arXiv subjects
Publications and source records attributed to Peter Nelson.
We show that, for each real number $α> 0$ and odd integer $k\ge 5$ there is an integer $c$ such that, if $M$ is a simple binary matroid with $|M| \ge α2^{r(M)}$ and with no $k$-element circuit, then $M$ has critical number at most $c$. The result is an easy application of a regularity lemma for finite abelian groups due to Green.
A matroid is $\text{GF}(q)$-regular if it is representable over all proper superfields of the field $\text{GF}(q)$. We show that, for highly connected matroids having a large projective geometry over $\text{GF}(q)$ as a minor, the property of $\text{GF}(q)$-regularity is equivalent to representability over both $\text{GF}(q^2)$ and $\text{GF}(q^t)$ for some odd integer $t \geq 3$. We do this by means of an exact structural description of all such matroids.
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.
We show that, if $k$ and $\ell$ are positive integers and $r$ is sufficiently large, then the number of rank-$k$ flats in a rank-$r$ matroid $M$ with no $U_{2,\ell+2}$-minor is less than or equal to number of rank-$k$ flats in a rank-$r$ projective geometry over GF$(q)$, where $q$ is the largest prime power not exceeding $\ell$.
We show that, if $q$ is a prime power at most 5, then every rank-$r$ matroid with no $U_{2,q+2}$-minor has no more lines than a rank-$r$ projective geometry over GF$(q)$. We also give examples showing that for every other prime power this bound does not hold.
We show for each positive integer $a$ that, if $\mathcal{M}$ is a minor-closed class of matroids not containing all rank-$(a+1)$ uniform matroids, then there exists an integer $c$ such that either every rank-$r$ matroid in $\mathcal{M}$ can be covered by at most $r^c$ rank-$a$ sets, or $\mathcal{M}$ contains the GF$(q)$-representable matroids for some prime power $q$ and every rank-$r$ matroid in $\mathcal{M}$ can be covered by at most $cq^r$ rank-$a$ sets. In the latter case, this determines the maximum density of matroids in $\mathcal{M}$ up to a constant factor.
We report the discovery by M. Linnolt on JD 2455665.7931 (UT 2011 April 14.29) of the sixth eruption of the recurrent nova T Pyxidis. This discovery was made just as the initial fast rise was starting, so with fast notification and response by observers worldwide, the entire initial rise was covered (the first for any nova), and with high time resolution in three filters. The speed of the rise peaked at 9 mag/day, while the light curve is well fit over only the first two days by a model with a uniformly expanding sphere. We also report the discovery by R. Stubbings of a pre-eruption rise starting 18 days before the eruption, peaking 1.1 mag brighter than its long-time average, and then fading back towards quiescence 4 days before the eruption. This unique and mysterious behavior is only the fourth known anticipatory rise closely spaced before a nova eruption. We present 19 timings of photometric minima from 1986 to February 2011, where the orbital period is fast increasing with P/dot{P}=313,000 yrs. From 2008-2011, T Pyx had a small change in this rate of increase, so that the orbital period at the time of eruption was 0.07622950+-0.00000008 days. This strong and steady increase of the orbital period can only come from mass transfer, for which we calculate a rate of 1.7-3.5x10^-7 Mo/yr. We report 6116 magnitudes between 1890 and 2011, for an average B=15.59+-0.01 from 1967-2011, which allows for an eruption in 2011 if the blue flux is nearly proportional to the accretion rate. The ultraviolet-optical-infrared spectral energy distribution is well fit by a power law with flux proportional to nu^1.0, although the narrow ultraviolet region has a tilt with a fit of ν^{1/3}. We prove that most of the T Pyx light is not coming from a disk, or any superposition of blackbodies, but rather is coming from some nonthermal source.
We report a long campaign to track the 1.8 hr photometric wave in the recurrent nova T Pyxidis, using the global telescope network of the Center for Backyard Astrophysics. During 1996-2011, that wave was highly stable in amplitude and waveform, resembling the orbital wave commonly seen in supersoft binaries. The period, however, was found to increase on a timescale P/P-dot=3x10^5 yr. This suggests a mass transfer rate of ~10^-7 M_sol/yr in quiescence. The orbital signal became vanishingly weak (<0.003 mag) near maximum light of the 2011 eruption. After it returned to visibility near V=11, the orbital period had increased by 0.0054(6) %. This is a measure of the mass ejected in the nova outburst. For a plausible choice of binary parameters, that mass is at least 3x10^-5 M_sol, and probably more. This represents >300 yr of accretion at the pre-outburst rate, but the time between outbursts was only 45 yr. Thus the erupting white dwarf seems to have ejected at least 6x more mass than it accreted. If this eruption is typical, the white dwarf must be eroding, rather than growing, in mass -- dashing the star's hopes of ever becoming famous via a supernova explosion. Instead, it seems likely that the binary dynamics are basically a suicide pact between the eroding white dwarf and the low-mass secondary, excited and rapidly whittled down, probably by the white dwarf's EUV radiation.
We show that, if $α> 0$ is a real number, $n \ge 2$ and $\ell \ge 2$ are integers, and $q$ is a prime power, then every simple matroid $M$ of sufficiently large rank, with no $U_{2,\ell}$-minor, no rank-$n$ projective geometry minor over a larger field than $\GF(q)$, and satisfying $|M| \ge αq^{r(M)}$, has a rank-$n$ affine geometry restriction over $\GF(q)$. This result can be viewed as an analogue of the Multidimensional Density Hales-Jewett Theorem for matroids.
We show for each positive integer $a$ that, if $\cM$ is a minor-closed class of matroids not containing all rank-$(a+1)$ uniform matroids, then there exists an integer $n$ such that either every rank-$r$ matroid in $\cM$ can be covered by at most $r^n$ sets of rank at most $a$, or $\cM$ contains the $\GF(q)$-representable matroids for some prime power $q$, and every rank-$r$ matroid in $\cM$ can be covered by at most $r^nq^r$ sets of rank at most $a$. This determines the maximum density of the matroids in $\cM$ up to a polynomial factor.
For a set $G$ of points in $\PG(m-1,q)$, let $\ex_q(G;n)$, denote the maximum size of a collection of points in $\PG(n-1,q)$ not containing a copy of $G$, up to projective equivalence. We show that \[\lim_{n\rightarrow \infty} \frac{\ex_q(G;n)}{|\PG(n-1,q)|} = 1-q^{1-c},\] where $c$ is the smallest integer such that there is a rank-$(m-c)$ flat in $\PG(m-1,q)$ that is disjoint from $G$. The result is an elementary application of the density version of the Hales-Jewett Theorem.
Let $\cM$ be a minor-closed class of matroids that does not contain arbitrarily long lines. The growth rate function, $h:\bN\rightarrow \bN$ of $\cM$ is given by $$h(n) = \max(|M|\, : \, M\in \cM, simple, rank-$n$).$$ The Growth Rate Theorem shows that there is an integer $c$ such that either: $h(n)\le c\, n$, or ${n+1 \choose 2} \le h(n)\le c\, n^2$, or there is a prime-power $q$ such that $\frac{q^n-1}{q-1} \le h(n) \le c\, q^n$; this separates classes into those of linear density, quadratic density, and base-$q$ exponential density. For classes of base-$q$ exponential density that contain no $(q^2+1)$-point line, we prove that $h(n) =\frac{q^n-1}{q-1}$ for all sufficiently large $n$. We also prove that, for classes of base-$q$ exponential density that contain no $(q^2+q+1)$-point line, there exists $k\in\bN$ such that $h(n) = \frac{q^{n+k}-1}{q-1} - q\frac{q^{2k}-1}{q^2-1}$ for all sufficiently large $n$.
For each proper minor-closed subclass $\cM$ of the $\GF(q^2)$-representable matroids containing all simple $\GF(q)$-representable matroids, we give, for all large $r$, a tight upper bound on the number of points in a rank-$r$ matroid in $\cM$, and construct a rank-$r$ matroid in $\cM$ for which equality holds. As a consequence, we give a tight upper bound on the number of points in a $\GF(q^2)$-representable, rank-$r$ matroid with no $\PG(k,q^2)$-minor.
For any positive integer $l$ we prove that if $M$ is a simple matroid with no $(l+2)$-point line as a minor and with sufficiently large rank, then $|E(M)|\le \frac{q^{r(M)}-1}{q-1}$, where $q$ is the largest prime power less than or equal to $l$. Equality is attained by projective geometries over GF$(q)$.
As an extension of the project in Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 61 SU UMa-type dwarf novae mainly observed during the 2009-2010 season. The newly obtained data confirmed the basic findings reported in Kato et al. (2009): the presence of stages A-C, as well as the predominance of positive period derivatives during stage B in systems with superhump periods shorter than 0.07 d. There was a systematic difference in period derivatives for systems with superhump periods longer than 0.075 d between this study and Kato et al. (2009). We suggest that this difference is possibly caused by the relative lack of frequently outbursting SU UMa-type dwarf novae in this period regime in the present study. We recorded a strong beat phenomenon during the 2009 superoutburst of IY UMa. The close correlation between the beat period and superhump period suggests that the changing angular velocity of the apsidal motion of the elliptical disk is responsible for the variation of superhump periods. We also described three new WZ Sge-type objects with established early superhumps and one with likely early superhumps. We also suggest that two systems, VX For and EL UMa, are WZ Sge-type dwarf novae with multiple rebrightenings. The O-C variation in OT J213806.6+261957 suggests that the frequent absence of rebrightenings in very short-Porb objects can be a result of sustained superoutburst plateau at the epoch when usual SU UMa-type dwarf novae return to quiescence preceding a rebrightening. We also present a formulation for a variety of Bayesian extension to traditional period analyses.
The first science flight of the balloon-borne \Sunrise telescope took place in June 2009 from ESRANGE (near Kiruna/Sweden) to Somerset Island in northern Canada. We describe the scientific aims and mission concept of the project and give an overview and a description of the various hardware components: the 1-m main telescope with its postfocus science instruments (the UV filter imager SuFI and the imaging vector magnetograph IMaX) and support instruments (image stabilizing and light distribution system ISLiD and correlating wavefront sensor CWS), the optomechanical support structure and the instrument mounting concept, the gondola structure and the power, pointing, and telemetry systems, and the general electronics architecture. We also explain the optimization of the structural and thermal design of the complete payload. The preparations for the science flight are described, including AIV and ground calibration of the instruments. The course of events during the science flight is outlined, up to the recovery activities. Finally, the in-flight performance of the instrumentation is briefly summarized.
We systematically surveyed period variations of superhumps in SU UMa-type dwarf novae based on newly obtained data and past publications. In many systems, the evolution of superhump period are found to be composed of three distinct stages: early evolutionary stage with a longer superhump period, middle stage with systematically varying periods, final stage with a shorter, stable superhump period. During the middle stage, many systems with superhump periods less than 0.08 d show positive period derivatives. Contrary to the earlier claim, we found no clear evidence for variation of period derivatives between superoutburst of the same object. We present an interpretation that the lengthening of the superhump period is a result of outward propagation of the eccentricity wave and is limited by the radius near the tidal truncation. We interpret that late stage superhumps are rejuvenized excitation of 3:1 resonance when the superhumps in the outer disk is effectively quenched. Many of WZ Sge-type dwarf novae showed long-enduring superhumps during the post-superoutburst stage having periods longer than those during the main superoutburst. The period derivatives in WZ Sge-type dwarf novae are found to be strongly correlated with the fractional superhump excess, or consequently, mass ratio. WZ Sge-type dwarf novae with a long-lasting rebrightening or with multiple rebrightenings tend to have smaller period derivatives and are excellent candidate for the systems around or after the period minimum of evolution of cataclysmic variables (abridged).
We present photometry of the first reported superoutburst of the dwarf nova VSX J074727.6+065050 during 2008 January and February. At its brightest the star reached magnitude 11.4 and this was followed by a slow decline at 0.09 mag/d for 19 days, corresponding to the plateau phase. There was then a rapid decline at 1.66 mag/d to a temporary minimum at magnitude 16.6 where it stayed for 2 to 3 days after which there were six remarkable echo outbursts before the star gradually faded back towards quiescence at ~magnitude 19.5. The overall outburst amplitude was at least 8 magnitudes and it lasted more than 80 days. During the plateau phase we observed common superhumps with Psh = 0.06070(6) d, but the period increased to Psh = 0.06151(5) d coinciding with the end of the plateau phase and the onset of the rapid decline. This corresponds to a continuous period change with P^dot = +4.4(9) x 10-5. During the echo outbursts there was a superhump regime with Psh = 0.06088(49) d. Evidence is presented which is consistent with the star being a member of the WZ Sge family of dwarf novae.