Islanders go the polls in the state primary on Tuesday to cast votes that will help choose Democratic and Republican candidates to run for the Massachusetts seat in the U.S. Senate left vacant in August when longtime Sen. Edward M. Kennedy — who held the seat for 46 years — died after a 14-month battle with brain cancer.

Polls are open from 7 a.m. to 8 p.m. in every town.

The four Democratic candidates are Massachusetts Attorney General Martha Coakley, Stephen Pagliuca, a managing partner of the Boston Celtics, U.S. Rep. Mike Capuano, and Alan Khazei, co-founder and former chief executive officer of City Year. The two Republican candidates are Scott P. Brow and Jack E. Robinson 3rd.

Two of the candidates have Island ties. Ms. Coakley is a seasonal visitor to West Tisbury, where her sister owns a home, and Mr. Robinson’s father, the late Jack E. Robinson 2nd, was an Oak Bluffs resident and owner of the Martha’s Vineyard Resort and Racquet Club. He died in December of 2006.

The special election to fill the late Senator Kennedy’s seat is on Jan. 19. Since August the seat has been held by interim appointee Paul Kirk, a longtime Kennedy aide who opted not to run for election to complete the term.

Senator Kennedy and his staff authored more than 300 bills that became law and was a champion of economic and social justice. Known as a liberal lion, he was also well known for reaching across the aisle to his Republican counterparts to find bipartisan compromise.

The four Democratic candidates vying for the Kennedy seat share many of his liberal views. All strongly support health care reform, a woman’s right to choose, the repeal of the Defense of Marriage Act, and the military’s Don’t Ask, Don’t Tell policy. But there are also differences among the candidates.

Ms. Coakley has voiced opposition to the controversial Stupak-Pitts Amendment in the health care bill that places limits on taxpayer-funded abortions.

She has said she would vote against the bill if the Stupak Amendment was still included, saying that fighting for women’s access to abortion is more important than passing the overall bill and providing coverage for 36 million people. “We should not pretend now that the House has passed this is real progress — it’s at the expense of women’s access to reproductive rights,” she said in an interview in a Boston radio station last month.

Her opposition to the bill has put her at odds with her three rivals for the Democratic nomination: especially Mr. Capuano, who voted in favor of the plan in the House and has blasted Coakley for her rigid opposition to the amendment.

“If she’s not going to vote for any bill that’s not perfect, she wouldn’t vote for any bill in history. She would have voted against Medicare, the Civil Rights bill,” Mr. Capuano said in a recent interview.

Ms. Coakley is arguably the most experienced of the four candidates. She served as district attorney of Middlesex County from 1999 to 2007 before being elected as the first woman to serve as Attorney General of Massachusetts. She is a strong supporter of green energy technologies, and led an 18-state coalition to oppose a 2007 U.S. Supreme Court ruling that the Environmental Protection Agency does not have the authority to regulate greenhouse gases under the Clean Air Act.

Earlier this year she filed a lawsuit against the U.S. Department of Health and Human services challenging the constitutionality of the Defense of Marriage Act. The complaint claims that Congress overstepped its authority and undermined states’ efforts to recognize marriage between same-sex couples.

A questionnaire from Ms. Coakley’s campaign that was provided to the Gazette states she supports the controversial Cape Wind project, even though Senator Kennedy was strongly opposed. “With the impact of global warming and our need to new energy sources, we need to move forward on this. It’s the only site in Massachusetts that would provide the size and scope that’s needed for such a project,” she said.

The same questionnaire states Ms. Coakley is opposed to a troop increase in Afghanistan unless “the goals we need to achieve are clearly articulated and we are sure our military is capable of carrying them out.” Ms. Coakley also supports President Obama’s plan to fully withdraw troops from Iraq by 2011.

Mr. Capuano represents the 8th district of Massachusetts, a seat once held by John F. Kennedy and Tip O’Neill, which includes the northern three-fourths of Boston plus Cambridge and Somerville. In 2006 he was appointed chairman of the Task Force on Ethics Enforcement by Speaker Nancy Pelosi, with whom he has a close relationship.

Mr. Capuano in a questionnaire said he also supports Cape Wind. Although he voted against the use of force in Iraq, he does support the use of force in Afghanistan. “I remain gravely concerned about the stability of Pakistan and the security of its nuclear arsenal,” he said.

Mr. Pagliuca has framed himself as a Beltway outsider, free from special interest influence, who would lean heavily on his business background to solve the nation’s ongoing economic problems. In addition to being a managing partner of the Boston Celtics, he is also the managing director of the private equity firm Bain Capital.

In a questionnaire filled out by his campaign, Mr. Pagliuca states that health care reform is the critical issue of this special election. “While traveling across the state I’ve met families who have faced down bankruptcy, illness and even death because they lack adequate health insurance coverage . . . I will stand up to cast the 60th vote needed to pass comprehensive health care reform with a robust public option that will give over 30 million Americans affordable coverage and bring down costs,” he said.

Mr. Pagliuca also supports Cape Wind, same sex marriage, and the withdrawal of troops from Iraq.

Mr. Khazei is probably the least known of the four Democratic candidates, and has cited his relative newcomer status to politics as a strength. He is founder and CEO of Be the Change Inc., a Boston-based organization dedicated to building national coalitions of nonprofits and citizens to enact legislation on issues such as poverty and education.

He cofounded City Year with Michael Brown, his friend and roommate at Harvard College and Harvard Law School. The company engages 17 to 24-year-olds in a year of service in one of 19 U.S. cities and in Johannesburg, South Africa. In 2006 U.S. and World Report named Mr. Khazei one of America’s 25 Best Leaders.

In his candidate questionnaire, Mr. Khazei states he also supports Cape Wind, as well as a strong national green energy policy.

“I view climate change as one of the greatest threats facing our country and our planet, and would rank combating it my highest environmental priority. We need to communicate a sense of urgency to spur action. I have made a commitment not to accept any lobbyist money, meaning I will be serving the American people, not the energy industry,” he said.

The two Republican candidates are both opposed to the health care reform plan recently approved by the House.

Mr. Brown, 50, is a graduate of Tufts University and Boston College Law School. He is also a former Wrentham selectman, and is a current state senator who also served three terms as a state representative. He is a 30-year member of the Massachusetts National Guard and holds the rank of Lieut. Colonel in the Judge Advocate Generals Corps.

Mr. Brown supports reasonable development of alternative energy sources, and also supports stronger immigration enforcement and an employment verification system with penalties for companies that hire illegal immigrants, according to his campaign Web site.

Mr. Robinson, 49, lives in Duxbury and is a graduate of Brown University, Harvard Law School and Harvard Business School.

He is a former executive in the airline industry and financial services industry and is the founder of the digital cellular company Oceanic Digital Communications — which he later sold to the world’s richest man, Mexican billionaire Carlos Slim. Mr. Robinson ran for the U.S. Senate in 2000 against Senator Kennedy and lost.

He also ran for Secretary of State in 2002 and lost to William F. Galvin, and for U.S. House of Representatives in Massachusetts’s 9th district in 2006, losing to Stephen Lynch. He grew up in the Roxbury section of Boston, in a family that was involved with the Republican party going back six generations.

While campaigning he has positioned himself as a respected entrepreneur, attorney and business leader combining an inspiring rags to riches personal story with over 25 years experience solving business problems and creating jobs. He has promised to create jobs, cut wasteful government spending, prevent job-killing tax increases, eliminate debt, and fix the economy.

Polling places for the state primary Tuesday are as follows: Edgartown town hall first-floor meeting room; Oak Bluffs Public Library; Tisbury American Legion Hall; West Tisbury Public Safety Building; Chilmark Community Center; Aquinnah town hall meeting room.