text:
visiting-industrial-fellowships-awarded-to-graduates
article Press releases 2014 January
Aston awards Visiting Industrial Fellowships
From l-r: Emma Jennings, Daniella Genas, Ollie Leggett, Paul Little, Indi Deol, Charles Rapson, Prof Mark Hart, Prof George Feiger, Rob Mannion, John Miller, Steph Chamberlain, Byron Dixon, David Lusty, Heather Forrester, Paula Whitehouse.
Aston University is proud to award Visiting Industrial Fellowships to thirteen Alumni of the Goldman Sachs 10,000 Small Businesses Programme, in recognition of the contribution they have made across the university to the understanding, experience and awareness of business growth and entrepreneurship.
This is the first time that members of the 10,000 Small Businesses programme alumni have been recognised in this way. The selected business owners, who will hold the title for a two year period, come from a broad range of business sectors and through their engagement to date have supported Aston University, its students, research and staff across a range of activities such as KEEN and KTP projects, mentoring through the BSEEN and SERV programmes, social impact projects with MBA students, involvement in policy development and lobbying through the university, recruiting students and graduates to their businesses, as well as acting as live case studies in taught modules.
The Visiting Industrial Fellows were awarded the title at a lunch event held at Aston Business School on 14th January 2014, attended by Professor Mark Hart, Professor of Small Business and Entrepreneurship and Academic Lead on Goldman Sachs 10,000 Small Businesses programme and Professor George Feiger, Executive Dean, Aston Business School.
Professor George Feiger said: "I am delighted that thirteen of the 10,000 Small Businesses programme alumni have been awarded Visiting Industrial Fellowships. We value the contribution these high growth, entrepreneurial business leaders are making to the work of Aston Business School and the key role they play in fostering relationships between the small business community and Aston University".
Stephanie Chamberlain, CEO of Magic Milestones, a consulting firm specialising in the field of digital product management is one of the alumni to be recognised as a Visiting Industrial Fellow. Stephanie has been involved in a number of consultations involving Lord Heseltine and the University's Enterprise Research Centre and also acts as a mentor to young entrepreneurs for the BSEEN programme.
Talking about receiving the title Stephanie said: "I am honoured to be made a Visiting Industrial Fellow by the University. Since joining 10,000 Small Businesses I have valued the support and opportunities I have had to engage with both Aston Business School and the wider University community. As the owner of a growing business within the region I particularly appreciate the opportunity to contribute to the discussion of enhanced government policy support for small businesses and for budding entrepreneurs."
The University plans to award these Fellowships annually to 10,000 Small Businesses alumni who demonstrate their commitment to supporting Aston Business School and the business community.
The thirteen Visiting Industrial Fellows are:
• Dan Barber, Standout Design & Marketing Ltd, Leicester (www.standoutuk.com/)
• Stephanie (Steph) Chamberlain, Magic Milestones, Birmingham (www.magicmilestones.biz/)
• Inderjit (Indi) Deol, Aidem Digital CIC, Birmingham (www.aidemdigital.org.uk)
• Byron Dixon, Micro-Fresh, Leicester (www.microfresh.co.uk)
• Heather Forrester, Research By Design, Birmingham (www.researchbydesign.co.uk/)
• Daniella Genas, Aspire4u, Birmingham (aspire4u.co.uk)
• Emma Jennings, thestudio Venue Company, Birmingham (www.studiovenues.co.uk)
• Oliver (Ollie) Leggett, IE Design, Birmingham (www.iedesign.co.uk)
• Paul Little, Coen Ltd, Birmingham (www.jcoen.co.uk)
• David Lusty, Lightpower Ltd, Birmingham (www.lightpoweronline.com)
• Rob Mannion, RNF Digital Innovation, Warwick (www.rnfdigital.com)
• John Miller, Base Group, Leicester and Birmingham (www.base-group.co.uk)
• Charles Rapson, Colebridge Enterprises (www.colent.org) and West Midlands School for Social Entrepreneurs (www.the-sse.org/schools/29/west-midlands), Solihull and Birmingham
BSEEN is part-funded by the European Regional Development Fund.
Aston University is renowned for the quality of its innovative learning and teaching, world leading research and for having a friendly and supportive culture. The School has strong business links, and offers life-transforming experiences that make a real difference to organisations, economies and the global society. Aston Business School is committed to helping small businesses realise their potential through dedicated services which are specifically tailored to meet their needs. The School also delivers cutting edge entrepreneurial research (especially on high growth firms) and is home to the Global Entrepreneurship Monitor (GEM) UK project and jointly hosts the new national Enterprise Research Centre with Warwick University.
10,000 Small Businesses UK
10,000 Small Businesses UK is an initiative to unlock the growth and job creation potential of small businesses and social enterprises across the United Kingdom through providing the resources they need to grow, including greater access to business education and business support services. It is based on the broadly held view of leading experts that a combination of education and support services best addresses the barriers to growth for small businesses.
The programme is based on an innovative and successful approach to supporting entrepreneurs, as developed through the Goldman Sachs 10,000 Women initiative and the 10,000 Small Businesses programme launched in the United States in 2009. A programme tailored specifically for the UK market was brought to Yorkshire in 2010 and then to the North West of England in 2011, the Midlands in autumn 2011 and London in early 2012. Programme partners include Saïd Business School (University of Oxford), Leeds University Business School, Manchester Metropolitan University Business School, Aston University Business School and University College London.
10,000 Small Businesses in the UK is funded by Goldman Sachs and the Goldman Sachs Foundation.
The BSEEN project is part financed by the European Regional Development Fund Programme 2007 to 2013. The Department for Communities and Local Government is the managing authority for the European Regional Development Fund Programme, which is one of the funds established by the European Commission to help local areas stimulate their economic development by investing in projects which will support local businesses and create jobs. For more information visit www.communities.gov.uk/erdf
David Farrow
d.farrow@aston.ac.uk
Aston academic awarded OBE for services to engineering and forensic science
Public lecture: Is bioenergy a sustainable resource?
Minority-led firms more likely to face "survival threats"
Aston students coach school children in launch of online maths platform
Aston University recognised in UK's Best Breakthroughs list
asian links
aston business school students final hult prize
aston campaign raises more than 11000 for for filipino town
aston graduate presented with prestigious award
aston student intake increase second highest in the uk
business minister visits european bioenergy institute
charity record label founded
inaugural lecture explores technological revolution
influential 500
lecture to explore sustainable growth
new head engineering applied science
nuclear programme wins training award
pioneering study investigates causes alzherimers
professor elected chair pharmacy schools council
professor named fellow of international society
santander branch opens
student founds company
student wins bowls tournament
visiting industrial fellowships awarded to graduates


"It's all about individuality," says makeup artist James Kaliardos about the transparent shades at Diane Von Furstenberg. "There's a strong casting that covers the reality of what our world is now, so we're using easy, natural tones." Orlando Pita also went natural, but gently helped Mother Nature by coaxing hair into light waves, then let it fall back behind their shoulders. "She wanted the girls to look the way they did when they came in for casting," explained Pita. "But when the reality is that they're coming from another show, we need to help get it there a little."


text:
Andrelândia ist eine Stadt im Süden des brasilianischen Bundesstaates Minas Gerais.
Sie liegt 998 Meter über dem Meeresspiegel, hat eine Fläche von etwa 1010 km², befindet sich ca. 300 km von Belo Horizonte, der Hauptstadt des Bundesstaates Minas Gerais, 396 km von São Paulo, 990 km von Brasília und 250 km von Rio de Janeiro entfernt. Die Stadt hat rund 12.000 Einwohner.

Geschichte
Die Kolonisierung des Andrelandia-Gebiets begann in der Folge des Goldbergbaus im Süden von Minas Gerais. Vor 1700 hielten sich bereits in dieser Gegend neben den ansässigen Bergbauern einige Abenteurer auf, die nach Gold suchten. Gegen 1736 wanderte der portugiesische Bauer André da Silveira in Brasilien ein und ließ sich in der Gegend nieder. André stammte wahrscheinlich aus einer reichen Familie, da er schreiben konnte, eine damals seltene Fähigkeit. Er hielt Sklaven, die seinen Bauernhof, die Fazenda das Bicas, bewirtschafteten.

1749 erhielt André da Silveira von dem Bischof Marianas, D. Manoel da Cruz die Genehmigung zum Bau einer Kapelle, die der Madonna von Porto geweiht wurde, und die später in Nossa Senhora do Porto da Eterna Salvação (Madonna von Porto der ewigen Rettung) umbenannt wurde. Sie befindet sich im heutigen Stadtzentrum. André da Silveira gab in Portugal ein Marienbild in Auftrag, das bis heute in dieser Kirche zu sehen ist.
André da Silveira war verheiratet mit Maria do Livramento und hatte zwei Töchter, Maria da Silveira und Tereza, die adoptiert war. Nach dem Tod seiner Frau zog er nach Piedade do Rio Grande und lebte dort bis zu seinem Tod.

Um diese Kapelle entstand eine Siedlung, viele Leute ließen sich in dem neuen Dorf nieder, das bald als Pfarrei anerkannt wurde.
Ab dem 17. Jahrhundert ließen sich in der Stadt Familien aus Libanon, Spanien, aus Portugal und Italien nieder, um nach Gold zu suchen. Auch bot der Bau der ersten Eisenbahn in der Region Verdienstmöglichkeiten für die Einwanderer.

Am 20. Juli 1868 erhielt die Siedlung in einer Sitzung des Gemeinderates den Namen Vila Bela do Turvo (Schönes Dorf des Turvos) und den Status einer Stadt. 1930 wurde die Stadt zu Ehren des André da Silveira in Andrelândia umbenannt.
Durch den Bau der Eisenbahn ab 1980 zwischen Andrelândia und Arantina und den damit verbundenen verbesserten Erwerbsmöglichkeiten nahm die Zahl der Bevölkerung stark zu und die Infrastruktur verbesserte sich.

Wirtschaft
Die wichtigsten Wirtschaftszweige sind Landwirtschaft, die Herstellung von Milchprodukten, Tourismus und Dienstleistungen.
Hergestellt werden mehrere Käsesorten und Joghurt.
Landwirtschaftliche Produkte sind vor allem Kaffee, Mais, Kartoffeln, Bohnen, Zuckerrohr und Tomaten. Die größte nutzbare Fläche besteht aus Plantagen zur Produktion von Eukalyptus- und Pinienholz. In kleinen Mengen wird ein Schnaps aus Zuckerrohr gebrannt, und es gibt eine geringe Weinproduktion.

Jedes Jahr findet die Exposição agropecuária im Parque de Exposições statt, auf der die Farmer der Region Produkte ausstellen und die besten Erzeugnisse prämiert werden. Die Ausstellung wird von einem reichhaltigen kulturellen Programm begleitet.

Sprache
Die Amtssprache in Andrelândia ist Portugiesisch. Menschen verschiedener Ethnien, die in die Region eingewandert sind, gaben häufig ihre Muttersprache auf und sprechen Portugiesisch, mit stärkerer mundartlichen Einfärbung in Minas Gerais.

Religion
Nach dem letzten Zensus sind 89 % der Bevölkerung katholisch, 9 % evangelisch, 1,5 % geben keine Religion an und 0,5 % gehören einer anderen Religionsgemeinschaft an.

Kultur
Die Musik in Andrelandia unterscheidet sich nicht von der üblichen Musik im Südost Brasiliens, wie Sertaneja, Pop oder MPB (brasilianische Volksmusik).

Veranstaltungen
  Festival de férias. Ein Mal pro Jahr findet das Festival de Férias statt, auf dem berühmte brasilianische Musikgruppen gastieren.
  Andréfolia, der Karneval. Der Karneval in Andrelândia wird von den so genannten Blocos organisiert. Blocos sind Gruppen oder Vereine, die unter einem bestimmten Motto Karnevalskostüme entwerfen und vorführen. Der "Bloco das Virgens" ist eine gemischte Gruppe, in der die Männer Frauenkleider tragen und die Frauen in Männerkleidern auftreten.

Weblinks

 Website der Stadtpräfektur (portugiesisch)

Ort in Minas Gerais
Município in Minas Gerais

redpajama_set_name: RedPajamaWikipedia


text:
> Business Aviation
Cosmic Radiation (5)
Valmont Industries, Inc.
Valmont Industries, Inc. is the first corporate jet operator to use the GlobaLog system to monitor the cosmic radiation of its aircrews
"We are very pleased with GlobaLog. The system makes it easy to comply fully with
EU directives and national regulations. GlobaLog also enables us to pursue a
health & safety strategy of ensuring the cosmic radiation load is shared equally
among those of our pilots exceeding 1.0 milliSievert annually.", TNT Airways
" GlobaLog is an excellent product that delivers on it's promise. We are about to
commence trans-Atlantic flights and expect GlobaLog will also play a role in
optimizing flight rostering. I know many of our pilots also make good use of the
GlobaLog electronic logbook.", Jet2.com
"GlobaLog has made it easy to provide our pilots and cabin crew members with a
personal cosmic radiation account. GlobaLog has helped increase understanding of cosmic radiation among aircrews and thus helped us fulfill our legal obligation to inform them about the health risks involved.", Thomas Cook Airlines
"We are well aware that the EU directive on cosmic radiation monitoring is currently not being enforced to the letter. It's a comfort factor knowing that with GlobaLog we are fully prepared for when that day comes and will not have to rush to implement technology for keeping individual radiation accounts.", Thomas Cook Airlines
" GlobaLog does everything it says and more. Setting up the data channel was easy and the level of service is good. My colleagues and I are convinced GlobaLog provides the most accurate picture of how much cosmic radiation our pilots and cabin crew are exposed to.", Icelandair

redpajama_set_name: RedPajamaCommonCrawl


on Work Stream 1 Recommendations as issued on 23 February 2016.
On 6 March 2016, the ALAC ratified the entire set of twelve Recommendations.
consensus of the remaining fourteen ALAC Members.
Recommendation 12 was ratified with full consensus by all fifteen ALAC Members.


Lake Lure Golf Club - "The Municipal Golf Course of Lake Lure"
The Lake Lure Golf Club is a great nine-hole course offering a challenging golf game amidst the beautiful scenery of Hickory Nut Gorge at the southeastern end of town.
The course is open year round and has a historic clubhouse, paved parking area, cart storage building, driving range and two putting greens.
The course is located at the southeastern end of town along US64/74. It sits on a 235-acre tract of land owned by the Town of Lake Lure.
From the white tees, this course is 2,738 yards for nine holes and par 35. The course underwent a major renovation in 2010 to return it to its original design and playing condition.
It has proven popular with golf leagues, women's teams and golfers looking for a challenging place to practice their shots.
There are no tee times at this course.


1. How screwed am I?
So, multitasking is a *****. Also, I'm a dumbfuck.
I had Don't Steamrve opened and paused. In the meantime, I updated my graphics card drivers (with the game still open). And then HEY, Under the Ocean finished downloading, I better check it out. Somewhere between that and the graphics driver updating Don't Starve crached.
...so yeah. Almost 15 hours wasted.
Am I completely screwed or what?
You are telling me this wasn't my doing?
Now I don't know if what broke the game was the drivers update or the new build that was just pushed.
I have an AMD Radeon HD 6800ish, if that helps, and I just installed the last driver available. I'm still downloading the Chrome version to see if it works.
Which build would that be?
I just downloaded 68792 and it's still broken. I guess we'll have to wait for Steam to propagate the update.
I think you're just delayed. it should be 68845.
Yay, kevin fixed the island!


Tony Lee is a New Zealand based singer/songwriter who writes authentic, salt of the earth tunes, big choruses with heartfelt lyrics worn on his sleeve.
I was commissioned by Cartel Records to write and create a music video to accompany the song based around the idea of an unappreciated superhero and this is the story I came up with.
Nominated for "Best Music Video" at the Limelight Film Awards in London.


I'm happy to announce that the Hart's Desire Print Shop is now open. You have two ways to shop. You can click on the Print Shop at the top of the page on this site to find affordable art prints for sale in various sizes or you can visit my Etsy Shop and find some of my images adorning blank greeting and Thank You cards.
There are 12 different card sets available in the Etsy Shop.
Each one is printed on textured paper which can also double as art prints after the cards are given.
Simply frame and hang up!
$10 of each set of this card set, featuring food out of my garden, will be donated to the Warren County Backpack Program which provides kids in need a backpack full of food.
Enough to feed that child over a weekend.
With each set of this card purchased, that's enough to feed TWO children over one weekend.
We already had our vacation plans set to go to the beach in June, but when an opportunity came up to spend an extra week at the beach? and at a beautiful sound-side home? we'd have to have been crazy to turn that down!
The most beautiful 'non beach' beach house I've ever set foot in.
It was originally a hunting/fishing lodge. The house has been restored and remodeled. The owners kept as much original as they could.
Original wood floors. Even the numbers on the old lodge doors were kept.
The 'softest blanket ever' was a gift right before this trip. He has slept with it every night since it was given to him.
What came first? The horses or the people? It's hard to tell as the horses aren't bothered by people at all.
These guys were literally right outside our door and crabbed all day. We were lucky enough to get almost a bushel of crabs before they hit the fish markets.
I find it amusing the things he decides to 'collect'. He was fascinated with the crab claws.
Congrats to Bridgett! Page County's latest High School graduate! I wish you nothing but good vibes and happiness as you start this new chapter in life.
Another year has gone by and she keeps getting more grown up and more beautiful.
I stopped by her house so she could show me her rabbit and new puppy.
We walked next door to her Grammie's. How great to grow up so close to family!


text:
Q: Do-While Loop in C doesn't repeat This code doesn't repeat if I answer a negative number like "-1.01".  How can I make it loop so that it will ask again for c?
#include <stdio.h>

main()
{
    float c;

    do {
        printf("O hai! How much change is owed? ");
        scanf("%.2f", &c);
    } while (c < 0.0);

    return(0);
}

A: The format strings for scanf are subtly different than those for printf. You are only allowed to have (as per C11 7.21.6.2 The fscanf function /3):

*

*an optional assignment-suppressing character *.

*an optional decimal integer greater than zero that specifies the maximum field width (in characters).

*an optional length modifier that specifies the size of the receiving object.

*a conversion specifier character that specifies the type of conversion to be applied.

Hence your format specifier becomes illegal the instant it finds the . character, which is not one of the valid options. As per /13 of that C11 section listed above:

If a conversion specification is invalid, the behaviour is undefined.

For input, you're better off using the most basic format strings so that the format is not too restrictive. A good rule of thumb in I/O is:

Be liberal in what you accept, specific in what you generate.

So, the code is better written as follows, including what a lot of people ignore, the possibility that the scanf itself may fail, resulting in an infinite loop:
#include <stdio.h>
int main (void) {
    float c;
    do {
        printf ("O hai! How much change is owed? ");
        if (scanf ("%f", &c) != 1) {
            puts ("Error getting a float.");
            break;
        }
    } while (c < 0.0f);
    return 0;
}

If you're after a more general purpose input solution, where you want to allow the user to input anything, take care of buffer overflow, handle prompting and so on, every C developer eventually comes up with the idea that the standard ways of getting input all have deficiencies. So they generally go write their own so as to get more control.
For example, here's one that provides all that functionality and more.
Once you have the user's input as a string, you can examine and play with it as much as you like, including doing anything you would have done with scanf, by using sscanf instead (and being able to go back and do it again and again if initial passes over the data are unsuccessful).

A: scanf("%.2f", &c );
//      ^^ <- This seems unnecessary here.

Please stick with the basics.
scanf("%f", &c);

If you want to limit your input to 2 digits,
scanf("%2f", &c);

redpajama_set_name: RedPajamaStackExchange


text:
Disk in the Active Galactic Nuclei observed by HALCA
Filed under Institute of Space and Astronautical Science (ISAS), Japan
The radio astronomy satellite HALCA is maintaining its space observations under the VLBI Space Observatory Program (VSOP), in cooperation with the global tracking network and the radio astronomical antenna network. Though the operation is slightly limited at present, because of a malfunction in one of HALCA's four reaction wheels a year ago, there is no serious problem in normal observation.
While VSOP spends most of its time observing jet phenomenon in Active Galactic Nuclei, we sometimes detect a disk perpendicular to the jet during observation. This is detectable in the radio galaxy NGC4261 that is about 130 million light-years distant. In this radio galaxy, there is long, massive radio jet that penetrates the center of the galaxy.
The Hubble Space Telescope (HST) has discovered a bright disk measuring about 1,000 light-years in diameter, whose axis matches that of the jet in the radio galaxy. With recent ground-based VLBI observations, the root of the jet has been observed with approximately one light-year resolution, which resulted in the discovery that the brightly glowing root is asymmetrical at the front and back of the core along the jet axis.
By observing radio galaxy NGC4261, VSOP observations produced persuasive results. The absorption by the disk that encircles the core can be clearly seen. The width of the disk is less than one light-year and 1/1,000th smaller in scale than that observed by HST. Because VSOP enables us to observe at relatively long wavelengths of 18cm and 6cm, the absorption by the disk (absorption of low-frequency electric waves by plasma) can be sensitively observed.
The optical disk (Hubble Space Telescope) of radio galaxy NGC4261
central nuclei and a VSOP wavelength image. The jet axis and
disk-rotation axis face from left to right in the illustration.


I am going to Maelstrom for the hotest weekend of the year (Not that there's a hell of a lot of competition). How would you like your Aquarion: baked, boiled or fried?
For the They Who Evolve World Cup Sweepstakes, I have drawn the Ivory Coast. Who are doomed, for no better reason than their connection to me.
The new Aquarionics design (v12) is mocked up and sitting in PSP. Soon, I will get around to implementing the blasted thing.


The battery within a laptop is the most important component to having a functioning laptop. If you are experiencing a poor battery lifetime in your HP Elitebook 840 G5, then please follow the step-by-step replacement guide for the battery below. As this replacement requires the backing to be completely removed, use caution during the replacement as the electrical components inside of your laptop will be exposed. Also ensure to carefully remove any connecting wires by the heads-not the wires themselves. This will prevent any wires from breaking during the replacement.
Use a Phillips #1 screwdriver to undo the five screws. The top three screws are 10 mm and the two side screws are 7 mm.
Unscrew the bottom three screws using the same screwdriver.
The bottom Phillips #1 screws don't remove from the back plate, but do need to be unscrewed.
Turn computer so that the hinged side is facing up.
Use the plastic opening tool to pry open the back plate.
Drag the plastic opening tool along the edge from left to right and use a second opening tool to pry open the top right corner.
Repeat the 3rd step for the other side.
You should be able to hear a pop when prying open the corners.
Grab the back plate and separate it slowly away from the device.
No wiring is connected to the back plate. Separate with caution, as there are electric components on the inside.
Remove the 4mm screws that are fastened on the battery with your T9 Torx screwdriver.
Carefully remove the power supply connector by tugging it from the sides of its head.
Make sure not to pull on the wires, as they could become damaged.
Slide the battery out and remove it from the device.


text:
\section{Introduction}

It is  now widely  accepted that the  gravitational pull exerted  by a
merging satellite galaxy can generate structure in the stellar disc of
its more-massive host. A striking example of the outcome of these kind
of  interactions is  the  system  composed of  M51  and its  companion
galaxy, NGC 5195 \citep[e.g.][]{oh,dobbs}. Previous studies have shown
that prominent spiral structure  is more commonly observed in galaxies
located within groups  or with companions \citep{kor,elma,elmb}. These
observations highlighted  the importance of tidal  interactions on the
structure of  galactic discs. Although  grand design spirals,  such as
the ones observed  in M51, are related to  massive companions (in this
case,  $M_{\rm  M51}  /  M_{\rm  NGC~  5195}  \gtrsim  0.3$),  several
theoretical studies  have shown that much less  massive satellites can
also    create    phase-space     structure    in    galactic    discs
\citep{qh93,tutu,kaza08,vh08,younger,quill09,min09,bird,
  gm12}. Morphological  features, such as spiral  arms, warps, flares,
central bars,  and low surface  brightness ringlike structures  in the
outskirts of  a disc  can be  the result of  either recent  or ongoing
accretion events.

Most  of  the previously-mentioned  morphological  features have  been
observed      in     the      disc     of      our      own     Galaxy
\citep[][]{levine,moma,cabre,pohl,new02,    yanny03},    and   various
formation  scenarios  have  been   explored  for  most  of  them.   An
interesting  example is the  Monoceros ring,  which is  a low-latitude
stellar structure  spanning about $180^{\rm o}$  in Galactic longitude
at nearly constant Galactocentric  distance. It has been proposed that
this structure  could be the remnant of  a tidally-disrupted satellite
galaxy   \citep{hnm,ibata03,conn,pena05}.    More  recently,   several
authors  have argued  that this  dynamically  cold ring  could be  the
result of a tidal perturbation from a satellite galaxy on the Galactic
disc \citep{kaza08,  younger,quill09}. In particular,  the Sagittarius
dwarf galaxy  (Sgr) has been proposed  as a possible  perturber of the
Milky  Way, causing the  emergence of  the Monoceros  ring as  the far
extension of a Galactic  spiral arm \citep{pur11} and also potentially
as a gravitational influence that circularised the orbit of a putative
dwarf galaxy that could have been  torn apart to become that same ring
\citep{md11}.  Motivated  by recent studies  on cosmological abundance
matching  \citep{cw09,bcw}, \citet[][hereafter  P11]{pur11} considered
models of Sagittarius with total masses as large as $\sim 10\%$ of the
Milky Way's  mass.  These models  can successfully reproduce  not only
dynamically cold structures such as the Monoceros ring, but also other
global morphological features observed in the Milky Way.  However, its
impact on the phase-space structure of the Solar neighbourhood has not
yet been explored.

As  first shown  by \citet{min09},  the  energy kick  imparted by  the
gravitational potential of a satellite  as it crosses the plane of the
disc can strongly perturb the  velocity field of disc stars located in
local  volumes such as  the Solar  neighbourhood.  In  stellar samples
close to the Sun (i.e.  distances $\leq 0.2$ kpc), these perturbations
can be observed in the $u$-$v$ plane as arc-like features traveling in
the direction  of positive $v$, where  $u$ and $v$ are  the radial and
tangential velocity  components, respectively.  In  a follow-up study,
\citet{gm12} showed that  the space defined by the  energy and angular
momentum  of  stars  is  a  better  choice  than  velocity  space,  as
substructure   remains    visible   even   in    much   larger   local
volumes. Furthermore, they also  showed that satellites with masses as
small as  $10\%$ of  the mass of  the host  can leave imprints  in the
phase-space  distribution  of  Solar neighbourhood-like  volumes  that
could  be  identified as  late  as  $\approx  5$~Gyr after  the  first
satellite's  pericentre passage.   Substructure  associated with  this
mechanism, known as  ``ringing,'' is expected to be  better defined in
the Galactic thick disc. This  is because these stars spend relatively
little  time near  the Galactic  plane, where  perturbations  from the
Galactic  bar, spiral structure,  and giant  molecular clouds  are more
vigorous.   Moreover,  the  thick  disc  is composed  of  a  very  old
population  of stars,  with ages  around  10 to  12 Gyr  \citep{sch06,
  bens07}. Thus, most of its stars must have been in place at the time
the hypothetical merger occurred.

An  obvious question  arises  from our  previous  discussion: Could  a
satellite  galaxy like  Sagittarius have  left imprints  of  its tidal
interaction  with the  Milky Way's  thick  disc in  the local  stellar
phase-space  distribution? Previous attempts  to describe  features in
the  velocity field  of the  Solar neighbourhood  have  been primarily
concerned with the dynamical  effects induced by non-axysimmetric disc
components,  such as  a central  bar or  self-gravitating  spiral arms
\citep[see,        e.g.,][]{walter,fux01,min07,min08,ant09,min10,ant11,
  quill11}.  These studies have  focused their attention on very small
local  volumes, dominated  mostly by  populations of  thin-disc stars.
However,  little attention  has been  paid to  the  identification and
characterisation of  substructure in local volumes of  the Milky Way's
thick  disc  that may  have  originated as  a  response  of the  tidal
interaction with a satellite galaxy \citep[see, e.g.,][]{min09}.

In  this work  we attempt  to fill  this gap  by analysing  a  full 6D
phase-space catalog  of F/G-type dwarf stars from  the Sloan Extension
for  Galactic  Understanding  and  Exploration (SEGUE;  Yanny  et  al.
2009).  The   great  advantage  of  this  catalog,   as  presented  by
\citet[][hereafter L11]{lee11b}, is that it contains accurate estimates
of $[\alpha/{\rm Fe}]$  and [Fe/H] ratios for a  large fraction of its
stars.  This enables  a chemical  separation of  the disc  system into
likely  thin-  and thick-disc  populations,  avoiding unwanted  biases
associated  with  methods  based  on  stellar  kinematics  or  spatial
distributions.   To  complement this  analysis,  we  also explore  the
distribution of disc stars from the \citet{sch06} catalog.

The paper's outline  is as follows. Section 2  presents a brief review
of  the main  properties  of ringing.  In  Section 3  we describe  the
stellar samples  analysed in this  work. The distribution of  stars in
energy  and   angular  momentum  space   of  the  F/G-dwarf   and  the
\citet{sch06}   catalogs   are   analysed   in  Section   4   and   5,
respectively.   In  Section   6  we   apply  the   same   analyses  to
high-resolution   N-body  simulations   of  the   interaction  between
Sagittarius and the Milky Way. A summary and conclusions are presented
in Section 7.

\section{Ringing in galactic discs}
\label{sec:model}

\begin{figure}

\hspace{-0.1cm}
\includegraphics[width=80mm,clip]{fig1a.eps}
\\
\includegraphics[width=69mm,clip]{fig1b.eps}
\caption{Top panel: $E-L_{z}$ distribution  of disc particles inside a
  sphere of 2.5~kpc radius located  at 8~kpc from the galactic centre,
  obtained from a  simulation with a mass ratio  of $M_{\rm host}^{\rm
    total}  / M_{\rm  sat}^{\rm total}  =  0.2$. The  total number  of
  particles enclosed within this volume is $N_{\rm part}^{\rm model} =
  976$.   The snapshot  corresponds to  a  time of  3.9~Gyr after  the
  satellite  was launched,  or to  1.9~Gyr after  the  satellite fully
  merged  with  the  host  galaxy. The  different  colours  (contours)
  indicate  different number of  particles. Note  the large  number of
  lumps with  nearly constant  energies associated with  density waves
  crossing  the  sphere.   Bottom  panel:  Kernel  histogram  (KH)  of
  energies,  $E$, obtained  from the  same distribution  of particles.
  Each  peak in  the kernel  histogram corresponds  to a  density wave
  observed in the top panel.}
\label{fig:model}
\end{figure}

\citet{min09}, followed by  \citet[][hereafter G12]{gm12}, showed that
relatively  massive minor-merger events  can generate  substructure in
the   velocity   field   of   disc   stars  located   in   the   Solar
neighbourhood. Merging  satellite galaxies with total  masses as small
as $10\%$ of the mass of  the Milky Way may excite density waves whose
signatures can be identified  even $5$~Gyr after the first satellite's
pericentre  passage.    The  space  of   $E$-$L_{z}$  is  particularly
well-suited to identify density waves, since the waves are surfaces of
constant  energy  \citep[see  also e.g.][]{hz00,hwzz99}.   Over  time,
these  constant-energy  features  associated  with the  density  waves
become  more   closely  spaced,  and  their  number   increases  as  a
consequence  of phase wrapping  (see Section  3 of  G12).  In  the top
panel  of Figure~\ref{fig:model}  we show,  in $E$-$L_{z}$  space, the
distribution    of   disc   particles    located   within    a   Solar
neighbourhood-like sphere of 2.5 kpc  radius, obtained from one of the
simulations analysed in  G12. The sphere is centred  at 8~kpc from the
galactic  centre and the  distribution was  obtained after  3.9~Gyr of
evolution, which corresponds  to a time since total  disruption of the
satellite galaxy of 1.9 Gyr.  In this simulation, the satellite galaxy
has a total initial mass equal to $20\%$ of the mass of the host. Note
that only $N_{\rm part}^{\rm model} = 976$ are located within this 2.5
kpc  sphere.  It  is  clear  that disc  particles  are distributed  in
different  lumps of nearly  constant energy,  each of  them associated
with  a   different  density-wave  crossing.   The   bottom  panel  of
Figure~\ref{fig:model}  shows  a Kernel  Histogram  (KH) of  energies,
$E$. To compute the kernel histogram, a Gaussian kernel with bandwidth
$\sigma = 0.011~\Delta E$ was assigned to each particle. Here, $\Delta
E = 4 \times 10^{4} {\rm ~km^{2} ~s^{-2}} $ is approximately the total
extent  of the  satellite in  energy  space within  this volume.   The
kernel histogram  is the  sum of all  of the Gaussian  kernels.  Since
density  waves  are  surfaces  of  nearly constant  energy,  they  are
observed in the KH as  well-defined peaks.  Note that larger values of
$\sigma$  tend  to  oversmooth  the  KH, erasing  some  of  the  peaks
associated with substructure observed in $E-L_{z}$ space.  Conversely,
smaller  values produce  noisier KHs.   In  what follows  we keep  the
values of $\sigma$ and $\Delta E$ fixed at these values.

\section{The stellar samples}

\subsection{The SEGUE F/G-Dwarf sample}
\label{sec:gdwarf}

The SEGUE F/G-dwarf sample analysed in this work was culled from $\sim
~70,000$ F and G type stars with available low-resolution spectroscopy
($R \sim  2000$), as provided  in SDSS DR8 \citep{aiha}.   Among them,
about $63,000$ stars  were targeted as G-dwarfs; hence,  our sample is
dominated  by  the  G-dwarf  candidates  used  by  L11.   The  G-dwarf
candidates  were   obtained  by  selecting  stars   with  colours  and
magnitudes in the range $0.48 <  (g-r)_{0} < 0.55$ and $r_{0} < 20.2$,
respectively, while the  rest of the sample covers  $0.2 < (g-r)_{0} <
0.48$, and $g_{0}  < 20.2$. Thanks to this  simple selection function,
the stellar sample is expected  to be completely unbiased with respect
to  kinematics, and  only  slightly biased  towards  metal poor  stars
\citep[see][]{katie}.

\subsubsection{Local sample}

In order to obtain a  local sample of stars with accurate measurements
of  their 6D  phase-space coordinates,  as well  as  metallicities and
$[\alpha/{\rm  Fe}]$ ratios,  a series  of  cuts were  applied to  the
complete catalog. Here we provide a brief summary of the criteria used
for the  sample selection, but we  refer the interested  reader to L11
for a more  detailed description of this procedure  as we follow their
prescription to select the final sample.

Stellar atmospheric parameters, such as effective temperature, $T_{\rm
  eff}$, surface gravity, $\log~g$, and metallicity, $[{\rm Fe}/{\rm
  H}]$, were determined using the SEGUE Stellar Parameter Pipeline,
SSPP \citep{lee08a,lee08b,ap08,smo}.  In order to obtain high-quality
estimates of both $[{\rm Fe}/{\rm H}]$ and $[\alpha/{\rm Fe}]$
\citep{lee11a}, only stars with spectra of signal-to-noise ratios
(S/N) greater than 30 ${\rm \AA}^{-1}$ were considered.  Importantly,
this also ensures that errors in the estimated radial velocities are
smaller than 5 km s$^{-1}$. Proper motions were obtained following
\citet{munn04}, after correcting for the systematic error described in
\citet{munn08}.  Distances to individual stars were estimated using
calibrated set of stellar isochrones \citep{an09b}, following the
prescription of \citet{an09a}.  To minimise possible distance bias
from stellar age effects near the main sequence turnoff, only stars
with $\log~g \geq 4.2$ were considered. In addition, to minimise the
errors on the estimates of phase-space coordinates, we only consider
stars with distances from the Sun $0.4 \lesssim d \leq 2$ kpc. Note
that the inner limit is imposed by the data itself, due to saturation
of the SDSS photometric scans for $g \lesssim 14.5$.

To  compute  Galactocentric  positions  and velocities  of  our  local
stellar  sample, we  assume  the Sun  to  be located  at $R_{\odot}  =
8$~kpc, and that it has a  peculiar velocity with respect to the Local
Standard  of  Rest  (LSR)  $(U,~V,  ~W)_{\odot}  =  (11.1,~12.2,~7.3)$
km~s$^{-1}$ \citep{scho10}.  We further assume  a velocity of  the LSR
with  respect  to   the  Galactic  centre  of  $V_{\rm   LSR}  =  220$
km~s$^{-1}$. Finally,  we discard stars with $[{\rm  Fe}/{\rm H}] \leq
-1.2$ and $V_{\phi}  < 0$ km s$^{-1}$ in  order to avoid contamination
(as much as  possible) from the stellar halo, as  well as the proposed
metal-weak thick-disc component of the Galaxy \citep{carollo10}.

\subsubsection{The thin- and thick-disc populations}
\label{sec:thin_thick}

As mentioned  in the Introduction, signatures of  ringing are expected
to be stronger in the thick disc than the thin disc because its stars
are   less  affected   by   perturbations  from   the  Galactic   bar,
self-gravitating  spiral  arms,   and  giant  molecular  clouds.  More
importantly, the thick  disc is mainly composed of  a very old stellar
population, with ages of $\sim 10-12$~Gyr \citep{sch06, bens07}. Thus,
most of its stars must have been  in place as recently as 5~Gyr ago --
a required condition  if, for example, we seek  to identify signatures
of a merger event that may have started approximately at that time.

Following L11, we split our local sample into likely thin- and thick-disc
populations on the basis of their stellar chemical abundances, i.e.,
$[\alpha/{\rm Fe}]$ and [Fe/H]. We assign stars to the thin-disc
(low-$[\alpha/{\rm Fe}]$) and thick-disc (high-$[\alpha/{\rm Fe}]$)
components according to the following scheme:

\begin{description}

\item[For stars] with [Fe/H] $\geq -0.8$

\begin{itemize}
\item thin disc, if $[\alpha/{\rm Fe}] < -0.08 ~ \cdot$ [Fe/H] $+ 0.15$
\item thick disc, if $[\alpha/{\rm Fe}] > -0.08 ~ \cdot$ [Fe/H] $+ 0.25$
\end{itemize}

\item[For stars] with [Fe/H] $< -0.8$

\begin{itemize}
\item thin disc, if $[\alpha/{\rm Fe}] < +0.214$
\item thick disc, if $[\alpha/{\rm Fe}] > +0.314$
\end{itemize}

\end{description}

While any old stellar population with high velocity dispersion would be
suitable for our investigation, by assigning stars to the different
components of the disc according to $[\alpha/{\rm Fe}]$ we avoid
introducing unwanted biases associated with methods based on stellar
kinematics or spatial distributions. Note the gap of 0.1~dex left in the
$[\alpha/{\rm Fe}]$ cuts between the thin disc and thick disc, which is
chosen to avoid misclassification of stars. For a detailed description of
the motivation behind this scheme, we refer the reader to section 3.1 of
L11.

\subsection{The Schuster et al. (2006) sample}
\label{sec:schuster}

The \citet[][hereafter SCH06]{sch06} catalog comprises a total of 1533
high-velocity and metal-poor stars. Positions and proper motions for these
stars were primarily derived from Hipparcos \citep{hip}, Tycho-2
\citep{tycho}, and the revised NLTT catalog \citep{sg03}, whereas radial
velocities were obtained from a number of different sources available in
the literature (see SCH06, and references therein). As in Section
~\ref{sec:gdwarf}, we compute Galactocentric velocities by assuming
$R_{\odot} = 8$ kpc, $(U,~V,~W)_{\odot} = (11.1,~12.2,~7.3)$~km s$^{-1}$
and $V_{\rm LSR} = 220$ km s$^{-1}$.

Metallicities estimated  via a  photometric calibration based  on {\it
  uvby-$\beta$} photometry are also provided for the entire sample. As
shown by  SCH06, it is  possible to discriminate stars  from different
Galactic  components by means  of the  $X$ parameter,  where $X$  is a
simple linear  combination of the rotational  velocity and metallicity
of the  stars. Following SCH06, we  discard from our  sample all stars
with $X  \geq 0$, in order  to avoid potential  contamination from the
Galactic halo\footnote{Note that only a fraction smaller than $3\%$ of
  our final F/G-dwarf thick-disc subsample has $X \geq 0$.}.

Note that estimates of $[\alpha/{\rm Fe}]$ are not provided in the SCH06
catalog. Thus, a subdivision between likely thin- and thick-disc stars
cannot be performed following the scheme described in
Section~\ref{sec:thin_thick}. Nevertheless, as shown by \citet{ns91} and
SCH06, the thin-disc population in this sample belongs to a very old disc
component, with the bulk of the population older than 10~Gyr, and the
remaining stars with ages between 10 and 4~Gyr. We thus ensure that most of
these stars were already part of the disc $\sim 5$ Gyr ago. It is important
to note that all disc stars in this sample are located at a distance from
the Sun $d < 0. 2$~kpc. Thus, this sample probes the innermost regions of
the Solar neighbourhood, complementing the more distant SDSS F/G-dwarf sample.

\section{The SEGUE F/G-Dwarf sample in $E-L_{z}$ space}
\label{sec:gdwarf_ener}

We now analyse the $E-L_{z}$ distribution of the stars present in our local
SEGUE F/G-dwarf sample. In order to obtain an estimate of the orbital energy
of these stars we first need to assume a shape for the Galactic potential.
We adopt a model consisting of three different components. These are:
(1) a Miyamoto-Nagai disc
\citep{mi-na}
\begin{equation}
\Phi_{\rm disc}=-\frac{GM_{\rm d}}{\sqrt{R^{2}+(r_{a}+\sqrt{Z^{2}+r_{b}^{2}})^{2}}},
\end{equation}
(2) a Hernquist bulge \citep{hernq},
 \begin{equation}
\Phi_{\rm bulge}=-\frac{GM_{\rm b}}{r+r_{c}},
\end{equation}
and (3) a NFW dark matter halo \citep{nfw}
\begin{equation}
\Phi_{\rm halo}=-\frac{GM_{\rm vir}}{r\left[\log(1+c)-c/(1+c)\right]}\log\left(1+\frac{r}{r_{s}}\right).
\end{equation}
\begin{table}
\begin{minipage}{90mm} \centering
  \caption{Parameters of the present day Milky Way-like potential used
    in this work. Masses are in M$_{\odot}$ and distances are in kpc.}
\label{table:model}
\begin{tabular}{@{}lll} \hline Disc & Bulge & Halo\\
  \hline $M_{\rm d} = 4 \times 10^{10}$ & $M_{\rm b} = 8 \times 10^{9}$ & $M_{\rm vir} = 1 \times 10^{12}$ \\ $r_{\rm a} = 6.5$ & $r_{\rm c} =0.7$ & $r_{s} = 21.5$ \\  $r_{\rm b} = 0.26$ & & $c = 12$ \\
  \hline
\end{tabular}
\end{minipage}
\end{table}

Table~\ref{table:model}  summarises   the  numerical  values   of  the
parameters used for our Galactic potential model. These parameters are
similar  to those  used by  other  authors \citep[e.g.,][]{bj05,gea10,
  pena10}  and fit the  Milky Way  rotation curve  \citep{kly02}. Note
that,  as  described by  \citet[][and  references therein]{gh10},  the
results are  not strongly  dependent on the  particular choice  of the
potential, since substructure in  integrals of motion space are robust
to small differences in the  mass distribution because we always focus
on  small volumes  in space.  Hence,  small changes  in the  potential
essentially  act  as a  zero-point  offset,  affecting  all the  stars
present in this volume in the same way.

\begin{figure}
\hspace{-0.08cm}
\includegraphics[width=85mm,clip]{fig2a.eps}
\\
\includegraphics[width=72.5mm,clip]{fig2b.eps}
\caption{Top panel: $E-L_{z}$  distribution of likely thick-disc stars
  located  within  2~kpc  of  the  Sun, obtained  from  our  F/G-dwarf
  sample. The  different colours (contours)  indicate different number
  of stars.  Only stars with total  errors in velocity  $V_{\rm err} <
  20$  km  s$^{-1}$ are  considered.  The  subsample contains  $N_{\rm
    stars}^{\rm  thick} = 3141$  high-$[\alpha/{\rm Fe}]$  stars. Note
  the  presence of a  series of  high-density features,  especially at
  large  values of energies.  Bottom panel:  kernel histogram  of $E$,
  obtained from both the thick-disc (red solid line) and the thin-disc
  (blue  dashed  line)  stellar  subsamples.  The  thin-disc  subsample
  contains $N_{\rm  stars}^{\rm thin} =  4903$ low-$[\alpha/{\rm Fe}]$
  stars.  The  shaded  areas  indicate  errors  associated  with  poor
  sampling   of   the  underlying   distributions   (see  text).   The
  high-density features observed in  the top panel correspond to peaks
  in the kernel histogram.  Note that the thin-disc subsample exhibits
  a smoother distribution relative to the thick disc. }
\label{fig:el_20}
\end{figure}

\subsection{Thin vs. Thick disc}
\label{sec:th_tk}

The  top panel  of  Figure~\ref{fig:el_20} shows  the distribution  of
$\alpha$-enhanced,  likely thick-disc  stars in  $E-L_{z}$  space. For
this figure we have only considered stars with $d \leq 2$ kpc from the
Sun  and a  total velocity  error $V_{err}  < 20$  km s$^{-1}$.   As a
result,  and because  of the  different cuts  applied to  the complete
catalog (see Section~\ref{sec:gdwarf}), we  are only left with a total
of  $N_{\rm stars}^{\rm  thick} =  3141$ likely  thick-disc  stars.  A
series  of  high-density  features  can  be observed  in  this  panel,
especially at  high values of  $E$ and $L_{z}$. These  features become
more evident in the kernel histogram of energies, shown as a red solid
line  in  the  bottom  panel  of the  same  figure.   Comparison  with
Figure~\ref{fig:model} clearly  indicates that, if  these features are
to be associated with ringing, they have a much smaller amplitude than
might be expected.  However, due  to the relatively large threshold in
total  velocity  errors  considered  (i.e.,  $V_{\rm  err}  <$  20  km
s$^{-1}$), these  peaks may  have been smoothed  out; we  explore this
issue further in Section 4.2. On the other hand, due to the relatively
low number  of stars, some of the  peaks may have arisen  due to noise
associated  with poor  sampling  of the  underlying distribution.   To
investigate  this, we  bootstrapped our  thick-disc  stellar subsample
2000  times  and computed  a  kernel histogram  for  each  one of  the
realisations. At each value of $E$,  we sort the results of the KHs in
ascending   order.   The  shaded   areas  in   the  bottom   panel  of
Figure~\ref{fig:el_20} show  the 25-75 percentiles  (light shadow) and
the  5-95 percentiles  (dark  shadow) of  the  distribution of  values
obtained  from the bootstrapped  KHs.  The  results of  this procedure
indicate that  only a few of  these peaks have  amplitudes with values
above  the noise  level. However,  in the  following sections  we show
that,  after accounting  for the  effects of  measurement  errors, and
through exploration of the SCH06  catalog, some of the remaining peaks
may indeed be real.

\begin{figure}
\includegraphics[width=80mm,clip]{fig3a.eps}
\\
\includegraphics[width=80mm,clip]{fig3b.eps}
\caption{Distribution of total errors  in positions (top panel) and
  velocities (bottom panel), extracted from our likely thick-disc SDSS F/G-dwarf
  subsample.}
\label{fig:errors}
\end{figure}

\begin{figure*}
\includegraphics[width=61.5mm,clip]{fig4a.eps}
\includegraphics[width=50mm,clip]{fig4b.eps}
\includegraphics[width=50mm,clip]{fig4c.eps}

\caption{Kernel histograms of normalised  energies, obtained  from the
  distribution of particles shown in Figure~\ref{fig:model}, after
  convolving with measurement errors. The red solid line in each panel
  shows the averaged kernel histogram obtained after 400 realisations of the error
  convolution. The maximum error in total velocity considered is indicated
  in the top right corner of each panel. The shaded regions indicate
  $1\sigma$ deviations from the mean. For comparison we show, with a dashed
  black line, the kernel histogram obtained from the same distribution of particles
  before convolution. When errors in total velocity as large as 20 km/s are
  considered, most of the peaks in the histogram are erased (left panel). These
  peaks are recovered when we reduce the magnitude of the maximum error to
  11 km/s (right panel).}
\label{fig:mod_errors}
\end{figure*}

The bottom panel of Figure~\ref{fig:el_20} also shows (blue dashed line) the
kernel histogram on $E$ of the stars associated with the low-$\alpha$, likely thin-disc
stars. In this case, the total number of stars in the subsample is $N_{\rm
stars}^{\rm thin} = 4903$. It is very interesting to observe that the
distributions associated with the thin disc and thick disc are shifted with
respect to one another. The thin-disc subsample comprises a population of
stars that, at least locally, is less tightly bound than that of the thick
disc. Note that, within volumes as small as the ones considered here, the
Galactic potential can be regarded as constant. Thus, for these stars, the
binding energy is mainly a function of their velocities. Since the thick
disc is composed of a population of stars with a lag in $V_{\phi}$ of $\sim
30$ km s$^{-1}$ relative to the thin disc (as shown in, e.g., L11), it is not surprising
to find that these stars have a larger binding energy\footnote{Note that
the mean radial and vertical velocity components for both populations are
$\sim 0$ km s$^{-1}$.}. It is also noticeable that the thick-disc stars
exhibit a much broader distribution in energy than their thin-disc counterparts. This
is a manifestation of the larger velocity dispersion (in all directions)
associated with the thick-disc component. Finally, note that the thin disc
exhibits a much smoother distribution when compared to that of the thick
disc. One has to bear in mind that the thin-disc
subsample is also $\sim 35\%$ larger than the thick-disc subsample. Thus,
noise associated with poor sampling is reduced. This is indicated by the
tighter blue and light-blue shaded regions, computed as discussed above.
Nevertheless, in Section~\ref{sec:errors} we show that this result holds
even when considering smaller stellar subsamples with more accurately
determined velocities.

\subsection{Characterising  the  effects   of  errors  on  phase-space
  coordinates}
\label{sec:errors}

As noted above, the  measurement errors in the phase-space coordinates
of  our local F/G-dwarf  stellar sample  may be  large enough  to either
smooth out  or erase  some of the  signatures of ringing  in $E-L_{z}$
space. To  characterise their effect  on the observed features  in the
kernel histograms, we have  extracted the distributions of errors from
our  thick-disc subsample, and  convolved them  with the  position and
velocities of the particles shown in Figure~\ref{fig:model}. Estimates
of  the errors were  obtained from  the SSPP  (see L11  and references
therein);       their      distributions       are       shown      in
Figure~\ref{fig:errors}. The left panel of Figure~\ref{fig:mod_errors}
shows the  results of  this convolution when  errors in  velocities as
large as  20 km$^{-1}$  are considered. The  red solid line  shows the
averaged  kernel  histogram of  normalised  energies, $E_{\rm  norm}$,
obtained after  400 different  realisations of the  error convolution,
whereas  the shaded  region  indicates its  standard deviation.  Here,
$E_{\rm norm} = (E_{i} - \min(E)) / \Delta E$, with $\Delta E$ defined
as  in Section~\ref{sec:model}.  It is  important to  remark  that, to
compute the energies of  the $N$-body particles after convolution with
errors, we have used the same analytic potential that was used for the
F/G-dwarf sample. Note that this  simulation was designed to emulate the
result of a minor merger experienced  by a Milky Way-like galaxy at $z
=  1$. Thus, the  properties of  this potential  were scaled  to those
expected at  $z=1$, as described  in Section 2 of  G12. Interestingly,
due  to the  large magnitude  of the  errors considered,  most  of the
structure associated  with ringing has been  erased. Furthermore, some
spurious peaks can  be observed.  For comparison we  show with a black
dashed line the  kernel histogram obtained from this  set of particles
before error  convolution. The middle  panel of this figure  shows the
results of  the same  procedure, now after  convolving with  errors in
velocity $V_{\rm  err} < 16$ km  s$^{-1}$. Note that  these errors are
still large  enough to erase most  of the signatures  of ringing. Only
when considering  errors in  velocity $V_{\rm err}  < 11$  km s$^{-1}$
(right panel) do we start recovering the previously-observed peaks.

This exercise clearly indicates that, in order to detect signatures of
ringing in the  Milky Way disc, very accurate  6D phase-space catalogs
must be  explored. A highly accurate  subset of stars  can be obtained
from  our local  F/G-dwarf  sample, at  the  expense of  significantly
reducing  the  total  number  of  stars analysed.  The  top  panel  of
Figure~\ref{fig:verr11} shows the kernel  histograms of the thick disc
(red solid  line) and  the thin disc  (blue dashed line)  obtained when
only stars with  total velocity errors $V_{\rm err}  < 11$ km s$^{-1}$
are considered. As a result of  this more restrictive cut, we are left
with  $N_{\rm  stars}^{\rm  thick}   =  968$  thick-disc  and  $N_{\rm
  stars}^{\rm      thin}       =      1132$      thin-disc      stars,
respectively.  Interestingly,  not only  do  we  recover  most of  the
features   already  observed   in  Figure~\ref{fig:el_20},   but  also
structure here is more sharply  defined (as expected from our previous
discussion). Note, however, that  errors associated with poor sampling
of the underlying distribution are larger due to the smaller number of
stars.  This is  evident  by the  wider  areas covered  by the  shaded
regions, obtained  from the bootstrap  analysis of our  subsample (see
Section~\ref{sec:th_tk}). Nevertheless,  it is important  to note that
the  number  of thick-disc  stars  in  this  more accurate  subsample,
$N_{\rm stars}^{\rm  thick}$, is approximately equal to  the number of
particles analysed in the  $N$-body model, $N_{\rm part}^{\rm model}$,
shown in Figures~\ref{fig:model} and \ref{fig:mod_errors}.

Alternately, it is possible to obtain a more accurate subsample simply by
analysing a much more local subset of stars. In the bottom panel of
Figure~\ref{fig:verr11} we show the kernel histogram of $E$ obtained from a sample of
stars with heliocentric distances projected onto the plane $R \leq 0.5$
kpc. Note that by reducing the radius of our Solar neighbourhood sphere
we are not only constraining errors in the velocities of the stars, but
also in their positions. After the cut we obtain a thick-disc subsample of
$N_{\rm stars}^{\rm thick} = 2441$ stars, whereas the thin-disc subsample
contains $N_{\rm stars}^{\rm thin} = 3021$ stars. Comparison with the top
panel of Figure~\ref{fig:verr11} and Figure~\ref{fig:el_20} shows again
that many previously-observed features are preserved. Furthermore, some of
the features have become {\it even more significant}, in particular, the peak
located at $E \approx -0.97 \times 10^{5}$ km$^2$ s$^{-2}$. It is also
interesting to note that, as previously discussed in Section
\ref{sec:th_tk}, the thin-disc population exhibits  a smoother
energy distribution relative to that of the thick-disc population in both
of these panels. Notice that now both subsamples have comparable numbers of stars.

\begin{figure}
\includegraphics[width=82mm,clip]{fig5a.eps}
\\
\includegraphics[width=82mm,clip]{fig5b.eps}
\caption{Top panel:  Kernel histograms of energies  obtained from the
  SEGUE F/G-dwarf  thick disc (red solid  line) and the  thin disc (blue
  dashed line), when errors in  total velocity smaller than 11~km/s are
  considered. The shaded regions  indicate errors associated with poor
  sampling      of      the      underlying     distribution      (see
  Section~\ref{sec:th_tk}). Note that  most of the previously-observed
  features  in  Figure~\ref{fig:el_20} are  more  sharply defined,  as
  expected from  this more accurate  subsample. Note as well  that the
  thin disc  presents a smoother  distribution in $E_{\rm  norm}$ with
  respect to the thick disc. Bottom panel: As above, for stars located
  within $R \leq 0.5$ kpc and  total velocity errors smaller than 20~km/s.}
\label{fig:verr11}
\end{figure}

\begin{figure}
\includegraphics[width=82mm,clip]{fig6a.eps}
\\
\includegraphics[width=82mm,clip]{fig6b.eps}

\caption{Top panel:  Kernel histogram of  $E$ obtained from  the SCH06
  sample of  disc stars with total  velocity error $V_{\rm  err} < 11$
  km/s, shown with a black dashed line. The sample contains a total of
  603 stars.  Note  the large number of peaks  located at very similar
  values of $E$ as in the kernel histogram of the F/G-dwarf subsample,
  indicated with a red solid line.  The slight shift between these two
  distributions can  be accounted for by the  different volumes probed
  by  the  samples  (see  text),  as  well as  poor  sampling  of  the
  underlying energy  distribution. Bottom panel: As in  the top panel,
  for a sample of disc stars  with total velocity error $V_{\rm err} <
  20$  km/s.  This  larger sample  contains 813  stars.   The coloured
  areas indicate  the approximate energy range of  the Arcturus stream
  (yellow), the Hercules stream (green), and the most significant peak
  identified in the SEGUE F/G-dwarf sample (light blue).}
\label{fig:sch}
\end{figure}

\section{The Schuster et al. (2006) sample in $E-L_{z}$ space}
\label{sec:schuster_ener}

The previously-observed  peaks in the  kernel histograms of  our SEGUE
F/G-dwarf sample might  be an indication of ringing  in our own Galactic
thick disc. However, due to  the relatively small number of stars with
the  necessary small measurement  errors, uncertainties  associated with
poor sampling  of the underlying distribution are  (for some features)
still  large.  It  is  therefore  important  to  look  for  additional
evidences of  ringing in other  stellar catalogs already  available in
the  literature.  The  SCH06  is  particularly  well-suited  for  this
analysis, as it comprises a set  of old and metal-poor disc stars (see
Section~\ref{sec:schuster}).  Furthermore,  the  disc  stars  in  this
sample are all located within $d  < 0.2$ kpc, thus they probe a region
of the Solar neighbourhood that is different than that explored by the
more distant SEGUE F/G-dwarf sample.

The black  dashed line on  the top panel of  Figure~\ref{fig:sch} shows
the kernel  histogram obtained from  a subsample of likely  disc stars
from the  SCH06 catalog.  Following our previous  discussion, we first
consider stars with  total errors in velocities $V_{\rm  err} \leq 11$
km s$^{-1}$.  As a consequence,  we are left  with a total of  603 old
disc stars.  Interestingly, a large  number of peaks can  be observed,
most of them  located at values of $E$  consistent with those observed
in the kernel  histogram of F/G-dwarf subsample, shown  with a red solid
line.  As we explain  in Section~\ref{sec:sag_ps},  due to  the strong
radial and azimuthal  dependance on the location and  amplitude of the
peaks,  together  with the  poor  sampling  of  the underlying  energy
distribution, it  is not surprising  to find features in  these kernel
histograms slightly shifted with respect to one another.

The bottom  panel of  Figure~\ref{fig:sch} shows the  kernel histogram
from the  SCH06 catalog, obtained  after considering stars  with total
velocity errors  of $V_{\rm  err} \leq 20$  km s$^{-1}$.   This larger
sample  contains 813  stars.  Again,  note that  many of  the features
observed in  the KHs of both  the SCH06 and the  F/G-dwarf samples are
located at very similar values of  $E$. The colour-coded areas in
  this  panel  indicate the  approximate  energy  range  in which  the
  Arcturus and the Hercules moving groups are expected to be found. To
  compute  these energy ranges,  for simplicity,  we have  assumed for
  each moving group:

\begin{itemize}

\item  a   characteristic  $V$  velocity   component,  $V_{\rm  LSR}$
  \citep[see,   e.g.,][]{walter08,fux01,ant08,nhf,klement}.  Since  this
  characteristic   V   velocity  is   subject   to  relatively   large
  uncertainties, to  compute each energy  range we assumed $V  = V_{\rm
    LSR } \pm 10$ km s$^{-1}$

\item a characteristic $U$ velocity component equal to zero

\item a Galactocentric distance $R = 8$ kpc

\end{itemize}

The bottom  panel shows  that both moving  groups could  be associated
with  peaks in our  KH.  Note  that, as  previously explained  in this
Section, it is not surprising to find slight shifts in the location of
the  peaks between  the  two  analysed samples  due  to the  different
volumes  probed.  M09  considered  the possibility  that the  Arcturus
moving  group is the  result of  a perturbation  in the  Galactic disc
induced by a  minor merger event.  They concluded  that a minor merger
that took place $\sim 1.9$ Gyr ago could explain not only the presence
of  the Arcturus  moving  group, but  also  other previously  observed
features in  the local velocity field  \citep[see e.g.][]{ari_fu}.  It
is important to note that  streams with velocities larger than $V_{\rm
  LSR} \sim \pm  50$ km s$^{-1}$ are less likely to  be related to the
Galactic bar.  Interestingly, the short timescale associated with this
event is  consistent with  the estimated age  of the Galactic  bar, as
measured by \citet{cw}  ($< 3$ Gyr ago).  This  suggests that the same
event that could  have caused the formation of  the Galactic bar could
have also  left the  stellar disc unrelaxed,  thus giving rise  to the
observed high-velocity  stream.  On the other hand,  many studies have
successfully described the presence of  the Hercules moving group as a
result   of   a  resonant   interaction   with   the  bar   \citep[see
e.g.][]{walter,min07}.  However, as  shown by \citet{ant09,ant11}, the
effect that bars  and spiral density waves have  on the velocity field
of  galactic  discs   is  highly  degenerate\footnote{Note  that  both
  mechanisms  could   be  acting  simultaneously.}.    Therefore,  the
scenario in which the Hercules moving group was formed as the response
of the Galactic disc to a minor merger event cannot be ruled out.

\section{The Sagittarius dwarf galaxy as a possible perturber}

The impact that the Sagittarius dwarf galaxy may have had on the Galactic
disc has been previously considered by several authors. Recently, using
high-resolution $N$-body simulations, P11 showed that its gravitational
interaction may play a significant role on shaping the morphology of the
Galactic disc, by inducing the formation of rings, influencing the Galactic
bar, and flaring the outer disc. Its interaction could also explain the
formation of the Monoceros rings \citep{new02,quill09,md11,pur11}. However,
until now, its influence on the phase-space distribution of disc stars
located within the neighbourhood of the Sun has not been explored. In this
section we analyse the simulations presented by P11 to characterise the
effect of Sagittarius within this volume.

\begin{table}
\begin{minipage}{90mm} \centering
  \caption{Initial  properties  of   the  two  $N$-body  simulations
    analysed in Section 6.}
\label{table:Nmodel}
\begin{tabular}{@{}llllr}
\hline
\hline
Host & & & \\
\hline
DM halo & & & $N_{\rm part} = 2.65 \times 10^{7}$ \\
\hline
Virial mass & $1 \times 10^{12}$ & & $[M_{\odot}]$ \\
Scale radius & $14.4$ & & [kpc] \\
\hline
Stellar disc & & & $N_{\rm part} = 3 \times 10^{6} $ \\
\hline
Mass & $3.59 \times 10^{10}$ & & [$M_{\odot}$] \\
Scale length & 2.84 & & [kpc] \\
Scale height & 0.43 & & [kpc] \\
\hline
Stellar bulge & & & $N_{\rm part} = 5 \times 10^{5} $ \\
\hline
Mass & $9.52 \times 10^{9}$ & & [$M_{\odot}$] \\
Effective radius & 0.56 & & [kpc] \\
S{\'e}rsic index & 1.28 & & \\
\hline
\hline
Satellites & & & \\
\hline
DM halo & {\it Light}  & {\it Heavy} &  $N_{\rm part} = 1.8 \times 10^{6}$ \\
\hline
Virial mass & $0.32 \times 10^{11}$ & $1 \times 10^{11}$  &[$M_{\odot}$] \\
Scale radius & $4.9$ & $6.5$ &  [kpc] \\
\hline
Stellar spheroid & & &  $N_{\rm part} = 5 \times 10^{4} $ \\
\hline
Core radius & $1.5$ & $1.5$ & [kpc] \\
Tidal radius & $4$ & $4$ & [kpc] \\
Central vel. disp. & 23 &  30 & [km s$^{-1}$]
\end{tabular}
\end{minipage}
\end{table}

\subsection{The simulations}

  Two  simulations with different models for  the Sagittarius dwarf
  galaxy progenitor were performed.  In both cases, the primary galaxy
  includes a  NFW dark matter  (DM) halo, an exponential  stellar disc
  and a central bulge following  a S{\'e}rsic profile.  The {\it Light
    Sgr}  and  {\it  Heavy  Sgr}  progenitors  were  self-consistently
  initialised  with a  NFW DM  halo and  a separate  stellar component
  following  a King  profile  \citep{king}.  Table  \ref{table:Nmodel}
  summarises  the numerical values  of the  parameters used  for these
  models.    Following   previous   work   on  the   Sgr   interaction
  \citep{kesel},  the  satellites were  launched  at  80~kpc from  the
  galactic centre in the plane  of the Milky Way, traveling vertically
  at 80~km  s$^{-1}$ toward the north galactic  pole.  The simulations
  reach a  present day configuration  after approximately 2.7  and 2.1
  Gyr of evolution, respectively.   Mass loss that would have occurred
  between  virial  radius  infall  and this  ``initial''  location  is
  accounted for by  truncating the progenitor DM halo  mass profile at
  the instantaneous Jacobi  tidal radius, $r_{\rm t} =  23.2$ and 30.6
  kpc, respectively.  This leaves a  total bound mass that is a factor
  of  $\sim 3$  smaller than  their effective  virial  mass originally
  assigned.  Each  of the model  Sgr progenitors experiences  two disc
  crossings, approaching  a third at  the present day.   The satellite
  first crosses the disc at a galactocentric distance of $\sim 20$ kpc
  approximately $\sim  1.75$ Gyr  ago, producing the  most significant
  perturbation.   The  progenitor loses  roughly  $75\%$  of its  dark
  matter mass (but little stellar  material) during this time.  In the
  bottom panel  of Figure~\ref{fig:xy_sag} we show  the time evolution
  of  the satellites'  galactocentric distance.   The initial  disc in
  both Sgr-infall models  is completely smooth at $t=0$  Gyr, and only
  develops a mild  bar when it is evolved in isolation  for a few Gyr.
  When compared to the isolated run, the {\it Light Sgr} model results
  in a  stronger bar  (see P11). Conversely,  as a result  of enhanced
  central  disc heating,  the  more massive  satellite suppresses  bar
  formation. The endstate  bar orientation, $\phi_{\rm bar}^{\rm sims}
  = 15^{o}  - 20^{o}$, is in  both cases consistent  with estimates of
  the long bar's orientation observed  in the center of the Milky Way,
  $\phi_{\rm  bar}^{\rm  MW} =  15^{o}  -  30^{o}$ \citep{biss}.   The
  simulations   used   the   parallel   $N$-body  tree   code   ChaNGa
  \citep{changa},  with  a   gravitational  softening  length  of  one
  parsec\footnote{ The  force softening  length is set  to roughly
      0.1 of the mean  disc interparticle spacing.}, and followed the
  evolution of 30 million particles with masses in the range 1.1 - 1.9
  $\times ~ 10^{4} {\rm M}_{\odot}$.

\subsection{The phase-space distribution of  Solar neighbourhood-like
  volumes}

\label{sec:sag_ps}

\begin{figure}
\begin{centering}
\hspace{-0.5cm}
\includegraphics[width=82mm,clip]{fig7a.eps}
\\
\includegraphics[width=79mm,clip]{fig7b.eps}
\caption{Top panel: Distribution  of particles in the X  - Y plane, as
  obtained from the {\it Heavy Sgr} simulation after approximately 2.1
  Gyr  of  evolution.    The  different  colours  (contours)  indicate
  different   numbers  of   particles.   As   a  consequence   of  the
  non-axisymmetrical  energy kick  imparted by  the  satellite, spiral
  features  are induced  in the  galactic disc.   The location  of the
  Solar       neighbourhood-like       volumes       analysed       in
  Section~\ref{sec:sag_ps} are indicated with solar symbols.  The cyan
  dot indicates the local  volume that best resembles the observations
  in the  Solar Neighbourhood.  The white dots  labelled as  ``1'' and
  ``2'' trace the regions where  the {\it Heavy Sgr} crosses the plane
  of the disc for the first and second time, respectively. Its current
  projection on  the X - Y  plane is indicated with  the symbol ``C''.
  Bottom panel:  Evolution of the galactocentric distance  of both Sgr
  models as a function of time. }
\label{fig:xy_sag}
\end{centering}
\end{figure}

\begin{figure*}
\hspace{-0.16cm}
\includegraphics[width=176.5mm,clip]{fig8a.eps}
\\
\includegraphics[width=175mm,clip]{fig8b.eps}
\\
\includegraphics[width=176mm,clip]{fig8c.eps}
\caption{Top panel:  Kernel histograms  of energies obtained  from the
  {\it Heavy  Sgr} simulation. Each  panel shows the  kernel histogram
  (KH)  obtained from  the distribution  of particles  within  a Solar
  neighbourhood-like  sphere  located  at a  different  galactocentric
  azimuthal angle,  $\theta$. The black solid lines  show KHs obtained
  after  computing  particle's  energy  using the  analytic  potential
  described  in Section~\ref{sec:gdwarf_ener}.  The  red dashed  lines
  show the  KHs obtained after computing particle's  energies from the
  $N$-body  potential. The shaded  regions indicate  errors associated
  with   poor   sampling   of   the   underlying   distribution   (see
  Section~\ref{sec:th_tk}).  The angle $\theta$ is measured clockwise,
  starting  from the  negative  Y axis  in Fig.~\ref{fig:xy_sag}.  The
  azimuthal  location of  the spheres  are indicated  in the  top left
  corner of each  panel. Note that all the  KHs exhibit multiple peaks
  associated with density  waves crossing the Solar neighbourhood-like
  volumes. Furthermore,  the locations of these  peaks strongly depend
  on  the azimuthal  location of  the sphere.  Note as  well  the good
  agreement between  the second panel  ($\theta \approx 18^{o}$  ) and
  the  KHs obtained for  our F/G-dwarf  thick-disc subsample  shown in
  Figures~\ref{fig:el_20}  and  \ref{fig:verr11}.  Middle  panels:  As
  above for the {\it Light Sgr} simulation. Note that, as expected for
  a less-massive  satellite, the peaks previously observed  on the KHs
  of the {\it Heavy Sgr} model  are either very mild or not present at
  all. Bottom panels: As above, now for spheres located at a different
  galactocentric radius, $R$. The  spheres are located at an azimuthal
  angles  $\theta =  0^{\rm o}$.  The galactocentric  distance  of the
  spheres  are indicated in  the top  left corner  of each  panel. The
  black solid  and blue  dashed lines show  the KHs obtained  from the
  from  the   {\it  Heavy  Sgr}  and  {\it   light  Sgr}  simulations,
  respectively. For the {\it  Heavy Sgr} simulation, the locations and
  amplitude  of the peaks  in the  KHs strongly  depend on  the radial
  position of the  spheres. Note as well the  similarities between the
  second panel ($R = 7.5$ kpc)  and the KHs obtained for our F/G-dwarf
  thick-disc  subsample.  For the  {\it  Light  Sgr} simulation,  mild
  signatures  of density  waves  can  be observed  only  in the  outer
  spheres,  where  the  perturbation  from  the  satellite  galaxy  is
  stronger.}
\label{fig:khh}
\end{figure*}

We now  characterise the phase-space distribution  of particles within
Solar neighbourhood-like volumes of 1~kpc radii. In these simulations,
according to  the location  of the Sagittarius  remnant and  its tidal
debris, the Sun should be located at approximately $(0,-8,0)$ kpc from
the  galactic centre.   In order  to examine  the dependencies  of the
particle's   phase-space  distribution   with  azimuthal   angle,  and
uncertainties  on the  location  of the  ``Sun''  associated with  the
model,  we  have  placed  5  spheres at  different  azimuthal  angles,
covering a  total of $\approx  58^{{\rm o}}$ around the  ``Sun.''  The
top panel of Figure~\ref{fig:xy_sag}  shows contour plots of the final
distribution of  particles in the X  - Y plane obtained  from the {\it
  Heavy Sgr} simulation.   The white dots trace the  regions where Sgr
crosses the plane  of the disc and its current projection  on the X- Y
plane. The locations of  our Solar neighbourhood spheres are indicated
with solar  symbols.  As shown  by P11, the  gravitational interaction
between  the  Sagittarius-like  satellite  and the  galactic  disc  is
sufficiently strong  to induce the formation of  transient spiral arms
or  rings.  These arms  can be  clearly observed  outside a  radius of
15~kpc, but not so clearly at  the Solar radius.  In the top panels of
Figure~\ref{fig:khh}  we show  the kernel  histograms of  $E$ obtained
from the  distribution of particles located within  these volumes. Let
us recall that throughout this work  we have kept fixed both the value
of $\Delta E$  and the value of the bandwidth  of the Gaussian kernel,
$\sigma$. The  black solid  lines show the  results obtained  when the
particle energies are computed using the analytic potential introduced
in  Section~\ref{sec:gdwarf_ener}, whereas  for the  red  dashed lines
energies were computed directly  from the $N$-body potential. The very
good agreement between the two KHs reflects the weak dependence of the
amount and distribution of features  with the particular choice of the
galactic potential.   Note that, for comparison, the  red dashed lines
have been slightly shifted in energy,  so that both KHs overlap in the
same energy  range. On average,  the number of particles  contained in
each sphere is $\approx 10,000$. It is interesting to observe that all
the analysed  volumes exhibit peaks  in their KHs; these  are features
associated  with  density waves.   We  see  strong  dependence of  the
distribution and  amount of peaks  with azimuthal angle,  $\theta$: as
$\theta$  is decreased,  power  from the  highest  amplitude peak  ($E
\approx  -1.01 \times  10^{5}$  km$^{2}$ s$^{-2}$  at $\theta  \approx
29^{o}$), or density wave, is  transferred towards a secondary peak at
higher energy  ($E \approx -0.96  \times 10^{5}$ km$^{2}$  s$^{-2}$ at
$\theta \approx -29^{o}$).  In addition,  the location of each peak is
shifted towards lower values of $E$ indicating that, on average, these
peaks are  populated by  more inner particles.   This is  the expected
behaviour from  a spiral pattern  traveling in this  angular direction
(see also Section  4.2 of G12).  Note the  similarities between the KH
in  the  second top  panel  of  Figure~\ref{fig:khh} ($\theta  \approx
18^{o}$)  with   the  KHs  obtained  from   our  F/G-dwarf  thick-disc
subsample,  shown  in  Figures~\ref{fig:el_20}  and  \ref{fig:verr11}.
This result  clearly indicates that  some of the features  observed in
the KH of the Milky Way  thick disc, especially the peak at $E \approx
-0.97 \times 10^{5}$ km$^2$ s$^{-2}$, could be associated with density
waves  excited   by  the  Sagittarius  dwarf   galaxy.   An  important
implication  of  the  strong  azimuthal  dependance  observed  in  our
simulations is  that the orbital  properties of the  Sagittarius dwarf
galaxy  could be  further  constrained by  fitting  the locations  and
amplitude of the significant peaks  in the models to those observed in
stellar samples.

In the  middle panels of  Figure~\ref{fig:khh} we show the  results of
the previous  analysis obtained  from the {\it  Light Sgr}  model. The
Solar neighbourhood-like spheres were placed at the same locations. As
before,  the black  solid lines  show the  kernel  histograms obtained
after  computing  particle  energies  using  the  analytic  potential,
whereas for the  red dashed lines the $N$-body  potential was used. As
expected from a less-massive  satellite (and thus a weaker perturber),
the peaks  previously observed  in the kernel  histograms of  the {\it
  Heavy Sgr} model  are either very mild or not present  at all. It is
interesting to note that, as previously discussed, the {\it Light Sgr}
model  results  in  a much  stronger  bar  than  the {\it  Heavy  Sgr}
model. The more massive satellite suppresses bar formation as a result
of enhanced central disc  heating. This clearly demonstrates that none
of the observed  features in these simulations could  be associated to
resonances  with the  galactic  bar.  Otherwise,  we  would expect  to
observe  higher-amplitude  features in  the  {\it  Light Sgr}  model's
kernel histograms  as a  result of the  interaction with  the stronger
bar. Thus,  models of the  Sagittarius dwarf galaxy progenitor  with a
total   mass  $\leq   10^{10.5}  {\rm   M}_{\odot}$  could   be  ruled
out. Moreover, note  that its total mass could  be further constrained
by comparing the  amplitudes of the significant peaks  observed in the
kernel histograms of models with those of the Milky Way disc.

In  the  bottom  panels   of  Figure~\ref{fig:khh}  we  explore  Solar
neighbourhood-like  spheres  of  1~kpc  radius  centred  at  different
galactocentric distances.   The spheres are separated by  0.5 kpc, and
are all  located at $\theta =  0^{\rm o}$. The black  solid lines show
the kernel histogram obtained from the {\it Heavy Sgr} model. A strong
dependence on  the amplitude of  each peak with  galactocentric radius
can  be observed. As  we move  towards the  galactic centre  we better
sample   inner  density   waves,   represented  by   peaks  at   lower
energies. Again, note the similarities between the KHs obtained in the
inner  spheres  (e.g.,  $R=7.5$  kpc)  and  those  obtained  from  our
F/G-dwarf sample  (see e.g.  Fig.~\ref{fig:verr11}).   The blue dashed
lines  in  the  bottom  panels  of Figure~\ref{fig:khh}  show  the  KH
obtained from the {\it Light  Sgr} model. As expected, mild signatures
of density waves can be observed  only in the outer spheres, where the
perturbation  from   the  satellite  galaxy  is   stronger.   In
  Figure~\ref{fig:kh_time} we  show the  time evolution of  the kernel
  histogram    of   particles   located    within   a    given   Solar
  neighborhood-like  sphere for  $ \approx  2.5$ Gyr.   To  track this
  volume over time,  our sphere is rotating with  an angular frequency
  set by the velocity of  the LSR, obtained after correcting the final
  mean rotational velocity profile for axysimmetric drift.  The KH are
  shown  at four  different  times: the  initial  conditions, the  two
  pericentre passages,  and the present day  configuration.  From this
  figure  it is  possible  to appreciate  the  smooth distribution  of
  particles in energy space at  $t=0$.  In addition, it is possible to
  observe  that  strong perturbations  in  the  disc particles  energy
  distribution are only excited  after the first pericentre passage of
  the {\it  Heavy Sgr}  satellite, as shown  by the black  solid line.
  Note that  the smaller number of peaks  in the KH of  the {\it Heavy
    Sgr} model with respect  to the KH shown in Figure~\ref{fig:model}
  is  due to  the  shorter period  of  time this  simulation has  been
  evolved. The blue dashed lines show KHs obtained from the {\it light
    Sgr} model. Notice the approximately smooth energy distribution at
  all times.

\begin{figure*}
\hspace{-0.16cm}
\includegraphics[width=176.5mm,clip]{fig9.eps}
\caption{  Kernel  histograms  of  energies  obtained  from  both  Sgr
  simulations at different times. Each  panel shows a KH obtained from
  a distribution of particles within a Solar neighbourhood-like sphere
  located at  $R = 8$ kpc  and rotating with an  angular frequency set
  set by  the velocity of  the LSR, after correcting  for axysimmetric
  drift.   The KH  are  shown  at four  different  times: the  initial
  conditions,  the  two  pericentre   passages  and  the  present  day
  configuration. The  black solid lines  show KHs obtained  {\it Heavy
    Sgr} model.  Note the smooth  distribution of particles  in energy
  space at  $t=0$.  Strong perturbation  in the disc  particles energy
  distribution are only excited  after the first pericentre passage of
  the satellite.  The  blue dashed line show the  KH obtained from the
  {\it  light  Sgr}  model.   Note  the  approximately  smooth  energy
  distribution at all times.}
\label{fig:kh_time}
\end{figure*}

\section{Summary and Conclusions}
\label{sec:conclu}

We  have analysed the  SEGUE F/G-dwarf  and the  Schuster et  al. (2006)
stellar samples in  search for imprints of minor  merger events in the
Milky Way disc.  In contrast  to a  number of previous  studies, we  look for
perturbations in the phase-space of  the host disc rather than merger
remnants.  We  apply  the  same  analyses  to  high-resolution  N-body
simulations of  the interaction between  the Sagittarius dwarf galaxy  and the
Milky Way. We summarise our results as follows:
\begin{itemize}

\item The alpha-enhanced, likely thick-disc F/G-dwarf subsample exhibits
significant peaks in the stellar energy kernel histograms (KH). Conversely,
the thin-disc subsample shows a much smoother distribution. This is
consistent with the expectation that merger-induced perturbations in the
host galaxy disc (e.g., the Milky Way) create structure in the stellar phase-space
density, which survives until later times only in the old, hotter stellar
population.

\item  We show that, to unambiguously identify merger-induced waves
(ringing), samples of stars with velocity errors $V_{\rm err} < 11$ km
s$^{-1}$ are required. This depends on the time since the waves were
excited, as well as on the mass of the perturber.

\item Complementary evidence of ringing can be obtained from the SCH06
  catalog.  The energy  kernel histogram  of stars  here  also reveals
  peaks, most of them remarkably consistent with those observed in the
  F/G-dwarf sample.

\item  Simulations of the  interaction between the Milky  Way and
    the  Sagittarius  dwarf  galaxy  show  that  a  relatively-massive
    progenitor (i.e., masses of $\approx 10\%$ of the host) can induce
    density  waves in  the Galactic  disc.  Furthermore,  the features
    seen in the energy kernel  histogram of the observational data can
    be qualitatively well reproduced  with these simulations.  This is
    interesting since,  by matching features in  the kernel histograms
    of  both models  and observations,  one could  attempt  to further
    constrain  the orbital  properties of  Sagittarius, thanks  to the
    strong  azimuthal and  radial  dependance of  the distribution  of
    peaks.  Note,  however,  that  other possible  origins  for  these
    perturbations need to be ruled  out before performing this kind of
    analysis.

\item On  the contrary, low-mass  models of Sagittarius  barely excite
  density  waves in the  disc. Thus,  if we  assume that  the observed
  peaks in the kernel histogram of the F/G-dwarf sample are the response
  of the  Galactic disc  to the tidal  interaction with Sgr,  we could
  rule  out  such  low-mass   models.  Furthermore,  by  matching  the
  amplitudes of the peaks, one  could attempt to further constrain the
  total mass of the Sagittarius progenitor.

\end{itemize}

Comparing  Figures \ref{fig:verr11}  and \ref{fig:khh},  we  note that
variations  in the  azimuthal and  radial  positions of  the Sun  with
respect to  the Sagittarius orbital plane  can result in  similar structure in
the  stellar energy  distribution. This  degeneracy can  be  broken by
studying in detail the variation of features in the stellar phase-space
distribution  when  position in  the  disc  is  varied. This  in  turn
requires  larger  and  deeper   stellar  samples,  which  will  become
available   in   ongoing   and   future  surveys,   such   as   APOGEE
\citep{apogee},  HERMES  \citep{hermes},  and  ultimately  {\it  Gaia}
\citep{gaia}.

Although  we cannot fully  discard the  possibility that  the observed
features  have   some  secular   origin,  the  much   smoother  energy
distribution of the thin-disc  population make this scenario unlikely.
If these  features had originated by resonant  interaction with, e.g.,
the Galactic  bar, we  would expect  them to be  stronger in  the thin
disc, rather than  in the thick disc.  This  result is consistent with
the  hypothesis  that features  associated  with  ringing should  last
longer in  the thick disc.   Thick-disc stars spend  relatively little
time near  the Galactic plane, where  heating from spiral  arms or the
bar and  scattering by  giant molecular clouds  is most  vigorous.  In
addition, features generated by the bar or spiral arms can be observed
as lumps in the u-v plane.   We have explored this plane, and found no
significant overdensities that could be linked to this kind of secular
perturbations.

In this study we considered  simulations with two different masses for
the  Sagittarius  progenitor, representing  a  lower  ($M_{\rm vir}  =
10^{10.5}~{\rm M}_{\odot}$)  and upper ($M_{\rm vir} =  10^{11} ~ {\rm
  M}_{\odot}$) limits.  We have found  that the {\it Light Sgr} cannot
explain the structure seen in  the energy distribution of our observed
samples. On the  other hand, the {\it Heavy  Sgr} model creates strong
disturbances in the  Milky Ways disc, resulting in  prominent peaks in
the energy kernel histogram in localised spatial volumes, perhaps even
stronger  than  what is  seen  in  the  observations (compare  Figures
\ref{fig:verr11} and \ref{fig:khh}). As  shown by G12, satellites with
masses $10\%$  and $20\%$ of the  mass of their  host generate density
waves, which can be followed for  no longer than 1 and 2~Gyr after the
satellite's full  disruption, respectively.  Close  encounters between
massive substructures and galactic  discs should be common occurrences
in a  $\Lambda$CDM cosmology since z  = 1 (Kazantzidis  et al.  2009).
However,  the short  relaxation time  scale involved  and the  lack of
observational evidence  of a merger  with such characteristics  in the
last 1-2 Gyr suggest that Sgr is the most likely perturber.

It is  important to  note that all  simulations analysed in  this work
considered initially stable, unperturbed  stellar discs. It remains to
be explored how a previously  perturbed disc, either by a merger event
or other dynamical process, would  react to the tidal interaction with
a  satellite  galaxy  such  as  Sgr. Future  studies  should  consider
simulations spanning a range of masses for the Sgr progenitor, between
the two  limits we  presented here, as  well as varying  Galactic disc
models,  which  can be  tuned  more finely  as  our  knowledge of  the
dynamics of the Milky Way expands.   In addition, it remains to be
  studied whether  perturbations from multiple  satellite galaxies can
  be successfully disentangled.

\section*{Acknowledgments}

We thank the anonymous referee for the useful comments and suggestions
that helped  to improve this work.  FAG was supported  through the NSF
Office of Cyberinfrastructure by grant PHY-0941373 and by the Michigan
State  University  Institute   for  Cyber-Enabled  Research.  BWO  was
supported in part  by the Department of Energy  through the Los Alamos
National  Laboratory Institute for  Geophysics and  Planetary Physics.
YSL and TCB  acknowledge partial support from grants  PHY 02-16783 and
PHY  08-22648: Physics  Frontiers Center/Joint  Institute  for Nuclear
Astrophysics (JINA), awarded by the U.S.  National Science Foundation.
DA acknowledges  support by the National Research  Foundation of Korea
to  the  Center  for  Galaxy  Evolution  Research.  \'AV  acknowledges
financial  support  from  the  European  Research  Council  under  the
European  Community's Seventh Framework  Programme (FP7/2007-2013)/ERC
grant agreement n. 202781.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the
U.S. Department of Energy. The SDSS-III web site is http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the
Participating Institutions of the SDSS-III Collaboration, including the
University of Arizona, the Brazilian Participation Group, Brookhaven
National Laboratory, University of Cambridge, University of Florida, the
French Participation Group, the German Participation Group, the Instituto
de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA
Participation Group, Johns Hopkins University, Lawrence Berkeley National
Laboratory, Max Planck Institute for Astrophysics, New Mexico State
University, New York University, the Ohio State University, University of
Portsmouth, Princeton University, University of Tokyo, the University of
Utah, Vanderbilt University, University of Virginia, University of
Washington, and Yale University.

redpajama_set_name: RedPajamaArXiv


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An award-winning fundraising consultant who has been in fundraising since 1985. In August 1997 he returned from a three- year spell in Australia and has since established his own fundraising consultancy business drawing on wide work experience gained in the UK, USA and Australia. He has held a number of senior posts including Executive Director of The Starlight Foundation and Director of Public Affairs at The Royal Melbourne Hospital.
He did his Geography degree at the School of Oriental & African Studies (University of London), is a qualified teacher (PGCE from University of Liverpool) and won a scholarship to undertake his Masters degree in Demography from the London School of Economics. He has been a speaker at Institute of Fundraising regional and national conferences. He gained his professional accreditation in Australia as a Certified Fund Raising Executive (CFRE) - one of the first British fundraisers to do so. He also won a national 'Excellence in Fundraising' Award from the Fundraising Institute of Australia and more recently was named Fundraising Adviser of the Year (UK) for 2017 by the Global Finance Monthly Magazine Awards.
Paddy is a member of the Association of Fundraising Consultants (13 years) and the Institute of Fundraising (27 years).
Paddy specialises in providing effective diagnosis of fundraising programmes and advising on improving these programmes and increasing fundraising income. Referral to and inclusion of other associates is provided when appropriate. Paddy also provides staff training in all aspects of fundraising technique and management. He loves to continue giving fundraising leads and tips to previous clients.
Paddy lives in Redhill, Surrey and has a second office base in Macclesfield, Cheshire.
Heidi is the associate fundraising consultant specialising in raising money from trusts, foundations and statutory sources. She has particular strengths in developing strong relationships by telephone, email and in person as appropriate. She has excellent research and writing skills, adapting proposals to the specific requirements of funders.
With a varied career background in the private and public sector Heidi can relate well to people from all sectors and backgrounds. She has experience on both sides of the fence: managing large scale funded projects and raising funds for other peoples' projects. She was Head of Fundraising for the Royal National College for the Blind (RNC) from 2008 to 2012, managing a team of four undertaking a whole variety of fundraising activities to conclude a £21.7 million capital fundraising programme and also to raise revenue funding for smaller projects and core costs. Prior to RNC, Heidi was Sector Manager for Business Link West Midlands where she managed a UK government and EU funded programme to support high growth small businesses to grow. During three years, the budget of over £3million supported more than 200 businesses to increase turnover and create new jobs. The programme was presented to Government office as a flagship for future business support. This role gave Heidi insights to working with UK and EU government offices and understanding requirements of statutory funders.
Heidi's original career background was in marketing, primarily within the drinks market, and she worked for Bulmers Cider in Hereford for many years.
Heidi lives in Hereford and has a second office base in Farnham, Surrey.
Matthew has a long experience of working with disability charities. He was head of legacy fundraising at the Stroke Association and at Action for Children he was in charge (amongst other responsibilities) of raising money to support residential homes for people with disabilities, both in the UK and in the Caribbean. For several years he was chair of the trustees of a small London based charity for young people aged up to 25 with severe disabilities.
He is currently engaged in leading a capital appeal at the Chailey Heritage Foundation, which will deliver a state of the art disability sports and recreation centre costing just under £3M.
He has a very strong track record in delivering funding from trusts and foundations, both for capital projects and revenue fundraising. Since January 2016 he has delivered about £3m in funding for clients from trusts and foundations.
Matthew prides himself on providing exceptional value for clients, working efficiently to deliver high quality work.
Finbar has worked in the voluntary sector for over twenty years and has been a prospect researcher since 1999. He was a senior researcher at Factary and worked for Children's Hospice South West on their major capital appeal for over two years. Finbar is an Associate Consultant with Paddy Hunter-Murphy and the International Fundraising Consultancy, and a Consultant with Action Planning. He has a prospect research blog on Howard Lake's UK Fundraising website, and was previously an associate editor of fResource.
He is an expert on prospect research for finding especially major donors (HNWIs) and trusts & foundations and researching to find out all about them. Finbar is a regular speaker at Institute of Fundraising and other conferences. He contributed to the chapter on research in Major Donor Fundraising by Margaret Holman & Lucy Sargent (2006 & 2011). In October 2013, ResearchPlus published a directory of (100+) "unpublished" grant-making trusts. All received donations of at least £100,000, usually from a single donor. In June 2012, ResearchPlus published a directory of (100+) "unpublished" Scottish grant-making trusts.
Each month, Finbar contributes to The Trust List, highlighting newly registered grant-making trusts worthy of particularly close attention.
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