text:
Public sector to lead green push and save $62.5m a year
Deputy Prime Minister Teo Chee Hean.PHOTO: LIANHE ZAOBAO
Melissa Lin, The Straits Times
Singapore's biggest employer plans to slash its consumption of electricity and water as part of a nationwide "go green" plan unveiled yesterday.
By 2020, the public sector will use 15 per cent less electricity and 5 per cent less water compared with 2013 levels, according to the Public Sector Sustainability Plan 2017-2020 announced by Deputy Prime Minister Teo Chee Hean.
The temperature setting for thermostats in air-conditioned public-sector offices will be set higher, Mr Teo said.
Such steps could save $62.5 million a year, apart from being gentler on the environment.
For a start, premises will be greener. All new public-sector buildings will attain the highest Green Mark Platinum standard and existing buildings will aim for at least the Green Mark Gold standard for environmentally-friendly buildings.
Events and functions will be held in venues with at least a Green Mark Certified rating - the basic certification grade.
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The public sector will also buy more green electronics and paper products for its offices.
Food waste will be recycled in public-sector premises and a floating solar test-bed will be set up in Tengeh Reservoir, in Tuas.
The sector will also continue to invest in green technologies and seek innovative ways to harness renewable energy.
'TRANSFORM'
"This will help transform the way the public sector operates and set an example for the wider community to adopt sustainability as our way of life," added Mr Teo, the Coordinating Minister for National Security.
The public sector is Singapore's largest employer, comprising 16 ministries and 64 statutory boards, and about 145,000 officers.
From 2013 to 2015, the sector accounted for an average of 4 per cent of Singapore's total electricity consumption and 3 per cent of total water consumption.
Under the 2016 Paris Agreement, Singapore has committed to reduce emissions intensity by 36 per cent from 2005 levels by 2030.
Teo Chee HeanEnvironmentSingapore


This page displays sold house prices for Hill House Cottages in Reading.
Hill House Cottages in Hare Hatch, Reading consists predominantly of terraced houses. Properties on Hill House Cottages typically have values around £250,000 - £350,000, with larger terraced houses and townhouses valued at around £350,000.
Map showing Hill House Cottages in Reading.


text:
Phil's Friday Stories: Best series of 2013 gives McCartney shot gold
PA 2013 Outdoor Features
Phil Grove
Photos by Don Rich, Patty Morgan, Kathy Leister and Jim Spisak
A series to remember (and the medal will help as well)
At the Penn Relays Carnival, Courtney McCartney was on top of her game, unleashing a 45-foot, 3-inch effort that enabled her to remain as the state's No. 1 entering Friday's Class AAA shot put. However, her heave in late April doesn't hold a candle to the series the Selingrove sophomore put together in capturing state gold.
A 44-2.25 opener was followed by the first of three 45-plus heaves. McCartney's longest in round 5 measured 45-5.5 and was more than 2 ½ feet ahead of a field that included five athletes over 41-4.
"By far this was my best series of the year," she said. "I was just doing my peak, and it set me up good for today."
Averaging over 44-3 on six legal throws, the winner closed out the competition with a pair of 45-footers as several other top placers also hit their best marks as the event came to a close.
"Honestly, I was just hoping to do well this season," McCartney said. "I didn't think I was going to be state champ, but it happened."
Freshman Emily Stauffer of Cocalico backed up her indoor state title with the runner-up slot at Shippensburg at 42-11.25, while seniors April Krivoniak of Greater Latrobe and Jayne Corbett of Corry Area moved up to the next two spots with throws of T-PA#7 42-8.5 and 42-8, respectively.
Record Attempt Eludes PA's Top Vaulter
Rebekah Petty was looking to make a little history Friday in the Class AA pole vault. In the end, history got in the way of the Greenville junior achieving one of her main goals at Seth Grove Stadium.
The junior won state gold with a first-try clearance of 11 feet, 9 inches, a mark that fell short of the meet record of 12-7 that she wanted to break.
"It was a great experience, good and bad," Petty said. "I still won gold, and we still having another year to try to get back and beat the record. I guess when you are a state champ on your worst day, you can't complain."
As Pennsylvania's top-ranked vaulter, Petty had a large advantage on the field in season bests, with her 12-8 at the District 10 meet being 14 inches ahead of her closest competitor. Despite the unseasonably cold temperatures, the Greenville coaches were optimistic that she might be able to duplicate that performance for a second consecutive week.
"It was one of those things where with the tailwind, I was hoping that she would be able to get settled in," Greenville pole vault coach Justin Lewis said. "With all of the different delays that we had – we waited for a hurdler, and then there was the 25-minute delay for these technicalities – we never could get into a groove."
Following a proven routine, Petty was the last to enter the competition when she attempted and cleared 10-6. A pass of 11-0 moved her and four others to 11-6, where eventual runner-up Bre Manzolillo of Schuylkill Valley jumped into the lead with her first-attempt clearance and Petty stayed alive on her second try.
The competition then ground to a halt as the next height for the remaining duo was debated and discussed – continue to add 6 inches and go to 12-0 or cut the increment in half for attempts at 11-9.
"What they have done in the past in both verticals, when they get down to two to three jumpers left, is they have split the increment," meet referee Jack Hedlund said of moving the bar up only 3 inches. "That's something that they have done down here for years, it's in the terms and conditions (of the meet)."
In addition to creating a delay in the vaulting, the debate over the next height broke up a planned, speedy assault on the record set three years ago.
"The mindset she had going into (11-9), she just wanted to clear the height," Lewis said of Petty, who was over on her first attempt for the win. "She was pretty upset. All it's done is create a little fuel in the belly to give her some motivation to go higher and work a little harder."
He noted that the junior, who also won a District 10 title in the 100 dash but scratched out of it for Shippensburg, had become faster down the runway as their workouts began to taper for the state final. Add in the gusty tailwind, and Petty had their hands full with the conditions.
"I was definitely under the whole day," she said of her takeoff point being too close to the pit. "That was really not good, that did not help the situation. I was getting yanked by the pole a bit."
Ryan Clips Sophomore for Third Long Jump Gold
One is a senior who already counted two state gold medals in the long jump amongst her prized possessions. The other is a sophomore who was looking for that breakthrough moment.
At seemingly different places in their high school athletic careers, Chambersburg's Marshay Ryan and Hempfield Area's Maddie Holmberg nevertheless covered almost the exact same chunk of real estate Friday in the Class AAA long jump.
In the narrowest margin of victory in the 2013 PIAA meet, Ryan collected her third consecutive event on the basis of her second-best jump as Ryan and Holmberg both were credited with state-leading jumps of 19 feet, 10 inches. The tie was broken on the basis of their second-best effort, with Ryan getting the nod by just a half-inch.
"This was probably the closest I've ever had to deal with coming down to the last everything, give-it-all-you've-got type of situation," Ryan said. "We were (almost at) exactly the same spot."
Ryan struck first as she went 19-10 in round 2, but Holmberg created the logjam in round 3. The Hempfield Area standout, whose jump is a PR by almost a foot, grabbed the lead in the tiebreak at 19-4.5 in round 5 before Ryan closed out the meet and claimed the gold with a 19-5 mark.
"I didn't know who had it until the guy came over to tell us our places and go line up," the winner said. "We really didn't know who had the second-best jump. Whew. It was a close one. More props to her because she definitely did really well. It was fun to compete like that."
More Articles In Series
Watch Videos of Courtney McCartney
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Boys 1500 Finals Section 1 - 8-10 YO VA Showcase (AAU) Jan 19, 2020
Girls 1500 Finals Section 1 - 8-10 YO VA Showcase (AAU) Jan 19, 2020
Courtney's Athlete Profile
Courtney McCartney
Tagged Meets
PIAA T&F State Championships
Survey: More Pennsylvania school districts require payment for playing sports Nov 20, 2013
Anonymous Donor Gifts Middle School $500K for Track Nov 11, 2013
Wellington Zaza lives, breathes and dreams track. Aug 7, 2013
Williams 3rd at US bobsled push championships | More Sports | Kentucky.com Aug 2, 2013
Every day, Deworski Odom gives back to the the sport and school that changed his life Aug 1, 2013
Tweets by PennTrackXC
MileSplit Pennsylvania Editor: Dan Beck, daniel.beck@flosports.tv

redpajama_set_name: RedPajamaCommonCrawl


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redpajama_set_name: RedPajamaGithub


Last weekend we hosted our very first Autumn inspired wreath making class at Batch with San Francisco based wreath maker, Maggie Philbin!
We invited 12 women in the Batch community to our showroom to mingle and craft beautiful wreaths for their homes just in time for the holiday season. We had so much fun learning how to style wreaths, that we wanted to share the inspiration with you so you too can try this DIY project at home!
Wreaths are quintessential for the holidays, and can be used in a variety of ways – like on top of your table with a candle as the centerpiece, or hanging on your front door, and given as a gift to a loved one.
Be sure to check out our step-by-step process below on how to create your very own fall wreath, and sign up for our newsletter to stay up to date about our workshop calendar so you can join us at our next event!


Better Prep makes eating healthy easy! We work directly with nutritionists and holistic practitioners to create restaurant quality meal prep that's anything but boring. If you're looking for delicious grab and go meals to get you through your busy week then we've got you covered. We offer inclusive meal prep solutions for those with special dietary requirements as well as a those looking to overhaul their health and nutrition.
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To see what's on the menu, click the link below!
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At Better Prep we invite all health and wellness professionals to utilize our services to provide an all encompassing experience for their clients. By taking the guesswork out of the kitchen, we make it easier to improve client compliance and increase success rates. We work with registered dieticians and holistic practitioners to create meal plans that you can feel confident offering to your clients. Spend less time writing plans and more time working on your practice. To inquire about how Better Prep can work for you, click the link below.
Hosting a luncheon or dinner party should be fun and give you time to catch up with old friends, not give you anxiety and a mountain of dishes to do. Rather than pour hours into making an elaborate feast, pour yourself a glass of wine and let Better Prep take care of the rest. You can even take the credit, we'll never tell!
Your event is as unique as you are which is why every menu is made to fit each event's taste, style, and budget. With dishes starting as low as $10 per person, there's even room for dessert.
Offering inclusive meals is so on trend right now. If you're interested in carrying Better Prep at your retail location we encourage you to hit us up, we'd love to hear from you! Send us a quick email letting us know who you are and include a link to your website or social media. Getting to know your business and values is important to us so we can make sure that we're a match made in heaven.


text:
\section{Introduction and background}\label{sec:intro}

Gravitational disc Instability (GI) theory for giant planet formation
\citep[e.g.,][]{Kuiper51,CameronEtal82,Boss97,Boss98} posits that
gravitational instability of the disc leads to formation of self-gravitating
gas fragments that later contract into present day planets. This view has been
strongly challenged in the last decade since it was shown that protoplanetary
discs do not cool rapidly enough to fragment onto gas clumps inside several
tens to a hundred AU
\citep{Gammie01,MayerEtal04,Rice05,Rafikov05,DurisenEtal07,SW08,Meru10}. This
would preclude the model from explaining most of the giant planets, since most
are detected at separations much smaller than this, all the way down to $\sim
0.05$~AU \citep[e.g.,][]{MQ95}.

However, \cite{Nayakshin10c} argued that giant planets could be born far out
but then migrate inward arbitrarily close to the parent star due to
gravitational torques of the disc
\citep[e.g.,][]{LinPap79,GoldreichTremaine80}. Crucially, GI planets are born
as fluffy (gas density $\rho \sim 10^{-13}$~g/cm$^3$) and cold (T$\sim 100$~K)
molecular gas fragments. In order to become dense Jupiter-like giant planets,
they must first contract to $T\lower.5ex\hbox{\gtsima} 2500$~K at which point a rapid dynamical
collapse occurs \citep[e.g.,][]{Bodenheimer74}. Tantalisingly, if the planets
migrate inward more rapidly than they contract, then they may be tidally
disrupted. The disruption leaves behind a rocky/icy core if grains inside the
planet managed to grow and sediment down into a core rapidly enough
\citep{McCreaWilliams65,BoleyEtal10}.  This scheme, named "Tidal Downsizing"
by \cite{Nayakshin10c}, may {\it potentially} explain any mass planets at
arbitrary separation from the host star within a single framework
\citep{ForganRice13b}.

Here we focus on giant gas planets within the GI/TD framework
specifically. While the rapid \citep[migration time $t_{\rm mig} \sim 10^4$
  years, see, e.g.,][]{BaruteauEtal11,Nayakshin10c} inward migration and tidal
disruption process of gas fragments is crucial to TD as a way of accounting
for terrestrial-like planets, this processes challenges the formation of the
gas giants themselves \citep{ZhuEtal12a}.  Firstly, since radiative
contraction time of even the Solar metallicity clouds is quite long
\citep[$\sim 10^6$ years, see, e.g.,][]{BodenheimerEtal80,VazanHelled12}, the
disruption process appears to be too efficient (see \S \ref{sec:under}), so it
is hard to explain how {\em any} close-in giant planets survive. Secondly,
radiative contraction of planets is slowed down at higher grain opacities
\citep{HB11}. Thus, tidal disruption in metal-rich environments should be even
more efficient. This would seem to contradict the well known fact that giant
planets are more abundant at higher metallicities
\citep[e.g.,][]{FischerValenti05,WangFischer14}. If this is true then close-in
giant planets must form via Core Accretion rather than GI \citep[see,
  e.g.,][]{Boley09}.

{There may appear to exist a simple solution to the conundrum of too long a
  radiative cooling time for GI clumps: a strongly decreased grain opacity due
  to grain growth. \cite{HB11} find that in models that include grain growth,
  opacity decrease cuts the planet contraction time scale to as short as $\sim
  10^3$ years. We do not favour this solution for two reasons.  Firstly, this
  would predict that protoplanetary discs of low metallicity stars would be
  ideal sites for gas giant planet formation. Instead, \cite{FischerValenti05}
  shows that low metallicity stars are the least likely to host a giant
  planet. Secondly, models of \cite{HB11} do not include collisional
  fragmentation of dust grain aggregates which are found to occur at
  relatively modest velocities in laboratory experiments
  \citep[e.g.,][]{BlumWurm08}. \cite{DD05} consider grain growth and opacity
  in protoplanetary discs of T Tauri stars. They find that models that neglect
  grain growth deplete the small grain population by a factor of a million in
  a few thousand years (see their figure 3), reducing the dust opacity
  significantly. However, the spectra of T Tauri sources clearly require a
  copious presence of small dust grains even at ages of a few Million
  years. To explain this, \cite{DD05} argue that high speed dust aggregate
  fragmenting collision must be also taken into account. This then results in
  a quasi steady-state for dust distribution in which the smallest grain
  abundance is suppressed only mildly even after about a Million years of
  grain growth (see their Fig. 7). For these two (observationally backed up)
  reasons, we discount the possibility that grain opacity in GI fragments is
  much lower than the interstellar one, although we do explore some grain
  opacity reduction below.

The solution to the too-slow-cooling conundrum that is proposed here is based
on another unexpected effect that grains have on GI clumps.}
\cite{NayakshinEtal14a} investigated the structure of the gas ``atmosphere''
around the massive solid core built within the TD gas fragments by grain
settling. Similar to CA theory, it was found that there exists a critical core
mass, $M_{\rm crit}$, beyond which the atmosphere may become self-gravitating
and too massive to be in hydrostatic balance
\citep{Mizuno80,Stevenson82}. Following CA arguments, the authors argued that
the atmosphere collapse sets off a phase of a rapid gas accretion onto the
dense core.  This may initiate a hydrodynamical collapse (termed Core-Assisted
Gas Capture instability; CAGS hereafter) of the whole gas fragment {\it
  before} a core-less fragment of same configuration would have collapsed,
thus providing a second and an unexplored way for the formation of giant
planets in the TD picture.

The original goal of this project was to follow up the work of
\cite{NayakshinEtal14a} with a hydrodynamical rather than hydrostatic code,
and to model the whole gas clump rather than only its centre. In addition, we
included external large grain deposition onto the planet, the so-called
"pebble accretion" \citep[e.g.,][]{JohansenLacerda10,OrmelKlahr10} of grains
on massive bodies embedded in protoplanetary discs. In doing so we discovered
that planets accreting grains can collapse more rapidly than those of fixed
metallicity. It turned out that this effect has nothing to do with formation
of the core directly, and instead originates in the fact that grain accretion
on a planet in itself is a form of cooling. Pending detailed analysis below,
this last statement can be understood qualitatively as follows.

Consider the total energy of the pre-collapse planet of mass $M_{\rm p}$ and
radius $R_{\rm p}$, $E_{\rm tot} \sim - GM_{\rm p}^2/R_{\rm p}$. It evolves in
time according to
\begin{equation}
{d E_{\rm tot}\over dt} = - L_{\rm rad} - {G M_{\rm p} \dot M_z\over R_{\rm p}}\;,
\label{equation1}
\end{equation}
where $L_{\rm rad}$ is the radiative luminosity of the planet, and the last
term on the right is the change in the gravitational potential energy of the
planet, $E_{\rm grav}$, due to grain accretion on it at the rate $\dot
M_z$. In the constant metallicity case (no pebble accretion) that was so far
studied in literature \citep{HB11}, the second term on the right is absent, so
that radiation is the only way for the planet to loose excess energy and
contract towards H$_2$ collapse. Increasing metallicity of the planet
increases dust opacity and decreases $L_{\rm rad}$, hence slowing down its
contraction. However, if $\dot M_z > 0$, then the planet "cools" due to
addition of metals, since $E_{\rm tot}$ becomes more negative. Deposition of
pebbles into a planet from outside may hence speed up rather than delay giant
planet formation.

The goal of this paper is to study the contraction of pre-collapse giant
planets due to grain accretion in detail. To not over-complicate this first
study by having to also study GAGC, we turn off grain growth in the planet,
with the result that grain sedimentation is negligible, and no core forms in
the planet's centre. The more general case is to be studied in a near future
paper.  We use a 1D spherically symmetric radiation hydrodynamics code as well
as analytic arguments to understand the planet's response to pebble deposition.

The paper is structured as follows. In \S \ref{sec:prelim}, the cooling
challenge of GI-born fragments is described, and the rate of pebble accretion
from the surrounding protoplanetary disc is estimated. In \S \ref{sec:methods}
and in Appendix \ref{appendix1}, numerical methods employed here are
presented.  \S \ref{sec:intro_runs} compares the evolution of planets enriched
by metals either at birth or by pebble accretion, and \S \ref{sec:theory}
outlines an analytical toy model that helps to understand why metal accretion
accelerates planet contraction. The analytical model is compared with
grain-dominated contraction of numerically integrated polytropic clouds with
fixed specific heats ratios ($\gamma$), as well as a more realistic molecular
planet in \S \ref{sec:real}. The conditions under which pebble accretion
dominates planet contraction are delineated in \S \ref{sec:grain_dom}. A
discussion is given in \S \ref{sec:discussion}.

\section{Preliminaries}\label{sec:prelim}

\subsection{The cooling challenge}\label{sec:under}

The properties of the first gas condensations in a self-gravitating disc
should be similar \citep{Nayakshin10a} to that of the ``first cores''
\citep{Larson69} in star formation, see also
\cite{Bodenheimer74,BodenheimerEtal80}.  The central temperature of these may
be as low as $\lower.5ex\hbox{\ltsima} 100$~K, Hydrogen is molecular, and the mass of the
fragment is of the order of a Jupiter mass to perhaps $10 \mj$
\citep{BoleyEtal10,ForganRice11,TsukamotoEtal14}.  If the fragments cool
sufficiently rapidly, reaching the central temperature of $\sim 2500$~K {\em
  before} they are tidally disrupted, then dissociation of molecular hydrogen
occurs.  Since post-collapse fragments are $\sim 3-5$ orders of magnitude
denser than pre-collapse ones, post-collapse fragments are much more likely to
survive as giant planets. H$_2$ collapse is hence a necessary step to
formation of a gas giant planet.

However, radiative cooling times of isolated Jupiter-mass pre-collapse
fragments are $t_{\rm rad}\sim 10^6$ years \citep[e.g.,][]{BodenheimerEtal80},
far longer than the disc migration times, $t_{\rm mig} \sim 10^4$ years
\citep[e.g.,][]{BaruteauEtal11,Nayakshin10c}. Figure \ref{fig:tcool} shows the
radiative cooling time of the pre-collapse planets, defined as
\begin{equation}
t_{\rm rad} = -{E_{\rm tot}\over 2 L}\;,
\label{trad}
\end{equation}
where $E_{\rm tot}$ is the total energy of the fragment, and $L$ is the
luminosity of the planet. The factor $2$ in the denominator is introduced
empirically to better match the numerical calculations of planet contraction
 (all the way to H$_2$ dissociation) reported below.

\begin{figure}
\psfig{file=tcool.eps,width=0.5\textwidth,angle=0}
  \caption{Radiative cooling times of pre-collapse planets of four different
    masses composed of a Solar mix of H/He and metals, as labelled on the
    figure, versus the central temperature of the planet, $T_{\rm c}$. Note
    that low mass planets are the least capable of contracting rapidly, and
    that the slowest evolution always occurs at $T_{\rm c}\lower.5ex\hbox{\gtsima} 1000$~K.
    Interstellar dust opacity is assumed for this figure.}
 \label{fig:tcool}
\end{figure}

In accord with previous results \citep{BodenheimerEtal80,HB11}, figure
\ref{fig:tcool} shows that more massive planets cool more rapidly. Also note
that, for all planetary masses, the initial cooling phase at $T_{\rm c}$ of a
few hundred K is much more rapid when the one at $T_{\rm c}\lower.5ex\hbox{\gtsima}
1000$~K. This is because the modulus of the total energy of the planet,
$|E_{\rm tot}|$, increases, whereas the luminosity $L(T_{\rm c})$ usually
drops with increasing $T_{\rm c}$ since the planet contracts and opacity in
the atmosphere rises. This implies that the cooling "bottle neck" for planets
of any mass is always at $T_{\rm c} \lower.5ex\hbox{\gtsima} 1000$~K, that is, the planets are
expected to spend more time contracting from $T_{\rm c}\sim 1000$~K to H$_2$
dissociation ($T_{\rm c}\sim 2200$~K or so, for most of our runs below) than
they spend contracting from their initial state towards $T_{\rm c}\sim
1000$~K.

Based on figure \ref{fig:tcool}, the expected outcome of GI fragment
contraction, while it also migrates inward rapidly, is that the fragment is
tidally disrupted before it collapses \citep{BoleyEtal10,Nayakshin10c}.  For
example, for $M_{\rm p} = 2\mj$, it takes more than $10^5$ years for this
collapse to take place. Furthermore, calculations by
\cite{CameronEtal82,VazanHelled12} show that irradiation from the parent star
and the surrounding disc slows the contraction of the fragments further, and
may in fact even reverse the heat flow from the planet. In this case the
planet puffs up rather than contracts with time. In the presence of tidal
shear from the parent star, this is clearly a receipt for destruction rather
than formation of a giant planet-to-be.

\subsection{The role of metals}\label{sec:metal_role}

Giant planets are observed to be over-abundant in metals
by a factor of a few to ten in the Solar System and beyond
\citep{MillerFortney11}. \cite{HB11} have shown that contraction of
pre-collapse giant planets is slowed down further at high metallicites if dust
opacity is proportional to the metallicity of the gas.

In the context of GI/TD models, we see two principal modes of metal enrichment
of pre-collapse fragments. Firstly, fragments can be enriched by solids at
birth by efficient aerodynamic capturing of grains into spiral arms of the
gravitationally unstable disc before it collapses onto fragments
\citep[e.g.,][]{BoleyEtal11a}. In this model, therefore, pre-collapse planets
are born more metal rich than the surrounding disc. For simplicity, we then
assume that the metallicity of such planets remain constant with
time. Secondly, metals can be gained by accretion from the disc, as we explain
now.

\subsection{Accretion of metals from the disc}\label{sec:mdot_grain}

\cite{JohansenLacerda10} and \cite{OrmelKlahr10} pointed out that "pebbles",
that is small solid bodies of $\sim 10$~cm-size can accrete efficiently on
planetesimals and rocky protoplanets embedded in a disc. This can potentially
speed up assembly of massive solid cores at tens of AU distances from the host
star, where core accretion via planetesimal capture is inefficient, and solve
the problem of too long core assembly time scale of CA theory
\citep[e.g.,][]{HB14} for planets such as Neptune and Uranus.

In this picture, the accretor follows a Keplerian circular orbit of radius
$a_p$ around the star of mass $M_*$, whereas the gas in the disc moves at a
velocity slightly smaller than the local Keplerian, and there is also the
local Keplerian shear, so that there is always gas streaming past the
accretor. The gas itself does not accrete onto the accretor since the gravity
of the latter is insufficient to overcome the pressure gradient force of the
gas. The small grains, on the other hand, are not supported against accretion
onto the protoplanet by a pressure gradient.

A similar situation may hold around a much more massive molecular gas
fragment.  \cite{NayakshinCha13} show that radiative pre-heating of the
surrounding disc material by the radiation from a young embedded protoplanet
is important in deterring gas accretion onto relatively low mass
proto-planets, $M_{\rm p}\lower.5ex\hbox{\ltsima} 6\mj$. Such planets are found to build a
hydrostatic-like atmosphere around themselves. The gas pressure gradient
around them is large enough to prevent accretion of gas from the
disc. Fragments with initial masses $M_{\rm p}\lower.5ex\hbox{\ltsima} 6\mj$ are found to
migrate inward rapidly at more or less constant fragment mass until they are
tidally challenged and eventually destroyed at $R\sim 20-30$~AU. More massive
protoplanets instead accrete gas rapidly, becoming proto brown dwarfs and
stalling at about their initial locations ($R\sim 80$~AU). These results imply
that, as far as planet formation is concerned, we need to limit our attention
to relatively low mass gas fragments of a few Jupiter masses as more massive
fragments may form low mass stars, and eventually turn the system into a
stellar binary, a situation that is well outside the scope of this paper.

\cite{LambrechtsJ12} recently presented analytical estimates and numerical
simulations of pebble accretion on large planetesimals and solid cores. We
rescale their results to the case of a pre-collapse giant planet embedded in a
protoplanetary disc.  Due to the substantial mass of the planet (compared to
planetesimals or solid cores), the accretion of pebbles on it is always in the
"Hill's regime", when pebbles are accreted from the whole of the Hill's
radius, $R_{\rm H} = a_p (M_{\rm p}/3M_*)^{1/3}$, where $a_p$ is the
planet-star separation, and $M_*$ is the mass of the host star. The maximum
rate, $\dot M_{\rm z}$, at which the grain particles can be accreted by the
planet in the this regime is \citep[see eq. 38 in ][]{LambrechtsJ12}
\begin{equation}
\max \dot M_z = \dot M_{\rm H} \approx 2 R_{\rm H} \Sigma_{\rm dust} v_{\rm H}\;,
\label{mdot_hill}
\end{equation}
where $\Sigma_{\rm dust}$ is the pebbles surface density in the
protoplanetary disc, Hill's velocity is $v_{\rm H} = \Omega_p R_{\rm H}$, and
$\Omega_p$ is the Keplerian angular speed at the location of the planet. In
reality only grains intermediately strongly coupled to the gas, such that
dimensionless stopping time, $\tau_f \equiv t_f \Omega_p$, $0.1\lower.5ex\hbox{\ltsima} \tau_f
\lower.5ex\hbox{\ltsima} 1$ are accreted as efficiently as equation \ref{mdot_hill}
suggests. The physical size of the particles in the strongly coupled
  regime, that is ``pebbles'' in our definition, depends on the protostellar
  disc properties and the radial distance from the star, $R$. For the Minimum
  Mass Solar Nebula disc, \cite{LambrechtsJ12} show that particles of size $a
  \sim \hbox{a few cm}\;\times R_{1}^{-3/2}$ are in the pebble regime, where
  $R_1 = R/(10$~AU). Thus, at the outer disc regions, $R\sim 100$~AU, pebble
  regime grains are actually about 1 mm or so.

Let us define the planet metallicity doubling time scale $t_{\rm z}$ as
\begin{equation}
{1\over t_{\rm z}} \equiv {\dot M_{\rm z} \over M_{\rm z}(0)}\;,
\label{tz0}
\end{equation}
where $M_z(0) \equiv z_0 M_{\rm p}$ is the initial mass of metals in the
planet. Let the fraction of mass in the  pebble regime, that is, in the
maximum efficiency accretion regime (compared to the total mass in grains in
the disc at radius $a_p$) be $f_{\rm max}< 1$. Further, $\Sigma_{\rm dust} =
z_0 \Sigma \sim z_0 M_{\rm disc}/(\pi a_p^2)$, where $\Sigma$ is the total
(dust plus gas) surface density of the disc, $M_{\rm disc}$ is the disc mass
at radius $a_p$, and we assumed that the disc metallicity is equal to the
initial metallicity of the planet, $z_0$. The end result is,
\begin{equation}
t_{\rm z} \approx {1\over 2 f_{\rm max}} {M_{\rm p}^{1/3} M_*^{2/3} \over
  M_{\rm disc}} {2\pi \over \Omega_p}\;.
\label{tz2}
\end{equation}
Now, in the early massive protoplanetary disc stage that is of interest here, the
disc can be as massive as $0.1 M_*$ or more. Picking this value for $M_{\rm disc}$ and
$M_{\rm p} = 1 \mj$, we then have
\begin{equation}
t_{\rm z} \sim 10^3 \hbox{ years } {1\over 2 f_{\rm max}} {\left(a_p\over 100
  AU\right)}^{3/2}\;.
\label{tz3}
\end{equation}
This shows that if the population of large grains is significant, e.g.,
$f_{\rm max}\lower.5ex\hbox{\gtsima} 0.1$, then the time scale to double the initial metal
content of the gas fragment is comparable or shorter than the typical
migration time, $t_{\rm mig}\sim 10^{4}$~years \citep{Nayakshin10c}. Tidal
Downsizing planets may then be non-trivially over-abundant in metals by the
time they migrate into the inner few AU of the protoplanetary disc region.

Clearly, $\dot M_{\rm z}$ and $t_{\rm z}$ are functions of the disc
properties, of the planet's location within the disc. Further, the disc itself
may be influenced by the interaction with the planet. For now we explore the
case of a fixed $t_{\rm z}$, in which the planet is loaded by pebbles (metals)
from outside at a constant rate as given by equation \ref{tz0}. The value of
$t_{\rm z}$ is varied in a broad range to study the parameter space.

\section{Numerical methods}\label{sec:methods}

The code used here is a spherically symmetric Lagrangian hydrodynamics code
first described in \cite{Nayakshin10a}, expanded and updated since then as
detailed in \cite{Nayakshin10b,Nayakshin11b,Nayakshin14b}.  Here we actually
simplify the dust-gas interactions module of the code to expose the
metal-loading effect most clearly. The simplified set of equations permits a
comparison with analytical solutions, which serves as a check of both the code
and our physical intuition. In the papers cited just above, the focus was on
formation of dense metal cores inside the fragment, and hence the relative
dynamics of gas and pebbles within the fragment was important and modelled by
two-fluid equations with aerodynamical gas force coupling the two species. In
this paper, we turn off grain growth and vaporisation physics, assuming that
grains are always "small", setting $a=1 \mu$m. In practice this means that
there is no relative motion of gas and grains and hence our equations reduce
to the standard one-fluid gas-dynamical equations. Physically, this limit
corresponds to the case when grains deposited into the outer reaches of the
planet either do not grow sufficiently rapidly or get vaporised quickly if the
fragment is too hot (e.g., water ice is vaporised already at $T\sim
150$~K). The grains can however be mixed in with the gas throughout the cloud
quickly by convection and turbulence
\citep[e.g.,][]{HelledEtal08,Nayakshin11b,HB11}, so that the metallicity of
the planet (related to the grain to gas mass ratio) is set to be uniform
inside the planet at all times. The more complicated situation, where a
relative gas-grain motion does occur, is of course of a significant interest
as well, but, due to a considerably expanded parameter space in that case
(e.g., has the core formed or not, and what is the chemical composition of
that core?) it is to be presented in the near future elsewhere. We emphasise
that the ``metal loading'' effect presented here exists when the grains are
allowed to sediment as well; it is however not possible to study that
analytically since grains are redistributed within the planet in a complicated
way.

Following \cite{HB11}, we make a reasonable assumption that dust opacity in
the fragment is directly proportional to the metallicity of the gas, $z$. The
opacity $\kappa(\rho, T)$ is then given by
\begin{equation}
\kappa(\rho, T) = f_{\rm op} \kappa_0(\rho, T) {z \over z_\odot}\;,
\label{kappa0}
\end{equation}
where $\kappa_0(\rho, T)$ are the interstellar gas plus dust opacities from
\cite{ZhuEtal09} which assume Solar metallicity, $z_\odot$, and $f_{\rm
  op}=$~const~$\le 1$ is a positive constant, set to 0.1 everywhere in this
paper, to account for possible opacity reduction due to grain growth. The main
conclusions of our paper are unchanged irrespectively of the value of $f_{\rm
  op}$, except that the parameter space where metal loading dominates as a
cooling process of course does depend on $f_{\rm op}$, as described below in
\S 7.

The full set of equations being solved for numerical experiments in this paper
is presented in the Appendix. The initial conditions are polytropic spheres of
a given central temperature $T_{\rm c}$, metallicity (usually Solar
metallicity), and total mass $M_{\rm p}$.

\section{The metal loading "paradox"}\label{sec:intro_runs}

Figure \ref{fig:exp1} shows contraction calculations for a planet of $M_{\rm
  p} = 4 \mj$ masses, with grain opacity reduced by a factor of $10$,
performed under two different assumptions about the planet's grain
content. The left hand panels show the cases of constant planet metallicity
(enrichment at birth model), where $z = 0.5, 1$ and 2 times the Solar
metallicity.  The right hand panels show the same calculation but for the
planets all starting with the Solar grain abundance at $t=0$ and then
metal-loaded by pebble deposition at five different (constant) rates as
labelled on the figure. In particular, the curves are computed for metal
loading times ranging from $t_z = 250$~years to $t_z = 4000$~years, in steps
of a factor of 2.  Note that the shortest $t_z$ values are unlikely to be
reached even in the inner disc regions \citep[unless radial drift of pebbles,
  see][significantly increases the local pebble abundance]{LJ14}. However,
such cases expose the metal loading effects clearly. In a follow up paper
(Nayakshin 2014, submitted), the pebble accretion rate is calculated
self-consistently from the surrounding disc properties, which is modelled in
some detail similarly to \cite{NayakshinLodato12}.

The constant metallicity cases, panels (a) and (b), are in a qualitative
agreement with results of \cite{HB10}. The time taken by the planet to
contract to the point of collapse increases with increasing $z$, somewhat less
rapidly than a linear proportion.

Panels (c) and (d) show a completely different evolution, however. The more
rapidly the metals are added to the planet, the more rapidly it contracts and
eventually collapses via H$_2$ dissociation. In the most rapid metal-loading
case, $t_z = 250$~years, the collapse time scale is shortened by a factor of
almost four compared with the Solar metallicity case. For this particular
case, the metallicity at collapse is $z\approx 0.12$, eight times larger than
the starting value, $z_0 = 0.015$. Based on the left hand side panels, one
would expect that collapse time scale for such a high metallicity fragment
would be a factor of $\sim 5$ longer than the solar metallicity case, not
shorter. There is thus over an order of magnitude difference in the collapse
time scale for this particular case between the enrichment at birth and a
gradual metal deposition models.

\begin{figure*}
\begin{minipage}{3.2in}
\psfig{file=sn_m4_fixedZ.eps,width=0.99\textwidth,angle=0}
\end{minipage}
\begin{minipage}{3.2in}
\psfig{file=sn_m4_Zdot.eps,width=0.99\textwidth,angle=0}
\end{minipage}
  \caption{Top left panel (a): evolution of the central temperature versus
    time for constant metallicity planets of $4 \mj$ masses. The bottom left
    panel (b) shows the (constant in time) metallicity, $z$, of the
    planets. Right panels (c) and (d): same but for planets loaded by grains
    at constant rates parameterised by the metallicity doubling time
    $t_z$. Note that the faster the metals are added to the planet, the
    quicker it collapses.}
 \label{fig:exp1}
\end{figure*}

Figure \ref{fig:exp2} shows another numerical experiment that helps to shed
more light on the situation. The planets here are started exactly as the ones
presented in figures 2c and 2d, with the same choices for the metal doubling
time, but grain accretion is termined when the central temperature reaches
$T_{\rm c} =700$~K. The exact numerical value of the termination temperature
is not important. Figure \ref{fig:exp2} shows that once grain accretion stops,
contraction of the cloud continues {\it at a slower} rate than that for a
non-metal-polluted planet, i.e., one recovers the main result of the fixed
metallicity cases shown in figure \ref{fig:exp1}a and \ref{fig:exp1}b. For
example, for the case of the most rapid metal loading, $t_z = 250$~years, the
fragment collapsed at less than 2,000 years in figure \ref{fig:exp1}(a), but
collapses only at $t\approx 9,000$~years when grain accretion is discontinued.

\begin{figure}
\psfig{file=sn_m4_Zdot_T700.eps,width=0.5\textwidth,angle=0}
  \caption{Same as the right hand side panels of figure \ref{fig:exp1} but
    grain accretion is (arbitrarily) turned off once the central temperature
    of 700 K is reached. Note that the faster the metals are loaded, the
    faster the fragments contract, but once grain accretion stops the
    situation reverses; the more metals are in the planet, the slower it
    contracts.}
 \label{fig:exp2}
\end{figure}

These results indicate that pebble deposition into a pre-collapse planet
produces two opposing effects, one delaying contraction of the planet, and the
other speeding it up.  The former effect is due to the increase in the dust
opacity which slows down radiative contraction of the fragment. In our opacity
model, this effect depends on the instantaneous amount of dust in the planet,
that is, its metallicity. The latter effect however depends not on the amount
of dust in the planet but on the rate of grain deposition into the planet, as
hinted in the Introduction.

\section{A toy model}\label{sec:theory}

To understand how grain accretion can accelerate collapse of a planet we turn
to a simple analytical model in which the planet is modelled as a polytropic
sphere of adiabatic index $\gamma = 1 + 1/n$. The equation of state (EOS) of
the gas in the sphere is
\begin{equation}
P = K \rho^{\gamma}\;,
\label{eos0}
\end{equation}
where $P$ and $\rho$ and the total (gas plus metals) pressure and density,
respectively, and $K$ is a constant throughout all of the planet. Constancy of
$K$ is assumed to be maintained by convection that is known to be the main
energy transfer mechanism within H$_2$ dominated planets
\citep[e.g.,][]{HS08}.

The theory is only approximate, since there is no single value of $\gamma$
that could describe a planet dominated by molecular hydrogen exactly. For gas
dominated by molecular hydrogen, $\gamma$ varies from $\gamma = 5/3$ at
$T\lower.5ex\hbox{\ltsima} 100$~K to $\gamma = 7/5$ in a relatively broad temperature range,
$200 \lower.5ex\hbox{\ltsima} T \lower.5ex\hbox{\ltsima} 1000$~K, and finally drops to $\gamma \approx 1.1-1.2$ at
$T\lower.5ex\hbox{\gtsima} 1500$~K \citep[see figure \ref{fig:H2_planets}a below,
  and][]{BoleyEtal07}. An H$_2$ dominated gas fragment spans a range of
temperatures, from the maximum at the centre, $T_{\rm c}$, to the minimum at
the atmosphere of the planet, $T_{\rm eff}$, which may be as low as tens of K
\citep{VazanHelled12}, so $\gamma$ varies within the planet
significantly. However, qualitatively, H$_2$ dominated gas fragments behave as
polytropes with $\gamma$ varying from $5/3$ at low $T_{\rm c}$ to $\gamma< 4/3$
at $T_{\rm c}\lower.5ex\hbox{\gtsima} 2000$~K.

The total energy of a polytrope of mass $M_{\rm p}$ and radius $R_{\rm p}$ is
\citep[e.g.,][]{Chandrasekhar57}
\begin{equation}
E_{\rm tot} = - {3-n\over 5-n} {G M_{\rm p}^2\over R_{\rm p}} \equiv -{3\gamma - 4\over
  5\gamma- 6} {G M_{\rm p}^2\over R_{\rm p}}\;,
\label{etot1}
\end{equation}
For $\gamma<4/3$, the total energy of the planet changes sign, which marks the
dynamical instability to gravitational collapse for gas with $\gamma<4/3$. In
the context of molecular hydrogen dominated fragments, the instability leads
to H$_2$ molecules dissociation and the gravitational collapse of the planet.

Consider now an instantaneous addition of grains of mass $\delta M_z\ll M_z
\ll M_p$ throughout the planet, where $M_z$ is the current mass of metals in
the planet, so that grain mass added within radius $R$ is $\delta M =
(M/M_{\rm p}) \delta M_z $, where $M$ is planet's mass interior to $R<R_{\rm
  p}$. If grains are not vaporised, then the thermal energy of the gas/grain
mixture does not vary appreciably due to this addition (kinetic energy in
Brownian motions of grains is negligible since the weight of a grain is much
larger than that of H$_2$ molecule). However, there is a change in the
gravitational potential energy of the planet,
\begin{equation}
\delta E_{\rm grav} = -\int_0^{M_p} \left( G {M+\delta M \over R} \left[d M+d
  \delta M\right] - {GM\over R} dM\right) \;.
\label{delta_grav1}
\end{equation}
Assuming that $R$ does not vary during this instantaneous mass variation, and
since $\delta M/M = \delta M_z/M_{\rm p} =$~const,
\begin{equation}
\delta E_{\rm grav} =  2 {\delta M_z\over M_p} E_{\rm
  grav}\;,
\label{delta_grav2}
\end{equation}
where $E_{\rm grav} = - \int (GM/R) dM = -(3/(5-n)) G M_{\rm p}^2/R_{\rm
  p}$. Due to energy conservation, $\delta E_{\rm tot} = \delta E_{\rm grav}$,
and hence total energy of the planet evolves according to
\begin{equation}
- {3-n\over 5-n} {d \over dt} {G M_{\rm p}^2\over R_{\rm p}} = - {6\over 5-n}
{G M_{\rm p}^2\over R_{\rm p}} \;{\dot M_z \over M_{\rm p}} \;.
\label{etot2}
\end{equation}
Now, since grain accretion is the only mass gain term for the planet, $\dot
M_p = \dot M_z$, and so equation \ref{etot2} integrates to
\begin{equation}
\ln {G M_{\rm p}^2\over R_{\rm p}} = {6\over 3-n}\ln M_{\rm p} +
\hbox{const}\;.
\end{equation}
It is apparent that as $M_{\rm p}$ increases, $| E_{\rm tot}|$ increases as well
(and rapidly if $n\rightarrow 3$).  If $M_{\rm p}^0$and $R_{\rm p}^{0}$ are
the initial planet mass and radius before grain accretion sets in, then the
constant in the above equation can be eliminated, resulting in
\begin{equation}
{G M_{\rm p}^2\over R_{\rm p}}= \left({G M_{\rm p}^2\over R_{\rm p}}\right)_0
\left[{M_{\rm p}\over M_{\rm p}^0}\right]^{6 \over (3-n)}
\label{etot3}
\end{equation}
The planet's mass is the sum of the mass of the gas and that of metals,
$M_{\rm p} = (1-z) M_{\rm p} + z M_{\rm p}$, and $M_{\rm gas} = M_{\rm p}
(1-z)=$~const. Thus, $M_{\rm p}/M_{\rm p}^0 = (1-z_0)/(1-z)$, where $z_0$ is
the initial metallicity of the planet. Equation \ref{etot3} can be now
re-written in terms of changing metallicity of the planet rather than its
total mass.

Provided that the mean molecular weight of the gas, $\mu$, is known, one can
find the central temperature of the polytrope,
\begin{equation}
T_{\rm c} =  A_n {GM_{\rm p}\mu \over k_{\rm b} R_{\rm p}}
\label{tc0}
\end{equation}
where $A_n = - [(n+1) \xi_1\theta'_n]^{-1} \sim 1$ is a function of $n$ but
not $M_{\rm p}$ or $R_{\rm p}$. For $n=5/2$, $A_n \approx 0.7$. Since we
neglect metal's contribution to pressure and internal energy of the mix and
assume a homogeneous spreading of metals inside the planet, $\mu \approx \mu_0
M_{\rm p}/M_{\rm g} = \mu_0/(1-z)$, where $\mu_0$ is the mean molecular weight
of H$_2$/He mixture. From equation \ref{tc0}, $T_{\rm c}\propto GM_{\rm
  p}^2/R_{\rm p}$, leading to
\begin{equation}
T_{\rm c} = T_0 \left( {M_{\rm p}\over M_{\rm p0}}\right)^{6\over 3-n} = T_0
\left[{1-z_0\over 1-z}\right]^{6\over 3-n}\;.
\label{tc1}
\end{equation}
This equation describes how temperature of the planet increases as its
metallicity increases.  In the limit $z_0 < z \ll 1$ it can be further
simplified by writing $(1-z_0)/(1-z) \approx 1 + (z-z_0)$, and using the
identity $(1+x)^b \approx \exp(bx)$ valid for $x\ll 1$:
\begin{equation}
T_{\rm c} = T_0  \exp\left[ {6\Delta z\over 3-n}\right]\;,
\label{tc_vs_z3}
\end{equation}
where $\Delta z = z - z_0$. This shows that if $6/(3-n) \gg 1$ then the planet
is very sensitive to addition of grains.

In particular, for di-atomic molecules, $\gamma=7/5$, or $n= 5/2$, which
yields
\begin{equation}
T_{\rm c} = T_0  \exp\left[ {12 \Delta z}\right] = T_0  \exp\left[ {0.18 {\Delta z\over z_\odot}}\right] \;,
\label{tc_vs_z}
\end{equation}
where $z_\odot=0.015$, the Solar metallicity. This suggests that
over-abundance of metals by a factor of $5-10$ in a gas fragment dominated by
molecular hydrogen may significantly increase $T_{\rm c}$, taking the planet
closer to the desired $T_{\rm c}\lower.5ex\hbox{\gtsima} 2000$~K point at which it can collapse
to much higher densities.

Figure \ref{fig:5gamma} show a comparison of the analytical theory (equation
\ref{tc1}) with numerical integrations of the metal loading effect performed
with our code, except that the H/He mix EOS was replaced by the polytropic gas
equation with a fixed $\gamma$. Five values of $\gamma$ are considered, as
labelled on the figure. The metal loading time is $t_z = 300$~years for all of
the curves. The black curves in top panel, fig. \ref{fig:5gamma}a, are
numerical integrations, whereas red lines are equation \ref{tc1}. Figure
\ref{fig:5gamma}b shows the metallicity evolution of the planets, which is
identical, all given by same value of $t_z = 300$ years. The agreement
between the theory and numerical simulations is acceptable to us. The curves
show, just as equation \ref{tc1} does, that the smaller the value of $\gamma$,
the stronger the planet reacts to addition of grains. This is because
$n=1/(\gamma-1)$ edges closer to the unstable value, $n=3$, as $\gamma$
approaches $4/3$ from above, and even a small amount of metals can cause a
significant contraction of the planet.

The same result (equation \ref{tc1}) can be also obtained from a polytropic
sphere relation between planet's radius, mass, and the "constant" $K$, if the
latter is allowed to vary as $z$ changes.  Namely, $K = P/\rho^{1 +1/n} = K_0
[(1-z)/(1-z_0)]^{1+1/n}$ in this case, where $K_0$ is the polytropic constant
at $z=z_0$. Since $K$ is related to entropy per unit mass of the planet, this
provides another interpretation of the metal loading effect: adding metals
decreases entropy of the cloud, just as radiative cooling does, so metal
accretion is effectively a cooling mechanism.

\begin{figure}
\psfig{file=m4_5gamma.eps,width=0.5\textwidth,angle=0}
  \caption{Evolution of polytropic gas fragments for five different values of
    $\gamma$, as labelled in the figure, when loaded with grains homogeneously
    throughout the cloud. The solid red lines are predictions of the
    analytical model (equation \ref{tc1}), whereas black curves are the
    results of the numerical integration.}
 \label{fig:5gamma}
\end{figure}

\section{Real H$_2$-dominated polytropes}\label{sec:real}

Having explored idealised polytropic models with a fixed value of $\gamma$
(or $n$), we turn to more realistic cases of H/He-dominated pre-collapse
planets. Figure \ref{fig:H2_planets}a shows adiabatic index $\gamma$ versus
gas temperature for a Solar composition H/He plus metals mix for the ideal EOS
used in this paper calculated for a fixed gas density of $\rho = 10^{-7}$
g/cm$^3$. As expected, $\gamma = 5/3$ at $T\lower.5ex\hbox{\ltsima} 100$~K when rotational and
vibrational degrees of freedom of molecular hydrogen are not yet excited; then
at higher $T$, $\gamma$ drops to $\approx 7/5$ appropriate for diatomic
gas. This persists until $T\sim 1500$~K when $H_2$ dissociation becomes
energetically possible. Due to H$_2$ dissociation at temperatures around
$2000$~K, $\gamma$ plunges to about 1.1.

Clearly, each pre-collapse planet configuration spans a range of densities and
temperatures, from the maximum in the centre to the minimum in the
atmosphere. To relate to the analytical theory derived in \S \ref{sec:theory},
we define effective $\gamma$ and $n$ for a planet by computing the
gravitational potential energy of that planet and then comparing it with that
of a polytropic planet of the same mass and radius, e.g.,
\begin{equation}
E_{\rm grav} = -{3\over 5-n} {G M_{\rm p}^2\over R_{\rm p}}\;,
\label{egrav}
\end{equation}
where $n = 1/(\gamma-1)$. The values of the $\gamma_{\rm eff}$ versus planet's
central temperature are plotted in figure \ref{fig:H2_planets}a for two
planetary masses, $M_{\rm p} = 1 \mj$ and $M_{\rm p} = 4 \mj$. These are very
similar all the way to $T_{\rm c} \approx 2000$~K. As can be expected,
$\gamma_{\rm eff}$ for a planet bears a strong resemblance to the $\gamma(T)$
function (the solid curve), except smoothed out somewhat due to the presence
of a range of temperatures inside a planet, and also shifted to higher
temperatures since $T_{\rm c}$ represents the maximum temperature in a given
planet, whereas $\gamma_{\rm eff}$ is probably related more closely to a mean
temperature in the planet.

Now, the analytical theory developed in \S \ref{sec:theory} predicts how the
central temperature of a polytropic planet varies with its metallicity when
grains are added to the planet, e.g., $T_{\rm c}\propto (1-z)^{-\sigma_{\rm
    z}}$ (equation \ref{tc1}), where we defined "metallicity exponent"
\begin{equation}
\sigma_{\rm z} = - {d \ln T_{\rm c}\over d\ln (1-z)} = {6\over 3-n}\;.
\label{sigmaz}
\end{equation}
The dependence of $\sigma_z$ on central temperature is plotted in figure
\ref{fig:H2_planets}b for the two planetary masses, and also for the solid
curve from figure \ref{fig:H2_planets}a (corresponding to fixed gas density of
$\rho=10^{-7}$ g/cm$^3$).

The dash-dotted curve passing through red triangles in the panel shows $-[d
  \ln T_{\rm c}/d\ln (1-z)]$ actually measured in simulations of planets of
mass $M_{\rm p} = 4 \mj$ loaded with metals. These (short) runs are started
with the planets initialised as polytropic spheres of Solar metal abundance
following the ideal EOS with $T_{\rm c}$ shown on the horizontal axis. The
metals are added to the planets in the same way as described in \S
\ref{sec:intro_runs}, with $t_z = 500$~years (the choice of $t_z$ is
unimportant for this plot). We then measure $\sigma_{\rm z}$ when $z$ varies
by a small increment. To make sure that radiative cooling of the planet, which
also drives evolution of $T_{\rm c}$ in realistic planets, does not corrupt
our measurement of $\sigma_{\rm z}$, we set the opacity multiplier to a very
large number ($10^{10}$) to turn off radiative cooling of the planet for
figure \ref{fig:H2_planets}.

The dash-dotted curve (measured $\sigma_{\rm z}$) should be compared with the
dashed one (predicted). These two are relatively close but do not coincide
exactly, which probably reflects the fact that our definition of $\gamma_{\rm
  eff}$ in equation \ref{egrav} is somewhat arbitrary, and is only one
possible way to define an effective $\gamma$ for a planet. Using the total
energy of the planet to define $\gamma$, for example, gives slightly different
values for $\gamma_{\rm eff}$. Nevertheless, the agreement appears reasonable
and hence the analytical theory has some utility in explaining contraction of
metal-loaded pre-collapse planets.

We also define the central temperature doubling metallicity, $z_{\rm d}$, as
metallicity at which $T_{\rm c}$ is twice its initial value, $T_0$. Given the
definition of $\sigma_{\rm z}$ and equation \ref{tc1},
\begin{equation}
z_{\rm d}  = 1 - \left(1-z_{\rm 0} \right) \, 2^{-1/\sigma_{\rm z}}
\label{zd1}
\end{equation}
where $z_0$ is the initial planet's metallicity. The doubling metallicity in
units of Solar metallicity, and assuming $z_0=z_\odot$, is plotted in figure
\ref{fig:H2_planets}c for the same models as in the two panels above it. We
can see that metal over-abundance of a factor of a few to ten in Solar
metallicity units is required to cause the planet to shrink by a factor of two
in radius (planet's radius is nearly exactly inversely proportional to $T_{\rm
  c}$). The required metal over-abundance is smaller at higher temperatures
because the planet is closer to the unstable value of $\gamma=4/3$ at higher
$T_{\rm c}$.

\begin{figure}
\psfig{file=a_vs_T.eps,width=0.5\textwidth,angle=0}
  \caption{Panel (a): the ratio of specific heats, $\gamma$, for our Solar
    composition EOS at a fixed gas density, $\rho = 10^{-7}$~g/cm$^3$ (the
    solid curve), and the effective $\gamma$ for two planetary masses as
    defined by equation \ref{egrav}. Middle panel (b): Metallicity exponent
    (equation \ref{sigmaz}) for the same cases as panel (a), plus one directly
    measured from a numerical experiment for $M_{\rm p} = 4\mj$ (dot-dashed
    curve passing through triangles). The larger $\sigma_z$, the more rapidly
    planet contracts as metals are loaded into it. Panel (c): the central
    temperature doubling metallicity $z_{\rm d}$, defined by equation
    \ref{zd1}, for the same cases as in panel (b), and plotted in units of the
    Solar metallicity, $z_\odot$.}
 \label{fig:H2_planets}
\end{figure}

\section{Grain-dominated planet collapse}\label{sec:grain_dom}

Having studied the contraction rates of planets loaded by metals, we can now
ask the question of when such a contraction is faster than that due to
radiative cooling. This happens when the rate of central temperature increase
due to radiative cooling rate is equal to the that due to metal loading. The
latter can be found via
\begin{equation}
{d T_{\rm c} \over dt} = T_{\rm c} {d \ln T_{\rm c}\over d\ln (1-z)}\;{d\ln (1-z) \over dt}\;.
\end{equation}
Now, using equation \ref{sigmaz} and definition $1-z = M_{\rm gas}/(M_{\rm
  gas} + M_{\rm z})$, where $M_{\rm gas}$ and $M_{\rm z}$ and the total mass
of gas and metals in the planet, we write
\begin{equation}
{d\ln (1-z) \over dt} = - {1\over M_{\rm p}} {d M_{\rm z} \over dt} = -
{M_{\rm z}(0)\over M_{\rm p} t_{\rm z}}
\label{dzdt1}
\end{equation}
The condition of the two contraction rates being equal to each other reads
\begin{equation}
{T_{\rm c} \over t_{\rm rad}} = T_{\rm c} \sigma_{\rm z} \;
{z_0\over t_{\rm z}}
\label{eq_rates}
\end{equation}
where we set $z=z_0$. This defines the critical metal loading time scale,
$t_{\rm crit}$, such that if metals are supplied to the planet on a time scale
shorter than $t_{\rm crit}$ then the planet contracts mainly due to the
increasing metal content rather than radiative cooling. According to equation
\ref{eq_rates}, the critical time is
\begin{equation}
t_{\rm crit} = t_{\rm rad} \sigma_{\rm z} z_0\;,
\label{tcrit1}
\end{equation}
Figure \ref{fig:tz_crit} plots the critical metal loading time versus planet's
central temperature for the same range of planetary masses as in figure
\ref{fig:tcool}. The curves showing $t_{\rm crit}$ are qualitatively similar
to those showing $t_{\rm rad}$ for obvious reasons save for the absolute
values, and the factor $\sigma_{\rm z}$ that is a function of $T_{\rm c}$.

This figure shows that loading the planet by metals at a typical $t_{\rm z}$
of a few thousand years, as estimated in \S \ref{sec:mdot_grain}, is not
likely to affect relatively massive planets, $M_{\rm p}\lower.5ex\hbox{\gtsima} 2 \mj$, at the
beginning of their evolution, but may affect them when they contract towards
$T\lower.5ex\hbox{\gtsima} 1000$~K. This finding is consistent with the right panels of figure
\ref{fig:exp1}, in which the central temperature evolution of metal-loaded
planets fed by metals at different rates was shown. The figure showed that
early evolution of planets, when $T_{\rm c}\lower.5ex\hbox{\ltsima} 500$~K, is
indistinguishable for different $t_{\rm z}$, at least in a rather broad range
of $t_{\rm z}$, from 250 years all the way to $t_{\rm z}=\infty$. This can now
be understood in terms of the radiation-dominated phase of the planet's
contraction: early on the planet contracts radiatively more rapidly than it
does due to metal loading, even at the shortest $t_{\rm z}$ explored in the
figure. At later times, however, depending on $t_{\rm z}$, the planets go off
the fixed metallicity (solid curve in figure \ref{fig:exp1}c) track and
accelerate onto the metal-dominated part of their evolution.

\begin{figure}
\psfig{file=t_crit.eps,width=0.5\textwidth,angle=0}
  \caption{Critical metal-loading time versus planet's central temperature for
    four different planetary masses and interstellar grain opacities, as
    labelled in the box in the figure. Metals must be added to the planet
    rapidly, so that $t_z < t_{\rm crit}$, in order for the metal loading to
    dominate over radiative cooling as a contraction mechanism.}
 \label{fig:tz_crit}
\end{figure}

On the other hand, figure \ref{fig:tz_crit} predicts that evolution of lower
mass gas fragments may be much more sensitive to deposition of metals. For
example, for $M_{\rm p} =0.5\mj$, even $t_{\rm z} = 10^4$ years is short
enough to dominate fragment's contraction. One preliminary conclusion from
this, which clearly needs to be explored more rigorously in a realistic
evolving protoplanetary disc setting, is that lower mass giant planets formed
by GI/TD may be more metal rich. Physically, it takes far longer for these
planets to contract (because their radiative cooling times are much longer,
see figure \ref{fig:tcool}). For this reason, they are likely to have a lower
central temperature for longer than their massive cousins. Based on the theory
developed above and figure \ref{fig:H2_planets}, their contraction due to
metal loading is therefore slower, and hence they may be able to absorb more
metals before they collapse.

While a full scale investigation of this prediction is outside the scope of
our paper, figure \ref{fig:M1M4} compares the evolution of two planets,
$M_{\rm p} = 4\mj$, which was already shown in figures \ref{fig:exp1}c,d with
the long dash curves, while the other planet has a lower mass, $M_{\rm p} =1
\mj$. The solid lines in figures \ref{fig:M1M4}a,b show the evolution of the
central temperature and metallicity, $z$, respectively, for $M_{\rm p} =1
\mj$. The dashed curve in figure \ref{fig:M1M4}b show the ratio of the
critical metal loading time scale to the actual value of $t_{\rm z}$
($4000$~years for both runs). Except for the earliest times, that ratio is
always greater than unity, suggesting that evolution of this planet is nearly
always metal dominated. This planet collapses at $t=0.12$~Myr almost entirely
due to metal loading rather than radiation. By the time the planet collapses,
its metallicity is very high, $z\approx 0.3$, e.g., some 20 times higher than
$z_\odot$.

The evolution of the more massive planet is distinctly different. Since such
planets are cooling much more rapidly (see fig. 1), metal loading is a
relatively minor effect in this case, with $t_{\rm crit}/t_{\rm z} < 1$
everywhere (see figure \ref{fig:M1M4}d). The evolution of a massive planet is
hence radiation-dominated. The critical loading time $t_{\rm crit}$ is
  calculated using equation \ref{tcrit1}, where the radiative time is found at
  each time step using the definition from equation \ref{trad}, the
  metallicity exponent $\sigma_z$ is computed using equation \ref{sigmaz} and
  definition of $n$ given by equation \ref{egrav}.

\begin{figure*}
\begin{minipage}{3.2in}
\psfig{file=sn_m1_tz4000.eps,width=0.99\textwidth,angle=0}
\end{minipage}
\begin{minipage}{3.2in}
\psfig{file=sn_m4_tz4000.eps,width=0.99\textwidth,angle=0}
\end{minipage}
  \caption{The central temperature (top panels, a and c) and metallicity
    (bottom panels, b and d) versus time for planets with mass $M_{\rm p} = 1
    \mj$ and $M_{\rm p} = 4 \mj$ (left and right panels, respectively). The
    dashed curve in the bottom panels show the ratio of the critical metal
    loading time scale to the actual value of $t_{\rm z}$ ($4000$~years for
    both runs). The dashed curves show that the evolution of the $M_{\rm p} =
    1 \mj$ is dominated by metal loading, whereas that of the $M_{\rm p} =
    4\mj$ is dominated by radiative cooling.}
 \label{fig:M1M4}
\end{figure*}

\section{Discussion}\label{sec:discussion}

In this paper we have shown that accretion of pebbles from the surrounding
protoplanetary disc is a surprisingly efficient way for pre-collapse H$_2$
dominated planets to contract and eventually collapse in high opacity
regime. The simplest way to understand this result is to (1) realise that a
gentle sedimentation of grains onto a planet brings in additional
gravitational potential energy but not thermal or kinetic energy, so that the
total energy of the cloud becomes more negative. (2) The reason for a
surprising sensitivity of molecular pre-collapse planets to metals is the fact
that the total energy of a polytropic cloud with index $n$ (equation
\ref{etot1}) with $n\rightarrow 3$ is very small compared to $G M_{\rm
  p}^2/R_{\rm p}$ (e.g., $(3-n)/(5-n) = 0.2$ for $n=5/2$), so it takes only a
little extra weight in metals to topple the planet over into the unstable
H$_2$ dissociation regime.

The implications of our results for TD hypothesis and GI-born planets are
potentially significant. First of all, metal loading makes it much more likely
that these planets are able to contract and collapse despite a rapid inward
migration. This may help to resolve the challenges to forming GI planets at
short separations by migration of fragments born at separations $\sim 100$~AU
emphasised by \cite{ZhuEtal12a} and \cite{VazanHelled12}. Secondly, metal
loading process may explain why giant planets are over-abundant in metals
\citep[e.g.,][]{MillerFortney11}. Finally, TD/GI planet survival may be
enhanced at high metallicities since the rates of pebble accretion are higher,
making the planets collapse sooner, while planet migration rates are unlikely
to depend on disc metallicity strongly. This may produce a positive giant
planet frequency -- host star metallicity correlation as needed to explain
observations \citep{FischerValenti05}. These issues will be addressed in a
separate forthcoming publication where the disc-planet interaction is modelled
in detail.

As discussed in the Introduction, low opacity in pre-collapse GI clumps
  may be another way to speed up the collapse \citep{HB11}, but it is not
  clear if opacity in the clumps is indeed much smaller than the interstellar
  one. \cite{DD05} argued that grain aggregate fragmentation in higher speed
  collisions is required by observations of T Tauri stars to maintain a high
  abundance of small grains despite the simultaneous presence of grains as
  large as $\sim1 $~cm in size. Furthermore, the low dust opacity picture
  would predict a very efficient formation of giant planets at low
  metallicities, which contradicts observations \citep{FischerValenti05}.

We also found that the response of giant planets to metal loading is a strong
function of their mass. More massive planets are less likely to be influenced
by metal accretion since they cool much more rapidly than their lower mass
cousins (see fig. \ref{fig:M1M4}). This gives us hope that there may be strong
trends in predictions of the TD model with fragment's mass that could
hopefully be used to contrast it with observations of exoplanets.

The main shortcomings of our numerical approach here are (i) the
simplification in the EOS that neglects metals' contribution to the internal
energy and pressure of the mix (see Appendix), and (ii) assuming a homogenous
spreading of the grains inside the planet. Both of these are made in order to
keep our treatment as transparent as possible and to enable a comparison to
the analytical model developed in \S \ref{sec:theory}. Furthermore,
preliminary results of simulations with a more complete EOS show that this
only strengthens the tendency of the fragments to collapse due to metal
loading because grain vaporisation must occur before the fragment collapses
(as $T\lower.5ex\hbox{\gtsima} 2000$~K at that point), and this process takes extra energy from
the gas due to the latent heat of vaporisation \citep[e.g.,][]{PodolakEtal88},
cooling the fragment yet more.  The assumption that grains are well mixed with
gas is reasonable if convection stirs the grains up quickly
\citep[e.g.,][]{HB11}, mixing newly accreted grains throughout the planet
efficiently. Nevertheless, we shall endeavour to relax these simplifications in
future publications.

\section{Acknowledgments}

Theoretical astrophysics research at the University of Leicester is supported
by a STFC Rolling grant. The author thanks Richard Alexander for useful
discussions.  This work used the DiRAC Complexity system, operated by the
University of Leicester, which forms part of the STFC DiRAC HPC Facility
(www.dirac.ac.uk). This equipment is funded by a BIS National E-Infrastructure
capital grant ST/K000373/1 and DiRAC Operations grant ST/K0003259/1. DiRAC is
part of the UK National E-Infrastructure.

\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


text:
Strategic Demolition
XGU
Geoffrey Pierini
Mr. Pierini's background in health care infrastructure construction spans two decades, having managed over $100 million in projects. Mr. Pierini has an extensive background in the pre-installation construction phase of diagnostic and surgical device installations across a broad range of platforms and manufacturers. Mr. Pierini has cultivated a specialized knowledge of the regulatory environments overseeing the healthcare and medical device industries.
Kathryn Pierini
A graduate of Stevens Institute of Technology with a Master of Science degree in Construction Management, Ms. Pierini has worked on such projects as the complete renovation of the Union Imaging Center in Union, NJ, where she was responsible for the pricing and ordering of all mechanical equipment and the scheduling of day and night crews for HVAC installations. She also was central to the installations performed at the Carroll County Medical Office Building in Westminster, MD. During this 1.1 million dollar medical imaging undertaking, Kathryn was assigned vital duties such as receiving and organizing sub-contractor bids.
Marie Lynch
Marie Lynch joined Excalibur Group in 2018 as Head of Operations. Prior to joining Excalibur, Ms. Lynch served as Director of Facilities and Construction at Kate Spade & Company, and also as Construction Manager at Liz Claiborne Inc.
Francesco Salerno
Director of Architecture and Engineering
Joining Excalibur Group in 2011, Francesco Salerno currently serves as the Director of Architecture and Engineering. Mr Salerno brings a vast amount of multidisciplinary knowledge to the team with over 14 years experience in designing medical facilities and working on large scale residential projects as well as several commercial developments. He obtained his Bachelor of Architecture degree from NJIT in 2001. Additionally, Mr Salerno has performed LEED design work in the areas of commercial design and construction.
Al Conklin
Serving as the Millwork Manager here at Excalibur Group, Al has over 35 years of experience in the cabinet making field and is a certified fabricator of Solid Surface Material. Mr. Conklin's daily responsibilities which consist of cabinetry design, safety review, job scheduling, and project forecasting as well as the overseeing of manufacturing.
© 2018 Excalibur Group LLC
Excalibur Announces partnership with Spartan Shielding to manufacture Modular Isolation Chambers for Hospital Patients and Staff Fighting COVID-19Read More
Excalibur: Nothing is Impossible!


my family's favorite sugar cookies.
And for something on the not-so-sweet side... sorry, no photo of the reuben spread recipe, next time I make some I will try to remember to take a photo.
-2 cups chopped pecans, toasted In a large mixing bowl (or kitchen aid bowl with paddle attachment), mix together the cream cheese, shredded cheese, and dressing mix. After beaten, form into a large ball. Roll in toasted pecans to coat to surface. Refrigerate for at least 2 hours before serving.
*To toast pecans, bake in oven at 350 F. for 10 minutes.
Mix all the ingredients together in a crock pot, let heat threw for 2 hours. Keep warm until ready to serve.


PLEASE NOTE THAT THIS EVENT IS AT FULL CAPACITY AND WILL NOT BE ABLE TO TAKE ANY MORE VOLUNTEERS.
Don't worry, though! We have loads of other One-Off Volunteering opportunities to choose from!
Volunteer Role: We are looking for friendly, reliable and patient volunteers to support our team of professionals at our summer schools. We are offering three different, week-long programmes for children aged seven to sixteen years old. In our courses, students make a musical in week: they will learn songs and dance routines from well-known films and West End shows, creating a show that they will perform to family and friends at the end of the course. We expect volunteers to work with our teachers to ensure the children are participating and enjoying their time at the school. Responsibilities may include assisting with costumes, learning lines in preparation for the end of week showing, and helping out with student registration at the start of the day.
When & Where: For the first two weeks (23 - 27 July and 30 July - 3 August), we're based at Chobham Academy. In week three (20 – 24 August) we're at Princess May. Classes are on all day, from 09:30 to 16:00. We are particularly keen to hear from volunteers who are able to commit to at least three days in any one week, but please do also get in touch if your availability is less, as we can be quite flexible.
We strive to make our volunteering opportunities as inclusive as possible and will try to make appropriate arrangements for anyone who wants to volunteer with us. Unfortunately Princess May School does not have step free access, so we're not able to accommodate volunteers who need this in week three (20-24 August).


text:
Why A Brick Wall Is Stumping The Internet
by Megan Grant
Pakin Songmor/Moment/Getty Images
If you're in the mood for your brain to explode, I've got just what you need: The latest photo sweeping the Internet and leaving everyone scratching their heads (or, alternatively, wanting to rip their hair out) is a brick wall optical illusion. It's apparently hiding something that's pretty tough for the human eye to spot. Honestly, when I was first looking at it, I was searching for a dead body or waiting for something to pop out and scare the buhjeezies out of me. Not sure what that says about me as a person, but, well, there you have it. Anyway, the image was posted to Facebook by Arron Bevin on May 16; it has garnered 74,000 likes and been shared over 55,000 times during the past three days, which should give you a pretty good idea of how into this whole thing we all are.
Alas, I was only slightly off in my suspicions. I didn't want to spoil the surprise, so I spent several minutes examining every square inch of the image like a complete moron, not coming any closer to a concrete answer. It's a wall. Made of bricks. It's a brick wall. Like, what do you want from me?
So I caved. I broke. I cheated and looked at the answer, because IFLScience made it really, really easy to do that. And once I saw it, I couldn't un-see it ever again. Now whenever I look at the image, all I see is this big, fat thing that doesn't belong. Take a look for yourself. Notice anything weird?
Look again. Reeeeeeeeeally look. Did you find it?
No? All right, here it is.
But first, check out our podcast The Chat Room for more talk about all things internet.
There's a freaking cigar sticking out of the middle of the wall. Sweet mother.
And that's it. That's the riddle. How did I not see that? Hoping to find justification for my inability to spot a cigar sticking out of a wall, I spent a little more time looking into how optical illusions even work — and it turns out that there is a scientific explanation behind optical illusions and why they're able to trick us. The complex process of optical illusions was more heavily studied starting as early as the 19th century, when scientists started to learn that while our senses are reliable, they can also be fooled. Here's the deal:
When you look at something, you're actually seeing all of the light that bounced off of it and hit your eyes. This bouncing light turns into electrical impulses, allowing your brain to create an image you can see. This is a rather miraculous process, when you think about it, and yet the entire thing occurs in about a tenth of a second! Here's the thing, though: Our eyes are constantly receiving streams of light, all the time. It's so much information that our brains can't process it all at once. So instead, our brains take their own little shortcuts so that we can focus only on the parts that are important. Our brain makes assumptions and judgments about objects largely based on the things surrounding it, which might help explain why many of us perceived the cigar in the wall to be merely part of the bricks — and why this wacky picture seen here can either be a profile or a flat-on view of half of a guy's face, depending on how you look at it:
So there. I now have a valid excuse — backed by science — for totally blanking on the whole cigar thing. And so do you. You're welcome.
Images: Pakin Songmor/Moment/Getty Images
Ashamed Of Your Screen Time Stats? Here's How To Change That
By Alexis Morillo
How To Turn Off TikTok Profile Views So You Can Stalk Other Accounts In Secret
Wait, Does Liking Someone's IG Story = Shooting Your Shot?
This Wordle Rival Is Taking Social Media By Storm


The cuisine on offer coupled with the breathtaking sea views on your doorstep and the spa is a winning combination.
Breathtaking design leans heavily on pastel shades and minimalist principles. We love the clean lines and whitewashed walls, which act as a striking counterpoint to the azure blue of the sea and the lush green of the gardens. The rooms and suites are complemented by four restaurants and five freshwater pools; there is an indoor pool and infinity pool at Almyraspa for 16 years +.
Almyra's eight acres of landscaped gardens have direct access to seafront and the Mediterranean Sea. The hotel is near to Pafos' many restaurants and attractions, including the House of Dionysos, a UNESCO World Heritage Site - containing Cyprus's world-renowned Roman mosaics.
Rooms combine simple, understated Mediterranean décor with a choice of garden or sea views, and either some with a private terrace or balcony. The seafront Kyma Suites with their private rooftop dining terrace are perfect for honeymoons. Aethon Sea View Rooms have stunning sea views and balconies. Their location near the spa makes them ideal for those looking to use this wonderful facility throughout their stay.


Flushing hubby down the drain is not news — Why NOT? Well, media bias, for one thing, but could there be another reason? What would it be?
Berlin – A woman in Germany put an end to her troubled marriage by chopping up her husband and flushing parts of him down the toilet, authorities said today.
The story apparently did not make the big news anywhere. Flushing hubby down the drain not news, while the killing of a cat by putting her in a microwave oven is (Canada, Jan. 5, 2008) most definitely is not and was not then.
Two Alberta teens who admitted to killing a cat in a microwave oven were sentenced Thursday to one year probation and 100 hours of community service.
Some of the preferential treatment of what is news-worthy and what is not is probably due to the maxim that "Dog Bites Man" is not news but "Man Bites Dog" is. It does not matter how one rationalizes it, media bias remains media bias, for any reason and by any other name.
It is fascinating that the media spent time (as was done in the article about the sentencing of the kids who killed the cat) in quite a few articles at the time about the sentence handed down for the killing of the cat. It is even more interesting that the killing of the husband (and let's be clear, he had suffered no less than the cat did, because he had been the victim in a long history of serious physical abuse against him, by his wife) was not discussed much in the media. Not only that, but the story about him being killed, chopped up and being flushed down the toilet never made the mainstream media, let alone the evening news or the front pages. A lot of people know about the two boys who killed the cat, and relatively few heard or read about the man who got killed by his wife, because flushing hubby down the drain is not news.
There is no escaping the reality that cats rank higher in the order of things than do men.
The woman had previously tried to poison her husband, and on one occasion she had seriously injured him with a hammer. Police were shocked that the long-suffering husband had never reported these incidents.
From the perspective of animal rights activists and feminists, it is a good thing that no one can get away scot-free with killing a cat, and that women who kill their husbands almost always will.
The woman who had been fatally abusing her husband, chopped him up and flushed him down the toilet never was sentenced for her deeds, not even to probation, because flushing hubby down the drain is not news. If the woman did not die, she is still around, and if you live in Macedonia, she could be your neighbour, your neighbour's wife, maybe even yours.
This entry was posted in Media Bias, The New World Order, Women's Violence. Bookmark the permalink.


text:
Q: Taking logarithm of column Im quite new to programming (in python) and I would like to create a new variable that is the logarithm of a column (from an imported excel file). I have tried different solutions from this site, but I keep getting an error. My latest error is AttributeError: 'str' object has no attribute 'log'.
I have already dropped all the values that are not "numbers', but I still don't know how to convert the values from strings to integers (if this is the case, because 'int(neighborhood)' doesn't work).
This is the code I have now:
import pandas as pd
import numpy as np

df=pd.read_excel("kwb-2016_del_col_del_row.xls")
df = df[df.m_woz != "."] # drop rows with values "."
neighborhood=df[df.recs=="Neighborhood"]
neighborhood=neighborhood["m_woz"]
print(neighborhood)

np.log(neighborhood)

and this is the error I'm getting:
AttributeError                            Traceback (most recent call last)
<ipython-input-66-46698de51811> in <module>()
     12 print(neighborhood)
     13
---> 14 np.log(neighborhood)

AttributeError: 'str' object has no attribute 'log'

Could someone help me please?

A: Perhaps you are not removing the data you think you are?
Try printing the data types to see what they are.
In a DataFrame, your column might be filled with objects instead of numbers.
print(df.dtypes)
Also, you might want to look at these two pages
Select row from a DataFrame based on the type of the object(i.e. str)
Pandas: convert dtype 'object' to int
Here's an example I constructed and ran interactively that correctly gets the logarithms (don't type >>>):
>>> raw_data = {'m_woz': ['abc', 'def', 1.23, 45.6, '.xyz'],
    'recs': ['Neighborhood', 'Neighborhood',
    'unknown', 'Neighborhood', 'whatever']}
>>> df = pd.DataFrame(raw_data, columns = ['m_woz', 'recs'])
>>> print(df.dtypes)
m_woz    object
recs     object
dtype: object

Note that the type is object, not float or int or str
Continuing on, here is what df and neighborhood look like:
>>> df
  m_woz          recs
0    42  Neighborhood
1   def  Neighborhood
2  1.23       unknown
3  45.6  Neighborhood
4  .xyz      whatever

>>> neighborhood=df[df.recs=="Neighborhood"]
>>> neighborhood

  m_woz          recs
0    42  Neighborhood
1   def  Neighborhood
3  45.6  Neighborhood

And here are the tricks...
This line selects all rows in neighborhood that are int or float (be careful to fix indents if you copy/paste this
>>> df_num_strings = neighborhood[neighborhood['m_woz'].
        apply(lambda x: type(x) in (int, float))]

>>> df_num_strings
  m_woz          recs
0    42  Neighborhood
3  45.6  Neighborhood

Almost there... convert the numbers to floating point from string
>>> df_float = df_num_strings['m_woz'].astype(str).astype(float)
>>> df_float
0    42.0
3    45.6

Finally, compute logarithms:
>>> np.log(df_float)
0    3.737670
3    3.819908
Name: m_woz, dtype: float64

redpajama_set_name: RedPajamaStackExchange


text:
Trump 2020 Campaign Raises Record $28.4 Million in First 24 Hours
President Donald Trump / Getty Images
Patrick Hauf - June 19, 2019 10:05 AM
President Donald J. Trump's reelection campaign raised a record $24.8 million in its first 24 hours, a total greater than the top five polling Democratic candidates combined.
"@realDonaldTrump has raised a record breaking $24.8M in less than 24 hours for his re-election," GOP Chairwoman Ronna McDaniel tweeted Wednesday morning. "The enthusiasm across the country for this President is unmatched and unlike anything we've ever seen!"
"THANK YOU! #Trump2020," Trump added.
https://twitter.com/realDonaldTrump/status/1141328504929300480
The $24.8 million figure for Trump's reelection was raised by three different entities: Trump Campaign, Trump Victory, and T-MAGAC.
Former vice president Joe Biden raised $6.3 million in the first 24 hours of his campaign. Bernie Sanders (D-VT) raised a similar $5.9 million. Elizabeth Warren raised $300,000 within 24 hours of announcing her exploratory campaign but did not provide a number for her official announcement. Pete Buttigieg raised $1 million within four hours of announcing his campaign but did not provide a number for 24 hours. Kamala Harris raised $1.5 million. Beto O'Rourke raised $6.1 million but is not polling in the top five for the Democratic nomination.
For those keeping score, that's more than the 5 highest polling Democrats – combined. https://t.co/krP2ehbfIw
— Michael Ahrens (@michael_ahrens) June 19, 2019
Trump kicked off his campaign with a rally in Orlando Tuesday night. According to the New York Post, his campaign set a fundraising goal of $7 million to reach by 11:59 p.m. Tuesday.
This entry was posted in Politics and tagged 2020 Election, Campaign Finance, Donald Trump. Bookmark the permalink.
Patrick Hauf is an intern reporting for Washington Free Beacon this summer through the National Journalism Center. He is an incoming junior at the University of Maryland at College Park, where he is studying journalism. He serves as vice president of Lone Conservative, a blog for right-of-center college students. His Twitter handle is @PatrickHauf. You can reach him at patrickjhauf@gmail.com.


text:
Click here to return to the media centre
Former teacher reckons science can be cool .. and this big win proves it
A former high school science teacher with a passion for inspiring kids has proven science can be cool by winning a major award.
(Courier Mail LINK)
A NUDGEE business has proven that science is cool, taking one of the top honours at the 2019 Telstra Business Awards.
Street Science, which has been bringing science to life for school kids across Australia for seven years, won the Small and Succeeding category at the awards.
Founder Steven Liddell and his team of scientists and educators could hardly contain their excitement when the result was announced during a gala night at Howard Smith Wharves.
After eight years in the classroom, Mr Liddell developed the Street Science concept - a hands-on, student-centred learning approach that teaches the Australian science curriculum in a fun, energetic and inspiring way.
He said that never in his wildest dreams did he imagine his team would win Australia's premier business award.
"Being acknowledged with such a prestigious award is testament to the hard work that we've been putting in over the past seven years. It's a great reward for the blood, sweat and tears on the rollercoaster that is small business," Mr Liddell said.
"Our team are dedicated, amazing people who love science. It is amazing to be recognised for what is our passion."
Mr Liddell is, at heart, a science educator who cares about improving student outcomes and providing opportunities for kids to step out of their comfort zone and find success through engaging styles of learning.
"I was a full-time high school teacher and I wanted to make learning more exciting," he said.
"By combining the national curriculum with a high energy show or interactive workshop, children from kindergarten to high school learn while having fun.
"I want more kids to study science. I was inspired to change the way science is taught in the classroom after seeing a significant drop in students taking on senior sciences through my work as a high school maths and science teacher."
Mr Liddell said running a business was very different to being a high school teacher.
"I have been on a massive learning curve over the past seven years. Nothing prepares you for the rollercoaster that is business.
"Winning an award like this shows that with hard work anything is possible.
"The last 12 months have been filled with great achievements - Kim, my wife, is now working in the business fulltime and earlier this year, we ran Brisbane Science Festival in Southbank.
"This festival engaged over 10,00 attendees by collaborating with several small businesses, government organisations and several university institutes to engage and excite our local community in STEM."
Street Science will now compete in the National Telstra Australian Business Awards in Melbourne on November 21.


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Linus Under Wraps, Fedora Tests Wayland & More…
By Larry Cafiero on March 13, 2015 |
Business, Distros, Hardware and Operating Systems
To be honest, I'm really not finished going through all the materials I picked up at the Open Compute Project 2015 U.S. Summit this week in San Jose. There is a lot of interesting stuff here to wade through, and I'm still going through it.
Meanwhile, much of what makes the FOSS world interesting didn't wait for me to finish. Like:
Linus Under Wraps? We all know Linus Torvalds. We "get it" — he's a guy with a big vocabulary who doesn't suffer fools gladly. Many of us are okay with "Linus being Linus," though some lately have begun to question how positive his criticisms can be. Earlier this week, Business Insider reported the Linux Foundation appeared to try to rein him in, slapping him on the wrist when they issued a new "Code of Conflict" policy that declared "personal insults or abuse are not welcome."
The "Code of Conflict" says that if "anyone feels personally abused, threatened, or otherwise uncomfortable" while working on Linux, they should report the situation to the Technical Advisory Board who will step in and mediate."
Greg Kroah-Hartman wrote it and submitted it as a "patch" to the Linux system, which meant ultimately Linus had to see the "patch" to approve it. He did, of course, adding the comment "Let's see how this works."
Let's see, indeed.
Fedora 22 Alpha out: It's nearly spring, and with the warmer weather and blooming flowers usually comes the even-numbered Fedora releases. The Fedora 22 Alpha is now ready for your test-driving pleasure, should you choose to give it a spin.
Hidden in the release notes in the link above is this morsel: "The login screen now uses Wayland by default. This is a step towards replacing X with Wayland, and users should not actually notice the difference." Okay, let's just see about that. If you want to see a preview of what that might look like, you can take a look here.
Fedora 22 Beta is scheduled for release in mid-April.
It's all in the terminology: I've always liked the term "Metal-as-a-Service" (MAAS). It invokes instantly conjuring up Judas Priest or Anthrax (the band, not the livestock disease) at a moment's notice, though I know that's not really what it means.
Strange bedfellows? The Microsoft booth at the 2015 OCP Summit in San Jose. (Photo: Larry Cafiero)
In any case, Canonical trumpets its partnership with Microsoft — yep, Microsoft — this week at the Open Compute Summit, where the Isle of Man reached across to Redmond to demonstrate how Canonical and Microsoft are working together to create scalable, OCP-compliant architecture.
"Canonical is supporting bare-metal provisioning on Microsoft's OCS hardware with our open source Metal-as-a-Service (MAAS) deployment product," the article states. "This support means Windows and Linux (Ubuntu, CentOS, SUSE) operating systems, as well as application software on top, can be one-touch provisioned on OCS hardware. At the summit, Canonical is demonstrating how to provision a multi-tier web architecture effectively, including content publishing and database to separate nodes in an OCS chassis."
What's mysteriously missing from that parenthetical in the previous paragraph? If you said Red Hat, you'd go on to the bonus round.
Okay then…get a room, you two. See you next week.
Larry Cafiero
Larry Cafiero, a.k.a. Larry the Free Software Guy, is a journalist and a Free/Open Source Software advocate. He is involved in several FOSS projects and serves as the publicity chair for the Southern California Linux Expo. Follow him on Twitter: @lcafiero
Published in Business, Distros, Hardware and Operating Systems
Mista Gee March 13, 2015
As famous as Linus has become, he's still Linus. A very smart man
is not so good with the public. He's misunderstood a lot, and yes he should do something about his vocabulary..
Fred McKinney March 13, 2015
Canonical in a partnership with Microsoft?!! Bye-bye Ubuntu, including any distro based on Ubuntu!
Hunkah March 13, 2015
How boring is open source going to be? Linus keeps things entertaining. Someone needs to speak up about the stupidity that keeps happening in the Open Source world.
People really need to stop being so fragile and quit wearing nerf diapers. If you're an idiot, no amount of petting is going to change the fact that YOU ARE A FRIGGIN IDIOT!. Get over yourself.
I say we give Linus a bigger podium. I'll hand out the popcorn.
digi_owl March 13, 2015
Time will tell how long it takes for someone to use this to shut him down when the RH mercenaries rides into town again.
Mike March 14, 2015
More corporate takeover of Linux.
Red Hat has their flunkies everywhere.
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