1,613 research outputs found
Asymptotic enumeration of dense 0-1 matrices with specified line sums
Let S=(s_1,s_2,..., s_m) and T = (t_1,t_2,..., t_n) be vectors of
non-negative integers with sum_{i=1}^{m} s_i = sum_{j=1}^n t_j. Let B(S,T) be
the number of m*n matrices over {0,1} with j-th row sum equal to s_j for 1 <= j
<= m and k-th column sum equal to t_k for 1 <= k <= n. Equivalently, B(S,T) is
the number of bipartite graphs with m vertices in one part with degrees given
by S, and n vertices in the other part with degrees given by T. Most research
on the asymptotics of B(S,T) has focused on the sparse case, where the best
result is that of Greenhill, McKay and Wang (2006). In the case of dense
matrices, the only precise result is for the case of equal row sums and equal
column sums (Canfield and McKay, 2005). This paper extends the analytic methods
used by the latter paper to the case where the row and column sums can vary
within certain limits. Interestingly, the result can be expressed by the same
formula which holds in the sparse case.Comment: Multiple minor adjustments. Accepted by JCT-
Pulse Profiles, Accretion Column Dips and a Flare in GX 1+4 During a Faint State
The Rossi X-ray Timing Explorer (RXTE) spacecraft observed the X-ray pulsar
GX 1+4 for a period of 34 hours on July 19/20 1996. The source faded from an
intensity of ~20 mCrab to a minimum of <~0.7 mCrab and then partially recovered
towards the end of the observation. This extended minimum lasted ~40,000
seconds. Phase folded light curves at a barycentric rotation period of
124.36568 +/- 0.00020 seconds show that near the center of the extended minimum
the source stopped pulsing in the traditional sense but retained a weak dip
feature at the rotation period. Away from the extended minimum the dips are
progressively narrower at higher energies and may be interpreted as
obscurations or eclipses of the hot spot by the accretion column. The pulse
profile changed from leading-edge bright before the extended minimum to
trailing-edge bright after it. Data from the Burst and Transient Source
Experiment (BATSE) show that a torque reversal occurred <10 days after our
observation. Our data indicate that the observed rotation departs from a
constant period with a Pdot/P value of ~-1.5% per year at a 4.5 sigma
significance. We infer that we may have serendipitously obtained data, with
high sensitivity and temporal resolution about the time of an accretion disk
spin reversal. We also observed a rapid flare which had some precursor
activity, close to the center of the extended minimum.Comment: 19 pages, 6 figures, accepted for publication in Astrophysical
Journal (tentatively scheduled for vol. 529 #1, 20 Jan 2000
Accretion column eclipses in the X-ray pulsars GX 1+4 and RX J0812.4-3114
Sharp dips observed in the pulse profiles of three X-ray pulsars (GX 1+4, RX
J0812.4-3114 and A 0535+26) have previously been suggested to arise from
partial eclipses of the emission region by the accretion column occurring once
each rotation period. We present pulse-phase spectroscopy from Rossi X-ray
Timing Explorer satellite observations of GX 1+4 and RX J0812.4-3114 which for
the first time confirms this interpretation. The dip phase corresponds to the
closest approach of the column axis to the line of sight, and the additional
optical depth for photons escaping from the column in this direction gives rise
to both the decrease in flux and increase in the fitted optical depth measured
at this phase. Analysis of the arrival time of individual dips in GX~1+4
provides the first measurement of azimuthal wandering of a neutron star
accretion column. The column longitude varies stochastically with standard
deviation 2-6 degrees depending on the source luminosity. Measurements of the
phase width of the dip both from mean pulse profiles and individual eclipses
demonstrates that the dip width is proportional to the flux. The variation is
consistent with that expected if the azimuthal extent of the accretion column
depends only upon the Keplerian velocity at the inner disc radius, which varies
as a consequence of the accretion rate Mdot.Comment: 7 pages, 5 figures, accepted by MNRAS. Included reference
The supermassive black hole in the Seyfert 2 galaxy NGC 5252
We present results from HST/STIS long-slit spectroscopy of the gas motions in
the nuclear region of the Seyfert 2 galaxy NGC 5252. The observed velocity
field is consistent with gas in regular rotation with superposed localized
patches of disturbed gas. The dynamics of the circumnuclear gas can be
accurately reproduced by adding to the stellar mass component a compact dark
mass of MBH = 0.95 (-0.45;+1.45) 10E9 M(sun), very likely a supermassive black
hole. Contrarily to results obtained in similar studies rotational broadening
is sufficient to reproduce also the behaviour of line widths. The MBH estimated
for NGC 5252 is in good agreement with the correlation between MBH and bulge
mass. The comparison with the MBH vs sigma relationship is less stringent
(mostly due to the relatively large error in sigma); NGC 5252 is located above
the best fit line by between 0.3 and 1.2 dex, i.e. 1 - 4 times the dispersion
of the correlation. Both the galaxy's and MBH of NGC 5252 are substantially
larger than those usually estimated for Seyfert galaxies but, on the other
hand, they are typical of radio-quiet quasars. Combining the determined MBH
with the hard X-ray luminosity, we estimate that NGC 5252 is emitting at a
fraction ~ 0.005 of L(Edd). In this sense, this active nucleus appears to be a
quasar relic, now probably accreting at a low rate, rather than a low black
hole mass counterpart of a QSO.Comment: Accepted for publication in A&
Angular Momentum Transfer in the Binary X-ray Pulsar GX 1+4
We describe three presentations relating to the X-ray pulsar GX 1+4 at a
workshop on magnetic fields and accretion at the Astrophysical Theory Centre,
Australian National University on 1998, November 12-13. Optical and X-ray
spectroscopy indicate that GX 1+4 is seen through a cloud of gravitationaly
bound matter. We discuss an unstable negative feedback mechanism (originally
proposed by Kotani et al, 1999), based on X-ray heating of this matter which
controls the accretion rate when the source is in a low X-ray luminosity state.
A deep minimum lasting ~6 hours occurred during observations with the RXTE
satellite over 1996, July 19-21. The shape of the X-ray pulses changed
remarkably from before to after the minimum. These changes may be related to
the transition from neutron star spin-down to spin-up which occurred at about
the same time. Smoothed particle hydrodynamic simulations of the effect of
adding matter with opposite angular momentum to an existing disc, show that it
is possible for a number of concentric rings with alternating senses of
rotation to co-exist in a disc. This could provide an explanation for the
step-like changes in Pdot which are observed in GX 1+4. Changes at the inner
boundary of the disc occur at the same timescale as that imposed at the outer
boundary. Reversals of material torque on the neutron star occur at a minimum
in L_X.Comment: 10 pages, 5 figures; accepted for publication by PAS
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