# Astronomy:Total electron content

**Total electron content** (or **TEC**) is an important descriptive quantity for the ionosphere of the Earth. TEC is the total number of electrons integrated between two points, along a tube of one meter squared cross section, i.e., the electron columnar number density. It is often reported in multiples of the so-called TEC unit, defined as TECU=10^{16}el/m^{2}.^{[1]}

TEC is significant in determining the scintillation and group and phase delays of a radio wave through a medium. Ionospheric TEC is characterized by observing carrier phase delays of received radio signals transmitted from satellites located above the ionosphere, often using Global Positioning System satellites. TEC is strongly affected by solar activity.

## Formulation

The TEC is path-dependent. By definition, it can be calculated by integrating along the path *ds* through the ionosphere with the location-dependent electron density *n _{e}(s)*:

- TEC = [math]\displaystyle{ \int n_e(s)\,ds }[/math]

The *vertical* TEC (*VTEC*) is determined by integration of the electron density on a perpendicular to the ground standing route, the *slant* TEC (*STEC*) is obtained by integrating over any straight path.

To first order, the ionospheric radio effect is proportional to TEC and inversely proportional to the radio frequency *f*. The ionospheric phase delay reads:^{[2]}^{:eq. (9.41)}

- [math]\displaystyle{ \tau_p^\mathrm{iono} = -\kappa \frac{\mathrm{TEC}}{f^2} }[/math]

while the ionospheric group delay has the same magnitude but opposite sign:

- [math]\displaystyle{ \tau_g^\mathrm{iono} = -\tau_p^\mathrm{iono} }[/math]

The proportionality constant *κ* reads:^{[2]}^{:eq.(9.21),(9.20),(9.19),(9.14)}^{[3]}

- [math]\displaystyle{ \kappa = q^2 / (8 \pi^2 m_e \epsilon_0) = c^2 r_e / (2\pi) }[/math]

where *q*, *m*_{e}, r_{e} are the electron charge, mass, and radius, respectively; *c* is the vacuum speed of light and *ϵ*_{0} is the vacuum permittivity. The value of the constant is approximately *κ* ≈ 40.308193 m^{3}·s^{−2};^{[4]}^{[5]} the units can be expressed equivalently as m·m^{2}·Hz^{2} to highlight the cancellation involved in yielding delays τ in meters, given *f* in Hz and TEC in m^{−2}.

## References

Original source: https://en.wikipedia.org/wiki/ Total electron content.
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