text:
## [1107.4322] Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order

Authors: Michele Levi

Date: 21 Jul 2011

Abstract: We calculate the next-to-next-to-leading order (NNLO) spin1-spin2 dynamics of a compact binary evaluated at fourth post-Newtonian (PN) order. We use an effective field theory (EFT) approach, and first demonstrate here the ability of the EFT approach to go at NNLO in the PN corrections of spin effects. The NNLO spin1-spin2 interaction sector includes contributions from diagrams, which are not pure spin1-spin2 diagrams, as they arise from other sectors. These diagrams contribute through the leading order spin accelerations and precessions, that should be first taken into account here. The EFT calculation is carried out in terms of the nonrelativistic gravitational (NRG) fields. The fact that the spin is derivative-coupled adds significantly to the complexity of computations. In particular, for the irreducible two-loop diagrams, which are the most complicated in this sector, irreducible two-loop tensor integrals up to order 4 are encountered. Moreover, not all of the benefits of the NRG fields apply to spin interactions, as all possible diagram topologies are realized at each order of G included. Still, the NRG fields remain advantageous, and thus there was no use of automated computations in this work. Our final result can be reduced, and a NNLO spin1-spin2 Hamiltonian can be derived from it.

#### Jul 31, 2011

1107.4322 (/preprints)
2011-07-31, 08:06

## [1107.5725] Measuring a cosmological distance-redshift relationship using only gravitational wave observations of binary neutron star coalescences

Date: 28 Jul 2011

Abstract: Detection of gravitational waves from the inspiral phase of binary neutron star coalescence will allow us to measure the effects of the tidal coupling in such systems. These effects will be measurable using 3rd generation gravitational wave detectors, e.g. the Einstein Telescope, which will be capable of detecting inspiralling binary neutron star systems out to redshift z=4. Tidal effects provide additional contributions to the phase evolution of the gravitational wave signal that break a degeneracy between the system's mass parameters and redshift and thereby allowing for the simultaneous measurement of both the effective distance and the redshift for individual sources. Using the population of O(10ˆ3-10ˆ7) detectable binary neutron star systems predicted for the Einstein Telescope the luminosity distance--redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations. We present the results of a Fisher information analysis applied to waveforms assuming a subset of possible neutron equations of state. We conclude that the redshift of such systems can be determined to O(10%) for z>1 and in the most optimistic case accuracies of 2% can be achieved.

#### Jul 31, 2011

1107.5725 (/preprints)
2011-07-31, 08:06

## [1107.5056] The final parsec problem: aligning a binary with an external accretion disc

Authors: Chris Nixon, Andrew King, Jim Pringle

Date: 25 Jul 2011

Abstract: We consider the interaction between a binary system (e.g. two supermassive black holes or two stars) and an external accretion disc with misaligned angular momentum. This situation occurs in galaxy merger events involving supermassive black holes, and in the formation of stellar--mass binaries in star clusters. We work out the gravitational torque between the binary and disc, and show that their angular momenta J_b, J_d stably counteralign if their initial orientation is sufficiently retrograde, specifically if the angle theta between them obeys cos(theta) < -J_d/2J_b, on a time short compared with the mass gain time of the central accretor(s). The magnitude J_b remains unchanged in this process. Counteralignment can promote the rapid merger of supermassive black hole binaries, and possibly the formation of coplanar but retrograde planets around stars in binary systems.

#### Jul 31, 2011

1107.5056 (/preprints)
2011-07-31, 08:06

## [1107.4987] Tests of gravity at the solar system scale

Authors: Marc-Thierry Jaekel, Serge Reynaud

Date: 25 Jul 2011

Abstract: As confirmed by tests performed in the solar system, General Relativity (GR) presently represents the best description of gravitation. It is however challenged by observations at very large length scales, and already at the solar system scale, tracking of the Pioneer 10/11 probes has failed to confirm their expected behavior according to GR. Metric extensions of GR, which are presented here, have the quality of preserving the fundamental properties of GR while introducing scale dependent modifications. We show that they moreover represent an appropriate family of gravitation theories to be compared with observations when analysing gravity tests. We also discuss different tests which could allow one to determine the metric extension of GR prevailing in the solar system.

#### Jul 31, 2011

1107.4987 (/preprints)
2011-07-31, 08:06

## [1107.4583] The Candidate Intermediate-Mass Black Hole in the Globular Cluster M54

Authors: J.M. Wrobel, J.E. Greene, L.C. Ho

Date: 22 Jul 2011

Abstract: Ibata et al. reported evidence for density and kinematic cusps in the Galactic globular cluster M54, possibly due to the presence of a 9400 solar-mass black hole. Radiative signatures of accretion onto M54's candidate intermediate-mass black hole (IMBH) could bolster the case for its existence. Analysis of new Chandra and recent Hubble Space Telescope astrometry rules out the X-ray counterpart to the candidate IMBH suggested by Ibata et al. If an IMBH exists in M54, then it has an Eddington ratio of L(0.3-8 keV) / L(Edd) < 1.4 x 10ˆ(-10), more similar to that of the candidate IMBH in M15 than that in G1. From new imaging with the NRAO Very Large Array, the luminosity of the candidate IMBH is L(8.5 GHz) < 3.6 x 10ˆ29 ergs/s (3 sigma). Two background active galaxies discovered toward M54 could serve as probes of its intracluster medium.

#### Jul 31, 2011

1107.4583 (/preprints)
2011-07-31, 08:06

## [1107.4294] Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries

Authors: Johannes Hartung, Jan Steinhoff

Date: 21 Jul 2011

Abstract: We present the next-to-next-to-leading order post-Newtonian (PN) spin(1)-spin(2) Hamiltonian for two self-gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincare algebra with the center-of-mass vector uniquely determined by an ansatz.

#### Jul 31, 2011

1107.4294 (/preprints)
2011-07-31, 08:06

## [1107.5064] Revealing the physics of r-modes in low-mass X-ray binaries

Authors: Wynn C. G. Ho, Nils Andersson (U Southampton), Brynmor Haskell (U Amsterdam)

Date: 25 Jul 2011

Abstract: We consider the astrophysical constraints on the gravitational-wave driven r-mode instability in accreting neutron stars in low-mass X-ray binaries. We use recent results on superfluid and superconducting properties to infer the core temperature in these neutron stars and show the diversity of the observed population. Simple theoretical models indicate that many of these systems reside inside the r-mode instability region. However, this is in clear disagreement with expectations, especially for the systems containing the most rapidly rotating neutron stars. The inconsistency highlights the need to re-evaluate our understanding of the many areas of physics relevant to the r-mode instability. We summarize the current status of our understanding, and we discuss directions for future research which could resolve this dilemma.

#### Jul 31, 2011

1107.5064 (/preprints)
2011-07-31, 08:06

## [1107.4106] The fate of Cyg X-1: an empirical limit on BH-NS merger rate

Authors: Krzysztof Belczynski, Tomasz Bulik, Charles Bailyn

Date: 20 Jul 2011

Abstract: The recent distance determination allowed precise estimation of the orbital parameters of Cyg X-1, which contains a massive 14.8 Msun BH with a 19.2 Msun O star companion. This system appears to be the clearest example of a potential progenitor of a BH-NS system. We follow the future evolution of Cyg X-1, and show that it will soon encounter a Roche lobe overflow episode, followed shortly by a Type Ib/c supernova and the formation of a NS. It is demonstrated that in majority of cases (>70%) the supernova and associated natal kick disrupts the binary due to the fact that the orbit expanded significantly in the Roche lobe overflow episode. In the reminder of cases (<30%) the newly formed BH-NS system is too wide to coalesce in the Hubble time. Only sporadically (1%) a Cyg X-1 like binary may form a coalescing BH-NS system given a favorable direction and magnitude of the natal kick. If Cyg X-1 like channel (X-ray active phase shorter than 10 Myr) is the only or dominant way to form BH-NS binaries in the Galaxy we can estimate the empirical BH-NS merger rate in the Galaxy at the level of 0.001 per Myr. This rate is so low that the detection of BH-NS systems in gravitational radiation is highly unlikely, generating Advanced LIGO/VIRGO detection rates at the level of only 1 per century. If BH-NS inspirals are in fact detected, it will indicate that the formation of these systems proceeds via some alternative and yet unobserved channels.

#### Jul 31, 2011

1107.4106 (/preprints)
2011-07-31, 08:06

## [1107.5707] The existence of a two-solar mass neutron star constrains the gravitational constant G_N at strong field

Date: 28 Jul 2011

Abstract: In General Relativity there is a maximum mass allowed for neutron stars that, if exceeded, entails their collapse into a black hole. Its precise value depends on details of the nuclear matter equation of state about which we are much more certain thanks to recent progress in low-energy effective theories.
The discovery of a two-solar mass neutron star, near that maximum mass, when analyzed with modern equations of state, implies that Newton's gravitational constant in the star cannot exceed its value on Earth by more than 8% at 95% confidence level. This is a remarkable leap of ten orders of magnitude in the gravitational field intensity at which the constant has been constrained.

#### Jul 31, 2011

1107.5707 (/preprints)
2011-07-31, 08:06

## [1107.4243] Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388

Authors: N. Lützgendorf, M. Kissler-Patig, E. Noyola, B. Jalali, P. T. de Zeeuw, K. Gebhardt, H. Baumgardt

Date: 21 Jul 2011

Abstract: Intermediate-mass black holes (IMBHs) are of interest in a wide range of astrophysical fields. In particular, the possibility of finding them at the centers of globular clusters has recently drawn attention. IMBHs became detectable since the quality of observational data sets, particularly those obtained with HST and with high resolution ground based spectrographs, advanced to the point where it is possible to measure velocity dispersions at a spatial resolution comparable to the size of the gravitational sphere of influence for plausible IMBH masses. We present results from ground based VLT/FLAMES spectroscopy in combination with HST data for the globular cluster NGC 6388. The aim of this work is to probe whether this massive cluster hosts an intermediate-mass black hole at its center and to compare the results with the expected value predicted by the $M_{\bullet} - \sigma$ scaling relation. The spectroscopic data, containing integral field unit measurements, provide kinematic signatures in the center of the cluster while the photometric data give information of the stellar density. Together, these data sets are compared to dynamical models and present evidence of an additional compact dark mass at the center: a black hole. Using analytical Jeans models in combination with various Monte Carlo simulations to estimate the errors, we derive (with 68% confidence limits) a best fit black-hole mass of $(17 \pm 9) \times 10ˆ3 M_{\odot}$ and a global mass-to-light ratio of $M/L_V = (1.6 \pm 0.3) \ M_{\odot}/L_{\odot}$.

#### Jul 31, 2011

1107.4243 (/preprints)
2011-07-31, 08:05

## [1107.3967] An Introduction to String Theory

Authors: James Bedford

Date: 20 Jul 2011

Abstract: These notes are based on lectures given by Michael Green during Part III of the Mathematics Tripos (the Certificate for Advanced Study in Mathematics) in the Spring of 2003. The course provided an introduction to string theory, focussing on the Bosonic string, but treating the superstring as well. A background in quantum field theory and general relativity is assumed. Some background in particle physics, group theory and conformal field theory is useful, though not essential. A number of appendices on more advanced topics are also provided, including an introduction to orientifolds in various brane configurations which helps to populate a relatively sparse part of the literature.

#### Jul 21, 2011

1107.3967 (/preprints)
2011-07-21, 04:36

## [1107.3866] Unexpected Formation Modes of the First Hard Binary in Core Collapse

Authors: Ataru Tanikawa, Piet Hut, Junichiro Makino

Date: 20 Jul 2011

Abstract: The conventional wisdom for the formation of the first hard binary in core collapse is that three-body interactions of single stars form many soft binaries, most of which are quickly destroyed, but eventually one of them survives. We report on direct N-body simulations to test these ideas, for the first time. We find that both assumptions are often incorrect: 1) quite a few three-body interactions produce a hard binary from scratch; 2) and in many cases there are more than three bodies directly and simultaneously involved in the production of the first binary. The main reason for the discrepancies is that the core of a star cluster, at the first deep collapse, contains typically only five or so stars. Therefore, the homogeneous background assumption, which still would be reasonable for, say, 25 stars, utterly breaks down. There have been some speculations in this direction, but we demonstrate this result here explicitly, for the first time.

#### Jul 21, 2011

1107.3866 (/preprints)
2011-07-21, 04:36

## [1107.2937] Electromagnetic counterparts of supermassive black hole binaries resolved by pulsar timing arrays

Authors: Takamitsu Tanaka, Kristen Menou, Zoltán Haiman (Columbia University)

Date: 14 Jul 2011

Abstract: Pulsar timing arrays (PTAs) are expected to detect gravitational waves (GWs) from individual low-redshift (z<1.5) compact supermassive (M>10ˆ9 Msun) black hole (SMBH) binaries with orbital periods of approx. 0.1 - 10 yrs. Identifying the electromagnetic (EM) counterparts of these sources would provide confirmation of putative direct detections of GWs, present a rare opportunity to study the environments of compact SMBH binaries, and could enable the use of these sources as standard sirens for cosmology. Here we consider the feasibility of such an EM identification. We show that because the host galaxies of resolved PTA sources are expected to be exceptionally massive and rare, it should be possible to find unique hosts of resolved sources out to redshift z=0.2. At higher redshifts, the PTA error boxes are larger, and may contain as many as 100 massive-galaxy interlopers. The number of candidates, however, remains tractable for follow-up searches in upcoming wide-field EM surveys. We develop a toy model to characterize the dynamics and the thermal emission from a geometrically thin, gaseous disc accreting onto a PTA-source SMBH binary. Our model predicts that at optical and infrared frequencies, the source should appear similar to a typical luminous active galactic nucleus (AGN). However, owing to the evacuation of the accretion flow by the binary's tidal torques, the source might have an unusually low soft X-ray luminosity and weak UV and broad optical emission lines, as compared to an AGN powered by a single SMBH with the same total mass. For sources near z=1, the decrement in the rest-frame UV should be observable as an extremely red optical color. These properties would make the PTA sources stand out among optically luminous AGN, and could allow their unique identification.

#### Jul 21, 2011

1107.2937 (/preprints)
2011-07-21, 04:36

## [1107.4014] The impact of a stochastic gravitational-wave background on pulsar timing parameters

Authors: J. Ellis, M. A. McLaughlin, J. P. W. Verbiest

Date: 20 Jul 2011

Abstract: Gravitational waves are predicted by Einstein's theory of general relativity as well as other theories of gravity. The rotational stability of the fastest pulsars means that timing of an array of these objects can be used to detect and investigate gravitational waves. Simultaneously, however, pulsar timing is used to estimate spin period, period derivative, astrometric, and binary parameters. Here we calculate the effects that a stochastic background of gravitational waves has on pulsar timing parameters through the use of simulations and data from the millisecond pulsars PSR J0437--4715 and PSR J1713+0747. We show that the reported timing uncertainties become underestimated with increasing background amplitude by up to a factor of $\sim10$ for a stochastic gravitational-wave background amplitude of $A=5\times 10ˆ{-15}$, where $A$ is the amplitude of the characteristic strain spectrum at one-year gravitational wave periods. We find evidence for prominent low-frequency spectral leakage in simulated data sets including a stochastic gravitational-wave background. We use these simulations along with independent Very Long Baseline Interferometry (VLBI) measurements of parallax to set a 2--sigma upper limit of $A\le9.1\times 10ˆ{-14}$. We find that different supermassive black hole assembly scenarios do not have a significant effect on the calculated upper limits. We also test the effects that ultralow--frequency (10$ˆ{-12}$--10$ˆ{-9}$ Hz) gravitational waves have on binary pulsar parameter measurements and find that the corruption of these parameters is less than those due to $10ˆ{-9}$--$10ˆ{-7}$ Hz gravitational waves.

#### Jul 21, 2011

1107.4014 (/preprints)
2011-07-21, 04:36

## [1107.3460] S. Chandrasekhar: White Dwarfs, $H^-$ ion,.., Black holes

Authors: Patrick Das Gupta

Date: 18 Jul 2011

Abstract: This is a concise review, addressed to undergraduate students, of S. Chandrasekhar's oeuvre in astrophysics, ranging from his early studies on white dwarfs using relativistic quantum statistics to topics as diverse as dynamical friction, negative hydrogen ion, fluid dynamical instabilities, black holes and gravitational waves. The exposition is based on simple physical explanations in the context of observational astronomy. Black holes and their role as central engines of active, compact, high energy sources have been discussed.

#### Jul 20, 2011

1107.3460 (/preprints)
2011-07-20, 04:24

## [1107.3528] Graviton mass bounds from space-based gravitational-wave observations of massive black hole populations

Authors: Emanuele Berti, Jonathan Gair, Alberto Sesana

Date: 18 Jul 2011

Abstract: Space-based gravitational-wave detectors, such as LISA or a similar ESA-led mission, will offer unique opportunities to test general relativity. We study the bounds that space-based detectors could place on the graviton Compton wavelength \lambda_g=h/(m_g c) by observing multiple inspiralling black hole binaries. We show that while observations of individual inspirals will yield mean bounds \lambda_g~3x10ˆ15 km, the combined bound from observing several events in a two-year mission is about ten times better: \lambda_g~3x10ˆ16 km (m_g~4x10ˆ-26 eV). This result is only mildly dependent on details of black hole formation and detector characteristics. The bound achievable in practice should be one order of magnitude better than this figure (and hence almost competitive with the static, model-dependent bounds from gravitational effects on cosmological scales), because our calculations ignore the merger/ringdown portion of the waveform. The observation that an ensemble of events can sensibly improve the bounds that individual binaries set on \lambda_g applies to any theory whose deviations from general relativity are parametrized by a set of global parameters.

#### Jul 20, 2011

1107.3528 (/preprints)
2011-07-20, 04:24

## [1107.3703] Recent Advances in the Numerical Simulations of Binary Black Holes

Authors: Pedro Marronetti, Wolfgang Tichy

Date: 19 Jul 2011

Abstract: Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of "things-we-know-how-to-do". Simulations of binary black holes in circular orbits, the holy grail of numerical relativity, are now tractable problems that lead to some of the most spectacular results in general relativity in recent years. We cover here some of the latest achievements and highlight the field's next challenges.

#### Jul 20, 2011

1107.3703 (/preprints)
2011-07-20, 04:18

## [1107.2872] Optimizing the Earth-LISA "rendez-vous"

Authors: Fabrizio De Marchi, Giuseppe Pucacco, Massimo Bassan

Date: 14 Jul 2011

Abstract: We present a general survey of heliocentric LISA orbits, hoping it might help in the exercise of rescoping the mission. We try to semi-analytically optimize the orbital parameters in order to minimize the disturbances coming from the Earth-LISA interaction. In a set of numerical simulations we include nonautonomous perturbations and provide an estimate of Doppler shift and breathing as a function of the trailing angle.

#### Jul 15, 2011

1107.2872 (/preprints)
2011-07-15, 06:48

## [1107.2819] Numerical simulations of black-hole binaries and gravitational wave emission

Authors: Ulrich Sperhake, Emanuele Berti, Vitor Cardoso

Date: 14 Jul 2011

Abstract: We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in three major areas of BH physics: (i) BHs as sources of gravitational waves (GWs), (ii) astrophysical systems involving BHs, and (iii) BHs in high-energy physics. We conclude with a list of the most urgent tasks for numerical relativity in these three areas.

#### Jul 15, 2011

1107.2819 (/preprints)
2011-07-15, 06:48

## [1107.2665] Toward Early-Warning Detection of Gravitational Waves from Compact Binary Coalescence

Authors: Kipp Cannon, Romain Cariou, Adrian Chapman, Mireia Crispín-Ortuzar, Nickolas Fotopoulos, Melissa Frei, Chad Hanna, Erin Kara, Drew Keppel, Laura Liao, Stephen Privitera, Antony Searle, Leo Singer, Alan Weinstein

Date: 13 Jul 2011

Abstract: Rapid detection of compact binary coalescence with a network of advanced gravitational-wave detectors will offer a unique opportunity for multi-messenger astronomy. Prompt detection alerts for the astronomical community might make it possible to observe the onset of electromagnetic emission from compact binary coalescence. We demonstrate a computationally practical filtering strategy that could produce early-warning triggers before gravitational radiation from the final merger has arrived at the detectors.

#### Jul 15, 2011

1107.2665 (/preprints)
2011-07-15, 06:48

## [1107.2904] Extending the effective-one-body Hamiltonian of black-hole binaries to include next-to-next-to-leading spin-orbit couplings

Authors: Enrico Barausse, Alessandra Buonanno (Univ. of Maryland)

Date: 14 Jul 2011

Abstract: In the effective-one-body (EOB) approach the dynamics of two compact objects of masses m1 and m2 and spins S1 and S2 is mapped into the dynamics of one test particle of mass mu = m1 m2/(m1+m2) and spin S* moving in a deformed Kerr metric with mass M = m1+m2 and spin Skerr. In a previous paper we computed an EOB Hamiltonian for spinning black-hole binaries that (i) when expanded in post-Newtonian orders, reproduces the leading order spin-spin coupling and the leading and next-to-leading order spin-orbit couplings for any mass ratio, and (iii) reproduces all spin-orbit couplings in the test-particle limit. Here we extend this EOB Hamiltonian to include next-to-next-to-leading spin-orbit couplings for any mass ratio. We discuss two classes of EOB Hamiltonians that differ by the way the spin variables are mapped between the effective and real descriptions. We also investigate the main features of the dynamics when the motion is equatorial, such as the existence of the innermost stable circular orbit and of a peak in the orbital frequency during the plunge subsequent to the inspiral.

#### Jul 15, 2011

1107.2904 (/preprints)
2011-07-15, 06:48

## [1107.1946] Assessing the redshift evolution of massive black holes and their hosts

Authors: Marta Volonteri, Daniel P. Stark

Date: 11 Jul 2011

Abstract: Motivated by recent observational results that focus on high redshift black holes, we explore the effect of scatter and observational biases on the ability to recover the intrinsic properties of the black hole population at high redshift. We find that scatter and selection biases can hide the intrinsic correlations between black holes and their hosts, with 'observable' subsamples of the whole population suggesting, on average, positive evolution even when the underlying population is characterized by no- or negative evolution. We create theoretical mass functions of black holes convolving the mass function of dark matter halos with standard relationships linking black holes with their hosts. Under these assumptions, we find that the local MBH - sigma correlation is unable to fit the z = 6 black hole mass function proposed by Willott et al. (2010), overestimating the number density of all but the most massive black holes. Positive evolution or including scatter in the MBH - sigma correlation makes the discrepancy worse, as it further increases the number density of observable black holes. We notice that if the MBH - sigma correlation at z = 6 is steeper than today, then the mass function becomes shallower. This helps reproducing the mass function of z = 6 black holes proposed by Willott et al. (2010). Alternatively, it is possible that very few halos (of order 1/1000) host an active massive black hole at z = 6, or that most AGN are obscured, hindering their detection in optical surveys. Current measurements of the high redshift black hole mass function might be underestimating the density of low mass black holes if the active fraction or luminosity are a function of host or black hole mass. Finally, we discuss physical scenarios that can possibly lead to a steeper MBH - sigma relation at high redshift.

#### Jul 15, 2011

1107.1946 (/preprints)
2011-07-15, 06:47

## [1107.1711] Accretion disks around kicked black holes: Post-kick Dynamics

Authors: Marcelo Ponce, Joshua A. Faber, James C. Lombardi Jr

Date: 8 Jul 2011

Abstract: Numerical calculations of merging black hole binaries indicate that asymmetric emission of gravitational radiation can kick the merged black hole at up to thousands of km/s, and a number of systems have been observed recently whose properties are consistent with an active galactic nucleus containing a supermassive black hole moving with substantial velocity with respect to its broader accretion disk. We study here the effect of an impulsive kick delivered to a black hole on the dynamical evolution of its accretion disk using a smoothed particle hydrodynamics code, focusing attention on the role played by the kick angle with respect to the orbital angular momentum vector of the pre-kicked disk. We find that for more vertical kicks, for which the angle between the kick and the normal vector to the disk $\theta\lesssim 30ˆ\circ$, a gap remains present in the inner disk, in accordance with the prediction from an analytic collisionless Keplerian disk model, while for more oblique kicks with $\theta\gtrsim 45ˆ\circ$, matter rapidly accretes toward the black hole. There is a systematic trend for higher potential luminosities for more oblique kick angles for a given black hole mass, disk mass and kick velocity, and we find large amplitude oscillations in time in the case of a kick oriented $60ˆ\circ$ from the vertical.

#### Jul 11, 2011

1107.1711 (/preprints)
2011-07-11, 03:24

## [1106.5056] Testing the black hole no-hair theorem at the galactic center: Perturbing effects of stars in the surrounding cluster

Authors: Laleh Sadeghian, Clifford M. Will

Date: 24 Jun 2011

Abstract: Observations of the precessing orbits of stars very near the massive black hole in the galactic center could provide measurements of the spin and quadrupole moment of the hole and thereby test the no-hair theorem of general relativity. Since the galactic center is likely to be populated by a distribution of stars and small black holes, their gravitational interactions will perturb the orbit of any given star. We estimate the effects of such perturbations using analytic orbital perturbation theory, and show that for a range of possible stellar distributions, and for an observed star sufficiently close to the black hole, the relativistic spin and quadrupole effects will be larger than the effects of stellar cluster perturbations. Our results are consistent those from recent numerical N-body simulations by Merritt et al.

#### Jul 11, 2011

1106.5056 (/preprints)
2011-07-11, 03:23

## [1106.6355] A detection pipeline for galactic binaries in LISA data

Authors: Tyson B. Littenberg

Date: 30 Jun 2011

Abstract: The Galaxy is suspected to contain hundreds of millions of binary white dwarf systems, a large fraction of which will have sufficiently small orbital period to emit gravitational radiation in band for space-based gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). LISA's main science goal is the detection of cosmological events (supermassive black hole mergers, etc.) however the gravitational signal from the galaxy will be the dominant contribution to the data -- including instrumental noise -- over approximately two decades in frequency. The catalogue of detectable binary systems will serve as an unparalleled means of studying the Galaxy. Furthermore, to maximize the scientific return from the mission, the data must be "cleansed" of the galactic foreground. We will present an algorithm that can accurately resolve and subtract >10000 of these sources from simulated data supplied by the Mock LISA Data Challenge Task Force. Using the time evolution of the gravitational wave frequency, we will reconstruct the position of the recovered binaries and show how LISA will sample the entire compact binary population in the Galaxy.

#### Jul 10, 2011

1106.6355 (/preprints)
2011-07-10, 01:40

## [1106.6313] Approximate Waveforms for Extreme-Mass-Ratio Inspirals in Modified Gravity Spacetimes

Authors: Jonathan R. Gair, Nicolas Yunes

Date: 30 Jun 2011

Abstract: Extreme-mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole, are prime candidates for detection with space-borne milliHertz gravitational wave detectors, similar to the Laser Interferometer Space Antenna. The gravitational waves generated during such inspirals encode information about the background in which the small object is moving, providing a tracer of the spacetime geometry and a probe of strong-field physics. In this paper, we construct approximate, "analytic-kludge" waveforms for such inspirals with parameterized post-Einsteinian corrections that allow for generic, model-independent deformations of the supermassive black hole background away from the Kerr metric. These approximate waveforms include all of the qualitative features of true waveforms for generic inspirals, including orbital eccentricity and relativistic precession. The deformations of the Kerr metric are modeled using a recently proposed, modified gravity bumpy metric, which parametrically deforms the Kerr spacetime while ensuring that three approximate constants of the motion remain for geodesic orbits: a conserved energy, azimuthal angular momentum and Carter constant. The deformations represent modified gravity effects and have been analytically mapped to several modified gravity black hole solutions in four dimensions. In the analytic kludge waveforms, the conservative motion is modeled by a post-Newtonian expansion of the geodesic equations in the deformed spacetimes, which in turn induce modifications to the radiation-reaction force. These analytic-kludge waveforms serve as a first step toward complete and model-independent tests of General Relativity with extreme-mass-ratio inspirals.

#### Jul 10, 2011

1106.6313 (/preprints)
2011-07-10, 01:40

## [1107.0766] A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source

Date: 5 Jul 2011

Abstract: The motion of a small compact object (SCO) in a background spacetime is investigated further in a class of model nonlinear scalar field theories having a perturbative structure analogous to the General Relativistic description of extreme mass ratio inspirals (EMRIs). We derive regular expressions for the scalar perturbations generated by the SCO's motion valid through third order in $\epsilon$, the size of the SCO to the background curvature length scale. Our expressions are compared to those calculated through second order in $\epsilon$ by Rosenthal in [E. Rosenthal, CQG 22, S859 (2005)] and found to agree but our procedure for regularizing the scalar perturbations is considerably simpler. Following the Detweiler-Whiting (DW) scheme, we use our regular expressions for the field and derive the regular self-force corrections through third order. We find agreement with our previous derivation based on a variational principle of an effective action for the worldline associated with the SCO thus demonstrating the internal consistency of our formalism. This also explicitly demonstrates that the DW decomposition of Green's functions is a valid and practical method of self force computation at higher orders in perturbation theory and, as we show in an appendix, at all orders in perturbation theory. Finally, we identify a master source from which all other physically relevant quantities are derivable. Knowing the master source perturbatively allows one to construct the waveform measured by an observer, the regular part of the field on the worldline, the regular part of the self force, and orbital quantities such as shifts of the innermost stable circular orbit, etc. The existence of a master source together with the regularization methods implemented in this series should be indispensable for derivations of higher-order gravitational self force corrections.

#### Jul 10, 2011

1107.0766 (/preprints)
2011-07-10, 01:37

## [1107.0996] Reliability of complete gravitational waveform models for compact binary coalescences

Authors: Frank Ohme, Mark Hannam, Sascha Husa

Date: 5 Jul 2011

Abstract: With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown gravitational waveforms from coalescing compact binaries by combining both descriptions into one complete hybrid signal. It is important to estimate the error of such waveforms. Previous studies have identified the PN contribution as the dominant source of error, which can be reduced by incorporating longer NR simulations. There are two outstanding issues that make it difficult to determine the minimum simulation length necessary to produce suitably accurate hybrids: (1) the relevant criteria for a signal search is the mismatch between the true waveform and a set of model waveforms, optimized over all waveforms in the model. For discrete hybrids this optimization is not possible. (2) these calculations require that NR waveforms already exist, while ideally we would like to know the necessary length before performing the simulation. Here we overcome these difficulties by developing a general procedure that allows us to estimate hybrid mismatch errors without numerical data, and to optimize them over all physical parameters. Using this procedure we find that, contrary to some earlier studies, ~10 NR orbits before merger allow for the construction of waveform families that are accurate enough for detection in a broad range of parameters, only excluding highly spinning, unequal-mass systems. Nonspinning binaries, even with high mass-ratio (>20) are well modeled for astrophysically reasonable component masses. In addition, the parameter bias is only of the order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the dimensionless spin magnitude. We take the view that similar NR waveform lengths will remain the state of the art in the Advanced detector era, and begin to assess the limits of the science that can be done with them.

#### Jul 10, 2011

1107.0996 (/preprints)
2011-07-10, 01:37

## [1107.1181] Mergers of black-hole binaries with aligned spins: Waveform characteristics

Authors: Bernard J. Kelly, John G. Baker, William D. Boggs, Sean T. McWilliams, Joan Centrella

Date: 6 Jul 2011

Abstract: We conduct a descriptive analysis of the multipolar structure of gravitational-radiation waveforms from equal-mass aligned-spin mergers, following an approach first presented in the complementary context of nonspinning black holes of varying mass ratio [Baker et al., Phys. Rev. D 78:044046 (2008)]. We find that, as with the nonspinning mergers, the dominant waveform mode phases evolve together in lock-step through inspiral and merger, supporting the previous waveform description in terms of an adiabatically rigid rotator driving gravitational-wave emission -- an implicit rotating source (IRS). We further apply the late-time merger-ringdown model for the rotational frequency introduced in Baker et al. (2008), along with an improved amplitude model appropriate for the dominant (2,+/- 2) modes. This provides a quantitative description of the merger-ringdown waveforms, and suggests that the major features of these waveforms can be described with reference only to the intrinsic parameters associated with the state of the final black hole formed in the merger. We provide an explicit model for the merger-ringdown radiation, and demonstrate that this model agrees to fitting factors better than 95% with the original numerical waveforms for system masses above ~ 150 MSun. This model may be directly applicable to gravitational-wave detection of intermediate-mass black hole mergers.

#### Jul 10, 2011

1107.1181 (/preprints)
2011-07-10, 01:37

## [1107.1267] Addressing the spin question in gravitational-wave searches: Waveform templates for inspiralling compact binaries with nonprecessing spins

Authors: P. Ajith

Date: 6 Jul 2011

Abstract: This paper presents a post-Newtonian (PN) template family of gravitational waveforms from inspiralling compact binaries with non-precessing spins, where the spin effects are described by a single "reduced-spin" parameter. This template family, which reparametrizes all the spin-dependent PN terms in terms of the leading-order (1.5PN) spin-orbit coupling term in an approximate way, has very high overlaps (fitting factor > 0.99) with non-precessing binaries with arbitrary mass ratios and spins. We also show that this template family is "effectual" towards a significant fraction of generic spinning binaries in the comparable-mass regime (m_2/m_1 < 10), providing an attractive and feasible way of searching for gravitational waves (GWs) from spinning low-mass binaries. We also show that the secular (non-oscillatory) spin-dependent effects in the phase evolution (which are taken into account by the non-precessing templates) are more important than the oscillatory effects of precession in the comparable-mass (m_1 ~= m_2) regime. Hence the effectualness of non-spinning templates is particularly poor in this case, as compared to non-precessing-spin templates. For the case of binary neutron stars observable by Advanced LIGO, even small spins (L_N . S/mˆ2 ~= 0.1) will cause significant de-phasing with non-spinning templates. This is contrary to the expectation that neutron-star spins may not be relevant for GW detection.

#### Jul 10, 2011

1107.1267 (/preprints)
2011-07-10, 01:37

## [1107.0854] Black-hole hair loss: learning about binary progenitors from ringdown signals

Authors: Ioannis Kamaretsos (Cardiff), Mark Hannam (Cardiff), Sascha Husa (Palma), B.S. Sathyaprakash (Cardiff)

Date: 5 Jul 2011

Abstract: Perturbed Kerr black holes emit gravitational radiation, which (for the practical purposes of gravitational-wave astronomy) consists of a superposition of damped sinusoids termed quasi-normal modes. The frequencies and time-constants of the modes depend only on the mass and spin of the black hole - a consequence of the no-hair theorem. It has been proposed that a measurement of two or more quasi-normal modes could be used to confirm that the source is a black hole and to test if general relativity continues to hold in ultra-strong gravitational fields. In this paper we propose a practical approach to testing general relativity with quasi-normal modes. We will also argue that the relative amplitudes of the various quasi-normal modes encode important information about the origin of the perturbation that caused them. This helps in inferring the nature of the perturbation from an observation of the emitted quasi-normal modes. In particular, we will show that the relative amplitudes of the different quasi-normal modes emitted in the process of the merger of a pair of nonspinning black holes can be used to measure the component masses of the progenitor binary.

#### Jul 10, 2011

1107.0854 (/preprints)
2011-07-10, 01:37

## [1107.1075] The case for testing MOND using LISA Pathfinder

Authors: Joao Magueijo, Ali Mozaffari

Date: 6 Jul 2011

Abstract: We quantify the potential for testing MOdified Newtonian Dynamics (MOND) with LISA Pathfinder (LPF), should a saddle point flyby be incorporated into the mission. We forecast the expected signal to noise ratio (SNR) for a variety of instrument noise models and trajectories past the saddle. For standard theoretical parameters the SNR reaches middle to high double figures even with modest assumptions about instrument performance and saddle approach. Obvious concerns, like systematics arising from LPF self-gravity, or the Newtonian background, are examined and shown not to be a problem. We also investigate the impact of a negative observational result upon the free-function determining the theory. We demonstrate that, if Newton's gravitational constant is constrained not be re-normalized by more than a few percent, only very contrived MONDian free-functions would survive a negative result. Finally we scan the structure of all proposed relativistic MONDian theories. We conclude that only the Einstein-Aether formulation would survive a negative result.

#### Jul 10, 2011

1107.1075 (/preprints)
2011-07-10, 01:37

format: plain


text:
Journal article Open Access

# RADIAÇÃO SOLAR EM PELOTAS, RS – ANÁLISE ESTATÍSTICA

Baptista da Silva, João; Llopart, Marta Pereira; Boiaski, Nathalie

### Dublin Core Export

<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:creator>Baptista da Silva, João</dc:creator>
<dc:creator>Llopart, Marta Pereira</dc:creator>
<dc:date>2019-09-18</dc:date>
<dc:description>The knowledge of the solar radiation (SR) and its interactions with other meteorological variables can help the planning of various activities. This variable is very important in studies of  agroclimatic zone seedling periods, potential productivity, necessity of irrigation and the development and use of the growth and culture yield models. Its also alternative source of energy in the moment that if has feeling the scarceness of the traditional source of energy. This paper reports the results of a study of the SR pattern in Pelotas, RS, Brazil, using records from the Estação Agroclimatológica de Pelotas during the 1961/2003 period (except the year of 1989). A preliminary study revealed that the SR monthly average follows the normal distribution, in all months. The results of the statistical analysis based on this assumption indicate that the SR monthly average decreases from january to june, where it reaches the highest value and increases until december, where it attains the maximum. Exactly the inverse that happens with the relative humidity. In the modelling of data to long of time, for the harmonic analysis, distinguish the annual wave with 99% of representativity</dc:description>
<dc:identifier>https://zenodo.org/record/3445439</dc:identifier>
<dc:identifier>10.5281/zenodo.3445439</dc:identifier>
<dc:identifier>oai:zenodo.org:3445439</dc:identifier>
<dc:relation>doi:10.5281/zenodo.3445438</dc:relation>
<dc:relation>url:https://zenodo.org/communities/0622</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:subject>descriptive statistics, climatology, periodic regression</dc:subject>
<dc:title>RADIAÇÃO SOLAR EM PELOTAS, RS  – ANÁLISE ESTATÍSTICA</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>publication-article</dc:type>
</oai_dc:dc>

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# What large cardinals are limits of Ramsey cardinals?

What large cardinal axiom, if any, implies that there are unboundedly many Ramsey cardinals below the large cardinal?

That is, is there a large cardinal axiom, such that if $$\kappa$$ is that large cardinal there are unboundedly many Ramsey cardinals $$< \kappa$$.

(I removed the past version of the answer, since I read "unboundedly many Ramsey cardinals" as "proper class of Ramsey cardinals", which is perhaps the more natural reading for a set theorist.)

If $$\kappa$$ is measurable then it is the limit of Ramsey cardinals, and in fact it is a measure $$1$$ limit of Ramsey cardinals. To see that, note that (1) measurable is Ramsey; and (2) if $$M$$ is an inner model that agrees with $$V$$ up to $$V_{\alpha+1}$$, then $$M$$ agrees with $$V$$ on whether or not $$\alpha$$ is a Ramsey cardinal, since being Ramsey is a 2nd order property.

Combine the two facts, and we see that if $$j\colon V\to M$$ witnessing that $$\kappa$$ is measurable, then $$V_{\kappa+1}\subseteq M$$, so $$\kappa$$ is Ramsey in $$M$$. But then the set of Ramsey cardinals below $$\kappa$$ has measure $$1$$.

Of course, we can just look at "worldly limit of Ramsey cardinals" or "inaccessible limit of Ramsey cardinals", etc. Much weaker axioms.

• Regarding the last paragraph: Woodin cardinals are not measurable, but are an inaccessible limit of measurable cardinals. Apr 25 '20 at 0:53
• (And, again, congratulations!) 🥳 Apr 25 '20 at 0:54
• @AndrésE.Caicedo: Thanks! :) Apr 25 '20 at 7:18


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Tag Info

Hot answers tagged mosfet

13

According to datasheet: But you're not driving the gate with 10V, rather it's close to 6-7V so RdsON will be higher. Note this is a guaranteed maximum value. Actual value may be lower. As Andy says in his answer, if the FET follows the "typical" characteristics graph, its RdsON will probably be around 0.7 ohms, but notice the text in the corner of ...

6

So what is it then? This is the correct graph: - Taken from this wiki page. Saturation refers to the channel being saturated and, as you said, no matter what $V_{DS}$ you apply, current remains constant. It is sometimes also referred to as the active region (not to be confused with the MOSFET being activated or ON). The linear (triode) or ohmic region is ...

5

I've builded this simple circuit that has the purpose to swiching on ad off a 12 V / 25 W lamp That's a load current of about 2 amps (25 watts divided by 12 volts). The IRF730 MOSFET just isn't very suitable for a 2 amp load: - Whether the gate control voltage is 6 volts or 10 volts you will get about 2.5 watts to 3 watts dissipated in the MOSFET and that ...

4

Capacitor: 40uF, DC Power Source: 100V, DC Switching time: ~us (originally nanoseconds) Current in a capacitor can be calculated from the derivative vs time of voltage across it: $i = C dv/dt$ With dt=1µs, dv=100V, C=40µF we got i=4000 A. This is quite impractical. If the charger does not use inductive energy storage, instead simply connecting a ...

4

On the IRF730's datasheet I can read that it can handle more than 7 A Never trust the current ratings given on a MOSFET datasheet. They are obtained under artificial lab conditions you will never achieve in practice and are essentially useless. You can use them as a metric to non-rigorously compare the relative current capability of MOSFETs, but that is ...

4

this circuit needs the mosfets to switch once every 5 minutes (not pwm, that's why I didn't put a driver), does 12V reach all gates? – Ricardo Casimiro 4 mins ago Yes all the current is drawn by the 10k resistor to 11.7V with Vce(sat) on the opto. or > 1mA This works well with 4mA input or more. If using 3.3V input (3.3V-1.2)/(220+25 cmos) = 8.5mA If ...

3

Two cascaded common emitter BJT amplifiers will have many more times the voltage and current gain of a single BJT amplifier. Because of this the threshold of the LED turning on and off is much more singular in nature as you adjust the potentiometer.

3

It's a P-channel MOSFET. But it's in backwards, so it's basically acting as a diode due to the body diode. That's ok, as I will explain below. Assume that the battery is one LiPo cell (3.7 ~ 4.1V max.) With the V_USB off, then the FET body diode is forward biased. The FET is also turned on (fun fact: current can flow in either direction in a FET.) Now turn ...

3

There are a lot of improvements that could be made to this design. Fundamentals that need to be taught Vgs gate voltage for low resistance needs to be at least 250% time the worst-case threshold Vt ( Vgs(th) ) for classic FET types from 2 to 4V. This means 10V min. for Vgs The subthreshold types <=1V only need >= 200% times the threshold voltage. ...

3

Capacitor: 40uF, DC Power Source: 100V, DC Switching time: ~ns Source Output impedance: ~50Ohm The charge/discharge rate should be in the nanosecond range To charge a 40 μF capacitor from a source with 50 Ω impedance cannot be done in nano seconds. The time taken to charge the capacitor to approximately 63.2% of 100 volts will be: - \text{50 Ω } \times \...

2

Your answer is approximation. The following is a graph of output characteristics for an arbitrary 2N7000 MOSFET:- Assume a fixed gate drive $V_{GS}$ of 5V and ignore all the other curves. So it's fixed. Consider the MOSFET then as an opaque component with only two legs, Drain and Source. As $V_{DS}$ (voltage across component) changes, $I_D$ (...

2

A 12V 50 W high beam+low beam bulb in series will limit current to 2.4A as the Cap charges up. dt= 33F * 12V / 2.4A = 165 seconds. The bulb will draw more current as it dims below visibility and speed up a bit.

1

Your wire is not defined on the schematic. Typically Delays are made for Half Bridges to delay turn-on to avoid short circuit or shoot -thru and depend on load inductance and FET Capacitance which I modelled here for a power FET with Ciss. The Turn-ON delay is circled and OFF is assumed to be x ns with low diode resistance. You must define more details on ...

1

If I pull up the IN pin to 3.3V or 5V will my MOSFET turn on, and if I give a logic 0 signal to IN pin will the MOSFET turn off. Yes. Applies to all three gate drivers mentioned. None of them have inverted inputs or outputs. You can look for the timing diagrams in the datasheets to see for yourself. That said, there’s a catch. None of the gate drivers you ...

1

to turn the mosfet on you need to put the gate voltage to be 3.3V above the source voltage. This means that if you want the battery voltage on the source you need more voltage than the battery has on the gate. these drivers all use capacitors to make the high voltage by adding VCC to it, but it only makes a pulse of charge, so if you're not occasionally ...

1

In Fig 2.6(c), it's not negative ions that are under the gate, but negative carriers (electrons) that are mobile and free to move in their plane. Underneath that there is an insulating depletion region (fixed negative charge from the p-type material where holes have been repelled from), and underneath that there is conductive p-type material. The depletion ...

1

Is this an acceptable way to drive a mosfet? Quite possibly not acceptable - you have to ensure that the gate drive voltage can fully turn on the MOSFET and, because the MOSFET source is expected to reach the same voltage as the +14.5 volt supply, the gate drive voltage needs to be several volts above that (anything between 4 volts and 10 volts higher). So ...

1

The circuit works fine as a high side power switch with bidirectional isolation when off. For example, if you use it with a battery, it can prevent the battery from both charging and discharging. But it cannot turn on when both A and B nodes are near or below ground. The reason is that the sources will be pulled down to ground and if A and B are both also ...

1

I've used this Electrical forum for the first time and I'm very impressed for the real high quality of all replays. I'm a teacher, as I said, and I've very appreciated all explanations supported by diagrams and datasheets. But let me go to my results (for now only simultated on Multisim). Setting Vds to 10 V, changes very little because the Pd is about 2,80 ...

1

Use a P-channel MOSFET eg. AO3401A to cut Vcc. Low to the gate = ON. simulate this circuit – Schematic created using CircuitLab Add a 1K resistor series with the TRIG input and make sure that you drive TRIG low before shutting off the Vcc and do not drive it high until after Vcc has been turned on. Also do not drive ECHO high as an output (it should ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
## FANDOM

25,675 Pages

April 2018: Tri-Beam, LAER, Elijah's LAER, Multiplas DPS updated.
March 2018: Calculations have been vastly improved and expanded upon.
Feb 2016: First release.

## Introduction

Figuring out the best weapon for a situation is very hard. It's probably more difficult than you realize. I will now attempt to figure out what the highest DPS weapon is in the game while taking into account as many variables as possible. If you want to just jump straight into the results, go ahead. But I think you will fail to appreciate just how far I've went to try to make my data as true as possible.

1. You don't care about sneak damage.
2. You are playing on PC and will use YUP to fix glitchy perks, but not other gameplay mods.
3. Gun condition is always 100%. (Anything but 100% CND means lower crit rate.)
4. Your character is maxed out. 10 SPECIAL, all the relevant perks, infinite supply of any ammunition, etc.
5. You are wearing the outfit that gives the highest critical chance.
7. You are not doing VATS, headshots, special attacks, or power attacks.
8. You use almost all drugs, except from poisons and Daturana Root.
9. Your primary concern is DPS.
10. You need to empty your clip and reload at least once before all the enemies are dead.
11. You will click attack exactly 5.5 times per second while aiming perfectly at the enemy.
12. Your attacks with explosive weapons are direct hits.
13. You are playing on Very Hard difficulty.
14. There are no enemy-specific perks that increase your DPS against the enemy you are facing.
15. You are not under the influence of the highly situational Atomic! perk.
16. The opponent does not have any DR.
17. You are primarily concerned about the DPS of weapons for the player, not the companions.

VATS increases 'base unarmed/melee damage' for non-thrown weapons by two. It also increases critical hit chance by 5-6%. Things like Camarader-E changes this. Perks like Center of Mass further muddies the water. The DPS values here assume the player does not have the perk or hits the enemy limbs instead. No, I can't calculate DPS factoring in accuracy. You have to decide what spread is good enough for a given purpose.

## Perks

No attack speed bonuses, be it from perks or consumables, work for automatic weapons. Nothing in the GECK states that this will happen, but that's what happens in practice. If you don't understand this you have no clue how DPS works in this game.

Perk Choices
The level 50 perk chosen is a major and irreversible decision (absent of console commands) that affects weapons a lot in different ways. There's +50% critical damage, +10% damage (and +100 max HP), and +20% firing rate. 20% firing rate is useless for automatics right off the bat. On top of this, there is a realistic speed cap for each weapon, and your weapon will wear out faster (decreasing combat effectiveness). It is very rarely the highest DPS perk to take so it's out. The luck bonus of Just Lucky I'm Alive is pointless given that you have 10 SPECIAL. On the other hand, most of the time it nets the highest DPS. Finally, Thought You Died still gives a good DPS boost and gives an extra 100 max HP, which is very useful. Crit damage tends to be better against heavily armored enemies, while damage perk tends to be the best in select circumstances against medium or lightly armored enemies.

Fast Shot: You will get more scope sway and a 20% penalty in accuracy, but in exchange you will get a 20% increase in attack speed for non-unarmed or melee weapons. In VATS the 20% decrease is mostly mitigated due to perks, but the same can't be said for free-fire. You also get 20% decrease in AP usage, but this article assumes VATS is not used. This is a more subjective decision. However, this trait is all downside for automatic weapons, so chose wisely. The chart you will soon see does not include the penalty of Fast Shot for automatic weapons, which they would have if you have Fast Shot and want to get the most out of your short-ranged or non-automatic weapons. It will assume that Fast Shot was used for all the non-automatic weapons, with its spread adjusted accordingly.

Heavy Handed: You get a 20% damage increase and a 60% decrease in critical damage. This perk always lowers DPS because critical damage is a huge part of melee and unarmed weapon DPS. It also doesn't affect guns, so this trait is objectively terrible.

Universal Perks & Chems
1.05 (Bloody Mess) * 1.04 (Lord Death) * 1.1 (Yao Gui Meat) * 1.25 (Slasher or Psycho) = 1.5015 or 50.15% damage boost.

Non-Universal Perks & Chems
Shotgun Surgeon - Enemy DT -10 for shotguns.
Cowboy - 25% damage boost to all revolvers, lever-action firearms, dynamite, knives, and hatchets.
Laser Commander - 15% damage boost to all laser weapons.
Grunt - 25% damage boost to many guns and a few knives. Note: Grunt does not affect DLC weapons outside of Honest Hearts without a bugfix mod.
Demolition Expert - 60% damage boost to explosive weapons.
Slayer - 30% speed increase for melee and unarmed attacks.
Melee Hacker - 10% speed increase for melee and unarmed attacks.
Pyromaniac - 50% damage boost to all fiery weapons.

Perks like Grunt do not affect weapons for other DLCs, but this is fixed in YUP. Rushing Water, Fast Shot, and Ain't Like That Now can all increase attack speed. Melee and unarmed weapons don't have Fast Shot but do have Slayer and Melee Hacker. Weapon Binding Ritual increases unarmed and melee by a flat 10. The Daturana Root increases unarmed damage by 1 but decreases agility by 2. The effect of the Daturana Root is too small to matter, and I have decided to ignore it.

## Critical Hit System

The DT of your opponent along with the chems, perks, critical chance/damage, and ammo type will affect which option nets the highest DPS. This article sidesteps almost all of those factors. Let's take a look at how the critical hit system works.

(Base Crit Chance * Weapon Crit Multiplier) + Flat Crit Modifiers = Actual Crit Chance

The 'base crit chance' can be found by typing "player.getav critchance". As you can see, "Flat Crit Modifiers" apply after the weapon multiplier and base crit chance are figured out.

A flat crit modifier is superior to a regular crit modifier. A good way to show this is with a high rate of fire weapon and a low base critical chance. Here's a quick comparison, assuming you have a minigun and a base critical rate of 10%. It has a weapon critical multiplier of 0.02.

(0.1 * 0.02) + 0.1 = 0.102
(0.2 * 0.02) + 0 = 0.004

Let's look at the highest critical chance build you can make in Fallout: New Vegas.
5% - 1st Recon Beret
5% - Ulysses Duster (NOT Elite Riot Armor, as you lose Light Touch.)
10% - 10 Luck
3% - Built to Destroy
5% - Finesse
10% - True Police Stories w/ Comprehension
---
38% Base Crit Chance

Flat Crit Modifiers:
5% - Light Touch
15% - Ninja (Unarmed/Melee) (Ninja is a base crit chance modifier due to a glitch. Patched on PC, it's a flat crit modifier.)
4% - Set Lasers for Fun (Energy Weapons)
10% - Laser Commander (Laser Weapons)
5% - VATS

Crit Chances w/o VATS:
Guns - (0.38 * Weapon Crit Chance) + 0.05
Energy Weapons - (0.38 * Weapon Crit Chance) + 0.19
Non-Laser Energy Weapons - (0.38 * Weapon Crit Chance) + 0.09
Melee & Unarmed - (0.38 * Weapon Crit Chance) + 0.20

Now let's look at critical damage. Fortunately, this part is pretty simple.

50% - Better Criticals
50% - Just Lucky I'm Alive
50% - Elijah's Ramblings (Melee)
---
Let's calculate the total critical damage if you are using a gun. 1.5 x 1.5 = 2.25. This means a weapon with a critical damage of 10 will now do 22.5 damage for its critical damage (add the base damage to get the total damage of the hit). I've actually tested the 225% figure myself. It is correct. Please note that Just Lucky I'm Alive is not always the best perk out of the three level 50 perks for a given weapon's DPS.

Crit Damage:
Melee - 337.5%
Non-melee - 225%

Critical Damage + Special Ammo vs Armor
No matter what difficulty you play on, the game treats the damage of your weapons the same up until the very end. This means that you will need the same amount of damage per projectile to negate the enemy's DT regardless of difficulty level.

Let's say you have a Medicine Stick, which for you does 78 dmg per bullet. You also have 225% critical damage. Let's assume you have 100% critical rate. You are using 45 Gov't SWC, which is x1.2 damage and enemy DT -6.

Medicine Stick + 45 Gov't SWC:
Weapon Damage: 78 + 175.5 = 253.5
Opponent DT: 100-6 (Bullet effect.)
(253.5 - 94) * (0.5 * 1.2) = 95.7 dmg (The 0.5 is from Very Hard penalty, and the 1.2 is from bullet effect.)

If enemy DT is 10 and your DAM (damage per projectile, not including any buffs except weapon mods) is 50, you will do 40 damage. DT can decrease your damage to a minimum of x0.2 it's normal amount. This is different if you are using ammunition that changes your damage (like hollow point or max charge). This process is convoluted, but if you are interested, there is a section after the results section that explains the process.

Because armor piercing ammo's DT effect applies before DT vs bullet damage calculation is done, using that over regular ammo helps the player jump over enemy DT. On the other hand, ammo that increases gun damage does not help the player jump over enemy DT because the extra damage effect of the bullet applies after DT vs bullet damage calculation is done. In other words, 15% damage boosting ammo is very different from -15 DT armor piercing ammo when dealing with armored targets.

Because perks that increase damage of a weapon are applied after the damage vs DT calculations are done, they are not useful for breaking through enemy armor. On the other hand, perks that increase critical damage (and by extension, critical chance) will help in that regard. Note that even things that do not break through enemy armor could increase DPS against armor. A simple example is Psycho.

Camarader-E boosts the base damage of a laser weapon. In other words, Camarader-E may help the player hop over enemy DT. This is a rare situation because non-critical-related perks and damage boosting ammunition do not to this. In addition, Camarader-E affects each projectile of a weapon, meaning it benefits the Tri-Beam Laser Rifle by a huge amount.

With Elijah's LAER which has 65 dmg (and no other perks but Camarader-E) against a Bighorner with 56 DT (ammo naturally has -2 DT effect, for a total DT of 54), I did 16 damage. Let's assume first that Camarader-E adds +5 to base damage of the weapon. We have 65+5 or 70 dmg. 70-54=16. The result matches. Let's assume Camarader-E adds +5 to damage after calculating DT vs dmg. 65 * 0.2 (we don't subtract because that would be below 65 * 0.2) = 13. If you add 5 to 13, you get 18. That's not 16.

And now to prove that Camarader-E affects every beam of the Tri-Beam Rifle: Against a Bighorner with 22 DT (again, net result 20 DT due to ammo), we get 30 damage. The rifle does 25x3 by default. If it was 30x3, then the result should be 3 * (30 - 20) = 30 damage. If it acted like the PipBoy claims, then it would be 3 * {[25 + (5/3)] - 10} = ~20 damage.

The DPS values of my chart take into account very hard difficulty level, critical chance, critical damage, ammunition types, perks, traits, chems, attack speed caps, ROF glitches, flawed damage formulas, weapons that reload one shot at a time, weapons that ignore DR/DT, and the whole nine yards. The DPS values in other parts of the wiki do not consider all the of the factors. Because we're looking at end DPS against an enemy with a certain DT, showing damage, regular DPS, critical chance, and critical multipliers is pointless.

Obviously melee and unarmed weapons cannot attack from a far distance away. A large reach with a melee or unarmed weapon is still useful, but its utility can't be calculated. Things like Gehenna's fire effect do not stack, but instead resets the timer on the effect.

Melee and unarmed weapons can use poisons. This make my calculations much more difficult because while the same poison doesn't stack in terms of damage, different ones do. While it would be technically superior to cycle through all the venoms and reapply them when all of them are used, that is a very masochistic way of playing the game. Also, consider how small the poison damage is relative to the best melee weapons. For example, Blood-Nap has 612 DPS against an enemy with 0 DT. Even if you get Bleak Venom and Cloud Kiss, Lethal down, that's 14 DPS increase. You'll have to hotkey the poisons too, otherwise the delay of pulling up the Pip-Boy and back down would cause a net loss in DPS. For the purposes of the chart below, the assumption will be that no poisons are used.

Explosive weapons are obviously able to damage more than one enemy at once at the expense of possible damage to oneself or their companions. Weapons that fall under Meltdown will cause explosive energy damage to appear when an enemy is killed. Elijah's LAER and LAER both do bonus damage to enemies in power armor and robots. This is noteworthy because high DT targets are often wearing power armor. LAER's bonus damage does not apply to NCR Heavy Troopers. If I had to estimate, I would say that the extra damage against robots and powder armor users is ~20% for 0DT enemies and <5% for 15 or 30DT enemies.

Missiles and mini-nukes come in cluster bomb varieties. Even when standing close enough to the target such that the player can take damage from the explosions once in a while, the accuracy of such ammunition is too low to be useful unless the enemy is standing next to a wall behind them. In that case the bombs will hit the wall nearby and detonate close to the target. Needless to say, highly explosive weaponry can cause massive collateral damage.

It is much easier to hold down fire with an automatic weapon compared to spam-clicking at a constant 5.5 clicks per second to maintain a good DPS on non-automatic weapons. For weapons fed a single round of ammunition at a time, I shot the weapon as soon as it got the last round in to maximize DPS. This is ver annoying to pull off in practice and is a ding against Medicine Stick.

Non-Hitscan Projectiles
There is a game bug where explosive projectiles do not do direct hit damage even when it's a direct hit outside of VATS. JIP fixes this bug.

A projectile that takes time to reach the enemy may require more leading as the enemy moves around in long range fights, making it harder to land hits outside of VATS. The time it takes to travel the distance also delays when you can start dealing damage at the initial point of the fight. The longer the fight, the less noticeable this effect is, but I doubt it is a large enough factor to matter in any situation.

## The Limits of Calculations

The attack speeds in the game are hard to calculate and glitched to some extent. Despite the wording in the game its files, ROF buffs only affect non-automatics. If ROF is too high and the player cannot click infinitely fast, the weapon may stop firing all of a sudden. This is why some weapons do not have Ain't Like That Now DPS values in the final comparison graph - since adding it to Fast Shot and Rushing Water glitches it out at 5.5 clicks per second, it cannot be the highest DPS setup for that weapon. Why 5.5 times per second? Because it's fast clicking that people should be able to sustain for some time.

To precisely figure out time to empty a clip and be ready to fire again (and by extension, ROF), I record footage of my autoclicking. In Premiere I find the ending frame and subtract it from the start frame and multiply the value by 0.16666 to get number of seconds. Then I divide it by the amount of reloads.

The damage formula listed in the combat page of the wiki is a great starting point but fails against armored targets in many situations. I could not come up with a better alternative that worked with other buffs like chems. To sidestep the issue with tricky calculations to a formula nobody understands, I used the weapon in the game against a Powder Ganger stuck on a cross in Nipton with Living Anatomy off. I had multiple hotkeys to change perks, DT, Fast Shot trait, view HP, and reset HP.

The critical chances are calculated instead of tested and using GECK information on rounds per clip, I can figure out the average amount of shots per clip that will be critical hits. Using damage values obtained from real world testing, I can figure out how much damage is done on an average clip when factoring in critical damage and chance.

The Fast Shot perk increases sway of the weapon, which can't really be calculated and quantified in any practical way. Aiming down sights reduces sway according to the wiki, but by how much is unknown.

Finally, the way the weapons glitch out when ROF is too high at 5.5 clicks per second is unpredictable. Due to this the margin of error of automatics is maybe 2-3%, while for non-automatics it goes up to 5-10%.

## Results

If you don't know what each column means, hover your cursor over the small icon at the top of the chart. The final thing to note here is that the chart assumes the enemy has 0 DR.

Weapon name Damage per second, 0 DT
Damage per second, 15 DT
Damage per second, 30 DT

.45 Auto SMG Honest Hearts 459 211 67 1.8
12.7mm SMG GRA Gun Runners' Arsenal 385 138 62 1.6
25mm grenade APWGun Runners' Arsenal 550 325 222 0.7
ww Alien blaster 308 283 262 0
A Light Shining in Darkness Honest Hearts 415 272 222 0.66
AER14 prototype 481 460 395 0.0225
All-American 241 199 141 0.035 (0.02275)
Annabelle 226 214 202 0.02
Assault carbine
(GRA) Gun Runners' Arsenal
247 134 87 0.9
Automatic rifle Dead Money 190 103 72 2.5
Ballistic fist 308 308 285
Blade of the East 281 281 251
Bozar HP Gun Runners' Arsenal 272 26 16 0.75 (0.4875)
Chance's knife 540 540 465
Christine's CoS silencer rifle¹ Old World Blues (add-on) 453 280 228 0.02
CZ57 Avenger 406 220 142 0.55
Elijah's jury-rigged Tesla cannon Old World Blues (add-on) 315 308 286 0
Esther Gun Runners' Arsenal 923 911 899 0.6
FIDO Old World Blues (add-on) 302 158 76 1.5
Wild Wasteland Fist of the North Rawr
480 480 448
Gatling laser 732 543 161 0.6
Gehenna Gun Runners' Arsenal 530 530 467
Gobi Campaign scout rifle 381 330 239 0.018
Grenade machinegun 222 165 114 1
Heavy incinerator 121 34 33 0.5
Holorifle¹ Dead Money 260 245 228 0.18
Hunting rifle 368 255 218 0.01
K9000 cyberdog gun Old World Blues (add-on) 304 129 33 1.35
Katana Gun Runners' Arsenal 358 358 311
Knock-Knock 318 318 285
La Longue Carabine 332 200 158 0.05
LAER³ Old World Blues (add-on) 810 720 647 0.096
Laser pistol²
(GRA) Gun Runners' Arsenal
216 187 106 0.1
Laser RCW 251 199 77 0.08
Laser rifle 484 563 589 0.025
Li'l Devil Gun Runners' Arsenal 448 292 196 1.08
Light machine gun 472 256 94 1.5 (0.975)
Lucky 260 163 134 0.3
Maria 336 162 113 0.2
Medicine Stick Gun Runners' Arsenal 357 253 207 0.06
Mercy 456 412 367 1.2
Minigun 392 213 131 0.65

Multiplas rifle 292 267 201 1.5
Mysterious Magnum 327 200 159 0.7
Nuka Breaker Gun Runners' Arsenal 517 517 487
Gun Runners' Arsenal
446 433 421
Paciencia Gun Runners' Arsenal 392 321 266 0.01
Q-35 matter modulator 372 360 325 0.2
Oh, Baby! 368 368 336
Plasma caster 445 428 378 0.7
Plasma Defender
(GRA) Gun Runners' Arsenal
296 277 235 0.3
Plasma pistol
(GRA) Gun Runners' Arsenal
295 246 202 0.5
Protonic inversal axe Old World Blues (add-on) 297 297 269
Ranger Sequoia 408 284 234 0.1
Riot shotgun 440 367 147 2.5
Saturnite fist super-heated² Old World Blues (add-on) 413 413 369
Service rifle 243 132 76 0.55 (0.3575)
Sleepytyme Gun Runners' Arsenal 271 64 36 1.7
Sprtel-Wood 9700 Gun Runners' Arsenal 611 491 192 0.5
Survivalist's rifle Honest Hearts 528 339 227 0.08
The Smitty Special Gun Runners' Arsenal 251 221 137 1.3
That Gun 386 215 177 0.5 (0.325)
This Machine 361 211 194 0.5
Trail carbine 229 142 117 0.06
Tri-beam laser rifle GRA Gun Runners' Arsenal 866 799 598 0.5
Two-Step Goodbye
Gun Runners' Arsenal
174 174 148
Vance's 9mm SMG 344 70 36 1.5

¹Damage over time effect is not calculated.
²Grunt fix does not affect this weapon. While a Bowie Knife is a knife used in combat, the combat knife is a specific category in the game and Bowie Knives are not in that category.
³Does not consider bonus damage against robots and non-NCR-Heavy-Troopers which use power armor.

To the right is a graph showing how a weapon/ammunition combo performs at various DT levels. To view it in full size, open the picture in a new tab. Melee weapons only show performance at 15 and 30 DT due to Pierecing Strike perk. Industrial Hand only has one data point because it ignores DR and DT. The second graph combines the best DPS of each ammo type for a weapon to make the graph more legible.

Finally, to the right is a chart showing how weapons, enemy DT, and level 50 perks interact. The green columns are DPS values with critical damage boost, purple has damage boost, and blue has rate of fire boost. Notice how the highest DPS values tend to go from Thought You Died to using Just Lucky I'm Alive as enemy DT increases.

## Conclusion

30DT = Robo-Scroption Boss
15DT = Deathclaw
0DT = Tunneler

HP ammo can actually be useful against armored targets if the weapon DAM is high enough. Generally it makes sense to switch between AP and HP ammo. Don't forget that match rounds increase accuracy.

The best level 50 perk to get for DPS is Just Lucky I'm Alive for the most part. It is the best perk for most instances and most weapons. Ain't Like That Now is a terrible choice, placing near last in every single situation. My opinion is to go for Just Lucky I'm Alive for maximum DPS or Thought You Died for good DPS and higher maximum health.

DPS Winner
The Industrial Hand is broken in how overpowered it is and you don't even need to spam click. However, it is a player-only weapon. Give Fist of Rawr! to Veronica instead. Elijah's LAER is the best for long range encounters against heavily armored enemies, but its weapon condition is very low (recall that lower than 100% CND means lower critical chance). Tri-Beam actually delivers higher DPS than Elijah's LAER at 15DT, with tied DPS at 0DT. Generally I recommend Tri-Beam over Elijah's LAER since 30DT enemies are rare, and the CND is just terrible. Esther is very high DPS, but it's a mininuke launcher and with Big Boy you will end up killing yourself half of the time. For guns, the Survivalist's Rifle is a great general gun, but the Paciencia is actually great against 30DT despite having to reload all of the time.

Old Glory vs Oh, Baby! vs Gehenna
Oh, Baby! is just terrible. Old Glory is great for those who don't want Blood-Nap despite its high DPS due to its short reach.

Blood-Nap vs Chance's Knife
Blood-Nap is simply better, even though Chance's Knife gets Grunt.

Medicine Stick vs Sequoia
Medicine Stick has far higher CND and accuracy but has lower DPS than Ranger Sequoia while being annoying to reload optimally.

Gatling Laser vs Minigun vs LMG

The lasers here deteriorate faster than the miniguns due to MC ammunition, but it's not a huge problem. LMGs on the other hand fire for days without a hitch but has low accuracy. Gatling Laser > Sprtel-Wood > Avenger > Minigun. Gatling loses some of its lead at high DT but still wins by a good margin. LMG beats minigun against 15 and 0DT but loses by a lot to Gatling.

Pistol King of the Hill
Li'l Devil is stronger than ALSID in terms of pure DPS except for 30 DT enemies. Firing Super Hand Loads, A Light Shining in Darkness has lesser CND compared to Li'l Devil, but Li'l Devil has notably lower accuracy. In terms of the king of pistols, Li'l Dvil, ALSID, and Sequoia all have their shining moments, but I think Sequoia wins out due to very high accuracy. Purely in terms of DPS, the Sequoia is for 30DT and Li'l Devil for 15 and 0DT.

12mm SMG vs .45 Auto SMG
The .45 Auto SMG has higher DPS than the 12mm SMG in all cases, but has slightly lower accuracy and much lower CND due to the use of Super Hand Load rounds. SMGs are generally very weak due to low DAM with a ROF still inadequate due to ROF buffs for non-automatics, while eating up ammo.

Annabelle vs Red Glare
Red Glare beats Annabelle except for 30DT opponents for DPS but loses in accuracy.

## Special Ammo vs DT

This section is purely academic, meaning that it has no effect on the data. So unless you want to read a bunch of useless stuff, skip this part. For the purposes of this section, assume I am talking about a character with no perks, no chems, max stats, normal difficulty, and unmodded weapons unless specifically stated otherwise. This is important.

First let's talk about the damage formula in the combat page of the wiki. DT vs DAM vs Ammo AP is calculated first, and only in the end are things like perks and ammo damage boosts (like hollow point or hand load) applied. Usually the resulting damage after DT vs DAM calculation is DAM - DT. The floor is 20% of the original DAM. There is a specific point where (DAM - DT) = (DAM * 0.2). I will just call this 'Magic DT' (the particular name isn't that important).

Let's write this out so it's easier to see what the wiki's combat page predicts.

DAM = 50
10 DT: 40 dmg (50 DAM - 10 DT)
11 DT: 39 dmg (50 DAM - 11 DT)
39 DT: 11 dmg (50 DAM - 39 DT)
40 DT: 10 dmg (50 DAM - 40 DT OR 50 * 0.2) Magic DT
41 DT: 10 dmg (50 DAM * 0.2)
1000 DT: 10 dmg (50 DAM * 0.2)

While that system makes intuitive sense, it gets weird when enemy DT is high and we are comparing ammunition types. I will show an extreme example to make things more clear.

DAM = 50
DT = 1000
AP Ammo (100% dmg, -25 AP): 10 dmg [Because: (50 * 0.2) > (50 - 1000 - 25)]
HP Ammo (150% dmg, x3 enemy DT): 15 dmg [Because: (50 * 0.2) > (50 - 3000); ((50 * 0.2) * 1.5) = 15]

If enemy DT is an insane 1000, then both HP and AP fail to penetrate armor so much, they both hit the floor (DAM * 0.2). This means any DT modifications here don't matter. The only thing that matters is the damage boost of the HP ammunition, which is calculated after DAM vs DT calculations. This means HP > AP ammunition against very high DT targets. We would also expect HP ammo in this case to hit its damage floor of 15 damage at 40 DT. This means that it makes no difference if the enemy has 40 DT or 1000 DT. The problem is that none of this is totally true.

To be clear though: If the player is not using special ammunition, the wiki's formulas are correct.

Weapon = Elijah's LAER (no mods)
DAM = 65

Ammunition: Regular microfusion cells (DT -2)
Magic DT = (65 * 0.8) + 2 = 54

Predicted Damage:
54 DT: 13 dmg Magic DT
55 DT: 13 dmg
1000 DT: 13 dmg

Actual Damage:
54 DT: 13 dmg Magic DT
55 DT: 13 dmg
1000 DT: 13 dmg

Verdict: Wiki's formula works perfectly.

Weapon = Elijah's LAER (no mods)
DAM = 65

Ammunition: Microfusion cell, max charge (DT -10, Dmg x 1.5)
Magic DT = (65 * 0.8) + 10 = 62

Predicted Damage:
61 DT: 21 [(65 - (61 - 10)) * 1.5]
62 DT: 19.5 ((65 * 0.2) * 1.5) Magic DT
63 DT: 19.5
...
1000 DT: 19.5

Actual Damage:
61 DT: 21
62 DT: 19.5 Magic DT
63 DT: 18 dmg (19.5 - 1.5)
64 DT: 16.5 dmg [19.5 - (1.5 * 2)]
65 DT: 15 [19.5 - (1.5 * 3)]
66 DT: 13.5 [19.5 - (1.5 * 4)]
67 DT: 13 dmg (Floor is 13)
...
1000 DT: 13 dmg

Verdict: Wiki's formula fails.

Remember the 'Magic DT'? If enemy DT is above the Magic DT and the player is using ammunition that changes weapon damage, the wiki's formula fails. I found a way to explain this behavior, but it fails when taking into account other buffs like perks.

Here is a group of formulas that accurately predicts damage of a weapon with ammunition with damage buffs. Note that these formulas were not tested for critical hits.

$MagicDT = (DAM \times 0.8 \times Effect_{HP}) + Effect_{AP}$

The HP Effect is 3 for 9mm HP, etc. The AP Effect is 10 for Max Charge, 5 for Optimized, 25 for 5mm AP, etc.

$Dmg_{Magic DT} = max[DAM \times 0.2, (DAM \times 0.2 \times DmgFactor_{Ammo})]$

$Dmg_{Magic DT + n DT} = max[DAM \times 0.2, (Dmg_{Magic DT} - (DmgFactor_{Ammo} \times n))]$

Ammo Damage Factor is 1.5 for Max Charge, 1.3 for Over Charge, etc. If you don't know how to read the formula above, realize that max[1, n -3] means the result is either 1 or whatever n - 3 is, picking the larger value of the two. This means (in this example) that 1 is the floor.

DAM is multiplied by 0.8 because it mathematically gives us the DT where DAM - DT = DAM * 0.2. Then, you account for the armor negation of some ammunition types by adding it to the result.

Look back at the example where I said the wiki's formula fails. Notice how the wiki's formula starts to fail after the Magic DT because Max Charge (x1.5 dmg) was used. The damage seems to be falling below the floor (predicted to be 19.5) at a rate of 1.5 damage per 1 increase in DT. x1.5 damage is the damage bonus of max charge ammo. This is not a coincidence. The damage the player does will continue to decrease by 1.5 per 1 increase in DT until it hits the floor of 13. 13 is the damage we would expect the player to do if Max Charge didn't have a x1.5 damage bonus. This is also not a coincidence.