This pulsating variable star does interest me and, as it is well observed, there are
aspects to its displayed behaviour that I find intriguing. I have discussed this star before but here I wanted to record some of the things I have said about it on the BAA discussion forum.
Firstly, on the 15th June 2022 I asked the following (under the title "What's happening to Z Ursae Majoris?"):-
"I am a new member of the BAA and new
to variable star observing. Like many others, I am sure, I have begun a
few observations of Z UMa and to find out a bit more about this star I
have been doing a bit of reading up. One of the most interesting papers
was by John Greaves in the VSS Circular 184
(pdf download). What got my attention was that over the last 50 years
or so John has determined that this star’s period of pulsation has been
changing. If I have got this right, based on BAA data prior to 1995
there were two contributing pulsation periods – one main one of 194.0
days and one less significant one of 204.8 days. After 1995 the period
has settled down to 189.0 days and there is no evidence for the less
significant period. What’s more after 2006 the visual magnitude range of
variations in this star has increased to about 2.8 magnitudes. John
concluded that the period and magnitude range change are making this
star more like a Mira variable rather than a semiregular.
So what is causing these changes? What
physical changes within the star are causing it to evolve? There is
another paper in the literature that I found Secular Evolution in Mira Variable Pulsations
which looked at the changes in the period of 547 Mira variables and for
about 10 percent of the sample statistically significant long-term
period changes were seen. Templeton and Mattei believe that changes
could be caused by thermal pulses (which I take it are caused by flashes
of nuclear burning in the core?). However, another possible reason that
they consider for evolutionary changes in the period is non-linear
behaviour in the physics of the pulsation mechanism.
I am interested to know what other
people understand about the evolution of these giant stars and whether
other semiregular stars are showing signs period change."
On the 3rd July 2022 I put up another post under the same topic heading:-
"Another aspect of the light curve of
this star that interested me was that from time-to-time the maxima
appear to be double peaked. This has been shown nicely by some recent
observations using CMOS detectors (see figure below which has been
produced from the BAA database). If you look at the light curve after
the 1st Jan 2022 you can see (green data points) that Z UMa reached a
maximum of about magnitude 6.6 around the 14th March, then it faded a
bit to about 7.7 around the 21st April before brightening again to about
magnitude 6.8 around the 22nd May (roughly 69 days from peak-to-peak).
The same double peak is seen in the visual data (black circles) but the
scatter in the CMOS data is much tighter. Looking back at the four
maxima prior to this the visual data (black circles) hint that this
double peaked behaviour has been been developing as time progresses.
If you go back further in time other
reasonably clear examples of a double peak can be seen in August 2016,
January 2008 to July 2009, January 1999, July 1999 and July 1995 (I
haven’t gone back further than this). So what is causing this? One
suggestion has been that this is due to the interaction of different
pulsation cycles within the star but this is not so easy to understand
if, as John Greaves says (see my first post), after 1995 there is
virtually only one pulsation period of 189 days. With more people
carrying out observations using more accurate electronic detectors it
will be interesting to see how often this double peaked behaviour
appears."
Finally, on the 31st March 2023 I added another item under this heading:-
"I was pleased to see that Z UMa has been highlighted in a recent facebook post.
I have added the light curve of this variable star from this post
below. As described, in the last year the maxima have become nicely
double peaked and it has been suggested that this is due to the
interaction of the two main periods of pulsation of this star. However,
how does this square with the analysis of John Greaves that after 1995
there is little evidence for two pulsation periods in the data (see my
earlier posts on this topic)?
I wondered if the timescales for the
evolution of the double peak fit in with the two periods of 194.0 and
204.8 days that John measured before 1995. If you imagine that the two
pulsation periods start out in phase, then after one period of each the
peak of the 194.0 day pulsation will be ahead of the 204.8 day pulsation
by 204.8 – 194.0 = 10.8 days. After n such periods, the shorter
pulsation would be ahead by n x 10.8 days. Looking at the light curve
for the star you can see that for the last double peak (September 2022
to November 2022) the two humps were separated by about 3 months or
roughly 60 days. This would seem to imply that the two periods would
have been in phase n = 60/10.8 ~ 6 periods earlier and this certainly
seems feasible looking at the light curve.
So how often would we expect double
peaks to be occurring if the two periods of 194.0 and 204.8 days
persist? The simple linear addition of two sine curves of the same
amplitude but different periods of A and B would result in another sine
curve of period 2AB/(A+B) which in this case would be 199.3 days but the
amplitude of this would be modulated by a cosine curve of 2AB/(A-B)
which is 7,358 days or about 20 years. However, a cosine curve passes
through zero twice every period, so the “beat” frequency is half this,
i.e. every 10 years. This is only a very rough guide because I am sure
that the behaviour is not linear but it seems reasonable given what I
said in my earlier posts about how often double peaks occur.
Interestingly, the amplitude of the light curve variations does decrease
as a double hump approaches.
What is says to me is that we really
need more accurate measurements of the light curve to better see what is
going on. Have the two pulsation periods begun to die out as John says
or are they being hidden in the noise of the data? Perhaps we need
regular digital detector monitoring over the next 20 or 30 years to
decide this. Anyone fancy this?"
All text and images © Duncan Hale-Sutton 2025 (except the images kindly provided by the BAA).
