There is no equilux

I learned a new word recently… sort of. An equilux is a day on which the durations of daylight and night are exactly equal. Contrast this with the more familiar equinox, or the time at which the center of the Sun passes through the Earth’s equatorial plane, so that the Sun is directly above the Earth’s equator. (If anyone is checking, the official definition of the equinox is slightly different than this, for technical reasons that we don’t really care about here.)

There are two equinoxes each year; for example, this coming year the first equinox of 2022 is on 20 March, at about 15:33:25 UTC, marking the unofficial start of spring in the northern hemisphere (or fall in the southern hemisphere).

We think of an equinox as also being the time at which there are roughly equal periods of daylight and darkness. The Wikipedia page linked above does a good job of explaining why this isn’t quite true: the Sun appears as not just a point but a disk, a sliver of which becomes visible at sunrise well before the center of the Sun appears above the horizon, and similarly a sliver remains visible in the evening after the center has dipped back below the horizon again.

Thus, even on the equinox, the day is slightly longer than the night. So, when is the “equilux,” where these periods of day and night are truly equal?

To see why this is tricky to answer, consider the figure below, showing the changes in length of day and night over the course of the coming year in the Washington, D.C., area:

Length of day and night in Washington, D.C., over the course of the year 2022. The inset is a zoomed-in view of the week near the spring equinox on 20 March.

This winter, the nights (shown in blue) are much longer than the days (shown in red). But over the next few months, the nights get shorter and the days get longer… until the middle of March, when we start to see more daylight hours than nighttime. This “crossing” happens around 16 March (see the zoomed-in view in the inset), when we see almost exactly 12 hours (plus a few seconds) of night beginning at sunset that evening, followed by about 12 hours– plus almost a full minute— of daylight on 17 March.

The motivation for this post is to observe that (1) this is still not exactly equal periods of daylight and darkness, still differing by nearly a minute; and that (2) such an exact equilux will almost surely never occur. An equinox is a precise instant in time– and the same instant independent of observer location on the Earth– that we can in principle measure as accurately as we wish. But an equilux, on the other hand, is two consecutive intervals of time, whose lengths are varying over the weeks surrounding the equinox by several minutes per day. Hoping that those lengths will meet in the middle exactly is hoping for a measure zero event.

Having said that, we can relax our definition somewhat, and consider when periods of daylight and darkness are “most closely equal,” minimizing the absolute difference between consecutive intervals as we did above. Things are still pretty unpleasant, for a couple of reasons. First, the times, and thus durations, of daylight and darkness depend on the location of the observer. The calculations and figure above are unique to Washington, D.C.; if we instead consider southern Virginia (or Oklahoma, or most of California), the nearest equilux is earlier, consisting of the daylight hours of 16 March followed by that night, as shown in the figure below.

Date of (spring) equilux across the globe. Equilux is earlier than the spring equinox (20 March) in the northern hemisphere, later in the southern hemisphere. Lighter colors indicate the equilux starts with daytime (sunrise to sunset) of the indicated date, followed by nighttime; darker colors indicate starting with evening of the date, followed by daytime of the following day.

I struggled a bit to make this figure clear and informative at the same time. In the northern hemisphere, the spring equilux is before the 20 March equinox, by a number of days indicated by the color. For the southern hemisphere, I “re-used” the same color palette, indicating the number of days after the equinox that the equilux occurs. In either case, the lighter color indicates starting with daytime (sunrise to sunset) of the indicated date, followed by the roughly equal nighttime; the darker color indicates that the equilux starts with evening of the indicated date, followed by daytime of the following day.

The light purple and green bands near the equator more coarsely indicate equiluxes that are more than a week before or after the equinox, respectively. Which brings us to the second problem with everything we’ve done so far: an equilux depends on how we choose to define the transition between what we consider “daylight” versus “darkness.” The sunrise and sunset used above are defined as the times when the center of the Sun’s disk is 50 arcminutes below the horizon. It’s arguably way too light at these times to call them a transition to or from “darkness.” A more reasonable transition would be at least “dawn” and “dusk,” defined as civil twilight (6 degrees below the horizon), if not nautical or even astronomical twilight (12 or 18 degrees, respectively). The figure below compares the sunrise/sunset equilux (shown in red) with the dawn/dusk civil twilight assumption (shown in blue), as a function of the observer’s latitude.

Date of equilux vs. observer latitude, assuming “day/night” transitions at sunrise/sunset (in red) or dawn/dusk twilight (in blue). The equinox on 20 March is shown in black for reference.

So, depending on how dark we think it needs to be to qualify as “not daylight,” the spring equilux in the mid-northern latitudes where I live could be as late as a few days before the equinox, or as early as mid-February. And however we choose to define it, the duration of daylight and darkness will still differ by a minute or three.