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:
Total light (energy) given off by a star
l = luminosity, in photons / sec, or
in erg / sec
Light flux received on Earth from the same star -- i.e., a point source.
φ = photon flux, in photons sec-1 cm-2,
orf = flux, in erg sec-1 cm-2
For light flux received on Earth from an extended (i.e. resolved) source,
like a nebula or galaxy -- measure flux coming from a
solid angle, called a surface brightness, often
written as Σ or μ :
Σ = SB, in photons sec-1 cm-2 steradian-1,
Σ = SB, in erg sec-1 cm-2 steradian-1
WARNING: The definitions of things like "luminosity", "flux",
"flux density", etc. used by astronomers are not the same as those used
in other disciplines (e.g., our "luminosity" is called "flux" in other
sciences, etc.) -- see Chapter 1 of Rieke about these differences.
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.
In the above cases we are referring to bolometric quantities, which
refers to a sum over all frequencies.
Practically this is a very hard thing to measure, since it requires
measuring the entire EM spectrum of a source, which is impossible with a
single type detector.
Thus, bolometric fluxes have to be inferred by knowledge of the
physics producing the luminous source for which you have partial information, o
r pieced together from
observations at all parts of the EM spectrum.
More commonly we work with fluxes at specific energies.
Monochromatic fluxes are defined as the fluxes within infinitesimally
small bands -- (ν, ν + δν) or (λ, λ + δλ) --
and are quoted either in wavelength or frequency units:
fν units: erg sec-1 cm-2 Hz-1.
fλ units: erg sec-1 cm-2Å-1.
The above quantities are also referred to as spectral flux densities.
Note that because
fνδν = fλδλ,
and ν = c / λ, one finds (prove to yourself!):
ν fν = λ fλ
The functions fν(ν) and
fλ(λ) are referred to as the spectral energy
distribution (SED) of the source.
When referring to bolometric fluxes, it is common to use units of
Janskys (Jy) (borrowed from radio astronomy):
1 Jy = 10-26 W m-2 Hz-1.
1 Jy = 10-23 erg sec-1 cm-2 Hz-1.
The actual energy flux received by an Earthbound instrument really given by:
stellar flux incident on Earth atmosphere
Tλ = transmission of
Rλ = efficiency of
telescope + detector
Sλ = transmission
function of filter
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.
Exception: Cosmological redshift dimming.
SB ~ ( 1 + z )-4
In an expanding universe, the total luminosity of a source drops with distance
by 1 / [ d ( 1 + z )]2, while the angular diameter drops as
1 / ( 1 + z ).
This is the basis of the Tolman SB test for an expanding universe.
--> It can be a severe limitation on studying stellar populations at
Magnitudes are a brightness scale, a logarithmic representation of the spectral
A device that allows an easy way to intercompare sources with immense
ranges in flux density.
But a bit arcane, not readily intuitive.
Now several definitions used.
Should be thought of as "band-specific", where "band" means a set
range of λ.
History of the concept of magnitudes:
Roots of idea extend to second century B.C. Greek astronomer Hipparchus.
Catalog of ~1000 naked eye stars.
6 "magnitude" classes:
1 = brightest
6 = faintest
But revisions required and made in last few centuries.
Extend scale to < 1 mag to include
Sun, Moon, bright planets on same scale.
Later, telescope invented - extend scale to > 6 mag.
1850 -- N. R. Pogson (British astronomer)
notices that, because eyes work logarithmically,
classical magnitude scale corresponds roughly to
set ratios of brightness between successive magnitudes.
Also notes that mag 6 is about 100X fainter than
Since Δm = 5 appears
to be 100x ratio in brightness, and
Pogson proposes to formalize scale so that
ratios between successive magnitudes are
Thus, two stars of integrated band fluxes (i.e., the
integral over some [λ, λ + δλ]
of the spectral flux density)
f2 have a magnitude difference
Note that the above equation also shows that fractions
of magnitudes are possible for stars with brightnesses
in between two integer magnitudes.
Note, to avoid confusion with backwards magnitude system, best to
avoid the words "smaller" and "greater" in describing luminosities
and magnitudes and get in habit of saying "brighter" and "fainter".
Measuring the brightness of one star compared to another is called
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.
Relative brightnesses are much more accurately
determinable than "absolute fluxes".
Note that the absolute flux of the Sun at visual wavelengths
is still not established to better than a few percent.
Comparison of magnitudes and fluxes derived for the Sun.
From Bessell et al. (1998, A&A, 333, 231).
Suggests use of sets of widely agreed upon "standard stars" to serve
We have seen the Pogsonian system which gives the following
permutations of the same equations above:
Δm = 5 be 100x
ratio in brightness
In these equations we are always comparing stars and
are on a relative scale.
No consideration of magnitude system 0 point,
only brightness ratios (magnitude differences) is
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:
The zero point of the magnitude system (i.e., "const" in the
above equation), being defined by Vega's SED
(fν, Vega ),
will be different for each filtered set of wavelengths (i.e. bandpass)
One is forced always to compare to Vega, or some other star already
carefully calibrated to Vega.
Note that Vega is too bright to observe for most telescope+detector
Not as straightforward to intercompare data in different bandpasses.
To do physics, must always go through the SED of Vega
to get ergs sec-1 cm-2 Hz-1
for a star (and assign this monochromatic flux to one specific,
representative wavelength in the bandpass).
For example, in the Vega-based magnitude system, we have
for the V passband and all stars with an SED like Vega:
BUT, the effective wavelength of the V passband
actually shifts based on the SED of the source (e.g., becoming
redder than 5450 A for later type stars) -- see next webpage.
Requires tedious and sensitive calibrations to produce
tables like the following:
Calibration of various bandpasses by Bessell et al. (1988,
A&A, 333, 231).
NOTE IMPORTANT ERROR: The values in the fourth
row are flipped with those in the fifth row of the table.
Prone to universal changes, or at least increasing vagaries:
Even now, the system has shifted with improved measurements
of the Vega SED.
E.g., Vega's V magnitude is now actually V = 0.03.
(This may seem odd, but the actual zero-points of the "Vega-based"
system are now defined by a large set of secondary standards
calibrated to the former measures of Vega. Easier to change magnitude
of Vega than all other stars in the system.)
There have been suggestions in the literature that Vega's SED
may be slightly variable.
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.
Popularity grew out of work in the 1970s to do spectrophotometry
(precise measurement of fν SEDs) of stars on the
Hale 200-inch telescope (e.g., see Oke 1974, ApJS, 27, 21).
-2.5 log10fν - 48.6
Simpler -- don't always have to know what Vega is doing
to define the magnitudes.
Directly obtain the SED of the source when know mν.
Usually write "AB" subscript for AB magnitudes, e.g.,
The "STMAG" System
Analogous to AB system, but for fλ.
-2.5 log10fλ - 21.1
Used now for Hubble Space Telescope photometry (giving name "STMAG").
Intercomparison of Magnitude Systems
All three magnitude systems are designed with the zero-points
yielding identical magnitudes for Vega at the same wavelength, intended
to be the effective wavelength of the Johnson V band (the curve
shown at the bottom of the plot below).
The three curves at the top correspond to the three standard SEDs
that define the zeropoint for mλ in the three
Note how the zeropoints for the AB and STMAG magnitude equations appear
in the definitions of the Vega-based magnitude equations in the footnote
to the above Bessell et al. table.
Magnitudes and Distances
Now, assume m1 and m2 are for same star,
different d. Then:
Star with magnitude m2 farther by 10, 100x fainter,
5 mags fainter (larger)
--> Rule of thumb: One mag difference is 2.5X flux ratio; for similar
source it represents a 1.6X distance ratio.
Absolute Magnitudes and the Distance Modulus
Apparent magnitude (m) -- magnitude of star as observed
Note that the apparent magnitude of a star depends
not only on its luminosity, but its distance, because
its observed flux is given by:
f = l / (4 π d 2)
In some cases, we are interested in separating the luminosity and
the distance effects. For example, consider comparing the luminosities
of different types of stars when placed at the same distance.
At uniform distance, flux differences are luminosity differences, or
ratios if on the logarithmic magnitude scale.
We define an absolute magnitude as the apparent
magnitude of star if placed at a distance of 10 parsecs.
To distinguish apparent magnitudes from absolute
magnitudes, we write the latter as capital "M".
A parsec is 3.25 light years.
The value of absolute magnitudes comes from the fact that
if somehow we can guess the absolute magnitude, M, of a star or other object,
and we measure its apparent magnitude, m, we can determine the distance
to that star by:
The difference between the apparent and absolute magnitude of
an object, (m-M), is called the "distance modulus" of that object, and
is directly related to the distance of the object.
One of the most important problems in astronomy (which we will
address more fully in distance ladder section) has to do
with determining the absolute magnitudes, M, for
objects in order that we can estimate distances.
A standard candle is a certain kind of object
(star, galaxy, or other object) that:
makes its identity known by some easily
observable characteristic, and
has a definable absolute magnitude.
Standard candles are extremely valuable in astronomy, because
if we find one, we can estimate its distance.
Different ways of identifying "standard candles" that have
supposed constant M:
E.g. certain kinds of stars like
RR Lyrae or Cepheids vary in brightness in easily identifiable
Supernovae explode with a reasonably well-defined light profile:
E.g. We can take a spectrum of the star and see what
kind of star it is: Spectral type (OBAFGKM) and luminosity
class (I,II=supergiant, III=red giant, IV=subgiant, V=main sequence).
For example, Sun is a G2V star (G type star, 2/10's of the way
to being a K star, and of luminosity class V=main sequence type).
All stars of same spectral type + luminosity class should be of same
Getting distances in this way is called measuring a
Identify "spectral type" by photometry in different filters,
which is like very coarse spectroscopy.
Getting distances this way is called measuring photometric parallaxes.
Unfortunately, colors alone can give ambiguities.
For example, red stars can be either very
luminous red giants or very dim red dwarfs.
Making a mistake in confusing the two can lead to
distance errors off by factors of 100 or more.
There are many kinds of blue stars, from blue supergiants
to white dwarfs. Errors in proper identification can lead to
distance errors off by factors of 10,000 or more.
E.g., Assume all globular clusters of certain concentration
are same absolute magnitude.
Or, assume all galaxies of one type (e.g., spirals with a certain
disk to bulge ration) have the same absolute magnitude.
E.g. Assume that the third brightest galaxy in cluster of galaxies
are typically all about same M; or the tenth
brightest giant star in globular cluster is of fixed M.
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,
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
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).
In this case the distance modulus, e.g., (m-M)V,
is the difference between the observed and real magnitudes of stars
with reddening effects still included (not useful for accurate distances
unless you know amount of extinction).
We write (m-M)o in the case that the
distance modulus has had extinction effects removed. We don't
need to specify a passband in this case, because the true distance
(modulus) is independent of the passband.
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
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.
The simplest way to keep things clear is to always use small
"m" to denote apparent magnitudes and large "M" for
We then subscript with the community-agreed-upon name for the passband.
Apparent B (blue) magnitude is written as
Absolute B (blue) magnitude is written as
Apparent magnitude in the DDO51 filter is written as
Absolute magnitude in the DDO51 filter is written as
Apparent magnitude in the Stromgren u filter is
is written as "mu ".
Absolute magnitude in the Stromgren u filter is
is written as "Mu ".
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 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
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.
By convention we pick
cA-cB based on
Vega (an A0 V type star) so that for Vega:
AB system (e.g., HST) uses
same constant for all filters.
Typically write colors with shorter wavelength
passband first, e.g.:
B - V
U - B
J - K (NIR)
In this way, smaller numbers always mean "bluer",
A - B < 0 means "bluer
than Vega" (in this color system)
A - B > 0 means "redder
than Vega" (in this color system)
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.
Observational data are used to constrain models.
Models are used to interpret data.
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.
This difference is a frequent source of uncertainty comparing theory to observation.
We need to know the ratio of the total predicted output luminosity to that
observed in a specific passband.
We define the bolometric magnitude as the total magnitude of a source measured
by an ideal detector with perfect quantum efficiency for all wavelengths.
You can think of this as the observed flux with a detector+filter
system that is equally and fully sensitive at all wavelengths.
The typical output of a stellar evolution model gives positions in
a theoretical equivalent of the Hertzsprung-Russell/color-magnitude
diagram with axes of effective or "surface"
temperature, Teff , and Mbol .
A standard observational version of the Hertzsprung-Russell diagram
is, of course, the color-magnitude diagram.
Thus, for testing/constraining models we need to convert,
using stellar atmospheres theory, the predicted bolometric
magnitude to the measured magnitude in a specific filter.
Since Mbol acts like the magnitude in an imaginary
bandpass that samples all wavelengths fully,
this bolometric correction acts like a color, specific
to each other filter/passband, X, that is being compared to:
Thus, for example,
B.C.V = Mbol - MV
There are several conventions for defining the constant
C1 (much like the AB versus Vega-based systems --
though, ironically, we DON'T technically use Vega-based here!):
For V-band work, the constant C1 is sometimes selected by convention so that
B.C.V for the Sun is 0.0, in which case C1 = 18.90
when the flux is measured in MKS units.
Another convention is to define C1 so that all
B.C. are negative.
This convention is actually similar to a Vega-based system since, with
log(Teff) = 3.96, you can see from the figure below that the
BC for Vega is practically 0.0.
The sun, at log(Teff) = 3.75, has
B.C.V = -0.19 in this method.
V -band bolometric corrections measured for stars of many
spectral types and luminosity classes by Flower (1996, ApJ, 469,
The shape of the BC- log(Teff) trends in the above figure should
make sense to you...
Thus, the total luminosity of a star in solar units,
when the flux of that star is measured in only the V
Similar conversions have to be done to determine the relative
fluxes expected between two filters in order to convert theoretical
Teff to a measured color index.
Of course, the color difference between two filters is given by the
difference in B.C.X for the two filters.
In practice, it is hard to measure the B.C.X.
In general, the measurement of B.C.'s are limited to bright,
Hard to observe all wavelengths (especially from the ground) and measure
the total flux at all wavelengths.
Making the translation of model to observed properties even more
challenging, it is also the case that it is hard to measure
Teff accurately (whereas it is easier to measure colors).
This means that deriving color-temperature
relations are also an important problem.
From Bessell, Castelli & Plez (1998, A&A, 333, 231).
Nevertheless, one tactic to getting the total luminosity of
a star is to try to measure stellar radii and distances and rely on the
L = 4 π R2 σTeff4
Thus, B.C.'s are well known for grids of solar metallicity stars, but
not well known for metal-poor, super metal-rich, or other non-Population I disk
stars (e.g., the Flower plot above).
Interpolate from grid for stars in between.
Conversion from the theoretical to observational plane also tricky and
generally takes several tacks:
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.
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.
Typically a blending of both of methods is used.
See the Bessell, Castelli & Plez (1997) reference above
as an example.
Mass to Light Ratios
For a given source, define NX = # of Suns required to produce
its absolute flux in a particular band X:
It is interesting to compare the total mass of the
system with the mass it would have if all the light came
from the equivalent # of Suns (NX), which is
NX MSun .
This mass-to-light ratio, M / L, is:
M / L is an important concept used in dark matter studies, and studies of galaxies in particular.
Systems laden with dark matter have high values of M / L.
Something often forgotten is that
the M / L ratio normally varies with filter X (unless the object's SED is identical with SEDSun).
So, e.g., a galaxy with B-K = 3.3 compared to the Sun (which has [B-K]Sun = 2.2) has:
Have to be careful! Have to name filter X whenever you specify M/L (e.g., most commonly a standard value given for a stellar system is "M/LV") or give a bolometricM/L
(but of course, this bolometric quantity is not measurable for most objects...)
Surface Brightness in Magnitudes
For extended sources, like resolved extragalactic systems, globular
clusters, nebulae, etc., we measure brightness per solid angle of
Recall, SB is constant with distance (except for large redshift).
Use magnitude/color system, but per unit area (e.g.,
mag / arcsec2).
Σ or μ symbols used --
and need to specify filter too.
S10(V) -- number of V=10 stars /
S10(B) -- number of B=10 stars /
Note, can be tricky to think in either of these sets of units... (see
μ surface brightnesses often used to define the extents of
"isophotal radius'' = radius at some specified SB level
"core radius'' = radius at which the SB is half that of
the peak SB for an object
(Note: The "half-light radius'' is the radius within which half
a system's total luminosity is enclosed.)
For example, galaxy reference catalogs (de Vaucouleurs et al., etc.)
D25 = diameter at 25 mag /
R25 = 1/2 D25 = "de Vaucouleur
"Holmberg radius" = 26.5 mag / arcsec2 =
What sorts of things do color indices measure?
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
Note limiting forms of the Planck function:
Wien's Law - hotter stars are bluer:
Thus with appropriate filters, can get a measure of a star (blackbody source)
F2 for hotter star
F2 for cooler star
Note that the wider the baseline, the greater the sensitivity
For example, according to Bolte, to determine the effective
temperature of an F-G type star to 100 K, the following
relative integration times needed:
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.
Tuned narrow band filters:
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
Conditions of Use)
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?
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).
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 to typical stars.
In older references, you
will often see so-called "mpg" magnitudes --
to magnitudes of stars as measured on photographic films.
This is similar to B band.
The B-V color (or the older [mpg-mV] color)
was envisioned to provide a measure of the temperature of (hotter)
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 all 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...
...as well as the color-color diagram below, which
shows the correlation of U-B with B-V
for solar metallicity dwarf and giant stars.
Two-color diagram from Binney & Merrifield, Fig. 3.7,
showing distinct loci for dwarfs and giants. Note,
however, this is not a good method to separate
dwarfs and giants photometrically.
If U-B is monotonically correlated with
B-V (temperature), what is the point??
The real advantage of the U band is that is sensitive
to a part of the spectrum -- the ultraviolet -- where metal
lines dominate, so U is particularly
metallicity-sensitive (we will explore this further elsewhere).
What is the source of the "wiggle" in the loci
for stars with B-V ~ 0 ?
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.
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.
In the photographic era, color-magnitude diagrams for globular
clusters were traditionally done as (B-V, V).
From Mihalas & Binney, Galactic Astronomy.
In the past decade there has been a shift, particularly for globular
clusters, to working with CMDs in the (V-I, V) system.
Easier to observe in these wavelengths:
Less atmospheric extinction in red.
Less atmospheric refraction in red.
Seeing better in the red.
CCDs more sensitive in red than blue.
Effects of dust lower in the red.
Almost all of the important work on cluster/extragalactic
CMDs with HST has been done in the HST equivalent of the
(V-I, V) system -- the F555W-F814W --
which may now be regarded as something of a "standard''
system for CMD/stellar populations work in Local
HST CMDs of globular clusters Testa et al. (2001, AJ, 121, 916).
Not to say other combinations abandoned:
M15 CMD from Yanny et al. (1994, AJ, 107, 1745).
Some unusual changes in perspective: for example,
the "horizontal branch" of (B-V, V) CMD no longer
so "horizontal'' in other filter combinations.
Note, it is still advantageous to work in (B-V,V)
for working on stellar pops when blue stars of interest (as
above and below).
CMD of the young open cluster NGC 2244 by Park et al. (2002,
AJ, 123, 892).
Unfortunately, the use of 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.
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
and spanning a similarly large range of wavelength
is the Stebbins and Whitford 6 Color System.
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.
Stromgren-Crawford Intermediate Band System
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.
Intermediate band filters: bright stars or big telescopes.
Two primary Stromgren indices defined from four filters:
c1 = (u-v)-(v-b) -->
Measures height of Balmer discontinuity.
m1 = (v-b)-(b-y) -->
Measure of continuum depression by metal lines.
In combination, give spectral type and luminosity class
in the c1-m1 diagram.
From Stromgren's (1966) important review article on
his photometric system in ARAA, 4.
Crawford (1958) introduces H beta index.
Added to Stromgren system (Stromgren-Crawford System)
because of usefulness for determining the absolute magnitudes of
earlier type main sequence type stars.
Difference between filters tells strength of Balmer line --
gravity sensitive in hot stars --> can convert to absolute magnitude.
Especially useful for evaluating main sequence turn-off stars --> getting
ages (not trivial to do in other ways).
Thus, c1, m1, (b-y), beta system -->
Teff, MV , [Fe/H], age for warm stars.
The intermediate band DDO system consists of strategically selected filters that aid in measuring
stellar properties for later stellar types.
Another passband system of note is the Thuan-Gunn system:
Invented by Trinh Thuan and James Gunn.
Often used for faint galaxy work.
The u and v filters measure the strength of the "Balmer jump".
The g-r color roughly 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.
Similar ideas motivate the filter system used in the Sloan Digital Sky Survey.
The near- and mid-infrared uses slightly modified Johnson bands.
Obviously particularly useful for the coolest stars and brown dwarfs.
Useful for working in heavily reddened regions (less affected by dust).
These bands are designed to sample available windows in atmospheric
transmission in the NIR.
Near- and mid-infrared bandpasses match terrestrial atmospheric
windows. Some far-infrared pass bands used on the IRAS satellite are shown.
Zoom in on the near- and mid-infrared bandpasses with
current definitions of Johnson IR bandpasses, from Allen's
Astrophysical Quantities. Click here
for a close-up view of the NIR bands.
Astronomers have tended toward a truncated Johnson
K band, called Ks (for Kshort)
as a means to minimize the effects of sudden onset of background of atmosphere
radiating as a 250 K blackbody.
Transmission curves for the 2MASS optical path
(thick line), including the telescope mirror reflectivity,
dewar window, antireflection coatings, dichroics, filters,
and the NICMOS detector quantum efficiency, but excluding
atmospheric absorption. The thin line shows the model
atmospheric transmission for the mean observing conditions
at Mount Hopkins. From Carpenter (2001, AJ, 121, 2851).
There is even a K' filter, extending Ks
slightly blueward, for
use on Mauna Kea, to take advantage of the atmospheric window
being a little broader at 14,000 feet.
The NIR background in comparison to NIR passbands.
Top ("Figure 3") shows the onset of thermal emission from the atmosphere.
The lower image ("Figure 2") shows that the 1-2 micron
flux is dominated by OH emission lines.
An interesting aspect of the NIR two-color diagram is
its ability to discriminate late type giants/supergiants from dwarfs,
due to a gravity
sensitive CO band appearing in the K band.
The CO index in the spectra of giants and supergiants.
Even these two types of stars can be separated with a special
CO filter than can discern gravity differences in these
two evolved stellar types (see figure below).
From Forster-Schreiber (2000, AJ).
NIR two-color diagrams, showing separation of late type
(crosses in lower figure) and dwarfs (squares).
The above figure shows how NIR photometry is useful for "decomposing"
contributions to galaxy SEDs from red giants, supergiants and dwarfs,
hot stars, hot dust, HII regions and the effects of reddening.