# Symbolic Units¶

This section describes yt’s symbolic unit capabilities. This is provided as quick introduction for those who are already familiar with yt but want to learn more about the unit system. Please see General Data Analysis and Visualizing Data for more detail about querying, analyzing, and visualizing data in yt.

Originally the unit system was a part of yt proper but since the yt 4.0 release, the unit system has been split off into its own library, unyt.

For a detailed discussion of how to use unyt, we suggest taking a look at the unyt documentation available at https://unyt.readthedocs.io/, however yt adds additional capabilities above and beyond what is provided by unyt alone, we describe those capabilities below.

## Selecting data from a data object¶

The data returned by yt will have units attached to it. For example, let’s query a data object for the ('gas', 'density') field:

>>> import yt
>>> dd = ds.all_data()
>>> dd['gas', 'density']
unyt_array([4.92775113e-31, 4.94005233e-31, 4.93824694e-31, ...,
1.12879234e-25, 1.59561490e-25, 1.09824903e-24], 'g/cm**3')


We can see how we get back a unyt_array instance. A unyt_array is a subclass of NumPy’s NDarray type that has units attached to it:

>>> dd['gas', 'density'].units
g/cm**3


It is straightforward to convert data to different units:

>>> dd['gas', 'density'].to('Msun/kpc**3')
unyt_array([7.28103608e+00, 7.29921182e+00, 7.29654424e+00, ...,
1.66785569e+06, 2.35761291e+06, 1.62272618e+07], 'Msun/kpc**3')


For more details about working with unyt_array, see the the documentation for unyt.

## Applying Units to Data¶

A unyt_array can be created from a list, tuple, or NumPy array using multiplication with a Unit object. For convenience, each yt dataset has a units attribute one can use to obtain unit objects for this purpose:

>>> data = np.random.random((100, 100))
>>> data_with_units = data * ds.units.gram


All units known to the dataset will be available via ds.units, including code units and comoving units.

## Derived Field Units¶

Special care often needs to be taken to ensure the result of a derived field will come out in the correct units. The yt unit system will double-check for you to make sure you are not accidentally making a unit conversion mistake. To see what that means in practice, let’s define a derived field corresponding to the square root of the gas density:

>>> import yt
>>> import numpy as np

>>> def root_density(field, data):
...     return np.sqrt(data['gas', 'density'])

>>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030')

>>> ds.add_field(("gas", "root_density"), units="(g/cm**3)**(1/2)",
...              function=root_density, sampling_type='cell')

>>> ad = ds.all_data()
unyt_array([7.01979425e-16, 7.02855059e-16, 7.02726614e-16, ...,
3.35975050e-13, 3.99451486e-13, 1.04797377e-12], 'sqrt(g)/cm**(3/2)')


No special unit logic needs to happen inside of the function: the result of np.sqrt will have the correct units:

>>> np.sqrt(ad['gas', 'density'])
unyt_array([7.01979425e-16, 7.02855059e-16, 7.02726614e-16, ...,
3.35975050e-13, 3.99451486e-13, 1.04797377e-12], 'sqrt(g)/cm**(3/2)')


One could also specify any other units that have dimensions of square root of density and yt would automatically convert the return value of the field function to the specified units. An error would be raised if the units are not dimensionally equivalent to the return value of the field function.

## Code Units¶

All yt datasets are associated with a “code” unit system that corresponds to whatever unit system the data is represented in on-disk. Let’s take a look at the data in an Enzo simulation, specifically the ("enzo", "Density") field:

>>> import yt
unyt_array([6.74992726e-02, 6.12111635e-02, 8.92988636e-02, ...,
9.09875931e+01, 5.66932465e+01, 4.27780263e+01], 'code_mass/code_length**3')


we see we get back data from yt in units of code_mass/code_length**3. This is the density unit formed out of the base units of mass and length in the internal unit system in the simulation. We can see the values of these units by looking at the length_unit and mass_unit attributes of the dataset object:

>>> ds.length_unit
unyt_quantity(128, 'Mpccm/h')
>>> ds.mass_unit
unyt_quantity(4.89045159e+50, 'g')


And we can see that both of these have values of 1 in the code unit system.

>>> ds.length_unit.to('code_length')
unyt_quantity(1., 'code_length')
>>> ds.mass_unit.to('code_mass')
unyt_quantity(1., 'code_mass')


In addition to length_unit and mass_unit, there are also time_unit, velocity_unit, and magnetic_unit attributes for this dataset. Some frontends also define a density_unit, pressure_unit, temperature_unit, and specific_energy attribute. If these are not defined then the corresponding unit is calculated from the base length, mass, and time unit. Each of these attributes corresponds to a unit in the code unit system:

>>> [un for un in dir(ds.units) if un.startswith('code')]
['code_density',
'code_length',
'code_magnetic',
'code_mass',
'code_metallicity',
'code_pressure',
'code_specific_energy',
'code_temperature',
'code_time',
'code_velocity']


You can use these unit names to convert arbitrary data into a dataset’s code unit system:

>>> u = ds.units
>>> data = 10**-30 * u.g / u.cm**3
>>> data.to('code_density')
unyt_quantity(0.36217187, 'code_density')


Note how in this example we used ds.units instead of the top-level unyt namespace or yt.units. This is because the units from ds.units know about the dataset’s code unit system and can convert data into it. Unit objects from unyt or yt.units will not know about any particular dataset’s unit system.

## Comoving units for Cosmological Simulations¶

The length unit of the dataset I used above uses a cosmological unit:

>>> print(ds.length_unit)
128 Mpccm/h


In English, this says that the length unit is 128 megaparsecs in the comoving frame, scaled as if the hubble constant were 100 km/s/Mpc. Although $$h$$ isn’t really a unit, yt treats it as one for the purposes of the unit system.

As an aside, Darren Croton’s research note on the history, use, and interpretation of $$h$$ as it appears in the astronomical literature is pretty much required reading for anyone who has to deal with factors of $$h$$ every now and then.

In yt, comoving length unit symbols are named following the pattern < length unit >cm, i.e. pccm for comoving parsec or mcm for a comoving meter. A comoving length unit is different from the normal length unit by a factor of $$(1+z)$$:

>>> u = ds.units
>>> print((1*u.Mpccm)/(1*u.Mpc))
0.9986088499304777 dimensionless
>>> 1 / (1 + ds.current_redshift)
0.9986088499304776


As we saw before, h is treated like any other unit symbol. It has dimensionless units, just like a scalar:

>>> (1*u.Mpc)/(1*u.Mpc/u.h)
unyt_quantity(0.71, '(dimensionless)')
>>> ds.hubble_constant
0.71


Using parsec as an example,

• pc Proper parsecs, $$\rm{pc}$$.

• pccm Comoving parsecs, $$\rm{pc}/(1+z)$$.

• pccm/h Comoving parsecs normalized by the scaled hubble constant, $$\rm{pc}/h/(1+z)$$.

• pc/h Proper parsecs, normalized by the scaled hubble constant, $$\rm{pc}/h$$.

## Overriding Code Unit Definitions¶

On occasion, you might have a dataset for a supported frontend that does not have the conversions to code units accessible or you may want to change them outright. yt provides a mechanism so that one may provide their own code unit definitions to yt.load, which override the default rules for a given frontend for defining code units.

This is provided through the units_override argument to yt.load. We’ll use an example of an Athena dataset. First, a call to yt.load without units_override:

>>> ds = yt.load("MHDSloshing/virgo_low_res.0054.vtk")
>>> ds.length_unit
unyt_quantity(1., 'cm')
>>> ds.mass_unit
unyt_quantity(1., 'g')
>>> ds.time_unit
unyt_quantity(1., 's')
>>> sp1 = ds1.sphere("c", (0.1, "unitary"))
>>> print(sp1["gas", "density"])
[0.05134981 0.05134912 0.05109047 ... 0.14608461 0.14489453 0.14385277] g/cm**3


This particular simulation is of a galaxy cluster merger so these density values are way, way too high. This is happening because Athena does not encode any information about the unit system used in the simulation or the output data, so yt cannot infer that information and must make an educated guess. In this case it incorrectly assumes the data are in CGS units.

However, we know a priori what the unit system should be, and we can supply a units_override dictionary to yt.load to override the incorrect assumptions yt is making about this dataset. Let’s define:

>>> units_override = {"length_unit": (1.0, "Mpc"),
...                   "time_unit": (1.0, "Myr"),
...                   "mass_unit": (1.0e14, "Msun")}


The units_override dictionary can take the following keys:

• length_unit

• time_unit

• mass_unit

• magnetic_unit

• temperature_unit

and the associated values can be (value, "unit") tuples, unyt_quantity instances, or floats (in the latter case they are assumed to have the corresponding cgs unit). Now let’s reload the dataset using our units_override dict:

>>> ds = yt.load("MHDSloshing/virgo_low_res.0054.vtk",
...              units_override=units_override)
>>> sp = ds.sphere("c",(0.1,"unitary"))
>>> print(sp["gas", "density"])
[3.47531683e-28 3.47527018e-28 3.45776515e-28 ... 9.88689766e-28
9.80635384e-28 9.73584863e-28] g/cm**3


and we see how the data now have much more sensible values for a galaxy cluster merge simulation.

## Comparing Units From Different Simulations¶

The code units from different simulations will have different conversions to physical coordinates. This can get confusing when working with data from more than one simulation or from a single simulation where the units change with time.

As an example, let’s load up two enzo datasets from different redshifts in the same cosmology simulation, one from high redshift:

>>> ds1 = yt.load('Enzo_64/DD0002/data0002')
>>> ds1.current_redshift
7.8843748886903
>>> ds1.length_unit
unyt_quantity(128, 'Mpccm/h')
>>> ds1.length_unit.in_cgs()
unyt_quantity(6.26145538e+25, 'cm')


And another from low redshift:

>>> ds2 = yt.load('Enzo_64/DD0043/data0043')
>>> ds2.current_redshift
0.0013930880640796
>>> ds2.length_unit
unyt_quantity(128, 'Mpccm/h')
>>> ds2.length_unit.in_cgs()
unyt_quantity(5.55517285e+26, 'cm')


Now despite the fact that 'Mpccm/h' means different things for the two datasets, it’s still a well-defined operation to take the ratio of the two length units:

>>> ds2.length_unit / ds1.length_unit
unyt_quantity(8.87201539, '(dimensionless)')


Because code units and comoving units are defined relative to a physical unit system, unyt is able to give the correct answer here. So long as the result comes out dimensionless or in a physical unit then the answer will be well-defined. However, if we want the answer to come out in the internal units of one particular dataset, additional care must be taken. For an example where this might be an issue, let’s try to compute the sum of two comoving distances from each simulation:

>>> d1 = 12 * ds1.units.Mpccm
>>> d2 = 12 * ds2.units.Mpccm
>>> d1 + d2
unyt_quantity(118.46418468, 'Mpccm')
>>> d2 + d1
unyt_quantity(13.35256754, 'Mpccm')


So this is definitely weird - addition appears to not be associative anymore! However, both answers are correct, the confusion is arising because "Mpccm" is ambiguous in these expressions. In situations like this, unyt will use the definition for units from the leftmost term in an expression, so the first example is returning data in high-redshift comoving megaparsecs, while the second example returns data in low-redshift comoving megaparsecs.

Wherever possible it’s best to do calculations in physical units when working with more than one dataset. If you need to use comoving units or code units then extra care must be taken in your code to avoid ambiguity.