Physical Constants Unit

The Physical Constants unit provides a set of common constants, such as Pi and the gravitational constant, in various systems of measurement units. The default system of units is CGS, so named for having a length unit in centimeters, a mass unit in grams, and a time unit in seconds. In CGS, the charge unit is the esu, and the temperature unit is the Kelvin. The constants can also be obtained in the standard MKS system of units, where length is in meters, mass in kilograms, and time in seconds. For MKS units, charge is in Coloumbs, and temperature in Kelvin.

For ease of usage, the constant PI=3.14159…. is defined in the header file constants.h. Including this file with #include “constants.h” is an alternate way to access the value of \(\pi\), rather than needing to include the PhysicalConstants unit.

Any constant can optionally be converted from the standard units into any other available units. This facility makes it easy to ensure that all parts of the code are using a consistent set of physical constant values and unit conversions.

For example, a program using this unit might obtain the value of Newton’s gravitational constant \(G\) in units of Mpc\(^3\) Gyr\(^{-2}M_\odot^{-1}\) by calling

call PhysicalConstants_get (“Newton”, G, len_unit=”Mpc”, time_unit=”Gyr”, mass_unit=”Msun”)

In this example, the local variable G is set equal to the result, \(4.4983\times 10^{-15}\) (to five significant figures).

Physical constants are taken from K. Nahamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010).

Available Constants and Units

There are many constants and units available within Flash-X, see and . Should the user wish to add additional constants or units to a particular setup, the routine PhysicalConstants/PhysicalConstants_init should be overridden and the new constants added within the directory of the setup.

Available Physical Constants
String Constant	Description
Newton	Gravitational constant G
speed of light	Speed of light
Planck	Planck’s constant
electron charge	charge of an electron
electron mass	mass of an electron
proton mass	Mass of a proton
fine-structure	fine-structure constant
Avogadro	Avogadro’s Mole Fraction
Boltzmann	Boltzmann’s constant
ideal gas constant	ideal gas constant
Wien	Wien displacement law constant
Stefan-Boltzmann	Stefan-Boltzman constant
pi	Pi
e	e
Euler	Euler-Mascheroni constant

Available Units for Conversion of Physical Constants
Base unit	String Constant	Value in CGS units	Description*
length	cm	1.0	centimeter
time	s	1.0	second
temperature	K	1.0	degree Kelvin
mass	g	1.0	gram
charge	esu	1.0	ESU charge
length	m	`1.0E2`	meter
length	km	`1.0E5`	kilometer
length	pc	`3.0 856775807E18`	parsec
length	kpc	`3.0 856775807E21`	kiloparsec
length	Mpc	`3.0 856775807E24`	megaparsec
length	Gpc	`3.0 856775807E27`	gigaparsec
length	Rsun	`6.96E10`	solar radius
length	AU	`1.49 597870662E13`	astronomical unit
time	yr	`` 3.15569252E7``	year
time	Myr	`3 .15569252E13`	megayear
time	Gyr	`3 .15569252E16`	gigayear
mass	kg	`1.0E3`	kilogram
mass	Msun	`` 1.9889225E33``	solar mass
mass	amu	`1.6 60538782E-24`	atomic mass unit
charge	C	`` 2.99792458E9``	Coulomb

Cosm ology-friendly units using :ma th:H_0 = 100 km/s/Mpc:
length	LFLY	`3.0 856775807E24`	1 Mpc
time	TFLY	`2.05759E17`	\(\ frac{2}{3H_0}\)
mass	MFLY	`9.8847E45`	`5.23e12` Msun

Applicable Runtime Parameters

There is only one runtime parameter used by the Physical Constants unit: PhysicalConstants/pc_unitsBase selects the default system of units for returned constants. It is a three-character string set to “CGS” or “MKS”; the default is CGS.

Routine Descriptions

The following routines are supplied by this unit.

PhysicalConstants/PhysicalConstants_get Request a physical constant given by a string, and returns its real value. This routine takes optional arguments for converting units from the default. If the constant name or any of the optional unit names aren’t recognized, a value of 0 is returned.
PhysicalConstants/PhysicalConstants_init Initializes the Physical Constants Unit by loading all constants. This routine is called by Driver/Driver_initFlash and must be called before the first invocation of PhysicalConstants_get. In general, the user does not need to invoke this call.
PhysicalConstants/PhysicalConstants_list Lists the available physical constants in a snappy table.
PhysicalConstants/PhysicalConstants_listUnits Lists all the units available for optional conversion.
PhysicalConstants/PhysicalConstants_unitTest Lists all physical constants and units, and tests the unit conversion routines.

The header file PhysicalConstants.h must be included in the calling routine due to the optional arguments of PhysicalConstants_get.

Unit Test

The PhysicalConstants unit test PhysicalConstants/PhysicalConstants_unitTest is a simple exercise of the functionality in the unit. It does not require time stepping or the grid. “Correct” usage is indicated, as is erroneous usage.