The Killing: When celibacy and sleuthing make for a fatal attraction

Sarah Lund's nonexistent love life adds to The Killing's appeal

The wool monty: Sarah Lund in 'The Killing'

Raymond Chandler would have approved of The Killing's Sarah Lund, although perhaps not of he casual jumper and jeans get-up – after all Philip Marlowe "dresses as well as can be expected", which in the 1940s would have meant a suit, tie and hat. Rather Marlowe's creator would have approved of the fact that Lund has so far eschewed becoming romantically embroiled – with either cop partners or suspects.

Reflecting on why a really good mystery movie had yet to be made, Chandler wrote in 1947: "The reason is that the detective in the picture always has to fall for some girl, whereas the real distinction of the detective's personality is that he falls for nobody. He is the avenging justice, the bringer of order out of chaos, and to make his doing this part of a trite boy-meets-girl story is to make it silly."

This is something that actress Sofie Grabol, who plays Lund, intuited during the making of the first series of The Killing, after chief writer Soren Sveistrup decided that Lund should have an affair with one of the suspects, Copenhagen politician Troels Hartmann. "I rushed into the writers' office and said: 'You are not doing that... It's a sell-out'," she recalls. "I remember saying: 'I am Clint Eastwood! He doesn't have a girlfriend!'"

Lund did of course once have a fiancé – the poor long-suffering Bengt, whose failure to lure Lund to a new life in Sweden provided the backdrop to the first series (loved the scene when she stopped the plane preparing to take off).

Already in the first two episodes of The Killing II, which began on BBC4 last weekend, Lund has rebutted the first tentative approaches of her new police partner, while her flyblown house near the ferry port suggested a loveless bachelorette existence. But I digress. The one exception that Chandler made in his sweeping statement about the failure of detective movies was The Maltese Falcon. And of course at the end of John Huston's film of Dashiell Hammett's novel, Sam Spade (played by Humphrey Bogart) sends the woman he loves, the mendacious Brigid O'Shaughnessy (Mary Astor) to the electric chair. That's the thing with femmes fatales – you know that it can never end happily ever after.

More recent television detectives have had – often tortured – love lives imposed upon them. They are either widowed (David Jason's "Jack" Frost in A Touch of Frost; Kevin Whately in Lewis), divorced (Kurt Wallander; Colin Buchanan's Peter Pascoe in Dalziel and Pascoe) or full of regret for unrequited love (Inspector Morse). Morse had multiple relationships with women, while Robbie Lewis has his eye on one woman – Clare Holman's pathologist Dr Laura Hobson. Even Sarah's Lund's nearest antecedent, Jane Tennison – Helen Mirren's DCI from the Prime Suspect series – maintained a series of shaky relationships that had little or nothing to add to Lynda La Plante's superb series.

But then back stories are the plague of the modern detective TV series. The makers of The Killing were so determined to retain Lund's mystique that they struggled in The Killing III (currently filming in Denmark) when Lund bought her own home. How to decorate it to reflect her personality? But perhaps the last words should be left to the most famous bachelor detective of them all. Near the end of The Sign of Four, Sherlock Holmes tells Watson: ". . . love is an emotional thing, and whatever is emotional is opposed to that true, cold reason which I place above all things. I should never marry myself, lest I bias my judgment."

'The Killing II' is on Saturdays at 9pm on BBC4