# Units and Constants¶

**pysynphot** understands some Flux Units and
Wavelength Units that are commonly used in astronomy.
Unit conversion can be easily done within spectral objects by using
`pysynphot.spectrum.SourceSpectrum.convert()`

(for flux and wavelength) and
`pysynphot.spectrum.SpectralElement.convert()`

(wavelength only, as
throughput is unitless) methods. As in IRAF STSDAS SYNPHOT, only lowercase
unit names are valid.

Unless explicitly stated otherwise in API documentations, all calculations are done in the following internal units first, and then presented in user-specified units:

- Angstrom for wavelength
`photlam`

for flux

## Constants¶

These are the constants used in unit conversion:

Constant | Description | Value |
---|---|---|

`pysynphot.units.C` |
Speed of light, c |
\(2.99792458 \times 10^{18} \; \AA \; \mathrm{s}^{-1}\) |

`pysynphot.units.H` |
Planck’s constant, h |
\(6.62620 \times 10^{-27} \; \mathrm{ergs} \; \mathrm{s}\) |

`pysynphot.units.ABZERO` |
`abmag` zero point |
-48.6 mag |

`pysynphot.units.STZERO` |
`stmag` zero point |
-21.1 mag |

## Flux Units¶

The recognized flux units for source spectrum and observation objects are as
tabulated below. For IRAF STSDAS SYNPHOT users, the unit name is equivalent to
`form`

, which has become `fluxunits`

in **pysynphot** (see
Examples). Most calculation and sampling results are
presented in the given flux unit (e.g.,
`sample()`

and
`effstim()`

).
Since all internal flux calculations are done using `photlam`

, no special
steps are necessary when an operation is done on source spectra with different
flux units.
Counts and Magnitudes further explains the units of `vegamag`

,
`abmag`

, `stmag`

, `obmag`

, and counts. The rest of the supported
flux units should be self-evident.

Name | Class Object | Unit |
---|---|---|

photlam | `Photlam` |
\(\mathrm{photon} \; \mathrm{s}^{-1} \; \mathrm{cm}^{-2} \; \AA^{-1}\) |

photnu | `Photnu` |
\(\mathrm{photon} \; \mathrm{s}^{-1} \; \mathrm{cm}^{-2} \; \mathrm{Hz}^{-1}\) |

flam | `Flam` |
\(\mathrm{erg} \; \mathrm{s}^{-1} \; \mathrm{cm}^{-2} \; \AA^{-1}\) |

fnu | `Fnu` |
\(\mathrm{erg} \; \mathrm{s}^{-1} \mathrm{cm}^{-2} \mathrm{Hz}^{-1}\) |

stmag | `STMag` |
\(-2.5 \times \log(\mathrm{flam}) - 21.1\) |

abmag | `ABMag` |
\(-2.5 \times \log(\mathrm{fnu}) - 48.6\) |

obmag | `OBMag` |
\(-2.5 \times \log(\mathrm{count})\) |

vegamag | `VegaMag` |
\(-2.5 \times \log(\mathrm{flux} \; / \; \mathrm{flux}_{\mathrm{Vega}})\) |

count counts |
`Counts` |
\(\mathrm{photon} \; \mathrm{s}^{-1}\) |

jy | `Jy` |
\(10^{-23} \; \mathrm{erg} \; \mathrm{s}^{-1} \; \mathrm{cm}^{-2} \mathrm{Hz}^{-1}\) |

mjy | `mJy` |
\(10^{-26} \; \mathrm{erg} \; \mathrm{s}^{-1} \; \mathrm{cm}^{-2} \mathrm{Hz}^{-1}\) |

ujy mujy microjy |
`muJy` |
\(10^{-29} \; \mathrm{erg} \; \mathrm{s}^{-1} \; \mathrm{cm}^{-2} \mathrm{Hz}^{-1}\) |

njy nanojy |
`nJy` |
\(10^{-32} \; \mathrm{erg} \; \mathrm{s}^{-1} \; \mathrm{cm}^{-2} \mathrm{Hz}^{-1}\) |

### Counts and Magnitudes¶

**pysynphot** supports counts and the following magnitude systems:

`obmag`

, the instrumental magnitude that is the logarithmic form of counts. Conversion involving counts and`obmag`

assumes a pre-defined telescope collecting area.`abmag`

, the \(\mathrm{AB}_{\nu}\) magnitude from Oke (1974), which is based on a constant flux density per unit frequency.`stmag`

, the \(\mathrm{ST}_{\lambda}\) or Space Telescope magnitude, which is based on a constant flux density per unit wavelength.`vegamag`

, which is defined by setting the magnitude of Vega to zero in all bands. The adopted Vega spectrum is defined over a wavelength range of 900 Angstroms to 300 microns.

`vegamag`

offers a reasonable approximation to many of the conventional
photometric systems that use the spectrum of Vega to define
magnitude zero in one or more passbands. In broadband photometry, the relevant
passband integral is calculated first for the source spectrum and then again
for the spectrum of Vega, and the ratio of the two results is converted to a
magnitude. This would not be a scientifically meaningful option for
spectrophotometry.

Meanwhile, `abmag`

and `stmag`

are appropriate for either spectrophotometry
or photometry. Their zero point values of 48.60 and 21.10 mag, respectively, are
chosen for convenience so that Vega has \(\mathrm{AB}_{\nu}\) and \(\mathrm{ST}_{\lambda}\) magnitudes close
to 0 in the Johnson *V* passband, as shown in the following figure:

Because the `abmag`

and `stmag`

systems are defined such that they result in
constant magnitudes for spectra having constant flux per unit frequency and
wavelength, respectively, they will not provide magnitudes on a conventional
system, such as *UBVRI*, without first deriving an appropriate transformation
onto the desired standard system.

`obmag`

and counts are used to predict detected count rates. For instance,
`countrate()`

calculates the
predicted number of detected counts per second integrated over the passband.
There are two important things to remember concerning this unit:

- The number of counts per channel depends on the width (in wavelength space)
of the channel in the wavelength grid that is used.
As stated above, all flux calculations are done internally in
the unit of
`photlam`

, so when the output unit of counts or`obmag`

is requested, the`photlam`

values are multiplied by the collecting area of the telescope and by the width (in Angstroms) of each channel in the wavelength grid. Therefore, in order to accurately predict the number of counts per channel for a spectroscopic instrument, it is necessary to use a wavelength grid that provides a good match to the dispersion properties of the selected instrument mode (see Wavelength Table). For supported HST instruments, the appropriate wavelength grid will be automatically selected. - The unit “counts” refers to the actual detector counts for the FOC, FOS, HRS, and HSP instruments. While for the WF/PC-1, WFPC2, NICMOS, WFC3, COS, ACS, and STIS instruments, it refers to electrons. In order to obtain counts in the unit of data number (DN) for some of the latter instruments, include the appropriate keyword for ADC gain, if supported (see Appendix B: OBSMODE Keywords).

## Wavelength Units¶

These are the recognized wavelength units for all spectrum objects:

Name | Class Object | Unit |
---|---|---|

m meter |
`Meter` |
SI base unit for length |

cm | `Cm` |
\(10^{-2} \; \mathrm{m}\) |

mm | `Mm` |
\(10^{-3} \; \mathrm{m}\) |

um micron microns |
`Micron` |
\(10^{-6} \; \mathrm{m}\) |

nm | `Nm` |
\(10^{-9} \; \mathrm{m}\) |

angstrom angstroms |
`Angstrom` |
\(10^{-10} \; \mathrm{m}\) |

1/um inversemicron inversemicrons |
`InverseMicron` |
\(10^{6} \; \mathrm{m}^{-1}\) |

hertz | `Hz` |
\(\mathrm{s}^{-1}\) |

## Examples¶

Create a source spectrum from arrays with default units:

```
>>> sp = S.ArraySpectrum(
... np.array([1000, 2000, 3000]), np.array([0.1, 0.2, 0.3]))
>>> print('{0}, {1}'.format(sp.waveunits.name, sp.fluxunits.name))
angstrom, photlam
```

Convert both wavelength and flux units:

```
>>> sp.convert('nm')
>>> sp.convert('flam')
>>> print('{0}, {1}'.format(sp.waveunits.name, sp.fluxunits.name))
nm, flam
>>> sp.wave
array([ 100., 200., 300.])
>>> sp.flux
array([ 1.98648479e-12, 1.98648479e-12, 1.98648479e-12])
```

To sample the spectrum in user units (i.e., nm and `flam`

), use its
`sample()`

method:

```
>>> sp.sample(200)
1.9864847851996004e-12
```

To sample the spectrum in internal units (i.e., Angstrom and `photlam`

),
use its `__call__()`

method:

```
>>> sp(2000)
0.20000000000000001
```