Torsion points on elliptic curves over number fields of small degree
We determine the set $S(d)$ of possible prime orders of $K$-rational points on elliptic curves over number fields $K$ of degree $d$, for $d = 4$, $5$, $6$, and $7$.
math.NT↗
arXiv subjects
William Stein
Publications and source records attributed to William Stein.
The Rise and Fall of the King: The Correlation between FO Aquarii's Low States and the White Dwarf's Spindown
The intermediate polar FO Aquarii (FO Aqr) experienced its first-reported low-accretion states in 2016, 2017, and 2018, and using newly available photographic plates, we identify pre-discovery low states in 1965, 1966, and 1974. The primary focus of our analysis, however, is an extensive set of time-series photometry obtained between 2002 and 2018, with particularly intensive coverage of the 2016-2018 low states. After computing an updated spin ephemeris for the white dwarf (WD), we show that its spin period began to increase in 2014 after having spent 27 years decreasing; no other intermediate polar has experienced a sign change of its period derivative, but FO Aqr has now done so twice. Our central finding is that the recent low states all occurred shortly after the WD began to spin down, even though no low states were reported in the preceding quarter-century, when it was spinning up. Additionally, the system's mode of accretion is extremely sensitive to the mass-transfer rate, with accretion being almost exclusively disk-fed when FO Aqr is brighter than V~14 and substantially stream-fed when it is not. Even in the low states, a grazing eclipse remains detectable, confirming the presence of a disk-like structure (but not necessarily a Keplerian accretion disk). We relate these various observations to theoretical predictions that during the low state, the system's accretion disk dissipates into a non-Keplerian ring of diamagnetic blobs. Finally, a new XMM-Newton observation from a high state in 2017 reveals an anomalously soft X-ray spectrum and diminished X-ray luminosity compared to pre-2016 observations.
astro-ph.SR↗
The Spin-Period History of Intermediate Polars
We report the detailed history of spin-period changes in five intermediate polars (DQ Herculis, AO Piscium, FO Aquarii, V1223 Sagittarii, and BG Canis Minoris) during the 30-60 years since their original discovery. Most are slowly spinning up, although there are sometimes years-long episodes of spin-down. This is supportive of the idea that the underlying magnetic white dwarfs are near spin equilibrium. In addition to the ~40 stars sharing many properties and defined by their strong, pulsed X-ray emission, there are a few rotating much faster (P<80 s), whose membership in the class is still in doubt -- and who are overdue for closer study.
astro-ph.SR↗
Repetitive Patterns in Rapid Optical Variations in the Nearby Black-hole Binary V404 Cygni
How black holes accrete surrounding matter is a fundamental, yet unsolved question in astrophysics. It is generally believed that matter is absorbed into black holes via accretion disks, the state of which depends primarily on the mass-accretion rate. When this rate approaches the critical rate (the Eddington limit), thermal instability is supposed to occur in the inner disc, causing repetitive patterns of large-amplitude X-ray variability (oscillations) on timescales of minutes to hours. In fact, such oscillations have been observed only in sources with a high mass accretion rate, such as GRS 1915+105. These large-amplitude, relatively slow timescale, phenomena are thought to have physical origins distinct from X-ray or optical variations with small amplitudes and fast ($\lesssim$10 sec) timescales often observed in other black hole binaries (e.g., XTE J1118+480 and GX 339-4). Here we report an extensive multi-colour optical photometric data set of V404 Cygni, an X-ray transient source containing a black hole of nine solar masses (and a conpanion star) at a distance of 2.4 kiloparsecs. Our data show that optical oscillations on timescales of 100 seconds to 2.5 hours can occur at mass-accretion rates more than ten times lower than previously thought. This suggests that the accretion rate is not the critical parameter for inducing inner-disc instabilities. Instead, we propose that a long orbital period is a key condition for these large-amplitude oscillations, because the outer part of the large disc in binaries with long orbital periods will have surface densities too low to maintain sustained mass accretion to the inner part of the disc. The lack of sustained accretion -- not the actual rate -- would then be the critical factor causing large-amplitude oscillations in long-period systems.
astro-ph.HE↗
Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. VIII: The Eighth Year (2015-2016)
Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 128 SU UMa-type dwarf novae observed mainly during the 2015-2016 season and characterized these objects. The data have improved the distribution of orbital periods, the relation between the orbital period and the variation of superhumps, the relation between period variations and the rebrightening type in WZ Sge-type objects. Coupled with new measurements of mass ratios using growing stages of superhumps, we now have a clearer and statistically greatly improved evolutionary path near the terminal stage of evolution of cataclysmic variables. Three objects (V452 Cas, KK Tel, ASASSN-15cl) appear to have slowly growing superhumps, which is proposed to reflect the slow growth of the 3:1 resonance near the stability border. ASASSN-15sl, ASASSN-15ux, SDSS J074859.55+312512.6 and CRTS J200331.3-284941 are newly identified eclipsing SU UMa-type (or WZ Sge-type) dwarf novae. ASASSN-15cy has a short (~0.050 d) superhump period and appears to belong to EI Psc-type objects with compact secondaries having an evolved core. ASASSN-15gn, ASASSN-15hn, ASASSN-15kh and ASASSN-16bu are candidate period bouncers with superhump periods longer than 0.06 d. We have newly obtained superhump periods for 79 objects and 13 orbital periods, including periods from early superhumps. In order that the future observations will be more astrophysically beneficial and rewarding to observers, we propose guidelines how to organize observations of various superoutbursts.
astro-ph.SR↗
Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks
Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava-Shankar studying the average sizes of $n$-Selmer groups, have given new upper bounds on the average algebraic rank in families of elliptic curves over $\mathbb{Q}$ ordered by height. We describe databases of elliptic curves over $\mathbb{Q}$ ordered by height in which we compute ranks and $2$-Selmer group sizes, the distributions of which may also be compared to these theoretical results. A striking new phenomenon observed in these databases is that the average rank eventually decreases as height increases.
math.NT↗
Beyond the black box
We describe the role the open-source software community plays in fixing bugs through a case study of a problem with integer determinant computations in SageMath.
math.HO↗
PM J03338+3320: Long-Period Superhumps in Growing Phase Following a Separate Precursor Outburst
We observed the first-ever recorded outburst of PM J03338+3320, the cataclysmic variable selected by proper-motion survey. The outburst was composed of a precursor and the main superoutburst. The precursor outburst occurred at least 5 d before the maximum of the main superoutburst. Despite this separation, long-period superhumps were continuously seen between the precursor and main superoutburst. The period of these superhumps is longer than the orbital period by 6.0(1)% and can be interpreted to reflect the dynamical precession rate at the 3:1 resonance for a mass ratio of 0.172(4). These superhumps smoothly evolved into those in the main superoutburst. These observations provide the clearest evidence that the 3:1 resonance is triggered by the precursor outburst, even if it is well separated, and the resonance eventually causes the main superoutburst as predicted by the thermal-tidal instability model. The presence of superhumps well before the superoutburst cannot be explained by alternative models (the enhanced mass-transfer model and the pure thermal instability model) and the present observations give a clear support to the thermal-tidal instability model.
astro-ph.SR↗
Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. VII: The Seventh Year (2014-2015)
Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 102 SU UMa-type dwarf novae observed mainly during the 2014-2015 season and characterized these objects. Our project has greatly improved the statistics of the distribution of orbital periods, which is a good approximation of the distribution of cataclysmic variables at the terminal evolutionary stage, and confirmed the presence of a period minimum at a period of 0.053 d and a period spike just above this period. The number density monotonically decreased toward the longer period and there was no strong indication of a period gap. We detected possible negative superhumps in Z Cha. It is possible that normal outbursts are also suppressed by the presence of a disk tilt in this system. There was no indication of enhanced orbital humps just preceding the superoutburst, and this result favors the thermal-tidal disk instability as the origin of superoutbursts. We detected superhumps in three AM CVn-type dwarf novae. Our observations and recent other detections suggest that 8% of objects showing dwarf nova-type outbursts are AM CVn-type objects. AM CVn-type objects and EI Psc-type object may be more abundant than previously recognized. OT J213806, a WZ Sge-type object, exhibited a remarkably different feature between the 2010 and 2014 superoutbursts. Although the 2014 superoutburst was much fainter the plateau phase was shorter than the 2010 one, the course of the rebrightening phase was similar. This object indicates that the O-C diagrams of superhumps can be indeed variable at least in WZ Sge-type objects. Four deeply eclipsing SU UMa-type dwarf novae (ASASSN-13cx, ASASSN-14ag, ASASSN-15bu, NSV 4618) were identified. We studied long-term trends in supercycles in MM Hya and CY UMa and found systematic variations of supercycles of ~20%.
astro-ph.SR↗
HW Bootis: an enigmatic cataclysmic variable star
We present the 13-year light curve of HW Boo between 2001 May and 2014 May. We identified 12 outbursts, which typically lasted 2 to 5 days, with an amplitude of 2.7 to 3.6 magnitudes. Time resolved photometry during two outbursts revealed small hump-like structures which increased in size as the outburst progressed, reaching a peak-to-peak amplitude of ~0.8 mag. They occurred on timescales of 15 min to an hour, but did not exhibit a stable period. Similar irregular hump-like variations of 0.1 to 0.8 magnitudes, at intervals of 7 to 30 minutes, were also detected during quiescence. We discuss whether HW Boo might be a dwarf nova of the SU UMa family or an Intermediate Polar, but require further observations to support classification.
astro-ph.SR↗
OT J075418.7+381225 and OT J230425.8+062546: Promising Candidates for the Period Bouncer
We report on photometric observations of two dwarf novae, OT J075418.7+381225 and OT J230425.8+062546, which underwent superoutburst in 2013 (OT J075418) and in 2011 (OT J230425). Their mean period of the superhump was 0.0722403(26) d (OT J074518) and 0.067317(35) d (OT J230425). These objects showed a very long growing stage of the superhump (stage A) and a large period decrease in stage A-B transition. The long stage A suggests slow evolution of the superhump due to very small mass ratios of these objects. The decline rates during the plateau phase in the superoutburst of these objects were lower than those of SU UMa-type DNe with a similar superhump period. These properties were similar to those of SSS J122221.7-311523, the best candidate for the period bouncer. Therefore, these two DNe are regarded as good candidates for the period bouncer. We estimated the number density of period bouncers roughly from our observations in the recent five years. There is a possibility that these WZ Sge-type dwarf novae with unusual outburst properties can account for the missing population of the period bouncer expected from the evolutionary scenario.
astro-ph.SR↗
Superoutburst of SDSS J090221.35+381941.9: First Measurement of Mass Ratio in an AM CVn-Type Object using Growing Superhumps
We report on a superoutburst of the AM CVn-type object SDSS J090221.35+381941.9 [J0902; orbital period 0.03355(6) d] in 2014 March-April. The entire outburst consisted of a precursor outburst and the main superoutburst, followed by a short rebrightening. During the rising branch of the main superoutburst, we detected growing superhumps (stage A superhumps) with a period of 0.03409(1) d. During the plateau phase of the superoutburst, superhumps with a shorter period (stage B superhumps) were observed. Using the orbital period and the period of the stage A superhumps, we were able to measure the dynamical precession rate of the accretion disk at the 3:1 resonance, and obtained a mass ratio (q) of 0.041(7). This is the first successful measurement of the mass ratio in an AM CVn-type object using the recently developed stage A superhump method. The value is generally in good agreement with the theoretical evolutionary model. The orbital period of J0902 is the longest among the outbursting AM CVn-type objects, and the borderline between the outbursting systems and systems with stable cool disks appears to be longer than had been supposed.
astro-ph.SR↗
Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. VI: The Sixth Year (2013-2014)
Continuing the project described by Kato et al. (2009, PASJ, 61, S395, arXiv:0905.1757), we collected times of superhump maxima for 56 SU UMa-type dwarf novae mainly observed during the 2013-2014 season and characterized these objects. We detected negative superhumps in VW Hyi and indicated that the low number of normal outbursts in some supercycle can be interpreted as a result of the disk tilt. This finding, combined with the Kepler observation of V1504 Cyg and V344 Lyr, suggests that the disk tilt is responsible for modulating the outburst pattern in SU UMa-type dwarf novae. We also studied the deeply eclipsing WZ Sge-type dwarf nova MASTER OT J005740.99+443101.5 and found evidence of a sharp eclipse during the phase of early superhumps. The profile can be reproduced by a combination of the eclipse of the axisymmetric disk and the uneclipsed light source of early superhumps. This finding confirms the lack of evince of a greatly enhanced hot spot during the early stage of WZ Sge-type outburst. We detected growing (stage A) superhumps in MN Dra and give a suggestion that some of SU UMa-type dwarf novae situated near the critical condition of tidal instability may show long-lasting stage A superhumps. The large negative period derivatives reported in such systems can be understood a result of the combination of stage A and B superhumps. The WZ Sge-type dwarf novae AL Com and ASASSN-13ck showed a long-lasting (plateau-type) rebrightening. In the early phase of the rebrightening, both objects showed a precursor-like outburst, suggesting that the long-lasting rebrightening is triggered by a precursor outburst.
astro-ph.SR↗
Study of Negative and Positive Superhumps in ER Ursae Majoris
We carried out the photometric observations of the SU UMa-type dwarf nova ER UMa during 2011 and 2012, which showed the existence of persistent negative superhumps even during the superoutburst. We performed two-dimensional period analysis of its light curves by using a method called "least absolute shrinkage and selection operator" (Lasso) and "phase dispersion minimization" (PDM) analysis, and we found that the period of negative superhumps systematically changed between a superoutburst and the next superoutburst. The trend of the period change can beinterpreted as reflecting the change of the disk radius. This change of the disk radius is in good agreement with the predicted change of the disk radius by the thermal-tidal instability (TTI) model. The normal outbursts within a supercycle showed a general trend that the rising rate to maximum becomes slower as the next superoutburst approaches. The change can be interpreted as the consequence of the increased gas-stream flow onto the inner region of the disk as the result of the tilted disk. Some of the superoutbursts were found to be triggered by a precursor normal outburst when the positive superhumps appeared to develop. The positive and negative superhumps co-existed during the superoutburst. The positive superhumps were prominent only during four or five days after the supermaximum, while the signal of the negative superhumps became strong after the middle phase of the superoutburst plateau. A simple combination of the positive and negative superhumps was found to be insufficient in reproducing the complex profile variation. We were able to detect the developing phase of positive superhumps (stage A superhumps) for the first time in ER UMa-type dwarf novae. Using the period of stage A superhumps, we obtained a mass ratio of 0.100(15), which indicates that ER UMa is on the ordinary evolutional track of CVs.
astro-ph.SR↗
Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. V: The Fifth Year (2012-2013)
Continuing the project described by Kato et al. (2009a, arXiv:0905.1757), we collected times of superhump maxima for SU UMa-type dwarf novae mainly observed during the 2012-2013 season. We found three objects (V444 Peg, CSS J203937 and MASTER J212624) having strongly positive period derivatives despite the long orbital period (Porb). By using the period of growing stage (stage A) superhumps, we obtained mass ratios for six objects. We characterized nine new WZ Sge-type dwarf novae. We made a pilot survey of the decline rate of slowly fading part of SU UMa-type and WZ Sge-type outbursts. The decline time scale was found to generally follow the expected Porb^(1/4) dependence and WZ Sge-type outbursts also generally follow this trend. There are some objects which show slower decline rates, and we consider these objects good candidates for period bouncers. We also studied unusual behavior in some objects, including BK Lyn which made a transition from an ER UMa-type state to the novalike (standstill) state in 2013 and unusually frequent occurrence of superoutbursts in NY Ser and CR Boo. We applied least absolute shrinkage and selection operator (Lasso) power spectral analysis, which has been proven to be very effective in analyzing the Kepler data, to ground-based photometry of BK Lyn and detected the dramatic disappearance of the signal of negative superhumps in 2013. We suggested that the mass-transfer rates did not vary strongly between the ER UMa-type state and novalike state in BK Lyn, and this transition was less likely caused by a systematic variation of the mass-transfer rate.
astro-ph.SR↗
WZ Sge-type dwarf novae with multiple rebrightenings: MASTER OT J211258.65+242145.4 and MASTER OT J203749.39+552210.3
We report on photometric observations of WZ Sge-type dwarf novae, MASTER OT J211258.65+242145.4 and MASTER OT J203749.39+552210.3 which underwent outbursts in 2012. Early superhumps were recorded in both systems. During superoutburst plateau, ordinary superhumps with a period of 0.060291(4) d (MASTER J211258) and of 0.061307(9) d (MASTER J203749) in average were observed. MASTER J211258 and MASTER J203749 exhibited eight and more than four post-superoutburst rebrightenings, respectively. In the final part of the superoutburst, an increase in the superhump periods was seen in both systems. We have made a survey of WZ Sge-type dwarf novae with multiple rebrightenings, and confirmed that the superhump periods of WZ Sge-type dwarf novae with multiple rebrightenings were longer than those of WZ Sge-type dwarf novae without a rebrightening. Although WZ Sge-type dwarf novae with multiple rebrightenings have been thought to be the good candidates for period bouncers based on their low mass ratio (q) from inferred from the period of fully grown (stage B) superhumps, our new method using the period of growing superhumps (stage A superhumps), however, implies higher q than those expected from stage B superhumps. These q values appear to be consistent with the duration of the stage A superoutbursts, which likely reflects the growth time of the 3:1 resonance. We present a working hypothesis that the small fractional superhump excesses for stage B superhumps in these systems may be explained as a result that a higher gas pressure effect works in these systems than in ordinary SU UMa-type dwarf novae. This result leads to a new picture that WZ Sge-type dwarf novae with multiple rebrightenings and SU UMa-type dwarf novae without a rebrightening (they are not period bouncers) are located in the same place on the evolutionary track.
astro-ph.SR↗
Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. IV: The Fourth Year (2011-2012)
Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we studied 86 SU UMa-type dwarf novae. We confirmed the general trends such as the relation between period derivatives and orbital periods. There are some systems showing positive period derivatives despite the long orbital periods. We observed the 2011 outburst of the WZ Sge-type dwarf nova BW Scl, and recorded an O-C diagram similar to those of previously known WZ Sge-type dwarf novae. The WZ Sge-type dwarf nova OT J184228.1+483742 showed an unusual pattern of double outbursts composed of an outburst with early superhumps and one with ordinary superhumps. We propose an interpretation that a very small growth rate of the 3:1 resonance due to an extremely low mass-ratio led to a quenching of the superoutburst before the ordinary superhumps appeared. We studied ER UMa-type dwarf novae and found that V1159 Ori showed positive superhumps similar to ER UMa in the 1990s. The recently recognized ER UMa-type object BK Lyn dominantly showed negative superhumps, and its behavior was very similar to the present-day state of ER UMa. The pattern of period variations in AM CVn-type objects were very similar to short-period hydrogen-rich SU UMa-type dwarf novae, making them helium analogue of hydrogen-rich SU UMa-type dwarf novae. SBS 1108+574, a peculiar hydrogen-rich dwarf nova below the period minimum, showed a very similar pattern of period variations to those of short-period SU UMa-type dwarf novae. The mass-ratio derived from the detected orbital period suggests that this secondary is a somewhat evolved star whose hydrogen envelope was mostly stripped during the mass-exchange. CC Scl, MASTER OT J072948.66+593824.4 and OT J173516.9+154708 showed only low-amplitude superhumps with complex profiles. These superhumps are likely a combination of closely separated two periods.
astro-ph.SR↗
The first confirmed superoutburst of the dwarf nova GALEX J215818.5+241924
In 2011 October an optical transient was reported in Pegasus as a possible nova. The object had an ultraviolet counterpart, GALEX J215818.5+241924. In this paper we present follow-up photometry of the object which revealed the presence of superhumps, with peak-to-peak amplitude of up to 0.22 magnitudes, diagnostic of it being a member of the SU UMa family of dwarf novae. The outburst amplitude was 4.6 magnitudes and it lasted at least 10 days, with a maximum brightness of magnitude 14.3. We determined the mean superhump period from our first 5 nights of observations as Psh = 0.06728(21) d. However analysis of the O-C residuals showed a dramatic evolution in Psh during the outburst. During the first part of the plateau phase the period increased with dPsh/dt = +2.67(15) x 10-4. There was then an abrupt change following which the period decreased with dPsh/dt = -2.08(9)x 10-4. We found a signal in the power spectrum of the photometry which we tentatively interpret as the orbital signal with Porb = 0.06606(35) d. Thus the superhump period excess was epsilon = 0.020(8), such value being consistent with other SU UMa systems of similar orbital period.
astro-ph.SR↗