Establishing a Relation between the Mass and the Spin of Stellar-Mass Black Holes

Stellar mass black holes (SMBHs), forming by the core collapse of very massive, rapidly rotating stars, are expected to exhibit a high density accretion disk around them developed from the spinning mantle of the collapsing star. A wide class of such disks, due to their high density and temperature, are effective emitters of neutrinos and hence called neutrino cooled disks. Tracking the physics relating the observed (neutrino) luminosity to the mass, spin of black holes (BHs) and the accretion rate ((M) over dot) of such disks, here we establish a correlation between the spin and mass of SMBHs at their formation stage. Our work shows that spinning BHs are more massive than nonspinning BHs for a given (M) over dot. However, slowly spinning BHs can turn out to be more massive than spinning BHs if (M) over dot at their formation stage was higher compared to faster spinning BHs.

A J-band detection of the sub-stellar mass donor in SDSS J1433+1011

We present time-resolved J-band spectroscopy of the short-period cataclysmic variable SDSS J143317.78+101123.3. We detect absorption lines from the sub-stellar donor star in this system, which contributes 38 +/- 5 per cent to the J-band light. From the relative strengths of the absorption lines in the J band, we estimate the spectral type of the donor star to be L2 +/- 1. These data are the first spectroscopic detection of a donor with a confirmed sub-stellar mass in a cataclysmic variable, and the spectral type is consistent with that expected from semi-empirical evolutionary models.

Using skew mapping, we have been able to derive an estimate for the radial velocity of the donor of K-d = 520 +/- 60 km/s. This value is consistent with, though much less precise than, predictions from mass determinations found via photometric fitting of the eclipse light curves.

Compact groups of galaxies selected by stellar mass: the 2MASS compact group catalogue

We present a photometric catalogue of compact groups of galaxies (p2MCGs) automatically extracted from the Two-Micron All Sky Survey (2MASS) extended source catalogue. A total of 262 p2MCGs are identified, following the criteria defined by Hickson, of which 230 survive visual inspection (given occasional galaxy fragmentation and blends in the 2MASS parent catalogue). Only one quarter of these 230 groups were previously known compact groups (CGs). Among the 144 p2MCGs that have all their galaxies with known redshifts, 85 (59?per cent) have four or more accordant galaxies. This v2MCG sample of velocity-filtered p2MCGs constitutes the largest sample of CGs (with N = 4) catalogued to date, with both well-defined selection criteria and velocity filtering, and is the first CG sample selected by stellar mass. It is fairly complete up to Kgroup similar to 9 and radial velocity of similar to 6000?km?s-1. We compared the properties of the 78 v2MCGs with median velocities greater than 3000?km?s-1 with the properties of other CG samples, as well as those (mvCGs) extracted from the semi-analytical model (SAM) of Guo et al. run on the high-resolution Millennium-II simulation. This mvCG sample is similar (i.e. with 2/3 of physically dense CGs) to those we had previously extracted on three other SAMs run on the Millennium simulation with 125 times worse spatial and mass resolutions. The space density of v2MCGs within 6000?km?s-1 is 8.0 X 10-5?h3?Mpc-3, i.e. four times that of the Hickson sample [Hickson Compact Group (HCG)] up to the same distance and with the same criteria used in this work, but still 40?per cent less than that of mvCGs. The v2MCG constitutes the first group catalogue to show a statistically large firstsecond ranked galaxy magnitude gap according to TremaineRichstone statistics, as expected if the first ranked group members tend to be the products of galaxy mergers, and as confirmed in the mvCGs. The v2MCG is also the first observed sample to show that first-ranked galaxies tend to be centrally located, again consistent with the predictions obtained from mvCGs. We found no significant correlation of group apparent elongation and velocity dispersion in the quartets among the v2MCGs, and the velocity dispersions of apparently round quartets are not significantly larger than those of chain-like ones, in contrast to what has been previously reported in HCGs. By virtue of its automatic selection with the popular Hickson criteria, its size, its selection on stellar mass, and its statistical signs of mergers and centrally located brightest galaxies, the v2MCG catalogue appears to be the laboratory of choice to study physically dense groups of four or more galaxies of comparable luminosity.

Star formation in a stellar mass-selected sample of galaxies to z=3 from the GOODS-NICMOS Survey

We present a study of the star-forming properties of a stellar mass-selected sample of galaxies in the GOODS (Great Observatories Origins Deep Survey) NICMOS Survey (GNS), based on deep Hubble Space Telescope (HST) imaging of the GOODS North and South fields. Using a stellar mass-selected sample, combined with HST/ACS and Spitzer data to measure both ultraviolet (UV) and infrared-derived star formation rates (SFRs), we investigate the star forming properties of a complete sample of ∼1300 galaxies down to log M_*= 9.5 at redshifts 1.5 < z < 3. Eight per cent of the sample is made up of massive galaxies with M_*≥ 10^11 M_⊙. We derive optical colours, dust extinctions and UV and infrared SFR to determine how the SFR changes as a function of both stellar mass and time. Our results show that SFR increases at higher stellar mass such that massive galaxies nearly double their stellar mass from star formation alone over the redshift range studied, but the average value of SFR for a given stellar mass remains constant over this ∼2 Gyr period. Furthermore, we find no strong evolution in the SFR for our sample as a function of mass over our redshift range of interest; in particular we do not find a decline in the SFR among massive galaxies, as is seen at z < 1. The most massive galaxies in our sample (log M_*≥ 11) have high average SFRs with values SFR_UV, corr= 103 ± 75 M_⊙ yr^−1, and yet exhibit red rest-frame (U−B) colours at all redshifts. We conclude that the majority of these red high-redshift massive galaxies are red due to dust extinction. We find that A_2800 increases with stellar mass, and show that between 45 and 85 per cent of massive galaxies harbour dusty star formation. These results show that even just a few Gyr after the first galaxies appear, there are strong relations between the global physical properties of galaxies, driven by stellar mass or another underlying feature of galaxies strongly related to the stellar mass.

Minor mergers and their impact on the kinematics of old and young stellar populations in disk galaxies

By means of N-body simulations we investigate the impact of minor mergers on the angular momentum and dynamical properties of the merger remnant. Our simulations cover a range of initial orbital characteristics and gas-to-stellar mass fractions (from 0 to 20%), and include star formation and supernova feedback. We confirm and extend previous results by showing that the specific angular momentum of the stellar component always decreases independently of the orbital parameters or morphology of the satellite, and that the decrease in the rotation velocity of the primary galaxy is accompanied by a change in the anisotropy of the orbits. However, the decrease affects only the old stellar population, and not the new population formed from gas during the merging process. This means that the merging process induces an increasing difference in the rotational support of the old and young stellar components, with the old one lagging with respect to the new. Even if our models are not intended specifically to reproduce the Milky Way and its accretion history, we find that, under certain conditions, the modeled rotational lag found is compatible with that observed in the Milky Way disk, thus indicating that minor mergers can be a viable way to produce it. The lag can increase with the vertical distance from the disk midplane, but only if the satellite is accreted along a direct orbit, and in all cases the main contribution to the lag comes from stars originally in the primary disk rather than from stars in the satellite galaxy. We also discuss the possibility of creating counter-rotating stars in the remnant disk, their fraction as a function of the vertical distance from the galaxy midplane, and the cumulative effect of multiple mergers on their creation.

A lower mass for the exoplanet WASP-21b

We present high-precision transit observations of the exoplanet WASP-21b, obtained with the Rapid Imager to Search for Exoplanets instrument mounted on the 2.0-m Liverpool Telescope. A transit model is fitted, coupled with a Markov chain Monte Carlo routine, to derive accurate system parameters. The two new high-precision transits allow us to estimate the stellar density directly from the light curve. Our analysis suggests that WASP-21 is evolving off the main sequence which led to a previous overestimation of the stellar density. Using isochrone interpolation, we find a stellar mass of 0.86 ± 0.04 Msun, which is significantly lower than previously reported (1.01 ± 0.03 Msun). Consequently, we find a lower planetary mass of 0.27 ± 0.01 MJup. A lower inclination (87?4 ± 0?3) is also found for the system than previously reported, resulting in a slightly larger stellar (R*= 1.10 ± 0.03 Rsun) and planetary radius (Rp= 1.14 ± 0.04 RJup). The planet radius suggests a hydrogen/helium composition with no core which strengthens the correlation between planetary density and host star metallicity. A new ephemeris is determined for the system, i.e. T0= 245 5084.519 74 ± 0.000 20 (HJD) and P= 4.322 5060 ± 0.000 0031 d. We found no transit timing variations in WASP-21b.

An upper mass limit for the progenitor of the Type II-P supernova SN 1999gi

Masses and progenitor evolutionary states of Type II supernovae remain almost unconstrained by direct observations. Only one robust observation of a progenitor (SN 1987A) and one plausible observation (SN 1993J) are available. Neither matched theoretical predictions, and in this Letter we report limits on a third progenitor (SN 1999gi). The Hubble Space Telescope (HST) has imaged the site of the Type II-P supernova SN 1999gi with the Wide Field Planetary Camera 2 (WFPC2) in two filters (F606W and F300W) prior to explosion. The distance to the host galaxy (NGC 3184) of 7.9 Mpc means that the most luminous, massive stars are resolved as single objects in the archive images. The supernova occurred in a resolved, young OB association 2.3 kpc from the center of NGC 3184 with an association age of about 4 Myr. Follow-up images of SN 1999gi with WFPC2 taken 14 months after discovery determine the precise position of the supernova on the preexplosion frames. An upper limit of the absolute magnitude of the progenitor is estimated (M-v greater than or equal to -5.1). By comparison with stellar evolutionary tracks, this can be interpreted as a stellar mass, and we determine an upper mass limit of 9(-2)(+3) M.. We discuss the possibility of determining the masses or mass limits for numerous nearby core-collapse supernovae using the HST archive enhanced by our current SNAP program.

Mass-metallicity relation explored with CALIFA I. Is there a dependence on the star-formation rate?

We studied the global and local ℳ-Z relation based on the first data available from the CALIFA survey (150 galaxies). This survey provides integral field spectroscopy of the complete optical extent of each galaxy (up to 2−3 effective radii), with a resolution high enough to separate individual H II regions and/or aggregations. About 3000 individual H II regions have been detected. The spectra cover the wavelength range between [OII]3727 and [SII]6731, with a sufficient signal-to-noise ratio to derive the oxygen abundance and star-formation rate associated with each region. In addition, we computed the integrated and spatially resolved stellar masses (and surface densities) based on SDSS photometric data. We explore the relations between the stellar mass, oxygen abundance and star-formation rate using this dataset. We derive a tight relation between the integrated stellar mass and the gas-phase abundance, with a dispersion lower than the one already reported in the literature (σ_Δlog (O/H) = 0.07 dex). Indeed, this dispersion is only slightly higher than the typical error derived for our oxygen abundances. However, we found no secondary relation with the star-formation rate other than the one induced by the primary relation of this quantity with the stellar mass. The analysis for our sample of ~3000 individual H II   regions confirms (i) a local mass-metallicity relation and (ii) the lack of a secondary relation with the star-formation rate. The same analysis was performed with similar results for the specific star-formation rate. Our results agree with the scenario in which gas recycling in galaxies, both locally and globally, is much faster than other typical timescales, such like that of gas accretion by inflow and/or metal loss due to outflows. In essence, late-type/disk-dominated galaxies seem to be in a quasi-steady situation, with a behavior similar to the one expected from an instantaneous recycling/closed-box model.

Mass assembly and morphological transformations since z ∼ 3 from CANDELS

We quantify the evolution of the stellar mass functions (SMFs) of star-forming and quiescent galaxies as a function of morphology from z ∼ 3 to the present. Our sample consists of ∼50 000 galaxies in the CANDELS fields (∼880 arcmin^2), which we divide into four main morphological types, i.e. pure bulge-dominated systems, pure spiral disc-dominated, intermediate two-component bulge+disc systems and irregular disturbed galaxies. At z ∼ 2, 80 per cent of the stellar mass density of star-forming galaxies is in irregular systems. However, by z ∼ 0.5, irregular objects only dominate at stellar masses below 10^9 M_⊙. A majority of the star-forming irregulars present at z ∼ 2 undergo a gradual transformation from disturbed to normal spiral disc morphologies by z ∼ 1 without significant interruption to their star formation. Rejuvenation after a quenching event does not seem to be common except perhaps for the most massive objects, because the fraction of bulge-dominated star-forming galaxies with M^*/M_⊙ > 10^10.7 reaches 40 per cent at z < 1. Quenching implies the presence of a bulge: the abundance of massive red discs is negligible at all redshifts over 2 dex in stellar mass. However, the dominant quenching mechanism evolves. At z > 2, the SMF of quiescent galaxies above M^* is dominated by compact spheroids. Quenching at this early epoch destroys the disc and produces a compact remnant unless the star-forming progenitors at even higher redshifts are significantly more dense. At 1 < z < 2, the majority of newly quenched galaxies are discs with a significant central bulge. This suggests that mass quenching at this epoch starts from the inner parts and preserves the disc. At z < 1, the high-mass end of the passive SMF is globally in place and the evolution mostly happens at stellar masses below 10^10 M_⊙. These low-mass galaxies are compact, bulge-dominated systems, which were environmentally quenched: destruction of the disc through ram-pressure stripping is the likely process.

Spectral states and accretion geometries in Galactic black hole binaries

Black hole X-ray binaries, binary systems where matter from a companion star is accreted by a stellar mass black hole, thereby releasing enormous amounts of gravitational energy converted into radiation, are seen as strong X-ray sources in the sky. As a black hole can only be detected via its interaction with its surroundings, these binary systems provide important evidence for the existence of black holes. There are now at least twenty cases where the measured mass of the X-ray emitting compact object in a binary exceeds the upper limit for a neutron star, thus inferring the presence of a black hole. These binary systems serve as excellent laboratories not only to study the physics of accretion but also to test predictions of general relativity in strongly curved space time. An understanding of the accretion flow onto these, the most compact objects in our Universe, is therefore of great importance to physics. We are only now slowly beginning to understand the spectra and variability observed in these X-ray sources. During the last decade, a framework has developed that provides an interpretation of the spectral evolution as a function of changes in the physics and geometry of the accretion flow driven by a variable accretion rate. This doctoral thesis presents studies of two black hole binary systems, Cygnus~X-1 and GRS~1915+105, plus the possible black hole candidate Cygnus~X-3, and the results from an attempt to interpret their observed properties within this emerging framework. The main result presented in this thesis is an interpretation of the spectral variability in the enigmatic source Cygnus~X-3, including the nature and accretion geometry of its so-called hard spectral state. The results suggest that the compact object in this source, which has not been uniquely identified as a black hole on the basis of standard mass measurements, is most probably a massive, ~30 Msun, black hole, and thus the most massive black hole observed in a binary in our Galaxy so far. In addition, results concerning a possible observation of limit-cycle variability in the microquasar GRS~1915+105 are presented as well as evidence of `mini-hysteresis' in the extreme hard state of Cygnus X-1.

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M(circle dot). The choice of the lower frequency cutoff is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

Nucleosynthesis in the accretion disks of type II collapsars

We investigate nucleosynthesis inside the gamma-ray burst (GRB) accretion disks formed by the Type II collapsars. In these collapsars, the core collapse of massive stars first leads to the formation of a proto-neutron star. After that, an outward moving shock triggers a successful supernova. However, the supernova ejecta lacks momentum and within a few seconds the newly formed neutron star gets transformed to a stellar mass black hole via massive fallback. The hydrodynamics of such an accretion disk formed from the fallback material of the supernova ejecta has been studied extensively in the past. We use these well-established hydrodynamic models for our accretion disk in order to understand nucleosynthesis, which is mainly advection dominated in the outer regions. Neutrino cooling becomes important in the inner disk where the temperature and density are higher. The higher the accretion rate (M) over dot is, the higher the density and temperature are in the disks. We deal with accretion disks with relatively low accretion rates: 0.001 M-circle dot s(-1) less than or similar to (M) over dot less than or similar to 0.01 M-circle dot s(-1) and hence these disks are predominantly advection dominated. We use He-rich and Si-rich abundances as the initial condition of nucleosynthesis at the outer disk, and being equipped with the disk hydrodynamics and the nuclear network code, we study the abundance evolution as matter inflows and falls into the central object. We investigate the variation in the nucleosynthesis products in the disk with the change in the initial abundance at the outer disk and also with the change in the mass accretion rate. We report the synthesis of several unusual nuclei like P-31, K-39, Sc-43, Cl-35 and various isotopes of titanium, vanadium, chromium, manganese and copper. We also confirm that isotopes of iron, cobalt, nickel, argon, calcium, sulphur and silicon get synthesized in the disk, as shown by previous authors. Much of these heavy elements thus synthesized are ejected from the disk via outflows and hence they should leave their signature in observed data.

Nucleosynthesis in the outflows associated with accretion disks of type II collapsars

We investigate nucleosynthesis inside the outflows from gamma-ray burst (GRB) accretion disks formed by the Type II collapsars. In these collapsars, massive stars undergo core collapse to form a proto-neutron star initially, and a mild supernova (SN) explosion is driven. The SN ejecta lack momentum, and subsequently this newly formed neutron star gets transformed to a stellar mass black hole via massive fallback. The hydrodynamics and the nucleosynthesis in these accretion disks have been studied extensively in the past. Several heavy elements are synthesized in the disk, and much of these heavy elements are ejected from the disk via winds and outflows. We study nucleosynthesis in the outflows launched from these disks by using an adiabatic, spherically expanding outflow model, to understand which of these elements thus synthesized in the disk survive in the outflow. While studying this, we find that many new elements like isotopes of titanium, copper, zinc, etc., are present in the outflows. Ni-56 is abundantly synthesized in most of the cases in the outflow, which implies that the outflows from these disks in a majority of cases will lead to an observable SN explosion. It is mainly present when outflow is considered from the He-rich, Ni-56/Fe-54-rich zones of the disks. However, outflow from the Si-rich zone of the disk remains rich in silicon. Although emission lines of many of these heavy elements have been observed in the X-ray afterglows of several GRBs by Chandra, BeppoSAX, XMM-Newton, etc., Swift seems to have not yet detected these lines.

Detailed properties of high redshift galaxies

Galaxies evolve throughout the history of the universe from the first star-forming sources, through gas-rich asymmetric structures with rapid star formation rates, to the massive symmetrical stellar systems observed at the present day. Determining the physical processes which drive galaxy formation and evolution is one of the most important questions in observational astrophysics. This thesis presents four projects aimed at improving our understanding of galaxy evolution from detailed measurements of star forming galaxies at high redshift.

We use resolved spectroscopy of gravitationally lensed z ≃ 2 - 3 star forming galaxies to measure their kinematic and star formation properties. The combination of lensing with adaptive optics yields physical resolution of ≃ 100 pc, sufficient to resolve giant Hii regions. We find that ~ 70 % of galaxies in our sample display ordered rotation with high local velocity dispersion indicating turbulent thick disks. The rotating galaxies are gravitationally unstable and are expected to fragment into giant clumps. The size and dynamical mass of giant Hii regions are in agreement with predictions for such clumps indicating that gravitational instability drives the rapid star formation. The remainder of our sample is comprised of ongoing major mergers. Merging galaxies display similar star formation rate, morphology, and local velocity dispersion as isolated sources, but their velocity fields are more chaotic with no coherent rotation.

We measure resolved metallicity in four lensed galaxies at z = 2.0 − 2.4 from optical emission line diagnostics. Three rotating galaxies display radial gradients with higher metallicity at smaller radii, while the fourth is undergoing a merger and has an inverted gradient with lower metallicity at the center. Strong gradients in the rotating galaxies indicate that they are growing inside-out with star formation fueled by accretion of metal-poor gas at large radii. By comparing measured gradients with an appropriate comparison sample at z = 0, we demonstrate that metallicity gradients in isolated galaxies must flatten at later times. The amount of size growth inferred by the gradients is in rough agreement with direct measurements of massive galaxies. We develop a chemical evolution model to interpret these data and conclude that metallicity gradients are established by a gradient in the outflow mass loading factor, combined with radial inflow of metal-enriched gas.

We present the first rest-frame optical spectroscopic survey of a large sample of low-luminosity galaxies at high redshift (L < L*, 1.5 < z < 3.5). This population dominates the star formation density of the universe at high redshifts, yet such galaxies are normally too faint to be studied spectroscopically. We take advantage of strong gravitational lensing magnification to compile observations for a sample of 29 galaxies using modest integration times with the Keck and Palomar telescopes. Balmer emission lines confirm that the sample has a median SFR ∼ 10 M_sun yr^−1 and extends to lower SFR than has been probed by other surveys at similar redshift. We derive the metallicity, dust extinction, SFR, ionization parameter, and dynamical mass from the spectroscopic data, providing the first accurate characterization of the star-forming environment in low-luminosity galaxies at high redshift. For the first time, we directly test the proposal that the relation between galaxy stellar mass, star formation rate, and gas phase metallicity does not evolve. We find lower gas phase metallicity in the high redshift galaxies than in local sources with equivalent stellar mass and star formation rate, arguing against a time-invariant relation. While our result is preliminary and may be biased by measurement errors, this represents an important first measurement that will be further constrained by ongoing analysis of the full data set and by future observations.

We present a study of composite rest-frame ultraviolet spectra of Lyman break galaxies at z = 4 and discuss implications for the distribution of neutral outflowing gas in the circumgalactic medium. In general we find similar spectroscopic trends to those found at z = 3 by earlier surveys. In particular, absorption lines which trace neutral gas are weaker in less evolved galaxies with lower stellar masses, smaller radii, lower luminosity, less dust, and stronger Lyα emission. Typical galaxies are thus expected to have stronger Lyα emission and weaker low-ionization absorption at earlier times, and we indeed find somewhat weaker low-ionization absorption at higher redshifts. In conjunction with earlier results, we argue that the reduced low-ionization absorption is likely caused by lower covering fraction and/or velocity range of outflowing neutral gas at earlier epochs. This result has important implications for the hypothesis that early galaxies were responsible for cosmic reionization. We additionally show that fine structure emission lines are sensitive to the spatial extent of neutral gas, and demonstrate that neutral gas is concentrated at smaller galactocentric radii in higher redshift galaxies.

The results of this thesis present a coherent picture of galaxy evolution at high redshifts 2 ≲ z ≲ 4. Roughly 1/3 of massive star forming galaxies at this period are undergoing major mergers, while the rest are growing inside-out with star formation occurring in gravitationally unstable thick disks. Star formation, stellar mass, and metallicity are limited by outflows which create a circumgalactic medium of metal-enriched material. We conclude by describing some remaining open questions and prospects for improving our understanding of galaxy evolution with future observations of gravitationally lensed galaxies.

A fast hybrid algorithm for exoplanetary transit searches

We present a fast and efficient hybrid algorithm for selecting exoplanetary candidates from wide-field transit surveys. Our method is based on the widely used SysRem and Box Least-Squares (BLS) algorithms. Patterns of systematic error that are common to all stars on the frame are mapped and eliminated using the SysRem algorithm. The remaining systematic errors caused by spatially localized flat-fielding and other errors are quantified using a boxcar-smoothing method. We show that the dimensions of the search-parameter space can be reduced greatly by carrying out an initial BLS search on a coarse grid of reduced dimensions, followed by Newton-Raphson refinement of the transit parameters in the vicinity of the most significant solutions. We illustrate the method's operation by applying it to data from one field of the SuperWASP survey, comprising 2300 observations of 7840 stars brighter than V = 13.0. We identify 11 likely transit candidates. We reject stars that exhibit significant ellipsoidal variations caused indicative of a stellar-mass companion. We use colours and proper motions from the Two Micron All Sky Survey and USNO-B1.0 surveys to estimate the stellar parameters and the companion radius. We find that two stars showing unambiguous transit signals pass all these tests, and so qualify for detailed high-resolution spectroscopic follow-up.