ....)

      where λ(0) is the wavelength on the optical axis, and where generally r / C << 1 so that the power series can be truncated after a few terms.

      If the variation is slow enough (depends on choice of C), it may not make a huge difference across a given field of view and one can act as if one has broadly the same range of wavelengths across the focal plane.

      This is what we have in the use of most narrow band filters.

    • But one can build an instrument where our Fabry-Perot system is tunable, either by allowing the size of the gap between the etalons to be variable (e.g., by separating the etalons with piezo-electric crystals), or by changing the pressure of a gas between the plates, which alters its index of refraction.

      This is the basis of scanning Fabry-Perot imaging, where we can take many narrow-band images of a scene with narrowly spaced differences in the wavelength.

      In this way we can build up a "data cube", with two dimensions of spatial information and a third dimension of wavelength.

      From "Automated Spectral Reduction in the IRAF Fabry-Perot Package", by Shopbell & Bland-Hawthorn 1995, asp conf. Series 77,
      A scan across one free spectral range is accomplished by changing the optical distance between the plates by λ/2, with multiple wavelength slices being made.

      However, it is important to keep in mind that for a single slice of the datacube, the transmitted wavelengths follows the F-P equation as a function of the angle of incidence of the rays.

      This means that in a Fabry-Perot datacube:

      • a single x-y slice in space will have a radial variation in wavelength, as above.

      • a surface of constant wavelength is actually a curved surface intersecting many x-y slices of the cube.

      Thus, reduction of F-P datacubes requires fishing out the constant wavelength images of a source from the multiple slices.

      The following images give some sense of this:

      The above figures show two planes of a F-P data cube. The left display is for a spatial plane. The lines of constant RA and DEC, in equal increments, are overlayed in yellow. Lines of constant wavelength, also in equal intervals, appear as red circles. The circles are not equally spaced in radius because of the r2 variation with wavelength. The display on the right is a plane with wavelength along the horizontal dimension and RA along the vertical dimension. Lines of constant wavelength and RA, in equal increments, are overlayed. Note the curvature of the wavelength grid and the night sky spectral lines. From "Spectral WCS Conventions", IRAF on-line manual, by Francisco Valdes,
    • In terms of making narrow band interference filters, one can see from the F-P equation, m λ = 2 n d cos α , that if d ~ 167 nm, n = 1.5 and we operate at near normal incidence, we can create a filter that will only allow wavelengths of light to pass that are centered at 500 nm (for m = 1), 250 nm (for m = 2), 167 nm (for m = 3), etc.

      If one sandwiches such an interference filter with a dye filter, we can pick which narrow wavelength region we want.

      Normally we work in the m = 1 order with interference filters.

      Obviously, by playing with n and d we can pick whatever wavelengths we want.

      Note that narrow band filters are generally used in the converging beam of the telescope (unlike the F-P systems shown above, which are working with collimated beams).

      • THOUGHT PROBLEM: Why would the transmitted wavelength through an interference filter change if we tilted the filter?

        (The answer shows why it is critical that the filter tilt we use be highly repeatable to avoid systematic photometric errors.)

      • THOUGHT PROBLEM: Why does the mean transmitted wavelength through an interference filter used with a telescope have a shift depending on the f/ratio of the telescope? On the temperature?

        (The answer to the first problem explains also why would we want to limit the f-ratio of a telescope used with an interference filter to minimize systematic variations across the focal plane.)

    • Note that antireflection coatings, so important on transmissive optics, are also based on the use of interference within/between thin films applied to optics to limit the amount of light that bounces off the surface of lenses (used in camreas, telescope optics, eyeglasses, etc.)

General Care and Feeding of Filters

If you become an observational astronomer, you will no doubt have to handle filters in the course of your career.

A few things to keep in mind:

  • As with any optical elements, one should take great care in handling filters, especially with regard to avoiding touching the non-edge surfaces with your fingers.

    Finger oils can be destructive to optical coatings.

    Use care when blowing dust off filters, which should only be done with dry air (from a tank or commercial canister) at oblique angles (to avoid embedding dust into the soft coatings).

    Avoid talking over filters to minimize spittle on the glass!

  • Note a common mistake installing filters at the telescope: Because interference filters, as well as some colored glass filters with certain optical coatings, reflect light -- you have to look through the filter to see the transmitted color.

    Don't judge the transmission of a filter by its reflected light!
  • (see picture of the dichroic below, as one extreme example)

  • Introduction of a filter (or any flat optical element with a different index of refraction, e.g., a dewar window) changes the effective focal length of the telescope beam because of Snell's Law:

    Shift in focal plane due to introduction of a filter. From Bill van Altena's (Yale University) lecture notes.
    If n' is the index of refraction of the filter/window, t is its thickness, and n is the index of refraction of the surrounding medium (e.g., air), you can show (!) that the shift in focal length will be:

    Δ f = t ( 1 - n / n' )

    or, with air (n = 1) and glass (n' = 1.5)

    Δ f = t / 3

    Note that the focus is moved away from the objective of the telescope.

    In general this means that the telescope has a different focus for each filter of varying thickness and index of refraction, and one has to map out at the beginning of an observing run the filter focus offsets for each filter.

    Obviously, it is of great benefit if one can design a set of filters with equal "optical thickness" to eliminate the need to refocus the telescope between filter changes.

    Such parfocal filters are made by padding the optically thinner filters with quartz cover glass to make up the difference with thickest filter.

  • Filters, especially interference filters, do not always age well. Check older filters for decay of dielectric materials, glass and coatings.

  • Another common mistake when using narrow band filters is to forget to account for Doppler shifts in the sources which may shift desired spectral features out of a filter bandpass.

  • A similar problem may occur if using a narrow band filter designed for one f/ratio beam in another f/ratio beam that will shift the wavelength range of the filter.

More Terminology Associated with Filters (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" (see plots below).

  • Dichroic filter: Reflects certain wavelengths, transmits other wavelengths. Make as an interference filter using multi-layer thin-films coated on a glass substrate with one layer totally reflective for some wavelengths.
  • Note the difference in the colors transmitted (to the right) compared to the light reflected (on the left) in this dichroic. From

    Extremely useful for making multiple beam instruments by splitting incoming light into different wavelength sections. For example:

    • Double beam spectrographs or imagers (increase λ coverage).

    • Simultaneous optical/NIR imaging (using different cameras).

    • Pick off "unused" wavelengths to send to telescope guider.

    Splitting the light from a source using a dichroic, which allows simultaneous imaging in two different parts of the spectrum, can greatly increase the efficiency of a telescope. From

  • 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.

      Lower image from NOAO RC Spec manual.

      CuSO4 filters are useful for blocking out the red leaks allowed by other filters, as is shown in the plot above showing UG and BG filters.

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

  • 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.
    • Another method used to separate light by polarization is to use a Wollaston prism, which is a device made of two pieces of crystalline quartz or calcite cut into prisms with different crystal orientations and then cemented together on their base to form two right triangle prisms with perpendicular optical axes.

      Because the different polarizations see effectively different indices of refraction, the device separates randomly polarized or unpolarized light into two orthogonal, linearly polarized diverging beams, with the angle of divergence determined by the prisms' wedge angle and the wavelength of the light.

      Enables observer to measure the intensity of BOTH polarizations simultaneously (say, as two distinct images on the same focal plane detector).

      Left image from Right image from Wikipedia.
      Conceptual schematics of a traditional AO polarimeter and the integral field polarimetry architecture developed for GPI, indicating the order of the various optical components. These figures are highly simplified, with many optics omitted and others shown as transmissive even though in practice most are reflective. Upper panel: in a conventional AO polarimeter, the orthogonally polarized PSFs are similar but not identical due to non-common-path wavefront errors and the wavelength dependence of the Wollaston prism's birefringence; modulation with a rotating waveplate mitigates these differences. The data shown here for the conventional AO polarimeter are observed PSFs from the Lyot Project coronagraph at the AEOS 3.6 m (Hinkley et al. 2009). Lower panel: in an integral field polarimeter, the light is optically divided by the lenslet array prior to any dispersion, largely eliminating sensitivity to non-common-path errors and chromatic birefringence and thus producing a difference image with speckles highly suppressed. (IMAGE AND CAPTION TAKEN DIRECLTY FROM )

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".


    Also used for monochromatic fluxes, e.g., m5450 for the flux at 5450 Å.

  • 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 ".


    • Apparent magnitudes are often written in shorthand with capital letters because the name of some of the filters includes capital letters.

    • To avoid confusion, astronomers always write absolute magnitudes in the "MV" style to be clear that what is meant is absolute.

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:

  • We generally write the color index as letters that denote filters, e.g.:
  • Note that since 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.

  • In the Vega-based system, by convention we pick cA - cB based on Vega so that for A0V type star:
  • In the AB and STMAG systems cA = cB = same constant for all filters [but 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 color index 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
    • Most normal stars are reasonably approximated as Blackbodies (perfect radiation - hole in wall of oven)
    • Energy emitted by unit area of BB given by Planck function:
    • Star of radius R:
    • The hotter the star, the more luminous for a given radius R
    • From

    • Note limiting forms of the Planck function:

      • Rayleigh-Jeans limit:

      • Wiens limit:

    • Wien's Law - hotter stars are bluer:
    • Thus with appropriate filters, can get a measure of the temperature of a star (blackbody source):
    • F1 > F2 for hotter star (m1 - m2 small)

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

      • Note that the wider the baseline, the greater the sensitivity in general.

          For example, according to Mike Bolte, to determine the effective temperature of an F-G type star to 100 K accuracy, the following relative integration times are needed:

          color relative time
          B-V 4.2
          B-R 1.7
          B-I 1.0
          V-R 11.5

        As may be seen, the color with the longest wavelength baseline, B-I, requires the least time to measure a stellar temperature to the same precision.

  • Other filters can be tuned to measure things such as:
    • Absolute magnitude - Hβ filter in the 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.
    • Atmospheric 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 chromosphere) -- 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 Hα (6563 Å) emission line. From

    • 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: Hα (6563 Å shown as red), OIII oxygen (4959 Å 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

    • Active nuclei - emission lines - QSOs, Seyferts
    • Spectrum of a quasar, showing its prominent, but wide, emission lines. From

    • 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

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.

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: 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:

The Johnson-Morgan UBV System

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

  • The Johnson-Morgan V band is meant to simulate and perpetuate measurements historically made by the human eye, to which it approximately matches.
  • The Johnson-Morgan 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 (and therefore the spectral type) of stars.
  • From Kitchin, Astrophysical Techniques.

  • 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.

      • 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.
    • 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.
  • Don't confuse blanketing vectors from metallicity effects with reddening vectors due to foreground dust.

    From Galactic Astronomy, by Mihalas & Binney.

    • Foreground dust reddens all colors (and the amount is written as an excess color, e.g., E(B-V)).

      We usually discuss the amount of reddening in a standard color E(B-V) even though we must be concerned with our actual color system:

      From Galactic Astronomy, by Mihalas & Binney.

    • It also makes things fainter (apparent magnitudes larger).

    • Dust effects bluer light more than red light, leading to specific relations between color excesses.

    • Thus, one also sees reddening vectors in color-magnitude diagrams in this same general direction (i.e. redder and fainter).

Red Extensions of The Johnson-Morgan System

  • The UBV system became so popular and useful, Johnson and other people later extended the UBV system to the red and infrared, with R,I,J,K,L,M,N bands.

    • For example, it was found that the UBV system did not work well for very cool stars, like K and M spectral types, but 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.
    In the optical, then, we have the UBVRI broadband system.

    • Unfortunately, the use of these redder filters has caused some confusion in the astronomical community, because of the number of different definitions of these filters that were adopted:

    • In addition, the original definitions were not necessarily optimized to the atmospheric windows in the infrared.

      • The original Johnson red and IR bands are rarely used anymore.
      • A horrible mess of different R and I band definitions have evolved:

        Examples of the many definitions of the R and I passbands, and the spectra of a late M type star. From Bessell (1986, PASP, 98, 1303).
    • Most astronomers tend to use the Cousins RI bands with the Johnson-Morgan UBV.

    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.

    • Developed 1935-1960.

    • Stebbins-Whitford used a lot for early extragalactic studies.

    • Now rarely used.

    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).
    • Invented by Canterna (1976, AJ, 81, 228) and developed by Geisler (1986, PASP, 98 762; 1990, PASP, 102, 344) for study of cooler stars.

    • Devised to use the the wideband sensitivity of GaAs phototubes and CCDs and makes use of the sensitivity of blue-violet colors to metallicity and gathers more violet light in cool stars.

    • Geisler (1984, PASP, 96, 723) pointed out the usefulness of adding the intermediate band DDO51 filter for luminosity classification of cool stars.

    Intermediate Band Systems

    • The first widely adopted intermediate band system was by Stromgren.

    • More sharply defined bandpasses (and more of them) allows greater sensitivity to various stellar properties (metallicity, temperature, surface gravity) for AF type stars.

    • Of course, this greater sensitivity comes at the expense of less photons, longer required integration times.

    • Absolute magnitude - Hβ filter is often added to Stromgren system (Stromgren-Crawford System) because of usefulness for determining the absolute magnitudes of earlier type main sequence type stars.

    • The 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:

    • Invented by (now UVa faculty member) Trinh Thuan and James Gunn.
    • Often useful for faint 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 radiates 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, which is somewhat more advanced with broader passbands.

    SDSS and LSST Filters

    Gaia Satellite Passbands

    The photon response functions of the Gaia G (astrometric instrument), BP and RP (spectrophotometer) and RVS (radial velocity spectrograph) passbands. From .

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    Interference filter image from Polarizer filter images from Filter curves taken from All other material copyright © 2002,2005,2007,2009,2011,2013,2015,2017 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 511 at the University of Virginia.