Terahertz to hertz: counting the cold universe
What this conversion does
It multiplies by a trillion, expanding a spectroscopic observation into whole cycles per second. Astronomers publish in terahertz because the interesting lines are close together at that scale, while the underlying physics is stated in hertz. The conversion is exact, so a measurement reported to three decimal places in terahertz keeps all of its precision when written out in full.
What the band reveals
Cool dust and gas between the stars radiates most strongly in this region, along with a number of molecular lines that are invisible at optical wavelengths because the material is too cold to emit visible light and too warm to be seen in the radio bands. Observing from the ground is difficult because the atmosphere absorbs much of the band, which is why the instruments tend to be on high, dry sites or on aircraft and satellites.
Terahertz to hertz conversion table
Astronomical lines and observing windows in both units, showing why a band with such short wavelengths is still described in frequencies.
| Terahertz (THz) | Hertz (Hz) |
|---|---|
| 1 | 1000000000000 |
| 2 | 2000000000000 |
| 10 | 10000000000000 |
| 100 | 100000000000000 |
| 300 | 300000000000000 |
| 1000 | 1e+15 |
Why astronomers abandoned wavelength here
In the optical tradition a line is identified by its wavelength in nanometres or microns, and in the radio tradition by its frequency. Terahertz astronomy inherited both habits, and frequencies won because the lines are compared with laboratory measurements of molecular transitions, which are tabulated that way. A single observation can therefore be quoted in terahertz by the observer and in hertz by the physicist checking it.
Twelve places, twice over
Multiplying by a trillion moves the decimal point twelve places to the right. A line at 1.4 THz therefore becomes fourteen digits long, beginning 1,400,000,000,000. Counting the digits is a faster check than counting zeroes.
Frequently asked questions
How do I convert terahertz to hertz?
Multiply by a trillion, which is a million million. A line at 1.4 THz is therefore 1,400,000,000,000 Hz. The multiplication is exact and moves the decimal point twelve places to the right.
How many hertz are in one terahertz?
A trillion, or 10¹². Four prefix steps of a thousand sit between hertz and terahertz — kilo, mega, giga, tera — so the total factor is a thousand raised to the fourth power.
Why do astronomers work in this band?
Because cold dust and gas in space radiate there. Material too cold to glow visibly and too warm to be bright in radio emission shows up in the terahertz region, and several molecules have distinctive lines that let their abundance be measured.
Is it possible to observe from the ground?
Only at a few windows where the atmosphere is transparent, and only from high, very dry locations, since water vapour absorbs strongly across most of the band. Aircraft and satellites avoid the problem by getting above most of the atmosphere altogether.
Does the converter lose accuracy at these magnitudes?
No. The multiplication is by a power of ten, which is exact, and the result is written in full rather than in exponent form when it remains readable. Very large results fall back to exponent notation only to keep the output legible.