ASTR 5610, Majewski [SPRING 2016]. Lecture Notes

## FLUXES, MAGNITUDES, COLORS, AND FILTER SYSTEMS

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

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,

or

f = 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,

or

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:

OR:

where:

fλo = stellar flux incident on Earth atmosphere

Tλ = transmission of atmosphere

Rλ = efficiency of telescope + detector

Sλ = transmission function of filter

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

Constancy of Detected Surface Brightness

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

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

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

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

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

Surface brightness is a distance-independent quantity.

• 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 high redshifts.

#### Magnitudes

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

• 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.

• Ptolemy's Almagest
• 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 mag 1.
• Since Δm = 5 appears to be 100x ratio in brightness, and
• Pogson proposes to formalize scale so that ratios between successive magnitudes are exactly 2.5119.

• Thus, two stars of integrated band fluxes (i.e., the integral over some [λ, λ + δλ] of the spectral flux density) f1 and f2 have a magnitude difference given by
• 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".

#### Relative Photometry

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

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

• 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 as references.

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 relative photometry

#### Absolute Photometry

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

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

Setting up a universal magnitude system means defining for the equation

a set flux value f2 corresponding to m2.

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

Several approaches to this problem have now evolved.

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

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

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

The disadvantages of this system are:

• 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) observed.

• 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 combinations.

• 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).

• Defined as:

mν = -2.5 log10 fν - 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., "VAB".

• The "STMAG" System

• Analogous to AB system, but for fλ.

• Defined as:

mλ = -2.5 log10 fλ - 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 magnitude systems.

• 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:
• Example :
• 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:

1. makes its identity known by some easily observable characteristic, and
2. 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:
• Variability (ironically)

E.g. certain kinds of stars like RR Lyrae or Cepheids vary in brightness in easily identifiable ways:

Supernovae explode with a reasonably well-defined light profile:

• Spectral type

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 luminosity/absolute magnitude.

Getting distances in this way is called measuring a spectroscopic parallax.
• Colors

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.
• Morphology

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.
• Ensembles

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.

#### Extinction by Dust

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

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

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

• 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 various problems.

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

The naming of magnitudes by the bandpass follows certain conventions.

• 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. For example:

• 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 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.

• By convention we pick cA-cB based on Vega (an A0 V type star) so that for Vega:
• AB system (e.g., HST) uses CA-CB = same constant for all filters.
• 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":
• A - B < 0 means "bluer than Vega" (in this color system)
• A - B > 0 means "redder than Vega" (in this color system)

#### Bolometric Fluxes/Colors

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

• 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, 355).

• 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 band, is:

• 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, nearby stars.

• 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 Stefan-Boltzmann Law:

L = 4 π R 2 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:

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

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

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

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

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

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

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

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

#### Mass to Light Ratios

• 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 bolometric M/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 sky.

• 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.

• Two systems used:

• Σ, μX in mag / arcsec2

e.g., μV = 21 mag / arcsec2

• S10(V) -- number of V=10 stars / deg2

S10(B) -- number of B=10 stars / deg2

• Note, can be tricky to think in either of these sets of units... (see HW problem)
• μ surface brightnesses often used to define the extents of things:

• "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 / arcsec2
• R25 = 1/2 D25 = "de Vaucouleur radius"
• "Holmberg radius" = 26.5 mag / arcsec2 = μpg ~ μB

#### 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:
• The hotter the star, the more luminous at radius R
• ##### From http://www.physics.utoledo.edu/~lsa/_color/05_bla.htm.

• 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 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 Bolte, to determine the effective temperature of an F-G type star to 100 K, the following relative integration times needed:

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

• 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

##### 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:

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

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

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

#### The Johnson-Morgan UBV System

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

• The 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 to typical stars.
• In older references, you will often see so-called "mpg" magnitudes -- corresponding 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) 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 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 ?
• Note that similar loci can be constructed in other filter combinations.

#### The RI Extension to the Johnson-Morgan UBV System

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

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

• 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 Group objects.
• ##### 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 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.

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.

DDO System

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

Thuan-Gunn System

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

• 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.

Infrared Systems

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.
##### 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.

##### NIR two-color diagrams, showing separation of late type evolved stars (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.

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