Johnson B band

• Comment: Far too many unsourced sections, plus it reads like a textbook. Ldm1954 (talk) 17:28, 31 July 2026 (UTC)

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Approximate response curves of the UBV photometric system. The Johnson B band covers the blue portion of the visible spectrum between the U and V bands.

The Johnson B band is a broad optical photometric passband in the Johnson–Morgan UBV photometric system. The letter B denotes blue. The band measures radiation primarily in the blue region of the visible spectrum, with a characteristic effective wavelength near 440 nanometres, although the exact value depends on the spectrum of the observed object and the adopted realization of the passband.

The B band was introduced during the development of the UBV system by American astronomers Harold Lester Johnson and William Wilson Morgan in the early 1950s. Together with the ultraviolet U band and visual V band, it provided one of the first widely standardized systems for photoelectric measurements of stellar brightness and color.

A magnitude measured through the band is written as B or m_B. The difference between B- and V-band magnitudes,

$B-V=m_B-m_V,$

is the widely used B−V color index. It is sensitive to stellar temperature, spectral type, interstellar extinction, and the combined stellar populations of unresolved objects such as star clusters and galaxies.

The Johnson B band is not defined solely by a particular piece of colored glass. A practical realization includes the wavelength-dependent transmission of the filter, telescope optics, detector response, and, for ground-based observations, Earth's atmosphere. Observations made with different instruments are transformed onto the standard system using stars with accurately established B magnitudes and B−V colors.

Passband characteristics

The B band is a broad passband rather than a narrow interval with sharply fixed boundaries. Its response rises through the violet portion of the spectrum, reaches maximum sensitivity in the blue, and decreases toward the green.

In Bessell's 1990 reconstruction of the standard Johnson system, the normalized B response extends approximately from 360 to 550 nm and reaches its maximum near 420 nm. The effective wavelength was calculated as 438.2 nm for an A0 V stellar spectrum and 453.7 nm for a K0 III spectrum.

Representative properties of the Johnson B band

Property	Approximate value	Notes
Spectral region	Blue visible light	Between the Johnson U and V bands
Approximate response range	360–550 nm	Based on the normalized passband reconstructed by Bessell
Peak normalized response	Approximately 420 nm	Depends on the adopted system-response function
Effective wavelength for an A0 V spectrum	438.2 nm	Bessell 1990 representation
Effective wavelength for a K0 III spectrum	453.7 nm	Shifted redward because of the different source spectrum
Original detector	RMA 1P21 photomultiplier tube	Used in the early Johnson–Morgan system
Magnitude system	Traditionally Vega based	Modern synthetic realizations require an explicitly stated passband and zero point

The table gives representative values rather than universal constants. Effective wavelength depends on the source spectrum because a blue star and a red star distribute their photons differently across the same response curve.

System response

The total response of a ground-based observing system can be expressed schematically as

$S_B(\lambda )=T_{\mathrm{f}\mathrm{i}\mathrm{l}\mathrm{t}\mathrm{e}\mathrm{r}}(\lambda )T_{\mathrm{o}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{s}}(\lambda )Q_{\mathrm{d}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}}(\lambda )T_{\mathrm{a}\mathrm{t}\mathrm{m}}(\lambda ),$

where:

• S_B(λ) is the total B-band system response;
• T_filter(λ) is the filter transmission;
• T_optics(λ) is the transmission or reflectivity of the telescope and instrument;
• Q_detector(λ) is the detector's quantum efficiency; and
• T_atm(λ) is atmospheric transmission.

For observations from above Earth's atmosphere, the atmospheric term is omitted. Even then, the telescope, filter, and detector together define the natural instrumental passband.

Effective wavelength

A commonly used source-dependent effective wavelength may be written as

${\lambda }_{\mathrm{e}\mathrm{f}\mathrm{f}}=\frac{\int \lambda f_{\lambda }(\lambda )S_B(\lambda )d\lambda }{\int f_{\lambda }(\lambda )S_B(\lambda )d\lambda },$

where f_λ(λ) is the spectral flux density of the source.

For a photon-counting detector, an additional wavelength weighting is required because a photon carries energy hc/λ. A photon-weighted form is

${\lambda }_{\mathrm{e}\mathrm{f}\mathrm{f},\mathrm{p}\mathrm{h}}=\frac{\int {\lambda }^2{f}_{\lambda }(\lambda )S_B(\lambda )d\lambda }{\int \lambda f_{\lambda }(\lambda )S_B(\lambda )d\lambda }.$

Consequently, a single quoted wavelength cannot fully define the B band. The complete response curve and the convention used to calculate the characteristic wavelength are also required.

Pivot wavelength

A source-independent characteristic known as the pivot wavelength may be defined as

${\lambda }_{\mathrm{p}\mathrm{i}\mathrm{v}}=\sqrt{\frac{\int \lambda S_B(\lambda )d\lambda }{\int S_B(\lambda )d\lambda /\lambda }}.$

The pivot wavelength depends only on the adopted passband. It is useful when converting between flux densities expressed per unit wavelength and per unit frequency.

History

Development of the UBV system

Before photoelectric photometry became widespread, stellar brightness was commonly measured visually or from photographic plates. Photographic emulsions were particularly sensitive to blue light, while the human eye is most sensitive at longer visible wavelengths. Differences between photographic and visual magnitudes provided an early measure of stellar color.

Johnson and Morgan developed the standardized U, B, and V system to replace less consistent photographic and visual measurements with reproducible photoelectric observations. Their 1953 study established fundamental photometric standards alongside the revised Morgan–Keenan system of spectral classification.

The three passbands represented:

• U — ultraviolet;
• B — blue; and
• V — visual.

The original B realization used a combination of Corning 5030 blue glass and 2-mm Schott GG13 glass with an uncooled RMA 1P21 photomultiplier tube.

An RMA 1P21 photomultiplier tube, the type of detector used to establish the original Johnson UBV system

A photometric system is ultimately defined by its standard-star measurements rather than only by its physical filters. Johnson's later observations and secondary standard-star catalogues extended the system to larger numbers of stars and a wider range of brightnesses.

Transition to modern detectors

The spectral sensitivity of a modern charge-coupled device differs substantially from that of a 1P21 photomultiplier. Simply placing the original colored-glass combination in front of a CCD would therefore not reproduce the historical B passband exactly.

Bessell reconstructed practical UBVRI passbands by comparing synthetic photometry with standard observations and recommended colored-glass combinations suitable for photoelectric detectors and CCDs. Bessell and Murphy later used modern spectrophotometric libraries to revise photon-counting passbands and synthetic zero points.

These reconstructions are frequently described as Bessell B passbands. The term refers to a practical realization intended to reproduce Johnson-system photometry; it does not denote an entirely separate astronomical color system.

Measurement of B magnitude

A detector does not directly measure astronomical magnitude. It records electrons, counts, or another signal proportional to the radiation transmitted by the observing system.

For a photon-counting detector, the expected B-band count rate is proportional to

$C_B\propto \int f_{\lambda }(\lambda )S_B(\lambda )\frac{\lambda }{hc}d\lambda ,$

where:

• C_B is the detected count rate;
• f_λ(λ) is the source spectral flux density;
• S_B(λ) is the dimensionless total system response;
• h is the Planck constant; and
• c is the speed of light.

The instrumental B magnitude may be written as

$b_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}}=-2.5{\log }_{10}{C}_B+C_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}},$

where C_inst is an arbitrary instrumental constant.

A calibrated magnitude is determined relative to a reference count rate or reference spectrum:

$m_B=-2.5{\log }_{10}\left(\frac{C_B}{C_{B,0}}\right),$

where C_B,0 is the count rate associated with zero magnitude in the adopted realization.

An equivalent flux-based expression is

$m_B=-2.5{\log }_{10}\left(\frac{F_B}{F_{B,0}}\right),$

where F_B is a band-integrated flux and F_B,0 is its zero-point value.

The exact zero-point flux depends on the adopted response curve, flux convention, and reference spectrum. For this reason, precise synthetic photometry should identify the passband source and zero-point definition instead of relying on a single generic B-band wavelength or flux.

The B−V color index

The B−V color index is the difference between a source's B and V magnitudes:

$B-V=m_B-m_V.$

Using the magnitude definition, it represents a logarithmic ratio of the radiation detected in the two bands:

$B-V=-2.5{\log }_{10}\left(\frac{C_B/C_{B,0}}{C_V/C_{V,0}}\right).$

In the traditional Johnson system, the zero points were selected so that unreddened A0 main-sequence stars had B−V values near zero. Vega was historically central to the calibration of the magnitude scale, although modern realizations do not necessarily assign exactly zero magnitude to Vega in every passband.

Relationship between B−V color and effective temperature for main-sequence stars. Reddening, metallicity, and surface gravity can alter the relation.

Hot stars emit a larger fraction of their visible light in the B band and generally have negative or small B−V values. Cooler stars emit proportionally less blue light and have larger positive B−V values.

Approximate examples for unreddened main-sequence stars are:

General stellar type	Approximate B−V behavior
Hot O and B stars	Negative B−V
A0 stars	Near zero
Solar-type G stars	Moderately positive
Cool K and M stars	Large positive B−V

The relationship is not determined by temperature alone. Surface gravity, chemical composition, absorption lines, molecular bands, and interstellar extinction also affect B−V.

Uncertainty

When B and V measurements have independent uncertainties, the uncertainty in the color index is approximately

${\sigma }_{B-V}=\sqrt{{\sigma }_B^2+{\sigma }_V^2}.$

When the measurements have correlated errors,

${\sigma }_{B-V}^2={\sigma }_B^2+{\sigma }_V^2-2\mathrm{Cov}(B,V).$

Correlated atmospheric or calibration errors can partly cancel in a color index, while other systematic errors can affect both passbands in a more complicated manner.

Interstellar reddening and extinction

Interstellar dust absorbs and scatters blue light more strongly than visible light at longer wavelengths. As a result, dust generally makes an astronomical source appear fainter in B and gives it a more positive B−V color.

The B-band extinction is

$A_B=m_{B,\mathrm{o}\mathrm{b}\mathrm{s}}-m_{B,0},$

where m_B,obs is the observed magnitude and m_B,0 is the magnitude that would be measured without extinction.

The B−V color excess is defined as

$E(B-V)=(B-V{)}_{\mathrm{o}\mathrm{b}\mathrm{s}}-(B-V{)}_0.$

Because

$E(B-V)=A_B-A_V,$

the B-band extinction can also be written as

$A_B=A_V+E(B-V).$

The ratio of total to selective extinction in the V band is

$R_V=\frac{A_V}{E(B-V)}.$

Therefore,

$A_B=(R_V+1)E(B-V).$

For the frequently adopted diffuse Milky Way value R_V ≈ 3.1,

$A_B\approx 4.1E(B-V).$

This is an approximation rather than a universal law. The extinction curve and value of R_V vary among different sightlines and environments.

The B and V bands are especially important in studies of extinction because their difference defines the commonly used quantity E(B−V).

Atmospheric extinction

Earth's atmosphere attenuates B-band radiation through molecular scattering, aerosols, and absorption. Blue light is more strongly affected by Rayleigh scattering than longer visible wavelengths.

For a first-order atmospheric correction,

$b_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}}=b_0+k_{B}X,$

where:

• b_inst is the measured instrumental magnitude;
• b₀ is the magnitude above the atmosphere in the natural instrumental system;
• k_B is the B-band atmospheric-extinction coefficient; and
• X is the air mass.

A more complete transformation may include a color-dependent extinction term:

$b_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}}=b_0+k_{B}X+k{\text{'}}_B(B-V)X.$

The coefficients vary with observing site, altitude, weather, aerosols, season, and instrument. They are usually measured by observing standard stars over a range of air masses during a photometric night.

Transformation to the standard system

Every telescope, detector, and filter combination has a natural system. Its response will generally differ slightly from the standard Johnson B passband.

A common transformation equation is

$B=b_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}}+Z_B-k_{B}X+c_B(B-V),$

where:

• B is the standard magnitude;
• b_inst is the instrumental magnitude;
• Z_B is the photometric zero point;
• k_B is the atmospheric-extinction coefficient;
• X is air mass; and
• c_B is a color-transformation coefficient.

Depending on the observing program, additional terms may be included:

$B=b_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}}+Z_B-k_{B}X+c_1(B-V)+c_2(B-V{)}^2.$

A substantial color term indicates that the natural passband does not closely reproduce the standard one. A linear transformation may work well for ordinary standard stars but fail for objects with unusual spectra, including:

• emission-line stars;
• heavily reddened stars;
• white dwarfs;
• carbon stars;
• supernovae;
• active galactic nuclei; and
• galaxies containing mixed stellar populations.

Bessell identified B-passband mismatch as an important source of systematic differences in U−B and B−V photometry.

Standard stars

A standard photometric system is maintained through observations of photometric-standard stars. Their magnitudes and colors are repeatedly measured under photometric conditions and used to determine nightly zero points, extinction coefficients, and color transformations.

Arlo Landolt published widely used UBVRI standards near the celestial equator covering a broad range of magnitudes and colors. Later observations extended and updated the equatorial standard-star network.

Peter Stetson developed an extensive network of fainter secondary standards in star clusters and resolved-galaxy fields, calibrated to the Landolt system.

Standard-star calibration does not make two very different passbands physically identical. Instead, it establishes a mathematical transformation that reproduces the standard magnitudes for the range of colors and spectra represented by the standards.

Synthetic photometry

Synthetic photometry calculates magnitudes by integrating a measured or modeled spectrum through a numerical response curve. It is used to:

• derive expected B magnitudes from spectra;
• compare alternative passband definitions;
• calculate color transformations;
• estimate zero points;
• generate stellar-population colors;
• calculate K correction for galaxies;
• test instrumental passband mismatches; and
• convert between photometric systems.

For a photon-counting response, a synthetic magnitude may be written as

$m_B=-2.5{\log }_{10}\left[\frac{\int f_{\lambda }(\lambda )S_B(\lambda )\lambda d\lambda }{\int f_{\lambda ,\mathrm{r}\mathrm{e}\mathrm{f}}(\lambda )S_B(\lambda )\lambda d\lambda }\right]+m_{B,\mathrm{r}\mathrm{e}\mathrm{f}},$

where f_λ,ref is the reference spectrum and m_B,ref is its assigned magnitude.

The passband, response convention, reference spectrum, and zero point must all be specified for reproducible synthetic photometry.

Scientific applications

Stellar temperature and classification

B−V is one of the most widely used broad-band indicators of stellar temperature. After correction for extinction, it can be used to estimate effective temperature and to compare stars with standard spectral sequences.

The relation between B−V and temperature is nonlinear. It also depends on surface gravity, metallicity, and spectral features. Precision work therefore uses empirical or model-based calibrations appropriate to the relevant type of star.

Color–magnitude diagrams

B and V observations are frequently used to construct a color–magnitude diagram with B−V on the horizontal axis and V or absolute V magnitude on the vertical axis. Such diagrams reveal:

• the main sequence;
• the main-sequence turnoff;
• the red-giant branch;
• the horizontal branch;
• white dwarfs;
• binary sequences; and
• effects of age, metallicity, distance, and reddening.

For a star cluster, comparison with theoretical isochrones can constrain age, distance, chemical abundance, and interstellar extinction.

Variable stars

Repeated B-band measurements produce a blue-light curve. Comparing B and V variations can show whether an object becomes bluer or redder during its brightness cycle.

UBVRI light curves of Delta Cephei, showing that the amplitude and phase of a variable star can differ among photometric bands

B observations are used in studies of:

• Cepheid variables;
• RR Lyrae variables;
• eclipsing binaries;
• pulsating stars;
• eruptive variables;
• cataclysmic variables; and
• supernovae.

Variability amplitudes are often larger in B than in V because temperature changes have a stronger effect at shorter visible wavelengths.

Stellar populations and galaxies

The integrated B−V color of a galaxy depends on its mixture of stellar populations, dust content, metallicity, and star-formation history. A galaxy dominated by young hot stars generally has a bluer B−V color than one dominated by older, cooler stars.

B-band luminosities have historically been used in galaxy luminosity functions, mass-to-light ratios, surface-brightness measurements, and morphological studies. Blue light is particularly sensitive to recent star formation but is also more affected by dust than red and infrared light.

Transient astronomy

Historical observations of novae and supernovae often include Johnson B magnitudes. B-band light curves are used to study color evolution, temperature changes, extinction, and comparisons with earlier events.

Because transient spectra can contain broad and rapidly changing absorption and emission features, transforming measurements from a mismatched instrumental B filter can produce systematic errors. Direct synthetic photometry or publication of the natural-system response may therefore be preferable.

Solar-system objects

B−V colors are also measured for asteroids, comets, planetary satellites, and other Solar System bodies. These colors provide broad information about surface reflectance, composition, and changes caused by rotation or activity.

Comparison with related blue passbands

The Johnson B band is not interchangeable with every filter labeled "B" or "blue".

Selected blue optical passbands

Passband	System or instrument	General relationship to Johnson B
Johnson B	Johnson–Morgan UBV	Historical standard blue passband
Bessell B	Johnson–Cousins realization	Designed to reproduce standard Johnson B photometry with modern detectors
BT	Tycho photometric system	Broader and generally bluer; requires color-dependent transformation
g, g′	Sloan photometric system	Extends over a different and generally redder spectral interval
GBP	Gaia	Much broader blue photometer response, not a Johnson B equivalent
F435W	Hubble ACS	Similar nominal wavelength but has an instrument-specific response
BJ	Photographic survey system	Photographic blue band with a distinct response and calibration

Conversions between systems are normally expressed as color-dependent equations. A generic transformation might take the form

$B=g+a(g-r)+b,$

but the coefficients depend on the source type, detector, filter realization, and color range. No single equation is valid for all stars, galaxies, or transients.

Limitations and systematic effects

The Johnson B band remains scientifically useful, but precise measurements require attention to several limitations.

Passband ambiguity

The term "Johnson B" has been applied to several practical realizations. Published measurements may use different:

• filter-glass combinations;
• detector technologies;
• atmospheric assumptions;
• standard-star networks;
• response definitions; and
• transformation procedures.

A study requiring high precision should publish or identify the complete response curve.

Source-dependent wavelength

Because the B band is broad, its effective wavelength changes with the spectrum of the source. A quoted central wavelength does not mean that all B measurements correspond to exactly that wavelength.

Spectral features

The band contains numerous stellar absorption features, including higher-order Balmer lines and metal-line absorption. Small passband shifts can therefore affect different spectral types unequally.

Line blanketing is especially important in cool and metal-rich stars. Galaxies and transients can contain emission or absorption features whose movement through the band with redshift or time alters the measured magnitude.

Atmospheric sensitivity

B-band measurements are more sensitive to atmospheric scattering than V-band observations. Thin clouds, aerosols, air mass, and variable extinction can introduce color-dependent errors.

Detector response

A CCD usually has a much redder and broader intrinsic sensitivity than the original 1P21 photomultiplier. The filter must compensate for this difference, and residual mismatch must be corrected through standard-star transformations.

Red leaks

Small transmission outside the intended passband can affect very red sources because they may emit much more flux at red wavelengths than in the B band. High-quality photometric filters require strong out-of-band blocking.

Low efficiency for red objects

Cool stars and dust-obscured objects emit relatively little radiation in the blue. B-band observations of such targets may require long exposure times and may have larger statistical and calibration uncertainties.

Dependence on adopted magnitude system

Published B magnitudes are traditionally Vega based, but synthetic datasets may instead use the AB magnitude or ST magnitude systems. The label "B" alone does not always identify the zero-point convention.

An AB magnitude is defined from spectral flux density per unit frequency:

$m_{\mathrm{A}\mathrm{B}}=-2.5{\log }_{10}\left(\frac{f_{\nu }}{3631\mathrm{J}\mathrm{y}}\right).$

A Vega-based B magnitude and an AB magnitude calculated through the same response curve differ by a passband-dependent offset.

Nomenclature

The band may be written as:

• Johnson B;
• B band;
• B-band;
• Johnson–Morgan B;
• Johnson–Cousins B; or
• Bessell B, when referring to a specific reconstructed realization.

In technical writing, B band should be accompanied by the photometric system or instrument when ambiguity is possible. A B filter on one telescope is not necessarily equivalent to the Johnson standard B passband.

The term should also not be confused with unrelated uses of "B band" in radio, microwave, or communications engineering.

See also

• Photometric system
• Stellar classification

Further reading

• Bessell, Michael; Murphy, Simon (February 2012). "Spectrophotometric libraries, revised photonic passbands, and zero points for UBVRI, Hipparcos, and Tycho photometry". Publications of the Astronomical Society of the Pacific. 124 (912): 140–157. arXiv:1112.2698. Bibcode:2012PASP..124..140B. doi:10.1086/664083.
• Bessell, Michael S. (September 2005). "Standard photometric systems". Annual Review of Astronomy and Astrophysics. 43: 293–336. Bibcode:2005ARA&A..43..293B. doi:10.1146/annurev.astro.41.082801.100251.
• Bessell, Michael S. (October 1990). "UBVRI passbands". Publications of the Astronomical Society of the Pacific. 102: 1181–1199. Bibcode:1990PASP..102.1181B. doi:10.1086/132749.
• Hearnshaw, John B. (1996). The Measurement of Starlight: Two Centuries of Astronomical Photometry. Cambridge: Cambridge University Press. ISBN 978-0-521-40393-1. Search this book on
• Sterken, Christiaan; Manfroid, Jean (1992). Astronomical Photometry: A Guide. Dordrecht: Kluwer Academic Publishers. ISBN 978-0-7923-1653-4. Search this book on

External links

• Johnson and Morgan's original 1953 UBV paper at the Astrophysics Data System
• Bessell's 1990 UBVRI passband reconstruction at the Astrophysics Data System
• Revised UBVRI photon-counting passbands and zero points
• SVO Filter Profile Service

This article "Johnson B band" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:Johnson B band. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

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