There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per 8.0×10^{4}  years. We infer the component masses of the binary to be between 0.86 and 2.26  M_{⊙}, in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range 1.17-1.60  M_{⊙}, with the total mass of the system 2.74_{-0.01}^{+0.04}M_{⊙}. The source was localized within a sky region of 28  deg^{2} (90% probability) and had a luminosity distance of 40_{-14}^{+8}  Mpc, the closest and most precisely localized gravitational-wave signal yet. The association with the γ-ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ-ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation, and cosmology.

/pdf/gw170817-observation-of-gravitational-waves-from-a-binary-q2x9byg981.pdf

GW170817: observation of gravitational waves from a binary neutron star inspiral

We present cosmological parameter results from the ﬁnal full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to signiﬁcant gains in the precision of other correlated parameters Improved modelling of the small-scale polarization leads to more robust constraints on manyparameters,withresidualmodellinguncertaintiesestimatedtoaﬀectthemonlyatthe05σlevelWeﬁndgoodconsistencywiththestandard spatially-ﬂat6-parameter ΛCDMcosmologyhavingapower-lawspectrumofadiabaticscalarperturbations(denoted“base ΛCDM”inthispaper), from polarization, temperature, and lensing, separately and in combination A combined analysis gives dark matter density Ωch2 = 0120±0001, baryon density Ωbh2 = 00224±00001, scalar spectral index ns = 0965±0004, and optical depth τ = 0054±0007 (in this abstract we quote 68% conﬁdence regions on measured parameters and 95% on upper limits) The angular acoustic scale is measured to 003% precision, with 100θ∗ = 10411±00003Theseresultsareonlyweaklydependentonthecosmologicalmodelandremainstable,withsomewhatincreasederrors, in many commonly considered extensions Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: HubbleconstantH0 = (674±05)kms−1Mpc−1;matterdensityparameterΩm = 0315±0007;andmatterﬂuctuationamplitudeσ8 = 0811±0006 We ﬁnd no compelling evidence for extensions to the base-ΛCDM model Combining with baryon acoustic oscillation (BAO) measurements (and consideringsingle-parameterextensions)weconstraintheeﬀectiveextrarelativisticdegreesoffreedomtobe Neﬀ = 299±017,inagreementwith the Standard Model prediction Neﬀ = 3046, and ﬁnd that the neutrino mass is tightly constrained toPmν < 012 eV The CMB spectra continue to prefer higher lensing amplitudesthan predicted in base ΛCDM at over 2σ, which pulls some parameters that aﬀect thelensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAOdataThejointconstraintwithBAOmeasurementsonspatialcurvatureisconsistentwithaﬂatuniverse, ΩK = 0001±0002Alsocombining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −103±003, consistent with a cosmological constant We ﬁnd no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0002 < 006 Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower ﬂuctuation amplitudes or matter density parameters), and in signiﬁcant, 36σ, tension with local measurements of the Hubble constant (which prefer a higher value) Simple model extensions that can partially resolve these tensions are not favoured by the Planck data

/pdf/planck-2018-results-vi-cosmological-parameters-3d8tp95x87.pdf

Planck 2018 results. VI. Cosmological parameters

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

/pdf/the-observation-of-gravitational-waves-from-a-binary-black-58srpupgg9.pdf

The Observation of Gravitational Waves from a Binary Black Hole Merger

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $\Lambda$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base $\Lambda$CDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $\Omega_c h^2 = 0.120\pm 0.001$, baryon density $\Omega_b h^2 = 0.0224\pm 0.0001$, scalar spectral index $n_s = 0.965\pm 0.004$, and optical depth $\tau = 0.054\pm 0.007$ (in this abstract we quote $68\,\%$ confidence regions on measured parameters and $95\,\%$ on upper limits). The angular acoustic scale is measured to $0.03\,\%$ precision, with $100\theta_*=1.0411\pm 0.0003$. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-$\Lambda$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4\pm 0.5)$km/s/Mpc; matter density parameter $\Omega_m = 0.315\pm 0.007$; and matter fluctuation amplitude $\sigma_8 = 0.811\pm 0.006$. We find no compelling evidence for extensions to the base-$\Lambda$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{\rm eff} = 2.99\pm 0.17$, and the neutrino mass is tightly constrained to $\sum m_\nu< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$\Lambda$CDM at over $2\,\sigma$, which pulls some parameters that affect the lensing amplitude away from the base-$\Lambda$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)

/pdf/planck-2018-results-vi-cosmological-parameters-gjusa8fy3b.pdf

SNEC: SuperNova Explosion Code

Early observations of supernova light curves are powerful tools for shedding light on the pre-explosion structures of their progenitors and their mass-loss histories just prior to explosion. Some core-collapse supernovae that are detected during the first days after the explosion prominently show two peaks in the optical bands, including the $R$ and $I$ bands, where the first peak appears to be powered by the cooling of shocked surface material and the second peak is clearly powered by radioactive decay. Such light curves have been explored in detail theoretically for SN 1993J and 2011dh, where it was found that they may be explained by progenitors with extended, low-mass envelopes. Here we generalize these results. We explore, first, whether any double-peaked light curve of this type can be generated by a progenitor with a "standard" density profile, such as a red supergiant or a Wolf-Rayet star. We show that a standard progenitor (1) cannot produce a double-peaked light curve in the $R$ and $I$ bands, and (2) cannot exhibit a fast drop in the bolometric luminosity as is seen after the first peak. We then explore the signature of a progenitor with a compact core surrounded by extended, low-mass material. This may be a hydrostatic low-mass envelope or material ejected just prior to the explosion. We show that it naturally produces both of these features. We use this result to provide simple formulae to estimate (1) the mass of the extended material from the time of the first peak, (2) the extended material radius from the luminosity of the first peak, and (3) an upper limit on the core radius from the luminosity minimum between the two peaks.

Supernovae with Two Peaks in the Optical Light Curve and the Signature of Progenitors with Low-mass Extended Envelopes

During accretion, a neutron star (NS) is spun up as angular momentum is transported through its liquid surface layers. We study the resulting differentially rotating profile, focusing on the impact this has for type I X‐ray bursts. The viscous heating is found to be negligible, but turbulent mixing can be activated. Mixing has the greatest impact when the buoyancy at the compositional discontinuity between accreted matter and ashes is overcome. This occurs preferentially at high accretion rates or low spin frequencies and may depend on the ash composition from the previous burst. We then find two new regimes of burning. The first is ignition in a layer containing a mixture of heavier elements with recurrence times as short as ≈5–30 minutes, similar to short recurrence time bursts. When mixing is sufficiently strong, a second regime is found where accreted helium mixes deep enough to burn stably, quenching X‐ray bursts altogether. The carbon‐rich material produced by stable helium burning would be importan...

The Turbulent Story of X‐ray Bursts: Effects of Shear Mixing on Accreting Neutron Stars

Material accreted onto a neutron star can stably burn in steady state only when the accretion rate is high (typically super-Eddington) or if a large flux from the neutron star crust permeates the outer atmosphere. For such situations we have analyzed the stability of nonradial oscillations, finding one unstable mode for pure helium accretion. This is a shallow surface wave which resides in the helium atmosphere above the heavier ashes of the ocean. It is excited by the increase in the nuclear reaction rate during the oscillations, and it grows on the timescale of a second. For a slowly rotating star, this mode has a frequency of approximately 20-30 Hz (for l=1), and we calculate the full spectrum that a rapidly rotating (>>30 Hz) neutron star would support. The short period X-ray binary 4U 1820--30 is accreting helium rich material and is the system most likely to show this unstable mode,especially when it is not exhibiting X-ray bursts. Our discovery of an unstable mode in a thermally stable atmosphere shows that nonradial perturbations have a different stability criterion than the spherically symmetric thermal perturbations that generate type I X-ray bursts.

http://export.arxiv.org/pdf/astro-ph/0311398

Unstable Nonradial Oscillations on Helium Burning Neutron Stars

We describe recent theoretical work on the final stage of accretion when material passes from an accretion disk onto a white dwarf surface. Our calculations focus on understanding the latitudinal spreading and differentially rotating profile of this material, so we call it the ``spreading layer'' (SL) model. The SL typically extends to an angle of 0.01-0.1 radians, with respect to the equator. At low accretion rates ($\dot{M}\la10^{18} {\rm g s}^{-1}$) the amount of spreading is small, so that the dissipated energy is radiated back into the accretion disk. When the accretion rate is high, such as in dwarf novae, symbiotic binaries, and supersoft sources, the material spreads to higher latitudes to be more easily observed. The SL may contain shallow surface modes, and we propose that such waves could produce dwarf nova oscillations (DNOs). This hypothesis naturally explains many key properties of DNOs, including their frequency range, sinusoidal nature, sensitivity to accretion rate, and why they are only seen during outburst.

Anthony L. Piro

Papers

SNEC: SuperNova Explosion Code

Supernovae with Two Peaks in the Optical Light Curve and the Signature of Progenitors with Low-mass Extended Envelopes

The Turbulent Story of X‐ray Bursts: Effects of Shear Mixing on Accreting Neutron Stars

Unstable Nonradial Oscillations on Helium Burning Neutron Stars

The Spreading Layer and Dwarf Nova Oscillations