text:
DOI:10.5852/EJT.2019.500
A new genus and three new species of mangrove slugs from the Indo-West Pacific (Mollusca: Gastropoda: Euthyneura: Onchidiidae)
@article{Dayrat2019ANG,
title={A new genus and three new species of mangrove slugs from the Indo-West Pacific (Mollusca: Gastropoda: Euthyneura: Onchidiidae)},
author={Beno{\^i}t Dayrat and Tricia C. Goulding and Munawar Khalil and Deepak Apte and Adam J. Bourke and Jos{\'e} Manuel Mart{\'i}nez Comendador and Shau Hwai Aileen Tan},
journal={European Journal of Taxonomy},
B. Dayrat, Tricia C. Goulding, +4 authors S. Tan
Mangroves of the Indo-West Pacific have remained poorly explored, so even the diversity of the onchidiid slugs, which are some of the most abundant animals in mangroves of the Indo-West Pacific, is not well known. Thanks to several years spent exploring mangroves in the Indo-West Pacific (more than 260 stations), especially in South-East Asia, the diversity of mangrove gastropods can now be addressed through revisions following an integrative taxonomy approach (nomenclature, field observations…
A new species and new records of Onchidium slugs (Gastropoda, Euthyneura, Pulmonata, Onchidiidae) in South-East Asia
B. Dayrat, Tricia C. Goulding, M. Khalil, D. Apte, S. Tan
ZooKeys
A new species of Onchidium melakense is described, a rare species with only nine individuals found at three mangrove sites in the Andaman Islands and the Strait of Malacca, which is delineated based on mitochondrial (COI and 16S) and nuclear (ITS2 and 28S) DNA sequences as well as comparative anatomy.
A new genus of air-breathing marine slugs from South-East Asia (Gastropoda, Pulmonata, Onchidiidae)
B. Dayrat, Tricia C. Goulding, +4 authors Shau Hwai Tan
Medicine, Geography
The present contribution shows again that species delineation is greatly enhanced by considering comparative anatomy and nuclear DNA sequences in addition to mitochondrial DNA sequences, and that thorough taxonomic revisions are the best and most efficient path to accurate biodiversity knowledge.
Systematic revision of the genus Peronia Fleming, 1822 (Gastropoda, Euthyneura, Pulmonata, Onchidiidae)
The taxonomy of the onchidiid slugs with dorsal gills is revised for the first time based on a large collection of fresh material from the entire Indo-West Pacific, from South Africa to Hawaii, to better establish species distributions.
View 28 excerpts, cites background, methods and results
Description of a new Peronia species (Gastropoda: Eupulmonata: Onchidiidae) from Iran, Persian Gulf.
F. Maniei, M. Espeland, M. Movahedi, H. Wägele
Zootaxa
Results on a new species of eupulmonate slug found in the Persian Gulf, a subtropical region with harsh conditions such as elevated salinity and high temperature compared to the Indian Ocean, are presented.
View 5 excerpts, cites results and methods
A DNA barcode library for mangrove gastropods and crabs of Hong Kong and the Greater Bay Area reveals an unexpected faunal diversity associated with the intertidal forests of Southern China
H. Bravo, Christine L. Y. Cheng, +6 authors S. Fratini
This study provides the first reference barcode library for mangrove-associated macrobenthic fauna in the Greater Bay Area and represents a reliable tool to management and conservation plans.
A new genus and four new species of onchidiid slugs from South-East Asia (Mollusca: Gastropoda: Pulmonata: Onchidiidae)
B. Dayrat, Tricia C. Goulding, D. Apte, Vishal Bhave, Quang Ngo Xuan
A new genus, Melayonchis Dayrat and Goulding gen. nov., and four new species are described, based on morphological characters and DNA sequences of the Onchidiidae, which ranges from the Andaman Sea to the South China Sea through the Strait of Malacca.
Integrative taxonomy of a new and highly-diverse genus of onchidiid slugs from the Coral Triangle (Gastropoda, Pulmonata, Onchidiidae)
Tricia C. Goulding, M. Khalil, S. Tan, B. Dayrat
Nine of the ten Wallaconchis species are found in the Coral Triangle (eastern Indonesia and the Philippines), with up to six species found on the island of Bohol (Philippines) and eight species overlapping in northern Sulawesi (Indonesia).
A new genus and a new species of onchidiid slugs from eastern Indonesia (Gastropoda: Euthyneura: Onchidiidae)
A new genus is described here for a new species, Alionchis jailoloensis Goulding & Dayrat, new species which is highly distinct from all other onchidiids, which is endemic to Halmahera, eastern Indonesia.
Integrative taxonomy of the genus Onchidium Buchannan, 1800 (Mollusca, Gastropoda, Pulmonata, Onchidiidae)
The genus Onchidium is redefined here as a clade including only three species which are strongly supported by both morphological and molecular data, and all three species are re-described here for the first time.
View 10 excerpts, references background and results
Review of the current knowledge of the systematics of Onchidiidae (Mollusca: Gastropoda: Pulmonata) with a checklist of nominal species
B. Dayrat
A checklist of all 143 species names available in Onchidiidae is provided, as a first step towards a systematic revision of systematics of this taxon.
A revision of Peronina Plate, 1893 (Gastropoda : Euthyneura : Onchidiidae) based on mitochondrial and nuclear DNA sequences, morphology and natural history
Tricia C. Goulding, S. Tan, +5 authors B. Dayrat
Invertebrate Systematics
Peronina species are described using an integrative approach (natural history, comparative anatomy and DNA sequences), and Mitochondrial COI and 16S sequences and nuclear ITS2 and 28S sequences are used to independently test species boundaries.
Distribution of Onchidium damelii Semper (Gastropoda, Onchidiidae)
R. Kenny, A. Smith
The pulmonate gastropod Onchidium damelii Semper has a widespread tropical Indo-Pacific intertidal distribution and shows habitat preference rather than a zonal (tidal pattern) distri bution within the mangroves; population density is associated with substrate particle size and organic content; and temperature relationships were investigated.
Anatomical Re-Description of the Terrestrial Onchidiid Slug Semperoncis montana (Plate, 1893)
The anatomy of Semperoncis montana, a terrestrial species that lives in high-elevation rain forests of the Philippines Islands, is redescribed based on 91 specimens representing ten populations and Ontogenetic changes in the shape of male organs are described and illustrated in detail, indicating that S. montana was described based on immature specimens of the later named Platevindex apoikistes.
Species diversity of Onchidiidae (Eupulmonata: Heterobranchia) on the mainland of China based on molecular data
Bianna Sun, Cheng Chen, Heding Shen, Kunxi Zhang, N. Zhou, Jing Qian
A phylogeny constructed using partial sequences of two mitochondrial genes and one nuclear ribosomal RNA gene from 32 samples comprising five genera showed that the taxa clustered in two main groups of six species, and it was clear that COI will be useful in discriminating onchidiid species-group taxa.
Phylogenetic relationships and evolution of pulmonate gastropods (Mollusca): new insights from increased taxon sampling.
B. Dayrat, Michele Conrad, +6 authors A. M. F. Martins
Phylogenetic relationships among higher clades of pulmonate gastropods are reconstructed based on a data set including one nuclear marker and two mitochondrial markers for a total of 96 species, with a special emphasis on sampling the Ellobiidae, Onchidiidae, and Veronicellidae.
View 6 excerpts, references background, methods and results

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to set total no. of days on x-aixs Want to display total no. of days at the bottom, it displays 365 days after that starts from day 1, is there any way show total no. of days please! display 425 instead of 060 at the end.

Have checked other relevant answers but I couldn't get succeed, your help is much appreciated! Thanks!!
    data1 = pd.read_csv(path1,names=['time','1','2','3','4','Value','6','7',],
                                sep=',', index_col=0, parse_dates=True, dayfirst=False)
    ax = pd.rolling_mean(data1['Value'],100).plot()
    date_fmt = '%j'
    formatter = dates.DateFormatter(date_fmt)
    ax.xaxis.set_major_formatter(formatter)
    plt.gcf().autofmt_xdate()

Thanks in advance...

A: Someone better at matplotlib may have a cleaner idea, but if you're willing to add a column or change the index, calculating the running number of days is relatively straighforward.  Assuming your data is already daily, this will work.
df['day'] = range(df.index[0].dayofyear, df.index[0].dayofyear + len(df))

If it's not even days, some logic like this should handle it.
import numpy as np
import calendar

df['day'] = ((df.index.dayofyear - df.index[0].dayofyear + 1) +
              (df.index.year - df.index[0].year) *
              np.where(df.index.map(lambda x: calendar.isleap(x.year - 1)), 366, 365))

redpajama_set_name: RedPajamaStackExchange


text:
Q: Email2Case: How to stop OOO replies updating cases This might be a known issue but I am unable to find any answers at present.
When an agent sends an email from a case which includes the case thread, we are trying to stop OOO from triggering a case to be reopened if received back as this will create false stats.
Can anyone advise of a way that this can be done?
Thanks
Scott

A: To fix this issue at the root would be to have your mail server configured in such a way that emails which contain key words, such as 'Out of office', are ignored. Although that would typically be an IT Helpdesk remit and not for a Salesforce Admin / Developer.
From a Salesforce Developer perspective, you can write a trigger which auto-deletes or prevents a new email thread hitting the case. This link gives some helpful information.
From a Salesforce Admin perspective, it may be worth researching an App on the AppExchange. Email to Case premium is very helpful for preventing email2case loops, but I am unsure if it prevents email threading of emails which contain key words. Also from a Salesforce Admin perspective, although this isn't ideal, you can create new custom fields and have workflows / process builders created which would ignore calculating case open times etc from threads which contain key words.


text:
006-i. Advice on ToR: EIA for village water supply Dosso - Niger
The NCEA was intended to advise on Terms of Reference (ToR) for the EIA for a rural water supply project in Dossa, Niger. The request for this support was however withdrawn and no advisory report was submitted.
The Dutch government proposed a project to improve rural drinking water supplies in the department of Dosso. The project would be titled 'Programme d'Hydraulique Villageoise Dosso (Phase III)'. Project activities would include drilling and repairing wells, and building a water supply system in a number of rural villages.
The NCEA was originally asked to provide support the project by advising on Terms of Reference (ToR) for the EIA. A working group had been established. The request for support was however withdrawn. The NCEA discontinued its activities and did not submit an advisory report.
Mr N. van Duivenbooden
Mr R.J.M. Gunst
Ms M. Nugteren
Chair: Mr D. de Zeeuw
Technical secretary: Mr R.A.M. Post
Country: Niger
Last modified: 10 May 2019


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Michael Killen will again take a break from producing interviews with guests who help explain CA's Climate Plan or their related message. On Sat. August 11, and starting at 11:30AM, he will produce interviews with three artists. They are with the artists Odis Schmidt of Compche, CA; Harry Cohen, Woodacre, CA and Dickens 44, from Marin, County, CA. Carl W. Laur will direct the productions.


Canada Goose Holdings Inc.'s forecast proved to be conservative again.
The luxury parka maker reported a profit in the fourth quarter while analysts had projected a loss. Earnings almost doubled for the fiscal year, the company said Friday, outpacing the at least 35 per cent growth outlook it provided seven months ago. Canada Goose predicted an increase of at least 25 per cent for the current year.
The shares surged as much as 31 per cent in Toronto in their biggest intraday gain since the company went public in March 2017.
Canada Goose, which is known for its Arctic-ready, US$1,000-plus parkas, has added stores in cities such as London and Chicago, expanded its presence online and introduced lighter products such as windbreakers. It's now betting on Chinese consumers' newfound willingness to spend and recently unveiled plans to open a Beijing flagship store and a shop in Hong Kong this fall.
"These results reinforce my belief that we are still just scratching the surface of our global potential," Chief Executive Officer Dani Reiss said in a statement.
After years of relying on wholesalers, the company's focus on more lucrative direct-to-consumer sales has paid off and helped the stock more than triple in value since its initial public offering last year.
Analysts have said the company tends to undershoot with its forecasts. In June 2017, Canada Goose said sales would grow in the mid-to-high teens for the next three fiscal years and predicted adjusted profit growth of about 20 percent. Just five months later, it revised its outlook for fiscal 2018 to at least 25 percent, and profit growth to at least 35 percent.
The forecast assumes "impressive growth to continue, yet looks conservative on Ebitda margins," Mark Petrie, an analyst at CIBC World Markets, said in a note to investors.
Excluding some items, earnings in the fiscal year that ended March 31 rose 95 percent to 84 Canadian cents. In the fourth quarter, the company posted profit of 9 Canadian cents, compared with analysts' projections for a loss of 9 cents.
Canada Goose climbed as high as $78.30 on Friday. They were already up 51 per cent this year through Thursday's close.
--With assistance from Brandon Kochkodin.


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I install new gas hot water systems, replace old hot water systems and repair Bosch hot water that's gone cold. I install gas cooktops and ovens and repair gas appliances that won't light or stay lit. I install new toilet suites, clear blocked drains, service and repair leaking taps, replace broken pipes and stop toilets from leaking. Give me a call to carry out annual backflow testing to certify your backflow prevention device.
Rail showers, water filtration, pressure testing, UV sterilisation, mixer taps, renovations, corroded sewer vents, gas leaks, garden taps, LP Gas systems, rainwater pumps, outdoor pool showers – you name it – if it involves water or gas around your home or place of business, call Josh's Gas & Plumbing to install it or repair it.
Hot water, blocked toilets and drains, leaking taps and toilets, rainwater pumps and filter taps. New plumbing work to additions and renovations is no problem either.
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Call Josh for annual backflow testing and certification, installing new backflow protection or repairing a valve that won't stop leaking.


text:
Cakung is a district (kecamatan) of East Jakarta, Indonesia. The district is roughly bounded by Bekasi Raya Road to the west, the Bekasi Raya Road - Petukangan canal to the north, a portion of Cakung river to the east, and the Jakarta-Bandung-Surabaya railway to the south. A large area in Cakung is allotted to industrial or agricultural use. The Pulo Gadung industrial complex is located in the district. The district is served by Jakarta Outer Ring Road.

The city hall of East Jakarta is located in Pulogebang Administrative Villages in Cakung. Newly built Pulo Gebang Bus Terminal, which is arguably the largest of its kind, is also located in this area.

The Cakung Drain is a flood canal that begins from Cakung, starting at the confluence of Cakung River and Buaran river, flows to the north, and flows out to the Jakarta Bay via Cilincing Administrative Village in Cilincing District of the city of North Jakarta.

Kelurahan (Administrative Villages)
The district of Cakung is divided into 7 kelurahan or administrative villages:

List of important places
 City Hall of East Jakarta
 Pulogadung Industrial area
 Pulo Gebang Bus Terminal, the largest bus terminal in Southeast Asia. It is integrated with Jakarta Outer Ring Road and railway. Starting on July 2, 2016 all buses to Central Java, Yogyakarta and East Java depart form Pulogebang bus terminal due to Rawamangun terminal and Pulogadung terminal are closed for the buses. TransJakarta serves Rawamangun-Pulogebang and Pulogadung-Pulogebang routes.
Jakarta Garden City
J-Sky

References

Districts of Jakarta
East Jakarta

redpajama_set_name: RedPajamaWikipedia


Nearly two decades ago Bob Miller was an altruistic bone marrow donor, today he is the recipient of a lifesaving kidney transplant from a stranger.
Organ donations in New Jersey broke records last year and soared 38 percent in the past five years.
The NJ Sharing Network reported 531 organs donations by New Jerseyans in 2015, up 37 percent from the year prior.
Jessica Melore, the programs director for NJ Sharing Network, shares her story of organ transplant and explains the process.


text:
\section{Introduction}
Ram pressure of the inter-galactic medium in the dense environments of
galaxy clusters and groups can significantly affect the interstellar
content of galaxies. Together with tidal stripping and gas outflows due
to galaxy mergers, ram pressure stripping is an efficient mechanism
removing their gas component. This quenches the star formation. Local
enhancement of the gas density by the ram pressure, however, can
increase the star formation rate in the central disk regions and in the
tail of stripped material \citep{kronberger08}. Current observations
showing gaseous tails and extra-planar gas
\citep[e.g.][]{crowl05,chung07}, and a number of numerical simulations
\citep[e.g.][]{vollmer01a, roedigerbruggen07} confirm the importance of
gas stripping in the evolution of galaxies. Although some gas tails
could be due to tidal interactions between galaxies in the cluster
\citep{chung07}, these are rapidly destroyed by the ram pressure
\citep{kapferer08}. Ram pressure then creates its own long gas tails
\citep{roedigerbruggen08}.

When the galaxy plunges into the intracluster medium (ICM), a complex
hydrodynamical interaction of the interstellar matter (ISM) and ICM
takes place. Several phases of ISM-ICM interaction were recognized by
\citet{roedigerbruggen06}: the initial ram pushing of the ISM out of
the disk, followed by stripping of elements accelerated to the escape
velocity, in a background supported by continuous stripping. A simple
estimate of the stripping amount suggests that if the ram pressure of
the wind exceeds the local gravitational restoring force per unit area,
the gas is released from the potential of the galaxy
\citep[][GG72]{gunngott72}. This approximation works well for face-on
cases with constant long-lasting flows of the ICM. However, in real
situations, galaxies experience a time-varying ram pressure due to
their evolving orbital velocity and radially changing ICM density. An
approximative criterion where the stripping is proportional to the
momentum of the ICM encountered along the orbit was introduced by
\citet{jachym07}.

A long-term ram pressure corresponding to the overall cluster ICM
density profile can be accompanied by short pressure spikes from local
clumps in the ICM distribution or wakes caused by previous stripping
events. \citet{tonnesenbryan08} studied the role of ICM
overdensities and their infalling motions, and suggested that even
small substructures in the ICM may evoke a stronger stripping than that
corresponding to the given position in the cluster. In short ICM-ISM
encounters, not all the ISM is accelerated to the escape speed and its
re-accretion can occur. Very recently, \citet{tonnesenbryan09} took
into account the multi-phase nature of the ISM, and found different
results, according to the clumpiness of the gas. \citet{vollmer09}
argue that ram pressure is more efficient on ionized gas, and they see
evidence of differential ram pressure efficiency according to the
nature of the multiphase gas.

The question of how the orientation of the galaxy relative to the
orbital direction influences the final stripping was touched on by many
authors \citep{quilis00, vollmer01a, schulzstruck01, hidakasofue02,
marcolini03, roedigerbruggen06}. For tilted galaxies the effect of the
hydrodynamical shielding is more pronounced in comparison to the
face-on case and yields weaker stripping. Moreover, due to galactic
rotation, near edge-on ram pressures evoke asymmetric shapes of the ISM
disks \citep[e.g.][]{roedigerbruggen06}.
From previous simulations, only close-to edge-on orientations were
identified as less efficient in the stripping than face-on cases
\citep{quilis00,roedigerbruggen06}. The tilted stripping was found to
be delayed compared to face-on \citep{vollmer01a}, and takes a
longer time \citep{faroukishapiro80}. Other features, like tails of
stripped material forming on the disk side where the gas rotates
against the wind \citep{phookunmundy95}, or annealing of inclined
galaxies by a stronger loss of angular momentum \citep{schulzstruck01},
were noticed. Mimicking the hydrodynamical shielding of tilted galaxies
with a simple geometrical prescription, \citet{vollmer01a} performed a
set of sticky-particle simulations with time-varying ram pressure
peaks. \citet{roedigerbruggen06,roedigerbruggen07}, using
hydrodynamical adaptive-mesh-refinement simulations, introduced models
of galaxies experiencing a constant ICM flow in a periodic boundary
box, or orbiting on realistic orbits in clusters.

What is the role of the galactic disk tilt angle in various
distributions of the ICM, and could a simple dependence between the
stripping amount and the tilt angle be found from simulations? To
answer these questions we perform in this paper an extensive grid of
Smoothed particle hydrodynamics (SPH) simulations with time-varying
large or small ram pressure peaks of
generally tilted ram pressure stripping events. This completes other
existing simulations based on different numerical approaches (AMR,
sticky-particles etc.) and follows our simulations on the face-on study
made by \citet{jachym07}.
Rather than describing in detail the process of stripping itself (that
shall be studied in a forthcoming paper), we focus on the quantitative
outcomes of the tilted ISM-ICM interactions. To isolate the effect of
the disk inclination, we deal with galaxies on strictly radial orbits
freely falling from the cluster outskirts. This condition however does
not imply a strong limitation since ram pressure profiles experienced
by galaxies along slightly elliptical orbits may be modeled with
strictly-radial ones through an ICM distribution with a lower value of
the central density and a lower concentration towards the center.
With the results of the simulation grid in hand, we use a simplified
test particle model to separate the various effects taking place in the
ISM-ICM interactions, and to search for a simple dependence
that would fit the numerical results.

Our model, initial conditions and simulation method are introduced in
Section~\ref{sec:model}. The results of simulations are presented and
analyzed in Sections~\ref{sec:proc} and \ref{sec:res}. Their comparison
with a simple test model is discussed in Section~\ref{sec:kin}. How can
the results of the tilted stripping be estimated? This question is
answered in Section~\ref{sec:analyt}, which deals with a momentum
delivery criterion. In the discussion of Section~\ref{sec:disc}, we
compare our results with outcomes of previous numerical simulations.

\section{Modeling}\label{sec:model}
\subsection{Galaxy model}
Our model galaxy is a late-type massive galaxy (LM-type in
\citealp{jachym07}): a three-component system with Plummer bulge
and dark halo, and with Toomre-Kuzmin-sech$^2(z/z_0)$ disk. The
values of the model parameters are $M_d=8.6\ 10^{10}$ M$_\odot$,
$a_d=4$ kpc, $z_0=0.25$ kpc, $M_b=1.3\ 10^{10}$ M$_\odot$, $a_b=0.4$
kpc, and $M_h=4.2\ 10^{11}$ M$_\odot$, $a_h=20$ kpc. All three
components are represented with particles (12~000 for the stellar disk,
12~000 for the halo, and 6000 for the bulge). Their
distribution is truncated at 16 kpc (disk), 4 kpc (bulge), and 40 kpc
(halo). The corresponding rotation curve is flat with a velocity of
about 250~km~s$^{-1}$. The ISM in the disk follows the same density
profile as the stellar component with the same radial scale ($a_d=4$
kpc). Its mass forms 10\% of the total disk mass. The ISM disk
consists of 12~000 SPH particles which provides sufficient resolution
for the large-scale effects of interest in this paper.

\subsection{Cluster model}
The galaxy cluster is modeled with dark matter (DM) and ICM gas. Their
volume densities follow a $\beta$-profile \citep{cavaliere76,
schindler99}: $\rho = \rho_0 (1 + R^2/ R_{\rm c}^2 )^{-3\beta /2}$.
For the {\it standard cluster model} we use $\beta_{\rm ICM}=1/2$,
$\rho_{\rm 0,ICM}=6.5\ 10^{-3}$ cm$^{-3} = 0.64\ 10^{-26}$ g~cm$^{-3}$
and $R_{\rm c,ICM} = 13.4$ kpc. The fixed DM, which provides the
gravitational potential, has $\rho_{\rm 0,DM}=3.8\ 10^{-4}$
M$_\odot\,$pc$^{-3}$,$R_{\rm c,DM} = 320$ kpc, and $\beta_{\rm DM}=1$.
The ICM is introduced with 120~000 SPH particles distributed within
a 140~kpc truncation radius about the cluster center. Initially, the
ICM particles are assigned velocity dispersions calculated from the
hydrostatic equilibrium equation of the cluster. The system then
slightly relaxes to a stable state. Particles that reach the truncation
radius of 140 kpc are relocated to the centrally symmetric position.
See \citet{jachym07} for more details.

\begin{table}[t]
\centering
\caption{\small
Set of basic simulation runs. We refer to $R1\rho1$ as to the
{\it standard run}. Values of $\Sigma_{\rm ICM}$ correspond to $R_{\rm
ICM}^{\rm trunc}=140\ $kpc.}
\begin{tabular}{lcccc}
\hline
\hline \rule{-3.pt}{2.6ex}
run & $R_{\rm c,ICM}$, $\rho_{\rm 0,ICM}$ & $p_{\rm ram}^{\rm
max}$ & $\Sigma_{\rm ICM}$\\
& (kpc,10$^{-3}$cm$^{-3}$) & cm$^{-3}$(km/s)$^2$ & ($M_\odot$pc$^{-2}$)\\
\hline \rule{-3.pt}{2.6ex}
$R4\rho8$&53.6 , 52   & 100~913& 114\\
$R4\rho4$&53.6 , 26   & 46~752 &  57\\
$R4\rho1$&53.6 , 6.5  & 10~993 &  14\\
$R4\rho0$&53.6 , 1.6  & 2705   & 3.6\\
\hline \rule{-3.pt}{2.6ex}
$R1\rho8$&13.4 , 52   & 89~214 &  41\\
$R1\rho4$&13.4 , 26   & 43~827 &  20\\
$R1\rho1$&13.4 , 6.5  & 10~810 &   5\\
$R1\rho0$&13.4 , 1.6  & 2693   & 1.3\\
\hline \rule{-3.pt}{2.6ex}
$R0\rho8$&3.4  , 52   & 86~549 &  12\\
$R0\rho4$&3.4  , 26   & 43~143 & 5.9\\
$R0\rho1$&3.4  , 6.5  & 10~769 & 1.5\\
$R0\rho0$&3.4  , 1.6  & 2689   & 0.4\\
\end{tabular}
\label{tab_runs}
\end{table}

\subsection{Initial conditions}
The model galaxy initially starts with zero velocity from the cluster
periphery ($R=1$ Mpc) and freely falls along a strictly radial orbit
towards the cluster center. In the standard model the galaxy reaches
the center at time $T=1.64$ Gyr with a velocity of about 1300
km~s$^{-1}$. The simulation is followed until $T=2$ Gyr
when the galaxy has already left the central part of the cluster
filled with ICM particles. Thus, each simulation run corresponds to one
orbit of the galaxy through the cluster center.

To treat various cluster environments, we vary the values of the
$R_{\rm c,ICM}$ and $\rho_{\rm 0,ICM}$ parameters, multiplying each
standard value by factors of 8, 4, 1, and 0.25. Table~\ref{tab_runs}
defines the basic set of simulation runs which are labeled with the
corresponding factors (0 stands for the factor of 0.25).
Table~\ref{tab_runs} gives for each run the combination of $R_{\rm
c,ICM}$ and $\rho_{\rm 0,ICM}$ parameters, the peak value of the ram
pressure along the orbit, and the column density of the ICM encountered
on the orbit. Note that narrow ICM distributions or those with low
values of density may represent ICM overdensities or debris structures
left over in the cluster from recent stripping events.

\citet{abadi99} warned against too massive ICM particles that can punch
holes in the gas disk and cause a large artificial drag on the ISM
particles. In our standard model ($R1\rho1$) one ICM particle has a
mass of about 5~10$^5$~M$_\odot$, which is almost equal to the mass of
an individual ISM particle. Concerning the ICM component setup, its
truncation radius of 140~kpc was chosen so that ram pressure in the
standard cluster exceeds at that distance the gravitational restoring
force in the disk outskirts of an approaching galaxy.

We introduce the tilt angle of the disk with respect to the orbital
direction of the galaxy as $i=0^\circ$ for edge-on and $i=90^\circ$ for
face-on orientation, throughout the paper.

\subsection{Simulation method}\label{sec:method}
The simulations were carried out with the tree/SPH code GADGET
\citep{springel01} adapted by \citet{jachym07} for calculations of
ISM-ICM interactions. Smoothed particle hydrodynamics
\citep[SPH,][]{lucy77,gingoldmonaghan77} in its standard formulation
has significant problems with contact discontinuities where the density
jump is very large. Across such contact discontinuities, fluid
instabilities can be suppressed \citep[e.g.][]{agertz07}, or other
artifacts can occur when the sampling is poor
\citep[e.g.][]{okamoto03}. The problem of ICM-ISM interaction is
basically a special case of this. \citet{jachym07} modified GADGET to
estimate smoothing lengths of either ICM or ISM particles separately
from neighbors of a corresponding phase.
This means that the search of the neighboring particles continues
until a desired number of proper neighbors are found, while ignoring
those of the second phase. It ensures that even a moderate number of
ICM particles will fully cover during the interaction the ISM disk, as
the ICM particles do not shrink when approaching the dense ISM in the
disk. This modified code was used by \citet{jachym07} for
simulations of face-on ram pressure stripping events.

Although large ICM particles result in a low spatial resolution
and ISM particles that lack pressure gradients from the wind,
our suggestion provides a simple way to avoid the above limitation
of the standard SPH method, and it may be used for the quantitative
purposes of this paper. An ideal solution could involve a new
self-consistent way to estimate densities that allows a better
representation of contact discontinuities -- e.g. based on a
tessellation scheme \citep[recently published by][]{springel09},
implementation of the particle splitting mechanism
\citep{kitsionaswhitworth07} into the standard SPH, or the new SPH scheme
of \citet{kawata09}.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig1.ps}
\caption{\small
Zero-order test vs. isolated evolution: Disk radii encompassing 95~\%,
90~\%, 80~\%, ..., 10~\% of the total ISM mass ({\it from top down}) as
functions of time in the case of the galaxy evolving at rest in the
center of the standard cluster ({\it solid curves}), and in an isolated
galaxy ({\it dashed}).
}\label{zero_test}
\end{figure}

\begin{figure*}[t]
\centering
\includegraphics[height=1.\textwidth,angle=270]{1469fig2.eps}
\caption{\small Pole-on views of the ISM disk crossing edge-on through
the $R4\rho1$ cluster. The disk rotates clockwise; the ram pressure
operates from the left. Color saturation corresponds to increasing
ISM density.}
\label{edge_snap}
\end{figure*}

\subsection{Zero-order simulation run}\label{zero}
In order to test the influence of the simulation technique used, and
the effect of resolution on the results of our stripping simulations,
we present a zero-order test: The galaxy is placed at rest at the
center of the cluster and left to evolve surrounded by the ICM for about
300 Myr (the time comparable to the duration of the standard ISM-ICM
interaction discussed later). The evolution of the galaxy's gaseous
disk is displayed in Fig.~\ref{zero_test} showing radii that
encompass fixed fractions of the total ISM mass (solid curves)
evolving with time. The ISM disk (or at least its outer layers) is
compressed by an abrupt introduction of the static external pressure of
the ICM on a time scale of about 100~Myr. After this period the
outer layers start to slightly oscillate while the disk slowly
continues to settle towards an equilibrium. All the ISM particles
during the simulation stay bound to the galaxy. The stellar disk
component is unchanged during the simulation. For comparison, the
evolution of the ISM disk of an isolated galaxy, not exposed to any
external pressure, is plotted in Fig.~\ref{zero_test} with dashed
curves.

The ISM component is treated isothermally in our simulations. This
simple approach is used to roughly mimic an efficient radiative cooling
of the ISM gas. The disk confinement in Fig.~\ref{zero_test} may thus
be understood in terms of an abrupt increase of the external pressure
after the galaxy has been placed into the ICM -- due to its
isothermality the ISM cannot heat up (to compensate the increased
external pressure) and is compressed instead. In Fig.~\ref{zero_test},
an extreme effect is shown due to a maximum pressure corresponding to
the cluster center. However, in the ram pressure stripping simulations
that we deal with further in this paper, the galaxy arrives at the
cluster center only gradually from its outskirts. This aspect will
be treated in the following section.

Concerning the influence of our numerical technique on the simulation
outputs, no Rayleigh-Taylor instabilities or spurious effects due to
the lack of resolution appeared in the zero-order test simulation.

\section{Process of stripping}\label{sec:proc}
\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig3.ps}
\caption{\small
Effect of the inclination: Evolution of the ISM mass bound to the
galaxy ({\it solid curves}) or enclosed within an evaluation cylinder
around the disk plane ({\it dashed}) in simulations with disk tilt
decreasing from face-on to edge-on ({\it from bottom up}) of the
standard $R1\rho1$ run.
}\label{M_tilt}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig4.ps}
\caption{\small
Mass flow of the ISM through the boundary of the evaluation cylinder
for five simulations of Fig.~\ref{M_tilt}.
}\label{Mdot}
\end{figure}

For non-face-on orientations of the galaxy with respect to the ICM
wind, the galactic rotation starts to play a role. Its effect is most
pronounced for near edge-on cases when it evokes an asymmetry in
the gaseous disk. This can be seen in Fig.~\ref{edge_snap} where
snapshots of the galaxy passing edge-on through the center of a wide
$R4\rho1$ cluster are depicted. (For illustrative purposes the
$R4\rho1$ run is studied here rather than the standard one where
edge-on stripping is less prominent.) Due to rotation, the disk side
moving parallel to the wind (upper side in Fig.~\ref{edge_snap})
experiences ram pressure that is lower by a factor of $(v-v_{\rm
rot})^2 / (v+v_{\rm rot})^2$ with respect to the opposite disk side;
$v$ is the orbital speed of the galaxy and $v_{\rm rot}$ is the
rotational velocity of the disk. However, as e.g. the second panel of
the Figure shows, the parallel-rotating side is more severely stripped
than the opposite one and it is thus not the highest ram pressure that
yields the strongest stripping. This paradox was noted by
\citet{roedigerbruggen06} as well. The explanation is in terms of time
delay: on the parallel-rotating side, the gas is accelerated towards
more rotational velocity and exits the galaxy almost at once. At the
opposite side, the gas is being braked from $v-v_{\rm rot}$ towards $v$
and with lower or no centrifugal force it has time to fall towards the
center of galaxy. Then, it still has to rotate half a turn around the
galaxy, and it has time to be re-accreted (or at least it stays around
the galaxy for a longer time).
Snapshots in Fig.~\ref{edge_snap} further show how, due to rotation,
the tail of the stripped material winds up around the disk.

To measure the actual level of stripping we set up a cylindrical zone
about the galactic disk plane ($r=16$ kpc and $|z|\leq3$ kpc), and
follow the enclosed ISM mass and the flow of the material through the
zone boundary. This is shown in Figs.~\ref{M_tilt} and \ref{Mdot} for
five simulations of the standard run with different tilt angles,
together with the ISM mass fraction bound to the galaxy (solid curves
in Fig.~\ref{M_tilt}). It confirms the expected trend: with the tilt
angle growing towards face-on, more material is stripped. The maximum
departure of the curves of the bound and in-the-zone-enclosed ISM mass
in Fig.~\ref{M_tilt} indicates the amount of material that is
re-accreted after the ISM-ICM interaction. The bound mass in
Fig.~\ref{M_tilt} is given by the sum of the ISM particles for
which $E_{\rm kin}+E_{\rm pot}<0$. Note that the system of the galaxy
is not closed -- it experiences a changing effect of the external
potential of the cluster and an external pressure. A slight growth of
the solid curves in Fig.~\ref{M_tilt} may be found at later simulation
times.

The "stripping rate" $\dot{M}_{\rm ISM}$, i.e. the flow of the ISM
through the boundary of the evaluation zone, exceeds almost 400
M$_\odot$yr$^{-1}$ for a face-on galaxy, the peak value decreases towards
the edge-on orientation to about 50 M$_\odot$yr$^{-1}$ (see
Fig.~\ref{Mdot}). This Figure shows not only the removal rate
($\dot{M}_{\rm ISM}<0$) but also a reversed re-accretion rate of the
shifted material ($\dot{M}_{\rm ISM}>0$) -- in the face-on case it
reaches about 50 M$_\odot$yr$^{-1}$ after the passage of the galaxy
through the central cluster part. (Note that the amount of re-accretion
is dependent on the extent of the evaluation zone.)

The re-accretion process may be better followed in Fig.~\ref{zbound}
which traces the actual distances of the bound ISM behind the galaxy (in
the direction of the wind) for face-on and edge-on cases. In the
face-on orientation, the ISM is by an increasing ram pressure first
gradually pushed out of the disk plane, and then rapidly "thrown" to
large distances, shortly after the cluster center passage. This material
returns to the disk at later simulation times.
In the edge-on orientation, the disk is first compressed by the rising
ram pressure, and then some material is shifted to larger distances.
The peak in Fig.~\ref{zbound} is, however, much smaller than in the
face-on case.
The reason why in near edge-on orientations the pushed material stays
close to the disk is in the conservation of the angular momentum of the
ISM particles rotating in the disk. When pushed by the ram pressure,
the particles wind up around the disk. We checked this behavior in a
more efficient run $R4\rho1$ where almost the same amount of ISM is
stripped as in the standard face-on run.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig5.ps}
\caption{\small
ISM re-accretion: Distances behind the galaxy (in the direction of the
wind) within which a certain fraction of actually bound ISM particles
are enclosed (from 95~\% to 80~\%, {\it curves from top down}). Face-on
({\it black}) and edge-on simulations of $R1\rho1$ run. (In the edge-on
case the distances are taken in absolute value as initially one half of
the particles occur ahead of the galactic mid-plane.)
}\label{zbound}
\end{figure}

Apart from the total stripped amount, no radical differences in the
duration of the stripping process of variously tilted galaxies can be
seen from our simulations. Several details, like a slight time shift of
the maximum of the stripping rate, or the course of re-accretion, look
different in edge-on and face-on orientations, however these effects
seem to be of secondary nature.

\subsection{Static vs. dynamic ICM pressure}
How does the effect of the disk radius reduction due to ram pressure
compete with the disk confinement due to the static ICM pressure
discussed in Section~\ref{zero}? In Fig.~\ref{calib} the rate of the
disk radius reduction caused by the ram pressure stripping in the
standard face-on run is compared with the upper curve of
Fig.~\ref{zero_test}. It shows that the effect of the ram pressure is
more important, even though the zero-order test took place in the
center of the standard cluster where the disk experienced the maximum
external pressure possible. In the ram pressure simulation the
in-flying galaxy enters the ICM distribution at the truncation radius
where the ICM density (and its pressure) is only small, and
plunges deeper towards the cluster center, which is crossed very fast.
Thus the actual role of the static ICM pressure will be even less than
in Fig.~\ref{calib}.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig6.ps}
\caption{\small
Ram pressure stripping vs. zero-order test: Actual estimate of the
stripping radius of the face-on galaxy in the standard $R1\rho1$
cluster ({\it solid}) as a function of time, vs. radius of the disk
confined by static ICM pressure ({\it dashed}, the 95~\% radius from
Fig.~\ref{zero_test}).
}\label{calib}
\end{figure}

Although the disk confinement due to the static ICM pressure operates
against ram pressure -- it does not strip the gas but makes the disk
more resistant to the ram pressure -- the tendency of the increasing
effect of the static ICM pressure in "larger" clusters goes in the same
direction as the effect of ram pressure stripping. Recently,
\citet{tonnesenbryan09} have taken into account the multi-phase nature
of the gas disk and found that the stripping radius is considerably
smaller for galaxies with radiative cooling, although the amount of
stripping is similar to that in galaxies without cooling. This goes in
the same direction as the above effect observed in our simulations.

We conclude that the disk confinement due to static external ICM
pressure is much less important than the stripping due to ram pressure
and we neglect this effect in analyzing the simulations in the
following sections.

\begin{table*}[t]
\centering \caption{\small List of performed simulations -- results.
From left to right: fraction of the stripped ISM mass for simulations
with decreasing inclination, stripped mass fraction estimate of GG72
criterion, corresponding stripping radii and the estimate of GG72.}
\begin{tabular}{lccccccccccccc}
\hline \hline \rule{-3.pt}{2.6ex} run & $M_{\rm strip}^{90^\circ}$ &
$M_{\rm strip}^{70^\circ}$ & $M_{\rm strip}^{45^\circ}$ & $M_{\rm
strip}^{20^\circ}$ & $M_{\rm strip}^{0^\circ}$ & $M_{\rm strip}^{\rm
GG72}$ & $r_{\rm strip}^{90^\circ}$ & $r_{\rm strip}^{70^\circ}$ &
$r_{\rm strip}^{45^\circ}$ & $r_{\rm strip}^{20^\circ}$ & $r_{\rm
strip}^{0^\circ}$ & $r_{\rm strip}^{\rm GG72}$\\
& (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (kpc) & (kpc) &
(kpc) & (kpc) & (kpc) & (kpc)\\
\hline \rule{-3.pt}{2.6ex}
$R4\rho8$& 93 & 91 & 89 & 86 & 70 & 93 & 1.5 & 0.9 & 1.4 & 0.8 & 1.2 & 1.5\\
$R4\rho4$& 85 & 85 & 80 & 72 & 52 & 83 & 1.6 & 1.8 & 1.6 & 1.6 & 2.0 & 2.4\\
$R4\rho1$& 59 & 56 & 48 & 34 & 24 & 57 & 2.5 & 2.6 & 2.6 & 3.7 & 5.1 & 4.5\\
$R4\rho0$& 26 & 25 & 18 & 10 &  6 & 36 & 6.0 & 6.2 & 6.5 & 6.5 & 7.1 & 6.8\\
 \rule{-3.pt}{3.6ex}
$R1\rho8$& 79 & 77 & 70 & 54 & 36 & 92 & 1.5 & 1.6 & 1.6 & 2.2 & 2.7 & 1.6\\
$R1\rho4$& 63 & 61 & 50 & 30 & 19 & 81 & 2.1 & 2.5 & 3.1 & 3.2 & 4.0 & 2.5\\
$R1\rho1$& 30 & 27 & 20 & 10 &  5 & 57 & 5.5 & 6.3 & 6.5 & 7.2 & 8.0 & 4.5\\
$R1\rho0$&  9 &  8 &  6 &  2 &  1 & 36 & 8.6 & 9.0 & 9.3 & 9.9 & 10.3 & 6.8\\
 \rule{-3.pt}{3.6ex}
$R0\rho8$& 37 & 35 & 27 & 13 &  7 & 92 & 5.5 & 4.6 & 6.1 & 6.5 & 7.2 & 1.6\\
$R0\rho4$& 22 & 21 & 14 &  6 &  3 & 81 & 6.8 & 7.7 & 8.0 & 9.2 & 9.2 & 2.5\\
$R0\rho1$&  5 &  5 &  3 &  1 &  1 & 57 & 9.8 & 9.9 & 10.2 & 10.6 & 10.7 & 4.5\\
$R0\rho0$&  1 &  1 &  0 &  0 &  0 & 36 & 11.1 & 11.1 & 11.2 & 11.4 & 11.5 & 6.8\\
\end{tabular}
\label{tab_results}
\end{table*}

\section{Results}\label{sec:res}
In this section the results of the basic set of simulation runs
introduced in Table ~\ref{tab_runs} are described. For each run listed
we have performed five simulations with increasing disk inclination: $i
= 0^\circ$ (edge-on), 20$^\circ$, 45$^\circ$, 70$^\circ$ and 90$^\circ$
(face-on). The overall Table~\ref{tab_results} provides the results:
mass fraction of the stripped material ($M_{\rm strip}$) at the end of
the simulation for five disk inclinations, stripped mass fraction
estimated with the GG72 formula, stripping radii $r_{\rm strip}$ for five
inclinations, and the stripping radius corresponding to GG72.

\subsection{Stripped amount}
The fraction of the ISM particles that is no longer bound to the
galaxy at the final simulation time yields the stripped mass fractions,
whose dependence on inclination is shown in Fig.~\ref{mstrip_inclin}.
The general tendency of the plot is evident -- with the inclination
decreasing from face-on to edge-on, the amount of stripping declines.
Furthermore:
\begin{itemize}
\item Previous simulations of \citet{quilis00},
\citet{roedigerbruggen06} and others have shown that there is almost no
difference between $i=70^\circ$ and face-on stripping ($i=90^\circ$). This is true in
Fig.~\ref{mstrip_inclin} for all runs.
\item For large pressure peaks (runs $R4\rho4$ and $R4\rho8$), the
stripping amount is almost independent of the inclination (for angles
higher than about 20$^\circ$).
\item The dependence of the stripping amount on inclination is more
pronounced for smaller ram pressure peaks.
\item Runs with the same value of $R_{\rm c,ICM} \cdot \rho_{\rm
0,ICM}$ quantity show close profiles of the $M_{\rm strip}(i)$ curves
-- e.g. ($R4\rho1$ and $R1\rho4$), or ($R4\rho0$, $R1\rho1$, and
$R0\rho4$).
\end{itemize}

The behavior with varying inclination is more clearly displayed in
Fig.~\ref{eff_inclin} which shows a new parameter $\eta$ that we
name the {\it stripping efficiency with respect to inclination}. It is
the ratio of the stripped mass fraction relative to the face-on case:
\begin{equation}\label{eq_eta}
\eta (i) = \frac{M_{\rm strip,\it i}}{M_{\rm strip, 90^\circ}} =
\frac{1-M_{\rm fin,\it i}/M_{\rm ini}} {1-M_{\rm
fin,90^\circ}/M_{\rm ini}}.
\end{equation}
Thus, $\eta$ characterizes the relative strength of a given ram
pressure profile to strip the ISM from an inclined galaxy with
respect to the face-on case. In Fig.~\ref{eff_inclin}, one observes
that the stripping efficiency always declines with decreasing
inclination angle. Moreover, both wider and higher ram pressure peaks
yield higher efficiencies. For smaller pressure peaks, $\eta$ falls
fastest at medium inclinations (between 20$^\circ$ and 70$^\circ$),
while for large peaks at inclinations smaller than $20^\circ$.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig7.ps}
\caption{ \small
Stripped mass fraction as a function of disk inclination for runs from
Table~\ref{tab_results}. Each run is labeled with the peak value of
the ram pressure. The inclination is 0$^\circ$ for edge-on and
90$^\circ$ for face-on orientation.}
\label{mstrip_inclin}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig8.ps}
\caption{ \small
Stripping efficiency with respect to inclination $\eta=M_{\rm
strip,i}/M_{\rm strip,90^\circ}$ as a function of the inclination (runs
$R0\rho1$ and $R0\rho0$ are not plotted).}
\label{eff_inclin}
\end{figure}

Stripping of face-on galaxies depends on the amount of the ICM
encountered along the trajectory \citep[Fig.~15 in][]{jachym07}:
galaxies crossing clusters with such combinations of $R_{\rm c,ICM}$
and $\rho_{\rm 0,ICM}$ parameters that $\Sigma_{\rm ICM}\sim \rm const$
were stripped to the same level. For inclined cases this hypothesis
is tested in Figs.~\ref{Mstrip_SigICM} and \ref{eff_SigICM}, which show
the stripped mass fraction and the stripping efficiency with respect to
inclination as a
function of the column density of the encountered ICM, respectively.
Different colors refer to simulations with different inclination
angles. The following trends are apparent
\begin{itemize}
\item with increasing amount of encountered ICM the stripped mass
fraction and the efficiency increase;
\item there is a tendency for the results from each inclination to
follow a certain close relationship, despite some systematic deviations
due to the different ICM density distributions;
\item for high $\Sigma_{\rm ICM}$, these relations saturate towards
complete stripping;
\item for lower ICM column densities, edge-on stripping is reduced
with respect to face-on by a constant factor.
\end{itemize}

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig9.ps}
\caption{ \small
Stripped mass fraction as a function of the column density of the
encountered ICM. The symbols denote the results of the SPH simulations
for various inclinations. The curves correspond to the fitting curve in
Eq.~\ref{fit}.
} \label{Mstrip_SigICM}
\end{figure}

All these results indicate that the column density of the ICM
encountered during the ISM-ICM interaction is the key parameter
determining the stripping outcome. It is much more important than the
maximum value of the ram pressure experienced along the orbit (GG72
criterion).

The numerical results in Fig.~\ref{Mstrip_SigICM} can be fitted with
the following formula
\begin{equation}\label{fit}
\frac{M_{\rm strip}}{M_{\rm ini}} = 1 - \exp\left[-0.01\, \Sigma_{\rm
ICM} (1 + 6 \sin^{1.5} i)\right].
\end{equation}
The exponent 1.5 provides a rather satisfactory match to the results
with intermediate inclinations, as can be seen in both
Figs.~\ref{Mstrip_SigICM} and \ref{eff_SigICM}.

In Table~\ref{tab_results}, the stripped mass fraction estimated with
the GG72 criterion is added. For the largest ram pressure peak ($R4\rho8$),
the values match well the face-on results of the SPH simulations. For
smaller peaks, however, GG72 overestimates the real stripped fraction.
Of course, no dependence on the tilt angle is included in the GG72
criterion, and its multiplication by a simple $\cos i$ term does not
resolve the problem, as it yields zero stripping in edge-on cases.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig10.ps}
\caption{ \small
Stripping efficiency with respect to inclination as a function of
the column density of the encountered ICM. The curves correspond to the
fitting curve in Eq.~\ref{fit}.
} \label{eff_SigICM}
\end{figure}

\subsection{Stripping radii}
Due to an asymmetric shape of the gas disk that develops, especially
after an inclined stripping event, the determination of its final
radius, i.e. the stripping radius, is not trivial
\citep[see][]{roedigerbruggen06}. In close to edge-on cases,
all the stripped and shifted material stays in the plane of the disk
and makes the determination difficult.

In Table~\ref{tab_results}, the given values of stripping radii
correspond to radii within which 90\% of the bound ISM is enclosed in
the final simulation time. This may slightly underestimate the radius
for the face-on orientation, while overestimating it for the edge-on case.
The values do not show a strong dependence for large and small peak
ram pressures; however, for medium pressure the trend of increasing
stripping radii towards edge-on orientations is visible.

As shown in Fig.~\ref{rstrip_inclin}, the stripping radii for all
simulations can be quite reasonably fitted with
\begin{equation}\label{fit_rstrip}
r_{\rm strip} = 12\, \mathrm{kpc}\, /\, [1 + \Sigma_{\rm ICM} (0.1 + 0.15
\sin i)].
\end{equation}

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig11.ps}
\caption{ \small
Stripping radii $r_{\rm strip}$ versus column density of the
encountered ICM. The symbols
are the same as in Fig.~\ref{Mstrip_SigICM}. The points are fitted with
the fitting function in Eq.~\ref{fit_rstrip}.
} \label{rstrip_inclin}
\end{figure}

The stripping radii estimated in the last column of
Table~\ref{tab_results} using the GG72 criterion show quite a good
agreement for the largest run. However, there is a tendency to
overestimate the SPH results. For smaller peaks, GG72 predicts less
stripping corresponding only to the peak ram pressure.

\section{A simple test particle model}\label{sec:kin}
In order to study the influence of the parameters more efficiently, and
to separate various effects -- the direct kinematics on the ISM induced
by the ram-pressure, and the related hydrodynamical consequences -- we
construct a very simplified model for the removal of gas from a
galaxy. The gas disk is represented by 10~000 point masses
distributed as in an exponential disk and held in the potential well
composed of the bulge, stellar disk, and dark halo, with parameters
identical to those used in the SPH computations. Initially, all
these particles are in circular orbits about the center of the
galaxy. Then, they are subjected to a Gaussian-shaped force pulse of
specified tilt angle with respect to the galactic plane, duration,
and maximum amplitude. The simulation starts at a time that is three
times the pulse duration before the maximum. In the computation of the acceleration,
the inertial mass of each particle is taken to be proportional to
the gas surface density of the exponential disk, in order to account
for the correct computation of the ram pressure in that part of the
disk. For each particle, the equation of motion is integrated, and
when the total energy becomes positive and the particle becomes
unbound, it is marked and counted as having been stripped. If all
particles were to experience this force pulse, the fraction of
stripped particles is independent of the tilt angle, because all
reach escape velocity within time-spans that depend little on their
initial position in the galaxy and the force tilt angle.

In order to simulate the thickness of the disk, we introduce a
shielding or shadowing of the particles downstream of those
particles facing the force. In this, we follow the modeling by
sticky particles by \citet{vollmer01a}. Particles that are
shielded by at least one upstream particle are assumed to experience
only the galaxy's internal forces. Experiments show that with the
choice of a suitable value for the shadowing radius (typically 200~pc),
we are able to reproduce well the amount of stripping for the
standard model of the SPH computations, as well as its dependence on
the tilt angle.

As is seen in Fig.~\ref{FigA}, the stripped mass fractions from these
simplified models behave in a very similar way as the SPH results.
While at high values of the ICM column density the stripping is less
severe and the relation is slightly flatter, the influence on the tilt
angle is nearly identical -- one obtains the same amount of stripping in
the edge-on configuration as in the face-on case for an ICM column density
that is larger by about a factor of 6. This indicates that this modeling
approach, and hence also the sticky-particle computations by
\citet{vollmer01a}, appears to be quite reliable in capturing the main
features of ram-pressure stripping. However, this simplified approach
has notable differences to the full hydrodynamical approach, in
features that we consider below.

\begin{figure}[t]
\centering
\includegraphics[clip=true,bb=73 72 543 745,height=0.48\textwidth,angle=270]{1469fig12.ps}
\caption{\small
The dependence of the stripped mass fraction on the column density of
the swept-up ICM, for different tilt angles. The dots are results from
a grid of simplified point-mass models, covering a range from 1/16 to
16 times in both duration and strength of the ram pressure force pulse,
centered about the value for our standard model. The curves are the
analytical fit to the SPH results. The symbols and colors are identical
to those of Fig.~\ref{Mstrip_SigICM}. Note that the range of parameters
in both axes is much wider.
}\label{FigA}
\end{figure}

The stripping efficiencies with respect to inclination (Fig.\ref{FigB})
show that the ratios of face-on and edge-on results are as large as
from the SPH models, but that there are some limitations. First
of all, at intermediate angles the simplified modeling gives results
that are closer to the face-on case than we find in SPH. Furthermore,
at high ICM column densities, one does not find such a steep increase of
stripping as experienced in SPH. We searched quite extensively in
parameter space, but could not find situations where the behavior
matched the SPH results more closely. Evidently, this is a
consequence of the limitations of the simplified treatment. We take
this as an indication that this kind of diagram is sensitive to the
different treatment of the (hydro-)dynamics of the problem.

\begin{figure}[t]
\centering
\includegraphics[clip=true,bb=73 72 543 745,height=0.48\textwidth,angle=270]{1469fig13.ps}
\caption{\small
Similar to Fig.~\ref{FigA}, but for the dependence of the stripping
efficiencies with respect to inclination as a function of the
column density of the encountered ICM.
}\label{FigB}
\end{figure}

The simplified modeling does allow us to separate the different
physical phenomena in the ram-pressure process. In particular it helps
to identify the hydrodynamical shielding by the matter lying
upstream as the principal cause for the dependence of stripping on
tilt angle, seen in our SPH results. The deviations seen with
respect to the SPH results suggest that the details of the behavior
changes with tilt angle comes from the finer details of the
hydrodynamics involved in the problem.

\section{Comparison with the analytical criterion}\label{sec:analyt}
From the consideration of the momentum provided by the in-streaming ICM
to the gas in the galactic disk \citet{jachym07} derived the
condition under which a volume element of disk gas (with column density
$\Sigma_{\rm ISM}$ for the face-on situation) would escape from a
galaxy,
\begin{equation}
\langle v\rangle_{\rho_{\rm ICM}} \Sigma_{\rm ICM} / \Sigma_{\rm ISM} =
v_{\rm after} > v_{\rm esc} = \sqrt{-2\Phi(r)},
\end{equation}
i.e. if the speed $v_{\rm after}$ exceeds the local escape speed. The
stripping radius would then be defined as the radius where $v_{\rm
after}$ = $v_{\rm esc}$ and the stripped mass fraction as the mass
exterior to that radius:
\begin{equation}
M_{\rm strip} = \int_{r_{\rm strip}}^{r_{\rm out}} 2 \pi \Sigma_{\rm
ISM}(r)\, r\, dr \ / \ M(r_{\rm out}),
\end{equation}
where $r_{\rm out}$ is the truncation radius of the disk.
For an exponential disk $\Sigma_{\rm ISM}(r) = \Sigma_0 \exp(-r/a_d)$
with $M_{\rm ISM} = 2\pi \Sigma_0 a_d^2$ we have
\begin{equation}
M_{\rm strip} = \frac{(a_d+r_{\rm out})\, e^{-r_{\rm out}/a_d} -
(a_d+r_{\rm strip})\, e^{-r_{\rm strip}/a_d}} {(a_d+r_{\rm out})\,
e^{-r_{\rm out}/a_d}-a_d}.
\end{equation}
On the other hand, the escape velocity as a function of galactocentric
radius is the sum of the contributions from all components, i.e. bulge,
disk, and dark halo. At the stripping radius the escape velocity equals
the speed $v_{\rm after}$, which is a function of the ICM column
density which we shall now take as the independent variable. Hence we
can compute the stripping radius as a function of ICM column density,
and with that we get the stripped mass fraction. This is easily
evaluated numerically by computing for each galactocentric radius the
mass fraction outside of that radius, and on the other hand the
quantity
\begin{equation}
\Sigma_{\rm ICM} = v_{\rm esc} \frac{\Sigma_{\rm ISM}(r)} {\langle
v\rangle_{\rho_{\rm ICM}}} = A \sqrt{-2 \Phi(r)}\, \frac{\Sigma_{\rm
ISM}(r)} {\langle v\rangle_{\rho_{\rm ICM}}}.
\end{equation}
Figure \ref{FigC} depicts the relation between $M_{\rm strip}$ and
$\Sigma_{\rm ICM}$ for our standard model. The above equation is able
to match the SPH results very closely, if we adopt $A=0.5$. In this
diagram, our fit formula to the SPH results (Eq.~\ref{fit}) gives a
function very similar in character to the one derived
from our analytical criterion. The choice of the outer disk radius
influences the shape of the curve in Fig.~\ref{FigC}; we find that a
value of 20 kpc gives a better match than the value of 16 kpc assumed
for the SPH models. This detail is not incorporated in the fit formula,
whose results therefore match the SPH results at low stripping less
well.

Although the SPH results from the edge-on case do exhibit a larger
scatter than the face-on data, it is quite remarkable that they can
still be matched by the analytical prediction for the face-on case, if
one simply increases the necessary ICM column density. This means that
the edge-on models can well be considered as having a lower stripping
efficiency, with a reduction factor of about 5. This factor may be
regarded as depending only on the tilt angle $i$, as
\begin{equation}
A(i) = 0.12 + 0.38 \sin i.
\end{equation}
A sine-type dependence could be understandable as a geometrical
projection effect, in that the edge-on galaxy presents a smaller cross
section to the ICM. If it were such a pure effect of the effective cross
sections, one should expect for our standard model a ratio of the areas
of $4/0.25 = 16$, from the disk radial scale being 4 kpc and its height
being 0.25 kpc. For the moment, we prefer to take our analytical formula
as a convenient expression which encapsulates essential features of the
problem rather than as giving a complete description.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig14.ps}
\caption{\small
The relation between stripped mass fraction and the column density of
the swept-up ICM gas, computed for our standard model from our
analytical criterion. The dots are results from the SPH models for the
face-on configuration, compared to the predictions, adopting a value of
$A=0.5$ ({\it solid curve}). The open circles are results in edge-on
orientation, and the dashed curves are the predictions with an adopted
value $A=0.12$. The dotted curves come from the fitting formula
Eq.~\ref{fit}.
}\label{FigC}
\end{figure}

\section{Discussion}\label{sec:disc}
We compare our results to the findings of previous numerical studies
which treated inclined ram pressure stripping. These investigations
differ in their numerical treatment of hydrodynamics, the model for the
galaxy, and the way the ICM gas flows around the galaxy.

\subsection{General trends}
The fraction of the ISM mass that is stripped in the simulations of
\citet{vollmer01a}, \citet{roedigerbruggen06},
\citet{roedigerbruggen07}, and \citet{schulzstruck01} is plotted in
Fig.~\ref{compare} as a function of inclination angle.
The curves join runs with different disk inclinations, and
are labeled by the maximum ram pressure. It must be stressed that for
different curves not only does the maximum value of the ram pressure
vary, but also its duration. These general features are apparent in
Fig.~\ref{compare}:
\begin{itemize}
\item for inclinations larger than about 50$^\circ$ there is very
little dependence of the stripped fraction;
\item towards the edge-on orientation, on the contrary, the amount of
stripping drops strongly;
\item the curves flatten for higher peak ram pressures.
\end{itemize}

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig15.ps}
\caption{\small Stripped mass fraction as a function of the disk
inclination, from \citet{vollmer01a} - {\it black},
\citet{roedigerbruggen06} - {\it red}, \citet{roedigerbruggen07} -
{\it green}, and \citet{schulzstruck01} - {\it blue}. Labels give
values of the peak ram pressure, in units of cm$^{-3}$(km/s)$^2$. For
\citet{roedigerbruggen07} the actual values of the inclination are
given for the instant of pericenter passage.
}\label{compare}
\end{figure}

Our results show the same features (cf. Fig.~\ref{mstrip_inclin}). A
closer comparison shows that the near edge-on models by
\citet{vollmer01a} are substantially more strongly stripped than ours
for the same peak ram pressure. However, since their Fig.~7 suggests
that the radial scale-length of the gas disk is longer than in our
model, one should expect that due to the higher ISM surface density
they should be stripped less severely. This suggests that the
shielding mechanism used by \citet{vollmer01a} is overly effective in
near edge-on orientations and thus overestimates the stripping, at
least in comparison to the full hydrodynamic treatment of
\citet{roedigerbruggen06} and our SPH approach.

For the same values of the stripped mass fraction, the simulations by
\citet{roedigerbruggen06} require a substantially lower value of the
peak ram pressure than our models or those by \citet{vollmer01a},
because \citet{roedigerbruggen06} consider the flow of the ICM
to be constant in time, hence much longer than in the other models.

The stripping efficiency with respect to inclination ($\eta$) measures
the relative stripping
potential of individual inclinations with respect to the face-on case.
It might thus serve as a good instrument for comparing results from
different numerical codes. From Fig.~\ref{compare_eta} it is obvious
that the results of different authors give very similar dependences
on the inclination angle. In spite of the basic difference in the
absolute values for the maximum ram pressure, the results of both
\citet{roedigerbruggen06} and \citet{vollmer01a} show that higher ram
pressures result in a lower dependence of the stripping on inclination
angle, i.e. making the inclined stripping as effective as the face-on
case. Thus, the features of the inclination dependence, which our
present study shows in a systematic way, has already been seen
in earlier studies.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig16.ps}
\caption{\small Stripping efficiency with respect to inclination as a
function of the angle for the same results as in Fig.~\ref{compare}.
}\label{compare_eta}
\end{figure}

\subsection{Vollmer's fitting formula}
\citet{vollmer01a} derived from their simulation results a formula
which relates the fraction of the final and initial total gas mass
to the peak ram pressure and inclination angle (their Eq.~21):
$M_{\rm ini}/ M_{\rm fin} = 0.25\, p_{ram}^{max}\, \sin^2 [0.9\,
(i+10^\circ)] + 0.84$, where $p_{ram}^{max}$ is normalized by
$p_0=100$ cm$^{-3}$ (km/s)$^2$. Using this fitting formula we
reproduce Vollmer's Fig.~17 in Fig.~\ref{vollmer_fit}: as a
function of angle we plot the stripping efficiency with respect to
inclination $\eta$. It shows that although the fitting function does
not match the simulations perfectly (and even gives for low ram
pressures negative values of $\eta$) the general trend corresponds well
to the numerical results, and to our findings as well: that for high
ram pressures the efficiency of stripping is high and less dependent on
the tilt angle than for low ram pressure values.

\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig17.ps}
\caption{ \small Curves of stripping efficiency with respect to
inclination $\eta$ as a
function of tilt angle as calculated from the fitting formula
of \citet{vollmer01a} for various values of the peak ram
pressure: 100, 300, 1000, 2000, 5000 and 10~000 cm$^{-3}$(km/s)$^2$
({\it from left to right}). Results of Vollmer's simulations
({\it dots}) correspond to the solid curves. Results of our
$R4\rho0$ and $R4\rho1$ runs with pressure peaks of $\sim 2700$ and
11~000 cm$^{-3}$(km/s)$^2$ are added ({\it triangles}).
} \label{vollmer_fit}
\end{figure}

\subsection{Dependence on ICM column density}
\begin{figure}[t]
\centering
\includegraphics[height=0.48\textwidth,angle=270]{1469fig18.ps}
\caption{\small
Stripping efficiency with respect to inclination $\eta$ as a function
of the column density of the encountered ICM for simulations of
\citet{roedigerbruggen06} ({\it green}) and \citet{vollmer01a} ({\it
black}).
}\label{compare_SigICM}
\end{figure}

To look for the dependence of the stripping results on $\Sigma_{\rm
ICM}$ in the previous simulations, we estimate these values from the
parameters of their runs. In \citet{roedigerbruggen06}, a constant flow
of ICM with three values of density (0.01, 0.1, and 1 $\times$
10$^{-26}$g$\,$cm$^{-3}$) provokes a wind at 800 kms$^{-1}$ lasting for
1 Myr. This yields values of the ICM column density of
0.4, 4, and 36 $M_\odot$pc$^{-2}$ for their weak, medium, and strong
pressure models, respectively. \citet{vollmer01a} approximate ram
pressure profiles with Lorentz functions, whose duration is determined
by the condition that 500~Myr before the peak, a constant pressure of
50 cm$^{-3}$(km/s)$^2$ is reached. For their four peak ram pressures of
1000, 2000, 5000, and 10~000 cm$^{-3}$(km/s)$^2$ we derive widths
$t_{\rm HW}=$ 115, 80, 50, and 35 kpc, respectively, which yield values
of $\Sigma_{\rm ICM}$: 4.4, 6.2, 9.4, and 13.5 $M_\odot$pc$^{-2}$.

Figure~\ref{compare_SigICM} compares the $\eta(\Sigma_{\rm ICM})$
dependence for the results of \citet{vollmer01a} and
\citet{roedigerbruggen06}. We do not include the results of
\citet{roedigerbruggen07}, as the tilt angle changes along the galaxy's
orbit. The results of both \citet{vollmer01a} and
\citet{roedigerbruggen06} show the same trend as that revealed in our
simulations: with increasing $\Sigma_{\rm ICM}$ the inclination
efficiency grows. It is worth noting that the increase is much steeper
in the case of \citet{vollmer01a}, in comparison to
\citet{roedigerbruggen06} and our own results. Since the parameters of
the model galaxies are rather similar and the stripping efficiency
$\eta$ measures the relative potential of inclined stripping with
respect to the face-on case, it could well be that these differences
are due to the different ways the hydrodynamics is treated.

\subsection{Limitations of strictly radial orbits}
To separate the effects of the disk tilt angle on the stripping results
we have focused in this paper on galaxies on strictly radial orbits.
Then the tilt angle stays constant along the orbit. In more realistic
orbits however, the disk inclination usually changes with time. Thus,
almost all galaxies are likely to experience once along their orbit
an efficient (close-to) face-on ram pressure phase. Its duration and
strength is then determined by the parameters of the orbit.
As the results of our simulations have shown, the tilt-variance might
be important for situations with compact ICM distributions where the
face-on stripping really is more efficient than the tilted ones. In
extended clusters, however, the dependence on the disk inclination
vanishes as the stripping tends to saturate.

Concerning the stripping potential of individual models, note that the
strictly radial orbits used in our calculations may be considered as
being equivalent to slightly elliptical ones: The ram pressure profile
along a strictly radial orbit through a given ICM distribution may well
be the same as the ram pressure profile along an elliptical orbit, however
through a modified ICM distribution that is more centrally peaked
(higher) and less extended (more compact). In other words, on an
elliptical orbit the galaxy passes through the slope of the ICM density
peak.

\section{Conclusion}
We have studied in detail the influence of disk tilt angle on the ram
pressure stripping efficiency in galaxy clusters. A grid of N-body/SPH
numerical simulations, varying the density of the ICM, the peak
ram-pressure, its duration, and the orientation of the galaxy was
performed. We summarize below the main results of the simulations:
\begin{itemize}
\item the stripping amount is lower for galaxies moving edge-on
with respect to the ICM wind, in agreement with previous
simulations;
\item apart from the total stripped amount, there is no
radical difference in the duration of the stripping process of
variously tilted galaxies;
\item due to conservation of angular momentum, ram pressure shifts
the ISM in near-edge-on orientations to smaller distances behind the
galaxy than in the face-on case;
\item the dependence of the stripping amount on the disk tilt angle
vanishes for large clusters, where the amount of the encountered
ICM ($\Sigma_{\rm ICM}$) is large;
\item on the other hand, for galaxies crossing small ICM overdensities
or debris structures left over in the cluster from recent stripping
events, the dependence on the tilt angle is more pronounced;
\item we emphasize the role of the amount of the encountered ICM
to the ram pressure stripping results;
\item the stripping efficiency with respect to inclination $\eta$ (i.e.
the ratio of the stripped mass fraction relative to the face-on case)
depends strongly on the disk tilt angle for small ram pressure peaks
but again vanishes for large values of $\Sigma_{\rm ICM}$ when
stripping saturates;
\item for non-face-on orientations, the sense of  rotation plays a
role: contrary to expectations, it is not the side with highest ram
pressure which is more stripped;
\item we propose a fitting formula (Eq.~\ref{fit}), which should now be
tested against observations, deriving the ICM density from X-ray
imaging of clusters, and the gas stripping from HI observations.
\end{itemize}

By comparison with a simple analytical stripping condition
\citep{jachym07}, the total momentum imparted by the encountered ICM on
the galaxy gas appears to be the main determinant of the stripping
result. Contrary to the GG72 criterion or the fitting formula of
\citet{vollmer01a} who assign the key role to the peak value of the ram
pressure, we stress the importance of the dependence on the amount of
the encountered ICM, together with the disk
inclination angle:
\begin{displaymath}
M_{\rm strip}/M_{\rm
init} \sim \Sigma_{\rm ICM} (a+b\,\sin^\alpha i).
\end{displaymath}
The values of $a$, $b$, and $\alpha$ depend on the ISM distribution in
the unperturbed disk. We use such a dependence to fit the outcome of
our numerical simulations -- the stripped mass fraction and the
stripping radius. The analytical stripping condition based on the
momentum balance yields similar formulae.

Using simple test particle models taking schematically into account the
"shadowing" of the gas disk by the material occurring upstream, we can
roughly obtain the main features of the stripping. The imparted momentum
$\langle v\rangle_{\rho_{\rm ICM}} \Sigma_{\rm ICM}$ proves to be the
key parameter of the ICM-ISM interaction. Such particle models however
fail to reflect the true dependence of the stripping efficiency on ICM
density and inclination revealed by the full hydrodynamics.

\begin{acknowledgements}
The authors gratefully acknowledge support by the Institutional
Research Plan AV0Z10030501 of the Academy of Sciences of the Czech
Republic, by the project 205/08/P556 of the Grant Agency of the Czech
Republic, and by the Center for Theoretical Astrophysics (LC06014). We
thank Volker Springel for valuable advice. The simulations have been
carried out on the Ond\v rejov Cluster for Astrophysical Simulations
(OCAS, Czech Republic) and the VIRGO computational cluster in Prague.
We thank Jim Dale for English revision of the text. We would like to
thank the referee for helping us to improve this paper considerably.
\end{acknowledgements}

\bibliographystyle{aa}

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