### spectral index

**(α)**
(power by which an object's flux depends on frequency)

The **spectral index** of an observed electromagnetic-radiation source is a scalar
measure describing an aspect of its spectrum, treating the
observed spectrum as a power law.
It is specifically the exponent of the frequency
that produces a term proportional to the observed radiant flux at
each frequency, i.e.,

S ∝ ν^{α}

- S - radiant flux.
- ν - frequency.
- α - spectral index.

(Some use the term **spectral index** to mean the negative this
exponent. Also, **spectral index** has been used to refer to an
exponent of the wavelength rather than of the frequency.
Some papers deliberately quote the formula they use to avoid confusion.
Comments below use the above definition/formula.)

The spectral index must be limited to a finite range/regime: otherwise
it would imply infinite energy emission and a frequency range limited
only by zero, with no upper limit. In actual practice, a
spectral index is used to describe the spectrum viewed over a portion
of the spectrum's full range, and describes an approximation of the
slope characteristics of radiant-flux-per-unit-frequency
over that particular portion.
Black-body radiation, which clearly is not a power
law over the whole spectrum, given its peak strength in the middle, does
approximate a power law of α = 2 over the lower frequencies,
as per the Rayleigh-Jeans law. If an observation is made in the
regime where this holds true (called spectrum's the **Rayleigh-Jeans regime**),
then black-body radiation is a possibility and parameters of the
spectrum indicate the temperature it suggests.

Other spectral indexes suggest other types of EMR production, e.g.,
synchrotron radiation or bremsstrahlung.

The term **emissivity index** (**β**) refers to the
spectral index minus two, basically comparing it to the low-frequency
end of the black-body spectrum.

Radio astronomy makes much use of the *spectral index*, and the
term **radio spectral index** is sometimes used to specify the spectral
index in the radio regime.

(*EMR,measure*)
**Further reading:**

http://en.wikipedia.org/wiki/Spectral_index

**Referenced by pages:**

anomalous microwave emission (AME)

CRATES

Lambda-CDM model (ΛCDM)

Parkes Multibeam Pulsar Survey (PMPS)

power law

spectral signature

stellar temperature determination

USS Sources

young stellar object (YSO)

Index