ZEN2: a narrow J-band search for z∼ 9 Lyα emitting galaxies directed towards three lensing clusters

We present the results of a continuing survey to detect Lyα emitting galaxies at redshifts   z ∼ 9  : the ' z equals nine' (ZEN) survey. We have obtained deep VLT Infrared Spectrometer and Array Camera observations in the narrow J -band filter NB119 directed towards three massive lensing clusters: Abell clusters 1689, 1835 and 114. The foreground clusters provide a magnified view of the distant Universe and permit a sensitive test for the presence of very high redshift galaxies. We search for   z ∼ 9 Lyα  emitting galaxies displaying a significant narrow-band excess relative to accompanying J -band observations that remain undetected in Hubble Space Telescope ( HST )/Advanced Camera for Surveys (ACS) optical images of each field. No sources consistent with this criterion are detected above the unlensed 90 per cent point-source flux limit of the narrow-band image,   F _NB= 3.7 × 10⁻¹⁸ erg s⁻¹ cm⁻²  . To date, the total coverage of the ZEN survey has sampled a volume at   z ∼ 9  of approximately 1700 comoving Mpc³ to a Lyα emission luminosity of  10⁴³ erg s⁻¹  . We conclude by considering the prospects for detecting   z ∼ 9 Lyα  emitting galaxies in light of both observed galaxy properties at   z < 7  and simulated populations at   z > 7  .     

The lens and source of the optical Einstein ring gravitational lens ER 0047–2808

We perform a detailed analysis of the optical gravitational lens ER 0047–2808 imaged with the Wide Field Planetary Camera 2 on the Hubble Space Telescope . Using software specifically designed for the analysis of resolved gravitational lens systems, we focus on how the image alone can constrain the mass distribution in the lens galaxy. We find that the data are of sufficient quality to strongly constrain the lens model with no a priori assumptions about the source. Using a variety of mass models, we find statistically acceptable results for elliptical isothermal-like models with an Einstein radius of 1.17 arcsec. An elliptical power-law model  (Σ∝ R ^−β)  for the surface mass density favours a slope slightly steeper than isothermal with  β= 1.08 ± 0.03  . Other models including a constant mass-to-light ratio (M/L), pure Navarro, Frenk & White halo and (surprisingly) an isothermal sphere with external shear are ruled out by the data. We find the galaxy light profile can only be fit with a Sérsic plus point-source model. The resulting total  M/L _B   contained within the images is  4.7  h ₆₅± 0.3  . In addition, we find the luminous matter is aligned with the total mass distribution within a few degrees. This is the first time a resolved optical gravitational lens image has been quantitatively reproduced using a non-parametric source.
The source, reconstructed by the software, is revealed to have two bright regions, with an unresolved component inside the caustic and a resolved component straddling a fold caustic. The angular size of the entire source is ∼0.1 arcsec and its (unlensed) Lyα flux is  3 × 10⁻¹⁷ erg s⁻¹ cm⁻²  .     

Probing the submillimetre number counts at f850 μm < 2 mJy

We have conducted a submillimetre mapping survey of faint, gravitationally lensed sources, where we have targeted 12 galaxy clusters and additionally the New Technology Telescope (NTT) Deep Field. The total area surveyed is 71.5 arcmin² in the image plane; correcting for gravitational lensing, the total area surveyed is 40 arcmin² in the source plane for a typical source redshift z ≈ 2.5. In the deepest maps, an image plane depth of 1σ rms ∼0.8 mJy is reached. This survey is the largest survey to date to reach such depths. In total 59 sources were detected, including three multiply imaged sources. The gravitational lensing makes it possible to detect sources with flux density below the blank field confusion limit. The lensing-corrected fluxes range from 0.11 to 19 mJy. After correcting for multiplicity, there are 10 sources with fluxes <2 mJy of which seven have submJy fluxes, doubling the number of such sources known. Number counts are determined below the confusion limit. At 1 mJy, the integrated number count is  ∼10⁴ deg⁻²  , and at 0.5 mJy it is  ∼2 × 10⁴ deg⁻²  . Based on the number counts, at a source plan flux limit of 0.1 mJy, essentially all of the 850-μm background emission has been resolved. The dominant contribution (>50 per cent) to the integrated background arises from sources with fluxes S ₈₅₀ between 0.4 and 2.5 mJy, while the bright sources S ₈₅₀ > 6 mJy contribute only 10 per cent.     

Multiwavelength observations of serendipitous Chandra X-ray sources in the field of A 2390

We present optical spectra and near-infrared imaging of a sample of 31 serendipitous X-ray sources detected in the field of Chandra observations of the A 2390 cluster of galaxies. The sources have  0.5–7 keV  fluxes of  (0.6–8)×10^-14 erg cm^-2 s^-1  and lie around the break in the  2–10 keV  source counts. They are therefore typical of sources dominating the X-ray Background in that band. 12 of the 15 targets for which we have optical spectra show emission lines at a range of line luminosities, and half of these show broad lines. These active galaxies and quasars have soft X-ray spectra. Including photometric redshifts and published spectra, we have redshifts for 17 of the sources, ranging from   z ∼0.2  up to   z ∼3  , with a peak between   z =1–2  . 10 of our sources have hard X-ray spectra indicating a spectral slope flatter than that of a typical unabsorbed quasar. Two hard sources that are gravitationally lensed by the foreground cluster are obscured quasars, with intrinsic  2–10 keV  luminosities of  (0.2–3)×10⁴⁵ erg s^-1  , and absorbing columns of   N _H>10²³ cm^-2  . Both of these sources were detected in the mid-infrared by ISOCAM on the Infrared Space Observatory , which when combined with radiative transfer modelling leads to the prediction that the bulk of the reprocessed flux emerges at ∼100 μm.     

The shape of the dark matter halo in the early-type galaxy NGC 2974

We present H  i observations of the elliptical galaxy NGC 2974, obtained with the Very Large Array. These observations reveal that the previously detected H  i disc in this galaxy is in fact a ring. By studying the harmonic expansion of the velocity field along the ring, we constrain the elongation of the halo and find that the underlying gravitational potential is consistent with an axisymmetric shape.
We construct mass models of NGC 2974 by combining the H  i rotation curve with the central kinematics of the ionized gas, obtained with the integral-field spectrograph SAURON. We introduce a new way of correcting the observed velocities of the ionized gas for asymmetric drift, and hereby disentangle the random motions of the gas caused by gravitational interaction from those caused by turbulence. To reproduce the observed flat rotation curve of the H  i gas, we need to include a dark halo in our mass models. A pseudo-isothermal sphere provides the best model to fit our data, but we also tested an NFW halo and modified Newtonian dynamics, which fit the data marginally worse.
The mass-to-light ratio M / L _I increases in NGC 2974 from 4.3 M_⊙/L_⊙, _I at one effective radius to 8.5 M_⊙/L_{⊙, I} at 5  R _e. This increase of M / L already suggests the presence of dark matter: we find that within 5  R _e at least 55 per cent of the total mass is dark.     

Near-infrared/optical counterparts of hotspots in radio galaxies

We present new high spatial resolution Very Large Telescope (VLT) and Very Large Array (VLA) observations of a sample of nine low-power (   P _1.4 GHz≤ 10²⁵  W Hz⁻¹) radio hotspots. Infrared/optical emission is definitely detected in four of the nine observed objects, resulting in a detection rate of at least 45 per cent. This emission is interpreted as synchrotron radiation from the electrons accelerated in the hotspots. The integrated spectra of these hotspots reveal typical break frequencies between 10⁵ and 10⁶ GHz, two orders of magnitude higher than typically found in high-power hotspots. This supports the idea that in low-power hotspots with their relatively low magnetic field strengths, electrons emit most of their energy at higher frequencies. A simple spectral ageing analysis would imply that the emitting electrons have been injected into the hotspot volume less than  ∼10³  years ago. We discuss possible scenarios to explain the lack of older electrons in the hotspot region. In particular, the extended morphology of the near-infrared/optical emission would suggest that efficient re-acceleration mechanisms rejuvenate the electron populations.     

Monopole gravitational waves from relativistic fireballs driving gamma-ray bursts

Einstein's general relativity predicts that pressure, in general stresses, plays a similar role to energy density,  ε=ρ c ²  (with ρ being the corresponding mass density), in generating gravity. The source of gravitational field, the active gravitational mass density, sometimes referred to as Whittaker's mass density, is  ρ_grav=ρ+ 3 p / c ²  , where p is pressure in the case of an ideal fluid. Whittaker's mass is not conserved, hence its changes can propagate as monopole gravitational waves. Such waves can be generated only by astrophysical sources with varying gravitational mass. Here we show that relativistic fireballs, considered in modelling gamma-ray burst phenomena, are likely to radiate monopole gravitational waves from high-pressure plasma with varying Whittaker's mass. Also, ejection of a significant amount of initial mass-energy of the progenitor contributes to the monopole gravitational radiation. We identify monopole waves with   h ¹¹+ h ²²  waves of Eddington's classification which propagate (in the z -direction) together with the energy carried by massless fields. We show that the monopole waves satisfy Einstein's equations, with a common stress-energy tensor for massless fields. The polarization mode of monopole waves is  Φ₂₂  , i.e. these are perpendicular waves which induce changes of the radius of a circle of test particles only (breathing mode). The astrophysical importance of monopole gravitational waves is discussed.     

Near-infrared properties of i-drop galaxies in the Hubble Ultra Deep Field

We analyse near-infrared Hubble Space Telescope ( HST )/Near-Infrared Camera and Multi-Object Spectrometer F 110 W ( J ) and F 160 W ( H ) band photometry of a sample of 27 i '-drop candidate   z ≃ 6  galaxies in the central region of the HST /Advanced Camera for Surveys Ultra Deep Field . The infrared colours of the 20 objects not affected by near neighbours are consistent with a high-redshift interpretation. This suggests that the low-redshift contamination of this i '-drop sample is smaller than that observed at brighter magnitudes, where values of 10–40 per cent have been reported. The J – H colours are consistent with a slope flat in   f_ν ( f_λ ∝λ⁻²)  , as would be expected for an unreddened starburst. However, there is evidence for a marginally bluer spectral slope  ( f_λ ∝λ^−2.2)  , which is perhaps indicative of an extremely young starburst (∼10 Myr old) or a top heavy initial mass function and little dust. The low levels of contamination, median photometric redshift of   z ∼ 6.0  and blue spectral slope, inferred using the near-infrared data, support the validity of the assumptions in our earlier work in estimating the star formation rates, and that the majority of the i -drop candidates galaxies lie at   z ∼ 6  .     

Depletion of background galaxies owing to the cluster lens CL0024+1654: U- and R-band observations

We have obtained U - and R -band observations of the depletion of background galaxies resulting from the gravitational lensing of the galaxy cluster CL0024+1654 ( z =0.39). The radial depletion curves show a significant depletion in both bands within a radius of 40–70 arcsec from the cluster centre. This is the first time that depletion is detected in the U band. This gives independent evidence for a break in the slope of the U -band luminosity function at faint magnitudes. The radially averaged R -band depletion curve is broader and deeper than in the U band. The differences can be attributed to the wavelength dependence of the slope of the luminosity function and to the different redshift distribution of the objects probed in the two bands. We estimate the Einstein radius, r _E, of a singular isothermal sphere lens model using maximum-likelihood analysis. Adopting a slope of the number counts of α =0.2 and using the background density found beyond r =150 arcsec, we find r _E=17±3 and 25±3 arcsec in the U and R bands, respectively. When combined with the redshift of the single background galaxy at z =1.675 seen as four giant arcs around 30 arcsec from the cluster centre, these values indicate a median redshift in the range 〈 z _S〉≈0.7 to 1.1 for the U _AB≥24 mag and R _AB≥24 mag populations.     

An ultradeep submillimetre map: beneath the SCUBA confusion limit with lensing and robust source extraction

Extracting sources with low signal-to-noise ratio (S/N) from maps with structured background is a non-trivial task which has become important in studying the faint end of the submillimetre (submm) number counts. In this paper, we study the source extraction from submm jiggle-maps from the Submillimetre Common-User Bolometer Array (SCUBA) using the Mexican hat wavelet (MHW), an isotropic wavelet technique. As a case study, we use a large (11.8-arcmin²) jiggle-map of the galaxy cluster Abell 2218 (A2218), with a 850-μm 1σ rms sensitivity of 0.6–1 mJy. We show via simulations that MHW is a powerful tool for the reliable extraction of low-S/N sources from the SCUBA jiggle-maps and nine sources are detected in the A2218 850-μm image. Three of these sources are identified as images of a single background source with an unlensed flux of 0.8 mJy. Further, two single-imaged sources also have unlensed fluxes <2 mJy, below the blank-field confusion limit. In this ultradeep map, the individual sources detected resolve nearly all of the extragalactic background light at 850 μm, and the deep data allow to put an upper limit of 44 sources arcmin⁻² to 0.2 mJy at 850 μm.     

Gravitational lensing of extended high-redshift sources by dark matter haloes

High-redshift galaxies and quasi-stellar objects (QSOs) are most likely to be strongly lensed by intervening haloes between the source and the observer. In addition, a large fraction of lensed sources is expected to be seen in the submillimetre region, as a result of the enhanced magnification bias on the steep intrinsic number counts. We extend in three directions Blain's earlier study of this effect.
First, we use a modification of the Press–Schechter mass function and detailed lens models to compute the magnification probability distribution. We compare the magnification cross-sections of populations of singular isothermal spheres and Navarro, Frenk & White (NFW) haloes and find that they are very similar, in contrast to the image-splitting statistics which were recently investigated in other studies. The distinction between the two types of density profile is therefore irrelevant for our purposes.
Secondly, we discuss quantitatively the maximum magnification, μ _max, that can be achieved for extended sources (galaxies) with realistic luminosity profiles, taking into account the possible ellipticity of the lensing potential. We find that μ _max plausibly falls into the range     for sources of     effective radius at redshifts within     .
Thirdly, we apply our model for the lensing magnification to a class of sources following the luminosity evolution typical for a unified scheme of QSO formation. As a result of the peculiar steepness of their intrinsic number counts, we find that the lensed source counts at a fiducial wave length of 850 μm can exceed the unlensed counts by several orders of magnitude at flux densities ≳100 mJy, even with a conservative choice of the maximum magnification.     

The SCUBA 8-mJy survey – II. Multiwavelength analysis of bright submillimetre sources

We present the results of a multiwavelength study of the 19 most significant submillimetre (submm) sources detected in the SCUBA 8-mJy survey. As described in Scott et al. , this survey covers ≃260 arcmin² using the submillimetre camera SCUBA, to a limiting source detection limit   S _850 μm≃8 mJy  . One advantage of this relatively bright flux-density limit is that accurate astrometric positions are potentially achievable for every source using existing radio and/or millimetre-wave interferometers. However, an associated advantage is that spectral energy distribution (SED) based redshift constraints should be more powerful than in fainter submm surveys. Here we therefore exploit the parallel SCUBA 450-μm data, in combination with existing radio and Infrared Space Observatory ( ISO ) data at longer and shorter wavelengths to set constraints on the redshift of each source. We also analyse new and existing optical and near-infrared imaging of our SCUBA survey fields to select potential identifications consistent with these constraints. Our derived SED-based redshift constraints, and the lack of statistically significant associations with even moderately bright galaxies allow us to conclude that all 19 sources lie at   z >1  , and at least half of them apparently lie at   z >2  .     

Luminosity and surface brightness distribution of K-band galaxies from the UKIDSS Large Area Survey

We present luminosity and surface-brightness distributions of 40 111 galaxies with K -band photometry from the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS), Data Release 3 and optical photometry from Data Release 5 of the Sloan Digital Sky Survey (SDSS). Various features and limitations of the new UKIDSS data are examined, such as a problem affecting Petrosian magnitudes of extended sources. Selection limits in K - and r -band magnitude, K -band surface brightness and K -band radius are included explicitly in the  1/ V _max  estimate of the space density and luminosity function. The bivariate brightness distribution in K -band absolute magnitude and surface brightness is presented and found to display a clear luminosity–surface brightness correlation that flattens at high luminosity and broadens at low luminosity, consistent with similar analyses at optical wavelengths. Best-fitting Schechter function parameters for the K -band luminosity function are found to be   M *− 5 log  h =−23.19 ± 0.04, α=−0.81 ± 0.04  and  φ*= (0.0166 ± 0.0008)  h ³ Mpc⁻³  , although the Schechter function provides a poor fit to the data at high and low luminosity, while the luminosity density in the K band is found to be   j = (6.305 ± 0.067) × 10⁸ L_⊙  h  Mpc⁻³  . However, we caution that there are various known sources of incompleteness and uncertainty in our results. Using mass-to-light ratios determined from the optical colours, we estimate the stellar mass function, finding good agreement with previous results. Possible improvements are discussed that could be implemented when extending this analysis to the full LAS.     

Deep inside the core of Abell 1795: the Chandra view

We present X-ray spatial and spectral analysis of the Chandra data from the central     of the cluster of galaxies Abell 1795. The plasma temperature rises outwards by a factor of 3, whereas the iron abundance decreases by a factor of 4. The spatial distribution of oxygen, neon, sulphur, silicon and iron shows that supernovae Type Ia dominate the metal enrichment process of the cluster plasma within the inner 150 kpc. Resolving both the gas density and temperature in nine radial bins, we recover the gravitational mass density profile and show that it flattens within 100 kpc as   ρ _DM∝ r ^-0.6  with a power-law index flatter than −1 at >3 σ level. The observed motion of the central galaxy and the presence of excesses and deficits along the north–south direction in the brightness distribution indicate that the central cluster region is not relaxed. In the absence of any non-gravitational heating source, the data from the inner ∼200 kpc indicate the presence of a cooling flow with an integrated mass deposition rate of about 100 M_⊙ yr⁻¹. Over the same cluster region, the observed rate of 74 M_⊙ yr⁻¹ is consistent with the recent XMM-Newton Reflection Grating Spectrometer limit of 150 M_⊙ yr⁻¹.     

Radial scalelengths of the galactic thin and thick disc with 2MASS data

This paper presents a global analysis of the 2MASS (Two Micron All Sky Survey) data as observed in seven fields at different galactic latitudes in our Galaxy. The data allow the preliminary determination of the scale parameters, which lead to strong constraints on the radial and vertical structure of the galactic thin and thick disc. The interpretation of star counts and colour distributions of stars in the near-infrared with the synthetic stellar population model gives strong evidence that the galactic thin disc density scalelength ( h _R ) is rather short (2.8±0.3 kpc). The galactic thick disc population is revisited in the light of new data. We find the thick disc to have a local density of 3.5±2.0 per cent of the thin disc, exponential scaleheight ( h _z ) of 860±200 pc and exponential scalelength ( h _R ) of 3.7±_0.5^0.8 kpc.     

The evolution of star formation in quasar host galaxies

We have used far-infrared data from IRAS , Infrared Space Observatory ( ISO ), Spitzer Wide-Area Infrared Extragalactic (SWIRE), Submillimetre Common User Bolometer Array (SCUBA) and Max-Planck Millimetre Bolometer (MAMBO) to constrain statistically the mean far-infrared luminosities of quasars. Our quasar compilation at redshifts  0 < z < 6.5  and I -band luminosities  −20 < I _AB < −32  is the first to distinguish evolution from quasar luminosity dependence in such a study. We carefully cross-calibrate IRAS against Spitzer and ISO , finding evidence that IRAS 100-μm fluxes at <1 Jy are overestimated by ∼30 per cent. We find evidence for a correlation between star formation in quasar hosts and the quasar optical luminosities, varying as star formation rate (SFR)  ∝ L ^0.44±0.07_opt  at any fixed redshift below   z = 2  . We also find evidence for evolution of the mean SFR in quasar host galaxies, scaling as  (1 + z )^1.6±0.3  at   z < 2  for any fixed quasar I -band absolute magnitude fainter than −28. We find no evidence for any correlation between SFR and black hole mass at  0.5 < z < 4  . Our data are consistent with feedback from black hole accretion regulating stellar mass assembly at all redshifts.     

Submillimetre imaging of NGC 3079

Submillimetre mapping observations of the active edge-on spiral galaxy NGC 3079 are presented. These maps at 850 and 450 μm were made with the Submillimetre Common User Bolometer Array (SCUBA) at the James Clerk Maxwell Telescope (JCMT).
The source structure at these wavelengths consists of a central unresolved source embedded in diffuse disc emission, similar to that displayed at 1.2 mm. The disc emission is fitted with two optically thin, isothermal dust models which give temperatures of 12 and 31 K, similar to those derived previously by Braine et al. The core component is well described by a single-temperature fit (∼32 K). The combined dust mass from these observations, using the same mass absorption coefficient as Devereux & Young (1990) is 3.5×10⁸ M_⊙, of which ∼90 per cent resides in the cold component of the galactic disc. The effect of the cold dust component detected by SCUBA is thus to reduce the global gas-to-dust mass ratio from ∼1400 found in the above study to 85, very similar to the Galactic level. Calculations using the models of Draine & Lee and/or alternative molecular gas mass estimates yield gas-to-dust mass ratios in the range 60–190.
The data presented here, together with previously published 1.2-mm mapping observations and IRAS data, are inconsistent with detections made with the Infrared Space Observatory ( ISO ). In particular, the latter give an excess of flux at 200 and 180 μm relative to that predicted by our simple model fits (approximately a factor of 2–3).     

The effects of resolved sources and blending on the detection of planets via gravitational microlensing

It has been shown that gravitational microlensing events towards the Galactic Bulge are sensitive to the presence of a planet orbiting the lensing star. The probability of planet detection is calculated here as a function of the binary geometry for mass ratios of     taking the effects of resolving the source and the inclusion of unlensed light (blending) into account. Source radii up to     θ _E are considered, at which point the detection probability becomes negligible. Small     mass ratio planets become undetectable at source radii of     θ _E . Blending has a slight adverse effect on planet detection. It is worst when the unblended detection probability is small and causes planets to become undetectable at smaller source radii than would be the case in the absence of blending. An alternative to current gravitational microlensing follow-up observations is investigated, where only the peaks of high amplification events are followed. Such a strategy promises to be at least twice as efficient at detecting planets as current observations, but requires a large number of high amplification events.     

Vertical distribution of Galactic disc stars and gas constrained by a molecular cloud complex

We investigate the dynamical effects of a molecular cloud complex with a mass ∼ 10⁷ M_⊙ and a size ∼ a few 100 pc on the vertical distribution of stars and atomic hydrogen gas in a spiral galactic disc. Such massive complexes have now been observed in a number of spiral galaxies. The extended mass distribution in a complex, with an average mass density 6 times higher than the Oort limit, is shown to dominate the local gravitational field. This results in a significant redistribution or clustering of the surrounding disc components towards the mid-plane, with a resulting decrease in their vertical scaleheights.
The modified, self-consistent stellar density distribution is obtained by solving the combined Poisson equation and the force equation along the z -direction for an isothermal stellar disc on which the complex is imposed. The effect of the complex is strongest at its centre, where the stellar mid-plane density increases by a factor of 2.6 and the vertical scaleheight decreases by a factor of 3.4 compared with the undisturbed stellar disc. A surprising result is the large radial distance of ∼ 500 pc from the complex centre over which the complex influences the disc; this is due to the extended mass distribution in a complex. The complex has a comparable effect on the vertical distribution of the atomic hydrogen gas in the galactic disc. This 'pinching' or constraining effect should be detectable in the nearby spiral galaxies, as for example has been done for NGC 2403 by Sicking. Thus the gravitational field of a complex results in local corrugations of the stellar and H  i vertical scaleheights, and the galactic disc potential is highly non-uniform on scales of the intercomplex separation of ∼ 1 kpc.     

Evolution of the mass function of dark matter haloes

We use a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15, in a  50 h ⁻¹ Mpc  volume containing 80 million particles. Our low-redshift results allow us to probe low-σ density fluctuations significantly beyond the range of previous cosmological simulations. The Sheth & Tormen mass function provides an excellent match to all of our data except for redshifts of 10 and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 per cent for the  10¹⁰–10¹¹ M_⊙  haloes sampled at redshift 15. Our results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. We provide an empirical fit to our data that corrects for the overprediction of extremely rare objects by the Sheth & Tormen mass function. This overprediction has implications for studies that use the number densities of similarly rare objects as cosmological probes. For example, the number density of high-redshift  ( z ≃ 6) QSOs  , which are thought to be hosted by haloes at 5σ peaks in the fluctuation field, are likely to be overpredicted by at least a factor of 50 per cent. We test the sensitivity of our results to force accuracy, starting redshift and halo-finding algorithm.