J0328-1219 Photometry Observations,Web Site #2
by Amateur Bruce L. Gary, Using a 16" Telescope at the Hereford Arizona Observatory (HAO)
Last updated: 2022.08.29, 22 UT

This web page is meant to be an archive of my light curve observations for "observing season #2" of white dwarf J0328 using the HAO backyard observatory 16" Ritchey-Chretien AstroTech telescope with a SBIG XME-10 CCD, g' band filter (link). Most of my web pages are meant for documenting observations and analysis results for myself (it's easier than using a filing cabinet). My web pages can sometimes serve to help with collaborations if I join with others to study the same star. This web page may serve these dual purposes since I'm aware of a group of astronomers (headed by Zachary Vanderbosch) that is engaged in a second observing season of observations following publication about the variable nature of J0328 during a first observing season. My Web Site #1 is located at http://www.brucegary.net/J0328/; it includes my observations during the first observing season (2020.12.02 to 2021.02.12).

To view the Season#3 web page for this star system, go to http://www.brucegary.net/J0328-3/   (2022.08.29 to now)

Latest Status Summary



The main dip "A" has decreased depth to ~ 16 % (as of Feb 08, and anew dip "B" (1/4 of an orbit trailing A) has grown to a depth of 21 %. The newly growing dip B is still narrow. Dip C is moving toward A and is deepening. As always, there is very little OOT time (maybe none). There is evidence that some dips have slightly different periods from each other, with dip A having the longest period (9.9324 hrs) and dip B having the shortest (P = 9.9292 hrs).


Figure 1.04. This is a phase-fold (using the A-system 's P = 9.931 hrs) for a 6-day set of 5 observing sessions in late January (observing session Group#3b, still "under construction").


Figure 1.03. This is a phase-fold (using the A-system 's P = 9.931 hrs) for my latest set of observations (observing session Group#3a & #3b, still "under construction").


Figure 1.02. This is a phase-fold (using the A-system 's P = 9.931 hrs) for early January observing sessions, Group#2. The "discrepancies" at certain phases are "good" because they may be due to the periodicities other than the A-system's 9.94 hrs (which will be derived by studying differences from the A-period best-fitting model, described below at link).


Figure 1.01. This is phase-fold LC for early December observing sessions, Group#1 (of this observing season).

General Information

RA/DE = 03:28:33.7 -12:19:45, g'-mag = 16.7, white dwarf type DZ, T_eff = 8750 (170) K (Guidry et al., 2020). Observing season is centered on Nov 18 (and extends from about Aug 01 to Mar 05).

List of Internal Links

    Observing session dates  
    Observing session LCs  
    Periodogram analyses 
    Trends   
    Finder image  
    Physical model suggestion  
    References  
    Related external links  


Observing Session Dates

2022.02.09   Data Exchange: Feb03 to Feb09  link
2022.02.08  
2022.02.07  
2022.02.06  
2022.02.05  
2022.02.04  
2022.02.03  


2022.01.31   Data Exchange Jan20 to Jan31 link
2022.01.30  
2022.01.28  
2022.01.27  
2022.01.26  
2022.01.25  
2022.01.24  
2022.01.22  
2022.01.21  
2022.01.20  

2022.01.06   Data Exchange Jan02 to Jan06 link (changed format)
2022.01.05  
2022.01.04  
2022.01.03  
2022.01.02  

2021.12.13   Data Exchange Nov10 to Dec13 link
2021.12.12  
2021.12.11  
2021.12.08  
2021.12.07  
2021.12.01  
2021.11.29  
2021.11.28  
2021.11.14  
2021.11.10  

Observing Session Light Curves


2022.02.09  




2022.02.08 



2022.02.07 




2022.02.06 


Expansion of B dip, showing how fast the dip developed. Depth went to 22 % is ~ 15 minutes. A point crosses the WD's equatorial path in 65 seconds, so the dust cloud went from leading edge to a full width of ~ 10 % the WD's  diameter along a orbit segment that was ~ 14 times the WD's diameter. This assumes a circular orbit, WD mass = 0.73 x Mass_earth and WD radius = 1.32 x Radius_earth.




2022.02.05 





2022.02.04 



2022.02.03  




2022.01.31  




2022.01.30 

About half of this observing session's data was rejected (due to clouds).



2022.01.28 

Power down at 4.3 UT.

2022.01.27 



2022.01.26  



2022.01.25 



2022.01.24 


2022.01.22  



2022.01.21  




2022.01.20 

This is the first observing session of "observing session Group#3."



2022.01.06  




2022.01.05 





2022.01.04  




2022.01.03  data

Notice that during the entire 6 hours of this date's observations there are dust clouds in our line-of-sight; no OOT level data. This agrees with the expectation using other data in a phase-folded LC.



2022.01.02  data




2021.12.13 


2021.12.12 




2021.12.11  



2021.12.08 




 2021.12.07  



2021.12.01  




2021.11.29  



2021.11.28  





2021.11.14  






2021.11.10  





Periodogram Analyses for 2022 Jan 02-06 Data

Here are two periodograms of the 2022 January 5-day observing sessions (Jan 2 - 6):


Figure P.01. Box Least-Squares periodogram.


Figure P.02. Lomb-Scargle periodogram.


Figure P.03. Lomb-Scarle periodogram of the A-system model that fits measured data, with no noise, showing importance of data gaps between 1-day interval of observing sessions.

The three peaks of this last periodogram (Pgram) are produced by frequency beats between the actual A-system variation with frequency = 1/ 0.4155 = 2.407 c/d and frequency = 1/0.9972 = 1.0028 c/d. The sum and difference of these two frequencies is 3.410 s/d and 1.404 c/d, corresponding to periods of 0.2937 day and 0.712 day (7.04 hrs and 17.09 hrs). In other words, the real A-system variation with P = 9.972 hrs and the interval between observing windows = 0.9972 days, caproduces the Pgram features with P = 7.0 and 17 hrs. This means we can ignore those peaks in the previous two figures.   

We are left with the following possibilities for periodicity:

Table 1. List of periodicities using HAO magnitudes.
System
 P [day]
 P[hrs]
A
 0.414 day
 9.931 hrs
B
 0.47 day
 11.3 hrs
C
 0.32 day
 7.68 hrs
D
 ~ 0.88 day
 ~ 21 hrs

The phase-folded LC for the A system is shown here:


Figure P.04. Phase-folded LC for the A system (P = 9.93 hrs). (Keep in mind that some of the scatter in this LC is due to B, C and D periodicities.)

 
Figure P.05. B-system LC (11.3 hrs). (Keep in mind that most of the scatter in this LC is due to the much larger amplitude A periodicity.)


Figure P.06. C-system LC (7.68 hrs). (Keep in mind that most of the scatter in this LC is due to the much larger amplitude A periodicity.)


Figure P.07. D-system LC (20.9 hrs). (Keep in mind that most of the scatter in this LC is due to the much larger amplitude A periodicity.)

My strategy for determining periodicities B, C and D is to remove the A-system periodicity and work with the residuals for a search for other periods.


Figure P.08. Least-squares fitted AHS model for HAO measurements phase-folded using the A-system ephemeris.

Differences off the AHS model fit exhibit the following periodogram:


Figure P.09. Lomb-Scargle periodogram for the differences off the A-system AHS model fit. Three candidate periodicities are present (in addition to the A-system).

Table 2. List of periodicities of HAO "differences of measurements with respect to the A-system AHS model fit"
System
 P[day]
 P[hrs]
B
 0.466 day
 11.2 hrs
C
 0.318 day
 7.63 hrs
D
 0.872 day
 20.9 hrs
E
 0.244 day
 5.84 hrs

The following 4 figures are LCs for these extra periodicities using data that are "differences of measurements with respect to the A-system AHS model fit" :


Figure P.10. Phase-folded LC for the B-system ephemeris (P = 11.18 hrs), based on differences off the A-system AHS model fit.


Figure P.11. Phase-folded LC for the C-system ephemeris (P = 7.63 hrs), based on differences off the A-system AHS model fit.


Figure P.12. Phase-folded LC for the D-system ephemeris (P = 21 hrs), based on differences off the A-system AHS model fit.


Figure P.13. Phase-folded LC for the E-system ephemeris (P = 5.84 hrs), based on differences off the A-system AHS model fit.

The following graphs are my AHS fits to the above "A-difference" data. For easy reference, here's a repeat of the previous table:




Figure P.14. Phase-folded LC for the B-system ephemeris (P = 11.2 hrs), based on differences off the A-system AHS model fit.


Figure P.15. Phase-folded LC for the C-system ephemeris (P = 7.63 hrs), based on differences off the A-system AHS model fit.


Figure P.16. Phase-folded LC for the D-system ephemeris (P = 21 hrs), based on differences off the A-system AHS model fit.


Figure P.17. Phase-folded LC for the E-system ephemeris (P = 5.84 hrs), based on differences off the A-system AHS model fit.

To summare, here are the periods and peak amplitudes derived from this periodicity analysis:

Table 3. List of periodicities of "differences w.r.t. A-system model fit"
System
 P[day]
 P[hrs]
 Peak Depth
 Confidence
A
 0.414 day
 9.931 hrs 14.3 %
 100 %
B
 0.466 day 11.2 hrs 4.0 %
 80 %
C
 0.318 day 7.63 hrs 3.0 %
 10 %
D
 0.872 day 20.9 hrs 2.0 %
 5 %
E
 0.244 day
 5.84 hrs
 2.0 %
 2 %

The B system may be reasonably well-established, but I suggest that the C, D and E systems should be viewed skeptically until more data is available that supports them.The last column in Table 3 is my subjective opinion about how confident I am that the periodicity system is real.

Periodogram Analysis of 2021 Nov 10 - Dec 13 Data

The next two graphs are Lomb-Scargle periodograms for different sets of measurements, the 2021 Nov/Dec data and the 2022 Jan data:


Figure P.18. Lomb-Scargle periodogram for the 2021 Nov 10 to Dec 13 data (Nov 14 data not present)..


Figure P.19. Lomb-Scargle periodogram for the 2022 Jan 02 - 06 data.

Recall that we have to ignore periods of 0.2937 day and 0.712 day (7.04 hrs and 17.09 hrs) because they are produced by the beating of frequencies corresponding to periodicities of the 0.4155 day signal and the 0.9972 day interval between observing sessions.

After removing a best fitting AHS model from the Nov/Dec data we find the following periodogram:


Figure P.20. Lomb-Scargle periodogram for the Nov/Dec differences off the A-system AHS model fit.

According to this periodogram no other periodicities are present during the Nov/Dec observations. An alternative interpretation is that the observing sessions span so long a range of dates (33 days) that any periodicities besides the main one would be "smeared." If this suggestion had merit then eliminating the first two observing sessions, leading to a date span of only 15 days, would show more structure in the periodogram, but it doesn't. One more alternative explanation for the lack of other periodicities in the Nov/Dec data is that the amplitude of the other periodicities was lower for the earlier observing dates and appeared in late December. If only the 11.2-hr periodicity is real then this suggestion is possible. Here's a 11.2 hr phase-fold LC for the Nov/Dec A-difference data:


Figure P.21. Phase fold LC for the Nov/Dec "A difference data." 

I conclude that the the C-, D- and E-system periodicities are unlikely to be real, and the B-system periodicity might have existed during 2022 January 2-6, but was not detectable in HAO data taken 2021 Nov 10 - Dec 13.

Obviously, more data would be welcome for additional analysis.

Trends

This observing season consists of 4 observing session groups: early Dec, early Jan, late Jan and early Feb (new moon times). I want to call attention to three dips that exhibit big changes, dips A, B and C. They are shown in the following sequence (most recent at top):









Here's a "waterfall" version of the previous LCs.



Phase drift and depth trends are shown in the next pair of graphs:





If the A and B dust clouds are in circular orbits they will be a mere 400 m apart.

Finder Image


Finder image. FOV = 15 x 10 'arc. North up, east left.

Physical Model Suggestion

J0328 resembles WD1145 in the following ways: 1) dips are present most of the time, 2) dips exist for weeks to months, 3) the inner-most orbit is the most active in producing dips, and 4) dust clouds are in orbits that can (or must) be close to the WD's tidal radius. J0328 differs from WD1145 in the following respects: 1) J0328 dips are present essentially all the time, whereas for WD1145 there are almost always prenty of OOT time per orbit, 2 ) the J0328 dust clouds are in a larger orbit , with P > twice the WD1145 Ps. 


Since the WD1145 dust cloud sources (fragments of a planetesimal source) are certainly related in some way to being on the verge of tidal disruption I suggest that the J0628 dust clouds are produced by the same mechanism. I propose that the fragments for both WD1145 and J0328 are being bombarded by a background of rock collisions that become exhausted at the fragment location after a few weeks to months. This replenishment of dust that is continually lost from Keplerian shear and radiation pressure amounts to a steady-state of production and loss, thus accounting for long timescale preservation of dust cloud shape (depth and width) that would not occur in the absence of continual collision bombardment.

When a fragment begins to be bombarded by a swarm of rocky debris it will start with a shape that is narrow and will deepen quickly, while eventually reaching a steady-state level of collisional bombardment. While the rate of rocky bombardment is constant the dip will have a quasi-constant shape (depth and width). As the background level of rocky debris diminishes the dip should broaden and become reduced in depth. These three life-cycle phases can be thought of as "early, "middle" and "late." Accordingly, this observing season's A dip is in a late phase whereas the B dip is in an early phase.

Whereas WD1145's planetesimal source for fragments is a planetary core (with density ~ 7 g/cc), the J0328 planetesimal source for fragments is an asteroid (with density ~ 2 g/cc).

My Collaboration Policy

Please don't ask me to co-author a paper! At my age of 82 I'm entitled to have fun and avoid work. Observing and figuring things out is fun; writing papers is work. My observations are "in the public domain" and are available for use by anyone. If my data is essential to any publication just mention this in the Acknowledgement section.

References

Vanderbosch, Zachary P., Saul Rappaport, Joseph A. Guidry, Bruce L. Gary and 13 others, "Recurring Planetary Debris Transits and Circumstellar Gas around White Dwarf ZTF J0328-1219," MNRAS arXiv

Xu, Siyi, Samuel Lai and Erik Dennihy, 2020, "Infrared Excesses around Bright White Dwarfs from Gaia and unWISE I," arXiv 

Guidry, Joseph A., Zachary P. Vanderbosch, J. J. Hermes, Brad N. Barlow, Isaac D. Lopez, Thomas M. Boudreaux, Kyle A. Corcoran, Bart H. Dunlap, Keaton J. Bell, M. H. Montgomery, Tyler M. Heintz, D. E. Winget, Karen I. Winget, J. W. Kuehne, 2020, "I Spy Transits and Pulsations: Empirical Variability in White Dwarfs Using Gaia and the Zwicky Transient Facility," submitted to ApJ, arXiv

Rappaport, Saul, Roberto Sanchis-Ojeda, Leslie A. Rogers, Alan Levine & Joshua Winn, 2013, "The Roche Limit for Close-Orbiting Planets: Minimum Density, Composition Constraints and Applications to the 4.2-Hour Planet KOI 1843.03," ApJ L, arXiv 


External Links of Possible Relevance

J0328 Photometry observations by Bruce Gary during observing season #1 (2020/2021)
WD1145 summary of 4 observing seasons
WD1145 for 2020/21 observing season
Resume of webmaster

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This site opened December12, 2021. Nothing on this web page is copyrighted.