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EME 807
Technologies for Sustainability Systems
1.2 Growth / No Growth Dilemma
Steady State Economy
Herman E. Daly (1938-), a renowned expert in ecological economics, who has been a longtime proponent of the concept of sustainable steady state economy (as opposed to economic growth), formulated several basic rules for sustainable society, known as Daly Rules:
Renewable resources - e.g., groundwater, biomass - must be used no faster than the rate at which they regenerate.
Nonrenewable resources - e.g., minerals, fossil fuels - must be used no faster than renewable substitutes for them can be put into place.
Pollution and wastes must be emitted no faster than natural systems can absorb them, recycle them, or render them harmless.
Sustainable steady state theory states that human societies can grow to a special state, where resource supply and consumption are balanced. This should be considered a sustainable steady state. After this balance point has been reached, only refinement of societies (via better use of available resources through more efficient technologies) instead of growth (increase in supply and consumption of resources) should be pursued.
According to Daly's theory, economic growth cannot be forever maintained because the planet and its resources have finite physical dimensions and capacity:
"If resources could be created out of nothing, and wastes could be annihilated into nothing, then we could have an ever-growing resource throughput by which to fuel the continuous growth of the economy. But the first law of thermodynamics says NO. Or if we could just recycle the same matter and energy through the economy faster and faster we could keep growth going. The circular flow diagram of all economics principles texts unfortunately comes very close to affirming this. But the second law of thermodynamics says NO." [Daly, 2009]
But is reaching a sustainable steady state in fact realistic and practically achievable? Daly argues that there is a practical alternative to economic growth paradigm. That would rely on a number of critical economic steps and policies. Daly's measures may seem controversial and somewhat radical at a national or international scale, but they touch an important scaling question: how large can a system be and keep its potential for sustainability?
Please click on the following link to review Daly's proposals: "From a Failed Growth Economy to a Steady-State Economy".
Note: This material will be related to the topic of our first forum discussion.
Oscillating Steady State
Contrary to the steady-state paradigm, an alternative view expressed in works by Howard T. Odum and collaborators (for example "Environmental Accounting: Emergy and Decision Making" 1995) considers the whole planet a self-organizing system, where storages of resources are continuously depleted and replaced at different rates, and matter recycling and reorganization is driven by solar, geothermal, and gravitational energies. It is hypothesized that one of the possible reasons for oscillating systems to be preferable over steady state systems is that they are governed by the system feedback to changing environmental conditions or depletion of one or other storage. The system should be able to tune its performance according to the changing environment.
As the diagram in Figure 1.2. illustrates, net primary production and storage of resources (expressed as Quantity Q) develop faster than consumer assets (expressed as Quantity C) until the system reaches a threshold where autocatalytic and higher order pathways are accelerated. At the threshold, consumer assets show a sudden increase at the expense of the environmental storage (consumer pulse). As the resources are used up quickly, consumer assets drop, allowing a new cycle of building resource storage to begin. In the case of global economy, the storages can be represented, for example, by oil, minerals, topsoil, and other slowly renewable resources, while the consumer assets are human economies and civilization. The theory presumes that this kind of pulsation can be sustained over time.
Figure 1.2. Pulsing growth paradigm.
Credit: Odum, 1988
Anthropogenic Ecology Theory
Some contemporary scientists find Daly's arguments overly pessimistic. For example, Erle Ellis, an associate professor of geography and environmental systems at the University of Maryland, Baltimore County, and a visiting associate professor at Harvard's Graduate School of Design, argues that over the course of the anthropogenic history, humans have almost never relied simply on the carrying capacity of natural ecosystems, but rather created specially engineered ecosystems. Such artificial eco-niches utilize intelligent approaches and technologies for extracting more usable resource from the nature. So, essentially, Ellis infers, there is no problem of limiting carrying capacity due to creative transformative powers of humankind.
Within the anthropogenic ecology theory, the emergence of new sociocultural niches in human society is represented as a novel evolutionary process in the Earth system. These niches are the result of re-shaping the biosphere into new organizational level which allows virtually unlimited upscaling of societies through culturally mediated changes.
Please click on the following link to learn more about Erle Ellis views: "Overpopulation is not the Problem"
To better understand and to analyze the dynamics of feedback and oscillations within socio-ecological systems, it would be useful for us to look at the basics of the systems thinking approach. This thinking framework is especially important to sustainability science, because it allows tracking logical interconnections between natural factors, economic factors, social motifs. More details are given further in Section 1.5 of this lesson.
‹ 1.1 Sustainability Definitions up 1.3 Principles of Sustainable Design ›
EME 807: Technologies for Sustainability Systems
Lesson 1: Principles of Sustainable Systems
1.1 Sustainability Definitions
1.3 Principles of Sustainable Design
1.4 Principles of Sustainable Engineering
1.5. Frameworks for Applying Sustainability Principles
Summary & Activities
Lesson 2: Technology Development and Lifecycle Assessment
Lesson 3: Metrics for Technology Evaluation
Lesson 4: Green Chemistry
Lesson 5: Resource Management Technologies
Lesson 6: Sustainable Water and Wastewater Systems
Lesson 7: High Performance Building Systems
Lesson 8: Applied Renewable Energy Technologies
Lesson 9: Energy Management and Power Systems
Lesson 10: Sustainable Transportation Technologies
Lesson 11: Behavioral Aspects and Feedbacks
Lesson 12: Course Project
Author: Mark Fedkin, Faculty, Department of Mechanical and Nuclear Engineering / Dutton e-Education Insitute. College of Earth and Mineral Sciences, The Pennsylvania State University


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2. The baseline ...
3. Analysis of the uncertainties
4. Discussion and conclusions
Maurizio Salaris1, Santi Cassisi2,3 and Adriano Pietrinferni2
1 Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
e-mail: M.Salaris@ljmu.ac.uk
2 INAF−Osservatorio Astronomico di Teramo, via M. Maggini, 64100 Teramo, Italy
e-mail: cassisi@oa-teramo.inaf.it, pietrinferni@oa-teramo.inaf.it
3 Instituto de Astrofísica de Canarias, Calle via Lactea s/n, 38205, La Laguna, Tenerife, Spain
We obtain stringent constraints on the actual efficiency of mass loss for red giant branch stars in the Galactic globular cluster 47 Tuc, by comparing synthetic modelling based on stellar evolution tracks with the observed distribution of stars along the horizontal branch in the colour-magnitude-diagram. We confirm that the observed, wedge-shaped distribution of the horizontal branch can only be reproduced by accounting for a range of initial He abundances, in agreement with inferences from the analysis of the main sequence, and a red giant branch mass loss with a small dispersion. We carefully investigated several possible sources of uncertainty that could affect the results of the horizontal branch modelling, stemming from uncertainties in both stellar model computations and cluster properties, such as heavy element abundances, reddening, and age. We determine a firm lower limit of ~0.17M⊙ for the mass lost by red giant branch stars, corresponding to horizontal branch stellar masses between ~0.65M⊙ and ~0.73M⊙ (the range driven by the range of initial helium abundances). We also derive that in this cluster the amount of mass lost along the asymptotic giant branch stars is comparable to the mass lost during the previous red giant branch phase. These results confirm, for this cluster, the disagreement between colour-magnitude-diagram analyses and inferences from recent studies of the dynamics of the cluster stars, which predict a much less efficient red giant branch mass loss. A comparison between the results from these two techniques applied to other clusters is required to gain more insights about the origin of this disagreement.
Key words: globular clusters: individual: 47 Tucanae / stars: evolution / stars: horizontal-branch / stars: low-mass / stars: mass-loss
Mass loss during the red giant branch (RGB) evolution of globular cluster (GC) stars has a generally negligible effect on their structure unless the RGB star is experiencing very high mass loss rates (Castellani & Castellani 1993). This mass loss is crucial, however, to interpreting the colour-magnitude-diagram (CMD) of the following horizontal branch (HB) phase, and affects the CMD and duration of the asymptotic giant branch (AGB) stage.
A comprehensive physical description of RGB mass loss processes is still lacking, and RGB mass loss rates are customarily parametrized in stellar evolution calculations by means of simple relations such as the Reimers formula (Reimers 1975) or, more recently, the Schröder & Cuntz (2005) formula. These prescriptions are essentially scaling relations between mass loss rates and global stellar parameters such as surface bolometric luminosity (L), gravity (g), effective temperature (Teff), and/or radius (R). The zero point of these scaling relations is typically set by a free parameter (η) that needs to be calibrated.
The more direct approach to study the mass loss in RGB stars is to detect outflow motions in the outer regions of the atmospheres, through the presence of asymmetries and coreshifts in chromospheric lines, (see e.g. Mauas et al. 2006; Vieytes et al. 2011), or detect the circumstellar envelopes at larger distances from the stars, for example through infrared dust emission (see e.g. Origlia et al. 2007, 2010; Boyer et al. 2010; Momany et al. 2012). Another traditional indicator of the efficiency of RGB mass loss is the CMD location and morphology of the HB of globular clusters, starting from the pioneering works by Iben & Rood (1970) and Rood (1973). Matching observed HBs with synthetic HB models traditionally requires that RGB stars lose a fraction of their initial mass with typical values of the order of ~0.2 M⊙ (see e.g. Lee et al. 1990; Catelan 1993; Salaris et al. 2007; di Criscienzo et al. 2010; Gratton et al. 2010; Dalessandro et al. 2013; McDonald & Zijlstra 2015, and references therein).
A very recent series of papers (Heyl et al. 2015b,a) has applied a completely different approach to estimate the mass lost by RGB stars in the Galactic GC 47 Tuc. Using HST images these authors determined the rate of diffusion of stars through the cluster core, using a sample of bright white dwarfs (WDs). They then compared the radial distribution of upper main sequence (MS), RGB, and HB stars, showing that they are nearly identical, even when only objects near the RGB tip are considered, whilst the radial distribution of young WDs is only slightly less concentrated than upper MS and RGB stars, indicating that there has been very little time for the young WDs to have diffused through the cluster since their progenitors lost mass. They estimated that most of the ~0.4 M⊙ that 47 Tuc stars lose between the end of the MS and the beginning of the WD sequence (the typical MS turn-off mass for 47 Tuc, as inferred from theoretical isochrones, is equal to ~0.9M⊙, whilst typical masses for bright WDs in GCs as determined from observations are ~0.53 M⊙, see Kalirai et al. 2009) is shed shortly before the start of the WD cooling. Quantitatively they estimated that mass loss greater than 0.2 M⊙ earlier than 20 Myr before the termination of the AGB can be excluded with 90% confidence and that mass loss larger than 0.2M⊙ during the RGB can be excluded at more than 4σ level. Also, a typical HB stellar mass of the order of ~0.65M⊙ is excluded by comparisons of the radial distribution of HB stars and ~0.65M⊙ MS stars.
Regarding more direct estimates of RGB mass loss in 47 Tuc, Origlia et al. (2007) derived that the total mass lost by individual RGB stars is ΔMRGB ~ 0.23 ± 0.07 M⊙ from the detection of their circumstellar envelopes by means of mid-IR photometry (see also Origlia et al. 2007; Boyer et al. 2010; Momany et al. 2012). This is in contrast with the Heyl et al. (2015a) result, but is consistent with published results from synthetic HB modelling, which require RGB stars to have lost typically more than 0.2 M⊙ (Salaris et al. 2007; di Criscienzo et al. 2010; Gratton et al. 2013). On the other hand, observations of the infrared excess around nearby RGB stars (not in GCs) led Groenewegen (2012) to determine a Reimers-like mass loss formula that when used in stellar model calculations predicts negligible mass loss for 47 Tuc RGB stars (Heyl et al. 2015a).
The Heyl et al. (2015a) result based on stellar dynamics clearly questions the accuracy of HB stellar models and/or their interpretation of HB morphologies. A solution for this discrepancy requires a robust assessment of the reliability of these two radically different techniques employed to determine the RGB mass loss of the cluster. To this purpose, we revisit in this paper the theoretical modelling of 47 Tuc HB, discussing various sources of potential uncertainties in synthetic models based on HB evolutionary tracks. Section 2 briefly describes our synthetic modelling and presents our baseline synthetic HB for this cluster with the estimated mean RGB mass loss (ΔMRGB). Section 3 discusses various potential sources of uncertainties in our baseline synthetic HB model and their impact on the estimated ΔMRGB. A critical discussion and conclusions close the paper.
2. The baseline synthetic HB model for 47 Tuc
We employed the accurate BVI cluster photometry by Bergbusch & Stetson (2009) in our analysis and selected stars between 400 and 900 arcsec of the cluster centre to minimize the effect of blending (see the discussion in Bergbusch & Stetson 2009) and field contamination. We present results for the HB modelling in the Johnson V − (B − V) CMD, but we verified that we reach the same conclusions when using the Johnson-Cousins V − (V − I) CMD instead. We also compared with our adopted photometry the V − (V − I) CMD of the cluster central region from the ACS survey of Galactic GCs, transformed from the equivalent HST ACS filters to the Johnson-Cousins system by Sarajedini et al. (2007). The HB morphology is the same in the ACS field with just an offset of about ~0.05 mag in the V magnitudes, as the ACS magnitudes are brighter.
The reddening estimates for 47 Tuc range between E(B − V) = 0.024 (Gratton et al. 2003) and E(B − V) = 0.055 (Gratton et al. 1997). Schlegel et al. (1998) reddening maps provide E(B − V) = 0.032, whilst the Harris (1996) catalogue of GC parameters reports E(B − V) = 0.04. The amount of differential reddening is negligible, E(B − V) varies around the cluster mean value by at most −0.007 mag and +0.009 mag, respectively, as recently determined by Marino et al. (2016) on a sample of stars taken from our adopted Bergbusch & Stetson (2009) photometry. As for the cluster chemical composition, Thompson et al. (2010) and Cordero et al. (2014) list a series of spectroscopic determinations of [Fe/H] and [α/Fe] for this cluster that can be summarized as [Fe/H] = −0.7 ± 0.1 and [α/Fe] = 0.3−0.4. The [Fe/H] measurements in a sample of 47 Tuc HB stars provide [Fe/H] = −0.76 ± 0.01 (rms = 0.06 dex), which is consistent with the range quoted above (Gratton et al. 2013).
In our baseline simulation of the cluster HB we assumed [Fe/H] = −0.70, [α/Fe] = 0.4 and E(B − V) = 0.024. We employed the lowest estimate of the cluster reddening because it leads to generally higher HB masses and, hence, minimizes the necessary RGB mass loss1.
Synthetic HB models were computed by employing HB tracks from the BaSTI stellar model library (Pietrinferni et al. 2004, 2006)2 and the code is fully described in Dalessandro et al. (2013). We made use of the BaSTI tracks for [Fe/H] = −0.7, [α/Fe] = 0.4 (corresponding to Z = 0.008), and varying Y.
Our calculations require the specification of four parameters, plus the cluster initial composition, age, and photometric error. Two of these parameters are related to the distribution of the initial He abundances among the cluster stars. We can choose between a Gaussian distribution with a mean value ⟨ Y ⟩ and spread σ(Y), and a uniform distribution with minimum value Ymin and range ΔY. The other two parameters are the mean value of the mass lost along the RGB, ΔMRGB, which for simplicity we assume to be the same for each Y, but can be made Y-dependent, and the spread around this mean value (σ(ΔMRGB)). The idea behind these types of simulations (see e.g. D'Antona et al. 2002; Gratton et al. 2010; Dalessandro et al. 2013; Milone et al. 2014, and references therein) is that the colour extension of the HB is driven mainly by the variation of Y rather than mass loss efficiency. A range of He abundances within individual clusters is expected theoretically given the well-established presence of CN, ONa, and MgAl abundance anti-correlations within single GCs (see Gratton et al. 2004). These abundance variations are most likely produced by high-temperature CNO cycling, hence one also expects He variations in addition to these anti-correlations.The actual amount of He variations depend on the nucleosynthetic site and the cluster chemical evolution (see e.g. Decressin et al. 2007; D'Ercole et al. 2010, for two different scenarios to explain the observed abundance patterns).
Indeed, studies of the optical CMDs of MS stars3 have disclosed the presence of ranges of initial He in several GCs (see e.g. Piotto et al. 2007; Milone et al. 2013; Nardiello et al. 2015, and references therein), including 47 Tuc (Milone et al. 2012). The synthetic HB modelling by di Criscienzo et al. (2010) and Gratton et al. (2013) also required a range of initial Y to reproduce the wedge-shaped HB in optical filters. On this issue, it may be worth recalling that in the past (see Dorman et al. 1989; Catelan & de Freitas Pacheco 1996) it was shown that at metallicities typical of 47 Tuc a wedge-shaped HB could be reproduced theoretically with a single but large initial Y of the order of Y ~ 0.30. With our synthetic HB calculations, we can obtain a shape roughly similar to that observed for Y = 0.34 and a negligible Y range (and ΔMRGB ~ 0.12 M⊙). However, the resulting distance modulus is ~0.3 mag too large compared to constraints from the cluster eclipsing binaries (see below) and, in addition, cluster R-parameter studies (see e.g. Cassisi et al. 2003; Salaris et al. 2004) exclude such high initial values of Y.
Finally, it is also important to mention that the observed CNONaMgAl abundance variations do not affect the stellar evolution tracks and isochrones as long as the CNO sum is unchanged (see e.g. Pietrinferni et al. 2009; Cassisi et al. 2013) as is generally true within the spectroscopic measurements errors with just a few exceptions. This justifies the use of standard α-enhanced models, only varying the initial He content.
To translate the RGB mass loss ΔMRGB into HB masses, we assume an age for the cluster that provides (from the theoretical isochrones) the initial value of the mass of the stars evolving at the tip of the RGB (denoted as RGB progenitor mass). Age estimates by Salaris & Weiss (2002), Gratton et al. (2003), Dotter et al. (2010), and VandenBerg et al. (2013) from CMD analyses provide a range between t = ~ 10.5 and t = ~ 12.5 Gyr, and for this simulation we assumed t = 11.5 Gyr, which corresponds to a RGB progenitor mass equal to 0.92 M⊙. Our assumed age is also consistent with the estimated value 11.25 ± 0.21(random) ± 0.85(systematic) Gyr by Thompson et al. (2010), based on theoretical mass-radius relations applied to the cluster eclipsing binary V69.
Comparison between the observed HB of 47 Tuc (triangles) with synthetic CMDs calculated with ΔMRGB = 0.23 M⊙ and Y = 0.256, 0.270 and 0.286 (filled large circles), respectively, plus a simulation for ΔMRGB = 0.28 M⊙ and Y = 0.256 (dots). Two HB tracks corresponding to Y = 0.256, and masses M = 0.8 and 0.9 M⊙ (corresponding to ΔMRGB = 0.12 M⊙ and 0.02 M⊙, respectively) are shown as solid lines. All the tracks and synthetic CMDs are shifted by E(B − V) = 0.024 and (m − M)V = 13.40 (see text for details).
Figure 1 displays a first test that shows clearly the need for a substantial mass loss and a range of initial Y values to match the location and morphology of the cluster HB. The three narrow synthetic sequences in the figure (filled circles) that overlap with the observed CMD were calculated for Y = 0.256 (the normal initial He for the chosen initial metallicity according to the ΔY/ ΔZ ~ 1.4 ratio employed in the BaSTI calculations, and a cosmological Y = 0.245) 0.270, and 0.286, respectively, ΔMRGB = 0.23, and a negligible Gaussian spread σ(ΔMRGB) = 0.001. The synthetic sequences were shifted in colour by applying the reference reddening E(B − V) = 0.024 and in magnitude by adding an apparent distance modulus (m − M)V = 13.40. This distance modulus is consistent with the estimates (m − M)V = 13.35 ± 0.08 (Thompson et al. 2010) and (m − M)V = 13.40 ± 0.07 (Kaluzny et al. 2007) from two eclipsing binaries in the cluster and has been chosen to match the bottom-right end of the observed HB with models calculated with the normal initial He.
The increase of initial He abundance at fixed mass loss moves the synthetic stars towards bluer colours and brighter magnitudes. This progressive shift in colours and magnitudes plus the increased extension of the blue loops in the synthetic populations reproduce well the wedge-shaped observed HB. For the reference age and metal composition, ΔMRGB = 0.23 M⊙ produces HB masses equal to 0.69, 0.66, and 0.63 M⊙ for Y = 0.256, 0.270, and 0.286, respectively (see also a similar discussion in Gratton et al. 2013). On the other hand, synthetic stars with Y = 0.256 and increased ΔMRGB = 0.28 M⊙ (dots) are displaced towards bluer colours but fainter magnitudes, confirming that the morphology of the cluster HB is driven by a range of Y rather than ΔMRGB.
We have shown also HB tracks for Y = 0.256 and masses equal to 0.8 and 0.9 M⊙ (in order of increasing colour and decreasing magnitude) that correspond to ΔMRGB = 0.12 M⊙ and 0.02 M⊙, respectively. These tracks are beyond the red edge of the observed HB and no variation of the adopted distance modulus can enforce an overlap with the data.
Our baseline synthetic model for 47 Tuc HB (filled circles) compared to the observed HB (open triangles). The number of observed and synthetic stars within the box enclosing the observed HB is the same (see text for details).
A full synthetic HB compared to the observed HB is shown in Fig. 2. For this complete simulation we had to assume a statistical distribution for the initial He abundances, which for simplicity we considered to be uniform. The range of Y values spans the interval 0.256−0.286 (Ymin = 0.256 and ΔY = 0.03) and ΔMRGB = 0.23 M⊙ as in Fig. 1 with a very small Gaussian spread of 0.005 M⊙. Photometric errors were assumed to be Gaussian with a mean value equal to 0.002 mag in both B and V magnitudes, as obtained from the photometric data. We restrict our comparison to the objects within the box highlighted in the CMD; the precise choice of the boundaries of the box is not crucial. The simulation contains a much larger number of stars than observed to minimize the Poisson error on the synthetic star counts, but for the sake of clarity we show a subset of synthetic objects that matches the number of observed stars. We considered the match to be satisfactory when the observed mean magnitude (⟨ V ⟩ HB = 14.07) and colour (⟨ (B − V)HB ⟩ = 0.80), plus the associated 1σ dispersions (0.04 mag in both cases) are reproduced within less than 0.005 mag, and the overall shape of the observed star counts as a function of both (B − V) and V is well reproduced. The mean (B − V) colour is matched for the assumed reddening E(B − V) = 0.024, and a distance modulus (m − M)V = 13.40 allows us to match the observed mean V magnitude as well.
Figure 3 shows the resulting histograms of observed and synthetic star counts as a function of V and (B − V); star counts from the synthetic CMD are rescaled to match the observed total number of HB stars. The agreement looks very good even with these simple assumptions about mass loss and He distribution.
Comparisons of synthetic (solid line) and observed (filled circles) star counts with Poisson error bars in V-magnitude (top panel: bin size equal to 0.04 mag) and (B − V) colour (bottom panel: bin size equal to 0.02 mag) bins, obtained from the data in Fig. 2 (see text for details).
Figure 4 indicates mass and Y distributions as a function of the colour of the synthetic stars shown in Fig. 2. There is an obvious correlation with (B − V) for both mass and Y, as expected from the constant ΔMRGB (irrespective of Y) and very small σ(ΔMRGB) assumed in the simulation, which is blurred by the blue loops of the HB tracks (see Fig. 1). This is clear from the top panel, which shows how stars with a fixed mass are distributed over a large range of colours. Redder stars on the ZAHB are on average more massive and less He enriched than bluer objects; the typical mass for the stars with normal Y = 0.256 is ~0.69 M⊙ and decreases to ~0.63 M⊙ for Y = 0.286. The average mass along the synthetic HB is equal to 0.66 M⊙ with a 1σ dispersion of 0.017 M⊙. The exact values of these two quantities depend on the assumed distribution of initial Y, but obviously the mean mass cannot be outside the range 0.63−0.69 M⊙. A general trend of increasing Y with decreasing colour is also fully consistent with the observed trend of increasing Na towards bluer colours along the cluster HB (see Gratton et al. 2013).
We could have tried to enforce a priori the constraint of perfect statistical agreement between the theoretical and observed star counts. However, a perfect fit rests on the precise knowledge of the statistical distribution of ΔMRGB and the initial Y among the cluster stars. Owing to the current lack of firm theoretical and empirical guidance, this distribution may be extremely complicated and/or discontinuous. The constraints imposed on the matching synthetic HB are however sufficient to put strong constraints on ΔMRGB, which is the main parameter discussed in this work, and the range of initial Y, which determines the region of the CMD covered by the observed HB.
In fact, only the observed shape of the HB enables a good determination of both the ΔMRGB and Y range, when E(B − V), age and initial chemical composition are fixed, as can already be inferred from Fig. 1. In greater detail, Fig. 5 shows how changing these two parameters affects the shape and location of the synthetic HB. Variations of ΔMRGB around the reference value, keeping the reference Y distribution fixed, move the location of the synthetic HB along the direction from the top right corner of the CMD to the bottom left corner. At the same time, the HB gets compressed when ΔMRGB is reduced (shorter loops in the CMD of the HB tracks of larger mass) and stretched when ΔMRGB is increased. No change in the cluster distance modulus can bring into agreement any of these two synthetic CMDs with the observed HB. Variations of ΔY, keeping the reference ΔMRGB unchanged, stretch or compress the synthetic HB along the direction from the top left corner of the CMD to the bottom right corner. Also, in this case, variations of the cluster distance modulus do not compensate for the change of Y distribution.
Distribution of stellar mass (top panel) and initial Y values (bottom panel) as a function of the colour (B − V) for the stars in the synthetic CMD shown in Fig. 2.
A decrease of ΔY to 0.025 and variations of ΔMRGB within less than 0.01 M⊙ do still allow a satisfactory fit to the observed HB, according to the criteria described above, but larger variations are clearly ruled out because the resulting synthetic HB would clearly have a different shape than observed. Values of ΔMRGB below 0.20 M⊙ are totally incompatible with the observed HB morphology and location in the CMD.
We also experimented with a mass loss that is linearly dependent on the initial Y distribution. Considering ΔMRGB = 0.23 M⊙ for the population with Ymin, a synthetic HB with ΔY = 0.03, and ΔMRGB increasing at most as 0.5 × ΔY provides a fit to the observations of comparable quality as the baseline simulation. This implies ΔMRGB is higher by just 0.015 M⊙ for the most He-rich component. Experiments with ΔMRGB decreasing with Y show that, at most, ΔMRGB can decrease as 0.15 × ΔY, implying a negligible decrease of the RGB mass loss as a function of Y.
As Fig. 2, but for the labelled values of ΔMRGB and ΔY (see text for details).
As an additional test, we calculated a synthetic HB by considering the reference ΔMRGB = 0.230 ± 0.005 (Gaussian spread) for all Y, but with a different distribution of initial He abundances. We considered, in this case, 70% of the stars with a Gaussian distribution of initial Y characterized by mean value ⟨ Y ⟩ = 0.275 and spread σ(Y) = 0.007, and the remaining 30% with a very narrow Gaussian distribution with ⟨ Y ⟩ = 0.258 and spread σ(Y) = 0.0008. This choice stems from the results by Milone et al. (2012), who found a bimodal MS for this cluster, corresponding to ~0.02 difference in initial Y. The adopted distribution in our simulations has a difference of ~0.02 between the mean values of the two Gaussians and a total range ΔY = 0.03 that is needed to cover the V − (B − V) region occupied by observed HB completely. The 70/30 ratio again comes from the Milone et al. (2012) analysis of the number ratio between the two populations of different initial He as a function of the distance from the cluster centre. For the same distance modulus of our reference simulation, mean V and mean (B − V) of the observed HB are again matched within 0.01 mag, although star counts as a function of colour and magnitude are slightly less well reproduced.
The main point of this simulation is that a change of the initial Y distribution of the HB stars does not affect the ΔMRGB required to match the CMD location of the observed HB.
In the previous section we found that for the adopted reference [Fe/H] = −0.7, [α/Fe] = 0.4, E(B − V) = 0.024, t = 11.5 Gyr, our synthetic HB simulations require that RGB stars lose ΔMRGB = 0.23 M⊙ (and have a range of initial He abundances ΔY = 0.03) to match the observed location and morphology of the HB, corresponding to stellar masses in the range 0.63−0.69 M⊙. This value of ΔMRGB (and ΔY) is broadly in line with previous results based on synthetic HB modelling (di Criscienzo et al. 2010; Gratton et al. 2013), but in total disagreement with the conclusions by Heyl et al. (2015a) about RGB mass loss, based on cluster dynamics. The Heyl et al. (2015a) results specifically exclude HB masses of the order of 0.65 M⊙. In the following we discuss quantitatively how our reference estimate of ΔMRGB may be affected by a series of observational and theoretical uncertainties.
3.1. Cluster reddening, age, and chemical composition
The first obvious source of systematics is related to the range of reddening, chemical composition, and age estimates found in the literature. We analyzed these effects by varying one parameter at a time. In all these cases the value of ΔY required to reproduce the observations is unchanged compared to the baseline case.
Increasing E(B − V) (our baseline simulation has employed the lowest estimate of cluster reddening) tends to increase ΔMRGB. For example, assuming the widely employed value E(B − V) = 0.04, we obtain ΔMRGB = 0.24 M⊙, whilst we obtain ΔMRGB = 0.26 M⊙ for the upper limit E(B − V) = 0.055; that is we need lower masses to match the observed HB. As already mentioned, Marino et al. (2016) determined star-to-star variations around the mean reddening by at most −0.007 mag and +0.009 mag, respectively with mean variations that are smaller than these extreme values. This amount of differential reddening hardly affects the value of ΔMRGB, as detailed below.
To maximize this effect, we assume that the stars at the red edge of the observed HB all have a reddening that is 0.007 mag lower than the mean value. To compare with theory, their colours should then be increased by 0.007 mag, and their V magnitudes increased by ~0.02 mag, to reduce the observed HB to a single value of E(B − V), causing a decrease of ΔMRGB by just ~0.01 M⊙ in this extreme case. At the same time, assuming all stars along the blue edge of the wedge have a reddening 0.009 mag that is higher than the mean value, their colours should be decreased by the same amount and their V magnitudes also decreased by ~0.03 mag. This would require a negligible increase of ΔY and ΔMRGB increasing with Y as 0.6 ×ΔY.
As for the age, a variation by ±1 Gyr around the reference value causes a change of the RGB progenitor mass by about ±0.02 (lower mass for increasing age). The best-fit synthetic HB requires the same HB mass distribution as the baseline case, but ΔMRGB varies by about ±0.02 (decreased when the age increases) because of the change of the RGB progenitor mass.
We then considered the range of [Fe/H] estimates [Fe/H] = − 0.7 ± 0.1. Increasing [Fe/H] of the models tends to increase ΔMRGB for two reasons. First, because at fixed age the RGB progenitor mass increases by ~0.01 M⊙ for a 0.1 dex increase of [Fe/H] due to longer evolutionary timescales at fixed mass; second, HB tracks are redder so that for a fixed reddening, lower HB masses are required to match the observed HB location. If we consider [Fe/H] = − 0.6 –the approximate upper limit of the spectroscopic determinations, keeping everything else unchanged, the best-fit synthetic HB model has ΔY = 0.03, ΔMRGB = 0.28 M⊙, and (m − M)V = 13.35. When employing the approximate lower limit [Fe/H] = − 0.8, after interpolation in metallicity amongst the grid of BaSTI models, we obtain a best match for ΔY = 0.03, ΔMRGB=0.18 M⊙, and (m − M)V = 13.47. In these cases the mean mass of the synthetic HB stars varies by ~0.03 M⊙ (increases when [Fe/H] decreases) around the mean value of the baseline simulation.
If we decrease [α/Fe] from 0.4 dex to 0.3 dex, keeping [Fe/H] and all other parameters unchanged, after interpolations amongst our models we found that ΔMRGB decreases by just 0.01−0.02 M⊙ and (m − M)V increases by ~0.02 mag compared to our baseline simulation. The HB mean mass changes by less than the ΔMRGB because of the corresponding variation of the RGB progenitor mass, as for the case of changing [Fe/H]).
To summarize, variations of the cluster chemical composition, age, and reddening do not change the ΔMRGB much and, in particular, the typical HB stellar mass, compared to the results of the baseline simulation. In the following we discuss whether considering a number of uncertainties in the theoretical models can help solve or at least minimize the disagreement with inferences from cluster dynamics.
3.2. Bolometric corrections and colour transformations
To compare the output of stellar evolution calculations (L and Teff) with observed CMDs, the use of bolometric corrections (BCs) and colour-Teff relationships is essential. One way to proceed is to calculate grids of model atmospheres and synthetic spectra that are integrated under the appropriate filter transmission functions to get fluxes in a given passband, which are then suitably normalized to calculate BCs and colours (see e.g. Girardi et al. 2002; Casagrande & VandenBerg 2014, and references therein). Our adopted set of models employs theoretical BCs and colours calculated from ATLAS9 model atmospheres and spectra (see Pietrinferni et al. 2004, 2006, for details). We also tested the results from PHOENIX model atmosphere calculations employed by the Dartmouth stellar model library (Dotter et al. 2008), and found that at the relevant metallicities the HB tracks become systematically redder than with ATLAS9 results. This shift would cause lower HB masses from synthetic HB modelling, hence higher ΔMRGB at fixed age, reddening, and chemical composition.
An alternative approach is to employ empirical or semi-empirical results, when available. Worthey & Lee (2011) recently presented essentially empirical BCs and colour-Teff relationships in various broadband filters based on a collection of photometry for stars with known [Fe/H].
HB evolutionary tracks for 0.7 (top panel) and 0.8 M⊙ (bottom panel), [Fe/H] = −0.7, [α/Fe] = 0.4, Y = 0.256 HB models shifted by E(B − V) = 0.024 and (m − M)V = 13.40, compared to the cluster HB. The dotted lines indicate BaSTI tracks with the adopted BaSTI BCs, and colour transformations, while the solid lines show the same tracks but employing the empirical Worthey & Lee (2011) BCs and colours. Dashed lines in each panel indicate the brightest and bluest, and the faintest and reddest extremes of the error range associated with Worthey & Lee (2011) transformations, respectively.
Figure 6 shows representative 0.7 M⊙ and 0.8 M⊙ HB tracks with our adopted reference chemical composition and Y = 0.256, shifted by E(B − V) = 0.024 and (m − M)V = 13.40 as in our baseline simulation. The same tracks are displayed after applying BCs and colour transformations from Worthey & Lee (2011), using the routine provided by the authors. This routine also gives the errors associated with the computed BCs and colours, and we show in the figure the brightest/bluest and faintest/reddest limits of the area covered by these error bars, which are of about 0.05 mag in BCV and ~0.02 mag in (B − V).
It is clear from the figure that these transformations make the tracks redder (and very slightly fainter) than the reference BaSTI models, but within the empirical error bars ATLAS9 transformations (adopted in the BaSTI library) are consistent with Worthey & Lee (2011) results. There is not much room for a substantial increase of the typical HB mass when considering these empirical results. Masses above ~0.7 M⊙ along the HB are still clearly excluded.
To get more quantitative results, we calculated synthetic HB models for the reference chemical composition and reddening using Worthey & Lee (2011) results. We found a best match to the observed HB for ΔMRGB = 0.24 M⊙, which is very close to the result of our baseline simulation of Sect. 2, (m − M)V = 13.38; all of the other parameters are the same as in our reference simulation of Sect. 2. By employing the bluest colours allowed by the error bars on Worthey & Lee (2011) results to minimize the value of ΔMRGB and the HB masses needed by the HB simulations, we obtained ΔMRGB = 0.22 M⊙, and a mean HB mass equal to ~0.67 M⊙. Considering also the errors on BCV would simply shift the synthetic HB vertically by ±0.05 mag, implying an adjustment of the derived (m − M)V by the same amount, that is still within the errors of the eclipsing binary distance estimates.
3.3. Model calculation, input physics
Before the start of the HB phase, GC stars go through the violent core helium flash at the tip of the RGB. Until recently, only few calculations were able to calculate the evolution of stellar models through this event, and traditionally HB models (including the BaSTI models employed in our analysis) were computed by starting new sequences on the HB, where the initial structure is taken from that at the tip of the RGB. The underlying assumption of such methods, which are consistent with the results of stellar evolution calculations that follow the helium flash evolution, is that during the helium flash the internal (and surface) chemical structure is not altered significantly, apart from a small percentage of C produced in the He-core during the flash.
The technique employed in BaSTI models (denoted as Method 2 in the work by Serenelli & Weiss 2005) envisages that a model at the beginning of the core helium flash is employed as the starting model for the ZAHB calculation. The core mass and chemical profile of the initial pre-flash configuration are kept unchanged. The total mass of the ZAHB model is either preserved or reduced (to produce a set of ZAHB models of varying total mass) by rescaling the envelope mass. The new model on the ZAHB is then converged and relaxed for a certain amount of time (typically 1 Myr) to attain CNO equilibrium in the H-burning shell (see e.g. Cassisi & Salaris 2013) before being identified as the new ZAHB model. A 5% mass fraction of carbon is added to the He-core composition, guided by requirement that the energy needed for the expansion of the degenerate helium core must come from helium burning (Iben & Rood 1970).
VandenBerg et al. (2000) and, in greater detail Piersanti et al. (2004) and Serenelli & Weiss (2005), compared the ZAHB location and HB evolution of models whose RGB progenitor evolution was properly followed through the He-flash with results from our method described before. Especially for red HB models, as in the case of 47 Tuc HB, differences in Teff, L and time evolution turned out to be negligible.
As additional potential sources of uncertainty in the determination of ΔMRGB employing synthetic HB modelling, we considered the effect of uncertainties in the current input physics adopted in stellar model calculations. We considered first the effect on the He-core mass at the He-flash and how this affects the HB tracks, and then the effect on the HB evolution at fixed core mass.
Since the calculation of the BaSTI model database, two relevant physics inputs, i.e. the reaction rate and the electron conduction opacities, have been the subjects of revised and improved determinations. The recent Cassisi et al. (2007) calculations of electron conduction opacities, larger than the Potekhin (1999) results used in the BaSTI calculations, cause a variation of the He-core mass at the He-flash (ΔMHec) by −0.006 M⊙, compared to our adopted HB models. On the other hand, the new Formicola et al. (2004) tabulations of the reaction rate, which is lower by a factor ~2 than the Angulo et al. (1999) rate used in our adopted model, induce an increase ΔMHec ~ 0.0025 M⊙ compared to the BaSTI calculations. The combined effect is a minor change ΔMHec ~ − 0.0035 M⊙ compared to the BaSTI models.
In addition, Valle et al. (2013) determined ΔMHec due to realistic uncertainties in the Formicola et al. (2004) reaction rate (±10%), the Cassisi et al. (2007) electron conduction opacities (±5%), plus the (±3%) and 3α (±20%) reaction rates, neutrino emission rates (±4%), and the radiative opacities (±15%) used in the BaSTI models. If we simply add together the effect of these uncertainties plus the systematic effect of including fully efficient atomic diffusion in the pre-HB calculations4 that increase MHec by ~0.004 M⊙ (see Table 7.2 in Cassisi & Salaris 2013 and the ΔMHec ~ − 0.0035 M⊙ discussed before), we obtain a (conservative) variation ΔMHec ~ ± 0.01 M⊙ around the value obtained from the BaSTI calculations.
As Fig. 6 but showing for the 0.8 M⊙ standard BaSTI track (solid line in both panels), the effect of changing the He-core mass at the He-flash by ±0.02 M⊙ (dashed lines in the left panel), the amount of He dredged to the surface by the first dredge up by δYFDU = ± 0.02 (dash-dotted lines in the left panel), the reaction rate (doubled and halved, respectively; dotted lines in the left panel), the mixing length αMLT by −0.15 (dashed line in the right panel), the Rosseland mean opacities by ±5% (dotted lines in the right panel), and the reaction rate from the Angulo et al. (1999) to the Formicola et al. (2004) tabulations (dash-dotted line in the right panel).
The left panel of Fig. 7 shows the effect of ΔMHec = ± 0.02 M⊙ on a 0.8 M⊙ HB track for the reference chemical composition Y = 0.256, [Fe/H] = − 0.7 and [α/Fe] = 0.4. To calculate this track, we varied the He-core mass by ±0.02 M⊙ around the value provided by the BaSTI models (MHec = 0.48 M⊙) and recalculated the HB evolution, as everything else was kept fixed. This variation is even larger than the estimates discussed before and takes two additional factors into account. First, there is a possible extra increase of MHec owing to the effect of rotation, as originally discussed by Castellani & Tornambe (1981) and Lee et al. (1994) in the context of synthetic HB modelling. Second, there is a potential additional decrease by ~0.008 M⊙ owing to the use of weak screening in the He-core during the whole RGB evolution, instead of the transition to intermediate and strong screening when appropriate, following the treatment by Graboske et al. (1973) as implemented in the BaSTI calculations.
It is clear from the figure that the expected shift in magnitude of the tracks (higher MHec corresponds to higher luminosity) is not accompanied by any major shift in colour. The ZAHB location is only very slightly redder for the lower core mass model and bluer for the higher core mass model and the extension of the loops in the CMD is only slightly altered. It may seem puzzling that such a large variation of MHec hardly affects the tracks. In fact HB tracks of a given total mass are generally sensitive to small variations of the He-core mass at the flash because of the changed efficiency of the H-burning shell due to the corresponding variation of the mass of the H-rich envelope. However, at this metallicity and for massive HB models, the efficiency of the burning shell is only weakly altered even by a ±0.02 M⊙ change of MHec because this corresponds to just a small percentage variation of the mass thickness of the envelope.
The same figure also shows the effect of arbitrarily altering the efficiency of the first dredge-up on the same 0.8 M⊙ HB track, keeping everything else unchanged. Our adopted BaSTI models predict an increase of the surface He mass fraction by 0.02 for the cluster RGB stars. This increased He abundance in the envelope impacts the efficiency of the H-burning shell during the HB phase. We tested a variation of the dredged-up He mass fraction δYFDU = ± 0.02 by recalculating HB models with this new envelope chemical abundance; the resulting tracks are simply shifted in luminosity (higher for increasing He abundance), but their colour location is unchanged.
We then considered the HB evolution of the same 0.8 M⊙ HB track keeping MHec fixed and varying the most relevant inputs one at a time as follows: for example the radiative opacities by ± 5%, the reaction rate from the Angulo et al. (1999) tabulations used in our adopted BaSTI models to the most updated Formicola et al. (2004) tabulations; the superadiabatic convection mixing length parameter by δαMLT = − 0.15, compared to the solar calibrated value (αml, ⊙ = 2.01) of the BaSTI calculations (see right panel of Fig. 7); and the reaction rate (doubled and halved, respectively, as shown in the left panel of Fig. 7).
As already mentioned, the Formicola et al. (2004) rate is about a factor of two lower than the Angulo et al. (1999) result, i.e. a variation much larger than the error associated with this improved rate. Regarding the variation δαMLT = − 0.15 with respect to the solar calibrated value, this is what the fitting formulas by Magic et al. (2015), based on the results of a large grid of 3D radiation hydrodynamics simulations, predict for the surface gravity-effective temperature regime of the 0.8 M⊙ HB track and a metallicity [Fe/H] = − 0.5, which is close to the value adopted in our calculations. We consider this adopted δαMLT as a qualitative estimate of the uncertainty on the efficiency of superadiabatic convection in the envelope of red HB stars. Regardless of the precise estimate of δαMLT, Magic et al. (2015) simulations (a similar behaviour is also found in an analogous 3D hydro-calibration by Trampedach et al. 2014, at solar metallicity) predict that αMLT should decrease towards higher effective temperature and/or lower surface gravity compared to the solar values. As for the reaction rate, we consider both an increase and a decrease by a factor of two with respect to the reference rate adopted in the BaSTI calculations (Kunz et al. 2001), along the lines of the analysis by Gai (2013) regarding the current uncertainties on this reaction rate.
It is clear from the figure that the variation of the opacity, in which higher opacity corresponds to lower luminosities, and reaction rate essentially alter only the brightness of the model and not the colour, as for the case of varying MHec and YFDU. The variation of the reaction rate alters only very marginally the extension of the bluewards loop in the CMD (more extended loop for an increase of the reaction rate). The variation of the mixing length obviously affects the model colours, but the decrease of αMLT predicted by the hydro-simulations makes the model redder, thus decreasing the mass of the HB models, hence increasing the RGB mass loss, needed to match the observed HB5.
Finally, we considered the effect of the treatment of core mixing during the HB phase. As is well known and was discussed recently again by, for example Gabriel et al. (2014) and Constantino et al. (2015), the treatment of convective boundaries during core helium burning is still an open question in stellar evolution calculations and is handled in different ways by different stellar evolution codes. Recent advances in asteroseismic observations and techniques (Bossini et al. 2015; Constantino et al. 2015) are starting to add very direct observational constraints to the core mixing process during the central He-burning phase, which coupled with theoretical inferences and indications from star counts in Galactic globular clusters (see e.g. Caputo et al. 1989; Gabriel et al. 2014; Cassisi et al. 2003, and references therein), make a strong case for the core mixed region to be extended beyond the Schwarzschild border. Questions exist however about the treatment of this extended mixing. The details do not affect the ZAHB location of the models, but can potentially modify the extension of the loops in the CMD and have some relevance for the determination of the mass range of the cluster HB population.
Our adopted BaSTI HB models include semi-convection in the core (see Castellani et al. 1971b,a, 1985) with the suppression of the breathing pulses in the last phases of central He-burning with the technique by Caputo et al. (1989), following the observational constraints discussed by Cassisi et al. (2003). Constantino et al. (2016) calculated and compared HB models with different treatment of core mixing beyond the Schwarzschild border and, in their Fig. 7, they compare HB tracks for a 0.83 M⊙, [Fe/H] = −1, initial Y = 0.245; this comparison is not very different from the case discussed in this section. Tracks with two different types of overshooting and with semi-convection are almost indistinguishable; one of these types of overshooting, the maximal overshoot case, reproduces best the asteroseismic constraints, as discussed by Constantino et al. (2015).
As a conclusion, none of the items on the large list of uncertainties discussed in this section appears to be able to shift onto the observed HB substantially more massive HB tracks compared to the baseline simulation.
In the previous sections we investigated in detail the constraints posed by the CMD of HB stars on the RGB mass loss in the Galactic globular cluster 47 Tuc using synthetic HB modelling. We confirm the results by di Criscienzo et al. (2010) and Gratton et al. (2013) about the need for a range of initial He abundances (we find ΔY = 0.03) to reproduce the observed HB morphology properly. This abundance range is broadly consistent with the range inferred from the analysis of the cluster MS. For the values of age (11.5 Gyr), metal content ([Fe/H] = − 0.7 and [α/Fe] = 0.4), and reddening (E(B − V) = 0.024) adopted in our baseline simulation, a total mass loss of individual RGB stars ΔMRGB = 0.23 M⊙ (with a very small dispersion) independent of Y is required to reproduce the observed HB location and morphology. This value for ΔMRGB is consistent with the estimates by Origlia et al. (2007) from mid-IR photometry and the results by di Criscienzo et al. (2010) and Gratton et al. (2013) from similar synthetic HB modelling. The mean mass of the synthetic HB stars in this simulation is equal to 0.66 M⊙.
To assess the robustness of this estimate of ΔMRGB and the HB masses, we then considered several possible sources of uncertainty that could affect the HB modelling, stemming from uncertainties in both cluster parameters and model calculations. Uncertainties in the cluster reddening, age, and [Fe/H] have the largest effect on the derived ΔMRGB. Considering an age of 12.5 Gyr, which is approximately the upper limit consistent with current estimates, [Fe/H] = −0.8, which is the lower limit of spectroscopic estimates, and the lowest reddening estimate E(B − V) = 0.024 could potentially lead to ΔMRGB< 0.20 M⊙. Younger ages, higher metallicities, and reddenings, within the range of current estimates, can however increase the estimated ΔMRGB up to ~0.30 M⊙. A fraction of this range of ΔMRGB values is due to the variation of the RGB progenitor mass with age and initial chemical composition, so that the actual variation of the typical HB masses is smaller than the full range of ΔMRGB.
There is however the additional constraint posed by the observed colour of the RGB that can be considered. As we show in the following, this narrows the range of ΔMRGB and HB masses allowed by the analysis of the cluster CMD. The upper panel of Fig. 8 shows the synthetic CMDs of our baseline simulation described in Sect. 2 ([Fe/H] = − 0.7, [α/Fe] = 0.4, E(B − V) = 0.024, age t = 11.5 Gyr, ΔY = 0.03, ΔMRGB = 0.23 M⊙, (m − M)V = 13.40) together with the corresponding RGB isochrone (also from the BaSTI models, using the reference ATLAS9 transformations) compared to the cluster photometry in the magnitude range around the HB. Obviously the theoretical RGB is too red compared to the data; given that E(B − V) = 0.024 is the lowest reddening estimate, there is no room for shifting to the blue the position of the theoretical RGB, that is virtually insensitive to age and initial Y for the relevant age and He-abundance ranges. This implies that our adopted models with [Fe/H] = − 0.7 are inconsistent with the observations.
As Fig. 2 but including also the observed and theoretical RGB sequences. The top panel displays the [Fe/H] = − 0.7 baseline simulation employing the BaSTI adopted BCs and colour transformations (ATLAS9). The bottom panel shows the result for the baseline simulation but employing the empirical Worthey & Lee (2011) BCs and colour transformations (solid line). The reddest and bluest limits of the RGB colours according to the errors on the Worthey & Lee (2011) transformations and BCs are displayed as dotted lines (see text for details).
The lower panel of Fig. 8 refers to the best-match synthetic HB simulation when applying the Worthey & Lee (2011) transformations to our adopted BaSTI stellar models, keeping [Fe/H] = − 0.7, [α/Fe] = 0.4, E(B − V) = 0.024, t = 11.5 Gyr, as in the baseline simulation of the top panel. We derive in this case, as already discussed, ΔY = 0.03, ΔMRGB = 0.24 M⊙, (m − M)V = 13.38. The position of the RGB is again largely inconsistent with observations, even allowing for the errors on the Worthey & Lee (2011) BCs and colour transformations shown in the figure.
Figure 9 shows an analogous comparison, but for [Fe/H] = − 0.8 ([α/Fe] = 0.4), t = 11.5 Gyr. In the top panel, the case with the ATLAS9 BCs and colours, the theoretical RGB matches the average colour of the observed RGB for E(B − V) = 0.035, and the best-match synthetic HB has ΔY = 0.03, ΔMRGB = 0.19 M⊙, (m − M)V = 13.46. The average mass along the synthetic HB is in this case equal to 0.69 M⊙ with a 1σ dispersion of 0.017 M⊙, and a full range between ~0.65 M⊙ and ~0.73 M⊙.
The bottom panel indicates the case with the Worthey & Lee (2011) transformations for [Fe/H] = −0.8 ([α/Fe] = 0.4), t = 11.5 Gyr, E(B − V) = 0.035. The only way to match the observed RGB is to consider the bluest colours allowed by the errors on these empirical transformations, whilst for the HB the reference BCs and colour transformations provided by Worthey & Lee (2011) allow a match with observations for ΔY = 0.03, ΔMRGB = 0.19 M⊙, (m − M)V = 13.44, which is almost identical to the case with the ATLAS9 transformations.
One can speculate whether considering the bluest limit of Worthey & Lee (2011) colour transformations also for the HB models, might decrease ΔMRGB because the synthetic HB should then be made redder while keeping reddening, age, and chemical composition fixed. However, an increase of the HB masses, hence a decrease of ΔMRGB below ~0.19 M⊙, would cause a shift to the red of the HB, but also a change of the HB morphology that is inconsistent with the observations, as in the case discussed in the lower left panel of Fig. 5. With increasing HB mass, the loops in the CMD shrink and it is impossible to match simultaneously the vertical and horizontal thickness of the observed HB by changing the Y distribution.
In summary, the additional constraint posed by the colour of the RGB narrows down the possible range of [Fe/H], E(B − V) and ΔMRGB. A fit for the minimum estimate E(B − V) = 0.024 could, in principle, be achieved, at least with the ATLAS9 transformations, considering a slightly higher [Fe/H] of between ~−0.8 and ~−0.75 dex; however, this would keep ΔMRGB, and the evolving HB masses, roughly unchanged because of the compensating effects of increasing [Fe/H] and decreasing reddening, as discussed in the previous sections.
As Fig. 8, but for simulations with [Fe/H] = −0.8 (see text for details).
A firm estimate of the minimum RGB mass loss allowed by our modelling is therefore ΔMRGB ~ 0.17 M⊙ if we consider a cluster age of 12.5 Gyr that is approximately the upper limit of current estimates. The maximum ΔMRGB is equal to ~0.21 M⊙, for an age of 10.5 Gyr. The resulting mass distribution of the HB stars is in both cases between 0.65 M⊙ and 0.73 M⊙, which is the full range determined mainly by the range of initial Y abundances of the progenitors (ΔY = 0.03). The derived distance modulus is consistent with constraints from the observed cluster eclipsing binaries.
We can also compare ΔMRGB with the expected mass loss during the following AGB phase (ΔMAGB). In the simulation that minimizes ΔMRGB, the initial progenitor mass of the HB stars is equal to ~0.89 M⊙ for the Y = 0.254 population and ~0.84 M⊙ for the Y = 0.284 population. Assuming that the final WD mass is equal to ~0.53 M⊙ (Kalirai et al. 2009) irrespective of the initial Y, the mass to be shed by the cluster stars during the AGB phase ranges between ΔMAGB ~ 0.19 M⊙ for the Y = 0.254 population and ~0.14 M⊙ for the Y = 0.284 population. The value of ΔMRGB is therefore expected to be similar to the average ΔMAGB, whose precise value depends on the distribution of initial Y. For a flat Y distribution the average ΔMAGB is equal to ΔMRGB.
On the whole our detailed analysis confirms the discrepancy between information coming from cluster dynamics and CMD modelling of the HB. The lower limit for ΔMRGB allowed by the HB modelling is only slightly lower than the 0.20 M⊙ value excluded with high confidence by the Heyl et al. (2015a) analysis. The predicted mass distribution of HB stars is between ~0.65 M⊙ and ~0.73 M⊙ with mean values, which depend on the exact Y distribution, and are not much higher than 0.65 M⊙; this latter is excluded by the Heyl et al. (2015a) analysis. On the other hand, the RGB mass loss allowed by the HB modelling is consistent with ΔMRGB ~ 0.23 ± 0.07M⊙ estimated from the detection of their circumstellar envelopes by means of mid-IR photometry (Origlia et al. 2007).
A comparison between the results from these two techniques applied to other clusters is required to gain more insights into the origin of this apparently major disagreement between CMD and dynamical results.
Higher reddenings require a larger shift to the red of the HB models, hence a lower HB mass at a given colour and an increased amount of RGB mass loss to match the observed HB location.
http://www.oa-teramo.inaf.it/BASTI
Light element anti-correlations do not affect the bolometric corrections for MS stars in optical CMDs, as shown by Sbordone et al. (2011).
The BaSTI models neglect atomic diffusion.
Somewhat surprisingly, the V-band magnitude of the model with changed mixing length is also affected, although this is exclusively due to the bolometric corrections, which change because of the decrease of the model effective temperature.
We thank the referee for comments that pushed us to improve the analysis of Sect. 3.3. S.C. warmly thanks the financial support by PRIN-INAF2014 (PI: S. Cassisi) and the Economy and Competitiveness Ministry of the Kingdom of Spain (grant AYA2013-42781-P). A.P. acknowledges financial support by PRIN-INAF 2012 The M4 Core Project with Hubble Space Telescope (P.I.: L. Bedin).
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The BaSTI Stellar Evolution Database: models for extremely metal-poor and super-metal-rich stellar populations
The horizontal branch of the Sculptor dwarf galaxy
Level of helium enhancement among M3's horizontal branch stars
Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations
On the missing second generation AGB stars in NGC 6752

redpajama_set_name: RedPajamaCommonCrawl


text:
/ Science and Technology
/ Biographies
/ Physics: Biographies
/ Lorentz, Hendrik Antoon
Lorentz, Hendrik Antoon
Lorentz, Hendrik Antoon hĕn´drək än´tōn lō´rĕnts [key], 1853–1928, Dutch physicist, a pioneer in formulating the relations between electricity, magnetism, and light. He was one of the first to postulate the existence of electrons. On this he based his explanation of the Zeeman effect (a change in spectrum lines in a magnetic field), for which he shared with Pieter Zeeman the 1902 Nobel Prize in Physics. He extended the hypothesis of G. F. Fitzgerald, an Irish physicist, that the length of a body contracts as its speed increases (see Lorentz contraction), and he formulated the Lorentz transformation, by which space and time coordinates of one moving system can be correlated with the known space and time coordinates of any other system. This work influenced, and was confirmed by, Einstein's special theory of relativity. Lorentz also discovered (1880), simultaneously with L. V. Lorenz of the Univ. of Copenhagen, the relations (known as Lorentz-Lorenz relations) between the refraction of light and the density of a translucent body. He was professor (1878–1912) at the Univ. of Leiden and director from 1912 of the Teyler laboratory, Haarlem. His works in English include The Theory of Electrons (1909) and Problems of Modern Physics (1927).
See his collected papers (9 vol., 1934–39); study ed. by G. L. de Haas-Lorentz (tr. 1957).
See more Encyclopedia articles on: Physics: Biographies


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Fake!!! Photo Of Bob Marley & Jimi Hendrix Playing Soccer Backstage
By raul on October 10, 2012 in Bob Marley, Jimi Hendrix
This photo of Bob Marley and Jimi Hendrix playing soccer backstage has been making the rounds for years.
I admit when I first saw it I was impressed, until common sense kicked in and I realized that Hendrix died in 1970 and this photo was taken later in Marley's career. After some research, the photo was taken on November 27, 1979 backstage at the San Diego Sports Arena. It was taken during Marley's "Survival Tour" as seen on the back of the shirt in the foreground in the un-cropped photo.
It is not a photoshop trick but rather a real person who (when blurred and from the side) happens to look like a lot like Hendrix. Here's a couple of photos of the unidentified man with the leather jacket on the same night with Marley. Clearly he's not Jimi Hendrix.
UPDATE: A feelnumb.com reader معاوية شاويش just gave us the info we have been searching for. The mystery man in the photo that looks like Hendrix is trumpet player Glen Dacosta from the Jamaican band Zap Pow. Here is cover to his album Mind Blowing Melody.
Jimi did meet lots of rock stars, just not Bob Marley and Bob Marley did meet George Harrison and Michael Jackson. At least the photo was real, these other two below are actually really good photoshop fakes…
Photo Of John Lennon And Bob Dylan Smoking Is A Fake!!!
Photo Of Axl Rose & Slash Together Again??? Gun's N' Roses Reunion???
Another Paul Is Dead Clue: Magical Mystery Tour Hidden Message "Love The 3 Beatles"
Kurt Cobain Looked Grungy But By All Accounts He Smelled Amazing
The Last Published Photos of Layne Staley Alive
Death Cab For Cutie Band Name Came From A Beatles Movie
Pink Floyd Ummagumma "Gigi" Soundtrack Album Cover
Scott Weiland Is A Huge University Of Notre Dame Football Fan
Geezer Butler's "Enjoy Cocaine" Bass Guitar Sticker
Iggy Pop's "The Idiot" & David Bowie's "Heroes" Album Cover Photos Were Insp...
John Lennon "Acoustic" Album Cover
Neil Young Once Bought 200,000 Of His Own "Comes A Time" Album And Shot Them With His Rifl...
The Details On Prince's "Purple Rain" Motorcycle
Days Inn Chicago 1991 - The Place Where Kurt Cobain & Courtney Love First Had Sex
Dave Grohl & Josh Homme's "Bromance"
Krist Novoselic's Cameo in Robin Williams Movie "World's Greatest Dad"
Layne Staley, Axl Rose, Taylor Hawkins, Jack White, Steven Tyler & Jay Z School Yearbook Photos
Kurt Cobain's Mosrite Mark IV Gospel Guitar With The "Fuck Elvis" Case
Nirvana "Smells Like Teen Spirit" Live With Flea On Trumpet
Nirvana "Smells Like Teen Spirit" Video Shoot Details
The Last Photos Of Jimi Hendrix Alive
Joseph Melville See Jr. Linda McCartney's Ex-Husband Was "JoJo" From Tucson, Arizona In The Beatles "Get Back"
The Clash Debut Album Cover Photo Location
Noel Gallagher's High Flying Birds Album Cover Location Beverly Hills, California
The Flaming Lips Wayne Coyne Caught In Bathtub By Google Street View
Best Of Led Zeppelin Album Covers Taken From Apollo 14 NASA Astronaut Photo
Free Pearl Jam "Amongst The Waves (Acoustic Version)" Download
The Hidden Walrus On The Cover Of The Beatles Sgt. Peppers Lonely Hearts Club Band Album


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Q: Preserving space within elements and removing blank space (empty rows) between elements XSLT, CSS Been trying to transform an xml document, using output html method, for display in browser using xsl stylesheet (with CSS). Would like to display the following code
 <paragraph>
 <content>Source                   A</content>
 </paragraph>
 <paragraph>
 <content>Color                       Yellow   </content>
 </paragraph>

as
Source                   A
Color                       Yellow
with space preserved between "Source" and "A", and space preserved between "Color" and "Yellow", but space (blank rows) removed between the rows. I am able to do either, for example wrapping the content nodes with pre nodes preserves space within the elements, and using

  { margin:0}

removes the blank space between the rows. However I haven't been able to accomplish both concomitantly. Played with various options such as whitespace:pre, xsl:preserve-space, and many other combinations without success.
Thanks

A: XSLT preserves whitespace. HTML just by default does not show it.
Use this CSS directive:
p {
  white-space: pre;
}

and XSLT like this:
<xsl:template match="paragraph">

<xsl:value-of select="content" />

</xsl:template>

redpajama_set_name: RedPajamaStackExchange


Think you're ready to own your own doggy day care? If so, it's important to know what to do when working with man's best friend for the first time. The work itself is very physically and mentally demanding, but the reward — both monetary and emotionally — is well worth the effort!
A good Camp owner is loving and understanding.
Unless you speak dog (which if you do, we suggest calling your local talk show, stat!), it can sometimes be difficult to understand what a dog needs or feels in a given moment. In order to work well with dogs, a Camp owner or counselor must be passionate, patient and understanding. Dogs are good judges of human character and can sense the love our Camp staff emits, making for a better experience all around.
To work with dogs, you must first be educated about them.
We've said it before, and we'll say it again — our golden rule when onboarding new franchisees or Camp staff members is that the individual "must love dogs." Dogs come in all shapes and sizes, and it's important to have a basic understanding of them in order to successfully work with and care for them. Knowing the basics is half the battle!
Customer service is a huge player in the game.
While we admit that a large portion of our day is spent romping and running about with the cutest dogs in town, that's not all it entails. Keep in mind that every dog that comes to Camp is loved and cared for deeply by their pet parents. A great Camp owner is able to communicate just as well with pet owners as he or she does with dogs. Likewise, we believe that "teamwork makes the dream work," which means that all Camp personnel should be able to band together and act as a Pack for the greater good of the animals.
Working with dogs may be a demanding field, but in the end, it's such a rewarding opportunity! Knowing what to do when working with dogs for the first time puts you at an advantage, both as a business owner and a dog lover.
So, what are you waiting for? To learn how you can join the Camp Bow Wow Pack, fill out the form below to receive your complimentary executive summary, or give us a call at (870) 600-2713.


Final quarter…..but we want more!
So we are in to October and the end of the year is rapidly approaching.
In September I paid a visit to Brands Hatch for the first time in about 20 years. A good mix of racing and some atrocious weather on the Sunday meant for an interesting weekend. Thanks for the questions and the banter. Sorry guys but I promise it won't be so long next time!
A good number of marshals helped out on the WRGB in North Wales. Unfortunately I was unable to go along and a shame we didn't have any local success to celebrate. Thanks to Pete Wilson for setting up the recruitment tent in Llandudno to seek new members. Recruitment is something we can all be involved in by talking to friends, colleagues and spectators. Spreading the word that we are volunteers and always looking for more people to join our ranks. If you would like to be involved please contact your local committee or Peter direct to offer to help at events or suggest events which would be suitable for us to consider attending. Derek Murphy has taken on the role of recruiting for rallies so if you can help with recruiting or looking after someone for a taster day please let him know.
The final Marshals Working Group of the year reviewed our activities regarding the PRC checks and responses. The overall consensus is that the checks are working and marshals are getting their PRCs signed correctly. We'll be checking other grades next year so make sure you sign up for training days to keep yours up to date. The Rally grading scheme has been adjusted and PRCs updated and going to print with the MSA. Next year we will be looking to tweak the grading scheme and PRC cards accordingly for Race and Speed grades. Training modules will also be updated and a few new ones created to keep everything in line. So 2020 will be one to aim for!
Now is the time of year when you get to have a louder voice than normal. At your local AGM of course! There is nothing to stop you contacting your local committees at any time but the AGM offers you the chance to hear what the committee has been doing for the last 12 months and ensuring that they have your interests at heart for the following year. I intend to put in an appearance at a few this year to offer my support and am open to questions – so look out for my surprise attendances!
This is also the time of year when you can renew for next year. Any new members at this time are also offered 15 months for the price of 12 months as limited activity at this end of the year – so welcome to you all. It's easy to renew on line and safe to do so.
We hope you recognise the benefits of being a member and the work we do to support you and thank you in advance for your renewal next year. (Direct debits will be taken on 4th January). However if you feel unable to rejoin we would really like to understand why. Maybe work or personal circumstances are difficult but do stay in touch even if you are not active on the bank. If there is something we haven't done or could do better – tell us please! We are your club, we are here for you but we can only do our best if you help us to understand.
Our request for applications for a brand manager role were well received and we will be putting a team together from all the applicants. Team leader to be determined and advised in due course with an overall remit for the team activities – watch this space!
Don't forget to check if you are this months prize winner!
As a mark of respect Barrie Williams will still appear as our President on the website and headed paper etc. until a suitable successor has been agreed.


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Rank calculations
Hello, I understand that the ranking system is based on a complex algorithm and your rank adjusts based on the ranking of the other players and your final position. However, once you become an expert it becomes extremely difficult to find good matches and if you want to play, you'll often end up playing against novices and beginners. You hardly get any points at all if you win, but if you loose it really socks it to your rank. I would like to suggest that the ranking algorithm be adjusted to ensure that you never loose more than 15% of your rank when you loose at expert or above. I've had a rank of 500 and it dropped down to 780 after one loss. At expert and above it's very difficult to find games against players you are matched with ... you are lucky to have an intermediate in the game. And losing hurts! Yes, you can create a game, but if you kick all the novices and beginners, the higher ranked players get impatient and just leave. Waiting forever for a "good match" isn't always realistic. But losing a quarter to half your rank for a single loss seems extreme. I think that at expert and above downward rank adjustments should be capped at 15%. That way we can continue to just play and have fun against everyone without being worried about huge rank swings. It's really not fair that at that level it takes 5 wins to recover from one loss. Each win is hard, made harder by the fact that many times people are just gunning for you because you have such a high rank. The solution of just playing against other high ranked players isn't always possible and we all just want to play! I did play chess for awhile and my rank didn't swing around this wildly. I understand that the system has been modified because there are multiple players and it depends on your final position. So changes happen a lot quicker, especially if you play a 6 person game. But I think capping downward adjustments, when upwards adjustments become minor and hard to come by, makes sense. Thanks.
Maxumus
You have to keep in mind that the 500 and 780 are placements against other people - not points. The only reason this changes so much is that there are so many people with very similar ranks, so losing seems to affect your rank a lot more than it actually does. In regards to taking multiple games to make up one loss, take the Clash Royale ranking system for example. A player who loses against someone ranked 300 points lower than them may lose 45 points, while they could have won only 15 against that person. Because winning against lower ranks is typically easier than someone your own rank, the amount of points gained is lower.
Christopher Balsamo
Totally agreed Dan. I love to play too, and the only way to play consistently is to play games filled with beginners and novices. Its next to impossible to maintain Grandmaster status. I've played 700 games, so there's no way 1 loss because a moron kamikaze novice guns for me should result in losing 300 ranking units!
I just stopped playing. Never even expected a like minded response. You know ... grandmasters aren't good at strategy, don't weigh the odds and take the risk needed to win. And that's on me. But ... I thought it was an impossible mission to become a grandmaster. I did it and was playing multiple games a day with ransoms. Maybe someone on support will read this ... but I am not going back to intermediate because people ganged up on me. I'm still a grandmaster and will leave it there.
Ransoms? I don't follow. I'm frequently at Grandmaster level and it bothers me when I drop back to Master, but i love to play.....so I take on all comers anyway!
I got to 216 and have a screenshot! How about you?
Sorry ... mistyped. Meant randoms ... But spellcheck changed it: it's not fun to be the one everyone else guns for. Have fun!
I lose one game and it literally takes me 5 wins to get back my rank. It shouldn't be about rank and I shouldn't care. But I worked really ... really ... hard to achieve grandmaster. And it means something to me.
I think I got into the 200s once. I'm around 700 now. I've played 693 games and won 280, and I only play 6 player games. It bothers me that I have such an enormous sample size and one bad result bc of a kamikaze when I'm in the 6th position and I don't cash cards until I collect 5....and it drops me 300+ places. What type of stats do you guys have?
True - I was ranked around 500... but once you reach Grandmaster level, it seems all the other players gang up on you lol
Next thing I know... I've lost 2 or 3 games and I'm ranked about 2,500 haha
Overall I've played almost 150 games and won over two thirds of them
Wow, winning 2/3 is huge. Are you playing 6 player games?
Yes, always 5/6 player games with Fixed Cards - the secret is putting the Turn Timer to 5/8 minutes... so you have plenty of time to think, which reduces the chance of you making bad moves lol


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Матеріал з Wikiquote
Larry Claxton Flynt (born November 1, 1942 – February 10, 2021) was an American publisher, the head of Larry Flynt Publications (LFP). LFP mainly produces pornographic content, including videos and magazines, most notably Hustler.
Quotes[ред.]
As I see it, the sole motivating factor behind the death penalty is vengeance, not justice, and I firmly believe that a government that forbids killing among its citizens should not be in the business of killing people itself.
Majority rule will only work if you're considering individual rights. You can't have five wolves and one sheep vote on what they want to have for supper
Carol LLoyd, Flynt's revenge, Salon, 1999-02-23.
My position has always been that there's two types of people opposed to pornography: those who don't know what they're talking about, and those who don't know what they're missing.
The Henry Rollins Show, episode 313.
My mother always told me that no matter how much you dislike a person, when you meet them face to face you will find characteristics about them that you like. Jerry Falwell was a perfect example of that. I hated everything he stood for, but after meeting him in person, years after the trial, Jerry Falwell and I became good friends. He would visit me in California and we would debate together on college campuses. I always appreciated his sincerity even though I knew what he was selling and he knew what I was selling.
Larry Flynt's Official Response to Jerry Falwell's Death. Pine Magazine (2007-05-16). Retrieved on 2009-05-12.
Larry Flynt: Don't Execute The Man Who Paralyzed Me (Guest Column). The Hollywood Reporter (2013-10-17). Retrieved on 2013-11-21.
About[ред.]
This is for Larry Flynt.
Kimora Lee Simmons after seeing a "party house", specifically after seeing an indoor hot tub with fur on the "rim" of it. Kimora: Life in the Fab Lane, episode Keepin' it Real Estate.
External links[ред.]
Отримано з https://en.wikiquote.org/w/index.php?title=Larry_Flynt&oldid=2949547
Businesspeople from the United States
Libertarians from the United States
Free speech activists
Anti-war activists
LGBT rights activists
Activists from the United States
Atheists from the United States
Autobiographers from the United States
United States presidential candidates, 1984
American publishers
People from Kentucky
Про Wikiquote


Colorado is a prime cannabis travel destination. Before the legalization of "Recreational Marijuana" in a variety of states, Americans had to pack a passport and cross the ocean to find their cannabis destination. Today, a select few states offer "Adult Use" marijuana, easing the burden of a big-budget international travel, to get the opportunity to spark up some of the most refined marijuana on the market. Travelers simply have to cross a few state lines, and maybe a few lakes and rivers to find their way to cannabis friendly destinations. These destinations are chock full of unique cultural experiences enhanced by marijuana.
There are some key things to keep in mind when venturing in to Colorado as your cannabis travel destination.
Travelers to Colorado should keep in mind that even though marijuana is legal, there are a few dos and don'ts when it comes to consumption. In Colorado, it is legal to purchase marijuana at "Recreational/Adult Use" dispensaries. However, it is not legal to spark up in the parking lot, in your car, in your hotel, rental property (unless it's 420 Friendly), street corners, etc. Wherever your cannabis destination, be sure to research their consumption laws prior to booking travel and accommodations.
In places like Colorado, platforms such as my420tours.com are a great resource. You're sure to find answers to your questions, as well as find and book 420 Friendly hotel accommodations.
There are also 420 Friendly house rentals, but once again, make note of the rules of the house. Often Colorado hotels and houses may not allow smoking flower, so if your vision for your trip to Colorado includes sparking up a joint with your travel companions, you should probably look elsewhere…like The Adagio Bud & Breakfast.
The Adagio's vintage charm and location are just two of the many assets it boasts for the cannabis traveler. At specifically 420 friendly places, you can smoke your choice of marijuana wherever you'd like – at the breakfast table, while enjoying a Wake & Bake Breakfast (not-infused), on the couches in the living room, while chatting and sharing stories with other guests, on the patio, while enjoying the Colorado outdoors.
Now that you're thinking about packing your bags and heading out on cannabis adventure, keep in mind, only local dispensaries can legally supply cannabis products. You may think Colorado has dispensary lined streets. Yes, it's true, Colorado does have more dispensaries (Medical Only and Recreational combined) than it has Starbucks and McDonald's combined. This makes exploring the vast cannabis industry's offerings exciting, and perhaps overwhelming. Do your research ahead of time so you can identify what dispensaries you would most like to visit!
What happens when you get to your cannabis destination? First things first, toss out any preconceived notions about what you think a marijuana dispensary would look like. Dispensaries come in all shapes and sizes. They are extremely clean, often very modern spaces, with ample staff to guide you through their product selections. But before you get to peruse the displays, you must show your ID prior to entering the separate purchasing area. Oh, and you must be at least 21 years of age.
Colorado Dispensary, Good Chemistry. Photo by Ellen Jaskol.
Dispensaries are where I hear my favorite cannabis tourist question, "So, I can buy marijuana here?!" It always makes me smile when the bud tender checking their ID says, in a normal volume, "You sure can." Remember, in Colorado cannabis has been around for long enough that for Coloradans, going to a dispensary is as normal as going to a pharmacy.
So, you have to decide where should you stop to make your purchase. With such an abundance of options, you should also look at the product menus to scope out what products you will want to purchase upon arrival.
Every dispensary has a wide variety of marijuana flower for sale at extremely reasonable prices. You'll find pre-rolled joints, blunts, a wide assortment of vape pens, and disposable vapes. You'll also find more specialized products such as concentrates with confusing names like "live resin" and "budder." Oh, and get ready to feast your eyes on every edible imaginable – including infused sparkling waters, tinctures, and topicals. How do you even know where to begin?
Cannabis industry professionals are passionate about marijuana, whether from a medicinal or recreational perspective. They have the answers you're looking for, and will guide you to the product that is right for you. Kyle Schwenn, Concentrate Buyer at Smoking Gun Apothecary, whose beautiful, pre-prohibition themed dispensary serves about 30% cannabis tourists, described his staff as tour guides. Although they hear a lot of the same questions from tourists, they never seem to tire of answering them.
If you have any questions at all regarding cannabis in general, ask! Colorado budtenders take the role of correcting misinformation very seriously. The basics of that misinformation generally center around public use, correct dosing, and transportation laws.
If your travels in Colorado take you north, to the quaint college town of Fort Collins, you'll find places like Infinite Wellness Center. Infinite Wellness Center is a highly awarded and recognized dispensary known as a pioneer in the Colorado cannabis industry. Since 2010, they have seen their share of regulatory hurdles, and overcame each of them to ensure that they can serve their customers. They serve locals, as well as tourists enjoying nearby Rocky Mountain National Park, and other Colorado lifestyle experiences such as camping and hiking.
Max Poling, of Infinite Wellness Center said, "It's not uncommon to see out of state IDs in Colorado." In a similar fashion to Denver dispensaries, customer education is paramount when interacting with all customers, especially tourists.
"Medical marijuana refugees" are Adult Use customers who book extended stays in Colorado to explore alternative treatments for ailments, without changing their residency to obtain a Medical Marijuana Card. If you are a medical marijuana refugee, seek out the dispensaries which have a medicinal focus. And make sure to go in the morning or other low traffic times so you can get all of your needs met by your budtender. Call ahead of time to figure out the best time to visit. The staff at Infinite Wellness is extremely passionate about helping people restore their quality of life, and they welcome customers with product questions to come in during the week, preferably in the early mornings, for detailed education. There are medicinally focused dispensaries throughout Colorado which love to serve medical patients and provide education and guidance needed. Take some time to seek out a location that appeals to you most!
Be sure you're clear on the consumption laws in your destination, be careful when using marijuana – it's a lot stronger than it used to be. And, NO, you cannot take it across state lines…or on a plane!
Even though cannabis tourist questions may be similar, each traveler is unique, coming from near and far to explore cannabis for their own personal reasons. Each dispensary goes above and beyond to educate each customer and will do the same for you.
When planning your trip, keep in mind that there are some factors to consider, both personally and legally. Do your own research. Not only will most of your questions be answered, but learning is part of the fun and excitement of experiencing legal marijuana. There are ample resources on the Internet so be sure you read up on local laws, products, proper dosing, and any other information you need to make informed decisions that will result in you having an incredible first experience into the world of legal marijuana.
NINA COMES TO YOU FROM THE HEART OF CANNABIS-LAND, DENVER, COLORADO. SHE'S A PASSIONATE INDUSTRY PROFESSIONAL, CONSUMER, MARIJUANA ADVOCATE. AND AUTHOR OF "UNICORNS AND DONUTS - THE ART OF CANNABIS SALES."