arXiv subjects

R. M. Rich

Publications and source records attributed to R. M. Rich.

At least 37 records · Page 2Linked to original sources

arXiv2024

Multi-iron subpopulations in Liller 1 from high resolution H-band spectroscopy

We present a high resolution chemical study of a representative sample of 21 luminous giant stars of Liller~1, a complex stellar system in the Galactic bulge, based on H band spectra acquired with the Near InfraRed Spectrograph at KeckII. 15 stars turn out to have a subsolar iron abundance and enhanced [$α$/Fe] and [Al/Fe], likely old that formed early and quickly from gas mainly enriched by type~II supernovae, and 6 stars with supersolar iron and roughly solar-scaled [$α$/Fe] and [Al/Fe], likely younger, thus formed at later epochs from gas also enriched by type~Ia supernovae. Moreover, both subpopulations show enhanced [N/Fe], as in the bulge field, about solar-scaled [V/Fe], and depletion of [C/Fe] and $^{12}$C/$^{13}$C with respect to the solar values, indicating the occurrence of significant mixing in the stellar interiors of these evolved stars. The current study has also made evident that the sub-solar subpopulation shows some structuring, and the presence of a third subcomponent with iron content and [$α$/Fe] enhancement somewhat intermediate between the metal-poor and metal-rich main subpopulations, has been statistically assessed, providing the chemical signature of an extended star formation with multiple bursts and of some self-enrichment.

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arXiv2024

Detailed chemical abundances of the globular cluster Terzan 6 in the inner bulge

We used near-infrared spectroscopy at medium-high resolution (R=8,000$-$25,000) to perform the first comprehensive chemical study of the intermediate luminosity bulge globular cluster Terzan~6. We derived detailed abundances and abundance patterns of 27 giant stars, likely members of Terzan~6, based on their accurate Hubble Space Telescope proper motions and line-of-sight radial velocities. From the spectral analysis of these stars, we determined an average heliocentric radial velocity of 143.3$\pm$1.0 km s$^{-1}$ with a velocity dispersion of 5.1$\pm$0.7 km s$^{-1}$ and an average [Fe/H]=$-0.65\pm0.01$ and a low 1$σ$ dispersion of 0.03 dex. We also measured some depletion of [Mn/Fe] with respect to the solar-scaled values and enhancement of for [Ca/Fe], [Si/Fe], [Mg/Fe], [Ti/Fe], [O/Fe], [Al/Fe], [Na/Fe], and, to a lower extent, for [K/Fe], consistent with previous measurements of other bulge globular clusters and favoring the scenario of a rapid bulge formation and chemical enrichment. Some spread in the light element abundances suggest the presence of first- and second-generation stars, typical of genuine globulars. Finally, we measured some depletion of carbon and low $\rm ^{12}C/^{13}C$ isotopic ratios, as in previous studies of field and cluster bulge giants, indicating that extra-mixing mechanisms should be at work during the post main sequence evolution in the high metallicity regime as well.

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arXiv2024

Chemical evolution of the Galactic bulge with different stellar populations

The metallicity distribution function (MDF) of the Galactic bulge features a multi-peak shape, with a metal-poor peak at [Fe/H]=-0.3 dex and a metal-rich peak at [Fe/H]=+0.3 dex. This bimodality is also seen in [alpha/Fe] versus [Fe/H] ratios, indicating different stellar populations in the bulge. We aim to replicate the observed MDF by proposing a scenario where the metal-poor bulge stars formed in situ during an intense star formation burst, while the metal-rich stars formed during a second burst and/or were accreted from the inner Galactic disk due to a growing bar. We used a chemical evolution model that tracks various chemical species with detailed nucleosynthesis, focusing on Fe production from both Type Ia supernovae and massive stars, including rotating massive stars with varying velocities. Our model also accounts for gas infall, outflow, and the effect of stellar migration. Results are compared to 13,000 stars from the SDSS/APOGEE survey within 3.5 kpc of the Galactic center. Our model successfully reproduces the double-peak shape of the bulge MDF and the alpha-element abundance trends relative to Fe by assuming (i) a multi-burst star formation history with a 250 Myr quenching of the first burst and (ii) stellar migration from the inner disk due to a growing bar. We estimate that about 40% of the bulge-bar's stellar mass originates from the inner disk. Nucleosynthesis models that assume either no rotation for massive stars or a rotational velocity distribution favoring slow rotation at high metallicities best match the observed MDF and [alpha/Fe] and [Ce/Fe] versus [Fe/H] abundance patterns.

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arXiv2024

X-shooter spectroscopy of Liller1 giant stars

We present the first comprehensive chemical study of a representative sample of 27 luminous red giant branch (RGB) stars belonging to Liller 1, a complex stellar system in the Galactic bulge. This study is based on medium-resolution near-infrared spectra acquired with X-shooter at the Very Large Telescope. We found a subpopulation counting 22 stars with subsolar metallicity ($<$[Fe/H]$>=-0.31\pm0.02$ and 1$σ$ dispersion of 0.08 dex) and with enhanced [$α$/Fe], [Al/Fe], and [K/Fe] that likely formed early and quickly from gas that was mainly enriched by type II supernovae, and a metal-rich population counting 5 stars with supersolar metallicity ($<$[Fe/H]$>$=+0.22$\pm$0.03 and 1$σ$ dispersion of 0.06 dex) and roughly solar-scaled [$α$/Fe], [Al/Fe], and [K/Fe] that formed at later epochs from gas that was also enriched by type Ia supernovae. Moreover, both subpopulations show enhanced [Na/Fe], as in the bulge field, about solar-scaled [V/Fe], and depletion of [C/Fe] and $^{12}$C/$^{13}$C with respect to the solar values. This indicates that mixing and extra-mixing processes during the RGB evolution also occur at very high metallicities. Notably, no evidence of a Na-O anticorrelation, which is considered the fingerprint of genuine globular clusters, has been found. This challenges any formation scenarios that invoke the accretion of a molecular cloud or an additional stellar system onto a genuine globular cluster. The results of this study underline the strong chemical similarity between Liller 1 and Terzan 5 and support the hypothesis that these complex stellar systems might be fossil fragments of the epoch of Galactic bulge formation.

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arXiv2023

Smooth kinematic and metallicity gradients reveal that the Milky Way's nuclear star cluster and disc might be part of the same structure

The innermost regions of most galaxies are characterised by the presence of extremely dense nuclear star clusters. Nevertheless, these clusters are not the only stellar component present in galactic nuclei, where larger stellar structures known as nuclear stellar discs, have also been found. Understanding the relation between nuclear star clusters and nuclear stellar discs is challenging due to the large distance towards other galaxies which limits their analysis to integrated light. The Milky Way's centre, at only 8 kpc, hosts a nuclear star cluster and a nuclear stellar disc, constituting a unique template to understand their relation and formation scenario. We aim to study the kinematics and stellar metallicity of stars from the Milky Way's nuclear star cluster and disc to shed light on the relation between these two Galactic centre components. We used publicly available photometric, proper motions, and spectroscopic catalogues to analyse a region of $\sim2.8'\times4.9'$ centred on the Milky Way's nuclear star cluster. We built colour magnitude diagrams, and applied colour cuts to analyse the kinematic and metallicity distributions of Milky Way's nuclear star cluster and disc stars with different extinction along the line of sight. We detect kinematics and metallicity gradients for the analysed stars along the line of sight towards the Milky Way's nuclear star cluster, suggesting a smooth transition between the nuclear stellar disc and cluster. We also find a bi-modal metallicity distribution for all the analysed colour bins, which is compatible with previous work on the bulk population of the nuclear stellar disc and cluster. Our results suggest that these two Galactic centre components might be part of the same structure with the Milky Way's nuclear stellar disc being the grown edge of the nuclear star cluster.

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arXiv2023

The Hubble Space Telescope Survey of M31 Satellite Galaxies II. The Star Formation Histories of Ultra-Faint Dwarf Galaxies

We present the lifetime star formation histories (SFHs) for six ultra-faint dwarf (UFD; $M_V>-7.0$, $ 4.9<\log_{10}({M_*(z=0)}/{M_{\odot}})<5.5$) satellite galaxies of M31 based on deep color-magnitude diagrams constructed from \textit{Hubble Space Telescope} imaging. These are the first SFHs obtained from the oldest main sequence turn-off of UFDs outside the halo of the Milky Way (MW). We find that five UFDs formed at least 50\% of their stellar mass by $z=5$ (12.6~Gyr ago), similar to known UFDs around the MW, but that 10-40\% of their stellar mass formed at later times. We uncover one remarkable UFD, \A{XIII}, which formed only 10\% of its stellar mass by $z=5$, and 75\% in a rapid burst at $z\sim2-3$, a result that is robust to choices of underlying stellar model and is consistent with its predominantly red horizontal branch. This "young" UFD is the first of its kind and indicates that not all UFDs are necessarily quenched by reionization, which is consistent with predictions from several cosmological simulations of faint dwarf galaxies. SFHs of the combined MW and M31 samples suggest reionization did not homogeneously quench UFDs. We find that the least massive MW UFDs ($M_*(z=5) \lesssim 5\times10^4 M_{\odot}$) are likely quenched by reionization, whereas more massive M31 UFDs ($M_*(z=5) \gtrsim 10^5 M_{\odot}$) may only have their star formation suppressed by reionization and quench at a later time. We discuss these findings in the context of the evolution and quenching of UFDs.

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arXiv2023

The AMIGA sample of isolated galaxies. XIV. Disc breaks and interactions through ultra-deep optical imaging

In the standard cosmological model of galaxy evolution, mergers and interactions play a fundamental role in shaping galaxies. Galaxies that are currently isolated are thus interesting, allowing us to distinguish between internal and external processes affecting the galactic structure. However, current observational limits may obscure crucial information in the low-mass or low-brightness regime. We use optical imaging of a subsample of the AMIGA catalogue of isolated galaxies to explore the impact of different factors on the structure of these galaxies. We study the type of disc break as a function of the degree of isolation and the presence of interaction indicators like tidal streams or plumes only detectable in the low surface brightness regime. We present deep optical imaging of a sample of 25 isolated galaxies. Through careful data processing and analysis techniques, the surface brightness limits achieved are comparable to those to be obtained on the 10-year LSST coadds. The extreme depth of our imaging allows us to study the interaction signatures of 20 galaxies, given that the presence of Galactic cirrus is a strong limiting factor in the characterisation of interactions for the remaining 5 of them. We detect previously unreported interaction features in 8 (40%) galaxies in our sample. We identify 9 galaxies (36%) showing an exponential disc (Type I), 14 galaxies (56%) with down-bending (Type II) profile and only 2 galaxies (8%) with up-bending (Type III) profiles. Isolated galaxies have considerably more purely exponential discs and fewer up-bending surface brightness profiles than field or cluster galaxies. We suggest that major mergers produce up-bending profiles while a threshold in star formation probably forms down-bending profiles. Unperturbed galaxies, evolving slowly with a low star formation rate could cause the high rate of Type I discs in isolated galaxies observed.

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arXiv2023

The formation history of our Galaxy's nuclear stellar disc constrained from HST observations of the Quintuplet field

Until recently it was thought that the nuclear stellar disc at the centre of our Galaxy was formed via quasi-continuous star formation over billions of years. However, an analysis of GALACTICNUCLEUS survey data indicates that >80% of the mass of the stellar disc formed at least 8 Gyr ago and about 5% roughly 1 Gyr ago. Our aim is to derive new constraints on the formation history of the nuclear stellar disc. We analysed a catalogue of HST/WFC3-IR observations of the Quintuplet cluster field. From this catalogue, we selected about 24000 field stars that probably belong to the nuclear stellar disc. We used red clump giants to deredden the sample and fit the resulting F153M luminosity function with a linear combination of theoretical luminosity functions created from different stellar evolutionary models. We find that >70% of the stellar population in the nuclear disc probably formed more than 10 Gyr ago, while ~15% formed in an event (or series of events) ~1Gyr ago. Up to 10% of the stars appear to have formed in the past tens to hundreds of Myr. These results do not change significantly for reasonable variations in the assumed mean metallicity, sample selection, reddening correction, or stellar evolutionary models. We confirm previous work that changed the formation paradigm for stars in the Galactic Centre. The nuclear stellar disc is indeed a very old structure. There seems to have been little star formation activity between its formation and about 1 Gyr ago.

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arXiv2023

Evidence of an age gradient along the line of sight in the nuclear stellar disc of the Milky Way

The nuclear stellar disc (NSD) is a flat dense stellar structure at the heart of the Milky Way. Recent work has shown that analogous structures are common in the nuclei of external spiral galaxies, where there is evidence of an age gradient that indicates that they form inside-out. However, the characterisation of the age of the NSD stellar population along the line of sight is still missing due to its extreme source crowding and the high interstellar extinction towards the Galactic centre. We aim to characterise the age of the stellar population at different average Galactocentric NSD radii to investigate for the first time the presence of an age gradient along the line of sight. We selected two groups of stars at different NSD radii via their different extinction and proper motion distribution. We analysed their stellar population by fitting their de-reddened $K_s$ luminosity functions with a linear combination of theoretical models. We find significant differences in the stellar population at different NSD radii, indicating the presence of an age gradient along the line of sight. Our sample from the closest edge of the NSD contains a significant fraction ($\sim40 \%$ of its total stellar mass) of intermediate-age stars (2-7 Gyr) that is not present in the sample from stars deeper inside the NSD, in which $\sim90 \%$ of the stellar mass is older than 7 Gyr. Our results suggest that the NSD age distribution is similar to the one found in external galaxies and they imply that bar-driven processes observed in external galaxies are similarly at play in the Milky Way.

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arXiv2023

Detailed $α$ abundance trends in the inner Galactic bulge

In this paper, we aim to derive high-precision alpha-element abundances using CRIRES high-resolution IR spectra of 72 cool M giants of the inner Galactic bulge. Silicon, magnesium, and calcium abundances were determined by fitting a synthetic spectrum for each star. We also incorporated recent theoretical data into our spectroscopic analysis (i.e. updated K-band line list, better broadening parameter estimation, non-local thermodynamic equilibrium (NLTE) corrections). We compare these inner bulge alpha abundance trends with those of solar neighbourhood stars observed with IGRINS using the same line list and analysis technique; we also compare our sample to APOGEE DR17 abundances for inner bulge stars. We investigate bulge membership using spectro-photometric distances and orbital simulations. We construct a chemical-evolution model that fits our metallicity distribution function (MDF) and our alpha-element trends. Among our 72 stars, we find four that are not bulge members. [Si/Fe] and [Mg/Fe] versus [Fe/H] trends show a typical thick disc alpha-element behaviour, except that we do not see any plateau at supersolar metallicities as seen in other works. The NLTE analysis lowers [Mg/Fe] typically by $\sim$0.1 dex, resulting in a noticeably lower trend of [Mg/Fe] versus [Fe/H]. The derived [Ca/Fe] versus [Fe/H] trend has a larger scatter than those for Si and Mg, but is in excellent agreement with local thin and thick disc trends. With our updated analysis, we constructed one of the most detailed studies of the alpha abundance trends of cool M giants in the inner Galactic bulge. We modelled these abundances by adopting a two-infall chemical-evolution model with two distinct gas-infall episodes with timescales of 0.4 Gyr and 2 Gyr, respectively. Based on a very meticulous spectral analysis, we have constructed detailed and precise chemical abundances of Mg, Si, and Ca for cool M giants.

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arXiv2022

The HST large programme on NGC 6752 -- IV. The White Dwarf Sequence

We present our final study of the white dwarf cooling sequence (WD CS) in the globular cluster NGC 6752. The investigation is the main goal of a dedicated Hubble Space Telescope large Program, for which all the observations are now collected. The WD CS luminosity function (LF) is confirmed to peak at m_F606W = 29.3+/-0.1, consistent within uncertainties with what has been previously reported, and is now complete down to m_F606W~29.7. We have performed robust and conclusive comparisons with model predictions that show how the theoretical LF for hydrogen envelope WD models closely follow the shape of the empirical LF. The magnitude of the peak of the observed LF is matched with ages between 12.7 and 13.5 Gyr, consistent with the cluster age derived from the main sequence turn off and subgiant branch. We also find that the impact of multiple populations within the cluster on the WD LF for m_F606W below 27.3 is negligible, and that the presence of a small fraction of helium envelope objects is consistent with the data. Our analysis reveals a possible hint of an underestimate of the cooling timescales of models in the magnitude range 28.1 < m_F606W < 28.9. Finally, we find that hydrogen envelope models calculated with a new tabulation of electron conduction opacities in the transition between moderate and strong degeneracy provide WD ages that are too small in comparison to the Main Sequence turnoff age.

astro-ph.SR↗

arXiv2022

The first r-process enhanced star confirmed to be a member of the Galactic bulge

Aims. Stars with strong enhancements of r-process elements are rare and tend to be metal-poor, with generally [Fe/H] <-2 dex and found in the halo. In this work we aim to investigate a candidate r-process enriched bulge star with a relatively high metallicity of -0.65 dex, and compare it with a previously published r-rich candidate star in the bulge. Methods. We reconsider the abundance analysis of a high-resolution optical spectrum of the red-giant star 2MASS J18082459-2548444 and determine its europium (Eu) and molybdenum (Mo) abundance, using stellar parameters from five different previous studies. Applying 2MASS photometry, Gaia astrometry and kinematics, we estimate distance, orbits, and population membership of 2MASS J18082459-2548444 and a previously reported r-enriched star 2MASS J18174532-3353235. Results. We find that 2MASS J18082459-2548444 is a relatively metal rich enriched r-process star that is enhanced in Eu and Mo but not substantially enhanced in s-process elements. It has a high probability of membership in the Galactic bulge based on its distance and orbit. We find that both stars show r-process enhancement with elevated [Eu/Fe]-values, even though 2MASS J18174532-3353235 is 1 dex lower in metallicity. Additionally, we find that 2MASS J18174532-3353235 plausibly has a halo or thick disc origin. Conclusions. We conclude that 2MASS J18082459-2548444 represents the first example of a confirmed r-process enhanced star confined to the inner bulge, possibly a relic from a period of enrichment associated with the formation of the bar.

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arXiv2022

Clues to the formation of Liller 1 from modeling its complex star formation history

Liller 1 and Terzan 5 are two massive systems in the Milky-Way bulge hosting populations characterized by significantly different ages ($Δt>7-8$ Gyr) and metallicities ($Δ$[Fe/H]$\sim1$ dex). Their origin is still strongly debated in the literature and all formation scenarios proposed so far require some level of fine-tuning. The detailed star formation histories (SFHs) of these systems may represent an important piece of information to assess their origin. Here we present the first attempt to perform such an analysis for Liller 1. The first key result we find is that Liller 1 has been forming stars over its entire lifetime. More specifically, three broad SF episodes are clearly detected: 1) a dominant one, occurred some 12-13 Gyr ago with a tail extending for up to $\sim3$ Gyr, 2) an intermediate burst, between 6 and 9 Gyr ago, 3) and a recent one, occurred between 1 and 3 Gyr ago. The old population contributes to about $70\%$ of the total stellar mass and the remaining fraction is almost equally split between the intermediate and young populations. If we take these results at a face value, they would suggest that this system unlikely formed through the merger between an old globular cluster and a Giant Molecular Cloud, as recently proposed. On the contrary, our findings provide further support to the idea that Liller 1 is the surviving relic of a massive primordial structure that contributed to the Galactic bulge formation, similarly to the giant clumps observed in star-forming high-redshift galaxies.

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arXiv2022

Ground Vibrational State SiO Emission in the VLA BAaDE Survey

Using a subsample of the Bulge Asymmetries and Dynamical Evolution (BAaDE) survey of stellar SiO masers, we explore the prevalence and characteristics of $^{28}$SiO $J=1-0, v=0$ emission. We identify 90 detections of maser, thermal, or composite $^{28}$SiO $J=1-0, v=0$ emission out of approximately 13,000 candidate spectra from the NSF's Karl G. Jansky Very Large Array (VLA). We find that the detected sources are likely asymptotic giant branch (AGB) stars belonging to a bright, foreground Milky Way stellar disk population. For the 32 sources showing thermal components, we extract values for outflow velocity by fitting thermal line profiles. We find a range of circumstellar envelope expansion velocities, and compare to previously recorded OH and CO expansion velocities. This preliminary survey is already the largest study of stellar ground-vibrational-state SiO masers to date, and will be expanded to include the entire VLA BAaDE dataset when data reduction for the 18,988 target sources is completed.

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arXiv2022

Science Cases for the Keck Wide-Field Imager

The Keck Wide-Field Imager (KWFI) is a proposed 1-degree diameter field of view UV-sensitive optical camera for Keck prime focus. KWFI will be the most powerful optical wide-field camera in the world and the only such 8m-class camera sensitive down to ~3000 A for the foreseeable future. Twenty science cases are described for KWFI compiled largely during 2019-2021, preceded by a brief discussion of the instrument, components, and capabilities for context.

astro-ph.IM↗

arXiv2022

The bending of the star-forming main sequence traces the cold- to hot-accretion transition mass over 0<z<4

We analyse measurements of the evolving stellar mass (M0) at which the bending of the star-forming main sequence (MS) occurs over 0 1.4 (for which we propose a revision in agreement with latest simulations). We hence argue that the MS bending is primarily due to the lessening of cold-accretion causing a reduction in available cold gas in galaxies and supports predictions of gas feeding theory. In particular, the rapidly rising M0 with redshift at z>1 is confirming evidence for the cold-streams scenario. In this picture, a progressive fueling reduction rather than its sudden suppression in halos more massive than Mshock/Mstream produces a nearly constant star-formation rate in galaxies with stellar masses larger than M0, and not their quenching, for which other physical processes are thus required. Compared to the knee M* in the stellar mass function of galaxies, M0 is significantly lower at z<1.5, and higher at z>2, suggesting that the imprint of gas deprivation on the distribution of galaxy masses happened at early times (z>1.5-2). The typical mass at which galaxies inside the MS become bulge-dominated evolves differently from M0, consistent with the idea that bulge-formation is a distinct process from the phasing-out of cold-accretion.

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arXiv2022

Preparing for low surface brightness science with the Vera C. Rubin Observatory: characterisation of tidal features from mock images

Tidal features in the outskirts of galaxies yield unique information about their past interactions and are a key prediction of the hierarchical structure formation paradigm. The Vera C. Rubin Observatory is poised to deliver deep observations for potentially of millions of objects with visible tidal features, but the inference of galaxy interaction histories from such features is not straightforward. Utilising automated techniques and human visual classification in conjunction with realistic mock images produced using the NEWHORIZON cosmological simulation, we investigate the nature, frequency and visibility of tidal features and debris across a range of environments and stellar masses. In our simulated sample, around 80 per cent of the flux in the tidal features around Milky Way or greater mass galaxies is detected at the 10-year depth of the Legacy Survey of Space and Time (30-31 mag / sq. arcsec), falling to 60 per cent assuming a shallower final depth of 29.5 mag / sq. arcsec. The fraction of total flux found in tidal features increases towards higher masses, rising to 10 per cent for the most massive objects in our sample (M*~10^{11.5} Msun). When observed at sufficient depth, such objects frequently exhibit many distinct tidal features with complex shapes. The interpretation and characterisation of such features varies significantly with image depth and object orientation, introducing significant biases in their classification. Assuming the data reduction pipeline is properly optimised, we expect the Rubin Observatory to be capable of recovering much of the flux found in the outskirts of Milky Way mass galaxies, even at intermediate redshifts (z<0.2).

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arXiv2022

Evidence for Cold-stream to Hot-accretion Transition as Traced by Lyα Emission from Groups and Clusters at 2 < z < 3.3

We present Keck Cosmic Web Imager (KCWI) observations of giant Lya halos surrounding 9 galaxy groups and clusters at 2<z<3.3, including five new detections and one upper limit. We find observational evidence for the cold-stream to hot-accretion transition predicted by theory by measuring a decrease in the ratio between the spatially extended Lya luminosity and the expected baryonic accretion rate (BAR), with increasing elongation above the transition mass Mstream). This implies a modulation of the share of BAR that remains cold diminishing quasi-linearly (logarithmic slope of 0.97+-0.19, 5 sigma significance) with the halo to Mstream mass ratio. The integrated star-formation rates (SFRs) and AGN bolometric luminosities display a potentially consistent decrease, albeit significant only at 2.6 sigma and 1.3 sigma, respectively. The higher scatter in these tracers suggests the Lya emission might be mostly a direct product of cold accretion in these structures rather than indirect, mediated by outflows and photo-ionization from SFR and AGNs; this is also supported by energetics considerations. Below Mstream (cold-stream regime) we measure LLya/BAR=10^{40.51+-0.16}~erg/s/Msun*yr, consistent with predictions, and SFR/BAR=10^{-0.54+-0.23}: on average 30_{-10}^{+20}% of the cold streams go into stars. Above Mstream (hot-accretion regime), LLya is set by Mstream (within 0.2~dex scatter in our sample), independent of the halo mass but rising tenfold from z=2 to 3.

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