You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'There is a strong spatial correlation between brightest cluster galaxies (BCGs) and the peak density and cooling rate of the intra-cluster medium (ICM). In this paper we combine integral field spectroscopy, CO observations and X-ray data to study three exceptional clusters (Abell 1991, Abell 3444 and Ophiuchus) where there is a physical and dynamical offset between the BCG and the cooling peak to investigate the connection between the cooling of the intracluster medium, the cold gas being deposited and the central galaxy. We find the majority of the optical line emission is spatially coincident with the peak in the soft X-rays. In the case of A1991 we make separate detections of CO(2-1) emission on the BCG and on the peak of the soft X-ray emission suggesting that cooling continues to occur in the core despite being offset from the BCG. We conclude that there is a causal link between the lowest temperature ($<$2keV) ICM gas and the molecular gas($\sim$30K). This link is only apparent in systems where a transitory event has decoupled the BCG from the soft X-ray peak. We discuss the prospects for identifying more examples of this rare configuration.'
author:
- |
    \
    \
    $^{1}$Institute for Computational Cosmology, Department of Physics, University of Durham, South Road, Durham DH1 3LE\
    $^{2}$School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia\
    $^{3}$Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada\
    $^{4}$Institute of Astronomy, Madingley Road, Cambridge CB3 0HA\
    $^{5}$LERMA, Observatoire de Paris, UMR 8112 du CNRS, 75014, Paris, France\
bibliography:
- 'bib.bib'
date: 'Accepted TBD; Received TBD; in original form September 2011'
title: 'The Relation Between Line Emission and Brightest Cluster Galaxies in Three Exceptional Clusters: Evidence for Gas Cooling from the ICM'
---

\[firstpage\]

galaxies: clusters: individual: A1991, A3444, Ophiuchus - galaxies: clusters: intracluster medium - galaxies: elliptical and cD

Introduction
============

Observations of the central regions of massive galaxy clusters show intense X-ray emission suggesting that the ICM is undergoing significant radiative cooling [@fab81]. X-ray emitting gas cools at a rate of $t_{cool}$ $\propto$ 1/$n$ (where $n$ is the gas density), suggesting a substantial mass ($\sim$10$^{12}$ M$_{\odot}$) of cool gas should be deposited into the central regions and form stars [for a review see @fab94]. In typical cases cooling rates of 50–100 M$_{\odot}$yr$^{-1}$ are expected rising as high as $>$500 M$_{\odot}$yr$^{-1}$ in the most extreme systems, although sub-mm observations did not detect this gas in molecular form [@ode94]. However, through systematic surveys for CO in clusters, molecular gas masses of $10^{9-11} M_{\odot}$ have been found [@edg01; @sc03]. More recent X-ray observations have revealed much reduced cooling rates ($\sim$1–10 M$_\odot$ yr$^{-1}$) with a sharp truncation in cooling at low ($<$ 1 keV) X-ray temperatures, suggesting a continuous feedback effect is reheating the gas. This heavily suppressed cooling has reduced the large discrepancy between gas deposition rate and observed molecular gas [see the review by @pf06].

The clusters X-ray luminosity and temperature relate closely to the intrinsic luminosity of the BCG [@sch87; @sch88; @es91b; @es91a]. This connection between the BCG and cluster properties makes BCGs an important tool for studying clusters. Since the dense environment at the centre of clusters means that BCG experiences a much higher ICM pressure than any other cluster member galaxy radiative cooling is at its strongest and gas cooling from the hot phase can be accreted onto the BCG, fuelling its evolution. However, these regions are also densely populated by other galaxies making the likelihood of interactions and mergers much more likely. Both mergers and gas accretion are therefore likely to play important roles in the growth and evolution of the BCG and cluster core [@tre90; @wil06].

Many BCGs of the most rapidly cooling cluster cores exhibit optical line emission [@cav08]. @cra99 found significant line emission in 32 per cent of a sample of 201 BCGs selected from the BCS X-ray selected sample [@ebe98]. This line emitting gas at 10$^4$ K traces filamentary structures around the BCG [@hat05; @hat06; @mcd11] and direct comparison has shown qualitatively similar structures in the 10$^7$ K X-ray [@fab08] and 30 K molecular [@sal11] gas. This structural similarity suggests that the gas phases are linked and as such, studying the line emitting gas can give an insight into the physical mechanisms operating within the cluster cores.

In order to measure the emission line structure of the gas within a more complete sample of clusters we have obtained spatially resolved spectroscopy around the redshifted H$\alpha$ emission of 77 BCGs (Hamer [*et al.*]{} [in preparation]{}). Here, we report observations of three extreme systems (Abell 1991, Abell 3444 and the Ophiuchus cluster) from our parent sample which show a significant component ( $>$ 50 per cent) of their line emission significantly offset from the central BCG. A1991 and A3444 are unique from the rest of the sample in that the rest frame optical line emission is significantly offset from the BCG. Figure \[fig:offsetcomp\] shows the physical offset between the BCG and the peak H$\alpha$ emission for the whole sample of 77 line emitting BCGs (Hamer [*et al.*]{} [in preparation]{}). It can clearly be seen here that the offsets for the majority of the sample fall below the seeing limit of the VIMOS observations (1.5$''$) with A1991 and A3444 having 9-13kpc offsets.

We first outline our observations and data reduction ($\S$\[sec:obs\]) followed by a summary of how we completed our analysis ($\S$\[sec:aly\]). In $\S$\[sec:res\] we present our results before discussing their implications in $\S$\[sec:dis\]. Finally a summary and conclusions are reported in $\S$\[sec:sum\]. We assume $\Omega_{m}=$0.27, $\Lambda=$ 0.73 and $H_{o}=$ 71 km s$^{-1}$ Mpc$^{-1}$ throughout. This corresponds to a physical scale of 1.12kpc/$''$ for A1991, 3.91kpc/$''$ for A3444 and 0.55kpc/$''$ for Ophiuchus.

Observations and Data Reduction {#sec:obs}
===============================

Observations of the BCG in A1991 were taken using the Visible Multiobject Spectrograph (VIMOS) instrument on the 8.2m Very Large Telescope (VLT) in April of 2008 and May of 2010. Observations were made at two positions one centred on the BCG and the second $\sim$ 10 $''$ north of the first to cover the peak in X-ray emission. At both locations a set of three 600 second exposures were performed with a pointing dither included between each exposure to account for bad pixels. The HR\_Orange Grism and GG435 filter (spectral resolution of R$\sim$$\Delta\lambda/\lambda$$\sim$2650 over the wavelength range 5250–7400 Å) were used to observe H$\alpha $ ($\lambda_{\rm rest} \ 6562.8 \rm$ Å) at the redshift of the cluster of 0.0587. Observations of A3444 where taken with VIMOS in June 2008 using the HR\_Red Grism and GG475 filter (spectral resolution R$\sim$$\Delta\lambda/\lambda$$\sim$3100 covering the wavelength range 6450–8600 Å) to observe H$\alpha $ at the cluster redshift of 0.2533. The observations were taken in a range of conditions, with a seeing of $\sim$ 0.7$''$–1.3$''$.

The raw data were reduced using the [*esorex*]{} package. This package performed the basic data reduction including bias subtractions, flat fielding and the wavelength and flux calibrations. To subtract the sky we masked any point-like objects to remove any stars within the field. The BCG was then removed from the field by masking all pixels within an isophote of half its peak intensity. The sky level for each quadrant was then calculated by taking the median value of the remaining pixels at each wavelength increment. This sky spectrum was then subtracted from each pixel in the four quadrants before they were combine into a single datacube. Finally we median combined the three exposures for each pointing in order to eliminate cosmic rays. To mosaic the two positions of A1991 we determine the exact offset between the BCG in both observations and combined them to create a cube with a $\sim$ 36$'' \times38''$ field of view.

The Ophiuchus cluster BCG (hereafter Ophiuchus) was observed by @edw09 using Gemini Multi-Object Spectrograph (GMOS) on the 8.1m Gemini South Telescope (Gemini). This object was selected from the literature as it is the best other example of a BCG showing significant offset between the BCG, the X-ray peak and the line emission [@ma09]. The observations of Ophiuchus consisted of four 1500 second exposures which were combined to give a total integration time of 6000 seconds. The R400+r grating (spectral resolution R$\sim$$\Delta\lambda/\lambda$$\sim$1918 covering the wavelength range 5620–6980 Å) was used to ensure coverage of H$\alpha$ at the cluster redshift of 0.0280 [@lah89]. The seeing during these observations was $\sim$ 0.8$''$ to 1$''$.

The data were reduced using GMOS specific tools in the Gemini IRAF package, which included bias subtraction, flat fielding and wavelength calibration. Sky subtraction was preformed by isolating the fibres from a secondary IFU situated $\sim$ 1$'$ away from the primary IFU. These fibres were then used to create a sky spectrum which was subtracted from the fibres containing the observations. Cosmic rays were then rejected by comparing the spectrum from each fibre to that from neighbouring fibres and rejecting any element which had a value exceeding ten times the Poisson noise. The individual exposures were then combined into a single datacube which covers a region centred on the BCG of $\sim 5'' \times 7''$.

We obtained IRAM 30m data for the CO(1-0) and CO(2-1) lines in A1991 on 21st April 2010. The observations were performed in reasonable conditions ($\tau_{\rm 225GHz}\sim 0.1-0.2$) with the EMIR receiver using a 4 GHz bandwidth covering each line. Two positions were observed, the BCG and the optical line peak 11$''$ north, each for 1 hour duration with wobbler switching with a 90$''$ throw. The observations reached a noise level of 0.6 mK and 1.3 mK in 44 km s$^{-1}$ bins (16 and 32 MHz) for CO(1-0) and CO(2-1) lines respectively. Both the 4 MHz and Wilma backends were used to sample the data but the noise performance of the 4 MHz backend was considerably better so only the 4 MHz data are presented here.

IRAM 30m observations of CO(1-0) in A3444 were obtained on 29th December 2006, before the VIMOS IFU observations, in very good conditions ($\tau_{\rm 225GHz}<0.1$) with the A/B100 receivers with a 400 MHz bandwidth for 1 hour duration using wobbler switching with a 90$''$ throw. These observations reached 0.8 mK in 52 km s$^{-1}$ bins (16 MHz). At the time of writing, we are aware of no observations of CO in Ophiuchus.

Analysis {#sec:aly}
========

We use the integral field spectroscopy to investigate the spatial variation of line emission and kinematics within the clusters. We fitted gaussian emission line profiles to the region of the spectra containing the H$\alpha$ ($\lambda_{\rm rest} \ 6562.8 \rm$ Å) and \[NII\] ($\lambda_{\rm rest} \ 6548.1/6583 \rm$ Å) in each lenslet. We used a $\chi^2$ minimisation procedure and allowed the velocity, intensity and linewidth of the H$\alpha$ line, as well as the continuum level to vary independently. The \[NII\] lines were fixed to the same velocity and linewidth as H$\alpha$, the \[NII\] intensity was allowed to vary but the ratio of \[NII\]6548.1/\[NII\]6583 was fixed to 0.3. The profiles were fitted to each 0.6$''$ pixel and adaptively binned to 1.8$''$ in regions with lower H$\alpha$ flux. As such the low surface brightness emission has a lower resolution than the brightest regions.

These fits were accepted as representing the data when they provided an improvement over a continuum only fit at the 7$\sigma$ significance level and when an acceptable fit was found the parameters of the best fit model were stored. These parameters were then used to produce maps of H$\alpha$ flux, relative velocity and linewidth(FWHM deconvolved for instrumental resolution). Continuum images of the region covered by the observations were also produced by taking the median of the emission from each lenslet over a region of the spectra containing no emission lines or sky line residuals (here after referred to as collapsing the cube).

Table \[tab:fits\].

Properties of the on source and offset components

  ------------ -------------- --------------- ------------------------------------- ------------------------------------- -------------------------------------------------- ---------------
  Target          Redshift       Velocity                H$\alpha$ Flux                         \[NII\] Flux                                  Continuum                           FWHM
                               (km s$^{-1}$)   ($10^{-16}$ erg cm$^{-2}$ s$^{-1}$)   ($10^{-16}$ erg cm$^{-2}$ s$^{-1}$)   ($10^{-16}$ erg cm$^{-2}$ s$^{-1} \rm$ Å$^{-1}$)   (km s$^{-1}$)
  Abell 1991                                                                                                                                                                 
  BCG           0.05935\[3\]    0 $\pm$ 11               10.3 $\pm$ 0.7                        23.7 $\pm$ 0.68                             6.41 $\pm$ 0.27                     205 $\pm$ 9
  Offset        0.05893\[2\]   124 $\pm$ 10              22.5 $\pm$ 1.2                        35.1 $\pm$ 0.87                             0.76 $\pm$ 0.41                     152 $\pm$ 5
  Connecting    0.05910\[3\]    71 $\pm$ 11              7.48 $\pm$ 0.4                        10.1 $\pm$ 0.35                             2.15 $\pm$ 0.19                     133 $\pm$ 7
  Abell 3444                                                                                                                                                                 
  BCG           0.25583\[6\]    0 $\pm$ 25               15.5 $\pm$ 0.7                         8.3 $\pm$ 0.6                               1.0 $\pm$ 0.2                     490 $\pm$ 21
  Offset        0.25550\[3\]   100 $\pm$ 19              16.5 $\pm$ 0.5                         7.8 $\pm$ 0.5                                  $<$ 0.5                         273 $\pm$ 9
  Connection    0.25503\[6\]   241 $\pm$ 26              10.0 $\pm$ 0.6                         8.2 $\pm$ 0.6                               0.4 $\pm$ 0.2                     450 $\pm$ 26
  ------------ -------------- --------------- ------------------------------------- ------------------------------------- -------------------------------------------------- ---------------

Table \[tab:coline\].

Properties of the CO(2-1) line in A1991

  -------- ----------------- ------------------------ --------------- --------------- ------------------------- --------------------
  Target     Significance     CO(2-1) Line Intensity     Velocity       Line width     Peak intensity T$_{mb}$     H$_2$ gas mass
            Sigma($\sigma$)      (K km s$^{-1}$)       (km s$^{-1}$)   (km s$^{-1}$)            (mK)             ($10^8$ M$_\odot$)
  On BCG          3.8             0.52$\pm$0.16         -22$\pm$10       60$\pm$18           7.8$\pm$2.2            9.9$\pm$3.0
  Offset          3.0             0.46$\pm$0.19         -62$\pm$17       79$\pm$35           5.5$\pm$1.8            8.8$\pm$3.6
  -------- ----------------- ------------------------ --------------- --------------- ------------------------- --------------------

Results {#sec:res}
=======

Abell 1991
----------

In Figure \[fig:offset\] we show the continuum image of A1991 (collapsed over $\lambda$ = 6000-7000 Å) and overlay contours of H$\alpha$ line emission. It is apparent that while there is a component of the H$\alpha$ emission centred on the BCG a more extended clump is present 9$''$ north lying off the bright stellar component, a projected physical offset of $\sim$ 10kpc at the cluster redshift of 0.0587 [@str99].

Table \[tab:fits\] shows the values of the variable parameters for the minimised fits to the emission on the BCG, off the BCG (labelled on Figure \[fig:offset\] as regions A and B respectively) and the emission from the connecting gas. These fits show that the offset clump contains the majority ($\sim$55 per cent) of the H$\alpha$ emission within the system.

A1991 also is known to have a significant offset ($\sim$ 10$''$) between the position of the BCG and the X-ray peak [@sha04s]. Figure \[fig:offset\] shows that the bright peak in the X-ray gas lies roughly 10$''$ (11kpc) to the north of the BCG and within 3kpc of a similar peak in H$\alpha$ emission. This bright X-ray peak corresponds to the lowest temperature gas in the cluster and the region where the gas is cooling most rapidly. This shows that the majority of the H$\alpha$ emitting gas is related to the most rapidly cooling region of the ICM rather than being co-located with the BCG. Analysis of the [*Chandra*]{} data indicates that the pressure in the core of the cluster is relatively uniform between the BCG and the cooler, offset peak implying that the enhanced density at the peak is balanced by a lower temperature [@sha04s].

In Figure \[fig:offset\] we show the velocity and linewidth maps produced from the fits to the individual lenslets. We note that the velocity map shows a continuous velocity gradient from the position of the BCG along a connecting filament to the offset emission. This suggests that the two components, while physically separated remain kinematically linked. To determine the velocity difference between the two components we extracted spectra from an 8$''$ by 7$''$ aperture centred on the BCG and on the offset component (marked A and B on the velocity map of Figure \[fig:offset\]). We find a velocity difference of 124 $\pm$ 10 km s$^{-1}$ between the two components. The linewidth (FWHM) of the emission from the BCG is greater (205 $\pm$ 9 km s$^{-1}$) than that from the offset component (152 $\pm$ 5 km s$^{-1}$).

Next, we combine the H$\alpha$ and the CO properties to investigate the relation between warm and cold gas within the cluster core. By virtue of the good conditions, the relative sensitivity between the two lines with EMIR strongly favours the CO(2-1) line. We obtain a significant detection of it in both positions (Figure \[fig:co21\]) of 3.8$\sigma$ on the BCG and 3.0$\sigma$ on the offset line emission. The significance of the line detection was calculated using the variance of the signal away from the line compared to the line strength. By this measure there are two candidate lines at -1250 and +930 km s$^{-1}$ in the offset observation but, if they are real, are unlikely to be related to the BCG.

The separation of the two positions is just smaller than the IRAM beam at this frequency (10.3$''$ vs 10.9$''$) and the measured velocity of the emission is offset by more than half the line width. &gt;From the separation and profile of the beam we estimate a less than 10 per cent contamination between the two pointings. Therefore the gas is likely to be spatially extended on a scale comparable, but not necessarily identical to, the optical emission lines. The velocity difference in CO(2-1) between the two positions is -40$\pm$20kms$^{-1}$ in the same direction as the shift we observe in H$\alpha$ but 84kms$^{-1}$. lower. This difference may be related to the bulk flow of the cold molecular gas or a different overall distribution with respect to the BCG compared to that traced by the optical lines. The significance of this velocity difference and its potential origin are beyond the scope of these single dish observations but could be addressed with deeper interferometry with PdBI or ALMA.

The detection of CO 10$''$ north of the BCG in A1991 makes this the fourth system where extended CO has been found (e.g. NGC1275 @sal06s, A1795 @sc04 and RXJ0821$+$07 @ef03). In all of these systems the extended CO coincides with extended H$\alpha$ emission. Within the system as a whole the implied total molecular gas masses of $\approx1.9 \times 10^9$ M$_\odot$ for A1991 is consistent with the correlation of molecular gas mass and optical line luminosity in @edg01 and with the star formation rate inferred from the MIR continuum [@ode08s]. However, current observations cannot spatially resolve whether the star formation in the offset gas follows the correlation found for gas within the BCG [@ode08s].

Abell 3444
----------

A3444 also shows a substantial factor ($\sim$63 per cent) of optical line emission offset from the BCG. In Figure \[fig:offset2\] we show a FORS2 $R$ band image of the central region of the cluster with contours from H$\alpha$ line emission. A clear extension in the line emission can be seen to the southwest where a secondary peak is apparent. This component is offset from the BCG by $\sim$ 3.2$''$ or $\sim$ 12.5kpc at the cluster redshift of 0.2533 [@str99]. In this cluster the line emission form the BCG and offset location are consistent within errors at $\sim$ 40% of the total line flux each (Table \[tab:fits\]).

The X-ray observations of this system show a weak but significant point like source (L$_{x}$(0.5-10 keV) $\sim$ 4 $\times$ 10$^{43}$ ergs s$^{-1}$ in a 1.5$''$ aperture and a power law spectrum) coincident with the BCG that has a relatively hard spectrum compared to the cluster emission (Figure \[fig:xrycomp\]) suggesting the presence of an AGN. While the point source is centred on the BCG (Figure \[fig:offset2\]), the soft X-ray emission shows an extension in the same direction as the offset optical line emission (Figure \[fig:offset2\]) although, like A1991, it is not exactly coincident with the offset peak in the line emission.

To determine the temperature of the gas in at the location of the BCG we fit a mekal thermal plasma model [@mew85; @mew86] to the 0.5–5.0keV emission from a 1.5$''$ aperture centred on the BCG. This found the temperature of the gas to be $>$ 7.5 keV which is high for a plasma model suggesting a contribution to the hard X-ray emission from an AGN component. The presence of an AGN in the BCG would produce increased X-ray counts which could shift the apparent centre of the cluster emission. As such the AGN contribution must be accounted for when determining the true centre of ICM cooling.

To subtract the AGN emission from the soft X-ray emission on the BCG (and find the true level of the extended cluster emission) we determine the normalisation of the point source in the 2.0–5.0keV band and apply this to the emission from the 0.5–1.5keV band. To do this we first determine the properties of the cluster 2.0–5.0 keV emission from an annulus surrounding the point source. We then fit an absorbed power law plus an absorbed mekal plasma model to the point source 2.0–5.0keV emission with the properties of the mekal component fixed to those from the surrounding annulus. Finally we apply the same model to the point source 0.5–1.5keV emission with the normalisation and photon index of the power law set to the values determine from the Hard X-rays and calculate the flux of the two components.

The total flux from the point source in the 0.5–1.5keV band is 2.45$^{+0.24}_{-0.20}$$\times$10$^{-14}$ erg cm$^{-2}$ s$^{-1}$, of which 0.55$^{+0.16}_{-0.13}$$\times$10$^{-14}$ erg cm$^{-2}$ s$^{-1}$ comes from the AGN contribution. We find that the cluster emission under the point source is 1.90$^{+0.18}_{-0.15}$$\times$10$^{-14}$ erg cm$^{-2}$ s$^{-1}$ while the extension to the southwest has a flux of 2.4$^{+0.20}_{-0.12}$$\times$10$^{-14}$ erg cm$^{-2}$ s$^{-1}$ suggesting that it represents the peak in the soft X-ray emission. Analysis of the [*Chandra*]{} data also shows that the pressure in the core of A3444 is relatively constant when the AGN emission is excised. Therefore, A3444 shows very similar X-ray properties to A1991 with an offset peak in soft X-rays but a constant pressure core on 50–100kpc scales. In the case of A3444, where the AGN in the BCG contributes significantly to the X-ray emission, the offset position in the soft X-rays represents the region of maximum cooling of the ICM.

Within this system the BCG and offset component are separated by a velocity of 100 $\pm$ 19 km s$^{-1}$. We also note that the connecting emission has a higher velocity offset (241 $\pm$ 26 km s$^{-1}$) than the offset peak. The linewidths in this system are higher in the BCG (FWHM= 490 $\pm$ 21 km s$^{-1}$) than in the offset component (FWHM= 273 $\pm$ 9 km s$^{-1}$) suggesting the gas is more disturbed within the galaxy or that it is the combination of several, related gas clouds. We also note that the lenslet from the centre of the BCG has FWHM $>$ 650 km s$^{-1}$ suggesting possible contribution from the AGN detected in the X-ray imaging, that can be seen in the linewidth map in Figure \[fig:offset2\].

In A3444, the smaller angular extent of the offset means that only a global measure of the cold molecular gas can be obtained from our IRAM observations in this system and its higher redshift restricts us to just CO(1-0). Our observation provides a marginal (2.0$\sigma$) detection of 0.33$\pm$0.11 K km s$^{-1}$ and a width of 172$\pm$69 km s$^{-1}$ at the velocity of the BCG. However, the restricted bandwidth of the A/B100 receiver means that a broader line could be present but is lost in the baseline subtraction. The implied total molecular gas masses of $\approx1.7 \times 10^{10}$ M$_\odot$ for A3444 is consistent with the correlation of molecular gas mass and optical line luminosity in @edg01.

Ophiuchus
---------

@edw09 studied the properties of the Ophiuchus cluster with the GMOS IFU and found line emission with a substantial ($\sim$ 4$''$) offset from the BCG (Figure \[fig:ophu\]). @edw09 attributed this offset line emission to another galaxy and not to the BCG itself but given the similarity with respect to the X-ray emission to A1991 and A3444 we reconsider this system. In our reanalysis of these data we also find that the line emission is offset from the BCG by $\sim$ 4$''$ which, at a redshift of z=0.028, corresponds to a projected separation of $\sim 2.2$kpc. The line emission within Ophiuchus shows no component on the BCG with 100 per cent of the H$\alpha$ emission coming from the offset component.

@mil10 also analyse [*Chandra*]{} X-ray data and find that the X-ray peak in the Ophiuchus cluster is offset from the BCG by $\sim$ 4$''$, a similar offset to that seen in the line emission. In Figure \[fig:ophu\] we compare the position of the X-rays and the offset line emission. We note that the [*GMOS*]{} field of view (shown by the dashed green line) ends along the north-east and north-west edges of the observed line emission but that otherwise the line emission lies towards the peak in X-ray surface brightness. While our analysis of these data find results consistent with those of @edw09 the alignment of the offset H$\alpha$ and X-ray emission suggests a situation similar to that in A1991 and A3444.

In this system, there is sufficient S/N in the continuum that we can determine the stellar velocity. We extracted a spectrum of the BCG and used a penalised pixel-fitting method [@cap04] to fit the Sodium D absorption from a catalogue of stellar templates. Comparison of the H$\alpha$ line with the Sodium D($\lambda$ 5889,5895) stellar absorption find that the line emitting gas is offset from the BCG by 603 $\pm$ 28 km s$^{-1}$. The velocity and line width maps are shown in Figure \[fig:kineophu\], the kinematics of the gas in this system are simple although some tentative evidence for a velocity structure is apparent to the east of the object (at the edge of the GMOS field of view). Other than this the velocity of the gas shows little variation ($\sigma$ = 31 km s$^{-1}$ or half the velocity resolution of $\sim$ 60 km s$^{-1}$) and the linewidth is uniform across the detected line emission (FWHM = 235 $\pm$ 38 km s$^{-1}$). Future, wider field IFU observations are required to map the full extent and velocity structure of the line emission.

Time scales
-----------

The conclusion we draw from our extensive optical IFU sample (Hamer [*et al.*]{} [in preparation]{}) is that the fraction of systems in which there is an offset between the majority of the optical line emission and the central galaxy of more than 8kpc is relatively small ($\approx 3$ in 77). In the narrow-band imaging survey of 27 groups and clusters [@mcd11], A1991 is the only object with a second component of the optical line emission that is offset from the BCG. Similarly, from X-ray observations of 24 line emitting clusters from the LoCuSS sample [@san09] only four are offset from the X-ray centroid by more than 8kpc (i.e. 15 per cent) (but none are offset by more than 15kpc).

We can use the statistics of offset line emission of our sample to estimate the lifetime of such offsets. Assuming that all clusters with a line emitting BCG may experience an offset at some stage, the fraction of BCGs showing this offset multiplied by the look-back time of the sample ($\sim$1 Gyr at the median redshift of our sample) gives an estimate on the lifetime of $\sim$40 Myr (3/77$\times$1 Gyr). With IFU observations, it is also possible to estimate the lifetime of the offset using the kinematics of the gas. Assuming the offset is orientated to the line of sight at an angle $\theta$, the actual separation of the BCG and X-ray peak is $D = D'/sin \theta$, where D is the actual separation and D’ is the projected separation that we observe. Similarly the projected and actual velocity difference is given by $V = V'/cos \theta$. We can determine the timescale of this separation to be $T = D'/V' \times cos \theta/sin \theta$.

Assuming that the likelihood of any orientation is uniform over the area a hemisphere, then the median orientation angle will correspond to the angle that splits the hemisphere into two equal areas. This implies that 2$\pi$r$^3$ cos$\theta_{2}$ = $\pi$r$^3$ and hence $\theta$=cos$^{-1}$ 0.5 $\sim$ 60$^{\circ}$.

A1991 has the most well constrained parameters of our three objects and therefore by setting a limit on the offset velocity and distance we can limit the range of angles over which we expect the offset to be orientated. We assume the maximum offset velocity to be 500 km s$^{-1}$ and the offset distance to be no more than 20kpc. These values correspond to an orientation ranging from $\sim$30$^{\circ}$–75$^{\circ}$. By applying the above equation with appropriate orientation angles we find that its most likely lifetime is 45 Myr with a possible range of 20–135 Myrs. These values are consistent with those calculated from the sample statistics suggesting that the lifetime of such offsets is a few tens to a hundred Myrs.

At a mass deposition rate of 10–20M$_{\odot}$yr$^{-1}$ [@sha04s] 2$\times$10$^7$–2.5$\times$10$^9$ M$_{\odot}$ could condense from the ICM within 20–135 Myr. With our most likely timescale of 45 Myr this corresponds to 5$\times$10$^8$–10$^9$ M$_{\odot}$ so the expected mass of gas is comparable to our detected CO gas mass. It should be noted that the lower mass deposition rate represents gas centred on the BCG which is at a higher temperature and lower density than that at the offset position so should be considered a lower estimate.

Discussion {#sec:dis}
==========

The most striking result from our observations is that the optical line emission is emitted predominantly from the region with the highest soft X-ray surface brightness and not the BCG. In the vast majority of clusters the peak in the X-ray emission is very close to the BCG [@per98; @hud10; @san09] so determining whether the optical lines are primarily related to the cooling of the ICM or the BCG is not possible. The direct relationship between the core X-ray properties (e.g. cooling time or entropy) and the optical line emission in any BCG has been established [@raf08; @cav08]. However, only in the very small minority of clusters where the ‘sloshing’ of the ICM resulting from major or minor cluster mergers [@asc06; @jon10; @mil10] or an episode of strong AGN activity temporarily results in the BCG not residing at the peak of the gas cooling is there an opportunity to make the direct test of whether the optical line emission is related primarily with the cooling gas or the BCG itself.

The presence of cold molecular gas in the cores of clusters can be explained through a number of mechanisms: mergers with gas-rich cluster galaxies or gas cooling from the intracluster medium. The gas mass observed in BCGs (10$^{9-11.5}$M$_\odot$) [@edg01; @sc03] is too large to be explained by galaxy mergers or stellar mass loss but is consistent with heavily suppressed cooling from the ICM [@pet03; @pf06; @snd10].

Given the close correlation between optical lines and CO found in other cluster cores the detection of ionised gas at the location of the X-ray peak suggests the presence of a reservoir of molecular gas offset from the BCG. In A1991 and A3444 we directly detect the presence of molecular gas in the form of CO. In one system, A1991 we also detect CO at the offset position, with a molecular gas mass of $\sim$10$^{9}$ M$_{\odot}$. The presence of such a high mass of molecular gas at the offset position clearly suggests that cooling is occurring despite the BCG and cluster core being separated.

Using the statistics from our sample we estimate that any offset of greater than 8kpc can only remain for around 10$^8$yrs. This is consistent with the dynamical timescale of the core implying that these “excursions” of the BCG from the X-ray peak are short-lived. If the molecular gas at the offset position is being produced in situ then it would have to cool from the ICM within this time frame. Within the central regions of the cluster core X-ray observations predict typical cooling rates of the order $\sim$ 1-10 M$_{\odot}$ yr$^{-1}$ [@pf06], at this rate of cooling the cluster core could deposit between 10$^{8}$ and 10$^{9}$M$_{\odot}$ of cold molecular gas in the $\sim$ 10$^8$ yrs which it is not coincident with the BCG. As such, the offset molecular gas observed in A1991 is consistent with the upper band of cooling from the ICM of 25 M$_{\odot}$ yr$^{-1}$ [@sha04s].

Although A3444 and Ophiuchus do not have separate detections of cold molecular gas at the offset position, their similarities to A1991 suggest that it may be present. Due to the smaller angular offset between BCG and X-ray peak in A3444 and Ophiuchus, resolving the molecular gas is not possible with single dish observations. However, with the start of ALMA operations there is now the possibility to directly map the molecular gas in such systems allowing the separate components of the gas to be resolved.

An alternative explanation for the morphology of the extended molecular and ionised gas is ram pressure stripping of gas related to the BCG when a merger induces large motion of the ICM relative to the BCG. This requires an efficient mechanism to entrain the dense molecular gas into the much more tenuous ICM. The effect of magnetic fields could enhance this stripping but would have to be very effective to explain the acceleration observed in Ophiuchus. The observations presented here cannot rule out ram pressure stripping. However, future mm-interferometry should be able to map the cold molecular gas and allow us to distinguish between these mechanisms. If ram pressure stripping is responsible we would expect the molecular gas to be stripped less effectively than the optical line-emitting gas, while in the case of local cooling we would expect a similar morphology between the two phases.

Similar objects
---------------

The offset between the BCG and X-ray peak in clusters is not unique to these objects, both Abell 1644 [@jon10] and RXJ1347.5-1145 [@jon11] have a small offset and show evidence of sloshing similar to that seen here. @mar03 also find that two thirds of clusters classified as cool cores by [@per98] show evidence of cold fronts associated with sloshing. An offset along the line of sight is not always obvious suggesting the existence of more objects in which the BCG is dissociated from the cluster core but cannot be detected by observations due to projection effects.

There are also a number of other systems where the peak of the line emission is coincident with the BCG but have less intense offset line emission in the form of extended envelopes and filaments. A1795 [@cra05] and RXJ0821$+$07 [@bay02] both show very extended optical emission that follows the highest X-ray emissivity in the cluster and also has associated cold molecular gas emission [@sc04; @ef03]. Most recently, @can11s present evidence for a filament of optical line emission extending from the BCG in A2146 which is undergoing a major merger where the peak in the X-ray emission is offset from the BCG by 37 kpc. The IFU data presented in @can11s doesn’t cover the X-ray peak so it can’t be established if A2146 is similar to the three clusters presented here but it illustrates that a significant merger is required to dissociate the BCG from the X-ray peak. In a major merger the disruption in the core will be significant. @rus10 show that the pressure profile in the core of A2146 is very asymmetric, unlike that in A1991 which is dynamically more quiescent. Therefore, the process of cluster-cluster merging, and the longer lived sloshing that it induces, may be required to produce the brief decoupling of the peak in the intracluster medium density from the BCG observed in all of these systems.

Another viable mechanism for inducing bulk motion of the ICM in a cluster core is the inflation of cavities due to AGN activity in the BCG. @bla11 show a close correspondance between filaments of high X-ray surface brightness and optical line emission in A2052 which has an extensive cavity network. The compressed gas in these filaments has a short cooling time so the optical line emission may also be related to local cooling. The systems presented in this paper do not resemble A2052 or exhibit the large cavities required to generate the observed offsets, so AGN feedback is unlikely to explain the lop-sided offsets we observe in A1991, A3444 and Ophiuchus. However, the small scale correlation between strongest X-ray cooling and optical line emission suggests a common mechanism behind them.

The existence of cold gas that is ‘orphaned’ in the cores of clusters may have a number of implications for more distant systems. For instance, in the high redshift radio galaxy TXS0828+193 ($z=2.6$), @nes09 find a cloud of cold molecular gas emitting at CO(3-2) that has no bright optical or near-infrared counterpart that is 80kpc from the radio galaxy itself. They speculate that this may be analogous to low redshift clusters but note that the gas tends to be associated with the central galaxy. While the total gas mass and physical offset are substantially larger in TXS0828+193 than in A1991 or A3444, the similarity between the systems may point to a common mechanism.

Summary {#sec:sum}
=======

Within the cores of most clusters there is a clear spatial coincidence between the position of the BCG and the peak of the ICM density. However there are a few clusters in which the BCG and cluster core are found to be decoupled. In such systems, it is possible to disentangle the effects of the cluster core and the BCG on the ICM and study each individually. Here we study three such systems selected from a parent sample of 77 massive X-ray selected clusters where we find that the optical, millimetre and X-ray observations of the cores show extended optical line emission and cold molecular gas directly related to the peak of the cooling of the intracluster medium and not the central galaxy. These three systems are the only clusters from our sample to show a significant offset between the BCG and cluster core suggesting that such a phenomenon is rare and transient. From our sample we find that a significant offset occurs in only 2–3 per cent of systems and that they likely have lifetimes lasting of the order of 20–100 Myr. We note however that it is possible for systems to have an offset along the line of sight which we would not detect so this fraction may be slightly higher and should be considered a lower limit.

The rarity of such significant offsets between the BCG, X-ray peak and optical line emission points to a large event in cluster evolution, a major cluster merger or possibly a powerful AGN outburst. Mergers are predicted to drive shocks through the core of the ICM at early times and cause sloshing as a later effect [@asc06; @jon10; @mil10; @zuh10; @zuh11] both of which are capable of separating the BCG from the cluster core. X-ray observations of A1991 suggest the passage of a cluster-wide shock through the core of the cluster and similar observations of Ophiuchus show sloshing of the ICM suggesting the possibility of a recent merger. Whatever the reason for the separation the gas cooling at the X-ray peak will continue and cooled gas will be deposited away from the BCG. This provides a unique opportunity to directly constrain the process of gas cooling without the presence of a BCG.

Acknowledgements {#acknowledgements .unnumbered}
================

SLH acknowledges the support received from an STFC studentship. AMS acknowledges an STFC Advanced Fellowship. HRR acknowledges generous financial support from the Canadian Space Agency Space Science Enhancement Program. ACF thanks the Royal Society for support.

Based on observations made with ESO Telescopes at the La Silla or Paranal Observatories under programme ID 081.A-0422 and 385.A-0955.

Based on observations carried out with the IRAM 30m Telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain)

Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina).

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