OT J071126.0+440405 is a cataclysmic variable star located in Auriga (07h 11m 25.98s, +44d 04' 05.0").  This star has a temporary designation instead of a permanent one since it was discovered just a few years ago.  OT J071126.0+440405 is thought to be a type of cataclysmic variable called a Polar.  A Polar is a binary system consisting of a white dwarf and a M-type (red) dwarf star.  The more massive white dwarf draws matter from its companion.  In most CVs this matter stream forms an accretion disk around the white dwarf.  In a Polar type system, the white dwarf has a strong magnetic field that disrupts the formation of any accretion disk, funneling material instead directly onto the magnetic poles.  The interaction of the matter stream with the magnetic field causes the emitted light to be highly polarized, hence the name 'Polar".

Polars are similar to dwarf novae but don't have outbursts.  They instead slowly vary between high and low states.  When in a low state, OT J071126.0+440405 is usually magnitude 17V or 18V.  During a high state, this variable can be as bright as magnitude 13V.  OT J071126.0+440405 is also an eclipsing variable since the orbit of its two components is nearly edge-on as seen from Earth.  The eclipses occur every 117 minutes and are up to 5 magnitudes deep.  These eclipses provide a way to measure many properties of the binary system, including the relative sizes and separation of the stars, masses, and mass transfer rates.


Observations

During March and April of 2009, OT J071126.0+440405 was seen in a high state.  CCD time series imaging of this star was obtained during several nights during that time period using my 8" f/5 Newtonian (March 16) and the CVAS 16” f/7 Newtonian at Indian Hill Observatory (April 17 and 18).  Each time series used either 30 or 20 second exposures made with a ST-7XME and a Clear filter.  I performed differential photometry on these sets of images using two nearby comparison stars:

V MagRc MagR.A. (2000)Dec. (2000)
13.91813.57407h 11m 13.16s+44d 03' 59.6"
14.15813.62107h 11m 35.50s+44d 04' 03.2"

Since the ST-7XME + Clear filter has a response closer to Cousins R than Johnson V, the Rc magnitudes of the comparison stars were used for the plots below.  The comparison stars’ differential brightness (K-C) is plotted also to show that conditions were good during each time series.


OT J071126.0+440405 light curve

Figure 1.  Light curve of OT J071126.0+440405 made from 288 CCD images on the night of March 16, 2009.  Due to the faintness of the variable during eclipse and because an 8" telescope was used, the variable was not seen on images during each eclipse and there is a gap in the data during those times.  There is also a gap near 3:34 UT due to a need to reposition the telescope during the long time series.  Click on the image for a larger version.


OT J071126.0+440405 light curve

Figure 2.  Light curve from Figure 1 with a Rc zero point applied.  Because the variable was too faint to see on individual frames during eclipse, several images during eclipse were stacked to see if the variable could be detected.  On the combined image for the first eclipse, a faint image of the variable was seen and measured.  For the second eclipse, no image of the variable was seen.  Errors for most data points are +/- 0.05 magnitude, increasing to +/- 0.3 magnitude for mid-eclipse.  Click on the image for a larger version.


OT J071126.0+440405 light curve

Figure 3.  Light curve of OT J071126.0+440405 made from 130 CCD images on the night of April 17, 2009.  Click on the image for a larger version.


OT J071126.0+440405 light curve

Figure 4.  Light curve from Figure 3 with a Rc zero point applied.  Errors for most data points are +/- 0.03 magnitude, increasing to +/- 0.3 magnitude for mid-eclipse.  Click on the image for a larger version.


OT J071126.0+440405 light curve

Figure 5.  Light curve of OT J071126.0+440405 made from 188 CCD images on the night of April 18, 2009.  Click on the image for a larger version.


OT J071126.0+440405 light curve

Figure 6.  Light curve from Figure 5 with a Rc zero point applied.  Errors for most data points are +/- 0.03 magnitude, increasing to +/- 0.3 magnitude for mid-eclipse.  Click on the image for a larger version.


The light curve from March 16 covers about 1.5 orbits of the OT J071126.0+440405 system.  During this time, two eclipses are seen as well as a pre-eclipse dip before the first eclipse and no dip before the second eclipse.  The eclipses are just over 117 minutes apart.  There is also a broader, sinusoidal variation that repeats every orbit.  This variation peaks around the time of each eclipse and is at its faintest about half an orbit later.

The light curves from April 17 and 18 show the entirety of the main eclipse, which is 4.5 to 5 magnitudes deep.  The onset of each eclipse is rapid but the rate of fading then slows until the star reaches minimum light.  The recovery is very rapid, usually taking less than a minute to go from minimum to maximum light.  The entire eclipse lasts 8 minutes.  A fade of 1 to 1.5 magnitudes is also seen before both eclipses.  This fade lasts 5 to 7 minutes and occurs about 18 minutes before the main eclipse.


OT J071126.0+440405 eclipse

Figure 7.  Above is a frame from a time-lapse animation of the eclipse that was imaged on April 18, 2009.   Click on the image to view the animation (7.6 MB).  This covers 27 minutes of time and shows the pre-eclipse dip and the main eclipse.  OT J071126.0+440405 is located just left of center and a magnitude 16.5V star lies just to the right and slightly above it.  The two comparison stars that where used for differential photometry are near the left (14.2V) and right (13.9V) edges of the cropped frame.  North is up.


Polars

To interpret the structure in the light curves, it is helpful to visualize what a typical Polar looks like.  Astronomers have studied dozens of Polars and have created models that best explain the variations in their light curves (see Figures 8, 9 and 10).  The standard model of a Polar has a M dwarf and white dwarf orbiting each other close enough that matter from the M dwarf is transferred to the more massive white dwarf.  This matter flows in a narrow accretion stream towards the white dwarf.  The accretion stream then encounters the white dwarf's strong magnetic field.  Matter in the stream becomes caught up in the magnetic field lines and follows them to the magnetic poles of the white dwarf.  Since the magnetic field lines converge on the poles, the matter is funneled onto them at very high velocities and pressures.  This results in a tremendous release of energy and light as well as copious amounts of X-rays.

In some models of Polars, the accretion stream is thought to split into two diverging streams as it first encounters the magnetic field of the white dwarf (see Figure 8).  These two narrow streams then follow the magnetic field lines to each pole.  However, other models suggest a more complex structure where the stream and magnetic field interact.  The density of matter in the stream probably varies.  Therefore, lower density matter will be diverted by the magnetic field sooner than higher density matter, which travels in a ballistic path farther around the white dwarf before being diverted by the magnetic field.  Thus the region where the accretion stream meets the magnetic field may resemble a curtain rather than a narrow stream.  Accretion curtains can be seen in Figures 10 and 11.

As mentioned above, the white dwarf's magnetic field acts like a funnel to focus the matter from the accretion stream or curtains onto a small area near each magnetic pole.  This "funnel" is also known as an accretion column.  Compressed matter flows through the accretion columns and onto the photosphere of the white dwarf.  The area where each accretion column meets the photosphere is called an accretion spot or hot spot.  The accretion spots are very small, only about 1% to 2% of the white dwarf's diameter.  The accretion columns and hot spots account for most of a Polar's light output.  In most Polars, one magnetic pole tilts towards the secondary star and most of the accreted matter flows towards that pole.  In that case, only one hot spot is usually seen.


polar

Figure 8.  Diagram of a Polar (courtesy of NASA).


polar

Figure 9.  Artist's concept of a Polar (courtesy of Russell Kightly Media).


polar

Figure 10.  Computer animation of a Polar (courtesy of OpenGL CV software).


In a Polar system, the light we see originates from the following sources (listed brightest to faintest):

  1. The accretion spot(s) near the white dwarf's pole(s) where the accretion stream contacts the white dwarf.
  2. The accretion stream (the curtain(s) and column(s) are the brightest parts of the stream).
  3. The white dwarf (primary).
  4. The M dwarf (secondary).

In an eclipsing Polar system, the main eclipses are caused by the secondary star covering the white dwarf and its associated accretion spot(s).


Discussion

Combining the results from all three nights allows for a better determination of the orbital period.  The data from March 16 indicates a period of 117.33 minutes (0.08148 days) between eclipses.  The data from April 17 and 18 indicates a period of 117.18 minutes (0.08138 days).  The difference between the two periods (0.15 minute) may not be significant given the errors associated with the timings.  The 117.18 minute period agrees best with what other observers have measured.

The 20 second exposures used on April 17 and 18 were not short enough to resolve the ingress and egress of each eclipse.  Especially with the egress, the star is very faint on one image and near full brightness on the next image.  This suggests that the actual duration of ingress/egress is considerably less than the length of the exposures.  (Indeed, other observers using larger telescopes and very fast exposure times have determined that ingress/egress each take about 1 second).  Although Polars can have two accretion spots (one near each magnetic pole), the lack of a step-like ingress/egress in the light curve implies that OT J071126.0+440405 has a single accretion spot.  The reason for having only one accretion spot could be that the magnetic field of the white dwarf tilts towards the secondary star, thus favoring the accretion of matter at mainly one pole instead of equally at both poles.

The sinusoidal variation seen on March 16 is most likely caused by the rotation of the white dwarf.  As the white dwarf rotates, the accretion spot is pointed towards us (just before and after the main eclipse).   About half a rotation later, the hot spot is pointed away from us and out of view behind the white dwarf.  Since the light curves show that the low point of the sinusoidal variation is about half a rotation from the main eclipses, this suggests that the accretion spot lies roughly along the line joining the white dwarf and the secondary.  This would be the case if the two stars are in synchronous rotation with each other.  A close look at the light curve shows that the low point of the sinusoidal variation is not exactly opposite the eclipses, but occurs 4 minutes earlier.  This implies that the accretion spot precedes the line between the white dwarf and secondary by about 13 degrees.

The light curves also suggest that the accretion stream is curved and precedes the secondary star.  The pre-eclipse dip is likely caused by the accretion stream eclipsing the accretion spot on the white dwarf.  If the accretion spot precedes the line between the white dwarf and secondary by about 13 degrees then it follows that the accretion stream is a curved line that precedes the secondary in its orbit.  The light curves also show an asymmetry during the later part of eclipse ingress.  The slower rate of fading then might be due to the secondary star gradually eclipsing the accretion stream after the ingress of the white dwarf.

The relative locations of the accretion spot and stream may vary with time.  Other observers have noted that the dip caused by the accretion stream was seen after the main eclipse.  Likewise, the accretion spot was seen to follow the line between the white dwarf and secondary by about 10 degrees.  The dip caused by the accretion stream is sometimes not seen (see the second eclipse in Figures 1 and 2), which suggests that the accretion stream either wanders a bit or sputters.

Some line drawings are shown in Figures 11a-d that illustrate what an eclipse of the OT J071126.0+440405 system might look like close-up as seen from the perspective of an Earth-based observer. 


polar eclipse

Figure 11a.  Illustration of the OT J071126.0+440405 system about 10 minutes before the start of the pre-eclipse fade caused by the accretion curtain.  Since this system has one dominant hot spot, only one accretion curtain and column are shown for clarity.  Main components are labeled.


polar eclipse

Figure 11b.  Illustration of the OT J071126.0+440405 system after the white dwarf has emerged from eclipse by the accretion curtain and just before the start of the main eclipse.


polar eclipse

Figure 11c.  Illustration of the OT J071126.0+440405 system just after the white dwarf has been eclipsed by the M dwarf.  The accretion stream and curtain will be eclipsed over the next few minutes.


polar eclipse

Figure 11d.  Illustration of the OT J071126.0+440405 system just after the white dwarf has emerged from eclipse by the M dwarf.  The leading edge (and brightest part) of the accretion curtain has also emerged at almost the same time as the white dwarf and hot spot.  This explains why the system brightens so rapidly at eclipse egress.


Summary

CCD time series imaging was performed on OT J071126.0+440405 on several nights in March and April of 2009.  The resulting light curves allowed several parameters of this Polar to be measured.  An orbital period of 117.18 minutes (0.08138 days) was measured.  Deep eclipses (~5 magnitudes) were observed with very rapid ingress/egress, which indicated that most of this system's light output was from a very compact source.  The accretion stream was indirectly detected both as it eclipsed the accretion hot spot near the white dwarf and as it was eclipsed by the secondary star.  The accretion stream was observed to vary in intensity and location.

OT J071126.0+440405 is an excellent example of a Polar and is very well placed for study during most of the year from the northern hemisphere.  Time series observations of eclipsing Polars such as this provide an effective method to measure many properties of these stars.  Parameters such as orbital period, relative sizes and orientations of the system components (primary, secondary, accretion stream and hot spots) and mass transfer (high/low states) can be determined.  Some of these parameters may change over time, so long-term study is warranted.  Ideally, any time series work should be done with large telescopes and high time resolution, but even modest amateur-sized telescopes can yield good results, especially when OT J071126.0+440405 is in a high state.


References

Thorne K., Garnavich P., Mohrig K., 2010, IBVS, 5923

O'Donoghue D., et al., 2006, MNRAS, 372, 151

AM Herculis - AAVSO page