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Tag: Ryan Getzlaf
Underestimating The Pace Of A Real Game
We all watched with our own eyes on Thursday night. Vegas' 5-2 victory over Anaheim got off to a quick but hectic start. In the opening eight minutes of the 2021 season, the two teams totaled four early goals. We know what happened later in the game, but let's focus on the first eight minutes of the game.
If you're playing in a normal season, and we get up two nothing like that the building is rocking. We got to learn to continue to push, we kind of let our foot off the gas after going up two nothing. -Mark Stone
In the initial 2:13 of the 1st period it looked like Vegas had turned the game into a one-sided contest. Jonathan Marchessault and Tomas Nosek nabbed their first goals of the season, temporarily giving the feel of a normal Golden Knights drubbing of the Ducks. Minutes later things quickly changed.
With their backs against the wall, Anaheim battled back and scored two of their own. Like the Golden Knights, the Ducks netted two in a matter of minutes.
The first eight minutes were messy but that wasn't a shock to the players or coaches involved.
With no preseason you have to evaluate your game. We had some breakdowns a little too much in front of our own net. Some mental breakdowns but we also battled back. We gave up two goals early and we were able to respond the way we wanted to. -Ryan Getzlaf, Ducks captain
After a long time off the ice and a short training camp, it was expected both teams would come out rusty. However, both offenses came out hot and surprised the defense and goaltenders right from the opening faceoff. According to Anaheim's head coach Dallas Eakins, the early flow of the game was sort of a reality check.
Ranking The Top Centers In The Pacific Division
This week the NHL Network ranked the league's twenty best centers. Lady Byng trophy winner William Karlsson came in at 17th place, not bad for a guy who wasn't rated in the top 100 last season. Connor McDavid, Anze Kopitar, Ryan Getzlaf and Leon Draisaitl were the other Pacific Division centers to make the NHL Network's list.
Karlsson is the 17th ranked Center in the league, and 3rd in the Pacific. Not bad. pic.twitter.com/QArrXeMgDy
— Jason R. Pothier (@JRPothier) August 6, 2018
So let's have some fun and rank the top centers in the Pacific Division.
1. Connor McDavid: There's not much to write. McDavid has 256 career points in 205 games, averaging 1.22 points per game. The Edmonton center has more points (208), goals created (77), assists per game (.84), and adjusted points (220) than any other player in the NHL since 2015-16. McDavid will continue to remain the top center in the division, and the league for many, many years.
2. Anze Kopitar: Again, this is another no-brainer. The Kings captain has averaged almost a point of game over his career, and put up his best (1.12) PPG average last season. After 12 NHL seasons, the Slovenian continues to get better. Kopitar ended the season with a career-high 92 points, and took home the Selke trophy. Also, he's a faceoff wizard. Against Vegas in the postseason, Kopitar posted a 60.4% faceoff win percentage. Pretty impressive, considering the puck was in his zone most of the series.
3. William Karlsson: I battled myself trying to be as objective as possible and at the end of the day, ranking Karlsson third behind McDavid and Kopitar was the only right decision. Most of the players on this list have consistently produced for multiple seasons. However, the overall skill Karlsson showcased leads you to believe he'll repeat his production from 2017-18.
A Different Anaheim Ducks Team On The Schedule Tonight
The Golden Knights are coming out of Christmas break in first place in the Pacific Division and eight points ahead of tonight's opponent, the Anaheim Ducks. Last time the two teams faced was on December 5th, when Vegas won in a shootout. After the loss, Anaheim players or coaches didn't seem to be upset. In fact, that's when Ducks Coach Randy Carlyle joked about the Golden Knights fortunate luck.
"What are the Golden Knights doing to beat you?" -SinBin
"They get lucky." -Randy Carlyle
"They played us much better in Anaheim than they did tonight. Ask me that question again at the end of the year." -Carlyle
(He was kidding, but kinda not really)
— SinBin.vegas (@SinBinVegas) December 6, 2017
At the time, I sensed a satisfied head coach leaving the toughest arena in hockey with one point. Carlyle knew his team wasn't complete and things could be different the next time they faced the Golden Knights. Since Captain Ryan Getzlaf returned on December 11th, the Ducks have earned nine points in seven games. Also, after trading for Adam Henrique, Anaheim has a point in nine of the twelve games he's played in. Not to mention, Henrique executed this season's most amazing goal.
Remember when this guy stoned six shootout attempts against the Ducks. Yeah, that was awesome. (Photo Credit: SinBin.vegas Photographer Brandon Andreasen)
When you add a center like Getzlaf back in the mix, the Ducks immediately become a playoff contender. The prototypical center is big, strong, plays all three zones, and has one of a kind ice vision. In limited action, Getzlaf leads the league with 1.08 assists per game. His career average over 13 seasons is 0.68 assists per game. To compare, David Perron leads Vegas with 0.71 assists per game.
Fantasy Free Agency: Edition 1.0
If you read Hockey blogs (like this one, or this one, or even this one, or click this one so we get another hit), then you know already NHL players love Las Vegas.
Recently, Superstar Defenseman Erik Karlsson took to social media to show off his one of a kind spiked Christian Loubotins bought on The Strip.
Players love to travel and party in town during the NHL Awards week. Ducks Captain Ryan Getzlaf even took his wife and three kids and admitted he couldn't wait to take the family on the High Roller. In fact, some NHL Players love Vegas too much… Ahem, Jarret Stoll.
With no income tax, nice weather and plenty to do, Las Vegas is perceived as a great place to lace up. What would you do if your only options were Las Vegas, Calgary or Columbus?
Some interesting names will be available via free agency in 2017. Some names are franchise players, but would they risk their career on a new franchise? And will The Creator go for a splash, or be content to build a team on smart money contracts and young talent?
Most of these questions can't possibly be answered for another two seasons but for now let's enjoy a fun game I'll be playing once in while called; Fantasy Free Agency.
Behind door number 1!!!
Victor Hedman– TB Def: UFA 2017
Hedman is a monster 6'6 defenseman from Sweden who in no doubt is a franchise blueliner. The 24-year-old will have a hard time making it to free agency only assuming Tampa will try and lock him down before he hits his last year. If the Las Vegas franchise were to bid for Hedman, they would have to be willing to pay $9-10 million a year and for multiple years. (Keep in mind P.K. Subban and Shea Webers contracts were 8 and 14 years respectively.)
Like I said this is Fantasy Free Agency, and that's why I opened up with Victor Hedman. He's almost guaranteed to get a long extension and signing bonus from the Lightning.
But if some reason the Bolts let Hedman the Great go to free agency, look out. This will be a bidding frenzy and whatever team that's lucky enough to sign him will have a strong blue line for years.
Hey, Victor, how's this look?


I just wanted to let you all know how impressed I was with your office and the way you treated me last Thursday. I was amazed at how easy the root canal procedure was and how Dr Barry and his assistant made me feel comfortable. I truly appreciate it.
I should start with this: I'm picky. Dental care is an investment in my total health and I've tried to make good choices. Recently I was shocked to discover out of the blue that two teeth (within the same week) suddenly were in terrible pain and needed root therapy. The pain was intense, and I couldn't sleep.
Remember I said I'm picky? I also work in a clinic so I see things other patients might not - for better and for worse... WITHOUT EXCEPTION, your clinic was OUTSTANDING. Two times in one week your team worked me in and showed incredible compassion and kindness for my comfort and care. Both doctors were that rare combination of highly skilled and great communicators. From scheduling to explaining my insurance and financials... from the dental assistants to the doctors, everyone was exceptional.


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« America's Term-Limit Monarchy | Main | One Cheer for Romney »
02 January 2012 3:48 PM
Prognosticators and Procrastinators
I never make New Year's resolutions, for fear I might be tempted to keep some of them, and I hardly ever make predictions about the coming year, lest I be held somehow responsible for my absurd jokes that always seem inevitably to come true.
Back in the late 1960's, I used to ask, "Women's rights? What's next, children's rights?" A little later, I used to ask, "Children's rights, what's next, Gay rights?" Then I found myself asking, "Gay rights, what's next? Animal Rights?" As the West slowly dissolves into driveling inanity, we may proceed from animal rights to vegetable rights to the rights of rocks and sand.
Actually, mineral rights--and I am not talking about coal, iron, and petroleum--are old hat. Ten or 15 years ago I gave a paper at a conference of environmental philosophers, one of whom denounced me for not acknowledging that a rock or cliff face had "intentionality." He was outraged that an insensitive sculptor had presumed to carve up Mt. Rushmore into the likeness of American presidents.
You don't have to be a prophet to have seen all this coming a very long time ago. There is hardly any idiocy in the world today that was not already on prominent display 100 years ago. In the 1920's French Surrealists were attacking anyone who defended western civilization, Christianity, or anything ever done by European man. They anticipated multiculturaism by several generations. The suicidal idiocy of the West is often blamed on the Great War, but G.K. Chesterton nailed it in the preface to The Napoleon of Notting Hill (1904). Speaking of the prophets of his day, Chesterton joked about the animal rights movement.
"There was Mr. Edward Carpenter, who thought we should in a very short time return to Nature, and live simply and slowly as the animals do. And Edward Carpenter was followed by James Pickie, D.D. (of Pocohontas College), who said that men were immensely improved by grazing, or taking their food slowly and continuously, after the manner of cows. And he said that he had, with the most encouraging results, turned city men out on all fours in a field covered with veal cutlets. Then Tolstoy and the Humanitarians said that the world was growing more merciful, and therefore no one would ever desire to kill. And Mr. Mick not only became a vegetarian, but at length declared vegetarianism doomed ("shedding," as he called it finely, "the green blood of the silent animals"), and predicted that men in a better age would live on nothing but salt. And then came the pamphlet from Oregon (where the thing was tried), the pamphlet called "Why should Salt suffer?" and there was more trouble..."
Most would-be prophets, Chesterton understood, make the same basic error: They fix their gaze on the recent past as a means of predicting the future. If global warming or social networking or radical Islam or the disintegration of the EU or the rising price of gold were big stories in 2011, then they will be even bigger stories in 2012. Economists like to tell the cautionary tale of predictions made in the late 19th century that by some date--say, 1930--London would be deep in horse manure. No one anticipated the horseless carriage.
In political prognostication the problem goes deeper than the inability to anticipate innovation. Ideology and what is called "political vision" often amount to no more than nostalgia for the world of our childhood, when the world was bathed in the warm rosey glow of naivete and inexperience. Sadly (I suppose) the 1950's are not coming back, nor, thank Heaven, are the 1970's.
Powerful lessons might be learned by studying distant ages we can look into as a magnifying mirror--Italy in the 6th century, for example, when Germanic hooligans (in this case, thuggish Lombards) were destroying the last vestiges of the Roman order. Short-term nostalgia, on the other hand, is the sentimental trap into which our modern prophets seem, inevitably, to fall. "When I was a boy...," one can almost hear them saying in preface to every prediction they utter.
Those who prate so much of "family values" long for the life depicted in Norman Rockwell covers and 1950's sitcoms. They refuse to acknowledge the emptiness of the postwar Potemkin village erected by American and European governments, in a vain effort to pretend that the social and cultural revolutions that erupted in the 1920's had been annulled. In America at least, something like no-fault divorce had become so common by the end of the 19th century that Lord Bryce, that great Americanophile, was dismayed. By the 1950's monogamy was still the norm, even in Hollywood, but it was the serial monogamy of Mickey Rooney, Clarke Gable, and Elizabeth Taylor.
More seriously, the erosion of family functions and their commodification (by schools, camps, counselors) accelerated its pace, prefiguring the shattered families of the post-apocalypse America in which we live, where home is a holding pen to contain parents and children between institutional appointments at the gymn, school, or recreational center.
The seeds of this social, moral, and spiritual destruction, which had been sown centuries earlier, were springing forth in full vigor in the sterile 1950's. It is thus small wonder that the literature of the United States and Britain was dominated by increasingly embittered old men (Eliot, Pound, Hemingway, Faulkner) and self-indulgent punks who struttered their mental and moral infirmities in public--the Beat Generation and the Angry Young Men. While they accomplished nothing of lasting value, the punks were a conspicuous symbol of a world in collapse.
The conservative response in America was Bill Buckley's The National Review, about which the less said the better. T.S. Eliot found it a waste of time, but it is a good thing he cannot see how infinitely more puerile it has become in the hands of Bill's successors. So-called conservativism, these days, is a classic illustration of the old proverb about shutting the barn-door when the horses are out. Alas, it is not a barn-door but the American mind that seems to have been permanently closed.
We all enjoy nostalgia, because it allows us to recapture that warm glow--the naivete and inexperience of childhood. Whenever I hear "In the Still of the Night," I am once again thirteen years old, slow-dancing with Donna or Jeanie or Tonie or whoever was the girl of my dreams at the moment.
Unfortunately, nostalgia also blinds us to the actual miseries that afflict us. Christendom did not fall to the assault of the Beatles and the Stones nor to combined might of Jerry Rubin and Danny the Red. It had been undermined, generation by generation, by thinkers, writers, statesmen, and theologians most conservatives revere--Montaigne and Voltaire, John Locke and Adam Smith, Tom Paine and Abe Lincoln and FDR. By 1945, there remained only a hollow shell of polite insincerities--very pleasant they were, too--which were blown away by the lightest breezes of revolution that sprang up in the late 1960's.
The chorus of conservatives, singing "gone are the days of my youth, too soon," drowns out any serious effort to understand how we got in this mess. If we cannot understand our past, we waste our time in prognosticating the future. I am reminded of one of Sean O'Casey's characters (in a once famous Irish play) who insults people with the terms prognosticator and a procrastinator. I have always assumed that he probably meant to say "prevaricator," but there is a deeper truth in the illiterate insult. The more we look back at the recent past in order to prognosticate the coming year or the coming decade, the less likely we are to know how to begin to solve the mess we have made of our world.
"Take short views, hope for the best, and Trust in God."
January 2, 2012 Comments (7) | Permalink
I took a look at Ms. Cosgrove's organization. At first glance, they have a goal that I heartily agree with. Children should play outside more! But then when you look into the specifics, it's just one bit of government meddling after another.
A new "programme" for kids to play. Changing speed limits and parking rules. "Fairness" in the "funding" of children's play. And a "PlayWise" bus programme that will cost only 12 million pounds a year to run! Cheap at the price, no doubt.
Maybe it's just me, but as a kid I played outside virtually every day, at zero cost to government. Of course back then there was no worry about law suits if kids fell on the playground (which was concrete). And there was little worry about sexual predators, perhaps because anyone caught attempting something would have the stuff beaten out of them by the local fathers and brothers, no police intervention needed thank you very much. And parents weren't meddling worry-warts concerned about not letting people park their cars on the street (how would you determine the end zone for your street pickup football game if not "touchdown is at the blue car"?).
Did we run smack into parked cars? Yup. Did we get bruised and bloody on a regular basis? We sure did. Did we come home at the end of the day exhausted and ready for bed without any pharmaceuticals? Indeed.
It's really pretty simple. But a meddler like Ms. Cosgrove doesn't grasp that what keeps children from playing outside these days is other meddlers like herself, and the velvet fist of the state.
Children do need "rights." They need the right to grow up under the supervision of their parents and the other adults in the neighborhood, not the snooping of government funded busy-bodies.
Posted by: peterike | 01/04/2012 at 04:55 PM
Come, there, now, Monsieur (or is it Madame?) Cosgrove. Do you really think there is less abuse among the "radical" bureaucratic social institutions who raise modern children than there where among the "traditional" households of the 19th century?
What it really comes down to this: should corrupt social workers and teachers control children or should corrupt parents? On principle, I'd have to go with corrupt parents.
I could not understand why Americans were going bonkers about Hungary's "New Constitution" or why the last place an Englishman would look for childish rights was towards "the future" and the Hague Tribunal -- for heaven's sake! Then I read Tom Fleming's, Prognosticators and Procrastinators, and the Hungarian Preamble. Tom Fleming wrote :
"Unfortunately, nostalgia also blinds us to the actual miseries that afflict us. Christendom did not fall to the assault of the Beatles and the Stones nor to combined might of Jerry Rubin and Danny the Red. It had been undermined, generation by generation, by thinkers, writers, statesmen, and theologians most conservatives revere--Montaigne and Voltaire, John Locke and Adam Smith, Tom Paine and Abe Lincoln and FDR." (I would add the damned fools who think paradise is just for kids, prisons for dead beat dads and the work place a lofty environment for real Mothers.) They hate the Church, except for everything they have made it, which is no doubt why Americans can't believe the Hungarians would say such things as ------------
[Preamble:]
We are proud that our king Saint Stephen built the Hungarian State on solid ground and made our country a part of Christian Europe one thousand years ago.
We recognise the role of Christianity in preserving nationhood. We value the various religious traditions of our country.
We do not recognise the suspension of our historical constitution due to foreign occupations. We deny any statute of limitations for the inhuman crimes committed against the Hungarian nation and its citizens under the National Socialist and Communist dictatorships.
We do not recognise the Communist constitution of 1949, since it was the basis for tyrannical rule; therefore we proclaim it to be invalid.
Article L
(1) Hungary shall protect the institution of marriage as the union of a man and a woman established by voluntary decision, and the family as the basis of the nation's survival.
(2) Hungary shall encourage the commitment to have children.
MY, MY, MY! What's next ? Ron Paul winning Iowa?
Jan your no doubt well meaning-?-though incoherent litany was irritating as it must be to any ordinary sensibility, because it didn't seem to intend to go anywhere except with its long list to Santa of complaints. It's an imperfect world is the short answer, made worse by the modern non-traditional context within which I realize you are now forced to function. A longer answer I see the author has already graciously supplied.
It is fascinating to see the mind of rights activists in action. A string of rhetorical questions and injunctions backed up by neither reason nor evidence is substituted for logical argument. A right in the modern sense is a claim against someone or some group. If children have rights, the claim is against their parents, and, since the children cannot enforce those rights, it means that paid agents of the government act on their behalf. Neoconservatives like to argue that the child-savers meant well and that the destruction of the family in modern times is an unintended consequence. That is much too easy. People who have been paid to stick their noses into other people's business--social workers, teachers, activists--should be held accountable for the destruction of so many lives. There never has been a perfect world, but the totalitarian societies policed by do-gooding rights activists is a nightmare. Fair Play for children, indeed! Try going to a Third World war zone and prating about the children's "right to play."
Children's Rights. Which do you think they shouldn't have? None of them? Gingrich = child labour? Youth curfews constitutional? Locking up kids for life, no parole? Corrupt judges send them to jail on trumped up charges as part of prison labour scam? The Texas youth abuse scandal? Penn State's current revelations? Syracuse? Kids don't need rights in America? Make sure they're treated right in your own country, concentrate your efforts there. Poverty in the richest nation in history, hitting kids the most. Tradition? Of what? Over-weening power of the most powerful? Tradition may be OK until it becomes the excuse for failing to change when that is the right thing to do. Segregation was tradition. Imprisoning gays was tradition. This article, harking back to a golden era that never was for the vast majority of human beings. From a segment of society never slow to trumpet its rights, the writers and pundits often paid to tell us how awful life is. The world should be fit for all our children to play in - it isn't, and it won't be right until it is.
Posted by: Jan Cosgrove National Secretary, Fair Play for Children | 01/03/2012 at 03:33 AM
Excellent advice; never take advice except from the excellent. Advice taken! And for me trust in God translates into the way station of CHRIST. I can't even climb that high never mind trying to leap above (or below) it.
Reason sadly shot Christ full of holes. Though upon discovering her own limits, instead points once again--when too terribly wearied and befuddled--to the way station our Tradition in the East and in the West. Tradition is another good tool since it remembers everything so you don't, like an idiot have to 'return to start'.
So it's best to make sure you've included tradition in your tool box right along with all the other limited, imperfect and important tools such as reason, science, intuition... remembering tradition too.
Because whether you do or not, it remembers you.

redpajama_set_name: RedPajamaCommonCrawl


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Q: Как ускорить программу? Два различных натуральных числа называются дружественными, если первое из них равно сумме делителей второго числа, за исключением самого второго числа, а второе равно сумме делителей первого числа, за исключением самого первого числа. Требуется найти все пары дружественных чисел, оба из которых принадлежат промежутку от M до N.
Входные данные:
В первой строке находятся числа M и N. 1 <= M <= N <= 1 000 000, все числа целые.
Выходные данные:
В каждой строке вывести по паре чисел через пробел. Первое число пары должно быть меньше второго. Строки должны быть отсортированы в порядке возрастания первого числа пары. Если пар дружественных чисел в промежутке нет, вывести "Absent".
Мой код:
def sd(k):
    s = 0
    m = int(k**0.5)
    for i in range(1, m+1):
        if k%i == 0:
            if i**2 == k:
                s += i
            else:
                s+=i
                s+=(k//i)
    s -= k
    return s

a = input().split()
n,m = int(a[0]), int(a[1])
f = 0
for i in range(n, m):
    for j in range(i+1, m+1):
        if sd(i) == j and sd(j) == i:
            print(i, j)
            f = 1
if f == 0:
    print('Absend')

Однако в системе на одном из тестов не заходит по времени, как ускорить программу?

A: первая итерация - вычислить сначала сумму делителей и только потом с ними работать
n = 10000

# получить соответствие число - делитель
numbers = [0,]

for value in range(1, n):
    dividers = 1
    for i in range(2, value):
        if value % i == 0:
            dividers += i
    numbers.append(dividers)

# вывести все пары дружественных чисел
for value1 in range(1, n):
    for value2 in range(1, value1 + 1):
        if value1 == numbers[value2] and value2 == numbers[value1]:
            print(value1, value2)

при этом рассматривать не все пары чисел, а только пары в которых первое число больше или равно второму (чтобы избежать дублирование пар)  - тогда будет выполняться всего n^2 / 2 действий
при этом самое долгое в данном алгоритме - вычисление делителей
про n=1000000 говорить не приходится (будет очень долго считаться, минуты)
вторая итерация - нет надобности проверять все делители от 2 до n, достаточно определять делители от 2 до n / 2 - это ускоряет алгоритм в 2 раза:
# получить соответствие число - делитель
numbers = [0,]

for value in range(1, n):
    dividers = 1
    for i in range(2, value // 2 + 1):
        if value % i == 0:
            dividers += i
    numbers.append(dividers)

итерация №3 - алгоритм поиска суммы делителей можно немного ускорить (в полтора-два раза) если переписать код через функции питона (не знаю почему так получается):
for value in range(1, n):
    dividers = 1 + sum(i for i in range(2, value // 2 + 1) if value % i == 0)
    numbers.append(dividers)

можно свернуть в чуть более короткий код (но такая же скорость работы)
# получить соответствие число - делитель
numbers = [(1 + sum(i for i in range(2, value // 2 + 1) if value % i == 0)) for value in range(1, n)]

итерация №4 - делители можно рассматривать до sqrt(value), но тогда необходимо дополнительно учитывать и вторые делители - value // i:
for value in range(1, n):
    dividers = 1 + sum((i + value // i) for i in range(2, int(math.sqrt(value)) + 1) if value % i == 0)
    numbers.append(dividers)

или
numbers = [(1 + sum((i + value // i) for i in range(2, int(math.sqrt(value)) + 1) if value % i == 0)) for value in range(1, n)]

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}
\label{sec:introduction}

Type~Ia supernovae (SNe~Ia; see \citealt{1997ARA&A..35..309F} for a review of SN classification) are remarkable cosmological standardisable candles that are consistently used to measure cosmological parameters \citep[e.g.,][]{1998AJ....116.1009R,1999ApJ...517..565P,2007ApJ...659...98R,2009ApJS..185...32K,2012ApJ...746...85S,2014ApJ...795...44R,2014A&A...568A..22B,2016ApJ...826...56R,2018ApJ...853..126R,2018ApJ...859..101S}. Observations of SNe~Ia provide a direct route to probe the nature of the dark energy that drives the accelerated expansion. As these studies become increasingly more precise, systematic uncertainties become a significant component of the error budget \citep[e.g.,][]{2011ApJS..192....1C}. Thus, one important consideration for their future use is how well we can understand the effect of underlying systematics and their evolution with redshift.

Theoretical studies suggested the progenitor metallicity could be one potential systematic that significantly alters SN~Ia luminosities. \citet{2003ApJ...590L..83T} showed that the amount of $^{56}$Ni (which powers the SN light curve) produced during the SN explosion will strongly depend on the progenitor metallicity. SNe~Ia with higher progenitor metallicities will generate more $^{14}$N during the hydrogen-burning stage and then convert to neutron-rich $^{22}$Ne during the helium-burning stage. This $^{22}$Ne will favour the production of stable and neutron-rich $^{58}$Ni instead of the radioactive $^{56}$Ni, resulting in fainter peak luminosity. The evolution of this metallicity effect is believed to have substantial bias on SN~Ia cosmology \citep[e.g.,][]{2006astro.ph..8324P}.

Technically, the direct measurement of SN progenitor properties is extremely difficult. Indirect methods like host-galaxy studies have been proven to be a profitable way to probe the astrophysical effects in SN progenitors \citep[e.g.,][]{2010ApJ...715..743K,2010ApJ...722..566L,2010MNRAS.406..782S,2011ApJ...743..172D,2013ApJ...770..108C,2014MNRAS.438.1391P}. Some studies found that SN~Ia luminosities correlate with the host-galaxy metallicities even after the empirical corrections for light-curve width and colour \citep[e.g.,][]{2011ApJ...743..172D,2013ApJ...770..108C,2014MNRAS.438.1391P}, in the sense that brighter SNe~Ia (after corrections) tend to reside in more metal-rich galaxies. However, the host metallicities measured by these studies are mostly on a galactic scale. The discrepancy from the metallicity of the progenitor can be expected to deviate from the galactic mean.

Another promising alternative to constrain the progenitor metallicity is through ultraviolet (UV) observations of SNe~Ia. Theoretical models suggested that the UV spectra of SNe~Ia should be sensitive to the progenitor metallicity. SNe with higher progenitor metallicity will increase the iron-group elements (IGEs) in the outer layers of the SN and cause greater UV line blanketing \citep[e.g.,][]{1998ApJ...495..617H,2000ApJ...530..966L}. Thus, we should see a more suppressed UV flux for SNe having higher progenitor metallicities. This metallicity effect will only dramatically change the UV spectrum but not the optical spectrum, as the electron scattering opacity (which is not sensitive to the line-blanketing effect) is a more dominant factor than the line opacity in the optical \citep[e.g.,][]{2008ApJ...674...51E}.

There have been many efforts to obtain UV spectra of SNe~Ia \citep[e.g.,][]{1993ApJ...415..589K,2008ApJ...674...51E,2008ApJ...686..117F,2012MNRAS.426.2359M}. However, most of the spectra from these studies do not probe $\lambda<2700$\,\AA\ (which by theory is most sensitive to the progenitor metallicity). Several studies were able to obtain high signal-to-noise ratio (SNR) UV spectra that probe shorter wavelengths \citep[down to $\sim1800$\,\AA; e.g.,][]{2012ApJ...753L...5F,2014MNRAS.439.1959M,2014MNRAS.443.2887F,2015MNRAS.452.4307P,2016MNRAS.461.1308F}, but the relatively small sample size makes them unable to cover the diversity of SNe~Ia and fully interpret the metallicity effect.

Recent observations of ``twin'' SN~2011by and SN~2011fe provide some evidence of a potential metallicity effect on SN~Ia UV spectra \citep{2013ApJ...769L...1F,2015MNRAS.446.2073G,2018arXiv180608359F}. These two SNe have nearly identical optical light-curve widths and spectra but very different UV spectra. Intriguingly, despite being so similar in the optical, SN~2011fe and SN~2011by present significantly different peak absolute magnitudes \citep[$\Delta M_{V}=0.335\pm0.069$\,mag;][]{2018arXiv180608359F}. These studies suggested that the difference in UV flux between the two SNe is likely due to their significantly different progenitor metallicities. However, these twin SNe might be rare. They must have very similar explosions but with the variations in their UV spectra primarily driven by the metallicity difference. For two random SNe, we will need to disentangle the metallicity and other explosion effects when comparing their UV spectra. In theory, this can be done by generating a SN~Ia UV spectral template with which we can derive the relative metallicity of any SN~Ia without needing a twin, but a large UV spectral sample which covers a wide range of parameter space will be necessary to achieve this purpose.

Recently, \citet[][hereafter P18]{2018MNRAS.479..517P} constructed a large UV spectral sample with the {\it Neil Gehrels Swift Observatory} \citep{2004ApJ...611.1005G}. Their study contains 120 UV spectra of 39 SNe~Ia, representing the largest UV ($\lambda<2900$\,\AA) spectroscopic sample of SNe~Ia to date. However, owing to the slitless design of the {\it Swift} UV grism, the target spectrum is more easily contaminated by nearby background sources. P18 developed an improved data-reduction procedure to produce more-accurate spectra. With this improved sample, we can probe a larger parameter space of SNe~Ia and construct better UV spectral templates than previous studies. In this second paper of the series, we perform detailed analysis of the {\it Swift} UV spectroscopic sample with the goal of constraining the metallicity effect on SN~Ia UV spectra.

An outline of the paper follows. In Section~\ref{sec:data} we describe our SN~Ia sample and the host-galaxy determination. We present the data analysis in Section~\ref{sec:analysis}. Our results are discussed in Section~\ref{sec:discussion} and our conclusions are in Section~\ref{sec:conclusion}.

\section{Data}
\label{sec:data}
\subsection{SN sample}
\label{sec:sample}
\begin{figure}
	\centering
		\includegraphics[scale=0.51]{plot/swift_subclass_branch.pdf}
		\caption{\ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda5972}\ pEW as the function of \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda6355}\ pEW.
               The sample and subclasses studied by \citet{2009PASP..121..238B}
               is plotted. The sample is split into four
               different subclasses: ``shallow silicon'' (open triangles),
               ``core normal'' (open circles), ``cool'' (open downward triangles),
               and ``broad line'' (open squares). The position of the near-peak sample
               in this work is overplotted (represented by the red filled stars).}
        \label{spec_subclass}
\end{figure}

\begin{figure}
	\centering
		\includegraphics[scale=0.46]{plot/ebv_compare.pdf}
		\caption{The comparison between the colour excess derived from the host-galaxy spectra ($E(B-V)_{\rm host}$) and SN light-curves ($E(B-V)_{\rm SN}$). Here we plot the difference between $E(B-V)_{\rm SN}$ and $E(B-V)_{\rm host}$ as the function of $E(B-V)_{\rm SN}$.}
        \label{ebv_compare}
\end{figure}

\begin{table*}
\caption{Summary of the SN~Ia near-peak sample in this work.}
\begin{tabular}{lccrcccrrc}
\hline\hline
SN Name         & Redshift $z$ & \ensuremath{\Delta m_{15}}($B$)$^a$ & Phase & Host name & $E(B-V)_{\rm host}$ & Morph.$^b$ & log\,$M_{\rm stellar}^c$ & 12 + log\,(O/H)$^d$ & AGN?$^e$\\
                &          &   (mag)          & (day) &      &       (mag)         &        &     (M$_{\odot}$)     &                   &          \\
\hline
SN~1992A$^f$    & 0.0062 & 1.47(05) & $4.9$  & NGC~1380      & 0.00(02)                & S0  & $11.451^{+0.033}_{-0.046}$ & $8.811^{+0.005}_{-0.005}$ & Y\\
SN~2005cf       & 0.0065 & 1.05(03) & $-1.0$ & MCG-01-39-03  & 0.10(03)                & S0  & $9.357^{+0.059}_{-0.200}$  & \nodata                   & N\\
SN~2005df       & 0.0044 & 1.12(00) & $0.7$  & NGC~1559      & 0.00(02)                & Sc  & $10.693^{+0.066}_{-0.827}$ & \nodata                   & \nodata\\
SN~2005ke       & 0.0049 & 1.76(01) & $-2.7$ & NGC~1371      & 0.04(01)                & Sa  & $10.283^{+0.495}_{-0.161}$ & \nodata                   & N\\
SN~2008Q        & 0.0079 & 1.41(05) & $-0.2$ & NGC~524       & 0.00(02)                & S0  & $10.572^{+0.380}_{-0.346}$ & \nodata                   & \nodata\\
SN~2009an       & 0.0092 & 1.44(00) & $2.7$  & NGC~4332      & 0.09(03)                & Sa  & $11.001^{+0.001}$          & $8.872^{+0.018}_{-0.024}$ & N\\
SN~2009ig       & 0.0088 & 0.89(00) & $1.3$  & NGC~1015      & 0.00(05)                & Sa  & $10.435_{-0.175}$          & \nodata                   & N\\
SN~2011ao       & 0.0107 & 1.00(00) & $-2.0$ & IC~2973       & 0.04(02)                & Scd & $9.854^{+0.117}_{-0.033}$  & $8.774^{+0.001}_{-0.000}$ & N\\
SN~2011by       & 0.0028 & 1.14(03) & $0.6$  & NGC~3972      & 0.07(01)                & Sb  & $9.294^{+0.028}_{-0.191}$  & $8.795^{+0.151}_{-0.087}$ & N\\
SN~2011fe       & 0.0008 & 1.11(00) & $0.6$  & NGC~5457      & 0.03(00)                & Sc  & \nodata                    & $8.717^{+0.003}_{-0.001}$ & N\\
SN~2011iv       & 0.0065 & 1.69(05) & $0.5$  & NGC~1404      & 0.00(03)                & E   & $11.407^{+0.024}_{-0.603}$ & \nodata                   & N\\
SN~2012cg$^f$   & 0.0014 & 0.86(00) & $-0.5$ & NGC~4424      & 0.18(04)                & Sa  & $8.793^{+0.063}_{-0.132}$  & $8.820^{+0.023}_{-0.009}$ & N\\
SN~2012fr       & 0.0055 & 0.85(05) & $0.9$  & NGC~1365      & 0.03(04)                & Sb  & $10.363^{+1.273}$          & $8.604^{+0.000}_{-0.001}$ & N\\
SN~2012ht       & 0.0036 & 1.39(05) & $-3.1$ & NGC~3447      & 0.00(02)                & Sm  & $6.516^{+0.278}_{-0.376}$  & $8.589^{+0.102}_{-0.112}$ & N\\
SN~2013aa       & 0.0040 & 0.80(03) & $-1.3$ & NGC~5643      & 0.00(05)$^g$            & Sc  & $10.474^{+0.086}_{-0.129}$ & $8.465^{+0.001}_{-0.001}$ & Y\\
SN~2013dy$^f$   & 0.0039 & 0.92(01) & $-0.8$ & NGC~7250      & 0.21(01)                & Scd & $8.752^{+0.034}_{-0.180}$  & \nodata                   & N\\
iPTF14bdn       & 0.0156 & 0.84(05) & $5.0$  & UGC~8503      & 0.00(05)$^g$            & Irr & $9.223^{+0.046}_{-0.124}$  & $8.437^{+0.023}_{-0.025}$ & N\\
ASASSN-14lp$^f$ & 0.0051 & 0.80(01) & $0.1$  & NGC~4666      & 0.32(01)                & Sc  & $11.072^{+0.000}_{-0.000}$ & $8.682^{+0.033}_{-0.037}$ & N\\
SN~2015F$^f$    & 0.0049 & 1.26(10) & $-0.3$ & NGC~2442      & 0.04(03)                & Sbc & $10.559^{+0.082}_{-0.163}$ & \nodata                   & \nodata\\
SN~2016ccz      & 0.0150 & 1.00(02) & $-1.2$ & MRK~685       & 0.00(05)$^g$            & Sb  & $9.044^{+0.022}_{-0.059}$  & $8.295^{+0.030}_{-0.036}$ & N\\
SN~2016coj      & 0.0045 & 1.33(03) & $-2.1$ & NGC~4125      & 0.03(05)$^g$            & E   & $10.794^{+0.406}_{-0.048}$ & \nodata                   & Y\\
SN~2016eiy      & 0.0087 & \nodata  & $0.6$  & ESO~509-IG064 & 0.00(05)$^g$            & Sab & $8.716^{+0.718}_{-0.258}$  & $8.540^{+0.001}_{-0.001}$ & N\\
SN~2016ekg      & 0.0171 & 1.00(00)  & $-0.7$ & PGC~67803     & 0.00(05)$^g$            & Sbc & $8.466^{+0.905}_{-0.881}$  & $8.490^{+0.001}_{-0.000}$ & N\\
SN~2016fff      & 0.0114 & 1.49(05) & $2.4$  & UGCA~430      & 0.00(02)                & Sd  & $8.267^{+0.954}_{-0.735}$  & $8.501^{+0.002}_{-0.001}$ & N\\
SN~2017cbv      & 0.0040 & 1.06(00) & $-4.6$ & NGC~5643      & 0.00(02)                & Sc  & $10.474^{+0.086}_{-0.129}$ & \nodata                   & \nodata\\
SN~2018aoz      & 0.0058 & 1.12(00) & $-1.2$  & NGC~3923     & 0.00(02)                & E   & $8.857^{+1.822}_{-0.118}$  & \nodata                   & N\\
\hline
\label{peak-sample}
\end{tabular}
\begin{flushleft}
$^a${The $B$-band decline 15~days after the peak brightness.}\\
$^b${Host-galaxy morphology from HyperLeda \citep{2014A&A...570A..13M}.}\\
$^c${Host-galaxy stellar mass.}\\
$^d${Host-galaxy gas-phase metallicity based on the PP04 O3N2 calibration \citep{2004MNRAS.348L..59P}.}\\
$^e${Is the host galaxy contaminated by an AGN?}\\
$^f${UV spectra observed by {\it HST}/STIS.}\\
$^g${$E(B-V)$ determined by fitting the host-galaxy spectrum.}\\
\end{flushleft}
\end{table*}

\begin{figure*}
	\centering
		\includegraphics[scale=0.49]{plot/mean_spec_dm15_max_log.pdf}
		\hspace{0.25cm}
		\includegraphics[scale=0.49]{plot/mean_spec_max_morph_log.pdf}\\
		\vspace{0.25cm}
		\includegraphics[scale=0.49]{plot/mean_spec_max_mass_log.pdf}
		\hspace{0.25cm}
		\includegraphics[scale=0.49]{plot/mean_spec_max_metal_log.pdf}
                \caption{The mean spectrum of the {\it Swift} near-peak sample with respect to $\ensuremath{\Delta m_{15}}$($B$) of SNe~Ia (upper left), host morphology (upper right), host stellar mass (lower left), and host gas-phase metallicity (lower right), respectively. The spectra are colour-coded based on the parameter range. The shaded regions represent the 68.27\% confidence region from the bootstrap resampling. All of the spectra are rebinned with a bin size of 15\,\AA.}
        \label{mean-spec}
\end{figure*}

A detailed description of the {\it Swift} data can be found in P18 and has been summarised below, along with any of the additions made to define our sample.

Our original sample contains 120 {\it Swift}/UVOT grism spectra of 39 SNe Ia. The redshift of that sample ranges from $z = 0.0006$ to 0.0214 (a median of 0.0079). The $\ensuremath{\Delta m_{15}}$($B$) (defined as $B$-band decline 15~days after peak $B$-band brightness) of that sample ranges from 0.6\,mag to 1.8\,mag, with three more SNe measured ($\ensuremath{\Delta m_{15}}(B) = 1.00$, 1.11, and 1.12\,mag for SN~2016ekg, SN~2017erp, and SN~2018aoz, respectively) since P18\footnote{The $\ensuremath{\Delta m_{15}}(B)$ of SN~2016ekg and SN~2017erp are determined from {\it Swift} UVOT $B$-band light curves. The $\ensuremath{\Delta m_{15}}(B)$ of SN~2018aoz is determined from a Swope $B$-band light curve.}.

Two-thirds of the SNe in our sample have multiple epochs of UV spectra, with a median phase of $-4.5$ and $-1.9$\,days for the first observation of a SN and all spectra, respectively. In this work, we focus our major analysis on the near-peak-brightness spectra (i.e., within 5\,days relative to the maximum light). This contains 28 SNe from our parent sample in P18.

Among the 28 SNe, we exclude SN~2014J owing to its high and uncertain reddening \citep[e.g.,][]{2014ApJ...784L..12G,2014MNRAS.443.2887F,2014ApJ...788L..21A}. The super-Chandra SN~2012dn is also excluded owing to its anomalous behaviour in the UV \citep{2014ApJ...787...29B}. Five SNe (SN~2008hv, SN~2009Y, SN~2010ev, SN~2013cg, and SN~2016gsb) were further excluded owing to either poor data quality or insufficient wavelength coverage for our analysis. To increase the sample size, we include 5 SNe (SN~1992A, SN~2012cg, SN~2013dy, ASASSN-14lp, and SN 2015F) which do not have near-peak {\it Swift}/UVOT grism spectra but rather near-peak {\it HST}/STIS UV spectra. We also include all other {\it HST} UV spectra studied by \citet{2016MNRAS.461.1308F} to our analysis when appropriate. Our final near-peak sample contains 26 SNe (see Table~\ref{peak-sample}).

Figure~\ref{spec_subclass} shows the subclasses of SNe~Ia according to the pseudo-equivalent width (pEW) of \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda6355}\ and \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda5972}\ \citep{2006PASP..118..560B}. \citet{2006PASP..118..560B} split the SN~Ia sample into four groups: A ``shallow-silicon'' group, which have low pEWs for both \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda6355}\ and \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda5972}\ lines (and include SN~1991T-like objects); a ``core-normal'' group, which have homogeneous and intermediate pEWs; a ``cool'' group \citep[similar to the FAINT group in][]{2005ApJ...623.1011B}, with strong \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda5972}\ lines relative to \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda6355}; and a ``broad-line'' group, which present strong \ensuremath{\mathrm{Si}\,\textsc{ii}\,\lambda6355}\ absorption lines. We also display our near-peak sample (where we were able to measure the pEWs from the optical spectra) in Figure~\ref{spec_subclass}.  It is clear that our sample covers all four subclasses and probes a larger parameter space (especially those in the broad-line group) than that of the {\it HST} UV sample of \citet{2016MNRAS.461.1308F}.

\subsection{UV Spectra}
\label{sec:spectra}
The spectroscopic observations were performed by the {\it Swift} UVOT \citep{2004SPIE.5165..262R,2015MNRAS.449.2514K}. Owing to the slitless design of the {\it Swift} UV grism observations, the target spectrum is easily contaminated by nearby background sources (e.g., host galaxy). Thus, we have developed an improved data-reduction procedure to mitigate this issue. A complete description of our methods can be found in P18. The details of the $\it HST$ UV spectra included in our sample are presented by \citet{2016MNRAS.461.1308F}.

We correct all spectra for foreground Galactic reddening using the calibrations of \citet{2011ApJ...737..103S}. We use the host-galaxy reddening determined from the SN light curves as reported by previous studies \citep{1999AJ....118.1766P,2009ApJ...697..380W,2010AJ....139..120F,2012ApJ...744...38F,2012ApJ...753L...5F,2013NewA...20...30M,2013MNRAS.430..869S,2014ApJ...782L..35Y,2015MNRAS.452.4307P,2015ApJS..221...22I,2016ApJ...826..144S,2017ApJ...845L..11H,2016ApJ...820...92M,2017RNAAS...1a..36K,2018ApJ...864L..35S,2018PASP..130k4504P}. Here we adopt $R_{V}=3.1$ and a \citet*[][CCM]{1989ApJ...345..245C} reddening law. Some of these SNe (4 out of 18) do not have uncertainties measured for host-galaxy reddening. Here we adopt a typical error of 0.02\,mag in their host $E(B-V)$, as determined from the mean value of those having uncertainties measured from their light curves in our sample. However, we find that our result is not sensitive to the assigned uncertainty or the choice of reddening laws (see Section~\ref{sec:flux-ratio} for a discussion).

For SNe without host extinction derived from their light curves (only 6 SNe in our near-peak sample), we dereddened their spectra with the colour excess given by the host spectrum fitting. This is done with the reddening model in \textsc{gandalf} (see Section~\ref{sec:host} for more details). By comparing the observed spectra to the unreddened spectral templates, \textsc{gandalf} can determine the diffusive dust throughout the whole galaxy that affects the entire host spectrum including emission lines and the stellar continuum. We compare the colour excess $E(B-V)$ derived from host-galaxy spectral fitting and SN light-curve fitting for those SNe having both measurements available; the result is shown in Figure~\ref{ebv_compare}. We find that the $E(B-V)$ values determined from the two different methods generally agree well with each other, with a dispersion of only $\lesssim0.05$\,mag. The dispersion becomes even smaller for those objects suffering lower extinction. This is likely to be the case for the 6 SNe measured with host-galaxy spectral fitting in our near-peak sample, where we find no or negligible extinctions from their host galaxies. We have incorporated this dispersion in estimating the uncertainty of host-galaxy reddening (for those determined from the host spectra).

Two SNe (SN~2016fff and SN~2018aoz) in our near-peak sample do not have host reddening derived from either method; we assume no host-galaxy extinction given their position in the outskirts of their host galaxies. The $E(B-V)$ of each host galaxy in the near-peak sample is listed in Table~\ref{peak-sample}.

\subsection{Host-galaxy properties}
\label{sec:host}
To investigate the relation between SN~Ia UV spectrum and host galaxy, we determine the host-galaxy parameters (e.g., morphology, stellar mass, and metallicity) with both photometric and spectroscopic data.

The morphology of the host galaxy is given by HyperLeda\footnote{http://leda.univ-lyon1.fr/} \citep{2014A&A...570A..13M}, with the numerical code for the host morphology defined by de Vaucouleurs morphological type in RC2 \citep{1976RC2...C......0D}. The host stellar mass is derived by fitting the multicolour photometry of the host galaxy with the photometric redshift code \textsc{z-peg} \citep{2002A&A...386..446L}. The host photometry is provided from SDSS \protect\hbox{$ugriz$}  \citep{2018ApJS..235...42A}, Pan-STARRS1 \protect\hbox{$grizy$}  \citep{2016arXiv161205560C}, and Skymapper \protect\hbox{$uvgriz$}  \citep{2018PASA...35...10W} catalogs. \textsc{z-peg} fits the observed galaxy colours with galaxy spectral energy distribution (SED) templates corresponding to 9 spectral types (SB, Im, Sd, Sc, Sbc, Sb, Sa, S0, and E). We assume a \citet{1955ApJ...121..161S} initial-mass function (IMF).  A foreground dust screen varying from a colour excess of $E(B-V)=0$ to 0.2\,mag in steps of 0.02\,mag is used. The photometry is corrected for foreground Milky Way reddening with $R_{V} = 3.1$ and a CCM reddening law.

To measure the host metallicity, we obtained optical spectra of the host galaxies, primarily with the Kast spectrograph \citep{Kast_spectrograph} on the Lick Observatory 3\,m Shane telescope and the Goodman spectrograph \citep{2004SPIE.5492..331C} on the SOAR telescope. We fit the emission lines and stellar continuum of the host spectrum using the Interactive Data Language (\textsc{IDL}) codes \textsc{ppxf} \citep{2004PASP..116..138C} and \textsc{gandalf} \citep{2006MNRAS.366.1151S}. A complete description of this process can be found in \citet{2014MNRAS.438.1391P}. Briefly, \textsc{ppxf} fits the line-of-sight velocity distribution (LOSVD) of the stars in the galaxy in pixel space using a series of stellar templates. Before fitting the stellar continuum, the wavelengths of potential emission lines are masked to remove any possible contamination.  The stellar templates are based on the \textsc{miles} empirical stellar library \citep{2006MNRAS.371..703S, 2010MNRAS.404.1639V}.  A total of 288 templates is selected with $[M/H]=-1.71$ to $+0.22$ in 6 bins and ages ranging from $0.063$ to $14.12$\,Gyr in 48 bins.

After the emission-line measurements from \textsc{ppxf} and \textsc{gandalf}, we calculate the host gas-phase metallicity with \textsc{pymcz} \citep{2016A&C....16...54B}, a python-based code that determines the oxygen abundances and their uncertainties with a Monte Carlo method. Here the PP04 O3N2 calibration \citep{2004MNRAS.348L..59P} is adopted. We further use BPT diagrams \citep*{1981PASP...93....5B} to check for potential contamination from active galactic nuclei (AGNs) in our host galaxies. The criteria proposed by \citet{2001ApJ...556..121K} are adopted to distinguish between normal and AGN host galaxies. For the host galaxies identified as AGNs, their gas-phase metallicity will be discarded from further analysis. The host-galaxy parameters measured for our near-peak sample can be found in Table~\ref{peak-sample}.

\begin{figure*}
	\centering
		\includegraphics[scale=0.74]{plot/ratio_uv_dm15.pdf}\\
		\vspace{0.1cm}
		\includegraphics[scale=0.74]{plot/ratio_uv_morph.pdf}\\
		\vspace{0.1cm}
		\includegraphics[scale=0.74]{plot/ratio_uv_mass.pdf}\\
		\vspace{0.1cm}
		\includegraphics[scale=0.74]{plot/ratio_uv_metal.pdf}
                \caption{Flux ratios for 2450--2620 ($f_{2535}$, left panels) and 2900--3150\,\AA\ ($f_{3025}$; right panels) as a function of $\ensuremath{\Delta m_{15}}$($B$) (top row), host morphology (second row), host stellar mass (third row), and host gas-phase metallicity (bottom row). The numerical code for the host morphology is defined by de Vaucouleurs morphological type in RC2 \citep{1976RC2...C......0D}. The solid line in each panel represents the best linear fit to the data. The dashed line in the top-right panel represents the linear fit with the two fastest decliners ($\ensuremath{\Delta m_{15}}(B)>1.6$\,mag) excluded. The dashed lines and dotted lines in the bottom panels show the same linear fit, but including SNe in the potential AGN hosts (represented by grey circles) and excluding one SN having the most metal-poor host galaxy in our sample ($Z=8.267$), respectively. The legend in each panel indicates the slope of the fitted line.}
        \label{flux-ratio}
\end{figure*}

\begin{table*}
\centering
\caption{The trends of UV flux ratios with SN and host parameters.}
\begin{tabular}{lcccccccc}
\hline\hline
   & \multicolumn{4}{c}{$f_{2535}$} & \multicolumn{4}{c}{$f_{3025}$}\\
\hline
   & linear trend & probability of & \multicolumn{2}{c}{correlation} & linear trend & probability of & \multicolumn{2}{c}{correlation} \\
   &              & negative slope & Pearson & Kendall &              & negative slope & Pearson & Kendall \\
\hline
$\ensuremath{\Delta m_{15}}$($B$) & $+0.043 \pm 0.030$ & 7.69\% & $+0.30$ & $+0.34$ & $-0.375 \pm 0.143$ & 99.4\% & $-0.52$ & $-0.35$\\
Morphology   & $-0.002 \pm 0.002$ & 79.1\% & $-0.18$ & $-0.12$ & $-0.002 \pm 0.011$ & 55.9\% & $-0.01$ & $+0.03$\\
Stellar Mass & $-0.009 \pm 0.007$ & 88.5\% & $-0.34$ & $-0.20$ & $-0.065 \pm 0.043$ & 94.0\% & $-0.33$ & $-0.30$\\
$Z$            & $-0.126 \pm 0.078$ & 94.9\% & $-0.60$ & $-0.27$ & $-0.051 \pm 0.389$ & 55.6\% & $-0.04$ & $+0.10$\\
$Z$ (incl. AGNs)& $-0.136 \pm 0.065$ & 97.9\% & $-0.66$ & $-0.32$ & $-0.204 \pm 0.336$ & 72.9\% & $-0.18$ & $-0.05$\\
\hline
\end{tabular}
\label{uvflux-statistic}
\end{table*}

\section{Analysis}
\label{sec:analysis}
\subsection{Mean spectra}
\label{sec:mean-spectra}
Here we produce the mean spectra to investigate potential correlation between the UV spectrum and other physical parameters, such as SN decline rate and host morphology, stellar mass, and gas-phase metallicity. The mean spectra are created using a bootstrap sampling method. The variance of the mean spectra is estimated with the range of spectra for the middle 68.27\% of spectra generated from the sample. All of the spectra are normalised with the median flux for a wavelength range of 4000--4500\,\AA. The results are shown in Figure~\ref{mean-spec}.

We first examine the dependence of UV spectrum on $\ensuremath{\Delta m_{15}}$($B$). Using {\it HST} spectra, \citet{2016MNRAS.461.1308F} found a strong trend between $\ensuremath{\Delta m_{15}}$($B$) and the flux level at $\sim3000$--3500\,\AA, with higher $\ensuremath{\Delta m_{15}}$($B$) (i.e., fast decliners) having lower flux level. Here we confirm their finding with the larger {\it Swift} sample. We also see some potential (but opposite) trend with $\ensuremath{\Delta m_{15}}$($B$) at $\lambda\lesssim2700$\,\AA, although it is less significant owing to the poorer SNR at shorter wavelengths.

We find trend between UV spectrum and host stellar mass, with SNe~Ia in more-massive galaxies tending to have lower flux levels at $\sim3000$--3500\,\AA. This trend is as expected given the tight correlation between SN decline rate and host stellar mass \citep[e.g.,][]{2014MNRAS.438.1391P}. A similar (but less significant) trend is also seen for the flux level below $3000$\,\AA. We find no clear trend between UV flux and host morphology.

The most intriguing result is probably from the relation with host metallicity. Here the split metallicity ($\rm12+\log(O/H)=8.6$) is selected to make approximately equally sized subgroups. We find a clear trend that SNe in more metal-rich galaxies (thus likely to have a metal-rich progenitor) tend to have lower flux levels at $\lambda<2700$\,\AA\ than their metal-poor counterparts, while the flux levels at longer wavelengths are similar for both subgroups. This is the first time we are able to see from observations that the host metallicity shows a correlation with SN~Ia UV spectra, and this metallicity effect apparently alters the flux exclusively at short wavelengths. We will discuss our findings in Section~\ref{sec:theory-compare}.

\subsection{UV flux ratio}
\label{sec:flux-ratio}
Following \citet{2016MNRAS.461.1308F}, we investigate the flux ratio of several spectral regions as a function of SN and host properties. In contrast to \citet{2016MNRAS.461.1308F}, here we are only able to examine two spectral regions owing to the smaller wavelength coverage of our {\it Swift} UV spectra; these correspond to the wavelength ranges of 2450--2620 and 2900--3150\,\AA. The flux ratio (labeled as $f_{2535}$ and $f_{3025}$, respectively) is then defined as the median flux of each region divided by the median flux for a wavelength range of 4000--4500\,\AA. The result is shown in Figure~\ref{flux-ratio}.

We see a trend between $f_{3025}$ and $\ensuremath{\Delta m_{15}}$($B$), with larger $\ensuremath{\Delta m_{15}}(B)$ having smaller $f_{3025}$. This is consistent with the mean spectra studied in Section~\ref{sec:mean-spectra}. Performing the linear fitting by using the Monte Carlo Markov Chain (MCMC) method \textsc{linmix} \citep{2007ApJ...665.1489K}, there is a $\sim99$\% probability that the slope is negative based on 10,000 MCMC realisations. We also derive a Pearson and Kendall correlation coefficient of $-0.52$ and $-0.35$, respectively. This trend still holds if we exclude two extremely fast decliners (with $\ensuremath{\Delta m_{15}}(B)>1.6$\,mag) from the fitting. There is also some trend that SNe having lower $f_{3025}$ tend to be found in more massive galaxies, but this trend is less significant than that of $\ensuremath{\Delta m_{15}}(B)$. No clear trend is found with other host properties, such as morphology and gas-phase metallicity.

We next examine the trend with $f_{2535}$. We see a moderate trend with $\ensuremath{\Delta m_{15}}(B)$ and host stellar mass, with SNe showing slower decline rates or found in more massive galaxies having smaller $f_{2535}$. No significant trend is found between $f_{2535}$ and host morphology. However, there is a $\sim2\sigma$ trend with host metallicity, in the sense that SNe in more metal-rich galaxies tend to have smaller $f_{2535}$. A $\sim95$\% probability of negative slope is determined, and a Pearson and Kendall correlation coefficient of $-0.60$ and $-0.27$, respectively. This result is also consistent with what we have seen using the mean spectra. The trend also holds if we further include the SN whose host was identified as a potential AGN in Section~\ref{sec:host}. The probability of a negative slope increases to 98\%, and the Pearson and Kendall correlation coefficients become $-0.66$ and $-0.32$, respectively. Excluding the SN hosted by the most metal-poor galaxy in our near-peak sample ($Z=8.267$) does not change the trend, but decreases its significance to the $\sim1\sigma$ level. In the future, a larger sample in this low-metallicity regime ($Z<8.5$) will be crucial to verify our results.

Our result is not sensitive to the uncertainty of the host-galaxy reddening or the choice of reddening laws. We performed a Monte Carlo experiment, where we assigned a random error in host $E(B-V)$ from 0 to 0.05\,mag for SNe without uncertainties measured in their host-galaxy reddening. A dispersion of only 0.003 ($\sim$2\%) is found for the slope of the $f_{2535}$ to host metallicity relation. This has a negligible effect on our result. We also compared our result with different reddening laws, such as the \citet{1999PASP..111...63F} law and two Large Magellanic Cloud reddening laws \citep{1999ApJ...515..128M}. The resulting differences in $f_{2535}$ are all $<1$\% and do not change the trends in Figure~\ref{flux-ratio}.

The results of the fitting and the correlation coefficients can be found in Table~\ref{uvflux-statistic}.

\begin{figure}
	\centering
		\includegraphics[scale=0.5]{plot/uv_spec_model_max_dm15.pdf}\\
		\vspace{0.25cm}
		\includegraphics[scale=0.5]{plot/uv_spec_model_max_metal.pdf}\\
                \caption{The data-driven templates created by SN~Ia UV near-peak spectra as a function of $\ensuremath{\Delta m_{15}}(B)$ (upper panel) and host gas-phase metallicity $Z$ (lower panel).}
        \label{model-spec}
\end{figure}

\subsection{Data-driven spectral template}
\label{sec:model}
\begin{figure*}
	\centering
		\includegraphics[scale=0.73]{plot/uv_spec_model_max_dm15_metal.pdf}
                \caption{Same as Figure~\ref{model-spec}, but with both $\ensuremath{\Delta m_{15}}(B)$ and $Z$ considered when fitting the template. Here we compare the templates generated by $\ensuremath{\Delta m_{15}}(B)=0.9$ and 1.4\,mag, each with $Z=8.4$ and 8.8.}
        \label{model-spec2}
\end{figure*}

\begin{figure*}
	\centering
		\includegraphics[scale=0.79]{plot/uv_spec_15F_model.pdf}\\
                \caption{{\it Upper panels}: the left panel shows the comparison between the near-peak UV spectrum of SN~2015F and our template parameterised with $\ensuremath{\Delta m_{15}}(B)$ only. The $\ensuremath{\Delta m_{15}}(B)$ for SN~2015F \citep[1.26\,mag;][]{2015ApJS..221...22I} is used to create the template spectrum. The right panel is the same as the left panel, but with our UV template parameterised with both $\ensuremath{\Delta m_{15}}(B)$ and host metallicity. Here we fix $\ensuremath{\Delta m_{15}}(B)$ and vary only the metallicities to match the data (with only by-eye inspection). {\it Lower panels}: fractional flux differences from the template spectra shown in the upper panels.}
        \label{15F-model}
\end{figure*}

Here we generate the data-driven UV spectral template with our near-peak sample. We first create the template spectra with $\ensuremath{\Delta m_{15}}(B)$ as the parameter. Following Eq.~(1) of \citet{2016MNRAS.461.1308F}, we generate a smoothed spectrum of each SN using an inverse-variance Gaussian filter \citep{2006AJ....131.1648B} and fit the smoothed flux for all spectra at each wavelength as a function of $\ensuremath{\Delta m_{15}}(B)$. Note that the fitting performed here is unweighted, and we do not estimate the uncertainties for our template spectra. The result is shown in the upper panel of Figure~\ref{model-spec}.

The template spectra generally follow the same trend as we found in the data (e.g., the mean spectra). There is a strong correlation between the $\ensuremath{\Delta m_{15}}(B)$ and the flux level at $\sim3000$--3500\,\AA. Similar to what was found by \citet{2016MNRAS.461.1308F}, our templates also show a pivot point at $\lambda\approx2700$\,\AA, where the templates tend to show an opposite trend blueward of 2700\,\AA\ in contrast to that redward of 2700\,\AA.

We next create the template spectra with host metallicity as the parameter. We fit the smoothed flux for all spectra in the sample at each wavelength as a function of host metallicity such that
\begin{equation}
\label{eq:model1}
f_{\lambda}=f_{8.6,\lambda}+s_{\lambda}\times(Z-8.6),
\end{equation}
where $f_{8.6,\lambda}$ represents the spectrum of a nominal SN~Ia of host gas-phase metallicity $Z=8.6$. The $s_{\lambda}$ is the deviation from that spectrum for a hypothetical SN~Ia of host $Z=9.6$. We present the parameters in Table~\ref{tab:model1}. The result is shown in the lower panel of Figure~\ref{model-spec}.

There is an obvious trend that the metallicity has a substantial effect in altering the flux level of our template spectra, and is particularly significant at $\lambda\lesssim2700$\,\AA. This implies that the near-peak UV spectra (at least for $\lambda\lesssim2700$\,\AA) could be promising indicators of SN~Ia progenitor metallicity.

As noted above, it is apparent that $\ensuremath{\Delta m_{15}}(B)$ and metallicity are both affecting the UV spectra of SNe~Ia (although likely in different ways). To disentangle this degeneracy, we try to construct UV templates based on both $\ensuremath{\Delta m_{15}}(B)$ and metallicity parameters to explore the two-dimensional parameter space. The formula we use for the fitting is
\begin{equation}
\label{eq:model2}
f_{\lambda}=f_{(1.1,8.6),\lambda}+s_{1,\lambda}\times(\ensuremath{\Delta m_{15}}(B)-1.1)+s_{2,\lambda}\times(Z-8.6),
\end{equation}
where $f_{1.1,8.6,\lambda}$ represents the spectrum of a nominal $\ensuremath{\Delta m_{15}}(B)=1.1$\,mag SN~Ia with the host galaxy having a gas-phase metallicity $Z=8.6$. Also, $s_{1,\lambda}$ is the deviation from that spectrum for a hypothetical SN~Ia of $\ensuremath{\Delta m_{15}}(B)=2.1$\,mag and host $Z=8.6$, while $s_{2,\lambda}$ is the deviation from the same spectrum for a hypothetical SN~Ia of $\ensuremath{\Delta m_{15}}(B)=1.1$\,mag and host $Z=9.6$. We present the parameters in Table~\ref{tab:model2}. The result is shown in Figure~\ref{model-spec2}. Our two-parameter templates clearly indicate that $\ensuremath{\Delta m_{15}}(B)$ and metallicity have distinct effects on the UV spectrum.

Figure~\ref{15F-model} shows the comparison between the UV spectrum of SN~2015F and our templates. The templates parameterised with only $\ensuremath{\Delta m_{15}}(B)$ and both $\ensuremath{\Delta m_{15}}(B)$ and host metallicity are compared. Since we do not have the host metallicity measured for SN~2015F, we fix $\ensuremath{\Delta m_{15}}(B)$ to that of SN~2015F (which is already known from the light-curve fitting) and only let the metallicity vary.  Note that the comparison made here is simply by-eye inspection; we did not fit our templates to the data.

It is clear that with the UV template having only a single parameterisation in light-curve shape, it is difficult to interpret the whole UV spectrum (especially for the behaviour at short wavelengths). The template which takes the metallicity into consideration is apparently more consistent with the data. By comparing the UV spectrum with our templates, we find that SN~2015F is likely to reside in a metal-rich host environment. This is probably not surprising given its relatively massive host galaxy ($\log\,(M_{\rm stellar}/{\rm M}_{\odot})=10.56$). Thus, it implies that SN~2015F could have a high-metallicity progenitor.

However, one should be cautious in using these templates. Firstly, we have only a relatively small number of SNe with measured host metallicities in certain regions of parameter space (especially those SNe at both ends of the $\ensuremath{\Delta m_{15}}(B)$ distribution of P18). A discrepancy between the host metallicity measured in this work and SN progenitor metallicity is also expected, but the relative trend existing in both mean spectra and spectral templates should be real. Secondly, the real mechanisms forming the UV spectra of SNe~Ia should be far more complicated than a simple description of a two-parameter template \citep[e.g.,][]{2000A&A...363..705M}. Other parameters (from the progenitor and/or explosion) could also play a role, but the strong dependence of SN~Ia UV spectra on light-curve shape and metallicity implies that they are likely important factors.

\begin{table}
\center
\caption{UV spectral template parameters for Eq.~(\ref{eq:model1}). The entire table is available online as supplementary material. A portion is shown here for guidance regarding its form and content.}
\begin{tabular}{lcc}
\hline\hline
Wavelength & $f_{8.6,\lambda}$  & $s_{\lambda}$\\
(\AA)      &                         &                           \\
\hline
2350  &   0.0757  &   $-0.1038$\\
2355  &   0.0887  &   $-0.1526$\\
2360  &   0.0926  &   $-0.1939$\\
2365  &   0.0938  &   $-0.2063$\\
2370  &   0.0934  &   $-0.1899$\\
2375  &   0.0885  &   $-0.1424$\\
2380  &   0.0802  &   $-0.0711$\\
2385  &   0.0737  &   $-0.0215$\\
2390  &   0.0716  &   $-0.0200$\\
2395  &   0.0700  &   $-0.0624$\\
\hline
\label{tab:model1}
\end{tabular}
\end{table}

\begin{table}
\center
\caption{The same as Table~\ref{tab:model1}, but for parameters in Eq.~(\ref{eq:model2}).}
\begin{tabular}{lccc}
\hline\hline
Wavelength & $f_{(1.1,8.6),\lambda}$ & $s_{1,\lambda}$ & $s_{2,\lambda}$\\
(\AA)      &                    &             & \\
\hline
2350  &    0.1431  &    0.2148  &   $-0.1363$\\
2355  &    0.1587  &    0.2460  &   $-0.2306$\\
2360  &    0.1625  &    0.2628  &   $-0.3171$\\
2365  &    0.1628  &    0.2836  &   $-0.3761$\\
2370  &    0.1621  &    0.3000  &   $-0.3994$\\
2375  &    0.1553  &    0.2941  &   $-0.3798$\\
2380  &    0.1443  &    0.2681  &   $-0.3234$\\
2385  &    0.1342  &    0.2264  &   $-0.2700$\\
2390  &    0.1261  &    0.1714  &   $-0.2405$\\
2395  &    0.1171  &    0.1160  &   $-0.2364$\\
\hline
\label{tab:model2}
\end{tabular}
\end{table}

\subsection{Spectral evolution}
\label{sec:evolution}
\begin{figure*}
	\centering
		\includegraphics[scale=0.35]{plot/sn2009ig_all.pdf}

		\includegraphics[scale=0.35]{plot/sn2011fe_all.pdf}

		\includegraphics[scale=0.35]{plot/sn2011iv_all.pdf}
                \caption{The UV spectral sequence of SN~2009ig (left), SN~2011fe (middle), and SN~2011iv (right). The phases in each panel are relative to $B$-band maximum light.}
        \label{uv-evolution}
\end{figure*}

Many SNe in our sample have a well-observed spectral sequence, making them ideal targets for studying the temporal evolution of UV spectral features.

In Figure~\ref{uv-evolution}, we present examples of UV spectral sequences for SNe with several different values of $\ensuremath{\Delta m_{15}}(B)$. The epochs of our spectral observations span $\sim\pm1$--2 weeks relative to the time of peak brightness. There is clear evolution for the UV feature at $\lambda\approx3000$--3500\,\AA. The flux level rises dramatically (relative to the flux at $\sim4000$\,\AA) with time after the SN explosion and peaks $\sim1$ week before optical maximum light. It then decreases slowly (relative to the rising) with time after peak brightness. This trend is similar for both low- and high-$\ensuremath{\Delta m_{15}}(B)$ SNe, although the high-$\ensuremath{\Delta m_{15}}(B)$ SNe generally exhibit much weaker (and more featureless) UV spectra than do low-$\ensuremath{\Delta m_{15}}(B)$ SNe at similar phases.

We examine the temporal evolution of the flux ratios $f_{2535}$ and $f_{3025}$ in Figure~\ref{uv-evolution2}. Similar to what we have seen in Figure~\ref{uv-evolution}, there is strong evolution of $f_{3025}$ with time. The feature also peaks $\sim1$ week before optical maximum light, indicating that early-time observations are more critical for the UV than for the optical. However, we do not see clear evolution for $f_{2535}$.

By examining each individual SN, we find that SN~2008hv and SN~2008Q are apparent outliers to these trends (in terms of their $\ensuremath{\Delta m_{15}}(B)$). They are noticeably bright in the UV despite their relatively fast decline rates ($\ensuremath{\Delta m_{15}}(B)=1.25$ and 1.40\,mag, respectively). We note that both SNe were classified as ``NUV-blue'' SNe~Ia by \citet{2013ApJ...779...23M}. This represents a relatively minor group of SNe~Ia (at least at low redshifts) which shows distinctly high NUV to optical ratios. SN~2011fe and SN~2011by were also classified as NUV-blue SNe~Ia. It is clear that their peak flux ratios $f_{3025}$ are higher than the majority of our sample. SN~2013dy and SN~2012cg are also similar to those NUV-blue events as described by \citet{2013ApJ...779...23M}. Intriguingly, we find that these NUV-blue SNe~Ia are not necessarily blue at shorter wavelength (e.g., $f_{2535}$). This implies that the UV spectrum at those wavelengths might be influenced by different physics (e.g., progenitor metallicity).

\section{Discussion}
\label{sec:discussion}
\subsection{Comparison with previous studies}
\label{sec:theory-compare}
\citet{2000ApJ...530..966L} modeled the effects of progenitor metallicity on SNe~Ia by modifying the metallicity of the unburned C+O layer in the W7 model of \citet{1984ApJ...286..644N}. They produced synthetic spectra of a variety of progenitor metallicities with wavelengths extended to the UV. They found that the UV continuum of the synthetic spectra is strongly affected by the metallicity in the unburned layer, with higher metallicities having lower flux levels. This trend is likely caused by the stronger UV line blanketing with increasing IGEs in the SN outer layers. Higher metallicity also results in a shallower line-forming region and causes the UV features to move blueward in the spectra.

Using a different spectral synthesis code, \citet{2008MNRAS.391.1605S} also showed that the variation of IGE abundance does not significantly affect the optical, but is significant in the UV part of the spectrum. However, they found that the UV flux level may either increase or decrease with increasing abundance of heavy elements, depending on the models they used. \citet{2012MNRAS.427..103W} adopted the radiative transfer codes based on \citet{2008MNRAS.391.1605S} but different explosion models to investigate the effect of metal content in the SN outer layers on the UV spectrum. They concluded that the flux at $\sim3000$--3500\,\AA\ relative to that near 4000\,\AA\ is a good tracer of metallicity.

In this work, we use the host-galaxy metallicity as a proxy for progenitor metallicity to examine the correlation with SN~Ia UV spectra. Our result is generally consistent with the predictions of \citet{2000ApJ...530..966L}. Their model spectra at 15~days after explosion (i.e., similar to the phase studied in this work) also reveal that the flux levels start to show increasingly large differences at $\lambda\lesssim2700$\,\AA\ between progenitor metallicities. This is consistent with both the mean spectra and data-driven spectral templates in this work. We do not see a significant trend between flux level at $\sim3000$--3500\,\AA\ and metallicity, which contradicts the model predictions of \citet{2012MNRAS.427..103W}.

\citet{2013ApJ...769L...1F} studied the ``twin" SN~2011by and SN~2011fe and found some evidence of a metallicity effect on the SN~Ia UV spectrum. These two SNe have nearly identical optical spectra and light curves but very different UV spectra. They compared the observed difference to those of model spectra in \citet{2000ApJ...530..966L} and concluded that the difference in their progenitor metallicities is likely the main source driving the discrepancy in the UV (without affecting the optical). Following their methods, we produce the near-peak flux-ratio spectrum of SN~2011fe to SN~2011by and present it in Figure~\ref{uv-model-compare}. By using flux ratios, we can avoid the differences of spectral features between models and data, and focus on the differences between models (e.g., the metallicity). We then compare the flux-ratio spectrum of the twin SNe to that of our data-driven templates as parameterised by the host metallicity. We find that SN~2011by is likely to have higher progenitor metallicity than that of SN~2011fe. For example, the flux ratio produced by 0.6\,$\rm Z_{\odot}$ and 1.0\,$\rm Z_{\odot}$ \citep[using the solar value of 8.69;][]{2001ApJ...556L..63A} template spectra could match the data quite well (the comparison made here is simply a by-eye inspection). The model flux-ratio spectrum of metallicity factor $Z_{1}/Z_{2}=1/30$ from \citet{2000ApJ...530..966L} is also overplotted for comparison.

Our results support the previous findings that SN~2011by and SN~2011fe could have solar (or above solar) and subsolar progenitor metallicities, respectively. Nonetheless, the ``direct'' interpretation or measurement of the progenitor metallicity using our templates could be problematic owing to a potential discrepancy between the host-galaxy and SN-progenitor metallicities. The metallicity measured close to the position of the progenitor system (e.g., determined from the local environment) should be considered to build more precise templates.

\begin{figure}
	\centering
		\includegraphics[scale=0.5]{plot/uv_evolution_2535.pdf}\\
		\includegraphics[scale=0.5]{plot/uv_evolution_3025.pdf}\\
                \caption{The temporal evolution of the UV flux ratios $f_{2535}$ and $f_{3025}$. The black and red symbols correspond to the SNe with $\ensuremath{\Delta m_{15}}(B)<1.2$\,mag and $\ensuremath{\Delta m_{15}}(B)>1.2$\,mag, respectively.}
        \label{uv-evolution2}
\end{figure}

\begin{figure}
	\centering
		\includegraphics[scale=0.49]{plot/uv_spec_model_max_metal2.pdf}
                \caption{The flux-ratio spectrum of SN~2011fe to SN~2011by observed by {\it HST}/STIS (in black). The red line represents the ratio of {\it Swift} template spectra of SNe~Ia in 0.6\,$\rm Z_{\odot}$ host galaxies relative to those in solar-metallicity host galaxies. The green line is the ratio of model spectra from \citet{2000ApJ...530..966L} with progenitor metallicity ratios of 1/30.}
        \label{uv-model-compare}
\end{figure}

\subsection{Implications for cosmology}
\label{sec:cosmology}
\begin{figure}
	\centering
		\includegraphics[scale=0.5]{plot/ratio_uv_hrs_2535.pdf}\\
		\vspace{0.25cm}
		\includegraphics[scale=0.5]{plot/ratio_uv_hrs_3025.pdf}\\
		\vspace{0.25cm}
		\includegraphics[scale=0.49]{plot/metallicity_hrs.pdf}
                \caption{The Hubble residuals from our near-peak sample as a function of flux ratios $f_{2535}$ (top) and $f_{3025}$ (middle), and host gas-phase metallicity (bottom). The red line in each panel represents the linear fit to the data. The dashed line in the middle panel shows the same linear fitting, but excluding the SN of highest $f_{3025}$ in our sample, which causes a significant trend with Hubble residual that is otherwise not present. The dotted line in each panel represents the line of zero residual.}
        \label{uvflux-hrs}
\end{figure}

Theory predicts that the amount of $^{56}$Ni produced during the SN~Ia explosion shows a strong dependence on the progenitor metallicity \citep[e.g.,][]{2003ApJ...590L..83T}. More metal-rich progenitors will likely generate more stable and neutron-rich $^{58}$Ni instead of the radioactive $^{56}$Ni, and therefore result in fainter SNe~Ia. Host-galaxy observations also suggested that SNe found in more metal-rich environments tend to be fainter than those in metal-poor environments \citep[e.g.,][]{2011ApJ...743..172D,2013ApJ...770..108C,2014MNRAS.438.1391P}. This dependence is significant even after the empirical corrections for SN light-curve width and colour. Given the underlying metallicity evolution with redshift \citep[e.g., $\sim0.2$\,dex from $z=0$ to 1;][]{2005ApJ...635..260S}, this could introduce substantial bias in the current cosmological analyses.

Theoretically, the UV spectrum of a SN~Ia should be a more direct probe of progenitor metallicity than the host galaxy. Accordingly, we inspect the correlation between the UV flux ratio and SN luminosity as parameterised by Hubble residuals to see if it shows a stronger trend than that with host galaxies. The Hubble residuals are defined as the difference between the observed rest-frame $B$-band SN apparent magnitude corrected for light-curve width and colour, and the peak SN magnitude expected in our assumed cosmological model. We use \textsc{salt2} \citep{2007A&A...466...11G} to fit the SN light curves, and we adopt similar procedures and cuts on light-curve width and colour as those described by \citet{2018MNRAS.475..193F}. However, we did not apply the correction for the host mass step as we are actually searching for potential variables which could have the same effect as host stellar mass (e.g., metallicity). For the 9 SNe having precise distances measured by \citet{2016ApJ...826...56R}, we use their Cepheid-based distance modulus instead of that derived from the cosmological models. For those without Cepheid distances, the distance modulus is determined by the \textsc{python} script \textsc{cosmos} and assumes $\rm H_{0}=67.7$\,km\,s$^{-1}$\,Mpc$^{-1}$ and a flat universe with $\Omega_{M}=0.3$.

The result is shown in Figure~\ref{uvflux-hrs}. Previous studies revealed that SNe in more metal-rich environments tend to have more negative Hubble residuals than their metal-poor counterparts \citep[e.g.,][]{2014MNRAS.438.1391P}. If the host metallicity traces the progenitor metallicity well, we should expect SNe with lower flux ratio $f_{2535}$ (caused by higher progenitor metallicity) to have more negative Hubble residuals. However, we do not see a significant trend with $f_{2535}$; if anything, SNe with lower $f_{2535}$ tend to have more negative Hubble residuals. There is a $\sim72$\% probability that the slope is positive based on 10,000 MCMC realisations. In comparison, we see an opposite trend with $f_{3025}$. We find this trend is likely caused by an outlier in the sample (see the middle panel of Figure~\ref{uvflux-hrs}), and which otherwise is not present. We also show the Hubble residuals as a function of host gas-phase metallicities (the bottom panel of Figure~\ref{uvflux-hrs}). However, we are unable to reproduce the significant trend found by previous host studies, although it is consistent with the absence of a trend we found with $f_{2535}$.

It is likely that our results suffer from large uncertainties, given that our sample is relatively small and nearby. At $z\lesssim0.01$, precise distance measurement becomes extremely difficult owing to peculiar velocities, and thus those Hubble residuals only very weakly depend on the cosmological model. It would be interesting to re-examine these relations by extending the current analysis to a higher-$z$ SN sample in the future.

\subsection{Early-time UV spectra}
\label{sec:early}
\begin{figure}
	\centering
	    \includegraphics[scale=0.47]{plot/mean_spec_premax_dm15_log.pdf}\\
		\vspace{0.25cm}
		\includegraphics[scale=0.47]{plot/mean_spec_premax_mass_log.pdf}\\
		\vspace{0.25cm}
		\includegraphics[scale=0.47]{plot/uv_mass_comp.pdf}
                \caption{{\it Upper}: The mean spectra of the {\it Swift} early-time sample ($t \approx -7$\,days) based on $\ensuremath{\Delta m_{15}}(B)$. The mean spectra of the slower decliners ($\ensuremath{\Delta m_{15}}(B)<1.05$\,mag) and faster decliners ($\ensuremath{\Delta m_{15}}(B)>1.05$\,mag) are shown with blue and red lines, respectively. {\it Middle}: Same as the upper panel, but with the host-galaxy stellar mass instead. The mean spectra of SNe in low-mass host galaxies ($\log\,(M_{\rm stellar}/{\rm M}_{\odot})<10$) and high-mass galaxies ($\log\,(M_{\rm stellar}/{\rm M}_{\odot})>10$) are represented with blue and red lines, respectively. {\it Bottom}: The flux-ratio spectra of low- to high-mass mean spectra for the early-time (in red) and near-peak (in green) samples, respectively. The solid circles represent the mean flux ratios in bins of wavelength. As in Figure~\ref{mean-spec}, all of the spectra here are rebinned with a bin size of 15\,\AA.}
        \label{mean-spec-premax}
\end{figure}

In this work, we have shown that the near-peak UV spectra are promising indicators of progenitor metallicity. However, theoretical models also predict that the progenitor metallicity should have a more significant effect at earlier epochs \citep{2000ApJ...530..966L}: the SN~Ia UV spectra are expected to show larger differences with progenitor metallicities, and diverge at longer wavelengths. This implies that the early-time UV spectra could be better metallicity indicators.

To test this, we build an early-time sample with the UV spectra observed $\sim1$\,week before peak brightness. Our early-time sample contains 14 SNe, with phases ranging from $-9$ to $-6$\,days (a mean phase of $-7.6$\,days). Following the procedure described in Section~\ref{sec:mean-spectra}, we produce the mean UV spectra based on $\ensuremath{\Delta m_{15}}(B)$ and host-galaxy stellar mass. Here the stellar mass is used instead of metallicity as it not only greatly increases the number of our early-time sample (13 out of 14 SNe have their host mass measured, but only half of them have host metallicity available), but also is a good proxy for metallicity \citep[e.g.,][]{2004ApJ...613..898T}. We then compare the flux-ratio spectra between the early-time and near-peak samples. The results are shown in Figure~\ref{mean-spec-premax}.

We find no significant difference between the slower decline and faster decline samples (here defined as $\ensuremath{\Delta m_{15}}(B)<1.05$ and $\ensuremath{\Delta m_{15}}(B)>1.05$\,mag, respectively), indicating that the decline rate is likely to have a negligible effect on the early-time UV spectra. However, there is an obvious trend that the mean spectra between low-mass and high-mass host galaxies present larger differences at $t \approx -7$\,days than that at peak brightness (see also Figure~\ref{mean-spec}). The spectra also tend to diverge at longer wavelengths. Using the stellar mass as the proxy for metallicity, this implies that the early-time UV spectra are better indicators of progenitor metallicity. Our finding is consistent with the theoretical predictions, although with large uncertainties owing to the small number of SNe with early-time observations available.

The fast turnaround of {\it Swift} makes it an ideal instrument for increasing the number of SNe with early-time UV spectra in the future. With earlier observations, we should be able to detect the metallicity differences more easily. This especially has the advantage of mitigating the problem that the SNR of {\it Swift} UV spectra generally deteriorates dramatically at shorter wavelengths, barely probing the region where metallicity just starts to take effect for the near-peak spectra (i.e., $\lambda \approx 2700$\,\AA).

\section{Conclusions}
\label{sec:conclusion}
Theoretical studies predicted that the SN~Ia UV spectrum is sensitive to the progenitor metallicity. However, it is extremely difficult to constrain such metallicity effects from observations owing to either limited wavelength coverage or sample size. In this work, we present the analysis of the largest UV ($\lambda<2900$\,\AA) spectroscopic sample of SNe~Ia observed by {\it Swift}. We constructed mean spectra and spectral templates to investigate the relation between UV spectra and both SN and host-galaxy properties.

\begin{enumerate}
\item[$\bullet$] We confirm previous findings that the UV flux shows a strong dependence on SN light-curve shape, with slower-decline SNe having higher flux levels at $\lambda\sim3000$\,\AA. There is also some potential (but opposite) trend with SN light-curve shape at $\lambda\lesssim2700$\,\AA.

\item[$\bullet$] Using host galaxy as a proxy for the SN progenitor system, we find a $\sim2\sigma$ trend between the UV spectrum and host metallicity. SNe found in more metal-rich galaxies (thus likely to have more metal-rich progenitors) tend to exhibit a lower UV flux level at $\lesssim2700$\,\AA. We find that this metallicity effect is nearly negligible at longer wavelengths. Our results are consistent with the theoretical predictions and provide strong observational evidence for a correlation between SN~Ia UV spectrum and progenitor metallicity.

\item[$\bullet$] Following \citet{2016MNRAS.461.1308F}, we generate UV spectral templates that depend on light-curve shape and host metallicity. While the UV templates with only a single parameterisation using light-curve shape agree quite well with the observations, they fail to describe the behaviour of the spectrum at shorter wavelengths (e.g., $\lambda\lesssim2700$\,\AA). The two-parameter templates which take both light-curve shape and metallicity into consideration are more consistent with the observations. Although other parameters could also play a role, the strong dependence of SN~Ia UV spectra on light-curve shape and metallicity implies that they are important factors.

\item[$\bullet$] We investigate the relation between UV spectra and SN luminosity as parameterised by Hubble residuals. We do not see a significant trend between UV spectra and Hubble residuals; if anything, the flux level at $\sim2500$\,\AA\ (which is sensitive to the progenitor metallicity) tends to increase with Hubble residuals. However, the determination of Hubble residuals for our sample suffers large uncertainties from SN distances, as most of our SNe are extremely nearby ($z\lesssim0.01$). That means they only weakly depend on the cosmological model. Future analyses of higher-$z$ SN samples will be necessary to examine the metallicity bias on Hubble residuals.

\item[$\bullet$] We find that early-time UV spectra are likely better metallicity indicators than near-peak UV spectra. We generate the mean spectra for SNe in low-mass and high-mass galaxies at earlier epochs ($t \approx -7$\,days) and find that their difference tends to be larger than that of the near-peak sample. This implies that the early-time UV observations could be better probes of progenitor metallicity.
\end{enumerate}

UV spectra are critical to understanding the explosion mechanism and progenitor systems of SNe~Ia. In particular, they are expected to be more direct probes of SN progenitor metallicity, which is believed to be able to significantly alter the SN luminosity and bias the distance measurement. Future studies with rest-frame UV spectra for higher-$z$ SNe will be critical for investigating the metallicity evolution and potential bias on cosmological analyses.

\section{Acknowledgements}
\label{sec:acknowledgements}
{\it Swift} spectroscopic observations were performed under programs
GI--04047, GI--5080130, GI--6090689, GI--8110089, GI--1013136, and
GI--1215205; we are very grateful to N.\ Gehrels, S. B.\ Cenko, and the
{\it Swift} team for executing the observations quickly.
Based in part on observations made with the NASA/ESA {\it Hubble Space
  Telescope}, obtained at the Space Telescope Science Institute
(STScI), which is operated by the Association of Universities for
Research in Astronomy, Inc., under National Aeronautics and Space
Administration (NASA) contract NAS 5--26555. These observations are
associated with Programmes GO--12298, GO--12592, GO--13286, GO--13646,
and DD--14925.  This manuscript is based upon work supported by NASA
under Contract No.\ NNG16PJ34C issued through the {\it WFIRST} Science
Investigation Teams Programme.

Y.-C.P. is supported by the East Asian Core Observatories Association (EACOA)
Fellowship. N.P.M.K. has been supported by the UK Space Agency.
The UCSC group is supported in part by NASA grant 14-WPS14-0048, NSF grant
AST-1518052, the Gordon \& Betty Moore Foundation, and by fellowships
from the Alfred P.\ Sloan Foundation and the David and Lucile Packard
Foundation to R.J.F. Additional financial assistance to A.V.F. was
provided by the TABASGO Foundation, the Christopher R. Redlich Fund,
and the Miller Institute for Basic Research in Science (U.C. Berkeley).

The national facility capability for SkyMapper has been funded through ARC LIEF grant LE130100104 from the Australian Research Council, awarded to the University of Sydney, the Australian National University, Swinburne University of Technology, the University of Queensland, the University of Western Australia, the University of Melbourne, Curtin University of Technology, Monash University, and the Australian Astronomical Observatory. SkyMapper is owned and operated by The Australian National University's Research School of Astronomy and Astrophysics. The survey data were processed and provided by the SkyMapper Team at ANU. The SkyMapper node of the All-Sky Virtual Observatory (ASVO) is hosted at the National Computational Infrastructure (NCI). Development and support the SkyMapper node of the ASVO has been funded in part by Astronomy Australia Limited (AAL) and the Australian Government through the Commonwealth's Education Investment Fund (EIF) and National Collaborative Research Infrastructure Strategy (NCRIS), particularly the National eResearch Collaboration Tools and Resources (NeCTAR) and the Australian National Data Service Projects (ANDS).

\bibliographystyle{mn2e}

redpajama_set_name: RedPajamaArXiv


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Music-making in the Hertfordshire Parish, 1760–1870 | University of Hertfordshire Press
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Home > Hertfordshire Publications > Music-making in the Hertfordshire Parish, 1760–1870
Music-making in the Hertfordshire Parish, 1760–1870
Author: Maggie Kilbey
Price: £16.99/$33.95
"Anyone with an interest in music, church social history, the education of singers and instrumentalists – in fact the music business in general, will find this book a mine of fascinating information. I read it from cover to cover with frequent smiles. Thank you, Dr Maggie Kilbey!"
-Ruth Jeavons,
Herts Past & Present
The standard of congregational singing in mid-eighteenth-century parish churches was often in a parlous state, a situation viewed with alarm by many influential clergy and social commentators. In this authoritative study, Maggie Kilbey explores attempts to improve parochial music-making over the following century and the factors that played a part in their success or failure.
Using Hertfordshire as a basis, original research by this respected author and historian uses a wide range of documentary evidence to reveal a complicated picture of influence and interaction between the gentry, clergymen and their parishioners.
Her innovative approach to the social history of church music-making sheds light on interactions between militia and church bands, singers, organists, the role of charity school children and the use of barrel organs.
Because of its proximity to London, Hertfordshire was particularly attractive to elites with an interest in the capital, and fell under the influence of metropolitan music-making more readily than less accessible parts of England.
The involvement of both fashion-conscious and socially aware gentry was mirrored by those further down the social scale, and formed part of a complex pattern of support for church music-making.
Unsurprisingly, this support was not universal, and often short-lived once initial enthusiasm or funding ran out. Consequently, although many attempts were made to 'improve' music-making in parish churches, sooner or later these were considered to be failures, swiftly forgotten — and then tried again.
To make matters worse, church rate disputes hampered efforts to improve or sustain parish music-making during the nineteenth century, resulting in financial hardship for organists and other church musicians. Yet this was followed by an 1850s 'singing craze' which led to the formation of many church choirs, alterations to the church fabric, and installation of organs.
This investigation into patterns of parochial music-making will appeal to both those with an interest in the history of music-making, and also those with a general interest in the social history of Hertfordshire.
About the Author/s:
Maggie Kilbey
Maggie Kilbey has a doctorate from the University of Oxford and lives in Hertfordshire.
ISBN: 978-1-912260-26-3 Format: Paperback, 304pp Published: Oct 2020
Other titles you may enjoy
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An Historical Atlas of Hertfordshire
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Contact us at UH Press if you have any queries or would like to find out more about this book.
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