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Tag: #WesternRomance
November #BookReviews! @bsmithnovelist @Sandra_Cox @teagangeneviene @JacqBiggar @michaelsvoice_2
Published on December 4, 2021 December 9, 2021 by Jan Sikes37 Comments
Welcome to my November Book Reviews! I hope you find something new that you can't resist! 🙂 I only post 4 or 5-star reviews, and all reviews are strictly my own opinions.
This post-apocalyptic book is like reading a diary. I had to keep reminding myself it is fiction. The author did a great job of drawing me into the story and into the struggle for survival after a devastating EMP. Whether it came from the sun or a radioactive blast, there was no way to know. But for Bea Crenshaw and her four grandchildren, it all came down to basic survival. When the EMP fries electric grids, a tremendous train wreck that releases chemical toxins begins this harrowing tale. The after-effects grow direr with each day that passes. Vehicles are rendered useless. There is no running water, no gas to cook with and no way to flush toilets. At first, Bea and her grandchildren are sure their lives will return to normal within a few days – surely government aid is on the way. However, as the days turn into months, it becomes apparent no help will arrive—EVER. Bea is more prepared than most. She's been stockpiling food and essentials for years, in a house she's kept a secret from everyone, including her husband. Continuing to keep it a secret becomes a matter of life and death. Looting takes place in every store within the first few days. As time passes, people are killed over a drink of water. Carrying arms becomes normality. The intensity builds throughout the story, as Bea and her grandchildren cope with this life-altering event. Bea's husband, Hank, and the children's parents had gone to Waco for a football game. So, the unanswered question as to what happened to them grates on frayed nerves as weeks turned into months with no return and no word. Bea is nothing short of a superhero in this book. While dealing with an illness and caring for the grandchildren, she brings the neighborhood together to work for a common goal—that of survival. Her stockpiles in the secret house save lives, that is until thugs break in and steal what they can. A grandchild dies because of no medical care. Bea never quite recovers from that blow. Then a stroke renders her helpless. This book is not a heart-warming feel-good story. It caused me some worry and sleepless nights, but I feel the message is not far off the target. Would you be able to survive in an apocalypse? This book might give you some ideas. I highly recommend it!
Silverhills is not just a story, it's a saga—a legacy.
Brandon Wade is a Texas rancher. He raises Longhorn cattle and has earned a reputation as a tough no-nonsense businessman as well as a ladies' man. He and his crew are on a cattle drive when a young boy wearing a six-shooter rides into their camp atop a wild back stallion. He's looking for work. Only Alex O'Malley isn't a boy at all. And she's desperate to keep that hidden. She's running from something that terrifies her more than rattlesnakes and scorpions. It takes a little while for Wade to realize Alex is not a boy, and he swears to protect her, although she makes it clear she can take care of herself. She has an Irish temper to match her auburn hair. She can rope, ride and shoot as well as or better than any man on the payroll. That is until she's captured by ruthless Comancheros. Wade will stop at nothing to rescue her. As much as he wants to ignore it, the feelings he's developing for Alex go beyond duty and honor. And that's just the beginning of the story. The author did a superb job of describing settings, life on a Texas ranch, and working with animals. Silverhills is the ranch, but it is so much more. It's an entire self-sufficient community. I loved all of the side characters, especially Jeff, Cookie, and Maria. The obstacles both Alex and Brandon Wade must overcome are daunting and seemingly impossible. The author did a great job of keeping Alex's secret until the last quarter of the book. But the story has more than a satisfying conclusion. From the plains of Kansas to Texas and on into Mexico, the characters cover a lot of territories. This is an action-packed nail-biting western drama with just the right touch of romance to satisfy any western romance reader!
I first heard of Michael A. Kroll when he interviewed my late husband, Rick Sikes, for a magazine article he was writing about inmates in Leavenworth Prison. So, when I saw Kroll had written a book, I grabbed it, and am I glad I did. This story goes deep into some very big social issues but does it in such a way that it is entertaining, yet while being brutally honest. The story begins with a traffic catastrophe on a bridge. Cars and people are stuck for hours. The main character, Harrison Ovitz, is an observer. He takes notice of each vehicle and person around him. Next to him is a pickup with a janitorial advertisement on the door. A black man sits in that pickup holding his phone to his ear but never speaking. When the man suddenly exits the pickup, Harrison makes eye contact with him, then locks his car door. That simple act of fear is reflected in the man's eyes as he calmly walks to the edge of the bridge and hurls himself off. That sets the story in motion. People flock to the side of the bridge to try and get a glimpse of the man, but the deep black waters have swallowed him up. Harrison looks in the pickup and finds a small dog curled up on the seat asleep next to a suicide note. Over the next few days, while taking care of the little dog, Harrison is haunted by what he witnessed, the way the man's eyes locked with his, and the horror that followed. It sends him on a mission. He is obsessed with discovering why Joshua Jeppards committed suicide. I do not want to leave any spoilers here. But I do want to express my thoughts about this story. It is well-written, as I would expect from a journalist, and it addresses some raw social issues such as sexual child abuse and racism. It also exposes an unspeakable incident that is a huge blight on American history which has all but been swept under the rug. I did not know about the tragedy that took place at Port Chicago, a Naval port in 1944. I do now, thanks to Kroll's story. If you enjoy a story that deals with real issues, the human psyche, and raw honesty, you will enjoy this book. I do highly recommend it!
This segment of Emlyn's journey is broken into two parts. We get a closer look at Haldis, The Watcher, and see her backstory. We also see that she is getting very old and tired, but her connection to the Lost Library is permanent and cannot be changed. She gives us a deeper look into the original powers and magic of the Daes Matres.
Emlyn and the Daes Matres are trapped in the Realm of the Dead and are unable to find the rip in the veil to return to the land of the living. Everything is dark and gray. The setting is creepy and energy levels are low. The group continues their search for the Lost Library and finds what only appears to be remnants of ruins long decayed. The omniscient POV the author writes in, also allows us to see through Arawan's eyes for a short minute. This gives more insight into his character. This segment ends with tension and I am eagerly looking forward to what's next.
This may be my favorite part of the story so far. When the Daes Matres finally discover the Lost Library, the author's description is stunning. I can picture the ancient walls, levels, and rows of books, rooms that appear as though they are still in use, although it's now been buried for hundreds of years. But the possession of Zasha by a former reincarnation of herself is a fascinating concept. We think of reincarnation only in terms of karmic debt or unfinished business, but Fotia fully possesses Zasha, even changing her physical appearance.
Emlyn's experience with the magic of the ancient staff is another favorite scene in this part of the story. Much is revealed about Emlyn and Osabide as well as Zasha here. Now, to see what they do with this new knowledge!
The author has a unique way of drawing the reader into the story and feeling each character's personality. I'm looking forward to the next segment.
A wonderful holiday story that leaves you feeling warm and fuzzy. Grace Donovan has moved with her six-year-old daughter, Cassie, to a new town. She is hopeful her daughter, who has Leukemia, can participate in a trial treatment program. What she hasn't bargained for is the kindhearted school principal that sets her heart racing. Widowed, Grace has not considered falling in love again.
But Cassie wants to see her mother happy and her Christmas wish is for someone to make her mother smile again. Well, and she also wants a puppy.
I loved all the characters from Avery, who quickly befriends Cassie, to Kyle the handsome school principal, and his twin brother, Keith. They are all realistic and believable.
This story has all the elements to create a wonderful holiday tale. From children to puppies, a sleigh ride, and a romance, it has it all. This is a short two-hour read and well worth the time. Jacquie Biggar is a talented writer and has the ability to draw the reader into the story with the characters. I highly recommend this story for any time of year, but especially around the holidays!
Categories Writing and Music•Tags #Apocapalyptic, #BookReviews, #ChristmasRomance, #dystopian, #Romance, #WesternRomance, Book Reviews, Brenda Marie Smith, Christmas Story, Fantasy, Jacquie Biggar, Michael A. Kroll, Racism, Sandra Cox, Sexual Child Abuse, Suicide, Teagan Geneviene
The Texans Favor – #NewRelease @dk_deters #WesternRomance @NetGalley @WildRosePress
Published on October 16, 2021 by Jan Sikes22 Comments
I received a copy of this book through NetGalley and Wild Rose Press. Opinions expressed are solely my own.
Jake Fontaine, a Texas Ranger, is hot on the trail of the vicious outlaw, Grizzly Duvall, when everything goes wrong.
Kat Collins is hellbent on escaping from her abusive uncle when she witnesses the ambush that will end the lawman's life. She makes a rash decision to fire at the attackers and her actions save him.
Now, Jake is obligated. But because she's dressed like a boy, he doesn't realize she's a woman until her hat falls off and her braid tumbles out. His Texas code of ethics won't allow him to leave a woman alone in the wilds of Kansas. Frustrated that this new turn of events causes him to lose the outlaw he is so determined to capture, he offers to accompany her to the ferry that will take her across the river to St. Louis.
Kat is strongly independent. She needs no one. She will make it to St. Louis and start a new life as a seamstress. So, when Jake insists on accompanying her, she makes it clear she does not need his help.
Thus begins a tumultuous relationship. Each struggles to deny any attraction they feel.
Things go sideways when Kat's uncle catches up to the pair and forces Jake to marry her. After all her uncle is a judge and the marriage is legal and binding. For me, this part of the story was not believable. That a man would go to all the trouble to track down his niece, then not force her to return with him seemed a little far-fetched.
But now they're married and when one night of passion brings them together, maybe they are going to work out their differences after all.
Not the case. While Jake is sleeping, Kat sneaks away, taking his horse with her.
Throughout the rest of the story, Kat is running and Jake is pursuing and each time they meet up, their relationship switches from cold to hot in seconds.
The story ramps up when Jake's grandfather goes to St. Louis to find Kat and get her out of his grandson's life forever. But instead, in five short weeks, he falls in love with the woman who has given birth to his great-granddaughter and on his dying bed, wills the ranch in Texas to her.
Now things get really complicated. Jake is betrothed to another. He has no idea he has a daughter.
He and Kat are like oil and water. I grew a little frustrated with both of them at different times during the story when they lied to each other and danced around the truth over and over.
However, the story does culminate into an action-filled shoot-out and happy ending.
If not for the frustration I felt while reading the story, and a couple of plot twists that were not believable, this would be a five-star read for me. However, I give it a four-star rating.
If you enjoy westerns, and tumultuous romances, you would enjoy this story.
Categories Writing and Music•Tags #historicalromance, #NewRelease, #Romance, #Western, #WesternRomance, D.K. Deters, Historical Romance, NetGalley, Romance, Western Romance, Wild Rose Press
May #BookReviews Part 2 – @stacitroilo @m_morganauthor @ErskineCaldwell
This is Part 2 of my May Book Reviews and I am thrilled to share my thoughts on these three books with you!
Life in the Colorado mountains isn't easy for immigrants Anita and Ottavio Notaro, particularly when they're isolated on a hillside and barely speak the language. Anita is carrying their first child, and Tav works many long, hard hours away from home. This isn't the American dream they were promised; this is a brutal life on the frontier. Tav has been saving money to make their lives easier, and he stumbles on a windfall. The only problem is, he isn't the only one who knows about it. Trouble befalls these two humble Italians, threatening their livelihoods—and their lives.
A strange posse made up of fellow countrymen ride to their rescue. But will they get there in time?
This short story sets the stage to begin the Medici Protectorate Series and after reading this introduction, I will be reading the rest of this series. The story gripped me from the first word on the first page to the last. A young Italian couple living on the rugged frontier in the Colorado mountains is struggling to survive. Ottavio and Anita Notaro have one dream and that is to return to their beloved homeland. Anita is heavy with their first child. Ottavio works hard and when he finds a treasure that will pay for their trip back home, he is overjoyed. But he isn't the only one who knows about the treasure. The tragedy that befalls Anita and Tav is heartbreaking. This story is written in rich narrative, heavily descriptive, and filled with emotion that drips off the pages. It includes folklore, history, and even a touch of mysticism. I am anxious to dive into book one of the Medici Protectorate Series to see what happens next!
Known as the Barbarian, Magnar MacAlpin is a fierce ruler for those under his command. As leader of the Wolves of Clan Sutherland, his loyalty and obedience lies with Scotland. However, the king's last demand is not something Magnar will tolerate.
After Elspeth Gunn's brother the Chieftain of Castle Steinn is murdered, she flees with her nephew, and finds safety amongst a band of men who are rumored to be part wolf. When the king forces her to wed a heathen Northman, she fears losing her heart and soul not only to the man, but the beast as well.
In order to restore peace to a shattered clan, Magnar and Elspeth travel a treacherous path that challenges their beliefs. When evil seeks to destroy ancient traditions, will Magnar be compelled to restrain his wolf or allow him free to protect those he loves?
This is the first book in the Wolves of the Clan Sutherland series. Set in Scotland in 1206, this story combines history, magic, folklore, and myth with reality. Magnar is the powerful and undisputed leader of the Sutherland Wolf Clan. All members of the clan are part man, part wolf but their power is in controlling the beast that resides within. They are fierce warriors and loyal to King William of Scotland. It would take a special kind of woman to win Magnar's heart, to love both him and the wolf, and that woman is Elspeth. When her brother, Chieftan of Steinn castle, is murdered by heathen Northmen, she escapes taking her small nephew with her. Little Erik is now Chieftan by default, at the age of 7. Starving, she steals bags from two horses, never suspecting she has stolen from the king. When she and the young chieftain are brought before King William, he offers shelter and protection. He then commissions Magnar and his clan to go and rid the castle of the marauders. But to bring peace to the clans, the King orders Magnar to marry Elspeth. What starts out as a cautious and untrusting marriage soon turns steamy. This is a fantastic story with layers of side plots, including a twin brother unknown to Magnar. The two are destined to clash. This author did a fantastic job of weaving all of the layers together seamlessly and depicting the time period perfectly. I devoured the book and am now anxious for book 2, Rorik. If you love a steamy romance from that time period in the setting of Scotland and the Orkney Islands, this book is for you! If I could give it more than five stars, I would!
Single father and poor Southern farmer Ty Ty Walden has a plan to save his farm and his family: He will tear his fields apart until he finds gold. While Ty Ty obsesses over his fool's quest, his sons and daughters search in vain for their own dreams of instant happiness—whether from money, violence, or sex. God's Little Acre is a classic dark comedy, a satire that lampoons a broken South while holding a light to the toll that poverty takes on the hopes and dreams of the poor themselves. This ebook features an illustrated biography of Erskine Caldwell including rare photos and never-before-seen documents courtesy of the Dartmouth College Library.
KINDLE PURCHASE LINK
I have always been a huge fan of Erskine Caldwell's writing and lucked out recently in finding several of his books in a half-price book store in Dallas. I bought all of them and am now rereading them. I started with "God's Little Acre." This book was first published in 1933 and there is no way on earth this book would be published in today's social climate. Erskine depicts poverty, attitudes, and social separations perfectly in this story. It opens with Ty Ty Walden digging deep holes all over his small Georgia farm. He is convinced there is gold under the ground. Two of his sons help him daily with the digging while sharecroppers make a half-hearted attempt to farm the land that isn't riddled with holes. Because Ty Ty is a god-fearing man, he has designated one acre of his farm as God's little acre with all profits realized from that acre to be donated to the church. However, when he thinks he is close to finding gold on that acre, he moves it. 🙂 Caldwell had such a distinct style of writing. The dialogue is original and true to the times and demographics of the story. Phrases such as "and that's a fact," follow many conversations. The loose morals of the women in this story are depicted in such a way that is believable but not offensive (at least to me.) As the story unfolds, there are two major plots. The first being gold fever and the second being a different life that depends on the cotton gin running to survive. When the big wigs shut down the gin to starve out the workers, Ty Ty's son-in-law takes the matter into his hands, determined to push past the guards, turn the power back on and return his people to work. It doesn't end well for him. This book could possibly be classified as a tragedy, or perhaps as a high-drama, but at best it is the work of an author who dared to blur the lines and be boldly "real." Caldwell's greatest strength is in portraying three-dimensional characters and what motivates each. He writes from multiple points of view (a no-no in today's literary world.) It is a classic no-holds-barred novel. If you have a weak stomach or strong social morals, this book is not going to be for you. But if you want to explore the writing genius of Erskine Caldwell, it's a great place to start. Interestingly enough, the story is classified on Amazon as dark humor, classic humor, and literary satire. In my opinion, none of that fits. I will be making my way through the collection that I purchased. On a final note, Caldwell died in 1987. Thank goodness the publishing houses didn't decide to keep publishing new work using a ghostwriter after his death.
Categories Writing and Music•Tags #Medieval, #MedievalRomance, #Viking, #WesternRomance, #Wolves, Dark Humor, Erskine Caldwell, God's Little Acre, Mary Morgan, Short Story, Staci Troilo, Viking Romance
May #BookReviews Part 1 – @LBroday @lisawellsauthor @1rburkey @CalebPirtle @CW_Hawes @jamesrcallan @virgilante
Published on May 21, 2021 May 20, 2021 by Jan Sikes49 Comments
I have had SUCH a great month of eclectic reading! I'm happy to share my thoughts on these books but it is going to take two posts to share them all. Please keep in mind I only share four and five star review reads.
Deacon Brannock is determined to make a name for himself and the saloon he's worked his whole life to afford. He was prepared for life in the Wild West, but he hadn't counted on Grace Legend…
Grace has always fought hard for what she believes in, and after her best friend is killed at the hands of her drunk and angry husband, that includes keeping alcohol out of her town. When the owner of the new saloon turns out to be a kind and considerate man, she can't help but wonder if they could have a future together…if they weren't on opposite sides of every issue.
I first met Grace Legend in book 2 of the Men of Legend Series. She was a baby, but a precocious one and soon had the calloused cowboys on the huge Lone Star Ranch wrapped around her little finger. In this book, she is all grown up and forging a life for herself. She's ambitious and sassy. She joins a Women's Temperance Movement and marches with other women into the notorious Hell's Half Acre in Fort Worth, known for the danger that lurks there. However, she isn't prepared for the handsome and kind owner she finds at the Three Deuces saloon. And when they smash his whiskey barrels, destroying his livelihood, things heat up. Deacon Brannock has gone through hell and back to establish his business and just when things are running smoothly, here come these women determined to destroy him. One of my favorite scenes in the book is when Grace Legend's father, the great Houston Legend, forces her to go to the saloon and clean up the mess she helped the women make. Then Houston replenishes Deacon's whiskey supply. The tension been Grace and Deacon is so thick you can't cut it with a sharp knife. It is highly unlikely that the two could ever be civil to each other, much less fall in love. This story is filled with such powerful imagery. Broday has depicted life in the rough and rowdy town of Fort Worth, Texas in the late 1880s perfectly. She uses all of the senses to bring the scenes to life. The characters are well-developed and layered, each with their own bag of secrets. If you love western romance, you are going to love this new book! I highly recommend it.
Librarian Kinley Foster wants to write erotic romance—the steamy, sexy, curl-your-toes kind of stuff. The problem? She desperately needs a little erotic inspiration. And at a romance convention in Vegas, she finds it…or rather him.
Literary agent Ian Thompson is a professional. Mentoring an aspiring author is one thing, giving her a thoroughly satisfying sexy education is quite another. Especially when she's as stunning and deliciously curvaceous as Kinley. Yet Ian can't help himself when Kinley makes him a wager he can't resist. A wager that will tempt Ian to cross every professional—and every sensual—boundary in the book…
Steamy with a Capital S!!! This was such a fun book to read and I immediately fell in love with both characters. Kinley Foster has an older brother, so grew up around all of his friends. She's had a major crush on his friend, Ian Thompson, since she can remember. But he rejected her and she's never forgotten. Now she's an aspiring author, writing steamy romance and heading to Las Vegas for a conference where she hopes to land a literary agent. To her surprise, the man she hasn't seen in ten years who picks her up at the airport is none other than Ian Thompson. He's every bit as handsome as she remembers. One debacle leads to another and she has to share a hotel suite with him. What a surprise to find that Ian Thompson is actually the acclaimed literary agent, I. Hartley. Kinley is in over her head after an indecent proposal from Thompson where he promises to teach her what she needs to know to write steamy romance. This is an off-the-charts steamy romance with a little light BDSM and a lot of hot sex with a series of missteps and mishaps. I won't leave a spoiler, but I will say I enjoyed this light read. It's a great way to escape from reality!
One photograph – A single image – A lonely boat on the edge of the sea.
Is it adrift? – Was it abandoned? – Did it wash ashore? – Was anyone aboard?
Did someone leave it behind? – Is anyone coming back? – Who knows.
The sea has washed the footprints away.
Look at the vessel and think: "If that old boat could talk, what stories it would tell."
Wonder no longer. Twelve members of Underground Authors all gazed upon the same image.
And to each, the photograph told a different story. Same boat. Same image. Different genres. From mystery and technothriller to romance and magical realism, from horror and historical fiction to fantasy and suspense with a little paranormal thrown in for good measure. These stories are presented in Beyond The Sea and are the handiwork of award-winning authors. The stories are all different as the boat had more than one secret to tell. It had a dozen.
This is a compilation of short stories from twelve different authors. Each story is unique and the twelve together cover a diverse compilation of genres. There is everything from mystery to apocalyptic to historical and suspense. While I enjoyed them all, there were a few that really stood out to me, as a reader. C.W. Hawes wrote a compelling short story that I didn't want to come to an end. His words came alive and I joined in with the characters in a hair-raising survival journey in a post-apocalyptic world. Great world-building and great writing! The Breakfield and Burkey writing duo wrote an inspiring tale about taking that proverbial leap of faith not knowing if it will end all the hopes, dreams, and goals of two ambitious young ladies. James R. Callan offers a nail-biting tale about an unexpected kidnapping and daring escape. Linda Pirtle took me on a mystery-solving journey while Kelly Marshall left me with goosebumps from her chilling tale of revenge. The theme of all of these stories is the boat you see on the cover. That is the common thread. It's so amazing to me how any group of people can view one photo and all see a different story in it. Again, while I enjoyed each story, these are just a few that stood out to me. If you are looking for entertaining diversity, this compilation of short stories is perfect as there is something for everyone! I highly recommend this book to all readers of all genres! And as a result of this book, I will be exploring other work by these authors.
Lizzie and the hat are back in action, only this time they're up against the most tragic monster of all, a werewolf.
This adventure is more like hunting an animal, and the werewolf is unlikely to come to any of their musical performances. This puts Lizzie out in the dark corners and wooded areas of the city. It may be more beneficial to get the monster to hunt Lizzie than to stalk him on his own turf. All she has to do is be quicker on the trigger than the wolf is on his feet.
At the same time, the police think they're after a serial killer. Lizzie tries to keep them alive while also keeping them out of her way. As the body count rises, so do the pressures. It doesn't help that people are blaming Lizzie and the hat for the killings. This involves an urban myth about them that the locals call Hellpox.
Pull on your boogie shoes and join the hunt. Designed as an afternoon read, this one is tons of supernatural fun.
This story, which is book 4 in The Hat series, is multi-layered. Lizzie St. Laurent and her magical sidekick, The Hat (a creature from another dimension) find themselves entrenched in a futile search for a killer. Not only a killer, but one who devours its victims, leaving behind only a few small body pieces and rivers of blood. This quickly earns him the nickname of "Sausage Maker" from the media. While Lizzie and The Hat normally hunt down vampires and ghouls, this one is different and The Hat tries to talk Lizzie out of pursuing it. The other plot unfolding in the story is police sergeant, Joe Yoder, who is grieving the death of his wife. He keeps a pomander drenched in her perfume (Emeraude) and smells it when he needs to feel her near or wants to communicate with her, which he does quite often. When he's assigned to the murder cases, he's at a loss. This doesn't seem like anything human. Yet, what else could it be? Everyone knows werewolves and vampires don't really exist, even if all of the killings do occur on the full moon. One of the things I've loved in each of The Hat books is the banter back and forth between Lizzie and The Hat. It adds a nice helping of humor to an otherwise dark story. The Hat loves surfing the internet and spending money. The Hat is also the manager for the band, Lizzie and the Pythons, where he plays the stand-up bass through Lizzie's fingers. In this book, we get a closer look at some of the other band members. Lizzie fears one of them could be the murderer. The way this book concludes, we get to see a softer more vulnerable side of Lizzie that's not been shown before. This is an entertaining read with fabulous world-building and engaging characters. I highly recommend this and the other books in The Hat series. Also, it's worth noting that you do not have to read the previous books before this one. It works well as a standalone
PART 2 OF MY MAY REVIEWS COMING UP!
Categories Writing and Music•Tags #BookReviews, #Erotica, #Fantasy, #historicalromance, #Romance, #ShortStory, #Werewolf, #WesternRomance, Book Review, Caleb Pirtle, Creature from Another Dimension, CS Boyack, CW Hawes, James Callan, Linda Broday, Lisa Wells, Rox Burkey, Short Story Collection, The Hat
#NewRelease – A Cowboy of Legend @LBroday @WesternRomance #Giveaway
Published on May 5, 2021 May 11, 2021 by Jan Sikes72 Comments
I am thrilled to announce the winner of the giveaway!!
Congratulations, Parris Afton Bonds!
You have won A Cowboy of Legend!
Thank you for having me, Jan. I'm so excited to be here talking about my new book.
Excuse me, what's Your Name?
This question wasn't asked much on the American frontier and if you were so bold, you were liable to get shot. The old West offered men (and women) a multitude of places to disappear into and leave behind whatever trouble he/she found themselves in.
No telephone. No internet. No Social Security numbers. Nothing. It was perfect.
There were probably hundreds of men back then looking to change their identities and disappear, and did. Outlaws checked into hotels and boardinghouses under an alias as did most politicians and famous people and still do today. In fact, in the 1800s it was such a common practice that, when introduced, people naturally assumed that the name was fake.
Elvis Presley used Jon Burrows when he sought anonymity. Frank Sinatra became Frankie Satin. Marilyn Monroe was Zelda Zonk.
In 1974, a singer/songwriter named Connie Converse told her family and friends that she'd had enough and was going to disappear. She packed up her Volkswagen Beetle and drove away. No one ever heard from her again despite many searches.
In my upcoming release, A Cowboy of Legend, Deacon Brannock has taken a fake name in order to disappear. All is well and good until firebrand Grace Legend marches into Hell's Half Acre with burning determination to shut down his saloon, The Three Deuces. She's a member of the Temperance Society and hellbent on running him out of business. All her life, she's taken up one cause after another but this one springs from her heart and is what she's most passionate about.
But here's the thing…Grace is also a reporter and writes a weekly column under her own alias in an attempt to hide it from her family. Like a bloodhound, she discovers that Deacon Brannock is hiding a humdinger of a juicy secret. Oh, I love it!
A Cowboy of Legend contains a lot of secrets. Writing about secrets is fun for an author. Where there are secrets there's conflict and those are what drives a story. I just love it when a book contains mysteries. I can't turn the pages fast enough.
You can find an excerpt on my webpage: https://lindabroday.com/books/lone-star-legends/a-cowboy-of-legend-1-lone-star-legends/
This is Book 1 of a new series called Lone Star Legends and released April 27th. Book 2 – A Cowboy Christmas Legend – follows in September.
My question: If you could change your identity and disappear, would you? My generation really overdid the Lindas and I've hated my name so I think I'd chose to be Sierra or maybe Summer or Sapphire. What new name would you choose if you were going to disappear?
I'm giving away an autographed copy (either print or ebook) so I wish you luck!
AMAZON BARNES & NOBLE APPLE KOBO
NY Times and USA Today Bestselling Author, Linda Broday
I'm a New York Times and USA Today bestselling author of historical western romance books and short stories. Here in the Texas Panhandle, I reside on ancient land that carries the voices of those who've gone before on the wind. If I close my eyes and get real still, I often hear them whispering stories in my ear.
My love of history and the Old West was born from watching TV westerns and visiting museums and libraries. I've always been an avid reader and books opened up entirely new exciting worlds that seemed limited only by my imagination.
Cowboys have always fascinated me and I often think I was born 150 years too late. I love writing about those men, their ladies, and the struggles they endure in trying to carve out a small place to call home. Western romance is my passion and I feel truly blessed. Humble roots and the love of family have become focal points in my stories. I sincerely hope readers enjoy what I strive to bring to life on the printed page.
I'm a mother, grandmother, and now a great grandmother. In my family, I'm the storyteller and the one who records our history. I come from a long line of poor but prideful people. That's okay. I'm happy with that. This is my legacy.
FOLLOW LINDA:
Categories Writing and Music•Tags #historicalromance, #WesternRomance, Linda Broday, Lone Star, Lone Star Legends, Sourcebooks Casablanca, Texas 1880, The Men of Legend Series, Western Romance
Once Upon A Mail Order Bride – Linda Broday #NewRelease @LBroday
Wow! I am super excited to get the opportunity to showcase my sister's latest book, "Once Upon A Mail Order Bride!" This is an amazing story. But I'll let Linda tell you about it!
Once Upon a Mail Order Bride is the fourth and final book of my Outlaw Mail Order Brides series and this makes my 30th publishing milestone. I warn readers to put their feet in the stirrups and hang on tight because this story is full of twists, turns, and surprises as Ridge and Addie fight tooth and nail for their happily ever after.
Ridge Steele is an ex-preacher weary of the outlaw life on the run and yearns for someone to share his days and nights with. He's excited when Adeline Jancy agrees to marry him sight unseen upon her release from prison.
She's as beautiful and kind as he'd dared hope for—except she can't speak a word, resorting to written communication only.
The look in her pretty eyes reveals fear that he'd send her back. Only he'd been through enough hard times to know he can't do that to her. He's in it for the long haul. But married life isn't easy. They both find it littered with one problem after another that threatens to steal their happiness and culminates in an on-the-edge-of-your-seat fight for justice…and a future glimmering ahead.
I think readers will find the story gripping. From the moment Ridge and Addie walked onto the page, I knew they were perfect for each other and that opinion never wavered. I hope you give their story a try.
"Broday concludes the Outlaw Mail Order Bride series with a sizzling finale that features a tantalizingly slow build to intimate trust that catapults into adrenaline packed ardor." ~Booklist
Accused of crimes he didn't commit, ex-preacher Ridge Steele is forced to give up everything he knew and make his home with outlaws. Desperate for someone to confide in, he strikes up correspondence with mail-order bride Adeline Jancy, finding in her the open heart he's been searching for. Upon her arrival, Ridge discovers Addie only communicates through the written word, but he knows a little of what trauma can do to a person and vows to stand by her side.
Addie is eager to start a new life with the kind ex-preacher and the little boy she's stolen away from her father―a zealot priest of a terrorized flock. As her small family settles into life at Hope's Crossing, she even begins to find the voice, and confidence, she'd lost so long ago.
But danger is not far behind, and her father will not be denied. While Addie desperately fights the man who destroyed her childhood, a determined Ridge races to the rescue. The star-crossed lovers will need more than prayers to survive this final challenge…and find their way back to each other again.
5.0 out of 5 stars Ridge and Addie will grab your heart! Reviewed in the United States on November 24, 2020
I loved everything about this story! The tough preacher turned outlaw, the woman who has endured more than anyone should ever have to, and the circumstances that bring them together are like an intricately woven blanket. These two have what seem to be insurmountable obstacles from the price on Ridge's head to Addie's inability to speak. They find ways to communicate, to heal, and to rebuild everything that is broken. If you love stories set in the old West with strong heroes and heroines, you will love this story from Linda Broday! I highly recommend it!
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Categories Writing and Music•Tags #Romance, #WesternRomance, Historical Western Romance, Linda Broday, Once Upon A Mail Order Bride, Sourcebooks Casablanca


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[Part 1] The Latest Wide-angle Zoom Technologies Canon Takes Pride in EF16-35mm f/4L IS USM & EF-S10-18mm f/4.5-5.6 IS STM
By Junichi Date- 2014-10-30 2019-08-20
In 2014, Canon has put in much effort to enhance the lineup of its interchangeable lenses, which includes the successive launch of two wide-angle lenses, the EF16-35mm f/4L IS USM and the EF-S10-18mm f/4.5-5.6 IS STM. In this article, I will go to the core of the technologies found on the latest lenses, which have a different focal length and maximum aperture value from other existing lenses.(Reported by: Junichi Date)
Photos (left to right)
Shota Shimada: ICP Group 1, Image Communication Products Operations, CANON INC./ Kunihiko Sasaki: ICP Development Center 1, Image Communication Products Operations, CANON INC./ Shunji Iwamoto: ICP Development Center 1, Image Communication Products Operations, CANON INC./ Makoto Nakahara: ICP Development Center 1,Image Communication Products Operations, CANON INC./ Masayasu Mizushima: Camera Development Center/ Masami Sugimori, ICP Development Center 1, Image Communication Products Operations, CANON INC.
Peripheral Image Quality Improved With 2 Aspherical Lens Elements
― First of all, can you describe the background that led to the release of the EF16-35mm f/4L IS USM?
Shimada It has been more than a decade since the EF17-40mm f/4L USM was released. During this period, the pixel count of cameras has increased significantly, and there are growing calls for lenses with a higher level of reproduction power. In particular, severe feedback has been received from Canon's customers regarding astigmatism that is found at the peripheral areas of the image. In response to these voices, we have strived to achieve a high level of optical performance that would meet the demand of users ranging from advanced amateurs to professionals when we developed the EF16-35mm f/4L IS USM, with emphasis placed on enhancing the peripheral image quality. Also, it is the first ultra wide-angle EF lens to be equipped with the IS (Image Stabilizer) feature. The aim of this feature is to help broaden the scope of expression, such as by enabling handheld shooting without the use of a tripod for dimly-lit scenes indoors, in the morning, or at dusk.
― One of the characteristics of the EF16-35mm f/4L IS USM is the "clear image quality up to the four corners of the image". What are the differences compared to other existing ultra wide-angle lenses? When I compare it with the lens construction of the EF16-35mm f/2.8L II USM, they do not seem very different except for the addition of the IS feature to the optical system.
Iwamoto Both the EF16-35mm f/2.8L II USM and the EF16-35mm f/4L IS USM employ two aspherical lens elements in the first group, but those used for the EF16-35mm f/4L IS USM are aspherical on both sides of the lens. To further improve the peripheral image quality, we have optimised the shape and material of these two aspherical lens elements.
― What are the key points for enhancing the peripheral image quality?
Iwamoto In the design of wide-angle lenses, it has remained a longstanding challenge trying to correct distortions while maintaining the focal plane flatness at the same time, which are two contradictory properties. For example, reducing distortions alone would lead to the loss of focal plane flatness. On the contrary, seeking focal plane flatness by minimising field curvature tends to result in larger distortions. To address this challenge, the material and shape of the two double-sided aspherical lens elements are optimised on the EF16-35mm f/4L IS USM to enable both focal plane flatness and the correction of distortions at a high level. Additionally, chromatic aberrations of magnification are improved with the introduction of two UD lens elements and the latest optical design.
UD Lens
UD lenses are capable of reducing chromatic aberrations. Two UD lens elements are used on the EF16-35mm f/4L IS USM to help effectively minimise chromatic aberrations of magnification around the peripheral areas of the image.
― Are there any existing lenses that also make use of double-sided aspherical lens elements?
Iwamoto The EF16-35mm f/4L IS USM employs two double-sided aspherical lens elements in the first group, one of which has a large diameter. It is the first time for us to adopt a double-sided aspherical lens with such a large diameter. Our success in establishing the technology necessary for the precise production of such a lens has helped to enhance the design performance of the EF16-35mm f/4L IS USM by a large extent.
Shimada Besides the EF16-35mm f/4L IS USM, the EF-S10-18mm f/4.5-5.6 IS STM has also contributed significantly to the advancement of our production technology. If we had come up with this design a few years earlier, we wouldn't have been able to create a lens with the same level of performance. Breakthroughs in both the optical design and production technology have led to the birth of the EF16-35mm f/4L IS USM and the EF-S 10-18mm f/4.5-5.6 IS STM.
― Between the EF16-35mm f/2.8L USM and the EF16-35mm f/4L IS USM, which is higher in image quality? Of course, the result may vary when the aperture is opened up fully and when it is stopped down.
Iwamoto The maximum aperture of the two lenses is not the same (f/2.8 and f/4), so it would be difficult to make a simple comparison. For example, if we take a shot with the aperture stopped down to f/8, the image quality of the EF16-35mm f/4L IS USM is higher because it is equipped with the latest optical technology. That being said, the f/2.8 lens is capable of expression with a shallow depth of field that is only achievable at the maximum aperture of f/2.8.
― The reproduction power of the EF16-35mm f/2.8L II USM is also excellent up to the area covered by the APS-H format sensor, but the image quality deteriorates markedly at the peripheral area. If we look at the MTF chart, the lines for the EF16-35mm f/2.8L USM are "wiggly" from the centre to the periphery. In contrast, the characteristics of the EF16-35mm f/4L IS USM are extremely straightforward, which decrease monotonically as it gets closer to the peripheral area. What is the reason for such a difference in the optical characteristics?
Iwamoto Generally speaking, the rippling MTF curve can, in many cases, be attributed to the curvature in the position where focus is achieved (focal plane). With the flatness of the focal plane improved on the EF16-35mm f/4L IS USM, the lines from the centre to the periphery become straighter and more gradual.
― The sagittal and meridional lines on the MTF chart are seen to diverge as it approaches the peripheral area. What type of aberration causes this to occur?
Iwamoto Generally, this is largely attributable to astigmatism. Astigmatism is a type of aberration due to differences in the position where image is formed in the sagittal and meridional directions. Divergence between the two lines increases when this difference is larger. The design of the EF16-35mm f/4L IS USM aims to minimise not just field curvature, but also astigmatism, so the divergence between the sagittal and meridional lines is relatively smaller.
― It would be difficult simply to maintain the peripheral image quality on an ultra wide-angle lens. Unless the image circle is sufficiently large, wouldn't correction by the IS feature cause the image quality in the peripheral area to deteriorate?
Iwamoto To prevent the image quality from deteriorating when correction is performed by the IS feature, we have optimised the lens construction and achieved a design that delivers a sufficiently high level of optical performance.
Lens Construction: EF16-35mm f/4L IS USM
Blue: Aspherical lens
Green: UD lens
Red: IS unit
Two double-sided aspherical lens elements are positioned in the front group to help improve the image quality in the peripheral area of the image.
Comparison of MTF Curve
EF16-35mm f/4L IS USM
EF16-35mm f/2.8L II USM
Spatial Frequency Max. Aperture f/8
S M S M
10 Lines/mm
The lines of the MTF curve for the EF16-35mm f/2.8L II USM are "wiggly". The resolution performance of 30 lines/mm is also comparatively low, and deteriorates markedly at the peripheral area. Meanwhile, the EF16-35mm f/4L IS USM maintains a high level of contrast and resolution up to the edges.
Optimising the Lens Layout For a More Compact IS Lens Body
― If the IS were not included in the design, would the lens be lighter and more compact?
Iwamoto Of course, without the IS unit, it is possible to come up with a smaller and lighter design. For this lens, we have adopted a lens layout that helps to prevent the body from becoming overly large due to the IS unit.
Sasaki The IS unit on the EF16-35mm f/4L IS USM has a compact size that is optimally designed for this lens. Although the overall length of the lens may be shorter if we had omitted the IS, the weight does not become considerably lighter, so I believe there are more advantages if we introduce the IS unit. We have also modified the shape of the hood for a more compact feel when it is attached to the lens.
― When I first held the EF16-35mm f/4L IS USM in my hands, I thought it was really light, but it is slightly heavier compared to the EF17-40mm f/4L USM. I suppose it feels lighter than its appearance, which is larger with a longer body. By the way, what is fluorine coating and what effects does it have?
Iwamoto The coating is water- and oil-repellent, which prevents dust from settling on it. Even when dust is attached to the surface, it can be wiped off easily. Lately, fluorine coating has become a standard feature on L lenses.
Size and Weight of 3 Wide-angle EF Lenses
The EF16-35mm f/4L IS USM is longer than the EF17-40mm f/4L USM in total length, and close to the size and weight of the EF16-35mm f/2.8L II USM.
― If the lens protect filter is not attached, will there be a higher risk of dirt and dust entering the lens during day-to-day use?
Sasaki For day-to-day use, there is no worry that dust or water droplets would enter the lens even if you do not attach the lens protect filter. However, due to its structure, dust or water droplets may be drawn into the lens unintentionally at the far end of the filter screw when the front lens moves forward or backward during zooming. To effectively protect the lens against dust and moisture in this case, it is recommended that you attach a lens protect filter.
― If a small amount of raindrops accumulate on the inner side of the lens tube when the camera is positioned almost horizontally, can I zoom the lens as usual?
Sasaki Of course, a small amount will not be an issue.
― Wouldn't it be possible to maintain a dust- and water-resistant structure even when the front lens moves, or adopt an optical system with the front lens remaining still?
Iwamoto In optical design terminology, many wide-angle zoom lenses select an optical system with the first group playing the role of a concave lens, and the first lens group is movable in most of the cases. If we adopt the inner zoom type, where the position of the front lens is fixed, the overall length of the lens would be longer and the diameter larger.
Front lens movable inside the lens tube
The front lens moves inside the lens tube, and the length of the lens remains unchanged during zooming. To ensure sufficient dust- and water-resistance in this case, the use of a protection filter is recommended.
― Instead of a structure with the lens moving inside the lens tube, wouldn't it help to eliminate the worry of water accumulating if the lens were able to extend out in the same way as conventional lenses?
Sasaki There are some users who prefer the front lens to remain still without the lens extending out or retracting. For the EF16-35mm f/4L IS USM, the lens tube is shortest not at the wide-angle end, but at the mid-telephoto zoom range. After taking into consideration the focal length at which the lens tube is shortest when retracted, and also the hassle during zooming, we decided that this design was the most well-balanced, since it would be easier to use and more robust if the lens tube does not extend out during zooming while the front lens moves inside the lens tube.
― I see. For an ultra wide-angle lens, the front lens is large and heavy, so instead of having the lens tube and the front lens extend out, the lens is able to better withstand external shock and hardly rattles due to wear and tear, am I right?
Sasaki Yes, exactly. In particular, the first group of an ultra wide-angle lens plays a very crucial role, so maintaining its precision is also the key to maximising the image quality according to the design value. Also, we paid meticulous attention to the slightest wobble in the focusing lenses, and made improvements to the mechanism for maintaining the optical system so as to achieve a stable level of optical performance. In addition, we were also mindful to enhance the position detection accuracy of the focusing lenses. While all these might sound very dull, it is the gradual enhancement in the precision through such accumulated efforts and revisions that lead to the overall improvement in the image quality.
Iwamoto We were also committed to maintaining the high level of optical performance we have achieved without any variation during mass production. Regardless of how excellent the design performance is, it would be meaningless if the lens is unable to deliver the inherent level of performance due to manufacturing errors. By working together with the production team to address the issue of how we can introduce the highest possible level of design performance into our products, we were able to maximise the performance of the EF16-35mm f/4L IS USM.
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Nauvoo, Illinois Temple
Nauvoo, Illinois Temple quantity
Nauvoo, Illinois, USA Temple
Originally dedicated privately by Orson Hyde and Joseph Young on April 30, 1846, it was publicly dedicated on May 1-3, 1846 by Orson Hyde. The Nauvoo temple became the first temple where baptisms for the dead were performed. Two years later, after the Saints had been forced to abandon it, an arsonist burned the interior of the building. In 1850 tornado category winds knocked down what remained of the exterior walls and by 1865 the building was no more; the stones having been scavenged for other buildings. April 4, 1999 it was announced that the Nauvoo Temple would be rebuilt. Dedicated June 27, 2002 this temple stands as a strong reminder that no matter how tough things get, no matter how beaten down we may become, through the power of the atonement we can be cleansed and renewed, being restored and becoming "Nauvoo", the Hebrew word for beautiful place, ourselves.
Anchorage, Alaska Temple
Bountiful, Utah Temple


text:
\section{Introduction}

The inclusion of a strong internal magnetic field can substantially affect the structure and mass-radius relation of white dwarfs and raise their limiting mass. Such Super-Chandrasekhar mass white dwarfs could be possible progenitors of over-luminous type-Ia supernovae \citep{howel06,hicken_07,yamanaka_09, Scalzo+2010, Tanaka+2010, Silverman+2011, Taubenberger+2011}. Several publications in the recent literature have addressed different aspects of this issue: for example, the effects of magnetic field on the equation of state \citep{das_m12, Paret+15, Zou+Meng15, Mukhopadhyay+2015}, Lorentz force and instability \citep{nitya14, Coelho+14}, possibility of electron capture \citep{chame13, chamel_14, Vishal+Mukhopadhyay2014} and total lepton number violation \citep{belyaev15}. In an earlier work (hereafter P1, \cite{bera_b14}) we have presented the mass-radius relation of strongly magnetized white dwarfs with self consistent inclusion of Lorentz force. In this work, the gravitational field was treated in a
Newtonian framework. Subsequently, \cite{das_m15} have pointed out that the inclusion of general relativistic (GR) effects may substantially reduce the upper mass limit. Here we revisit our earlier work with GR treatment of gravity and find that the reduction in the upper mass limit is at most $\sim$ 2.2\%.

Another important factor that affects the mass-radius relation of the white dwarfs is the equation of state (EoS) of the constituent material. In P1 we have used a pure Fermi degenerate electron EoS to describe the pressure density relation. However, as shown by \cite{salpeter61}, many body effects can have a significant effect on the EoS. In this work, we also explore the effects of many body corrections to the EoS on the mass-radius relation of magnetic white dwarfs. We find that for a white dwarf composed of carbon, this leads to a further reduction in the mass limit by about 2\%.

While the above discussion pertains to a purely poloidal configuration of the magnetic field, in reality the field configuration can be more complex. We have therefore also explored configurations with purely toroidal as well as mixed toroidal and poloidal fields. Our results in these cases show that the mass limit of equilibrium configurations could be substantially higher than that for pure poloidal configuration. While such a trend has been reported also by \cite{das_m15}, masses obtained by us lie well above the limits quoted by them.

In our work, we impose a constraint that the maximum of the mass density should occur at the center of the star. Recent work by \cite{Franzon+Schramm2015}, relaxing this assumption, finds that even higher mass equilibria may be obtained in a doughnut-shaped density distribution within the stellar interior.

In general, a white dwarf may possess fast rotation and this may affect its structure. However, we do not include the effects of rotation in the present work. The results presented here pertain to non-rotating white dwarfs with axisymmetric magnetic field distribution.

    The paper is structured as follows. In Section \ref{sol_method} we present in brief the method of solving the stellar structure equations and describe the equation of state (EoS) used by us. The results for different field configurations are presented in Section \ref{results}. Our conclusions are summarized in Section \ref{conclusions}.

\section {Equilibrium configurations with axisymmetric magnetic field} \label{sol_method}

To solve for the equilibrium configuration we use the spherical polar coordinates ($r$, $\theta$, $\phi$) with origin at the stellar center and the pole located along the axis of symmetry. We assume that the material has infinite conductivity, satisfying the ideal MHD condition with no electric field. The general approach we have followed to solve the stellar structure is modeled on the so-called ``Self Consistent Field method'' for both Newtonian and GR cases. These methods are briefly described in the subsections below. Further details on these methods may be found in \cite{hachi86, tomim05, lande09, bera_b14, bonazzola93, bocquet95, pili14}. To obtain the solution in Newtonian gravity, we use our earlier code \citep{bera_b14}, whereas we use publicly available codes $XNS$ \citep{Bucciantini11, pili14} and $Lorene$ \footnote{http://www.lorene.obspm.fr/} to obtain GR configurations. The XNS code finds self-consistently the axisymmetric equilibrium solution of the relativistic compact star with rotation and
magnetic field assuming approximate gravity with a conformally flat
condition (CFC) in GR 3+1 formalism. This code, capable of handling polytropic EoS, has been used to generate equilibrium structure of magnetized neutron stars with different field geometry \citep{pili14, pili15, bucciantini15}. It has also been used to study white dwarf configurations by approximating the Fermi degenerate EoS as a polytrope  \citep{das_m15, Subramanian+Mukhopadhyay2015}. We have modified the XNS code to use the full form of electron degenerate equation of state, thus avoiding the polytropic approximation. To obtain magnetized white dwarf configurations in full general relativistic gravity we use the {\em magstar} module of the spectral code {\em Lorene} which iteratively solves for the axisymmetric stellar configuration in 3+1 formalism. The output of {\em magstar} have been widely used to study stellar configurations and as input to the study of the evolution of poloidal fields \citep{liebling+10, gabler+12, gabler+13, haskell+14}. The advantage of using {\em magstar} is that it uses GRV2
and GRV3 to test the accuracy of
the result. GRV2 and GRV3 are similar to the virial condition in general relativity in 2d and 3d respectively \citep{bonazzola94, gourgoulhon94}.

\subsection{Newtonian Calculation}

In the presence of a magnetic field, there will be effects of Lorentz force on the stellar structure. In the Newtonian limit the stellar structure equations are
\begin{align}\label{hydro_eui}
\frac{1}{\rho}\mathbf{\nabla} P &=-\mathbf{\nabla} \Phi_g+\frac{1}{\rho}\left( \mathbf{j}\boldsymbol\times\mathbf{B}\right) \\
\mathbf{\nabla}^2\Phi_g &= 4\pi G \rho
\end{align}
\\where $P$, $\rho$, $\Phi_g$, $\mathbf{j}$ and $\mathbf{B}$ are pressure, mass density, gravitational potential, current density and  magnetic field respectively. In the ideal MHD condition, the magnetic field satisfies the following Maxwell's equations.
\begin{align}
 \nabla \cdot \mathbf{B} &= 0,  \\
 \nabla \times \mathbf{B} &= \mu_0 \mathbf{j} .
 \label{maxwell}
\end{align}
where $\mu_0$ is the free space permeability.

In axisymmetry, the set of equations ($\ref{hydro_eui}-\ref{maxwell}$) can be transformed, for Fermi degenerate EoS, to the following integral form using the Hachisu Self-Consistent-Field technique \citep{hachi86, tomim05, lande09}.

\begin{align}\label{intro_c}
 \dfrac{1}{\mu_{\rm e} m_{\rm B}} E_{\rm F} +\Phi_{\rm g} &=\mathcal M+C,
\end{align}
where $\mu_{\rm e}$ is the mean molecular weight per electron, $m_{\rm B}$ is the baryon mass, $E_{\rm F}$ is the Fermi energy, $\mathcal M$ is the function which expresses the magnetic influence on the structure and $C$ is a constant of integration. The functional form of $\mathcal M$ can be adjusted to give poloidal, toroidal or mixed field configurations. Equation ($\ref{intro_c}$) is used repeatedly at the grid points, along with proper boundary conditions, to converge on the stellar configuration iteratively.

For the poloidal and the mixed field geometry in axisymmetry, $\mathcal M$ is a function of the flux-function $u=r\sin\theta A_\phi$ where $A_\phi$ is the $\phi$ component of the magnetic vector potential. For simplicity, we assign to $\mathcal M$ a functional form proportional to $u$.
\begin{align}
 \mathcal M &= \rm{const.}\times \it{u},\\
 \mathbf B &=\frac{1}{r\sin\theta}\left( \boldsymbol\nabla u\boldsymbol\times \boldsymbol{\hat\phi}\right)+B_{\phi}\boldsymbol{\hat\phi}. \label{pol_B}
\end{align}
The $\phi$-component of the field $B_\phi$ is related to an arbitrary function of $u$: $B_\phi=f(u)/r\sin\theta$. Whereas for pure toroidal field $\mathcal M$ and $B_\phi$ are functions of $\rho r^2\sin^2\theta$, and these may be written as
\begin{align}
 \mathcal M &= -\frac{mK_m^2}{2m-1}(\rho r^2\sin^2\theta)^{2m-1}, \\
 B_\phi &= K_m\frac{(\rho r^2\sin^2\theta)^m}{r\sin\theta}, 	\label{tor_B}
\end{align}
here the index $m\geq 1$ and $K_m$ is a constant.

A stationary solution of the equilibrium structure is expected to satisfy the stellar virial condition, expressed as
\begin{equation}
 3\Pi+W+\mathscr{M}=0
\label{virial}
\end{equation}
\noindent
$$\text{here}\hspace{5mm}\Pi:\text{ contribution of internal energy}=\int PdV;$$ $$W:\text{ gravitational potential energy}=\frac{1}{2}\int\rho \Phi_{\rm g}dV;\hspace{2mm}$$\\and $$\mathscr{M}:\text{ magnetic energy}=\int\frac{B^2}{2\mu_0} dV; $$\\
where $V$ is the space volume.

The stellar configuration obtained from the self consistent field calculation is tested for the virial condition, the deviation being expressed in a non-dimensional form,
\begin{equation}
\vert VC \vert=\frac{\vert 3\Pi+W+\mathscr{M}\vert}{\vert W\vert}.
\end{equation}
The solution is said to converge when the relative change of the configuration parameters fall below a pre-set limit. In all the configurations presented by us, the values of $\vert VC \vert$ are $\sim 10^{-5}$.
\subsection{General Relativistic Calculation}

To obtain the stellar configuration in the general relativistic case it is required to solve the Einstein equation
\begin{align}
R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = \frac{8\pi G}{c^4} T_{\mu\nu}.
\end{align}
Here, the stress-energy tensor $T_{\mu\nu}$ contains matter and electromagnetic source terms
\begin{align}
T^{\mu \nu} = (e+P)u^\mu u^\nu + Pg^{\mu \nu} + \frac{1}{\mu_0}\left[F^{\mu\gamma}F^\nu_\gamma-\frac{1}{4}g^{\mu\nu}F_{\gamma\delta}F^{\gamma\delta}\right],
\end{align}
where $e$ is the total energy density, $\mathbf{u}$ is the fluid 4-velocity and $\mathbf{F}$ is the electromagnetic field tensor, which can be expressed using the potential 1-form $\mathbf{A}$ as:
\begin{align}
 F_{\mu\nu} = A_{\nu,\mu}-A_{\mu,\nu}.
\end{align}

$R_{\mu\nu}$ and $R$ are the Ricci tensor and Ricci scalar respectively. The metric tensor components $g_{\mu\nu}$ are used to express the line element as
\begin{align}
ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu}.
\end{align}
Following 3+1 formalism in axisymmetry the metric tensor can be expressed in spherical like coordinates $(t, r, \theta, \phi)$ as
\begin{align}
g_{\mu\nu}&dx^{\mu}dx^{\nu} = - N^2 dt^2 \notag\\
&+ A^4\left[B^2r^2\sin^2\theta(d\phi-N^\phi dt)^2 + \frac{1}{B^2}(dr^2+r^2d\theta^2)\right],
\label{Lorene_metric}
\end{align}
where $N (= e^\alpha)$, $N^\phi$, $A$ and $B$ are functions of ($r, \theta$) \citep{bocquet95}.

If the non-sphericity of the configuration is small, then the metric may be further assumed to be conformally flat in spatial dimension and the above expression approximated as \citep{pili14},
\begin{align}
g_{\mu\nu}dx^{\mu}dx^{\nu} &= - N^2 dt^2 \notag\\
&+ A^4\left[dr^2+r^2d\theta^2 + r^2\sin^2\theta(d\phi-N^\phi dt)^2\right].
\label{XNS_metric}
\end{align}

The projection of the energy-momentum conservation equation $T^{\mu \nu}_{~~;\mu}=0$ on time hyper-surfaces gives a 3-vector equation for the matter momentum density. The equation of stationary motion for perfect fluid with pure poloidal field can be expressed as:
\begin{align}
\frac{1}{e+P}\frac{\partial P}{\partial x^i} + \frac{\partial \alpha}{\partial x^i} = \frac{1}{e+P} j^\phi \frac{\partial A_\phi}{\partial x^i}
\label{GR_euler}
\end{align}
equation ($\ref{GR_euler}$) can be integrated to obtain an expression similar to that in equation ($\ref{intro_c}$),
\begin{align}
H + \alpha = \mathcal  M + \rm{const.}
\label{GR_C}
\end{align}
Here, $H$ is the heat function defined in terms of baryon number density $n$ as,
\begin{align}
H(n) = \int_0^n \frac{1}{e(n_1)+P(n_1)}\frac{dP}{dn}(n_1)dn_1.
\end{align}
where $e$ is the internal energy density.
Here too the functional form of $\mathcal  M$ decides the field configuration.

Equation (\ref{GR_C}) is used by the XNS and Lorene codes to find the stellar configuration. XNS uses the approximate line element form expressed in equation (\ref{XNS_metric}) whereas the full line element form of equation (\ref{Lorene_metric}) is used by the Lorene $magstar$ code. XNS has been designed to give solutions for poloidal, toroidal and mixed field conditions but $magstar$ handles only a pure poloidal field geometry. Pure toroidal configurations using the full metric of equation (\ref{Lorene_metric}) can be similarly obtained \citep{Kiuchi+Yoshida2008, Frieben+Rezzolla2012}, but we have not attempted this in the present work. The functional form of the magnetic term $\mathcal  M$ required to model a pure poloidal or a pure toroidal field is similar to that mentioned in the Newtonian case.

\subsection {Equation of State (EoS)}
White dwarfs are dense objects and their interior temperature is small compared to the Fermi temperature ($T_F$) of electrons. So the EoS is very similar to that of a zero temperature Fermi electron gas, of which the relation between the baryon density ($\rho$) and pressure ($P$) may be expressed as follows:
\begin{align}
n_{\rm e} &=  \frac{1}{3\pi^2\lambda_{\rm e}^3}x_{\rm F}^3\\
\rho &=\mu_{\rm e} m_{\rm B}n_{\rm e}	\\
e &= \frac{\pi m_e^4c^5}{h^3}\left[ x_{\rm F}(1+2x_{\rm F}^2)\sqrt{1+x_{\rm F}^2}-\sinh^{-1}x_{\rm F}\right] \\
P &=\frac{\pi m_e^4c^5}{3h^3}\left[ x_{\rm F}(2x_{\rm F}^2-3)\sqrt{1+x_{\rm F}^2}+3\sinh^{-1}x_{\rm F}\right].
\end{align}
Here, $n_{\rm e}$ is the electron number density, $\lambda_{\rm e}=\frac{\hbar}{m_{\rm e}c}$, $x_{\rm F}=\frac{p_{\rm F}}{m_{\rm e}c}$, $p_{\rm F}$ being the Fermi momentum, $e$ is the internal energy density, $h$ is the Plank constant, $\hbar$ = $h/2\pi$ and $c$ is the speed of light.

Corrections to the above equation of state may arise from a number of effects. Coulomb interaction in the ion lattice is one source of such corrections. \cite{salpeter61} considered corrections to the pressure and energy expressions from i) Coulomb energy due to ion lattice, ii) Thomas-Fermi effect due to non-uniform charge distribution, iii) spin-spin interaction and exchange energy between electrons and iv) correlation energy term. At very high densities the electron Fermi energy becomes high enough to enable neutronisation to occur via inverse beta decay. The
Neutronisation Threshold for He and C are 20.596 and 13.37 MeV respectively \citep{shapi83}. Beyond this the configuration becomes unstable. \cite{hamada_sol61} have presented the mass radius relation of non-magnetic white dwarfs, including these corrections. We investigate in this work the effect of these same corrections on the mass-radius relation of strongly magnetized white dwarfs. The relativistic Feynman-Metropolis-Teller EoS \citep{rotondo+11} is an improvement over the Salpeter one, but yields corrections very similar to the Salpeter EoS.

The strong magnetic field may itself modify the equation of state of white dwarf matter by trapping electrons in quantized Landau levels. The effects of this are most severe when electrons inhabit only the lowest Landau levels. However, the condition in a realistic stellar configuration always distributes electrons over several tens of levels, minimizing such impact \citep{bera_b14}. Strong internal magnetic fields may affect the many-body interactions and modify the Salpeter corrections, however, we have not included the effect of Landau quantization and magnetic modifications of the many-body interactions in the work presented here.

\section{Results}\label{results}
In the following sections, we present the results obtained using the methods outlined in the previous section. Initially different magnetic field configurations from the Newtonian calculation are constructed and then we compare pure poloidal and toroidal field configurations with their GR results. Next we present the effects of inclusion of the ion interactions in the EoS for poloidal field configurations, in general relativistic gravity. We use the baryon mass to represent the mass of the configuration and adopt a value of $1.9885\times10^{30}$ kg for the solar mass unit (M$_\odot$). In all GR configurations, explored by us, the gravitational mass differs from its baryon mass by less than $10^{-3}$. In representing the mass-radius relation of non-spherical configurations, we use either the polar or the equatorial radius, whichever is larger.

\subsection {Magnetic configurations for different field geometry : Newtonian calculation}

\subsubsection{Poloidal field}
In our calculations, the poloidal field is specified through a current distribution which is purely toroidal. The functional form of the toroidal current distribution is expressed  as $J_\phi = r\sin\theta \rho \alpha_0$. The parameter $\alpha_0$ describes the strength of the current. An example of a resulting configuration is shown in Fig. \ref{poloidal_den}. This object has a central density $2\times10^{13}\rm{kg.m^{-3}}$ and a central field strength 59.6$\times10^9$ T. The Newtonian calculation gives a mass of 1.896 M$_\odot$ and a radius of 875.3 km for this object. A star with such a strong poloidal field has an oblate shape. The ratio of polar to equatorial radius in this case is about 0.68 and the ratio of magnetic to gravitational energy is about 13\%. Near the equatorial plane in deep interior of the star the Lorentz force rises to become almost equal and opposite to the gravitational force. However the plasma beta remains high throughout most of the stellar configuration.

\begin{table*}
 \begin{tabular}{c|c|c|c}
  \hline
    \bf        		&	\bf{SCF}		&	\bf{XNS}		&	\bf{Lorene}	\\
  \hline \hline
	\bf CONDITIONS	&				&			&\\

	grid 		&	512$\times$512		&	 \begin{tabular}[c]{@{}c@{}} NR = 500, NTH = 100\\($R_{max}=2500$)\end{tabular}	&	\begin{tabular}[c]{@{}c@{}} nr = 129 (inside star) nt = 65\\ nr = 65  (outside star) nt = 65\end{tabular}	\\

	$\rho_c$	&	2$\times10^{13}$ kg.m$^{-3}$&	2$\times10^{13}$ kg.m$^{-3}$&	2$\times10^{13}$ kg.m$^{-3}$	\\
	Field parameter	&	$B_{core}$ = 59.621 GT	&	$k_{pol}$ = 0.01164, $\xi$ = 0	&	CFA = 950 \\
	\hline

	\bf   RESULTS	&				&\\
	Mass (M$_\odot$)&	1.8965			&  	1.8557  	 	&  	1.8540		\\
	R$_{eq}$ (KM)	&	875.26			&  	860.16	  		&  	865.95		\\
	R$_p$/R$_{eq}$	&	0.6758			&	0.6738			&	0.6767		\\
	B$_{max}$ (GT)	&	59.621 			&	59.893			&	59.621		\\
	$|\mathcal{M}/W|$	&	0.1288		&	0.1305			& 	0.1276		\\
	Virial test	&	$\mid$VC$\mid$ = 7.84$\times10^{-6}$	&	-			&	\begin{tabular}[c]{@{}c@{}} $\mid$GRV2$\mid$ = 2.98$\times10^{-8}$\\ $\mid$GRV3$\mid$ = 1.56$\times10^{-8}$\end{tabular}	\\
  \hline
 \end{tabular}
\caption{Pure poloidal field configurations from Newtonian SCF calculation and from GR codes XNS and Lorene.}
\label{poloidal_XNS_Lorene_SCF}
\end{table*}

For a given central density and field geometry, a higher field strength leads to a larger mass of the equilibrium configuration. The mass-radius relation of strongly magnetized white dwarfs is thus dependent on the field parameters (as shown in Fig. 4. of P1 or Fig. $\ref{poloidal}$). Here we have used the central field strength or the ratio of magnetic field energy to gravitational energy to represent the field parameter. For a fixed central field strength, as the central density is reduced the magnetic energy becomes more dominant, causing the mass-radius relation to deviate strongly from that of non-magnetic configurations. We present here solutions in which the component of Lorentz force just opposite to gravity never exceeds in magnitude the gravitational force itself. Violation of this would move the density maximum away from the stellar centre, as shown by \cite{Franzon+Schramm2015}.
\begin{figure*}
\centering
\includegraphics[width=0.95\textwidth]{poloidal_XNS_Lorene.pdf}
\includegraphics[width=0.65\textwidth]{poloidal_SCF_fm_fg.pdf}
\caption{The distribution of mass density and magnetic field strength inside a white dwarf configuration with a strong poloidal field from the Newtonian SCF calculation. The stellar outer boundary is indicated by a thick line. \textbf{A.} The density distribution shows an oblate structure, \textbf{B.} The radial profile of mass density along polar and equatorial directions, \textbf{C.} The 2-d poloidal field distribution, \textbf{D.} The radial distribution of magnetic field strength along polar and equatorial directions. \textbf{E.} The Lorentz force component along the gravitational force, the dashed white contour marking the region where the Lorentz force is 90\% in magnitude of the gravitational force, and opposite in direction. \textbf{F.} The distribution of plasma beta, the ratio of matter pressure to magnetic pressure in this configuration, the dotted contour indicating the value of 0.5. Plasma beta is seen to be high through most of the interior. }
\label{poloidal_den}
\end{figure*}
\subsubsection{Toroidal field}

A star with a pure toroidal field ($\mathbf{B} = B_\phi\hat\phi$) is prolate and the field is fully confined within the star with zero surface field strength \citep{fujisawa+eriguchi15}. We model such a magnetic field distribution by setting $m=1$ in equation ($\ref{tor_B}$), i.e. $B_\phi=K_m r \sin\theta\rho$, where $K_m$ is a constant. Pure toroidal field configurations have zero field at the center and along the axis of symmetry. Therefore in this case we use the total magnetic energy as the representative magnetic field parameter. A typical stellar configuration arising from such a field distribution is shown in Fig. $\ref{toroidal_2d}$. In this example the central density is 2$\times10^{13}$ kg.m$^{-3}$ and the ratio of magnetic energy to gravitational energy ($|\mathcal{M}/W|$) is about 39\%.
\begin{table*}
 \begin{tabular}{c|c|c}
  \hline
  \bf        		&	\bf{SCF}			&	\bf{XNS}	\\
  \hline \hline
	\bf CONDITIONS	&					&			\\
		grid	&	 1024$\times$1024		&	\begin{tabular}[c]{@{}c@{}}NR = 1000, NTH = 250\\ ($R_{max}=10000$)\end{tabular}\\
		$\rho_c$&	2$\times10^{13}$ kg.m$^{-3}$	&	2$\times10^{13}$ kg.m$^{-3}$	\\
	Field parameter	&	$|\mathcal{M}/W|$ = 0.3928, m = 1		&	$K_m$ = 7, m = 1\\
	\hline
	\bf   RESULTS	&\\
	Mass (M$_\odot$)&  	5.1611  	 		&  	4.9490	\\
	R$_{eq}$ (KM)	&	7854.6 		  		&	7774.6	\\
	R$_{p}$/R$_{eq}$&	1.1441				&	1.1386		\\
	$|\mathcal{M}/W|$	&	0.3928			&  	0.3928	\\
	virial condition&	$\mid$VC$\mid$ = $6.27\times10^{-5}$	&	-	\\
  \hline
 \end{tabular}
\caption{Pure toroidal field configurations from SCF Newtonian calculation and from XNS code.}\label{toroidal_XNS_SCF}
\end{table*}

\begin{figure*}
\centering
\includegraphics[width=0.95\textwidth]{toroidal_XNS_SCF.pdf}
\includegraphics[width=0.65\textwidth]{toroidal_SCF_fm_fg.pdf}
\caption{Same as Fig. \ref{poloidal_den} but with pure toroidal field. \textbf{A.} The density distribution shows that the structure is prolate. \textbf{B.} The radial density profile along polar and equatorial directions. \textbf{C.} The 2-d toroidal field distribution. \textbf{D.} The equatorial field strength profile. \textbf{E.} The Lorentz force component along the gravitational force, the white dashed contour indicating the region where gravity is being opposed by a Lorentz force component that is 90\% as strong. \textbf{F.} Distribution of plasma beta inside the configuration, the dotted contour indicating a value of 0.5. The beta values are much lower in this configuration than in the poloidal case.}
\label{toroidal_2d}
\end{figure*}

For strong toroidal fields, highly massive stellar configurations are obtained as the Lorentz force is able to reduce the effective inward gravity for most of the interior (see Fig. $\ref{toroidal_2d}$ \textbf{F}). The value of plasma beta is less than unity almost everywhere except a small region near the axis. Such configurations are likely to be  strongly prone to interchange instabilities.

Fig.~$\ref{toroidal_M_R}$ displays the mass radius relation for white dwarfs with pure toroidal field in the interior, as obtained from Newtonian SCF calculations.  Several curves for different values of  $|\mathcal{M}/W|$ are shown.  As the field energy increases, both the mass and the radius of the configuration increase in comparison to   non-magnetic configurations. As seen in the figure, for $|\mathcal{M}/W|=10\%$ the maximum mass is about 1.76 M$_\odot$, while for $|\mathcal{M}/W|=40\%$ the maximum mass reaches a value as high as 5.6 M$_\odot$.

\begin{figure}
\centering
\includegraphics[width=0.47\textwidth]{toroidal_N_M_R2.pdf}
\caption{Mass-radius relation of white dwarfs with strong toroidal magnetic field, as derived from Newtonian SCF calculations. Curves for different values of $|\mathcal{M}/W|$ are shown. Masses here can far exceed the traditional Chandrasekhar limit.}
\label{toroidal_M_R}
\end{figure}
\subsubsection{Mixed field}

In order to investigate structures with a mixture of poloidal and toroidal fields, we use a functional form $f(u)=\frac{\kappa_0}{k+1}(u-u_{max})^{k+1}$, in equation (\ref{pol_B}). We set $k=0$ and $\mathcal M = \alpha_0 u$ and carry out a Newtonian SCF calculation. Comparing with a pure poloidal field structure of the same central density and central field strength, we find that the introduction of a toroidal field increases both the total mass and the oblateness of the configuration. As listed in Table \ref{mixed_SCF}, the mass increases from 1.896 M$_\odot$ to 2.11 M$_\odot$ and then to 2.55 M$_\odot$ as the fraction of the field energy in the toroidal component is increased from zero to 4.7\% and to 7\%. The corresponding oblateness also increases, with R$_p$/R$_{eq}$ going from 0.68 to 0.62 and 0.53 respectively. The field distribution shows that the toroidal field is confined near the stellar surface with its strength reaching a maximum where the poloidal field attains zero magnitude (Fig. \ref{mixed_2d}).
The values of plasma beta remain high in the interior parts, indicating a relatively stable structure.

\begin{table*}
 \begin{tabular}{|c|c|c|c|}
  \hline
    \bf        	Code : SCF	&	\bf{Mixed field conf. I}	&	\bf{Mixed field conf. II}\\
  \hline \hline
  	\bf CONDITIONS	&			&\\
	$\rho_c$	&	2$\times10^{13}$ kg.m$^{-3}$&	2$\times10^{13}$ kg.m$^{-3}$\\
	Field parameter	&	B$_{core}$ = 59.621, $\hat{\kappa_0}$ = 5 	&	B$_{core}$ = 59.621 GT, $\hat{\kappa_0}$ = 8		\\
	\hline
	\bf   RESULTS	&				&			\\
	Mass (M$_\odot$)&  	2.1128		&	2.5552	\\
	R$_{eq}$ (KM)	&  	913.32		&	1000.7	\\
	R$_p$/R$_{eq}$	&	0.6211		&	0.5352	\\
	B$_{max}$ (GT)	&	59.621		&	59.621	\\
	$|\mathcal{M} /W|$	&	0.1797	&	0.2612	\\
	$|\mathcal{M}_{tor} /\mathcal{M}|$	&	4.6753$\times10^{-2}$	&	7.0047$\times10^{-2}$	\\
	Virial test		&	$\mid$VC$\mid$ = 2.29$\times10^{-5}$	&	$\mid$VC$\mid$ = 5.39$\times10^{-5}$	\\
  \hline
 \end{tabular}
\caption{Mixed field configurations from Newtonian SCF calculation with different toroidal field parameter $\hat{\kappa_0}$ for a fixed central mass density and central field strength. Here $\hat{\kappa_0}$ is a non-dimensional constant that appears in the function $f(u)$.}
\label{mixed_SCF}
\end{table*}

\begin{figure*}
\centering
\includegraphics[width=0.95\textwidth]{mixed_field_SCF.pdf}
\includegraphics[width=0.65\textwidth]{mixed_SCF_fm_fg.pdf}
\caption{Same as Figure~\ref{poloidal_den} but for a mixed poloidal and toroidal field, as in configuration conf.~II of Table \ref{mixed_SCF}. \textbf{A.} The density distribution shows a highly oblate structure. \textbf{B.} The radial distribution of mass density along polar and equatorial directions. \textbf{C.} The field distribution in the interior: the poloidal and toroidal components are plotted separately in the left and the right halves respectively. The white contours represent the field lines. \textbf{D.} The polar and equatorial distribution of the field strength. \textbf{E.} The Lorentz force opposing gravity rises to a maximum of about 75\% in this case, the white dashed contour indicating 50\%.  \textbf{F.} Plasma beta value is very high over most of the star. The dotted contour indicating plasma beta value of 0.5 is located close to the stellar surface.}
\label{mixed_2d}
\end{figure*}

\subsection{GR effects on white dwarf structure}

In order to quantify the effect of General Relativity on the mass and radius of a magnetic white dwarf, we intend
to compare the configurations obtained using Newtonian and GR methods for the same central density and magnetic field strength. However this is not straightforward  because the field strength cannot be directly specified in XNS and Lorene codes as input, instead other custom parameters are used. The field distribution obtained can only be quantified in the output solution. Therefore, an iterative adjustment of input parameters to these codes is required to obtain the desired interior field strength. We compare here solutions of these three codes when their field strengths differ by less than 1\%, for the same value of central density.

\subsubsection {Non-magnetic configuration: comparison of XNS, Lorene and TOV results}

\begin{table*}
 \begin{tabular}{c|c|c|c|c|c}
  \hline
  \bf        &  TOV  &  XNS &  relative difference (XNS \& TOV)  &  Lorene  & relative difference (Lorene \& TOV)	\\
  \hline
  \bf  Mass  &  1.4158 M$_\odot$  &  1.4155 M$_\odot$	&  0.02\%  &  1.4167 M$_\odot$ & 0.06\% \\
  \bf  Radius&  1075 km  &	1067 km &  0.74\% &  1072 km & 0.3\%	\\
  \hline
 \end{tabular}
\caption{Non-magnetic configurations with Fermi degenerate EoS. Here central density = 2$\times10^{13}$ kg.m$^{-3}$, XNS grid : NR = 500, NTH = 100, Lorene grid : nr = 129 nt = 65 (inside star) \& nr = 65 nt = 65 (outside star).}\label{TOV_XNS}
\end{table*}

We have modified the GR codes XNS and Lorene to use the full form of the Fermi degenerate EoS for the white dwarf structure. To validate the modifications of these codes, we first compare the results for non-magnetic spherically symmetric configurations with those obtained from the Tolman-Oppenheimer-Volkoff (TOV) equation \citep{tolman39,oppenheimer+volkoff39}.

\begin{figure}
\centering
\includegraphics[width=0.47\textwidth]{GR_mass_modification.pdf}
\caption{Comparison of Newtonian and GR estimates of masses and radii of non-magnetic White Dwarfs.  The maximum mass values are 1.45 M$_\odot$ and 1.41 M$_\odot$ in Newtonian and GR calculations respectively. The circles represent the percentage of mass modification upon inclusion of GR effects.}
\label{TOV_MR}
\end{figure}

The mass-radius relation of white dwarfs resulting from the TOV equation is compared with that from Newtonian calculations in Fig. $\ref{TOV_MR}$. For low mass and larger radius the GR mass-radius curve closely follows the Newtonian results, but for very compact configurations the curve turns around to smaller masses, indicating gravitational instability. To quantify the effect of GR, we compare the masses derived for the same central density in Newtonian and GR calculations. The relative difference between these values show that the change in mass due to GR effects is less than 2\% for the stable configurations (see Fig. $\ref{TOV_MR}$).

\begin{figure}
\centering
\includegraphics[width=0.47\textwidth]{TOV_XNS_Lorene.pdf}
\includegraphics[width=0.47\textwidth]{diff_poloidal_XNS_Lorene.pdf}
\includegraphics[width=0.47\textwidth]{diff_toroidal_XNS_Lorene.pdf}
\caption{\textbf{A.}: Comparison of the density profiles obtained from TOV, Lorene and XNS calculations of the non-magnetic white dwarf configuration presented in Table~\ref{TOV_XNS}. The difference in the density distribution with respect to the TOV solution is displayed here.  The XNS calculation was terminated at a lower density threshold of $10^7$ kg.m$^{-3}$, about $ 10^{-6}$ times the central density. The peak discrepancy between the density profiles is less than 1\%, while the total mass differs by less than 0.1\%, validating the modifications we have made to the Lorene and XNS codes. \textbf{B.}: The difference between the density (upper panel) and field strength (lower panel) distributions obtained from GR and Newtonian calculations of a white dwarf configuration with strong poloidal magnetic field (Table~\ref{poloidal_XNS_Lorene_SCF}). XNS and Lorene results, and polar (p) and equatorial (eq) profiles are shown separately as indicated. Deviations in the profiles due to GR are limited to within $\sim 1$\% of the maximum, while the total mass differs by $\sim 2$\%. \textbf{C.}: Same as panel \textbf{B} but for pure toroidal field (Table \ref{toroidal_XNS_SCF}).  The GR correction here goes up to 10\% of the maximum in the profiles and $\sim 4$\% in total mass.}
\label{XNS_Lorene}
\end{figure}

The XNS and Lorene results using our modifications are compared with the TOV results in Table \ref{TOV_XNS} and Fig \ref{XNS_Lorene}\textbf{A}. As it is seen, the maximum difference in mass is less than 0.1\% and that in radius is less than 1\% for the same central density. The density distribution in the stellar interior matches closely in all three cases.

\subsubsection {Magnetic configurations in General Relativity}

To illustrate the effect of GR on a magnetic white dwarf configuration, we compare in Tables \ref{poloidal_XNS_Lorene_SCF} \& \ref{toroidal_XNS_SCF} the results of GR and Newtonian calculations for a central density 2$\times10^{13}$ kg.m$^{-3}$.   The two tables correspond to poloidal and toroidal field geometries respectively. The poloidal field configuration is constructed by specifying a toroidal current distribution of the form $J^\phi = (e+P) k_{pol}$. We set $k_{pol} = 0.01164$ and $\xi =0$ in XNS to yield a central field strength of 59.6 GT. This combination of central density and field strength yields a near-limiting mass configuration.  In Lorene code the same field strength is achieved by setting the parameter CFA = 950. With these settings the GR calculations yield masses 1.855 M$_\odot$ (XNS) and 1.854 M$_\odot$ (Lorene), with radii of 860 km and 866 km respectively (Table \ref{poloidal_XNS_Lorene_SCF}). Comparison with the corresponding Newtonian configuration shows that the mass of this
configuration is reduced by $\sim$2\% when general relativistic effects are included. The density and field distributions of the GR and Newtonian configurations differ very little, as seen in Fig. \ref{XNS_Lorene}\textbf{B}.

\begin{figure}
\centering
\includegraphics[width=0.47\textwidth]{mag_GR_mass_modification.pdf}
\caption{Mass-radius relation of white dwarfs with poloidal magnetic field. Lines are derived from Newtonian SCF calculations and symbols along them indicate the assumed central field strength (expressed in units of  $B_c \equiv$ 4.41$\times10^9$~T). Configurations with a fixed central magnetic field start to deviate from the non-magnetic curve as the central density is reduced. Configurations with a fixed ratio of magnetic energy to gravitational energy are described by a mass-radius relation similar to that of non-magnetic ones, but shifted to a higher mass. The curve for $|\mathcal{M}/W| =10$\% is shown, it has a maximum mass of about 1.79 M$_\odot$. The squares indicate the percentage of modification in mass if  general relativistic effects are included.}
\label{poloidal}
\end{figure}

We construct a number of poloidal field configurations with different central densities and field strengths to evaluate the difference in mass derived from Newtonian and GR treatments. The results are shown in Fig. $\ref{poloidal}$. As expected, the difference is larger for more compact configurations. The difference is large also for stronger magnetic fields as they yield more massive configurations.

For a pure toroidal field with $|\mathcal{M}/W|~ \sim$ 39\% and the central density the same as above, the resulting XNS configuration has a mass of 4.95 M$_\odot$, which is $\sim 4$\% smaller than the Newtonian result (Table \ref{toroidal_XNS_SCF}). The radial distribution of density and field agree well in the two cases (Fig. \ref{XNS_Lorene}\textbf{C}).

We have not carried out a similar comparison of GR and Newtonian results for mixed field confgurations, but expect the general trend of reduction in mass by a few percent to apply in this case as well.

\subsection{Salpeter EoS}

So far we have used ideal Fermi degenerate EoS to obtain configurations with different field geometry. We now investigate the consequence of including many body effects in the EoS, \'a la \cite{salpeter61}. Table \ref{poloidal_Salpeter_Lorene} presents a comparison of the pure poloidal field configurations using ideal Fermi EoS, and those using Salpeter EoS for Helium and Carbon compositions respectively. The computations here are carried out in full GR, using the Lorene code. All three configurations have the same central density, 2$\times10^{13}$ kg.m$^{-3}$ and the central magnetic field strength is adjusted to be as close to each other as possible ($\sim$ 59.6 GT). We see that the mass of the configuration is reduced upon inclusion of the many-body effects. The reduction is $\sim$ 0.7\% in case of He composition and $\sim$ 2\% in case of Carbon. In the absence of the magnetic field, the same central density would give masses of 1.403 M$_\odot$ and 1.386 M$_\odot$ with Salpeter EoS, for He and C
composition respectively. The central density chosen is below the neutronisation threshold in either case. However if the composition is Fe, then the neutronisation threshold is $1.1\times10^{12}$ kg.m$^{-3}$ which yields a maximum stellar mass of 1.45 M$_\odot$ with strong poloidal field.

\begin{table*}
 \begin{tabular}{|c|c|c|c|}
  \hline
    \bf        Code : 	Lorene	&	\bf{Ideal degenerate EoS}	&	\bf{Salpeter EoS for He} &	\bf{Salpeter EoS for C}\\
  \hline \hline
  	\bf CONDITIONS	&			&				&\\

	$\rho_c$	&	2$\times10^{13}$ kg.m$^{-3}$&	2$\times10^{13}$ kg.m$^{-3}$	&	2$\times10^{13}$ kg.m$^{-3}$	\\
	Field parameter	&	CFA = 950 	&	CFA = 954	&	CFA = 959.5\\
	\hline
	\bf   RESULTS	&			&			&\\
	Mass (M$_\odot$)&  	1.8539		&	1.8405		&	1.8194	\\
	R$_{eq}$ (KM)	&  	865.95		&	861.47		&	856.28\\
	R$_p$/R$_{eq}$	&	0.6767		&	0.6752		&	0.6749\\
	B$_{max}$ (GT)	&	59.621		&	59.607		&	59.592\\
	$|\mathcal{M} /W|$&	0.1276		&	0.1284		&	0.1285\\
	Virial test	&	\begin{tabular}[c]{@{}c@{}} $\mid$GRV2$\mid$ = 2.98$\times10^{-8}$\\ $\mid$GRV3$\mid$ = 1.56$\times10^{-8}$\end{tabular}	&	\begin{tabular}[c]{@{}c@{}} $\mid$GRV2$\mid$ = 2.694$\times10^{-7}$\\ $\mid$GRV3$\mid$ = 1.696$\times10^{-7}$\end{tabular}
	&	\begin{tabular}[c]{@{}c@{}} $\mid$GRV2$\mid$ = 2.336$\times10^{-7}$\\ $\mid$GRV3$\mid$ = 2.135$\times10^{-7}$\end{tabular}\\
  \hline
 \end{tabular}
\caption{Pure poloidal field Configurations using ideal degenerate EoS and Salpeter EoS for Helium and Carbon from relativistic code Lorene.}
\label{poloidal_Salpeter_Lorene}
\end{table*}

\section{Conclusions}\label{conclusions}

In this paper, we have computed strongly magnetized axisymmetric white dwarf configurations, considering poloidal, toroidal and mixed poloidal-toroidal field geometries. In all cases, the increase of magnetic energy in a configuration increases its mass. We carry out our calculations in both Newtonian and GR, and quantitatively evaluate the magnitude of corrections introduced by GR effects. For a typical white dwarf, the radius is about a thousand times larger than its Schwarzschild radius, indicating that the GR corrections are expected to be small. From our calculations we find that the correction to the mass of the configuration is at most 2-4\% depending on the field geometry.   Our main results are :

\begin{enumerate}
 \item The Lorentz force has a strong effect on the structure of the stellar configuration. The magnitude and the orientation of the Lorentz force depend on the field geometry. For pure toroidal field configuration the magnetic effects could be extremely large and configurations with mass more than 5 M$_\odot$ can be obtained.
 \item The inclusion of general relativistic effects in the calculation of stellar structure, in general, reduces the stellar mass and radius. The percentage of modification is dependent on the compactness of the configuration. For a pure poloidal field geometry, GR reduces the maximum mass by about 2\% and for a pure toroidal field geometry ithe maximum correction is about 4\%.
 \item The inclusion of many body interaction effects in the EoS also modifies the stellar configuration and reduces the maximum mass. The extent of reduction in mass is dependent on the composition of the white dwarf. For Carbon or heavier atoms, this correction is larger than that due to GR effects.
\end{enumerate}

The configurations presented here satisfy conditions of equilibrium, but are not tested for stability. We restrict the interior density below the neutronization threshold and the GR instability threshold. However the strong magnetic field in the interior may itself drive interchamge instabilities in short time scales \citep{bera_b14}. Further, pure poloidal and pure toroidal magnetic field distributions are not stable by themselves and may evolve over Alf\' ven time scale \citep{marke73, tayler1973, mitchell+2015}. An appropriate mixture of poloidal and toroidal fields may provide stability \citep{braithwaite09, braithwaite06}. The mixed field configurations explored by us have, however, a relatively small toroidal component ($|\mathcal{M}_{tor} /\mathcal{M}| \le$ 7\%), which may not be sufficient to achieve stability. It appears unlikely that mixed field configurations with ($ \ge$ 10\%) magnetic energy in the toroidal component could be constructed in axisymmetry \citep{ciolfi+rezzolla13,armaza+15},
and more complex, non-axisymmetric structures may be responsible for the $\ge$ 2 M$_\odot$ white dwarf progenitors of over-luminous Type Ia supernovae.

\section{Acknowledgement}
PB thanks CSIR, India for Research Fellowship grant.

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