text:
namespace AgpuMetal
{

struct AgpuShaderAttachment
{
    agpu::shader_ref shader;
    agpu_shader_type stage;
    std::string entryPoint;
};

class AMtlGraphicsPipelineBuilder : public agpu::pipeline_builder
{
public:
    AMtlGraphicsPipelineBuilder(const agpu::device_ref &device);
    ~AMtlGraphicsPipelineBuilder();

    static agpu::pipeline_builder_ref create(const agpu::device_ref &device);

    virtual agpu::pipeline_state_ptr build() override;
    virtual agpu_error attachShader(const agpu::shader_ref &shader) override;
    virtual agpu_error attachShaderWithEntryPoint(const agpu::shader_ref &shader, agpu_shader_type type, agpu_cstring entry_point) override;
    virtual agpu_size getBuildingLogLength() override;
    virtual agpu_error getBuildingLog(agpu_size buffer_size, agpu_string_buffer buffer) override;
    virtual agpu_error setBlendState(agpu_int renderTargetMask, agpu_bool enabled) override;
    virtual agpu_error setBlendFunction(agpu_int renderTargetMask, agpu_blending_factor sourceFactor, agpu_blending_factor destFactor, agpu_blending_operation colorOperation, agpu_blending_factor sourceAlphaFactor, agpu_blending_factor destAlphaFactor, agpu_blending_operation alphaOperation) override;
    virtual agpu_error setColorMask(agpu_int renderTargetMask, agpu_bool redEnabled, agpu_bool greenEnabled, agpu_bool blueEnabled, agpu_bool alphaEnabled) override;
    virtual agpu_error setFrontFace(agpu_face_winding winding) override;
    virtual agpu_error setCullMode(agpu_cull_mode mode) override;
    virtual agpu_error setDepthBias(agpu_float constant_factor, agpu_float clamp, agpu_float slope_factor) override;
    virtual agpu_error setDepthState(agpu_bool enabled, agpu_bool writeMask, agpu_compare_function function) override;
    virtual agpu_error setStencilState(agpu_bool enabled, agpu_int writeMask, agpu_int readMask) override;
    virtual agpu_error setStencilFrontFace(agpu_stencil_operation stencilFailOperation, agpu_stencil_operation depthFailOperation, agpu_stencil_operation stencilDepthPassOperation, agpu_compare_function stencilFunction) override;
    virtual agpu_error setStencilBackFace(agpu_stencil_operation stencilFailOperation, agpu_stencil_operation depthFailOperation, agpu_stencil_operation stencilDepthPassOperation, agpu_compare_function stencilFunction) override;
    virtual agpu_error setRenderTargetCount(agpu_int count) override;
    virtual agpu_error setRenderTargetFormat(agpu_uint index, agpu_texture_format format) override;
    virtual agpu_error setDepthStencilFormat(agpu_texture_format format) override;
    virtual agpu_error setPrimitiveType(agpu_primitive_topology type) override;
    virtual agpu_error setPolygonMode(agpu_polygon_mode mode) override;
    virtual agpu_error setVertexLayout(const agpu::vertex_layout_ref &layout) override;
    virtual agpu_error setShaderSignature(const agpu::shader_signature_ref &signature) override;
    virtual agpu_error setSampleDescription(agpu_uint sample_count, agpu_uint sample_quality) override;

    agpu::device_ref device;
    agpu::shader_signature_ref shaderSignature;
    agpu::vertex_layout_ref vertexLayout;
    MTLRenderPipelineDescriptor *descriptor;
    MTLDepthStencilDescriptor *depthStencilDescriptor;
    MTLStencilDescriptor *backStencilDescriptor;
    MTLStencilDescriptor *frontStencilDescriptor;

    std::string buildingLog;
    agpu_uint renderTargetCount;
    agpu_pipeline_command_state commandState;
    agpu_bool depthEnabled;
    agpu_bool stencilEnabled;

    agpu_bool hasDepthBias;
    agpu_float depthBiasConstantFactor;
    agpu_float depthBiasClamp;
    agpu_float depthBiasSlopeFactor;

    std::vector<AgpuShaderAttachment> attachedShaders;
};

} // End of namespace AgpuMetal

#endif //AGPU_METAL_PIPELINE_BUILDER_HPP


What leads to the development of the General Comment?
Looking at the explanation provided under the first paragraphs, there are three main reasons which convinced the Committee to develop a General Comment on article 6 of the African Children's Charter.
The first is related to the observations that the Committee has derived from State Party Reports on the status of the implementation of the right to birth registration. The Committee notes that the right to birth registration, unfortunately, is one of the rights that consistently appear not to be fully implemented by States Parties (Para 3 of the General Comment). This can be inferred from the concluding observations and recommendations to State Parties that have submitted their Reports including Kenya, Tanzania, Burkina Faso, Cameroon, Libya, Mali and Uganda.
The second reason relates to the gravity of the problem of unregistered births in Africa. The Committee notes that currently millions of children go unregistered every year. According to the UN News Centre, a 2013 UNICEF Report reveals that 230 million children under the age of five had not had their birth registered, and the lowest rate of birth registration globally is in South Asia and in Sub-Saharan Africa. This results in children becoming vulnerable to all sorts of abuses such as recruitment into armed forces, sexual exploitation, being victims of child labour, human trafficking, early marriage, disinheritance, etc.
The recognition of the strong link between lack of effective birth registration system and the increasing prevalence of statelessness is also another reason. The difficulty of realizing of children's right to acquire nationality is ascribed to the lack of an effective and universal birth registration system. Even though the right to birth registration does not confer nationality by itself, the Committee notes that it is a proof of the nationality of the parents or the place of birth which are the grounds of acquiring nationality.
It is considering these facts that the Committee decided to hold a day of general discussion on birth registration and the rights of the child during its 20th Ordinary Session which was held in November 2012. At the conclusion of this day, the Committee decided to develop a General Comment on Article 6 of the Charter, hence the General Comment was developed and adopted in April 2014.
Addressing the challenges of statelessness among children requires an understanding of the causes of child statelessness. Statelessness among children is often a direct result of their parents' stateless status. Most countries in the world observe a Jus Sanguinis, as opposed to Jus Soli, nationality regime, whereby citizenship is granted only to those children whose parents are recognized citizens. It is important to note that the applications of these systems could be the cause of statelessness in a situation where people change their place of residence. Statelessness could also be caused by nationality regimes that discriminate against women as many countries around the world prohibit women married to foreign spouses from passing on their nationality to their children. Situations of State succession might also contribute for statelessness among children. Children who belong to ethnic minorities are particularly vulnerable to statelessness when States break up and a new States are created. More importantly to the issue under consideration, statelessness among children could also be attributed to administrative practices such as excessive fees on birth registration, insufficient proof of documents and failure to register births. Therefore, the need for effective, free, universal birth registration should be in place so that children born in the territory of a State can acquire the nationality of that State where they would otherwise be stateless.
The principle of universality of birth registration, according to the Committee, means 'the right to birth registration is for all the children, anywhere and anytime'.(Para 50 of the General Comment) The universality of birth registration particularly applies to address the challenges of registration of children born out of wedlock, children of minority groups, children with disability, children of refugee, asylum seeking or migrant families, children born to indigenous parents, and children of imprisoned mothers.
Including advanced principles, the Committee in considerable detail discusses the principle of free and accessible birth registration. The Committee sets the principle of free birth registration by means of universal, accessible, simple, expeditious and effective registration procedures without discrimination of any kind. This principle includes cases where there is late registration of births. (Para 72 of the General Comment). The Committee also innovatively approaches the principle of free birth registration by introducing the concept of de facto limitations and obstacles to birth registration. In this regard, the Committee persuasively states that free birth registration does not simply mean abolition of the fee applicable to registering a child or the cost of obtaining the birth certificate. Free birth registration cannot be effective unless the associated costs are catered for by States parties. (Para 73 of the General Comment).
The Committee further advances the interpretation of the rights to birth registration in relation to the principle of confidentiality. If registration is not made in a secure and confidential manner, it may expose a child to unnecessary risks since personal information may be misused, including for discriminatory purposes. In consideration of this fact, the Committee notes that States Parties must put in place a legal framework for protection of sensitive personal data that includes birth registration details and other vital statistical data.
The General Comment's approach to this element of birth registration is also unprecedented. Article 6 of the African Charter provides for registration of every child immediately after birth. The word 'immediately' is very vague and countries might interpret it in various ways, which could be detrimental to the rights to the child. The Committee, therefore, interprets 'immediately' to mean 'as soon as possible, with due regard to cultural and local practice related to maternity and infant rearing'. (Para 79 of the General Comment) However, at the same time it should be construed narrowly and the word 'immediately' should be taken to mean that birth registration shall occur within a few days or weeks after birth and not months or years later. In cases where parents adduce disincentives to birth registration, including transport and associated costs, the Committee recommends that the impact of disincentives can be mitigated by the removal other fees associated with immediate registration. Furthermore, the Committee also recommends States parties to establish birth registration desks at all places where a birth certificate is required for a service, such as upon entry to school, or when registering for social security and poverty alleviation programmes.
In conclusion, the General Comment includes principles and explanation which guide member States to establish a functioning, well managed, resourced, integrated, universal, free and accessible birth registration system with a view of, among other things, preventing statelessness.
Ayalew obtained his LLB from Makelle University Ethiopia in 2006 and an LLM in Human Rights in Democratisation in Africa from the University of Pretoria, South Africa in 2011. He lectured law at the Makelle University and he was the editor in chief of Makelle University Law Journal. He is currently a legal researcher at the Secretariat of the ACERWC.


text:
Walter Afanasieff
Walter Afanasieff (born February 10, 1958),[1] formerly nicknamed as Baby Love in the 1980s, is a Brazilian-American musician, songwriter, record producer and composer of Russian descent. He is known for his long association with Mariah Carey, for whom he was co-producer and co-writer for several years, beginning in 1990. He won the 1999 Grammy Award in the Record of the Year category for producing "My Heart Will Go On" by Celine Dion, and the 2000 Grammy Award for Non-Classical Producer of the Year.[2]
Vladimir Nikitich Afanasieff
Baby Love (in the 1980s)
(1958-02-10) February 10, 1958 (age 61)
Walter Afanasieff Production Co.
Wallyworld
www.walterafanasieff.com
Aside from Carey and Dion, Afanasieff has also written and produced music for many other recording artists as well, such as Richard Marx, Whitney Houston, Thalía, Lionel Richie, Luther Vandross, George Benson, Destiny's Child, Kenny G, Michael Bolton, Toni Braxton, Andrea Bocelli, Johnny Mathis, Kenny Loggins, Barbra Streisand, Christina Aguilera, Ricky Martin, Leona Lewis and Idina Menzel.
Life and workEdit
Afanasieff was born Vladimir Nikitich Afanasieff[3] (Russian: Владимир Никитич Афанасьев) in São Paulo, SP, Brazil to Russian parents Nikita and Tatiana.[1] His father is from Leningrad and his mother is a Harbin Russian from China. His parents met in Brazil in the early 1950s.[4] Beneath the senior portrait in his high school yearbook, Afanasieff wrote that his goal was to "write and play better than Keith Emerson" of Emerson, Lake & Palmer.[citation needed]
Starting out as a working jazz musician in 1980, Afanasieff initially played keyboards with the jazz/fusion violinist Jean-Luc Ponty. Later, he formed The Warriors[5] with another former Ponty sideman, guitarist Joaquin Lievano, and with leading 1980s music producer/songwriter and drummer Narada Michael Walden, and these experiences gave him the background and confidence to take an active role as a producer.[6]
Walden hired Afanasieff as a staff producer/arranger and began using him as a keyboardist on a large number of recording projects, including Whitney Houston's self-titled debut album released in 1985, which went on to become the artist's best-selling studio album to date. It was also during this time that Afanasieff and Walden began writing pop songs together. Together with his mentor Narada, Afanasieff's first major production was the title track of the James Bond movie Licence to Kill, sung by Gladys Knight and co-written by Afanasieff and Walden.[7]
One of Afanasieff's biggest hits as a producer was the smash hit "My Heart Will Go On", the theme tune to the 1997 film Titanic, sung by Celine Dion.[2] The song became the world's best-selling single of 1998.[8] Afanasieff produced and arranged other successful motion picture soundtracks, including Disney's Beauty and the Beast (the Celine Dion/Peabo Bryson title-track duet), Aladdin ("A Whole New World") and The Hunchback of Notre Dame ("Someday").[2] Afanasieff was also the producer and arranger for "Go the Distance", the Oscar-nominated Michael Bolton song from the animated film Hercules.
Afanasieff performs on most of his recordings (mainly keyboards, synthesizers and drum programming).
Afanasieff spent a significant part of his career creating music with Mariah Carey: 1988-1998. He had a role in some of Carey's most successful songs, including "Hero", which he co-produced, co-wrote, and on which he played all of the music tracks. "Hero" was released as the second single from Carey's album Music Box, and reached number one on the Billboard Hot 100 chart on December 25, 1993. It remained at the top of the chart for four weeks. "Hero" has become one of Carey's signature songs, and Carey closes many of her concerts with it.[9] Carey and Afanasieff also wrote "One Sweet Day", a duet between Carey and Boyz II Men, which holds the record for the longest run at number 1 on the Billboard Hot 100 (16 weeks total, a record later matched in 2017 by Despacito). The song was nominated for the 1996 Grammy Awards for Record of the Year and Best Pop Collaboration with Vocals, and received the ASCAP Song of the Year Award for 1996. In 1994, Carey released the Christmas song "All I Want for Christmas Is You". He and she produced and composed the song for Columbia Records. As of December 2018, the song has earned cumulative worldwide sales of over 14 million copies.
In 2009 Walter started working with Russian singer Yulia Nachalova. Their album "Wild Butterfly" was released in 2012 on iTunes. They later produced a video "Zhdi menya" (Wait for me) in Russian, released on iTunes in 2015.[citation needed]
In 2014 Walter became head of the composers/producers department at Isina, a worldwide talent search and development mentorship for those seeking to pursue a career in music.[10][11][12]
In 2015 he became one of the mentors of the Russian TV project Glavnaya Stsena ("Main Stage"), the Russian version of The X Factor.
Afanasieff has three children, Christina, Isabella, and Andrei Afanasieff from previous marriages.
Afanasieff married his longtime girlfriend Katie Cazorla November 2017 in Zihuatanejo Mexico.
AwardsEdit
1999 Grammy Award in the Record of the Year category for producing "My Heart Will Go On" by Celine Dion
2000 Grammy Award in the Producer of the Year, Non-Classical category
Main article: Walter Afanasieff discography
List of songs written by Walter Afanasieff
^ a b Walter Afanasieff biography at AOL Music Archived 2009-09-16 at the Wayback Machine
^ a b c Featured writers: Walter Afanasieff at Sony/ATV Music Publishing.
^ Walter Afanasieff biography at Musicianguide.com
^ Focus Taiwan article on Afanasieff and Lin yu-Chun partnership.
^ Joaquin Lievano personal Web site.
^ Mixonline.com interview with Afanasieff Archived 2010-01-17 at the Wayback Machine.
^ Licence to Kill at Discogs.com
^ Songs from the year 1998 at Tsort.info. Archived January 18, 2010, at WebCite
^ Classic Songwriter Story: How Walter Afanasieff Wrote The Classic Hit, "Hero," With Mariah Carey.
^ http://isina.com/departments/composer
^ http://www.campuscircle.com/review.cfm?r=20942
^ http://www.huffingtonpost.com/mike-ragogna/christmas-chats-with-farm_b_6375938.html
Mixonline.com interview with Walter Afanasieff
SongwriterUniver interview with Walter Afanasieff on how he wrote "Hero" with Mariah Carey
Walter Afanasieff biography at Musicianguide.com
Biography of Walter Afanasieff at AOL Music
Retrieved from "https://en.wikipedia.org/w/index.php?title=Walter_Afanasieff&oldid=900139843"

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to call a module from a function I have a module that returns the title of a youtube video when provided its id and it works fine the issue is when I call the module from within a function it replies undefined whereas when I call outside a function it works fine and prints the title. Why is it not working Inside a function and how can I make it work? Any help is appreciated. Thanks in advance.

//Works
const line = "zPfvActHhTQ"
getYoutubeTitle(line, function(err, title) {
  console.log(title)
})

//Doesn't work
function tester() {
  const line = "zPfvActHhTQ"
  getYoutubeTitle(line, function(err, title) {
    console.log(title)
  })
}
tester()

redpajama_set_name: RedPajamaStackExchange


Members of staff at Specsavers in Wellington are delighted to be increasing their wide selection of designer specs with the release of the brand-new Balmain range.
The collection, true to Balmain's style, is inspired by its long tradition as a historic French fashion house. All the frames are marked with subtle, Balmain brand details in gold including a signature 'B' on the temple tips.
Alongside the latest frame styles from the most fashionable names around, Balmain glasses will now be available from the Wellington store.
Emma Davies, store director, said: 'We are really excited for the release of this range - the frames are beautiful and incredibly popular among the team. The brand is worn by a number of high-profile actresses, celebrities and style icons so we're thrilled to have the specs as part of our offering here in Wellington.


text:
Docuseries
ST Kitts and Nevis with Inida
I wish to use the occasion of the 73rd Anniversary of Independence of the Republic of India to congratulate the government and people of the world's largest democracy for the enormous strides they have made since obtaining independence.
I wish particularly to congratulate Prime Minister Narendra Modi on winning a historic second term with an improved mandate to build on the impressive social and economic reforms of the last five years which have made India a much better place in which to live, work and do business.
In recent years, India has done miraculously well in reducing poverty, improving health and sanitation standards, revolutionizing its education system to become a global leader, and investing in public infrastructure to create a modern Indian society ready for global leadership. What is also truly impressive about India's rise as a modern economic powerhouse is that business investment has been a cornerstone of its success story. India is without question a global leader on the economic front, a testimony to which it is the world's third largest economy at purchasing power parity.
The Indian success story is not just in the homeland. As the Prime Minister of a Caribbean country for 20 years, I have seen first hand the highly significant role that the global Indian community has played across the Caribbean, and its contributions to both the social and business life our region.
I could not omit to make particular mention of the vital contributions that the Indian Community in St. Kitts and Nevis has made to the development and welfare of our country. Indian businesses in manufacturing, retail, medicine and educational services are an enormous part of the economic mainstay of our country. The involvement of the Indian community in sports and various other aspects of the social sphere of our country add to the richness of the Caribbean experience.
It is why my administration between 1995 and 2015 created an environment that celebrated diversity, subsequently enabling the Indian community to expand. I am pleased that St. Kitts-Nevis is one of a few countries in the Caribbean where many Indians are in fact first generation. I want to further encourage that kind of development. It pleases my heart when I see Diwali being celebrated in our country. It further adds to the rich diversity that we unceasingly encourage.
Further afield, the global Indian diaspora has grown exponentially, not just in population, but in the number and type of leadership positions in the world of politics, business, technology and social change, with key figures emerging in North America (USA & Canada) and Europe, through to the Pacific Islands of Fiji.
As I look forward to leading on initiatives for the further development of our country and Caribbean region in the coming year, I am committed to exploring further partnering with India in the critical areas of Education, Technology, Arts and Culture (particularly, developing the film industry and providing local onsite filming for Bollywood), Manufacturing, Financial Services, and Tourism. I believe that our region will become one of the preferred destinations for Indian weddings.
It is my sincere pleasure to extend warm Caribbean congratulations to the government and people of India, including those who work and do business in the wider global community. My wish for your great country is that you continue to prosper and to positively influence global social and economic trends.
By signing up to the Global Indian newsletter you agree to receive electronic communications from us that may sometimes include advertisements or sponsored content.
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text:
Rails.application.routes.draw do
  root to: 'visitors#index'
  devise_for :users

  resources :users
  resources :feeds
  resources :entries, only: [:index, :destroy] do
    member do
      post 'mark_seen'
      post 'mark_unseen'
      post 'toggle_mark'
    end
  end
end

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
Compact Steep-spectrum Sources (CSSs), defined to be $\mbox{\raisebox{-0.3em}{$\stackrel{\textstyle <}{\sim}$}}$20 kpc in size
(for $H_0$=100 km s$^{-1}$ Mpc$^{-1}$ and $q_0$ = 0.0) and having a steep
high-frequency radio spectrum  ($\alpha \geq 0.5$ where  S$_{\nu} \propto \nu^{-\alpha}$),
have received a great deal of attention in recent years.
The general consensus is that these are largely young sources seen at an
early stage of their evolution (e.g., Carvalho 1985; Fanti et al.\ 1995;
Readhead et al. 1996a,b; see O'Dea 1998 for a review).
Related to the CSSs are the very small ($\leq 1$ kpc)
Gigahertz-Peaked-Spectrum (GPS) sources (e.g., Gopal-Krishna, Patnaik \& Steppe 1983;
Stanghellini et al.\ 1998).
The smallest double-lobed radio sources have been christened as the
Compact Symmetric Objects (CSOs, Wilkinson et al.\ 1994; Readhead et al. 1996a;
Taylor, Readhead \& Pearson 1996; Owsianik, Conway \& Polatidis 1998)
which are believed to evolve into the
Medium-sized Symmetric Objects (MSOs, Fanti et al.\ 1995)  and later to the
standard large double-lobed (FR II) radio sources (e.g.\ Snellen 2003, and references therein)

High-resolution images of CSSs (e.g. Sanghera et al.\ 1995; Dallacasa et al.
1995, 2002 and references therein) showed that
there is a large range of structures associated with CSSs, ranging from double-lobed and
triple sources to those with complex structures.
Saikia et al.\ (1995, 2001, 2002) showed that,
as a class, the CSSs were more asymmetric than larger radio sources.
They also performed statistical tests of the orientation-based unified scheme,
(Barthel 1989; Urry \& Padovani 1995), and
concluded that there were differences between the CSS
radio galaxies (RGs) and quasars (QSRs) that were consistent with the
unified scheme; however, there was
also substantial evidence for more intrinsic asymmetries in CSSs than those which
were seen for the
larger sources.  Arshakian \& Longair (2000) studied the  FR II sources
in the 3CRR complete sample and also concluded that intrinsic/environmental
effects are more important for sources with small physical sizes; they also
found intrinsic asymmetries more important for sources of
higher radio luminosities.
Furthermore, while comparing the hotspot-size ratio in
radio sources, Jeyakumar \& Saikia (2000) found that CSSs are generally
more asymmetric in this parameter as well; explaining such large
ratios of hotspot sizes seems to require an intrinsic origin for the size difference.

Detailed polarization observations of individual sources,
such as 3C147, show huge differential rotation measures between the two
oppositely directed lobes, suggesting their evolution in an asymmetric
environment (Junor et al.\ 1999). VLBA observations of 3C43 show evidence of high rotation
measure where the jet bends sharply, suggesting collision of the jet with a dense cloud of gas
(Cotton et al.\ 2003).
The radio galaxy 3C459 has a highly asymmetric structure:
the eastern component is brighter, much closer to the nucleus
and is much less polarized than the western one, again suggesting
interaction of the jet with a dense cloud of gas. HST images of
the optical galaxy shows filamentary structures, suggestive of
tidal interactions (Thomasson, Saikia \& Muxlow 2003). Statistically,
CSS objects exhibit a higher degree of asymmetry in the polarization
of the outer lobes at cm wavelengths compared with the larger sources
(Saikia \& Gupta 2003; see Saikia et al.\ 2003 for a summary).
These asymmetries in the central regions of
active galaxies may be intimately related to the supply of fuel to the
central engine in these objects, possibly due to interactions with companion galaxies.

\begin{figure*}[t]
\begin{center}
 \psfig{file=1564fig1.ps,bbllx=24pt,bblly=580pt,bburx=587pt,bbury=711pt,width=17.8cm,clip=}
\end{center}
\caption[]{Analytic models for jets propagating through
asymmetric media: (a) the density distributions, $n(D)$,
as a function of distance, with side 1 on the right and 2 on the left;
since $\eta_1 = \eta_2$ there is a discontinuity
at $R_2$; (b) the arm-length ratio,
$r_D(t)$; (c) the luminosity ratio, $r_L(t)$ and
(d) the $r_D-r_L$ diagram, with both quantities now in log units.
The open and filled circles
represent the times $T_1$ and $T_3$ respectively and the open
and filled triangles represent the times $T_2$ and $T_4$
respectively. The unit of time is 1 Myr. \label{analytical}
}
\end{figure*}

All of these studies have indicated substantially greater asymmetries
for small radio sources. It is clearly worthwhile to attempt models of
their propagation so as to see if these differences can be understood.
In this paper we develop a simple analytical model that enables us to treat
both arm-length asymmetries and luminosity asymmetries (Section 2).
We then extend the analytical model to include relativistic effects so
as to allow properly for Doppler boosting and time delays if the
sources are ejected closer to the line-of-sight (Section 3). In Section 4 we
summarize results of our two-dimensional and three-dimensional hydrodynamical
models of jets propagating through
an asymmetric dense core, a symmetric galactic interstellar medium,
and finally, a symmetric uniform intracluster medium (ICM). We discuss the similar
results from the analytical and numerical models in Section 5.

\section{Analytical Models for Jets Propagating in an Asymmetric Environment}

To estimate the distances out to which jets with equal beam powers, but
propagating out through different interstellar media (ISMs), would reach at various times, we
further generalize the ram pressure balance calculations discussed for
constant density media by Scheuer (1974) and extended to jets leaving a
power-law ISM and entering intracluster media by Gopal-Krishna \& Wiita (1987)
and Rosen \& Wiita (1988).  Such models assume that the jets start with
conical cross-sections and that their heads, and associated hot-spots,
propagate sub-relativistically.
We also estimate the ratios of radio luminosities of the two lobes
as functions of time by
expanding upon the calculations of Eilek \& Shore (1989) and Gopal-Krishna
\& Wiita (1991). The latter authors suggested that an ``excess'' ISM in the
nuclear regions (central few kpc), perhaps due to the interactions of galaxies, could
lead to a larger fraction of CSS sources at higher redshifts. Such
interactions could both trigger a phase of jet production from the central
engine and easily lead to asymmetric distributions of gas in the inner
regions for at least the $<$10$^{7}$ yr  during which the jets propagate
through the galactic ISM.  The propagation through denser media also implies
higher efficiencies for conversion of jet power to radio luminosity (Gopal-Krishna
\& Wiita 1991; Blundell, Rawlings \& Willott 1999); this concept is supported
by the recent findings of Arshakian \& Longair (2000) that more luminous
sources are more asymmetric.

Our model calculations assume two intrinsically symmetric jets
propagating outwards in opposite directions in pressure balance
between the momentum flux density of the beam and ram pressure of the
external medium, so the equation for the growth of one jet is
(e.g., Scheuer 1974),
\begin{eqnarray}
 n(D){\left(\frac{dD}{dt}\right)}^2 &=& {4 K L_b} \over {\pi c \mu {m}_{h} {\left(D \theta \right)}^2}
\end{eqnarray}
where $K$ is an efficiency factor assumed to be a constant and of order unity,
$\mu {m}_{h}$ is the mean particle mass where ${m}_{h}$ is the mass of the hydrogen atom,
$L_b$ is the power of the beam, $D$ is the distance from the nucleus and $\theta$
is the full-opening angle.  We assume the
gas density of the interstellar medium (ISM) to be declining as
\begin{eqnarray}
n(D) = \eta n_0 \left[1+(D/a)^{2}\right]^{-\delta}.
\end{eqnarray}
For $D \gg a$, $ n(D) \approx \eta n_0 { \left(D/a\right)}^{-2\delta}. $
This approximation is assumed for the analytical model considered here. To allow
for asymmetrically distributed gas in the central regions, the slopes on
opposite sides of the nucleus denoted by the subscripts 1 and 2,
$ \delta_{1,2} $ are taken as shallower, and the core radius $a_c$ smaller,
in the interior regions, but the slope can be steeper in the
exterior regions. We have considered the possibility that the ISM
density levels off to a constant ICM density at large radii. Standard central
densities of $n_0 \approx 10^{-1}$cm$^{-3}$ and $a \approx 2$ kpc are typical
of large elliptical galaxies (Forman, Jones \& Tucker, 1985).  Excess central gas,
requiring $\eta \approx 10$ and extending out to a few kpc (i.e.,
with $a_c \ll 1$ kpc) is sufficient to confine reasonably powered jets to
CSS dimensions for significant lengths of time (e.g., Gopal-Krishna \& Wiita 1991;
Carvalho 1998).

We consider a model physically corresponding to jet propagation initially through
an asymmetric nuclear region, followed by a symmetrical galactic scale ISM,
and finally, through a constant ICM.
The central ambient medium is characterized by
$\eta=\eta_{1}$ and $\delta=\delta_{1}$ on one side, with the corresponding values
on the opposite side being $\eta_{2}$ and $\delta_{2}$. For the sake of
simplicity, we take the core radius for both as
$a_{c}$.  The jet propagating outwards on side 1 reaches a distance $R_1$ after a time
$T_{1}$, while the one on the opposite side reaches $R_{2}$
 after a time
$T_{2}$.  Beyond $R_{1}$ and $R_{2}$, the density distribution on both sides is
described directly by equation (2), with $a \gg a_c$.
The evolution after a distance $R_3 (> R_1 )$ on side 1 and
$R_4 ( > R_2 )$ on side 2, is governed by a constant
density, with
$T_3$ and $T_4$ the times taken by  the corresponding jets to reach the
distances  $R_3$ and $R_4$, respectively (Fig.~\ref{analytical}).
Although we will usually assume $R_2 = R_1$ and $R_4 = R_3$, the times
at which those radii are reached will be different for the opposite
sides even for jets of
identical powers, and it is certainly possible that
$R_2 \neq R_1$ or $R_4 \neq R_3$, so it is useful to retain this
more general notation.  Quite clearly, the jet propagating through
the denser side (with shallower $\delta$ or higher $\eta$) will take
longer to get to any fixed distance.
Note that there must be a density discontinuity, either at $D = 0$ if
$\eta_1 \neq \eta_2$, or at $R_2$ if $\eta_1 = \eta_2$; the latter case is shown
in the left panel of Fig.~\ref{analytical}.
Such discontinuities
are most likely to arise through
an asymmetric distribution of gas from a recent merger that may
be responsible for triggering the nuclear activity (e.g. Gopal-Krishna \& Wiita 1991).
However, it is relevant to note that any realistic situation would have steep
gradients and not discontinuities.
Note that even if $\delta > \delta_{1,2}$ (as explicitly assumed below),
because $a \gg a_c$ the
absolute rate of decline in
density at $D>R_{1,2}$ is slower than at $D < R_{1,2}$ where the inner
core distributions dominate.

Using Eq.\ (2), for  $D \gg a$,
equation (1) reduces to
$D^{(1-\delta)}(dD/dt)=\eta^{-1/2}\tau^{-1}a^{2-\delta}$,
where
\mbox{
$\tau={\left[{\mu n_0 c \pi {m}_{h} {\theta}^2} / {4 K L_b}\right]}^{1\over2}a^2.$}
Integrating the above equation yields
$D = [ (2-\delta){\eta^{-{1\over2}} }
{\tau^{-1}} t]^{1/(2-\delta)} a$.
For $D=R$ at $t=T$, this can be expressed as $ D=R{({t/T})}^{1/(2-\delta)}.$
We use the above expression to estimate the distances
$D_1$ and $D_2$ to the lobes 1 and 2 respectively.

When the distances of propagation of the jet on both sides
satisfy $D_1<R_1$ and $D_2<R_2(=R_1)$
then
\begin{eqnarray}
 D_{1,2}=R_{1,2} {({t/T_{1,2}})}^{1/(2-\delta_{1,2})}.
\end{eqnarray}
But once
$D_1>R_1$,
\begin{eqnarray}
D_1 = {\left[{{{2-\delta} \over {2 - \delta_1}} \left( {{t \over T_1} -1} \right)
+ 1 }\right] }^{ 1/(2 - \delta)} R_1.
\end{eqnarray}
For $t\gg T_1$ this can be expressed as \\
\mbox
{$D_1=  R_1 \left([(2-\delta) / (2-\delta_1)][t/T_1]\right)^{1/ (2-\delta)}$.}
Similarly, for the jet propagating on the opposite side,
for $D_2>R_2$,
\begin{eqnarray}
D_2 = {\left[  { F
\left( {{t \over T_2} -1} \right) + 1 } \right] }^{ 1/(2 - \delta)} R_2, \ \
\end{eqnarray}
\noindent with
\begin{eqnarray*}
F = {{2-\delta} \over {2 - \delta_2}} \left({{\eta_2} \over {\eta_1}}\right)^{1\over 2}
{(a_c/R_2)^{\delta_2-\delta} \over (a_c/R_1)^{\delta_1-\delta}}
= {{2-\delta} \over {2 - \delta_2}}\left({{a_c} \over {R_1}}\right)^{\delta_2-\delta_1},
\end{eqnarray*}
\noindent where the last equality holds when $\eta_1 = \eta_2$ and
$R_1 = R_2$.  For $t\gg T_2$,
$D_2= R_2(F/T_2)^{1/(2-\delta)} t^{1/(2 -\delta)}$.

We now estimate the ratios of separations, $r_D$, and luminosities, $r_L$, for
the lobes during different stages in the evolution of the source for this model.
We choose the
slopes of the density distributions such that  $\delta > \delta_1 > \delta_2$, and
$ \eta_2 = \eta_1$
so that  $D_1$ is greater than or equal to $D_2$ when evaluated at the same time,
though we leave some dependences on $\eta$ explicit in the following expressions.
For $t < T_1$ and $t < T_2$, when both the jets are within the asymmetric
environment,
$r_D= [T_2^{1/(2 - \delta_2)}/ T_1^{1/(2-\delta_1)}] t^{(\delta_1 - \delta_2)/[(2 -\delta_1)(2-\delta_2)]}$.
Using the approximate result that the radio luminosity on each side scales as
$L_R \propto n(D)^{3(1+\alpha)/10} \propto n(D)^m $ (Eilek \& Shore 1989;
Gopal-Krishna \& Wiita 1991) we find that
\begin{eqnarray*}
r_L = \left[{\eta_1 \over \eta_2} \left({R_1 \over a_c}\right)^{-2(\delta_1-\delta_2)}
T_1^{2\delta_1 \over 2-\delta_1}
T_2^{-2\delta_2 \over 2-\delta_2} t^{-4(\delta_1-\delta_2) \over (2-\delta_1)(2-\delta_2)} \right]^m,
\end{eqnarray*}
where we have taken $R_1 = R_2$.
With $\alpha \approx 1.0, m \approx 0.6$. For the case shown in Fig.\ 1, where
$\delta=0.75$, $\delta_1=0.675$ and $\delta_2=0.3$, $r_D \propto t^{0.17}$, and
$r_L \propto t^{-0.40}$. Thus, at this early phase of the evolution,
$r_D$ increases with time while $r_L$ decreases with time.

For $t \gg T_1$ and $t < T_2$,
\begin{eqnarray*}
r_D = \left({2-\delta \over 2-\delta_1}\right)^{1 \over 2-\delta}  T_1^{-1 \over 2-\delta}
T_2^{1 \over 2-\delta_2}
t^{ \delta - \delta_2 \over  (2 -\delta)(2-\delta_2)};
\end{eqnarray*}
\begin{eqnarray*}
r_L = \left[{\eta_1 \over \eta_2}\left({2-\delta \over 2-\delta_1}\right)^{-2\delta \over 2-\delta}
\left({R_1 \over a_c}\right)^{2(\delta_2-\delta_1)}
{T_1^{2\delta \over 2-\delta} \over T_2^{2\delta_2 \over 2-\delta_2} }
t^{-4(\delta-\delta_2) \over (2-\delta)(2-\delta_2)} \right]^m,
\end{eqnarray*}
\noindent where we have used the continuity of density at $R_1$ to eliminate
$\eta$ and $a$ through the relation
$\eta a^{2\delta}  = \eta_1 a_c^{2\delta_1} R_1^{-2 (\delta_1 - \delta) }$.
For the above values of the $\delta$'s and $m$ we see that the rise in $r_D$ and
the decline in $r_L$ both become slightly stronger, with $r_D \propto t^{0.21}$
and $r_L \propto t^{-0.51}$.

For $t > T_3$, when the faster jet crosses $R_3$, the distance travelled by lobe
1 is given by
\begin{eqnarray}
D_1 = {\left[{2 \over {2 -\delta_1}} \left({R_1 \over R_3}\right)^{2-\delta}
        \left({t\over T_1} - {T_3 \over T_1} \right) +1 \right]}^{1\over2} R_3.
\end{eqnarray}
\noindent For $t \gg T_3$ this result can be expressed as
\mbox{
$ D_1 = R_3 [2/(2-\delta_1)]^{1\over 2}
(R_1/R_3)^{1-\delta/2} (t/T_1)^{1/2}$. }

During the last intermediate phase, when $t \gg T_3$ but $T_2 \ll t < T_4$,
\begin{eqnarray*}
r_D = \left({2 \over 2-\delta_1}\right)^{1/2} F^{-{1 \over 2-\delta}}
\left({R_3 \over R_1}\right)^{\delta \over 2}
T_1^{-{1 \over 2}} T_2^{{1 \over 2-\delta}} t^{-{\delta \over 2(2 -\delta)}},
\end{eqnarray*}
\noindent and
\begin{eqnarray*}
r_L = \left[ \left( {R_1 \over R_3} \right)^{2\delta} \left( {F t \over T_2} \right)
^{2\delta/(2-\delta)} \right]^m.
\end{eqnarray*}
For the above choice of the parameters for the density profile, $r_D \propto t^{-0.30}$. Thus
at moderately late times $r_D$ slowly decreases with time, while $r_L$
more rapidly approaches unity from below, since $r_L \propto t^{0.72}$.

Finally, once $t > T_4$, and the slower progressing lobe also enters the uniform
intracluster medium,
\begin{eqnarray}
D_2 = \left[ G \left({t\over T_2} - {T_4 \over T_2}\right) +1 \right]^{1\over2} R_3,
\end{eqnarray}
\noindent where

\begin{eqnarray*}
G = {\left[{2 \over 2 -\delta_2} \left({\eta_2 \over \eta_1}\right)^{1\over 2}
a_c^{\delta_2-\delta_1}R_1^{\delta_1-\delta_2+2-\delta}R_3^{\delta-2}\right]}.
\end{eqnarray*}
For $t \gg T_4$, this simplifies to  $ D_2 = R_3 G^{1 \over 2} (t/T_2)^{1 \over 2}$.
Thus, when the jets have traversed well beyond $R_3$ and $R_4$, so that $t \gg T_3, T_4$,
$r_D  \longrightarrow 1 $,  while
$r_L \simeq 1$ as soon as both lobes are in the constant density ICM.

In summary, the size ratio grows monotonically until $T_2$, after which it
declines slowly toward unity.  The flux-density ratio varies more dramatically, and
with more complexity,
dropping quite a bit until $T_2$ and  then rising rapidly at that time, because of our
assumption of a density discontinuity at $R_2$.
Both before and after $T_3$, the flux-density ratio of the components
 becomes symmetric
more rapidly than does the separation ratio,
 with $r_L \propto r_D^{-4m}$,
but because of its earlier severe deviations from unity, it remains
more asymmetric.
 Finally, once lobe 2 also crosses the outer interface (at  $T_4$) and the constant density
ICM is entered, the ratio $r_L$ very quickly approaches
unity, but $r_D$ does so only asymptotically.

\subsection{Results of basic analytical models}
Fig.~\ref{analytical} shows the variation of density with distance from
the nucleus on opposite sides,  the variations of
the separation ratio, $r_D$, and the flux density ratio, $r_L$,
with time as the jets propagate outwards, as well as an $r_D$--$r_L$ diagram.
The time axis is in units of $10^6$ yr.
The times $T_1$, $T_2$, $T_3$, and $T_4$
when the jet crosses the interfaces at $R_1$, $R_2$, $R_3$, and $R_4$,
respectively, are marked on the trajectories.
Our calculations of such trajectories provide an explanation for the observed
points in the $r_D-r_L$ diagram which have $r_D$ greater than 1 and $r_L$
smaller than 1 (see Saikia et al.  1995, 2001).
Our calculations also show that after the jets have left the
asymmetric environment, and are passing through similar media on opposite
sides, the source tends to become symmetric quite rapidly. Thus most
large FR II sources, which tend to be quite symmetric in both distances
(cf.\ Arshakian \& Longair 2000) and
luminosities of the oppositely directed lobes, may still have passed through an
asymmetric environment in early phases of their evolutions. This is consistent
with the possibility that most sources may have undergone  CSS phases during
the early stages of their evolutions, as discussed in Section 1.
In only a few of the CSS sources, such as
3C 119 (Ren-dong et al.\ 1991) and  3C 48 (Wilkinson et al.\ 1991),
does it appear that the jets may have been disrupted by interaction
with the clumpy external medium so that they never evolve into  large sources
(e.g.\ De Young 1993; Higgins, O'Brien, \& Dunlop 1999; Wang, Wiita, \& Hooda 2000).

For a specific reasonable example,
consider a jet of a beam power of $7\times10^{46}$
erg s$^{-1}$ and an opening angle of 0.04 rad,
 propagating through a medium with $n_0=1$ cm$^{-3}$,
core radii $a_c = 0.45$ kpc and $a = 2.0$ kpc, with $\delta$=0.75, $\delta_1$=0.675, $\delta_2$=0.3.
 The times required to reach $R_1$=5 kpc,
$R_2$=5 kpc, $R_3$=25 kpc, and $R_4$=25 kpc are 0.025, 0.047, 0.19, and 0.22
$\times$ 10$^{6}$ yr, respectively. The above times for a weaker jet of
power $2\times10^{45}$ erg s$^{-1}$, with an opening angle of 0.1 radian propagating
in a medium with smaller $a_c = 50$ pc and higher
central density $n_0=10$ cm$^{-3}$, but otherwise identical parameters,
are 0.26, 1.1, 2.0 and 2.9 $\times$ 10$^{6}$ yr, respectively. These ages are
smaller than any plausible age estimates for larger sources (e.g.\ Leahy, Muxlow \&
Stephens 1989; Scheuer 1995; Blundell \& Rawlings 2000).
The brief times during which our models produce sources which
would be classified as GPSs (well within $R_1$) are consistent with the different analytical
approximations employed by Carvalho (1998) for jets passing through
extra dense (but uniform) matter.

If there is substantially less gas on one side than the other, as is the case
either if the power-law of the central fall-off is substantially less steep on
one side than on the other, say $\delta_{1} - \delta_{2}\approx 0.4$,
or if $\eta_2 \approx 4 \eta_1$,
we can obtain fairly wide ranges in the predicted ratios of separations and
radio luminosities, and explain the very asymmetric sources. For most sources,
a modest difference in $\delta$ of about 0.15 turns out to be adequate to
produce the observed asymmetries, even assuming symmetric
jets of equal powers are launched from the central engine.

\section{Relativistic and Viewing Angle Effects}

For more detailed comparison with the observations,
two other important effects must be included:
the observed luminosities are boosted or depressed via possible bulk relativistic
motions; and the observed positions are affected by light travel time effects.

In this section the subscript `a' will denote the lobe approaching the observer
and the subscript `r' will denote the receding component. So
 $D_a$ and $D_r$ are the distances from the core to the approaching and receding lobes,
respectively, while
$D_{1,2}(t)$ are the distances traveled
by the jets propagating through the less dense and denser media,
respectively, as in the previous section;
let $\varphi$ be the angle between the approaching jet and the line of sight to
the observer.

In the core's rest frame we are observing at time $t$.  The corresponding times at which
emission arises from the approaching/receding lobe are:
$t_a = t/(1 - \beta_a {\rm cos}\varphi)$;
$t_r = t/(1 + \beta_r {\rm cos}\varphi)$, where $\beta = v/c$.
Including light travel-time effects, where the appropriate velocity is
the mean speed of advance to that point,
the {\it observed} distances of the approaching and receding lobes are:
\begin{eqnarray*}
d_a(t) = D_a(t) {\rm sin}{\varphi}/(1 - [D_a(t)/(ct)] {\rm cos}\varphi);  \\
d_r(t) = D_r(t) {\rm sin}{\varphi}/(1 + [D_r(t)/(ct)] {\rm cos}\varphi).
\end{eqnarray*}
Thus, the distance ratio, including projection and light-travel time effects is
\begin{eqnarray}
r_D^*(t) \equiv {\frac{d_a(t)}{d_r(t)}} =\frac{D_a(t)}{D_r(t)} ~~{\frac{1 + [D_r(t)/(ct)] {\rm cos}\varphi}
{1 - [D_a(t)/(ct)] {\rm cos}\varphi}},
\end{eqnarray}
where the superscript $*$ indicates that relativistic effects have been
included.

The luminosity corrections also will depend upon the Doppler boosting
factor, which could be significant if much of the emission comes from the hotspots
moving at mildly relativistic speeds, which is plausible for young sources,
such as GPS and CSS objects.
For a hot-spot or knot within a jet, bulk motions produce a change in
flux density, so that (Scheuer \& Readhead 1979)
\begin{eqnarray*}
S_{obs (a,r)}(\nu) = S_{em}(\nu)[\Gamma (1 \mp \beta {\rm cos}\varphi)]^{-(3+\alpha)},
\end{eqnarray*}
where the Lorentz factor, $\Gamma \equiv (1-\beta^2)^{-1/2}$.
The suitable values of $\beta$ are
the instantaneous rates of advance of the lobes.

In the notation of \S 2, $S_{em} = L_R$ and $L_R \propto n(D)^m$.
Therefore, the above equations tell us that the observed luminosity
ratio is:
\begin{eqnarray}
r_L^*(t) = {\frac{S_{obs,a}(t)}{S_{obs,r}(t)}}
 = {\frac{L_{R,a}(t_a)[\Gamma_a^*
(1-\beta_a^*{\rm cos}\varphi)]^{-(3+\alpha)}}
{L_{R,r}(t_r)[\Gamma_r^*(1+\beta_r^*{\rm cos}\varphi)]^{-(3+\alpha)}}}.
\end{eqnarray}
Where
$\beta_a^* \equiv {\frac{1}{c}}{\frac{dD_a(t_a)}{dt_a}}$, ~
$\beta_r^* \equiv {\frac{1}{c}}{\frac{dD_r(t_r)}{dt_r}}$, and
$\Gamma^*_{a,r}$ are determined from these
 {\it instantaneous} $\beta^*$s evaluated at the
approaching (or receding) times.
To evaluate this precisely, albeit in a model dependent fashion,
explicit formulae for $L_{R,a}(t_a)$ and
$L_{R,r}(t_r)$ should be used (e.g., Eilek \& Shore 1989; Blundell, Rawlings \& Willott 1999;
Manolakou \& Kirk 2002), and no further simplification is possible.
However, the boosting term will typically dominate over
the light-travel time factors for the luminosity ratio, even for the low values of $\beta \le 0.2$
derived from spectral aging and other considerations (Scheuer 1995; Gopal-Krishna
\& Wiita 1996; Arshakian \& Longair 2000).  Therefore, for analytical work
Eq.\ (9) can be approximated as
\begin{eqnarray}
r_L^*(t) \simeq  {\frac{L_{R,a}(t)}{L_{R,r}(t)}}~ {\frac {[\Gamma_a^*
(1-\beta_a^*{\rm cos}\varphi)]^{-(3+\alpha)}}
{[\Gamma_r^*(1+\beta_r^*{\rm cos}\varphi)]^{-(3+\alpha)}}}. ~~~~~~~~~~
\end{eqnarray}

\begin{figure*}[ht]
\hbox{
\includegraphics[width=15.5cm,bbllx=12pt,bblly=365pt,bburx=596pt,bbury=711pt,clip=]{1564fig2.ps}
}
\caption{
Evolutionary tracks for $r_D^*, r_L^*$ and  $r_D^*-r_L^*$ diagrams for different viewing angles to the line of sight. The upper panels are for Case 1 while the lower  panels are for Case 2. The solid, dashed,  dot-dashed and dotted lines indicate a viewing angle,
$\varphi$, of 10, 45, 75 and 90 degrees, respectively.
The symbols marking the time have same meaning as in
Fig.~\ref{analytical}, and the unit of time is 1 Myr.
\label{fig2}
}
\end{figure*}

\subsection{Evolutionary tracks in the $r_D-r_L$ diagram}
{\bf Case 1:}
Here we consider the situation where the jet approaching us is propagating
through the less dense medium.
Then both density and travel-time
effects act to increase the observed arm-length ratio, $r^*_D$.
However the  travel-time and density induced luminosity changes work against
 the relativistic effects in finding the luminosity ratio, $r^*_L$.
Since the side approaching us comes through a lower density medium, it
is both farther out and observed at a ``later'' time, so that the density
is even lower (or at most the same) as it was for the receding lobe; both of these
effects imply a lower emissivity; however, the approaching lobe is Doppler boosted.
Meanwhile, the receding lobe is still in a higher density region (at
least until both have reached the ICM), and is observed at
an earlier time in its history, so $n(D_r)$ is even higher, implying relatively
enhanced emissivity; but it is weakened by the Doppler effect.

Here the appropriate values are $D_a(t)=D_1(t)$ and $D_r(t)=D_2(t)$, where
$D_{1,2}$ are obtained
from Eqs.\ (3--7), with the appropriate equations used depending
upon the distances the two lobes have travelled.
Then, recalling
that $r_D(t) \equiv D_1(t)/D_2(t)$ we have for the observed ratio,
\begin{eqnarray}
r_D^*(t) \equiv {\frac{d_a(t)}{d_r(t)}} = r_D(t) ~~\left[ {\frac{1 + [D_2(t)/(ct)] {\rm cos}\varphi}
{1 - [D_1(t)/(ct)] {\rm cos}\varphi}} \right].
\end{eqnarray}
and
\begin{eqnarray}
r_L^*(t) \simeq  r_L(t) ~~\left[{\frac {\Gamma_2^*
(1+\beta_2^*{\rm cos}\varphi)}{\Gamma_1^*(1-\beta_1^*{\rm cos}\varphi)}}\right]^{(3+\alpha)}
\equiv ~r_L(t) {\cal D}_1(t).
\end{eqnarray}

The observed $r^*_D$ is increased more for smaller viewing angles as shown
in the upper-left panel of Fig.\ 2.
Although $r_L$ can be quite small at very early times,
the ratio of the Doppler boosting factors, ${\cal D}_1$, is usually
greater than unity, and this raises  $r^*_L$.  Even for modest $\beta (< 0.2)$
it can invert the ratio and let the lobe more distant from the
nucleus  appear brighter {\it
if it is approaching} the observer.
At early  times, the density effects dominate and
the sources fall below the $r^*_L=1$ line, unless $\varphi$
is very small, in which case $r^*_L$ may initially exceed unity
before quickly dropping below it. Later on, the value of $r_L$
rises above 1 for $\varphi < 90^{\circ}$, and for most viewing
angles
 the source spends a considerable amount of time within a factor of a few
of the $r_L=1$ line, as shown in the upper-middle panel of Fig.~\ref{fig2}.
The evolutionary tracks move to the right on the $r_L^* - r_D^*$ plane as the
jet points closer to the line-of-sight (Fig.\ 2, upper-right).
Therefore, this scenario can explain  sources observed to have
fairly substantial ($\sim 10$) asymmetries in distance and/or luminosity; those
asymmetries can be correlated or anti-correlated, depending
on viewing angle and evolutionary phase.

\noindent{\bf Case 2:} In this situation the side approaching us comes through the
denser medium, so $D_a(t) = D_2(t)$ and $D_r(t) = D_1(t)$.  Now,
\begin{eqnarray}
r_D^*(t) \equiv {\frac{d_a(t)}{d_r(t)}} = {\frac{1}{r_D(t)}}~~
{\frac{1 + [D_1(t)/(ct)] {\rm cos}\varphi}
{1 - [D_2(t)/(ct)] {\rm cos}\varphi}},
\end{eqnarray}
and
\begin{eqnarray}
r_L^*(t)  \simeq \frac{1}{r_L(t)}  {\left[\frac{\Gamma_1^* (1+\beta_1^* {\rm cos}\varphi)}
{\Gamma_2^* (1-\beta_2^* {\rm cos}\varphi)}\right]}^{3+\alpha}
\equiv  \frac{{\cal D}_2(t)} {r_L(t)}.
\end{eqnarray}

Since $1/r_L(t) > 1$, both of the factors in the above
expression enhance the luminosity
ratio, $r_L^*$, and at very early times it can be very high.
However, the two effects work oppositely for the arm-length ratio, $r_D^*$.
Although $1/r_D(t) < 1$, for smaller viewing angles and  at very early times,
$r_D^*$ can be well above unity; such sources have $r_L^* > 1$
but are less asymmetric in $r_D^*$ compared to Case 1,
as shown in Fig.~\ref{fig2}.
Up until $T_2$, $r_D^*$ falls; around then the density effects
are comparable to the
light travel time effects.  At later times $r_D^*$ rises a bit,
but by $T_4$ it starts to asymptotically approach unity.
Although we have plotted $r_D^*$ (from Eq.\ 13) as less than 1 in the lower-left
panel of Fig.\ 2,  since the observed arm-length ratio is defined to be $>1$,
we invert both $r_D^*$ and $r_L^*$
for the $\varphi = 90^{\circ}$ curve in the bottom-right panel of Fig. 2,
showing that the evolutionary track in the $r_D^* - r_L^*$ plane
is similar to that of an unbeamed source (Fig.\ 1).
A similar procedure is adopted for $\varphi = 75^{\circ}$ in the time range
when $r_D^* < 1$.
The typical outcome of this  scenario is a source observed to be
nearly symmetric in $r_D$ but possibly very asymmetric in $r_L$.

\begin{figure*}
\psfig{file=1564fig3.ps,bbllx=56pt,bblly=235pt,bburx=572pt,bbury=637pt,width=6.0in}
\caption{Two-dimensional simulations, set up to nearly
reproduce our analytical model in the plane of the sky
($\varphi = 90^{\circ}$).  The natural logarithm
of the density
is shown for Runs A2 (upper image in each panel) and B2
(lower) at $t=0.80$ (top panel)
and $t=2.05$ (bottom panel). The computation is conducted
on the upper
half of the illustrated region and symmetry about the
propagation axis
is assumed in plotting the density.  The total length of the grid is 35 kpc,
with $R_1=$ 5 kpc and $R_3 =$ 25 kpc; here the unit of time is 0.6 Myr.
\label{2Dimage}
}
\end{figure*}

\section{Numerical Simulations}
We have examined some of our analytical estimates using numerical
simulations of propagating jets. To follow the jets with very high
resolution for the extended
distances that are necessary if we are to examine their evolution
for situations involving the multiple external media in our models,
we are constrained to perform two-dimensional axisymmetric computations.
To allow for some physically realistic breaking of axisymmetry, we have also
performed three-dimensional simulations, albeit at lower resolution.
We used the well-tested general purpose ZEUS 2D  and 3D (v.3.4) codes which are
described in depth in Stone \& Norman (1992a,b), Stone, Mihalas, \& Norman (1992),
Clarke \& Norman (1994), and Clarke (1996a).
As we could not implement the magnetohydrodynamical
version of ZEUS (e.g., Clarke 1996b), we cannot make even the quasi-realistic
estimates of the source luminosities that can arise from codes that
include magnetic fields.  Therefore, these simulations are useful for
examining $D(t)$ and $r_D(t)$, but not $L(t)$ or $r_L(t)$.
We now briefly summarize results from these efforts.

\subsection{2-D Simulations}
For the first set of simulations we used the ZEUS 2-D code
as modified by Hooda et al.\ (1994).
Our 2-D work used cylindrical coordinates with 900 zones
along the axial (jet propagation) direction and 200 zones in the radial
direction.  The jet radius has been scaled to 0.05 kpc, with the
entire grid running from 1--35 kpc in the axial direction and 0--2 kpc in the radial
direction.  With these choices, 25 zones are included within the initial jet radius, and
adequate resolution of internal shocks and rarefactions are achieved.

The density within the ISM exactly follows the profile as defined by Eqn.\ (2),
and does not make the pure power-law assumption used in \S 2.
In this work the important parameters are:  the jet Mach number,
${M_j = {u}/{a_{\rm in}}}$, with $a_{\rm in}$ the jet sound speed and $u$ the
velocity of the jet;
$\zeta \equiv \rho_{\rm jet}$/$\rho_0$, with $\rho_0$ the initial ambient
density and $\rho_j$ the density of the jet. Our numerical simulations
also assume initially conical jets, i.e.,
we set the half opening angle to 0.05 rad in these computations
(cf.\ Wiita, Rosen \& Norman 1990; Wiita \& Norman 1992.)

\begin{table}[h]
\caption{The parameters of the numerical runs}
\label{ptable}
\begin{tabular}{l|ll|ll}
\hline
 & \multicolumn{2}{c|}{2D}  & \multicolumn{2}{c}{3D} \\
 & A2 & B2 & A3 & B3 \\
\hline
$\zeta$  & 0.001  & 0.001 & 0.001 & 0.001 \\
$M_j$   & 26  & 26 & 26  & 26 \\
$\theta_j$(radian)   & 0.05  & 0.05 & 0.02  & 0.02 \\
$R_1$(kpc)   & 5  & 5 & 5 & 5 \\
$R_3$(kpc)   & 25  & 25 & 25 & 25 \\
$a_c$(kpc)   & 0.05  & 0.05 & 0.45 & 0.45 \\
$a$(kpc)   & 1.0  & 1.0 & 2.0  & 2.0 \\
$\delta$   & 0.75  & 0.75 & 0.75 & 0.75\\
$\delta_1$   & $-$  & 0.675  & $-$ &  0.675\\
$\delta_2$   & 0.3  & $-$ & 0.3  & $-$\\
$R_0$(kpc)   &0.05  &0.05 & 1.0 & 1.0 \\
\hline
\end{tabular}
\end{table}

We performed two simulations (A2, B2, where A2 corresponds to $D_2$
and B2 to $D_1$ of Sect. 2) with
parameters given in Table 1.
Beyond 25 kpc both densities were
constant and equal.
In both cases, the jets are assumed to be in initial pressure balance
with the external medium. All individual portions of the external gases
are taken as isothermal
and the interfaces are pressure matched; thus in Case A2 there is an
abrupt density drop by a factor of 0.03 at the first interface at 5 kpc
(easily seen in the uppermost panel of Fig.~\ref{2Dimage}), and there is
a corresponding rise in $T$ by a factor of 33 across that interface.

\begin{figure}[t]
\psfig{file=1564fig4.ps,width=3.5in}
\caption{The ratios of the location of the Mach disk and
bow shock
of Run B2 to those of A2, $r_D$, as  functions of time
scaled to units
of Myr. The triangle denotes the bow shock $r_D$ and the
circle denotes the Mach disk
$r_D$.
}
\end{figure}

Although the code is not relativistic, the simulation can be
reasonably scaled so that it is applicable
to FR II radio sources. For a value of the initial jet radius $R_0$ = 0.05 kpc
and  $T_{ISM}$ = 10$^6$K, one time unit corresponds to 0.6 $\times$ 10$^6$yr.
The velocity of the jet flow with respect to the ambient medium is $0.4c$
and the power of the jet is $L_b \simeq 2\times10^{45}$  erg s$^{-1}$ for a central
ambient density of $n_0 = 10$ cm$^{-3}$.

Figure~\ref{2Dimage} shows gas density for the two
simulations (A2 and B2) at the same early (set of two at the top) and late
(2.5 times greater; set of two at the bottom) times.
The early time is chosen to correspond to the point when the slower
jet (A2) just emerges from the denser inner core. At that same time, the identical
jet propagating through the less dense inner core (B2) has long since blasted
though its more rapidly declining inner medium
($\delta_{B2} \equiv \delta_1 > \delta_{A2} \equiv \delta_2$),
and has gone a good way out into the symmetric ISM.  So at that time, the ratio
of distances propagated is nearly maximal, since the
asymmetry produced by the differences between the central media is
fully felt.  At the late time shown, just before the less impeded jet leaves the grid,
the ratio of distances is substantially reduced, in that the early asymmetry in
environment is mitigated by the longer phase of propagation through symmetric
media.
Figure 4 illustrates the 2-D results for $r_D$ defined using both
the Mach disk and the bow shock positions; we see that for these simulations
there is essentially no difference between them, as the jet always terminates
just a short distance behind the bow shock.
Since CSS sources are restricted by definition to sizes in which
galactic halos and any irregularities in them will play a large role, the
much greater asymmetries observed for them (as compared to substantially bigger FR II
RGs) are easily accommodated.

\begin{figure*}[t]
\psfig{file=1564fig5.ps,bbllx=80pt,bblly=498pt,bburx=545pt,bbury=709pt,width=7.0in}
\caption{The natural logarithm of the density (with white the densest and black the
least dense) is shown for
Runs A3 (top) and B3 (bottom) at three times:
$t= 0.021$, left; $t=0.080$, middle; $t=0.144$, right; here the unit of time
is 6.0 Myr.
Note that these are slices through a 3-D computation and no
symmetries are imposed, so that non-axisymmetric motions are clearly visible in the rightmost
 panels. The grid runs from 1--35 kpc along the propagation direction and $\pm 12$kpc
in the transverse direction.
\label{3Dimage} }
\end{figure*}

\subsection{3-D Simulations}
Three-dimensional simulations allow for the generation of
non-axisymmetric modes and instabilities.
The parameters of our 3-D simulations are
also given in Table 1, and are similar to those of the
2-D simulations.
The main differences are the need to use a larger values of  $R_0$ (1.0 kpc),
$a_c$, and $a$ and a somewhat smaller value of $\theta_j$,
these changes being necessary to allow sufficient resolution in the necessarily
coarser 3-D simulations.
These three-dimensional simulations were run on
150$\times$50$\times$50 active zones,
extending out to 35$R_0$ (35 kpc) along the initial direction of propagation,
$x$, and  to $\pm$12$R_0$ ($\pm$12 kpc) in both directions perpendicular to it.
To provide marginally adequate resolution in the most important region, 14
uniform zones span the jet diameter, with the rest of the zones
logarithmically scaled (e.g. Hooda \& Wiita 1996; 1998).
This set-up allows the jets sufficient time to propagate through each medium
so that the effects of the different ambient media on the jets
can be ascertained; see Saikia et al.\ (2003).  We believe these to be the first 3-D extragalactic jet
simulations to employ non-zero opening angles.

With the exception of  a relatively wider jet
(in comparison to the size of the core and main galaxy, which is required to
provide adequate resolution within the jet), and minor differences
in the scale heights, the parameters for the
first two 3-D simulations are identical to those of the 2-D
simulations. Therefore we can quite quickly see the differences produced
by adding a third dimension.

Figure~\ref{3Dimage} displays densities from simulations A3 and B3 at early, middle and
late times in the evolutions.
For a canonical value of $R_0$ = 1 kpc and $T_{\rm ISM} = 10^6$K,
the unit of time is now 6.0 $\times$ 10$^6$ yr.
A major difference between the 2-D and 3-D runs is that the bow shocks run ahead
of the Mach disks by much greater amounts in 3-D than they do in 2-D.
At early times, when the jet is still in a transient initial state, the bow shocks for these $M_j = 26$ jets
proceed out through the inner halo very quickly, and open a large gap between
the bow shocks and the working surfaces at the ends of the jets.
Our analytical models assume that these two locations stay very close together,
so these simulations reveal that this assumption is an oversimplification
for such high Mach numbers and low jet densities.
A similar behaviour is also seen in axisymmetric simulations, using a different
3-D code, of very light cylindrical
jets propagating through constant density media (Krause 2003).

 The finite opening angles
are fairly well preserved in the first phases of the evolution (both in the central
halo and for some distance into the more steeply declining ISM), despite the
presence of a recollimation shock.
Once the jets are at a substantial distance into the ISM, the jet becomes
better collimated and then propagates nearly as a cylinder (see the middle panel
of Fig.~\ref{3Dimage} for B3 and the right panel for A3).  At this point,
our analytical models, which assume the opening angle stays constant,
lose more of their validity, as the slowing down of propagation predicted by
the spreading jet picture is replaced by a situation of more nearly constant
velocity.
We see a slow breaking of axisymmetry through these simulations, despite
the symmetric initial conditions.  This can be attributed primarily to numerical
errors introduced by our setting up of a conical flow within a relatively coarse
Cartesian grid.  Unsurprisingly, the non-axisymmetric effects
are stronger for A3, which crosses a density jump; such a discontinuity
helps to induce the growth of perturbations (cf.\ Hooda \& Wiita 1996, 1998).

\begin{figure}[t]
\psfig{file=1564fig6.ps,bbllx=53pt,bblly=200pt,bburx=375pt,bbury=504pt,width=3.5in,clip=}
\caption{The arm-length ratios, $r_D(t)$ defined for both
the bow shock and Mach disk locations of Runs A3 and B3 as functions
of time rescaled to units of Myr. The triangles
denote the bow shock ratio and the circles denote the Mach
disk ratio. \label{3Dratio}
}
\end{figure}

Figure~\ref{3Dratio} shows the arm-length ratio, $r_D(t)$ for B3 to A3; this is plotted
using both the bow-shock locations and the Mach disk locations.  We see that
the Mach-disk ratio basically follows the trend we would expect, with a substantial
increase at early times while the faster jet escapes the denser core and
enters the ISM, and then a more gradual decline after both jets reach
the ISM.  Unfortunately, our simulations could not be followed long enough to
see the ratio continue to decline once both jets were in the constant density
ICM, as the faster one leaves the grid before the slower one gets to that second
interface (Fig.~\ref{3Dratio}).  The bow-shock ratio is less variable, but,
after first rising, and then slightly declining, it again rises at moderate times
as the Mach disk in B3 catches up with the bow shock, while the Mach disk in A3
is only starting to do so.  These simulations can be scaled so
as to fit FR II
radio sources. For a temperature of the external gas of about
$10^6$K, the velocity of the jet with respect to the ambient medium
is $0.4c$ and the power of the
jet is $L_b \sim 7\times10^{46}$  erg s$^{-1}$ for a central ambient density
of  $n_0 = 1$ cm$^{-3}$.  We have used this value of $L_b$ in our analytical
calculations (\S 2 and 3) for scaling the time units.

\section{Discussion and Conclusions}
The asymmetric models considered above can explain the observed trend
in the  asymmetry parameters $r_D$ and $r_L$
(Saikia et al.\ 1995, 2003; Arshakian \& Longair 2000).
Our model for  jets in an asymmetric environment oriented in the
plane of the sky explains the large number of galaxies and quasars
having $r_D > 1$ and $r_L < 1$.
Our simulations of the  jets
propagating in asymmetric environments show a similar trend in arm-length
asymmetry as that produced in our analytical calculations.
We note that  the observed ranges of $r_D$ and $r_L$ can be
easily accommodated with the kind of asymmetric density profile discussed here.
The inclusion of time-delay and Doppler boosting effects can explain
the rarer sources with $r_L > 1$, and the fact that these are relatively
more common for CSS quasars (presumably seen at smaller $\varphi$) than
for CSS radio galaxies.

Although our analytical model for radio source evolution is certainly oversimplified,
somewhat more sophisticated models (e.g.\ Kaiser, Dennett-Thorpe
\& Alexander 1997; Blundell et al.\ 1999;
 Manolakou \& Kirk 2002; Barai et al.\ 2004), yield similar trends for distances and radio powers
with jet power, external medium density and time.  Larger differences emerge
at late times and at high redshifts, when different treatments of adiabatic
losses and our neglect of inverse Compton losses become important; however,
these are not relevant for the young CSS sources, since the synchrotron
losses from these compact lobes will always exceed the inverse Compton
losses (e.g., Blundell et al.\ 1999).  The key advantage our
simple model has over those more complicated approaches is that we avoid
the necessity of
performing numerical integrals to obtain values for $L_R$, so the estimates
of Sects.\ 2 and 3 are thus possible.

Although the analytical and numerical models agree in a qualitative sense,
it is not surprising that there are differences between the analytical and the numerical
calculations for the arm-length ratio.
Both the 2-D and 3-D numerical simulations show a
peak value for $r_D$ of about 2.7. At later times the numerically estimated
$r_D$'s  seem to approach
asymptotic values greater than 1, although the simulations could not be
continued long enough to confirm this. The analytical maximum $r_D$ is
about 1.7.
The time taken to reach the first interface is similar in both analytical
and numerical calculations, but in the simulations the second interface
is reached later compared to the times they are reached in the
analytical calculations.  This implies that
even though the calculated and simulated velocities are similar at early times,
the velocity of
the numerical jet, particularly for the 3-D case, is slower than our
simple ram pressure balance calculations would indicate.
These lower velocities in the numerical simulations can be
understood because the effective working surface in the simulations
is somewhat larger than the analytical model's jet width,
particularly at early times.  These slower speeds,
which are more pronounced for the jet propagating
through the denser gas, also explain most
of the discrepancies between the maximum values attained by $r_D$,
and the longer times needed for $r_D$ to decrease towards unity.

A possible reason why the jet in the 3-D simulation slows even more with respect
to the analytical estimate is that the simulated jet becomes  elliptical and rotates
about its own axis, as expected from theoretical calculations
of the fastest growing perturbations (e.g.\ Hardee, Clarke \& Howell 1995).
The jet eventually produces an oblique
 Mach disk, effectively  making the jet thrust smaller while narrowing
the transverse width of the Mach disk
(e.g.\ Norman 1996; Hooda \& Wiita 1996). Thus, allowing
for non-axisymmetry in the computations
basically acts to preserve the asymmetry
in $r_D$, and could explain  the larger asymmetry seen in these simulations as
well as the slower velocities at later times, as compared to the
simplified analytical calculations.

Recently Carvalho \& O'Dea (2002a,b) compared the propagation of jets
of many different values of $\zeta$ and $M_j$.  These simulations also
used the ZEUS 2-D code and were restricted to axisymmetry, but they
considered both propagation through constant density media and declining
power laws.
Although several parameters are different from our study, we made rough estimates
of arm-length ratios using their high $M_j$ simulations through an ambient
medium of constant density
($\delta=0.0$), and declining density ($\delta=0.75$),
at a time of 0.5 Myr;  $r_D$ is
about 2.0, 1.3 and 1.1 for $\zeta$ of 0.0276, 0.0542 and 0.1106, respectively.
The ranges of the observed $r_D$ thus argue for a small $\zeta (< 0.01)$ for
extragalactic radio jets.
Such low $\zeta$ values have long been known to be
favoured by the observed widths of cocoons seen in FR II radio sources
(Norman et al.\ 1982).

Carvalho (1998) performed analytical calculations of jets
``scattering'' or penetrating
through clouds in an otherwise uniform medium; the asymmetry is produced
due to the statistical variance in the
 number of clouds the jets cross through. The arm-length
asymmetry produced in his model decreases as the jet propagates
forward but the symmetrization occurs at much smaller scales.
To explain the corresponding flux density ratios would require the shorter
arm to be colliding with a cloud at the time of observation or at least
the presence of more contrast in
densities between the clouds and regular ISM on the side with the  shorter  arm
(Saikia et al.\ 1995, 2002).   In our simulations  the asymmetry
builds up  as time progresses before getting symmetrized at much later times
with the corresponding flux density ratio changing in the correct sense.

Recent 3-D simulations  of
jet/cloud interactions typically either show the jets destroying the clouds
or being halted by them; for a small range of jet/cloud parameters,
some  highly distorted structures and
deflected arms can be produced (Higgins et al.\ 1999; Wang et al.\
2000).
Such simulations may be applicable to only a small number of CSSs.
These cloudy medium models can confine the
CSS sources to sub-galactic sizes with ages of the order of the larger
radio sources (Carvalho 1998). But most observational evidence
(Fanti et al.\ 1995; Readhead et al.\ 1996a,b; Pihlstr{\"o}m et al.\ 2003)
suggests that the CSS sources are young, not ``frustrated''. Our model
predictions fit the
observational studies connecting CSS sources with both youth and
higher degrees of asymmetry.

An analysis of the breaks in the spectra of 50 CSS sources, which
included many measurements at 230 GHz, supports the picture that
they are very young, with most having estimated ages of $< 10^5$yr
(Murgia et al.\ 1999).  Our models correspond to
ages in the observationally estimated ranges of $<10^5$--$10^6$yr.
Our models also have the key advantage of producing the types of asymmetries in
arm-lengths and luminosities that are characteristic of smaller sources.

\acknowledgements
We thank Gopal-Krishna and Kandaswamy Subramanian for their comments on
the manuscript, and Srianand for his help.  We are grateful to the
anonymous referee for finding an error in the original manuscript and for
suggestions that have improved its clarity.
The two-dimensional numerical simulations were performed on the Pittsburgh
Supercomputer Center Cray C90, under an award to PJW funded by the NSF.
SJ thanks Georgia State University for hospitality and PJW is grateful
for hospitality at NCRA, RRI, and Princeton University Observatory.  This work
was supported in part by NASA grant NAG 5-3098 and by RPE and
Strategic Initiative Funds to PEGA at GSU.

redpajama_set_name: RedPajamaArXiv


text:
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