Search

The quest for high-redshift quasars has led to a series of record-breaking sources, with the current record holder at $z=7.642$. Here, we show how future detections of $z>8$ quasars impact the constraints on the parameters for black hole growth and seed models. Using broad flat priors on the growth parameters (Eddington ratio $\,f_{\rm Edd}$, duty cycle ${\cal D}$, seed mass $M_{\rm \bullet, seed}$ and radiative efficiency $\epsilon$), we show that the large uncertainties in their determination decrease by a factor $\sim 5$ when a quasar's detection redshift goes from $z=9$ to $z=12$. In this high-redshift regime, $\epsilon$ tends to the lowest value allowed, and the distribution for $M_{\rm \bullet, seed}$ peaks well inside the heavy seed domain. Remarkably, two quasars detected at $z > 7$ with low accretion rates (J1243+0100 and J0313-1806) already tighten the available parameter space, requiring $M_{\rm \bullet, seed} > 10^{3.5} \,{\rm M_\odot}$ and $\epsilon < 0.1$. The radiative efficiency is a crucial unknown, with factor $\sim 2$ changes able to modify the predicted mass by $\sim 3$ orders of magnitude already at $z\sim 9$. The competing roles of inefficient accretion (decreasing $\epsilon$) and black hole spin-up (increasing $\epsilon$) significantly impact growth models. Finally, we suggest that yields currently predicted by upcoming quasar surveys (e.g., Euclid) will be instrumental for determining the most-likely seed mass regime. For example, assuming thin-disk accretion, a detection of a quasar with $M_\bullet \sim 10^{10} \,{\rm M_\odot}$ by $z\sim 9-10$ would exclude the entire parameter space available for light seeds and dramatically reduce the one for heavy seeds., Comment: Accepted for publication in MNRAS. This is the final version of the manuscript. 8 pages, 5 figures

Aquatic biospheres reliant on oxygenic photosynthesis are expected to play an important role on Earth-like planets endowed with large-scale oceans insofar as carbon fixation (i.e., biosynthesis of organic compounds) is concerned. We investigate the properties of aquatic biospheres comprising Earth-like biota for habitable rocky planets orbiting Sun-like stars and late-type M-dwarfs such as TRAPPIST-1. In particular, we estimate how these characteristics evolve with the available flux of photosynthetically active radiation (PAR) and the ambient ocean temperature ($T_W$), the latter of which constitutes a key environmental variable. We show that many salient properties, such as the depth of the photosynthesis zone and the net primary productivity (i.e., the effective rate of carbon fixation), are sensitive to PAR flux and $T_W$ and decline substantially when the former is decreased or the latter is increased. We conclude by exploring the implications of our analysis for exoplanets around Sun-like stars and M-dwarfs., Comment: Accepted for publication in MNRAS; 40 pages; 5 pages; 1 table

As the sensitivity of gravitational wave (GW) instruments improves and new networks start operating, hundreds of merging stellar-mass black holes (SBHs) and intermediate-mass black holes (IMBHs) are expected to be observed in the next few years. The origin and distribution of SBH and IMBH binaries in various dynamical environments is a fundamental scientific question in GW astronomy. In this paper, we discuss ways tidal disruption events (TDEs) may provide a unique electromagnetic window into the assembly and merger of binary SBHs and IMBHs in nuclear star clusters (NSCs). We discuss how the host NSC mass and density and the slope of the black-hole mass function set the orbital properties and the masses of the binaries that undergo a TDE. For typical NSC properties, we predict a TDE rate of $\sim 10^{-6}$--$10^{-7}\ {\rm yr}^{-1}$ per galaxy. The lightcurve of TDEs in NSCs could be interrupted and modulated by the companion black hole on the orbital period of the binary. These should be readily detectable by optical transient surveys such as the Zwicky Transient Facility and LSST., Comment: 13 pages, 7 figures, 1 table, accepted by MNRAS

We combine the latest observationally motivated constraints on stellar properties in dark matter haloes, along with data-driven predictions for the atomic (HI) and molecular (H$_2$) gas evolution in galaxies, to derive empirical relationships between the build-up of galactic components and their evolution over cosmic time. At high redshift ($z \gtrsim 4$), the frameworks imply that galaxies acquire their cold gas (both atomic and molecular) mostly by accretion, with the fraction of cold gas reaching about 20% of the cosmic baryon fraction. We infer a strong dependence of the star formation rate on the H$_2$ mass, suggesting a near-universal depletion timescale of 0.1-1 Gyr in Milky Way sized haloes (of masses $10^{12} \ M_{\odot}$ at $z = 0$). There is also evidence for a near-universality of the Kennicutt-Schmidt relation across redshifts, with very little dependence on stellar mass, if a constant conversion factor ($\alpha_{\rm CO}$) of CO luminosity to molecular gas mass is assumed. Combining the atomic and molecular gas observations with the stellar build-up illustrates that galactic mass assembly in Milky-Way sized haloes proceeds from smooth accretion at high redshifts, towards becoming merger-dominated at late times ($z \lesssim 0.6$). Our results can be used to constrain numerical simulations of the dominant growth and accretion processes of galaxies over cosmic history., Comment: 8 pages, 6 figures, accepted for publication in MNRAS

We analyze triple systems composed of the super massive black hole (SMBH) near the center of M87 and a pair of black holes (BHs) with masses in the range $10-10^3$ $M_{\odot}$. We consider the post Newtonian precession as well as the Kozai-Lidov interactions at the quadruple and octupole levels in modeling the evolution of binary black hole (BBH) under the influence of the SMBH. Kozai-Lidov oscillations enhance the gravitational wave (GW) signal in some portions of the parameter space. We identify frequency peaks and examine the detectability of GWs with LISA as well as future observatories such as $\mu$Ares and DECIGO. We show examples in which GW signal can be observed with a few or all of these detectors. Multi-Wavelength GW spectroscopy holds the potential to discover stellar to intermediate mass BHs near the center of M87. We estimate the rate, $\Gamma$, of collisions between the BBHs and flyby stars at the center of M87. Our calculation suggests $\Gamma < 10$ $\rm{Gyr}^{-1}$ for a wide range of the mass and semi-major axes of the inner binary., Comment: 9 pages, 10 Figures, 2 Tables. Published in MNRAS

The Fundamental Plane (FP) of Black Hole (BH) Activity in galactic nuclei relates X-ray and radio luminosities to BH mass and accretion rate. However, there is a large scatter exhibited by the data, which motivated us for a new variable. We add BH spin as a new variable and estimate the spin dependence of the jet power and disk luminosity in terms of radio and X-ray luminosities. We assume the Blandford-Znajek process as the main source of the outflow, and find that the jet power depends on BH spin stronger than quadratically at moderate and large spin values. We perform a statistical analysis for 10 AGNs which have sub-Eddington accretion rates and whose spin values are measured independently via the reflection or continuum-fitting methods, and find that the spin-dependent relation describes the data significantly better. This analysis, if supported with more data, could imply not only the spin dependence of the FP relation, but also the Blandford-Znajek process in AGN jets., Comment: Accepted for publication in MNRAS

As the Sun moves through the surrounding partially ionized medium, neutral hydrogen atoms penetrate the heliosphere, and through charge exchange with the supersonic solar wind, create a population of hot pick-up ions (PUIs). Until recently, the consensus was that the shape of the heliosphere is comet-like. The termination shock crossing by Voyager 2 demonstrated that the heliosheath (the region of shocked solar wind) pressure is dominated by PUIs; however, the impact of the PUIs on the global structure of the heliosphere has not been explored. Here we use a novel magnetohydrodynamic model that treats the PUIs as a separate fluid from the thermal component of the solar wind. The depletion of PUIs, due to charge exchange with the neutral hydrogen atoms of the interstellar medium in the heliosheath, cools the heliosphere, ‘deflating’ it and leading to a narrower heliosheath and a smaller and rounder shape, confirming the shape suggested by Cassini observations. The new model reproduces both the properties of the PUIs, based on the New Horizons observations, and the solar wind ions, based on the Voyager 2 spacecraft observations as well as the solar-like magnetic field data outside the heliosphere at Voyager 1 and Voyager 2. A magnetohydrodynamic model of the interaction between the solar wind and the interstellar medium shows that our heliosphere has a round shape, not a tail-like shape as usually assumed. The model reproduces the observations from Cassini, New Horizons and the two Voyager probes.

We demonstrate how pulsar timing arrays (PTAs) can, in principle, yield a purely gravitational wave (GW) measurement of the luminosity distance and comoving distance to a supermassive black hole binary source, hence providing an estimate of the source redshift and the Hubble constant. The luminosity distance is derived through standard measurement of the chirp mass, which for the slowly evolving binary sources in the PTA band can be found by comparing the frequency of GW-timing residuals at the Earth compared to those at distant pulsars in the array. The comoving distance can be measured from GW-timing parallax caused by the curvature of the GW wavefronts. This can be detected for single sources at the high-frequency end of the PTA band out to Gpc distances with a future PTA containing well-timed pulsars out to $\mathcal{O}(10)$ kpc, when the pulsar distance is constrained to less than a GW wavelength. Such a future PTA, with $\gtrsim 30$ pulsars with precise distance measurements between 1 and 20~kpc, could measure the Hubble constant at the tens of percent level for a single source at $0.1 \lesssim z \lesssim 1.5$. At $z \lesssim 0.1$, the luminosity and comoving distances are too similar to disentangle, unless the fractional error in the luminosity distance measurement is decreased below 10%. At $z\gtrsim 1.5$, this measurement will likely be restricted by a signal-to-noise ratio threshold. Generally, clarification of the different types of cosmological distances that can be probed by PTAs, and their relation to pulsar distance measurements is important for ongoing PTA experiments aimed at detecting and characterizing GWs., Submitted to Physical Review D. Comments welcome

The long wait for the detection of merging black hole -- neutron star (BH--NS) binaries is finally over with the announcement by the LIGO/Virgo/Kagra collaboration of GW200105 and GW200115. Remarkably, the primary of GW200115 has a negative spin projection onto the orbital angular momentum, with about $90\%$ probability. Merging BH--NS binaries are expected to form mainly through the evolution of massive binary stars in the field, since their dynamical formation in dense star clusters is strongly suppressed by mass segregation. In this paper, we carry out a systematic statistical study of the binary stars that evolve to form a BH--NS binary, considering different metallicities and taking into account the uncertainties on the natal kick distributions for BHs and NSs and on the common envelope phase of binary evolution. Under the assumption that the initial stellar spins are aligned with the binary angular momentum, we show that both large natal kicks ($\gtrsim 150$ km s$^{-1}$) and high efficiencies for common envelope ejection are required to simultaneously explain the inferred high merger rates and the large spin-orbit misalignment of GW200115., 5 pages, 4 figures, accepted by ApJL

The Event Horizon Telescope (EHT), a global very long baseline interferometric array observing at a wavelength of 1.3 mm, detected the first image of the M87 supermassive black hole (SMBH). M87 is a giant elliptical galaxy at the center of Virgo cluster, which is expected to have formed through merging of cluster galaxies. Consequently M87* hosted mergers of black holes through dynamical friction and could have one or multiple binary companions with a low mass ratio at large separations. We show that a long-term monitoring of the M87 SMBH image over $\sim$1 year with absolute positional accuracy of 1$\approx\mu as$ could detect such binary companions and exclude a large parameter space in semi major axis ($a_0$) and mass ratio ($q$), which is currently not constrained. Moreover, the presence of the accretion disk around M87* excludes a binary companion with $a_0\approx$ of order a mili parsec, as otherwise the accretion disk would have been tidally disrupted., Comment: accepted for publication at MNRAS Letters

Mergers of black hole (BH) and neutron star (NS) binaries are expected to be observed by gravitational wave observatories in the coming years. Until now, LIGO has only set an upper limit on this merger rate. BH-NS binaries are expected to merge in isolation, as their formation is suppressed in star clusters by the mass segregation and the strong heating by BHs in the cluster core. Another viable scenario to BH-NS mergers is in triple systems. In this paper, we carry out a systematic statistical study of the dynamical evolution of triples comprised of an inner BH-NS binary by means of high-precision $N$-body simulations, including Post-Newtonian (PN) terms up to 2.5PN order. We start from the main sequence massive stars and model the supernovae (SN) events that lead to the formation of BHs and NSs. We adopt different prescriptions for the natal velocity kicks imparted during the SN processes and illustrate that large kicks lead to more compact and massive triples that merge on shorter timescales. We also show that BH-NS merging in triples have a significant eccentricity in the LIGO band, typically much larger than BH-NS merging in isolated binaries. Finally, we estimate a rate of $\Gamma_\mathrm{BH-NS}\approx 1.0\times 10^{-3}-3.5\times 10^{-2} \ \mathrm{Gpc}^{-3}\ \mathrm{yr}^{-1}$, for non-zero velocity kicks, and $\Gamma_\mathrm{BH-NS}=19 \ \mathrm{Gpc}^{-3}\ \mathrm{yr}^{-1}$, for no natal kicks. Our rate estimate overlaps with the expected BH-NS rate in isolated binaries and within the LIGO upper limit., Comment: 8 pages, 5 figures, 1 table, accepted by MNRAS

We show that planets around M-dwarfs with $M_\star \lesssim 0.2 M_\odot$ may not receive enough photons in the photosynthetically active range of $400$-$750$ nm to sustain Earth-like biospheres. As a result of the lower biological productivity, it is likely that biotic molecular oxygen would not build up to detectable levels in the atmospheres of habitable planets orbiting low-mass stars, consistent with prior work by Lehmer et al. (2018). We also estimate the minimum flaring rate for sustaining biospheres with Earth-like productivity and permitting the build-up of atmospheric oxygen, and find that the overwhelming majority of M-dwarfs are unlikely to exceed this threshold., Accepted for publication in MNRAS; 6 pages; 2 figures

Recently, a nitrogen iceberg was proposed as a possible origin for the first interstellar object, 1I/2017 U1, also known as `Oumuamua. Here, we show that the mass budget in exo-Pluto planets necessary to explain the detection of `Oumuamua as a nitrogen iceberg chipped off from a planetary surface requires a mass of heavy elements exceeding the total quantity locked in stars with 95\% confidence, making the scenario untenable because only a small fraction of the mass in stars ends in exo-Plutos., Comment: 3 pages, 2 figures; accepted for publication in New Astronomy

We examine the case of a random isotropic velocity field, in which one of the velocity components (the "radial" component, with magnitude $v_z$) can be measured easily, while measurement of the velocity perpendicular to this component (the "transverse" component, with magnitude $v_T$) is more difficult and requires long-time monitoring. Particularly important examples are the motion of galaxies at cosmological distances and the interpretation of Gaia data on the proper motion of stars in globular clusters and dwarf galaxies. We address two questions: what is the probability distribution of $v_T$ for a given $v_z$, and for what choice of $v_z$ is the expected value of $v_T$ maximized? We show that, for a given $v_z$, the probability that $v_T$ exceeds some value $v_0$ is $p(v_T \ge v_0 | v_z) = {p_z(\sqrt{v_0^2 + v_z^2}})/{p_z(v_z)}$, where $p_z(v_z)$ is the probability distribution of $v_z$. The expected value of $v_T$ is maximized by choosing $v_z$ as large as possible whenever $\ln p_z(\sqrt{v_z})$ has a positive second derivative, and by taking $v_z$ as small as possible when this second derivative is negative., Comment: 6 pages, 4 figures, references and discussion added

Quasars whose broad emission lines show temporal, bulk radial velocity (RV) shifts have been proposed as candidate sub-parsec (sub-pc), binary supermassive black holes (BSBHs). We identified a sample of 16 BSBH candidates based on two-epoch spectroscopy among 52 quasars with significant RV shifts over a few rest-frame years. The candidates showed consistent velocity shifts independently measured from two broad lines (H$\beta$ and H$\alpha$ or Mg${\rm \,II}$) without significant changes in the broad-line profiles. Here in the third paper of the series, we present further third- and fourth-epoch spectroscopy for 12 of the 16 candidates for continued RV tests, spanning $\sim$5--15 yr in the quasars' rest frames. Cross-correlation analysis of the broad H$\beta$ calibrated against [O${\rm\,III}]\,\lambda 5007$ suggests that 5 of the 12 quasars remain valid as BSBH candidates. They show broad H$\beta$ RV curves that are consistent with binary orbital motion without significant changes in the broad line profiles. Their broad H$\alpha$ (or Mg${\rm \,II}$) lines display RV shifts that are either consistent with or smaller than those seen in broad H$\beta$. The RV shifts can be explained by a $\sim$0.05--0.1 pc BSBH with an orbital period of $\sim$40--130 yr, assuming a mass ratio of 0.5--2 and a circular orbit. However, the parameters are not well constrained given the few epochs that sample only a small portion of the hypothesized binary orbital cycle. The apparent occurrence rate of sub-pc BSBHs is $\lesssim$13$\pm$5% among all SDSS quasars, with no significant difference in the subsets with and without single-epoch broad line velocity offsets. Dedicated long-term spectroscopic monitoring is still needed to further confirm or reject these BSBH candidates., Comment: 38 pages, 11 figures, MNRAS accepted

Mergers of black hole (BH) and neutron star (NS) binaries are of interest since the emission of gravitational waves (GWs) can be followed by an electromagnetic (EM) counterpart, which could power short gamma-ray bursts. Until now, LIGO/Virgo has only observed a candidate BH-NS event, GW190426\_152155, which was not followed by any EM counterpart. We discuss how the presence (absence) of a remnant disk, which powers the EM counterpart, can be used along with spin measurements by LIGO/Virgo to derive a lower (upper) limit on the radius of the NS. For the case of GW190426\_152155, large measurement errors on the spin and mass ratio prevent from placing an upper limit on the NS radius. Our proposed method works best when the aligned component of the BH spin (with respect to the orbital angular momentum) is the largest, and can be used to complement the information that can be extracted from the GW signal to derive valuable information on the NS equation of state., 6 pages, 3 figures, accepted by MNRAS

We present a comprehensive analysis of the shape of dark matter (DM) halos in a sample of 25 Milky Way-like galaxies in TNG50 simulation. Using an enclosed volume iterative method, we infer an oblate-to-triaxial shape for the DM halo with median T ≃ 0.24. We group DM halos into three different categories. Simple halos (32% of the population) establish principal axes whose ordering in magnitude does not change with radius and whose orientations are almost fixed throughout the halo. Twisted halos (32%) experience levels of gradual rotations throughout their radial profiles. Finally, stretched halos (36%) demonstrate a stretching in the lengths of their principal axes where the ordering of different eigenvalues changes with radius. Subsequently, the halo experiences a “rotation” of ∼90° where the stretching occurs. Visualizing the 3D ellipsoid of each halo, for the first time, we report signs of a reorienting ellipsoid in twisted and stretched halos. We examine the impact of baryonic physics on DM halo shape through a comparison to dark matter only (DMO) simulations. This suggests a triaxial (prolate) halo. We analyze the impacts of substructure on DM halo shape in both hydrodynamical and DMO simulations and confirm that they are subdominant. We study the distribution of satellites in our sample. In simple and twisted halos, the angle between satellites’ angular momentum and the galaxy’s angular momentum grows with radius. However, stretched halos show a flat distribution of angles. Overlaying our theoretical outcome on the observational results presented in the literature establishes a fair agreement.

Since the first signal in 2015, the gravitational-wave detections of merging binary black holes (BBHs) by the LIGO and Virgo collaborations (LVC) have completely transformed our understanding of the lives and deaths of compact object binaries, and have motivated an enormous amount of theoretical work on the astrophysical origin of these objects. We show that the phenomenological fit to the redshift-dependent merger rate of BBHs from Abbott et al. (2020) is consistent with a purely dynamical origin for these objects, and that the current merger rate of BBHs from the LVC could be explained entirely with globular clusters alone. While this does not prove that globular clusters are the dominant formation channel, we emphasize that many formation scenarios could contribute a significant fraction of the current LVC rate, and that any analysis that assumes a single (or dominant) mechanism for producing BBH mergers is implicitly using a specious astrophysical prior., Comment: 4 pages, one figure, matches version in RNAAS

The question of whether Cosmic Microwave Background (CMB) temperature and polarization data from Planck favor a spatially closed Universe with curvature parameter $\Omega_K, Comment: 30 pages, 6 figures. The busy reader should skip to Fig. 1 and Tab. 3 for the main results, and to Fig. 5 and Tab. 4 if they are interested in the extended parameter space results. "Piatto" = "flat" in Italian, "Note added" between conclusions and acknowledgements explains our choice of title. v2: abstract shortened, references added, version accepted for publication in ApJ. Comments are welcome

The equilibrium and fluctuations of an ideal gas in a rigid container are studied by every student of statistical mechanics. Here we study the less well-known case when the box is floating freely; in particular we determine the fluctuations of the box in velocity and position due to interactions with the gas it contains. This system is a toy model for the fluctuations in velocity and position of a black hole surrounded by stars at the center of a galaxy. These fluctuations may be observable in nearby galaxies., 5 pages, no figures, submitted to American Journal of Physics

We use the IllustrisTNG (TNG) cosmological, hydrodynamical simulations of galaxy formation to measure the velocity dispersion profiles of dark matter and star particles in Milky Way-mass, galaxy group, and cluster-scale dark matter halos. The mean profile calculated from both dark and luminous tracers are similar in shape, exhibiting a large degree of halo-to-halo scatter around the average profile. The so-called "splashback" radius demarcates the outer boundary of the halo, and manifests as a kink in the velocity dispersion profile, located on average between $\sim 1.0-1.5r_{200m}$, where $r_{200m}$ is the radius within which the enclosed density of the halo equals 200 times the mean background density of the universe at that redshift. Interestingly, we find that this location may also be identified as the radius at which the (stacked) velocity dispersion profile drops to 60% of its peak value (for line-of-sight motions of stellar and dark matter particles in TNG halos). We further show that the scatter in the velocity dispersion profiles may be attributed to the variations in the assembly history of the host halos. In particular, this segregates the profile into two regimes: one within $\sim0.1r_{200m}$, where the scatter in the velocity dispersion within is set by the early assembly history of the halo, and the other beyond this radius where the scatter in the velocity dispersion is influenced more strongly by its late-time assembly. Finally, we show that a two-parameter model can be used to fit the measured velocity dispersion profiles and the fit parameters can be related directly to two fundamental halo properties: mass and concentration. We describe a simple model which allows us to express the stellar velocity dispersion profile in terms of the mass and concentration of the host halo as the only free parameters., 17 pages, 9 figures, Accepted for publication in ApJ

The spin of the massive black hole (BH) at the center of the Milky Way, SgrA$^*$, has been poorly constrained so far. We place an upper limit on the spin of SgrA$^*$ based on the spatial distribution of the S-stars, which are arranged in two almost edge-on disks that are located at a position angle approximately $\pm 45^\circ$ with respect to the Galactic plane, on a milliparsec scale around the Galactic Center. Requiring that the frame-dragging precession has not had enough time to make the S-star orbital angular momentum precess, the spin of the massive BH at the center of the Milky Way can be constrained to $\chi\lesssim 0.1$., Comment: 3 pages, 2 figures, accepted by ApJ Lett

We investigate the prospects for the past or current existence of habitable conditions deep underneath the surfaces of the Moon and Mars as well as generic bound and free-floating extrasolar rocky objects. We construct a simple model that takes into account the thermal limits of life as well as the size, surface temperature, and relative radionuclide abundance of a given object and yields the spatial extent of the subsurface habitable region. We also investigate the constraint imposed by pressure on habitability, and show that it is unlikely to rule out the prospects for life altogether. We estimate the maximum biomass that might be sustainable in deep subsurface environments as a function of the aforementioned parameters from an energetic perspective. We find that it might be a few percent that of Earth's subsurface biosphere, and three orders of magnitude smaller than Earth's global biomass, under ideal circumstances. We conclude with a brief exposition of the prevalence of rocky objects with deep biospheres and methods for detecting signatures of biological activity through forthcoming missions to visit the Moon and Mars., Published in The Astrophysical Journal Letters; 8 pages; 3 figures

Tidal dissipation due to turbulent viscosity in the convective regions of giant stars plays an important role in shaping the orbits of pre-common envelope systems. Such systems are possible sources of transients and close compact binary systems that will eventually merge and produce detectable gravitational wave signals. Most previous studies of the onset of common envelope episodes have focused on circular orbits and synchronously rotating donor stars under the assumption that tidal dissipation can quickly spin up the primary and circularize the orbit before the binary reaches Roche-lobe overflow (RLO). We test this assumption by coupling numerical models of the post main sequence stellar evolution of massive-stars with the model for tidal dissipation in convective envelopes developed in Vick & Lai (2020) $-$ a tidal model that is accurate even for highly eccentric orbits with small pericentre distances. We find that, in many cases, tidal dissipation does not circularize the orbit before RLO. For a $10~M_\odot$ ($15~M_\odot$) primary star interacting with a $1.4~M_\odot$ companion, systems with pericentre distances within 3 AU (6 AU) when the primary leaves the main sequence will retain the initial orbital eccentricity when the primary grows to the Roche radius. Even in systems that tidally circularize before RLO, the donor star may be rotating subsynchronously at the onset of mass transfer. Our results demonstrate that some possible precursors to double neutron star systems are likely eccentric at the Roche radius. The effects of pre-common envelope eccentricity on the resulting compact binary merit further study., 15 pages, 9 figures, Accepted to MNRAS

The coalescence of massive black hole binaries (with masses $10^4 - 10^7 M_{\odot}$) leads to gravitational wave emission that is detectable out to high redshifts ($z \sim 20$) with the forthcoming LISA observatory. We combine the theoretically derived merger rates for dark matter haloes at various redshifts, with an empirically motivated prescription that connects the mass of a dark matter halo and that of its central black hole. Using the expected constraints on the (chirp or reduced) masses of binary black holes, their mass ratios and redshift uncertainties, we forecast the measurement precision on the occupation fraction, normalization and slope of the black hole mass - halo mass relation at various redshifts, assuming a five-year LISA survey for three different confidence scenarios. We use the expected sizes of the LISA localization ellipses on the sky to estimate the number of electromagnetic counterparts to the gravitational wave sources which are detectable by future wide-field optical surveys, such as LSST., 17 pages, 3 figures; version accepted for publication in JCAP

We show that an equal-mass, temporary binary companion to the Sun in the solar birth cluster at a separation of $\sim 10^3 \; \mathrm{\; AU}$ would have increased the likelihood of forming the observed population of outer Oort cloud objects and of capturing Planet Nine. In particular, the discovery of a captured origin for Planet Nine would favor our binary model by an order of magnitude relative to a lone stellar history. Our model predicts an overabundance of dwarf planets, discoverable by LSST, with similar orbits to Planet Nine, which would result from capture by the stellar binary., 5 pages, 2 figures; accepted to ApJL

HR 6819 was recently claimed to be a hierarchical triple system of a Be star in a wide orbit around an inner binary system of a black hole (BH) and a B III type star. We argue that this system is unlikely to be a hierarchical triple due to three reasons: (i) Given that this system is discovered in a magnitude limited Bright Star Catalog, the expected number of such systems in the Milky Way amounts to about $10^4$ while the estimate for the MW budget for such systems is between $10^2-10^3$ systems under generous assumptions. Such a large gap cannot be reconciled as it would otherwise likely overflow the MW budget for BHs; (ii) The dynamical stability of this system sets lower bounds on the orbital separation of the outer Be star, while it not being resolved by Gaia places an upper limit on its projected sky separation. We show that these two constraints would imply a narrow range for the outer orbit without resorting to geometrical fine-tuning; (iii) The triple system should have survived the stellar evolution prior to the formation of the BH in the inner binary. We perform numerical simulations starting with conservative initial conditions of this system and show that a small parameter space for BH progenitor star's mass loss, BH natal kicks, and initial orbital separation can reproduce HR 6819. Therefore, we propose this system is a chance superposition of a Be star with a binary., Matches the published version at ApJ Letters

Planck's residuals of the CMB temperature power spectrum present a curious oscillatory shape that resembles an extra smoothing effect of lensing and is the source of the lensing anomaly. The smoothing effect of lensing to the CMB temperature power spectrum is, to some extent, degenerate with oscillatory modulations of the primordial power spectrum, in particular if the frequency is close to that of the acoustic peaks. We consider the possibility that the lensing anomaly reported by the latest Planck 2018 results may be hinting at an oscillatory modulation generated by a massive scalar field during an alternative scenario to inflation or by a sharp feature during inflation. We use the full TTTEEE+low E CMB likelihood from Planck to derive constraints on these two types of models. We obtain that in both cases the $A_L$ anomaly is mildly reduced to slightly less than $2\sigma$, to be compared with the $2.8\sigma$ deviation from $A_L=1$ in $\Lambda$CDM. Although the oscillatory features are not able to satisfactorily ease the lensing anomaly, we find that the oscillatory modulation generated during an alternative scenario alone, i.e. with $A_L=1$, presents the lowest value of $\chi^2$, with $\Delta\chi^2=-13$ compared to $\Lambda$CDM. Furthermore, the Akaike Information Criterion suggests that such an oscillation constitutes an attractive candidate since it has a value $\Delta{\rm AIC}=-5$ with respect to $\Lambda$CDM, comparable to the $A_L$ parameter. We also obtain that the equation of state parameter in the alternative scenario is given at $1\sigma$ by $w=0.13\pm0.17$. Interestingly, the matter bounce and radiation bounce scenarios are compatible with our results. We discuss how these models of oscillatory features can be tested with future observations., Comment: revised version

There is evidence that ejecta from nearby supernovae have rained down on Earth in the past. Supernovae can accelerate pre-existing dust grains in the interstellar medium to speeds of $\sim 0.01 \mathrm{\;c}$. We investigate the survival and impact of dust grains from supernovae on the moon, finding that supernova dust grains can form detectable tracks with widths of $\sim 0.01 - 0.07 \mathrm{\; \mu m}$ and depths of $\sim 0.1 - 0.7 \mathrm{\; mm}$ in lunar rocks. These tracks could potentially shed light on the timings, luminosities, and directions of nearby supernovae., Comment: 4 pages, 2 figures; accepted for publication in ApJL

Recently, a 30-cm object was discovered to graze the Earth&rsquo, s atmosphere and shift into a Jupiter-crossing orbit. We use the related survey parameters to calibrate the total number of such objects. The number of objects that could have exported terrestrial microbes out of the Solar System is in the range 2 &times, 10 9 &ndash, 3 &times, 10 11 . We find that 10 7 &ndash, 10 9 such objects could have been captured by binary star systems over the lifetime of the Solar System. Adopting the fiducial assumption that one polyextremophile colony is picked up by each object, the total number of objects carrying living colonies on them upon capture could be 10&ndash, 10 3 .

Gravitational waves (GWs) are produced by colliding particles through the gravitational analogue of electromagnetic bremsstrahlung. We calculate the contribution of free-free emission in the radiation-dominated Universe to the stochastic GW background. We find that the energy density of the resulting GW radiation is heavily dependent on the number of elementary particles, $N_{\mathrm{tot}}$, and the maximum initial temperature, $T_{\mathrm{max}}$. We rule out $N_{\mathrm{tot}}\gtrsim N_{\mathrm{SM}}$ for $T_{\mathrm{max}}\sim T_{\mathrm{Planck}}\approx10^{19}$ GeV and $N_{\mathrm{tot}}\gtrsim10^{13}\times N_{\mathrm{SM}}$ for $T_{\mathrm{max}}\sim10^{16}$ GeV, where $N_{\mathrm{SM}}$ is the number of particles in the Standard Model. In the case of inflation, existing cosmological data constrain $T_{\mathrm{max}}\lesssim10^{16}$ GeV. However, alternative models to inflation such as bouncing cosmologies allow for $T_{\mathrm{max}}$ near $T_{\mathrm{Planck}}$. At the energy scales we are considering, the extra number of particles arise naturally in models of extra dimensions., 5 pages, 2 figures, submitted to PRL, comments welcome

We model explosions driven by the coalescence of a black hole or neutron star with the core of its massive-star companion. Upon entering a common envelope phase, a compact object may spiral all the way to the core. The concurrent release of energy is likely to be deposited into the surrounding common envelope, powering a merger-driven explosion. We use hydrodynamic models of binary coalescence to model the common envelope density distribution at the time of coalescence. We find toroidal profiles of material, concentrated in the binary's equatorial plane and extending to many times the massive star's original radius. We use the spherically-averaged properties of this circumstellar material (CSM) to estimate the emergent light curves that result from the interaction between the blast wave and the CSM. We find that typical merger-driven explosions are brightened by up to three magnitudes by CSM interaction. From population synthesis models we discover that the brightest merger-driven explosions, $M_V \sim -18$ to $-19$, are those involving black holes because they have the most massive and extended CSM. Black hole coalescence events are also common; they represent about 50% of all merger-driven explosions and approximately 0.3% of the core-collapse rate. Merger-driven explosions offer a window into the highly-uncertain physics of common envelope interactions in binary systems by probing the properties of systems that merge rather than eject their envelopes., 23 pages, 11 figures, submitted to APJ, comments are welcome

We explore the contributions of Tidal Disruption Events (TDEs) to the flares in Active Galactic Nuclei (AGN) at high redshifts. Using the latest data available from X-ray and optical observations of high-redshift galaxies, in combination with the evolution of their central supermassive black holes, we calculate the contribution of TDE to AGNs as a function of their luminosities. We find that at low redshifts ($z < 1$), a few percent of all AGN with bolometric luminosities $L_{\rm Bol} \lesssim 10^{44}$ erg s$^{-1}$ may be attributable to possible TDEs. However, this fraction can significantly increase at earlier cosmic times, including up to several tens of percent of the population of AGN at $z \gtrsim 3$. TDEs may comprise a significant fraction of the Compton-Thick (CT) AGN population at $z \gtrsim 3$. The above findings motivate further calibration with upcoming X-ray missions and spectroscopic surveys targeting TDE-AGN., 6 pages, 5 figures; accepted for publication in A&A

Fast radio bursts (FRBs) are highly energetic radio pulses from cosmological origins. Despite an abundance of detections, their nature remains elusive. At least a subset of FRBs is expected to repeat, as the daily FRB rate surpasses that of any known cataclysmic event, which has been confirmed by observations. One of the proposed mechanisms to generate repeating FRBs is supergiant pulses from young and highly spinning NSs, in which case FRBs could inherit the periodicity of their parent NS. Here we examine the consequences of such a population of periodic fast radio bursts (PFRBs). We calculate the rate and lifetime of PFRB progenitors, and find that each newly born highly spinning NS has to emit a number $N_{\rm PFRB}\sim 10^2$ of bursts during its active lifetime of $\tau\sim 100$ years, after which it becomes too dim and crosses a PFRB "death line" analogous to the pulsar one. We propose several tests of this hypothesis. First, the period of PFRBs would increase over time, and their luminosity would decrease, due to the NS spin-down. Second, PFRBs may show modest amounts of rotation measure, given the lack of expelled matter from the pulsar, as opposed to the magnetar-sourced FRBs proposed to explain the first repeater FRB 121102. As an example, we study whether the second confirmed repeater (FRB 180814) is a PFRB, given the preference for an inter-pulse separation of 13 ms within its sub-bursts. We show that, if confirmed, this period would place FRB 180814 in a different category as FRB 121102. We develop tests that would identify---and characterize---the prospective population of PFRBs., Comment: 8 pages, 1 figure. Comments are welcome

It is shown that a gravitationally bound system with a one-dimensional velocity dispersion sigma can at most dissipate a fraction ~36(sigma/c)^3 of the gravitational wave energy propagating through it, even if their dynamical time is shorter than the wave period. The limit is saturated for particles with a mean-free-path equal to the size of the system, such as hot protons in galaxy clusters, strongly-interacting dark matter particles in halos, or massive black holes in clusters. For such systems with random motions and no resonances, the dissipated fraction, 5 pages, accepted for publication in The Astrophysical Journal Letters

Planet Nine has been proposed to potentially be a black hole in the outer solar system. We investigate the accretion flares that would result from impacts of small Oort cloud objects, and find that the upcoming LSST observing program will be able to either rule out or confirm Planet Nine as a black hole within a year. We also find that LSST could rule out or confirm the existence of trapped planet-mass black holes out to the edge of the Oort cloud, indirectly probing the dark matter fraction in subsolar mass black holes and potentially improving upon current limits by orders of magnitude., Comment: 4 pages, 2 figures; accepted for publication in ApJL

Several large-scale experimental facilities and space-missions are being suggested to probe the universe across the gravitational-wave (GW) spectrum. Here we propose Gravitational-wave Lunar Observatory for Cosmology (GLOC) - the first concept design in the NASA Artemis era for a GW observatory on the Moon. Using feasible interferometer technologies, we find that a lunar-based observatory is ideal for probing GW frequencies in the range between deci-Hz to 5 Hz, an astrophysically rich regime that is very challenging for both Earth- and space-based detectors. GLOC can survey binaries with neutron stars, stellar and intermediate-mass black holes to $\gtrsim 70\%$ of the observable volume of our universe without significant background contamination. The sensitivity at $\mathcal{O}(1~\mathrm{Hz})$ allows a unique window into calibrating Type Ia supernovae. At its ultimate sensitivity limits, GLOC would trace the Hubble expansion rate up to redshift $z \sim 3$ and test General Relativity and $\Lambda$CDM cosmology up to $z\sim 350$., Comment: Published in the Journal of Cosmology and Astroparticle Physics (24 June 2021)

Here, we show that the detection of Borisov implies that interstellar objects outnumber Solar system objects in the Oort cloud, whereas the reverse is true near the Sun due to the stronger gravitational focusing of bound objects. This hypothesis can be tested with stellar occultation surveys of the Oort cloud. Furthermore, we demonstrate that $\sim 1 \%$ of carbon and oxygen in the Milky Way Galaxy may be locked in interstellar objects, saturating the heavy element budget of the minimum mass Solar nebula model., Comment: 4 pages, 4 figures; accepted for publication in MNRAS Letters

Black holes across a broad range of masses play a key role in the evolution of galaxies. The initial seeds of black holes formed at $z \sim 30$ and grew over cosmic time by gas accretion and mergers. Using observational data for quasars and theoretical models for the hierarchical assembly of dark matter halos, we study the relative importance of gas accretion and mergers for black hole growth, as a function of redshift ($0 10^8 \, \mathrm{M_{\odot}}$ and $z>6$; and (ii) growth by mergers is dominant at $M_{\bullet} < 10^5 \, \mathrm{M_{\odot}}$ and $z>5.5$, and at $M_{\bullet} > 10^8 \, \mathrm{M_{\odot}}$ and $z, Comment: Accepted for publication in The Astrophysical Journal. This is the final version of the manuscript. 12 pages, 5 figures

The LIGO/Virgo Collaboration (LVC) recently reported the detection of GW190814, a merger of a $23^{+1.0}_{-0.9}~M_{\odot}$ primary black hole (BH), and a $2.6^{+0.08}_{-0.08}~M_{\odot}$ secondary. The secondary's mass falls into the mass-gap regime, which refers to the scarcity of compact objects in the mass range of 2-5 $M_{\odot}$. The first clue to the formation of the GW190814 lies in the fact that the primary is a very massive BH. We suggest that the secondary was born as a neutron star (NS) where a significant amount of the supernova ejecta mass from its formation remained bound to the binary due to the presence of the massive BH companion. The bound mass forms a circumbinary accretion disk, and its accretion onto the NS created a mass-gap object. In this scenario, LIGO/Virgo will only detect mass-gap objects in binary mergers with an extreme mass ratio. We also predict a correlation between the mass of the secondary and the mass of the primary in such asymmetric mergers. Our model can be tested with future data from the LVC's third-observing run., Comment: Accepted for publication in ApJ Letters

In this paper, we explore from a conceptual standpoint the possibility of using natural astrophysical sources to accelerate spacecrafts to relativistic speeds. We focus on light sails and electric sails, which are reliant on momentum transfer from photons and protons, respectively, because these two classes of spacecrafts are not required to carry fuel on board. The payload is assumed to be stationed near the astrophysical source, and the sail is subsequently unfolded and activated when the source is functional. By considering a number of astrophysical objects such as massive stars, microquasars, supernovae, pulsar wind nebulae, and active galactic nuclei, we show that terminal speeds approaching the speed of light might be realizable under idealized circumstances provided that sufficiently advanced sail materials and control techniques exist. We also investigate the constraints arising from the sail's material properties, the voyage through the ambient source environment, and the passage through the interstellar medium. While all of these considerations pose significant challenges to spacecrafts, our analysis indicates that they are not insurmountable in optimal conditions. Finally, we sketch the implications for carrying out future technosignature searches., Comment: Published in The Astrophysical Journal; 22 pages; 4 figures

Stellar winds shape the evolution of stars through the loss of mass. In binary systems, they also shape the stars' evolution by modifying the orbit. In this paper, we use hydrodynamic simulations to study the emergence of nearly-isothermal winds from identical-twin binaries. We vary the degree to which model stars fill their Roche lobes and the temperature of the wind. Initialized at rest on the stellar surfaces, winds accelerate away from the binary components through a sonic surface to supersonic outward velocities. In cases where the binary fills its Roche lobe, a shared subsonic region surrounds both components. We find that mass loss rates from close twin-star binaries are enhanced relative to the expectation from two single-object winds. This binary enhancement is best modeled as a function of the ratio of wind velocity to orbital velocity. Similarly, we find that the specific angular momentum with which winds emerge can vary between that of the binary components and that of the outer Lagrange points depending on the ratio of wind velocity to orbital velocity. Given that mass and angular momentum loss can be modeled as simple functions of wind velocity, our results may be broadly applicable to the evolution of close, equal-mass binaries. One particularly important potential application is to massive, close binaries which may be progenitors of binary black hole mergers through the chemically-homogeneous evolution channel., Comment: Submitted to AAS Journals for review -- we welcome comments and feedback. Software to reproduce simulation analysis as well as extended figure sets are available at https://github.com/morganemacleod/TwinWinds Raw data release is also being arranged as soon as possible via zenodo, will be linked from github

We employ holographic duality to compute $\langle T_{\mu \nu} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{\mu \nu} \rangle$. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant $H_c$ for which de Sitter space is unstable when $H < H_c$ and mode stable when $H > H_c$., Comment: 11 pages, one figure, clarifications added in v2

The first and second Gravitational Wave Transient Catalogs by the LIGO/Virgo Collaboration include $50$ confirmed merger events from the first, second, and first half of the third observational runs. We compute the distribution of recoil kicks imparted to the merger remnants and estimate their retention probability within various astrophysical environments as a function of the maximum progenitor spin ($\chi_{\rm max}$), assuming that the LIGO/Virgo binary black hole (BBH) mergers were catalyzed by dynamical assembly in a dense star cluster. We find that the distributions of average recoil kicks are peaked at about $150$ km s$^{-1}$, $250$ km s$^{-1}$, $350$ km s$^{-1}$, $600$ km s$^{-1}$, for maximum progenitor spins of $0.1$, $0.3$, $0.5$, $0.8$, respectively. Only environments with escape speed $\gtrsim 100$ km s$^{-1}$, as found in galactic nuclear star clusters as well as in the most massive globular clusters and super star clusters, could efficiently retain the merger remnants of the LIGO/Virgo BBH population even for low progenitor spins ($\chi_{\rm max}=0.1$). In the case of high progenitor spins ($\chi_{\rm max}\gtrsim 0.5$), only the most massive nuclear star clusters can retain the merger products. We also show that the estimated values of the effective spin and of the remnant spin of GW170729, GW190412, GW190519, and GW190620 can be reproduced if their progenitors were moderately spinning ($\chi_{\rm max}\gtrsim 0.3$), while for GW190517 if the progenitors were rapidly spinning ($\chi_{\rm max}\gtrsim 0.8$). Alternatively, some of these events could be explained if at least one of the progenitors is already a second-generation BH, originated from a previous merger., Comment: 6 pages, 5 figures, accepted by MNRAS

LIGO and Virgo have reported the detection of GW190521, from the merger of a binary black hole (BBH) with a total mass around $150$ M$_\odot$. While current stellar models limit the mass of any black hole (BH) remnant to about $40 - 50$ M$_\odot$, more massive BHs can be produced dynamically through repeated mergers in the core of a dense star cluster. The process is limited by the recoil kick (due to anisotropic emission of gravitational radiation) imparted to merger remnants, which can escape the parent cluster, thereby terminating growth. We study the role of the host cluster metallicity and escape speed in the buildup of massive BHs through repeated mergers. Almost independent of host metallicity, we find that a BBH of about $150$ M$_\odot$ could be formed dynamically in any star cluster with escape speed $\gtrsim 200$ km s$^{-1}$, as found in galactic nuclear star clusters as well as the most massive globular clusters and super star clusters. Using an inspiral-only waveform, we compute the detection probability for different primary masses ($\ge 60$ M$_\odot$) as a function of secondary mass and find that the detection probability increases with secondary mass and decreases for larger primary mass and redshift. Future additional detections of massive BBH mergers will be of fundamental importance for understanding the growth of massive BHs through dynamics and the formation of intermediate-mass BHs., Comment: 8 pages, 5 figures, accepted by ApJ Lett

Binary systems undergoing unstable Roche Lobe overflow spill gas into their circumbinary environment as their orbits decay toward coalescence. In this paper, we use a suite of hydrodynamic models of coalescing binaries involving an extended donor and a more compact accretor. We focus on the period of unstable Roche Lobe overflow that ends as the accretor plunges within the envelope of the donor at the onset of a common envelope phase. During this stage, mass is removed from the donor and flung into the circumbinary environment. Across a wide range of binary mass ratios, we find that the mass expelled as the separation decreases from the Roche limit to the donor's original radius is of the order of 25% of the accretor's mass. We study the kinematics of this ejecta and its dependencies on binary properties and find that it assembles into a toroidal circumbinary distribution. These circumbinary tori have approximately constant specific angular momentum due to momentum transport by spiral shocks launched from the orbiting binary. We show that an analytic model with these torus properties captures many of the main features of the azimuthally-averaged profiles of our hydrodynamic simulations. Our results, in particular the simple relationship between accretor mass and expelled mass and its spatial distribution, may be useful in interpreting stellar coalescence transients like luminous red novae, and in initializing hydrodynamic simulations of the subsequent common envelope phase., Comment: The Astrophysical Journal, Volume 895, Issue 1, id.29. Software to reproduce these results availible at: https://github.com/morganemacleod/PreCEMassLoss, software to model pre-CE unstable mass transfer and circumbinary material based on simulation results availible at: https://github.com/morganemacleod/RLOF

Stellar engines are hypothesized megastructures that extract energy from the host star, typically with the purpose of generating thrust and accelerating the stellar system. We explore the maximum potential speeds that could be realizable by stellar engines, and determine that speeds up to $\sim 0.1\,c$ might perhaps be attainable under optimal conditions. In contrast, natural astrophysical phenomena in the Milky Way are very unlikely to produce such speeds. Hence, astrometric surveys of hypervelocity stars may be utilized to conduct commensal searches for high-speed stellar engines in the Milky Way. It may be possible to derive bounds on their abundance, but this requires certain assumptions regarding the spatiotemporal distribution of such engines, which are not guaranteed to be valid., Comment: Accepted for publication in The Astrophysical Journal; 9 pages; 0 figures

In the local universe, black hole masses have been inferred from the observed increase in the velocities of stars at the centres of their host galaxies. So far, masses of supermassive black holes in the early universe have only been inferred indirectly, using relationships calibrated to their locally observed counterparts. Here, we use the latest observational constraints on the evolution of stellar masses in galaxies to predict, for the first time, that the region of influence of a central supermassive black hole at the epochs where the first galaxies were formed is $\mathit{directly \ resolvable}$ by current and upcoming telescopes. We show that the existence of the black hole can be inferred from observations of the gas or stellar disc out to $> 0.5$ kpc from the host halo at redshifts $z \gtrsim 6$. Such measurements will usher in a new era of discoveries unraveling the formation of the first supermassive black holes based on subarcsecond-scale spectroscopy with the $JWST$, $ALMA$, and the $SKA$. The measured mass distribution of black holes will allow forecasting of the future detection of gravitational waves from the earliest black hole mergers., 9 pages, 3 figures; version accepted for publication in JCAP

Aquatic photosynthesis plays a major role in carbon fixation and O$_2$ production on Earth. In this Letter, we analyze the prospects for oxygenic photosynthesis in aquatic environments on modern Earth-analogs around F-, G-, K- and M-type stars. Our analysis takes into account the spectral type of the host star, attenuation of light by aquatic organisms, and rates of respiration and photosynthesis. We study the compensation depth ($\mathcal{Z}_\mathrm{CO}$) and the critical depth ($\mathcal{Z}_\mathrm{CR}$), defined respectively as the locations where the net growth rates and vertically integrated net growth rates of photoautotrophs become zero. Our analysis suggests that $\mathcal{Z}_\mathrm{CO}$ declines by more than an order of magnitude as one moves from the habitable zones around Sun-like stars to late-type M-dwarfs, but $\mathcal{Z}_\mathrm{CR}$ decreases by only a modest amount ($\sim 40\%$). For M-dwarf exoplanets, we propose that the photosynthetic red edge may constitute a more robust biosignature of aquatic photosynthesis compared to atmospheric O$_2$., Published in The Astrophysical Journal Letters; 7 pages; 3 figures