Time domain astronomy and fastest eclipsing binary ZTF J1539+5027 (+20 mag, 6.91 minutes): How to measure its minimum brightness?

Question

Per Wikipedia's ZTF J153932.16+502738.8

ZTF J153932.16+502738.8 is a double binary white dwarf with an orbital period of just 6.91 minutes. [...] The light curve shows eclipses. One dip in the light curve is 15%, and the other is close to 100%.

Below is a light curve plotted on a linear scale in Fig. 1a of Burdge et al, (2019) General Relativistic Orbital Decay in a 7 Minute Orbital Period Eclipsing Binary System. The dip at 0 phase is deep.

A logarithmic magnitude scale might tend to show just how deep but noting that the minimum is dimmer than +21.5 mag and probably lasts only a tiny fraction of the orbital period (i.e. a few seconds) makes a good measurement of the minimum quite a challenge.

It seems to me like this might be a situation where a photomultiplier tube and photon counting might be competitive with photometry based on CCD imaging and clever readout schemes.

Questions:

1. What are the technical challenges to measuring the minimum brightness of this eclipsing pair?
2. If it could be measured, would such a result even be particularly useful in this case?

---

Figure 1: Lightcurve of ZTF J1539+5027 a) The binned CHIMERA g' lightcurve of ZTF J1539+5027, phase-folded on the 6.91 minute orbital period. At phase 0, the lightcurve exhibits a deep primary eclipse, indicating that the hot primary star is producing most of the observed light. Outside of eclipse, there is a quasi-sinusoidal modulation because the primary star heavily irradiates one side of its companion. At phases ±0.5, the secondary eclipse occurs as the hot primary transits the irradiated face of its companion. b) The phase-folded ZTF g-band lightcurve of the object. We were able to discover the object because of its periodic behavior. c) A binned g' lightcurve obtained with KPED, phase-folded on the orbital period. Error bars are 1σ intervals.

Answer 1

Unless I've done my maths wrong, the period of total eclipse is about 18 seconds.

The CHIMERA camera at Mt Palomar, the instrument which followed up the discovery of this system, can take exposures at up to 8 full 1k$\times$1k frames/second and considerably higher if windowed on an object. There is no need for photon-counting equipment for such a slowly varying source. Indeed, the CHIMERA observations used 3 second exposures.

The problem in time resolution I suspect is just how faint the object is. So moving to photomultiplier technology, which would mean a hit in terms of efficiency, is not going to help here. The hot primary has $g = 20.38 \pm 0.05$. Given the the ratios of radii and temperatures in the discovery paper - $R_1/R_2 = 0.5$ and $T_1/T_2 > 4.9$ - then just a simple bolometric scaling suggests the flux from the secondary is $>144$ times smaller (or 5.4 mag).

It is quite challenging to accumulate much in the way of signal-to-noise on a magnitude $\sim 26$ object in $\sim 10$ seconds, even on the biggest telescopes on Earth. Probably the best bet would be to use a standard CCD camera on say the Gemini-N telescope (or Subaru) and just take a ten second exposure exactly at the predicted time of the minimum and then exposures either side (to confirm you were in the right place!). This can be repeated every 6.91 minutes for a whole night if necessary.

It doesn't look hopeful though. I used the Gemini-N integration time calculator with a $g=26$ source of spectral-type $\sim$A0V (ok for a white dwarf) observed in the darkest skies. It would take $215\times 10$s exposures to get a signal-to-noise ratio of 5, and the the noise is dominated by sky background at that magnitude. So basically unfeasible.

Determining the effective temperature of the unheated side of the secondary would be interesting because it might give you a constraints on its intrinsic luminosity, its cooling age, and hence on the evolutionary pathway that led to the less massive, but larger secondary helium white dwarf forming before the hotter primary C/O white dwarf.