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Thank you, Jeremy. This makes sense. I have submitted all the data.
CG Dra has an interesting curve at quiescence today. Assuming I interpret this correctly, the bright spot ingress begins at 59747.95, but then it gets temporarily dimmed by ~ 0.1 mag at 59747.99, then returns back to the normal brightness, followed by the “main” eclipse event at 59748.00, which is, I assume the eclipse of the accretion disk and/or the bright spot. What is also interesting is the brief ~ 0.1 mag dimming at 59748.06 after the egress, although this could be an artifact. I assume the dips are flickering events.
Max
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Poor seeing, but interesting data nevertheless. CG Dra on the rise. Broad U-shaped eclipse, profile similar to that in quiescence 2 days ago. I guess the broad component is the disc. Egress still at a lower magnitude than ingress, so bright spot still observable. Although the eclipse depth is about the same, the profile is different from the eclipse of, say, May 28th at quiescence where we saw a bright spot followed by a V-shaped dip to ~17.1 mag. Does this mean the bright spot changed its position and is now eclipsed for a longer duration?
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CG Dra in outburst. Good quality data today with two eclipses visible. Eclipse profiles are now narrower, some asymmetricity, but not as pronounced as before. The bright spot orbital hump is barely visible, if at all. I assume the accretion disk is now fully lit in the outburst and is now as bright as the bright spot itself, so we do not see a pronounced ingress orbital hump anymore, and the profile appears to be corresponding to the eclipse of the disk, somewhat similar to that during the outburst of June 11th.
Max
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CG Dra fading, right after outburst. Good quality data. The eclipse profile is back to V-shape with gentle egress. Mild bright spot hump – I assume the accretion disk is still contributing to the overall brightness immediately after the outburst. Initially I thought that the eclipse profile change may be correlated with outbursts, as EX Dra, for example, shows V-shaped eclipses on the rise and during its outburst stages, but its eclipses become U-shaped on the decline and during the quiescence. But this is not the case with CG Dra, as we have seen very prominent V-shaped eclipse with pronounced bright spot orbital hump on May 28th. My quiescence eclipse profile folder contains a wide variety of V and U shapes.
Max
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CG Dra Eclipse Zoo. First attempt at systematization. I see 7 eclipse profiles. Some may be artifacts. QROF on the right is whether profile has been seen in Quiescence, Rising, Outburst and Fading stages.
Some comments:
1) What is the difference between Broad-U/N/A and U/N/A profiles? It looks like the width of the “U” shape signifies the size of the accretion disk, i.e. we are seeing larger accretion disk during the rise and the fade, and smaller disk during the quiescence. Could as well be a flickering artifact, i.e. this is a single profile type.
2) U/L/S profile is expected during the outburst and fading stages, with bright accretion disk and relatively dim “bright” spot with the lack of the orbital hump.
3) Why we see V/N/A profiles during outbursts? The light curve is supposed to be dominated by the accretion disk, and here we see bright spot during the outburst in an asymmetric profile, i.e. a mix of a bright spot and accretion disk eclipse. Is this expected for dwarf novae?
4) What is the difference between V/L/S and U/L/S states?
5) V/H/HA and Sharp-V/H/HA are expected near quiescence, as the flux is dominated by the compact bright spot in a highly asymmetric light curve, and we see a sharp eclipse of it.
Max
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CG Dra fading, pair of eclipses visible, medium quality data. The latter appears to be of U/N/A type – U-shaped, normal orbital hump height, asymmetric. The former eclipse was interrupted by clouds, so the shape is indistinguishable, filed it as ?/N/A. Both types expected during the fading stage.
I have also updated the eclipse type table. I have removed the Broad-U/N/A type, as it appears to be the same as U/N/A, measured eclipse widths – the differences appear to be insignificant. I am also beginning to suspect that U/N/A and V/N/A, and U/L/S and V/L/S represent the same events, except that V-shaped counterparts simply exhibit more flickering during the minima or it is simply a chance alignment of measurement points that produce the V shape. I will leave them as separate types for now, but they are probably candidates for merger.
This data also uses new calibration files, had to redo everything for -15C Moravian C3-61000 main sensor cooling, as the -20C setpoint was pushing the coolers way too much – it’s pretty warm in Sierra del Segura mountains even during the night time. I was waiting to shoot flats for a few weeks. We should have gone for the enhanced cooling option, but we’ll live with -15C for now.
Max
CG Dra in quiescence. Looks like a U/N/A type eclipse of accretion disk and a bright spot.
Max
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Introduction
It is always interesting – what other information can we exctract from the light curve and available data? How CG Draconis looks like? What happens there and what’s the deal with out of phase components and impossible orbital configuration? It turns out, the disc instability model provides us with a way to visualize this engimatic star.
Thanks to Jeremy Shears from the British Astronomy Association, I’ve got myself a copy of the “Cataclysmic Variable Stars” by Hellier (2001). This book provides fantastic encyclopaedic review of these stellar systems, including dwarf novae. It showcases an argument put forward by Osaki (1974) to support the disc instability model – back when researchers still weren’t sure if the outbursts are actually caused by changes in mass transfer rates from the secondary star or due to something going on in the accretion disc around the white dwarf.
Basically, the premise of the model lies in that the secondary star donates material which overfills its Roche lobe and then falls onto the accretion disc around the white dwarf, creating so called bright spot (sometimes called the hot spot.) The flow of the material is constant. Viscuous forces in the accretion disc limit the flow: if a critical mass is reached, the disc becomes unstable and more viscious. This increases the accretion rate on the white dwarf rapidly and produces the outburst. Once the increased flow is accreted and processed in the outburst, the system fades back into the quiescent state, material begins to build up in the disc again, and the cycle repeats.
Now, to illustrate that this model is actually preferrable to the secondary star instability hypothesis, Osaki offers us a quantitative check. Imagine the red dwarf secondary feeding material. The material builds up in the accretion disc, then it dumps onto the white dwarf, producing the outburst. We have two accretion flows here – on the disc, regulating the luminosity of the bright spot as:
Lspot ~ G * M / r * Q_disc, (1)
where Lspot is the luminosity of the bright spot, M is the mass of the white dwarf, r is the distance of the bright spot from the white dwarf, and Q_disc is the mass accumulation rate. And, then, the second flow when all this mass excess is dumped on the white dwarf:
Lmax = G * M * Q_wd / R, (2)
where Lmax is the luminosity of the system during the outburst, Q_wd is the accretion rate on the white dwarf and R is the radius of the white dwarf. Assuming that no material leaves the system, Osaki establishes the relationship between these flows, so that:
Q_wd / Q_disc ~ tau_R / tau_outburst (3)
where tau and tau_outburst are the period and the duration of the outburst respectively. Combining all the above equations, we get:
Lmax / Lspot ~ r / R * ( tau / tau_outburst ), (4)
…
Hence, in order to measure the distance of the bright spot from the white dwarf, r, the only missing component we need is the white dwarf’s radius. Webbink (1990) comes to help. He provides average mass of the primary, 0.91 +/- 0.08, measured for 21 dwarf novae with orbital period P > 2.4 h, which appears to be a rather tight range for our purpose. We can then convert the average mass of the white dwarf to the average radius, R, we can use, using the known white dwarf mass-radius relationship from Hellier (2001):
R = 0.779 ( M ^ ( 2 / 3 ) – M ^ ( 2/3 ) ) ^ ( 1 / 2 ) * 10 ^ 7 m (5)
Measuring CG Dra Bright Spot Distance
Measuring the shoulder of the bright spot, converting magnitudes to linear fluxes (obtaining both L), using the average R from above, and tau taken from the light curve, we can begin plugging some numbers… With the last observed U/N/A-type eclipse (sorry, this is my own nomenclature, means U-shaped, normal orbital hump and asymmetric profile, improvement suggestions are welcome) typically observed at quiescence, I get r = 2.77 x 10^9 cm, or about 0.04 solar radii. Not sure what helps to visualize this – this is about 4.36 Earth radii – that’s the distance of the point on the accretion disc from the white dwarf where the flow from the secondary star lands to.
What is great is that we can measure this length in the radii of the primary star – the white dwarf itself, so the unknown r cancels itself out. This gets us the distance from the bright spot to the white dwarf at 4.52 white dwarf radii at CG Dra quiescence. With this type of the eclipse the contribution of the bright spot is approximately 20% of the total light of CG Dra.
Repeating the same exercise for the Sharp-V/H/HA-type eclipse, also at quiescence, I get 5.43 white dwarf radii, and also about 20% contribution by the bright spot to the total light. If we search dwarf novae visualizations, this looks about right.
For the CG Dra outburst state, I took the V/L/S-type eclipse – V-shaped, low hump, symmetric. The contribution of the spot is only 5% now, as it is outshone by the accretion disc. Plugging the numbers, the bright spot is at the 9.11 white dwarf radii now. Assuming that the bright spot is located somewhere at the edge of the accretion disc, this means the disc grows about twice in size during the outburst. This is in line with the disc instability model, and also looks similar to how the accretion discs are known to behave in dwarf novae, e.g. EX Dra.
Next Steps
All the derived numbers are rough, as I have determined measurement points visually at different phases of the system, and there are myriads of assumptions, but should be a good starting point. I need to implement and standardize routines to determine bright spot ingress and peak points and averaging procedures. And, of course, all this completely ignores the engima of the secondary star in CG Dra and assumes we are dealing with a normal dwarf nova.
REFERENCES
Hellier, C. 2001, in Cataclysmic Variable Stars, Springer-Praxis
Osaki, Y. 1974, PASJ, 26, 429
Webbink, R. F. 1990, in Accretion-Powered Compact Binaries, ed. C. W. Mauche, Cambridge University PressThis is 24th eclipse of CG Dra observed at quiescent state. Good quality data with check star sigma = 0.04 despite being pretty dim. A hole near the start of the session was due to the ACP observatory crash, for some reason the software just dies in the middle sometimes with nothing in the logs.
Flickering is on the order of 0.01 mag, characteristic for the system, continuing into the minima and present on the whole duration of the curve tonight.
The bright spot rotates into view raising the magnitude from ~ 16.82 to 16.72 peak, amplitude of ~ 0.1 mag. The bright spot contributes approximately 10% of the total luminosity of the system.
The eclipse is V-shaped, likely due to the presence of flickering at the minimum. Ignoring the flickering, I think the minimum can be placed at 17.02 mag. The shape is asymmetric due to the bright spot, hence, the eclipse is of type V/N/A which is the second of this type observed at quiescence. This is expected.
There is an unusual 0.16 mag increase of flux on the egress, followed by a sudden drop to the expected curve.
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That post egress brightening and subsequent drop is most intriguing Max. Testament to the high quality of your data
Thank you, Jeremy. Does this signify anything? I wonder if this is the bright spot peaking from the other side of the eclipse, or, perhaps, an overflow? Does the accretion disk size look alright for low-amplitude DN systems like this one?
Eclipses No(s): 25, 26
State: Quiescent
Data Quality: Good (check star sigma = 0.041)CG Dra keeps surprising. We see a pair of eclipses, on a single night, with quite different profiles. The time between the eclipses is about 4 hours, so the system is so active that significant changes can be observed in such a short period of time.
Eclipses are of type U/N/A (first) and V/N/A (second), which is typical for CG Dra. The minima appear to be V-shaped in the former, and U-shaped in the latter eclipse. I guess the shape appears different due to the flickering and chance alignment of measurement points, the orbital alignment of both events should be similar. Flickering amplitude appears to be 0.5 to 1 mag. I think the shape difference can be ignored, but look at the slope of the ingress curves!
There is now a dashed red line that shows the light curve smoothed with the Gaussian filter. Although I didn’t get the early phase of the bright spot appearance in the first eclipse, it should be similar to that of the second, at 16.86 mag. The first bright spot peaks at 16.77 mag and has the amplitude of 0.09 mag. The second bright spot peaks at 16.78, so the amplitude is 0.08 mag. So as both spots have about the same amplitude, why the ingress curve in the second eclipse is steeper, and why the eclipse itself is deeper? The minimum of the first eclipse is at 16.94 mag, while the second is 16.98 mag. My guess it is again due to the flickering.
Note, also, ~ 0.08 mag temporary brightening on the egress of the first eclipse, with gradual return to the normal curve, although this time there is no plateau like yesterday. Similar temporary brightening event is observed later between the eclipses.
There is a smooth brightening curve in the middle-left portion of the chart after the first egress. I wonder if this is the relection effect from the red dwarf.
There appears to be a standstill on the egress of the second eclipse. This corresponds to a compact bright spot according to Cook & Warner (1984), although again I could be imagining things due to the high amount of flickering present.
Max
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Eclipses No(s): 27, 28
State: Quiescent
Data Quality: Good (check star sigma = 0.045)Holy cow. What’s going on here? I thought there was something wrong with my telescope.
How do you measure the bright spot here? I assume the quiescence is somewhere in the middle of the chart, at 16.89 mag, and the bright spot before the second eclipse pushes it all the way up to 16.75 mag – an amplitude of 0.14 mag. Note two-step increase in brightness in the orbital hump – first to 16.85 mag, then the second one to 16.89 mag.
The profile is a new type, U/H/A, never seen before. It is similar to U/L/S, except that here we see a very prominent bright spot.
Lots of flickering – at the bright spot apperance, orbital hump, at the minimum, and the egress. Note the post-egress 0.05 mag dip, then sudden rise of 0.1 mag, then ~ 0.5 mag dip. Flickering? I don’t think so. Exactly the same structure is visible in both eclipses tonight. Is this the second bright spot or, perhaps, stream overflow? Could the second bright spot/stream explain the 2-step rise, and the post-egress hump?
LOTS of questions.
Max
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Eclipses No(s): 27, 28
State: Quiescent
Data Quality: Good (check star sigma = 0.045)Holy cow. What’s going on here? I thought there was something wrong with my telescope.
How do you measure the bright spot here? I assume the quiescence is somewhere in the middle of the chart, at 16.89 mag, and the bright spot before the second eclipse pushes it all the way up to 16.75 mag – an amplitude of 0.14 mag. Note two-step increase in brightness in the orbital hump – first to 16.85 mag, then the second one to 16.89 mag.
The profile is a new type, U/H/A, never seen before. It is similar to U/L/S, except that here we see a very prominent bright spot.
Lots of flickering – at the bright spot apperance, orbital hump, at the minimum, and the egress. Note the post-egress 0.05 mag dip, then sudden rise of 0.1 mag, then ~ 0.5 mag dip. Flickering? I don’t think so. Exactly the same structure is visible in both eclipses tonight. Is this the second bright spot or, perhaps, stream overflow? Could the second bright spot/stream explain the 2-step rise, and the post-egress hump?
LOTS of questions.
Max
I have been following this thread with interest and the quoted post, expressing a degree of incomprehension over the star’s behaviour, prompted me to contact an old friend, Phil Charles. Phil is a notionally retired but still very active professional astronomer who has specialized in the study of CVs of various types. He has given me permission to pass on his response.
Have to confess I’m not familiar with CG Dra, but that’s a very good light-curve for an almost 17th mag star (as expected for a 0.4m telescope in presumably a good site). It’s an eclipsing U Gem-type dwarf nova, here in quiescence, but I just looked at the AAVSO long-term light-curve and you can see that it outbursts quite frequently. That means it will be undergoing continuous mass transfer from the donor into the disc, and that displays itself as enhanced light when viewing either side of eclipse by the donor. In fact the hump here is quite broad, so it’s definitely an active system, and it’s clearly growing the disc in preparation for its next outburst.
Given the obvious data noise that is also visible in the comparison star, my reaction is that there’s nothing that unusual here. Let me know if you think I’ve missed anything.
Paul, thank you very much for sharing this. Glad this is of interest. And Phil was right – CG Dra went into outburst the following day. I couldn’t capture the whole night as ACP crashed, but here’s the curve from tonight, 28th.
Eclipses No(s): 29,30
State: Rising
Data Quality: Very good (check star sigma = 0.022)Two U-shape/Low hump/Symmetric (U/L/S) eclipses, expected at this state. Bright spot ~ 0.08 mag amplitude – close to normal asymmetric eclipse mode, but this signifies the accretion disk is getting brighter. Mild flickering throughout, although there’s a prominent small hump at the minimum – likely the flickering source is not eclipsed – inner accretion disk or bright spot extending? Some egress standstill on the first eclipse.
Max
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You’re welcome.
Now wondering if that sort of very detailed TS photometry could be used to predict the time of an imminent outburst perhaps to within a few hours. I doubt many people have tried to do it before.
Paul, I wonder if we can use the size of the accretion disk to predict outbursts – something to look into.
Eclipses No(s): 31, 32
State: Outburst
Data Quality: Very good (check star sigma = 0.025)Expected symmetric eclipses with low orbital hump – the accretion disk is now as bright as the bright spot, concealing it almost completely.
The first eclipse appears to be V-shaped (V/L/S) with standstill on egress, signifying compact bright spot. The second eclipse appears to be U-shaped (U/L/S) without standstill – amazing the amount of changes seen in just 4 hours.
The character of flickering has changed, especially during the second eclipse. Note how smooth the minimum in the second eclipse is. This is not usually seen in quiescent eclipses where bright spot flickering is prominent during the minima.
Max
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I think the long term light curve covering multiple outbursts will be a good probe of how the AD changes, especially at the beginning of an outburst. That is the advantage of studying a system that outbursts so often. I say “outburst”, although it is by no means clear these are traditional DN outbursts (they are quite small and their profile is different).
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