A century of the same answer
Taking noon in each year, the solar longitude on this date has ranged over a little more than a degree in a hundred and six years. Put another way, someone born on 2 February 1930 and someone born on 2 February 2035 have their Suns within a degree and a half of each other.
That is not what most people assume. The common expectation is that dates slide about, which is why sign date ranges differ between sources. The sliding is real but small, and it only shows up at the boundaries where a small shift crosses a line.
Why the calendar holds the orbit in place
The Earth takes about 365.2422 days to go round the Sun. A calendar of 365 days therefore falls behind by roughly a quarter of a day each year, and the Sun appears about six hours further along on any given date. After three such years the accumulated error is close to a full day, and the leap day removes it.
The correction is slightly too generous, which is why century years are usually not leap years. What remains after all of that is a drift of about a degree per century, and that drift is precisely the width of the range above. The calendar and the orbit stay in step by design, and a fixed date keeps returning to nearly the same point.
One consequence is that the sign date ranges printed in newspapers are not wrong so much as rounded. A range like 20 January to 18 February is an average of boundaries that move by roughly a day. For any date more than a day or two inside the range, the rounding never matters.
What sits at thirteen degrees of Aquarius
Thirteen degrees falls in the second decan, the ten degree band running from ten to twenty. Its Chaldean ruler is Mercury, and the triplicity scheme assigns it to Gemini, which is also Mercury's. The sign around it is Aquarius, fixed air, ruled by Saturn in the traditional scheme and by Uranus in the modern one.
Tradition reads the Aquarius Sun as observational and committed to a principle, and the Mercury decan as adding articulation to that. Those are interpretations the tradition carries, and they are set out here as tradition rather than as findings.
A degree is also the unit aspects are measured in, so the figure is not only a label. A Sun at thirteen degrees of Aquarius makes exact contacts with anything near thirteen degrees of the other signs, and that is where the number starts doing work beyond naming a decan.
The rest of the chart moves freely
The stability of the Sun on this date is not shared by anything else. The Moon covers a sign in about two and a half days, so across years it has been everywhere, and within a year it can shift sign during the day. The Ascendant runs through all twelve signs between one midnight and the next, so it is set by your minute of birth and by how far from the equator you were born.
The widget above computes your own degree from your year, hour and birthplace and reports how far you sit from the nearest sign boundary. On 2 February that distance is large, so the answer is never in doubt.
It is also worth saying what stays fixed besides the Sun. The outer planets move slowly enough that their signs can be read from a date alone, and Jupiter and Saturn change sign only every year or few. The fast material, the Moon and the angles, is the part that needs your details.
Questions people ask about this
What sign is 2 February?
Aquarius, every year. The date sits roughly a fortnight past the Capricorn boundary and a fortnight before the Pisces one, so it is about as far from either as an Aquarius birthday can be.
What degree of Aquarius is 2 February?
About 12.5 to 13.9 degrees at noon, taken across 1930 to 2035. The widget above narrows that to a single figure using your year, hour and birthplace.
Why is the range so narrow across a century?
Because the leap year rule was built to keep the calendar aligned with the orbit. The Sun slips about six hours later each ordinary year and the leap day returns it, leaving only about a degree of drift per century.
Does the drift ever change my sign?
Only for dates that sit within a day or so of a sign boundary. This date is nowhere near one, so the drift shows up as a slightly different degree and nothing more.
Which decan and ruler apply here?
The second decan of Aquarius, ten to twenty degrees, ruled by Mercury in the Chaldean order and assigned to Gemini, and so again to Mercury, by the triplicity scheme.
Do I need a birth time on this date?
Not for the Sun or the decan, both of which are settled. You need one for the rising sign always, and usually for the Moon, which can change sign during the day.